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200 | what is the maximum weight a sabre can hold | Sabre (fencing) electrically separates the handle and the guard. The conventional handle of the sabre is shaped so that it may be held so that the hand may slide down to gain further extension of the weapon relative to the fencer. Other grips which form various shapes are incompatible and impractical with sabre as they limit the movement of the hand, and are likely to be ergonomically incompatible with the guard. The entire weapon is generally 105 cm (41 inches) long; the maximum weight is 500g, but most competition swords are closer to 400g. It is shorter than the foil or épée, | My friend and I are trying to settle a debate on how many people a bull moose could carry. How much weight could a moose hold? | military are no longer intended for use as weapons, and now serve primarily in ornamental or ceremonial functions. One distinctive ceremonial function a sabre serves in modern times is the Saber arch, performed for servicemen or women getting married. The modern fencing sabre bears little resemblance to the cavalry sabre, having a thin, long straight blade. Rather, it is based upon the Italian dueling saber of classical fencing. One of the three weapons used in the sport of fencing, it is a very fast-paced weapon with bouts characterized by quick footwork and cutting with the edge. The only allowed target | The Dennis Sabre is a purpose-built fire engine produced by Dennis Specialist Vehicles of Guildford, Surrey, England from 1995 to 2007. It was the last full-size fire appliance produced by the company before its closure in 2007.
Features
Built as a low-cost alternative to the Dennis Rapier with increased equipment load capacity, the Sabre was available in three sizes: Sabre, Sabre ML, Sabre XL, with most of the coachbuilding on these chassis being undertaken by John Dennis Coachbuilders of Guildford, England. Over the Sabre's thirteen year production run it underwent several subtle styling changes, mainly to the grille, and later shared styling similarities with the compact Dennis Dagger. Production ceased in 2007 with the closure of Dennis Specialist Vehicles.
Like the Rapier, the Sabre is powered by a Cummins C Series turbocharged six-cylinder diesel engine and has an Allison MD five-speed automatic transmission. It also uses a double-wishbone suspension with semi-elliptical multileaf and coil springs with telescopic dampers, and the gearing allows a governed top speed of . The Sabre holds of water and seats six people in a stainless steel tilting cab.
Operators of the Dennis Sabre include fire brigades in the West Midlands and North East England, Hereford and Worcester, the city of Dublin and the Hong Kong Fire Services Department. The Dublin Fire Brigade are unique in ordering the only Sabre turntable ladders on the Sabre HD (Heavy Duty) chassis, while the Sabre HD was also popular with the Singapore Civil Defence Force as a conventional fire engine. Sabres were also sold to fire brigades in the Czech Republic, Slovakia, South Africa and the Netherlands.
References
External links
Dennis Sabre online brochure
JDC (John Dennis Coachbuilders) Sabre brochure
Firefighting equipment
Sabre
Sabre | What is the second heaviest weight category in boxing? | Holds 8 - 20 crossbow bolts with broad heads with no problem. I found the upper rubber retainer needed no modification to hold the bolts which are 11/32 diameter. Very pleased with this as I could find no other quiver to meet this need. Construction seems to be quality, The straps, when adjusted, have tails which I tied down with electrical tape. | I used 4 of these to temperarily hand a 4'x3'x3' metal hood over my bench in the garage. Held the weight just fine while I could mount the hood properly. Had no problem holding a 600W HPS, 2 held a 4" duct fan.
will be buying more for other random uses. | Weigh station to state. They are typically operated by the state's Department of Transportation (DOT) or Department of Motor Vehicles (DMV) in conjunction with the state highway patrol or state police, thus enabling enforcement of applicable laws. The federal maximum weight is set at 80,000 pounds. Trucks exceeding the federal weight limit can still operate on the country's highways with an overweight permit, but such permits are only issued before the scheduled trip and expire at the end of the trip. Overweight permits are only issued for loads that cannot be broken down to smaller shipments that fall below the federal weight | 200 | Sabre (fencing) electrically separates the handle and the guard. The conventional handle of the sabre is shaped so that it may be held so that the hand may slide down to gain further extension of the weapon relative to the fencer. Other grips which form various shapes are incompatible and impractical with sabre as they limit the movement of the hand, and are likely to be ergonomically incompatible with the guard. The entire weapon is generally 105 cm (41 inches) long; the maximum weight is 500g, but most competition swords are closer to 400g. It is shorter than the foil or épée, | how does the sabre separate the handle and the guard | what is the name of the part of the weapon which is gripped by the fencer | Fencing at the 2004 Summer Olympics – Men's team sabre | classical fencing uses which two grips | Should I take up Sabre Fencing? | Fencing at the 2010 Asian Games – Men's team sabre | what nationality is the pommel grip used in fencing | What are diffrent parts of fencing swords are called? |
201 | Method for manufacturing display device | The present invention provides a method of manufacturing a display substrate, a display substrate and a display device, the method comprising: an organic thin film layer formed on the non-display region of the display substrate; release organic thin film layer; organic functional layer is printed on the display substrate to remove the organic functional layer region except the display. The present invention can remove the non-display area of the print to the organic functional layer, while avoiding the generation of particles during the purge, affect the appearance. | PURPOSE: A display device and a method for manufacturing the same are provided to achieve improved reliability by preventing ingress of moisture or oxygen which causes degradation in characteristics. CONSTITUTION: A display device comprises a first substrate(10); a thin film transistor formed on the first substrate; an inter-layer insulation film(12) formed on the thin film transistor; an opening formed at the inter-layer insulation film; a protection film(14) formed on the opening; a second substrate(11) arranged on the inter-layer insulation film; and a sealing material(13) arranged on the inter-layer insulation film such that the first substrate and the second substrate are adhered with each other through the sealing material. The opening is formed in a peripheral portion of the first substrate. | A method for manufacturing a structure, - the present invention is active for the display device-matrix a) a plurality of row-line (RL) and a plurality of column-line (as the step of providing a matrix substrate (MS) having a SL), the row-line (RL) of one line of the said column-line ( step in which the feed-through (D) passing through the substrate is assigned, - RL) matrix to form a pixel on each intersection between a line of b) wherein a layer made of a p- silicon (TC) a matrix comprising: - providing a substrate (MS), c) for each pixel, n d) has a particle containing electronic ink matrix, and a step of depositing a layer on the free surface of the final structure is manufactured by the steps c) - single layer or an organic light emitting diode made of a material. In addition, the active prepared according to the method - is given also structure-matrix. | The invention relates to a method of manufacturing a display panel plasma.The method comprises the steps of: forming a layer of photosensitive paste composition on a support film; transferring the photosensitive paste composition layer on a substrate; exposing the photosensitive paste composition layer; removing the carrier film; and firing the layer of composition exposed to manufacture at least one of separating bars, electrodes, resistors, dielectrics, luminescent substances, color filters of rows, and a black matrix. | The invention provides a display apparatus and a method of manufacturing the same. The display apparatus includes a substrate including a plurality of organic layers and a plurality of inorganic layers, a display unit formed on the substrate and an encapsulation unit formed on the display, wherein the plurality of organic layers and the plurality of inorganic layers comprise at least a first organic layer, a first inorganic layer, a second organic layer, and a second inorganic layer which are sequentially stacked, and wherein an interfacial adhesion strength of the second organic layer is higher than an interfacial adhesion strength of the first organic layer. | A display device operation method according to an embodiment of the present invention comprises the steps of: outputting first content on a screen of the display device; receiving a screen link request for linking a first screen of the display device and a second screen of another display device connected to the display device; and controlling the display device and another display device such that the first content is output on a merged screen in which the first screen and the second screen are merged according to the received screen link request. | A method of manufacturing a flexible display device, the method including forming a sacrificial layer on a carrier substrate such that the sacrificial layer includes a hydrogen trap material and amorphous silicon; forming a support layer and a thin film transistor on the sacrificial layer; and separating the support layer from the carrier substrate by irradiating a laser to the sacrificial layer. | The present invention discloses a method of manufacturing an image display apparatus manufacturing method, the manufacturing method of a support and an image display unit, the processing member decomposition apparatus, the image display. Specifically disclosed is decomposed by inserting an object between the image display unit and the support of the image display apparatus embodiment. | 201 | According to one embodiment, it is disclosed a method of manufacturing a display device. The film material layer is formed on the supporting substrate. A first temperature to form a film layer, the second heating process for the second area surrounding the first area in the first heating step and a second temperature higher than the first temperature for the film material layer is made . The first region is provided in a central portion of the film layer. Forming a display layer on the first region and forms a peripheral circuit on at least a portion of the second area. A third temperature wherein the second temperature is higher than the film of the layer is at least a third heating step is performed for a portion of the film layer. In addition, the film layer is peeled from the supporting substrate. | A method of manufacturing a display substrate, a display substrate and a display device | Display device and method of manufacturing thereof | Substrate having buried structure, display device including the substrate, method of making the substrate and method for fabricating the display device | Display method and electronic device | Display Apparatus And Method Of Manufacturing The Same | Processing apparatus for processing a substrate for semiconductor and liquid crystal display device | Apparatus for organic layer deposition, method for manufacturing of organic light emitting display apparatus using the same, and organic light emitting display apparatus manufactured by the method | Display apparatus and method for inputting of display apparatus |
202 | Trader Joe's weaponizes idpol language to justify firing of employee for sending CEO letter on Covid safety precautions | My company is firing workers instead of laying them off.
I work for a company that has a large 'prestigious' brand image.
They comp high and are very selective in whom they chose.
Recently, they have been hit hard by the pandemic, in a very embarrassing manner.(Due to their own mismanagement, not due to the virus itself.)
Now, here is where the dis ingenuity is coming in play.
They want to retain their brand image, and not risk future talent from not-applying here.
The CEO is also very image and ego focused. Layoffs are an admittance of a company's mismanagement whereas a firing, places the blame on to the employee.
They are crafting false narratives, and firing people for fault.
People that have been high/strong performers their entire tenure are suddenly getting written up for trivial nonsensical things.
Employees are being gas-lit, and being told, "this is a recurring theme, we've discussed your timeliness issues before".
What recourse do people have? They are deliberately creating paper trails, and its not possible to fight each of these. They have 3-4 directors group up anytime you attempt to fight these write ups.
It sucks, and I do not believe anyone is entitled to a job. I would happily take a layoff so I could collect unemployment.
But this way, the $company$ protects its brand image, you have a stain on your employment record (for being fired), and you may potentially/likely not be able to collect unemployment.
It makes it even more painful, because this company proudly boasts about integrity and fairness as its pillars publicly.
Even if we were to collect unemployment, its extremely mentally stressful to be gaslit, and go through this emotional turmoil where your confidence is shattered.
What would you do in this case? Would you resign or plow through the waterboarding? | Once its legally his name, I think he has a better defense, and you know how predatory corporations are getting - like Gibson-level. | I've been a long time reader of this subreddit, and I've always read with the small businesses that they can fire you and there are zero repercussions due to current laws. Yet with corporate America, firing someone seems to be dragged out so long, I just don't get it.
I have a friend who works for a Fortune 500 company, maybe 100, and the stories they tell me just boggles my mind. She has one employee she's talked about for over a year that everyone knows underperforms, always messes up, causes problems, but nothing ever happens. Management wants her gone, they say it's in process, they say these things take time, and say that the person will be gone soon. Yet here they are, 6 months beyond that conversation and nothing has changed.
So with that said, it made me think of this subreddit. Why doesn't corporate America just fire people like they do in small business situations? I have to imagine there is lots of money flying out the door due to disgruntled coworkers of bad employees, loss revenue due to bad employees, etc. You'd think they'd just fire them and be done with it. | This study examines how employees’ messages about a corporate crisis affect external publics’ attitudes and behaviors toward an organization. Specifically, the study investigates whether the valenc... | By . Associated Press . and Daily Mail Reporter . General Motors says a 'pattern of incompetence and neglect' is to blame for a long-delayed recall on dangerously defective ignition switches which have been linked to the deaths of 13 drivers. Company CEO Mary Barra released the results of a 'deeply troubling' internal investigation on Thursday, which found that many employees who could have uncovered the problem didn't speak up. Barra has since fired 15 employees - including the ignition's designer - and has announced intentions to start a compensation fund for victims' families. Scroll Down for Video . Sorry: General Motors CEO Mary Barra says a 'pattern of incompetence and neglect' led to a long-delayed recall of faulty ignitions in their Chevy Cobalt . The fund will be administered by compensation expert Kenneth Feinberg, who handled the victims funds for September 11, the Boston Marathon bombing and BP oil spill. The fund will begin taking claims on August 1, but it's still unclear how much money will be involved. Paying back: Georgia nurse Brooke Melton is one of the 13 official victims of the faulty ignition. Barra also announced on Thursday intentions to set up a fund for victims' families, such as Melton's parents Ken and Beth Melton . Barra said the company would 'do the right things for those who were harmed' and 'everything in our power to make sure this never happens again.' Barra called the investigation, which . she ordered in March, 'brutally tough and deeply troubling.' It took GM . more than a decade to report the deadly switch failures to regulators . and the public, and to recall the cars. 'I . hate sharing this with you just as much as you hate hearing it,' Barra . told employees in a town hall meeting at GM's suburban Detroit technical . center. 'But I want you to hear it. I want you to remember it. I want . you to never forget it.' Barra then promised to 'fix the failures in our . system.' The crisis began . in February, when GM recalled 780,000 older-model Chevrolet Cobalt and . Pontiac G5 small cars because of defective ignition switches. GM soon . added the Saturn Ion and other small cars to the recall, which ballooned . to 2.6 million cars worldwide. The . switches in the cars can slip out of the 'run' position and shut down . the engine. That disables the power-assisted steering and brakes and can . cause drivers to lose control. It also disables the air bags. GM . reiterated Thursday that it only links 13 deaths to the problem, but . trial lawyers suing the company put the death toll closer to 60. Barra . said attorney Anton Valukas interviewed 230 employees and reviewed 41 . million documents to produce the report, which also makes . recommendations to avoid future safety problems. The government was . expected to release the report later Thursday. Barra . said the report found that the company was operating in 'silos,' and . individuals who could have helped uncover the problem didn't speak up. 'Because . of the actions of a few people, and the willingness of others in the . company to condone bureaucratic processes that avoided accountability, . we let these customers down,' Barra said. She again apologized to the . families of those who died. Bad machine: The faulty switches would cause the cars to slip out of the run position and shut down the engine, which led drivers to lose control of the vehicle. Above, consulting materials engineer Mark Hood holds up one of the ignitions in March 2014 . Last . month, GM paid a $35 million fine — the largest ever assessed by the . National Highway Traffic Safety Administration — for failing to report . the problem quickly to federal regulators. GM knew about problems with . the ignition switches as early as 2001, and in 2005 it told dealers to . tell owners to take excess items off their key chains so they wouldn't . drag down the ignition switch. In . 2006, GM engineer Ray DeGiorgio — who designed the switch — approved a . change in the switch design, but didn't inform the government or change . the corresponding part number. In subsequent years, that made it harder . for other GM engineers to figure out why older Cobalts performed worse . than newer ones. Barra confirmed Thursday that two employees placed on leave in April have been fired; DeGiorgio was one of those employees. GM . began repairing the cars in April, and had fixed 86,000 as of Thursday. But it has said it doesn't expect to fix them all until October. GM . says the cars are safe as long as customers only use the key and have no . extra items on their key chains. Impacts: Melton's crashed Chevy Cobalt is pictured above. It's still uncertain how much victims' families will be entitled to from the new GM fund. The company will begin accepting claims on August 1 . Disappointed: Barra said she was 'deeply troubled' by the reports findings. Pictured above at the Thursday announcement . Barra . named a new safety chief at GM in March and pledged to quickly work . through a backlog of potential recalls. As a result, the automaker has . recalled a record 15.8 million cars and trucks in North America so far . this year. The company took a . $1.3 billion charge in the first quarter to pay for the recalls. It . expects to take a $400 million recall-related charge in the second . quarter. The report doesn't . complete GM's recall saga. The automaker still faces a criminal . investigation by the U.S. Department of Justice — led by the same team . that recently reached a $1.2 billion settlement with Toyota over its . 2010 sudden acceleration recall. It also faces multiple lawsuits from . victims and from owners whose say their cars have lost value. Barra, who testified before House and Senate committees in April, will also likely be called back to Washington. Sen. Claire McCaskill, D-Mo., chairman of the Senate Commerce, Science and . Technology Committee's consumer protection subcommittee, said she . intends to hold a hearing on the delayed recalls later this summer. 'I . won't be letting GM leadership, or federal regulators, escape . accountability for these tragedies,' she said in a statement. 'The . families of those affected deserve no less.' | ambassador to France, Craig Roberts Stapleton, asked Washington to "calibrate a targeted retaliation list that [would cause] some pain across the EU", targeting countries that did not support the use of GM crops. This activity transpired after the US, Australia, Argentina, Brazil, Canada, India, Mexico and New Zealand had brought an action against Europe via the World Trade Organization with respect to the EU's banning of GMOs; in 2006, the WTO had ruled against the EU. Monsanto was a member of EuropaBio, the leading biotechnology trade group in Europe. One of EuropaBio's initiatives is "Transforming Europe's position on GM food". | I was looking through the F.B.I. wall of info and noticed something strange. I'll admit it's probably nothing, but I was hoping someone might have an explanation.
James Plouffe is the name of the E Corp EVP of Technology according to Season 1, Episode 10.
James Hobbes is the name of a deceased E Corp I.T. employee with a N.Y.P.D. case investigating the death as a suicide, according to Season 2, Episode 12.
Full shot of the F.B.I. board.
Close shot of the F.B.I. board.
So, is this meant to be the same person or a different one? Am I missing something?
This James Plouffe...
...is a cyber security professional and has worked as a consultant on the show. Would this have anything to do with the show retroactively changing the character's name?
edit: Thanks to the commenters who noticed that James Hobbes is the name of the I.T. guy at E Corp who Tyrell and Gideon talk to on the phone but is never seen, and not the same guy who shoots himself on live television. I wonder if we'll go back in time a bit in season 3 and see a bit of his involvement and why he is deceased or if that will just be one of the many questions left behind unanswered. | W-YRU....ON THE AIR. Your source for the latest and most exciting events of this political campaign.
<<Footage: An exterior shot of a restaurant called Bonne Chance French restaurant. The front window is exploded inwards and Knight Errant is on scene. An intrepid reporter standing out front looking intrepid as he can>>
"Are we on? What? OK!"
"AHEM! Behind me is the scene of the most blatant assassination attempt I have ever encountered in my three years of reporting the news! While details are still coming in it appears that Alex Dewitt, candidate Delacroix campaign manager was the victim a violent mid day attack. From what your W-YRU action crew has been able to gather the attack took place when Mr. DeWitt and his wife Mona were having lunch in Bonne Chance, behind me. A pair of metahumans that the kitchen staff described as "A bearded madman," and "a bald elf with some sort of polynesian face tattoo," crashed through their door. The elf yelled something about being part of a reality trideo program.
When the two attackers entered the dining area security converged on them and attempted to intercept them. However, the attackers were according to one witness "moving like they were on combat drugs of some kind."
The leader of the attack, an ork yelled, "Molly Mayhem says you need to eat some humble pie," in a thick Russian accent before hitting Mr. DeWitt in the face with what looked like a pie.
Security attempted to subdue him with less than lethal weapons while a third accomplice a scruffy human with obvious cyberlimbs crashed through the display window. Soon after a toyota gopher followed through. The elf used illegal magics to assist their accomplice in subduing the security while dragging their incapacitated leader to their get-away vehicle.
DocWagon was dispatched immediately and Mr. and Mrs. DeWitt were taken to receive medical treatment for their injuries. According to witnesses Mr. DeWitt received severe chemical burns to his face and hands, and Mrs. DeWitt had minor burns from a taser attack by the group's leader.
Knight Errant has gone on the record about this event.
<< Footage of a KE officer standing in front of a Mitsubishi Nightsky with the slogan "Vote Mayhem in '75" written on the side>>
Officer: Clearly this was attack was perpetrated by fanatics following the terrorist that calls herself "Molly Mayhem," he indicates the limousine and says, "While the attack on Mr. and Mrs. DeWitt was taking place this slogan was sprayed on an unrelated patron's vehicle. This Molly Mayhem is wanted by Knight Errant for multiple accounts of murder, property damage and crimes against metahumanity. This is just a recent example of her growing influence over the Seattle underworld. We're asking the public to notify us of any suspicious activities in their area, these fanatics are not to be approached. Contact Knight Errant right away."
<< Camera Returns to the reporter >>
"You heard it here first folks, W-YRU..On the air." | 202 | Tweet gaining some traction, pretty clownish use of idpol language to paint safety concerns as harmful. And it seems to be a rallying cry for unionization at Trader Joe's to prevent it from happening again
| Fox's self-promoting media hype--and deceptive jeremiad against shale gas extraction | Something critical to note as it relates to the Epstein story is that this seems personally to me to be a very high level of propaganda at its apex. | [NEWS] Buzzfeed - Trump's Twitter Rampage | who has called net neutrality the 'free speech issue of our time ' | What's going on with the recent spike in US covid tweets linking unreliable sources? | The Rachel Maddow Show: GOP Steps Up Vote Suppression; Native Americans Stand Up to Targeting; Twitter Reveals Massive Russian Operation; Possible Saudi Fall Guy for Khashoggi Disapperance; Trump Helping Saudis in Cover-Up (October 17, 2018) | Anybody notice/ have an explanation for the shift in market cultists hand-waving criticisms with "corporatism" instead of the old "crony capitalism" | Twitter Advanced Search help for "fake news" research |
203 | Touches get stuck at bottom left of screen | most people cannot tell that its even on the phone. It did introduce a touchscreen issue on the left side of the screen, just have to press a little harder. I believe you have to position it just right to prevent that. | Recently my 3ds bottom screen has been a bit wonky. When I touch the middle of the screen it clicks on something on the top right corner, when I touch anywhere else I touches the screen randomly on the top. I've tried to wipe it and even clean it with a toothbrush to no avail. I even tried recalibration what should I do now ? I've had it for a few years now | See this gif for a demonstration:
After some Windows 10 update the other day, whenever I open up my laptop, I get ghost touches in one corner of the screen making the laptop impossible to use. If I "massage" the screen a little bit, the touches will stop, as crazy as it sounds. Any ideas? | I try to tap something or scroll, it works for like a millisecond, then it stops registering my finger that is still on the screen? I tested my touchscreen with a touchscreen test app and I see nothing out of the ordinary on there, when I glide my finger over the screen it just draws fine. Anyone know whats up here? | This has been happening for months now.
Every now and then, my touch screen starts acting up and thinks that I'm holding the top left corner of the screen, and so I can't even navigate the menus in some games, this doesn't always happen, but when it happens, it's really annoying.
What might be the cause of this issue and what can I do> | As the title says, the top portion of my screen has pretty much stopped responding to touch. The entire screen also becomes unresponsive from time to time. I am able to get the notification drawer to slide down by actually pressing down harder on the screen, but nothing else does the trick.
I've tried a factory reset, flashing the stock images, using a custom ROM, but none of all that worked, which lead me to believe something was wrong with the digitizer. My phone was still on warranty from where I once got it repaired, so I took it back. They replaced the entire display assembly, but the problem persists, so no one really knows what's going on now.
Anyone had a similar issue? Or any ideas as to what might be wrong? | I'm serious. my finger doesn't slider naturally on the screen, it moves in a stop start motion. Does anyone else have this problem or a solution? Right now my screen is naked, I have a screen protector in the post which I hope will improve things. Other than that I may just sand off my fingerprint. | Hi all,
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I just recently bought a spectre folio and it came with a stuck subpixel that is pretty much always red. I've tried to do the jscreenfix, but that didn't work. I want to try to but pressure on it, but since it is a touch screen, I feel like the pressure I'm putting on the screen isn't really effecting it as it would a normal monitor and I'm afraid to press harder.
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Has anyone had any luck fixing a stuck pixel on a touch screen display? I really don't want to have to exchange it and wait (since I bought the LTE version and there is a 6 month free data promotion that is going to expire next week). | 203 | I've had this problem for a while.
But quite often my phone thinks I'm touching and holding down on the very bottom left corner of the screen without me even going near it.
Since I have Show Touches enabaled, I can see that the phone is registering a touch at the bottom left
This problem can happen randomly or when the device starts heating up. The only way to stop it is it shut off my screen and hope it went away | [Help] All of a sudden phones touch screen has become unresponsive sometimes | Touchscreen stops working after a certain amount of touches. | Unresponsive touch after lollipop update | Windows 10 turning on when touch anything | Almost 2 yrs with this phone and atill the ghost touch issue hasnt gone away | Phantom Touch Problem | Touch Screen Issues may be fixed by removing Screen Protector | Help, touchscreen acting up |
204 | Who you all find harder between FC and TL? | Under GAS tier whale guilds, the outcome of TW is pretty much totally dependent on which guild has the most Padmes, because there isn't a counter to this team (Higher powered teams are not counters - counter means that a weaker team in terms of power beats a stronger team). This has made TW totally uninteresting in terms of strategy and basically the outcome is decided as soon as the match is set. When will they put in a Padme counter, in the same way that Padme is a Darth Revan counter, DR, counters JKR, etc. GAS and GL don't count obviously, I'm talking about for normal players. | Just curious what character is out that you really want and have never gotten for me it's Teq Final Form Frieza he would now fit my team perfectly as well just won't drop! | I have seen one top team LOL tournament. But I have only very basic knowledge of LOL and I know nothing about their champions so I don't understand much about what's going on. I know even less about DOTA2 and have never seen a game.
What I do know is that HOTS is much shorter, the map objectives force a lot of fights and the shared XP allows for very different play than the other MOBAs. And having multiple maps with different layouts and objectives allows for multiple heroes and strategies to be viable. From my understanding you have a lot more fixed roles in LOL and DOTA2 with top, mid, bot, support and jungle. This is one thing that makes HOTS so interesting for me to watch.
Drafting in HOTS is very interesting and I wonder how that compares to the other two. You can see games that are pretty much decided on the draft alone and drafts that look weak that in game is really strong. ETC and Muradin are considered the best tanks by some but we have seen drafts without them being neither picked nor banned. Zeratul was highly contested in NA but rarely seen in EU.
We saw Murky vs Cho'Gall yesterday and it was interesting both to see the draft and the game. And today we saw a comp with two heavy tanks, two support and Li-Ming. We have even seen a first pick Stitches today. There are players well known for some heroes that aren't in the meta. Athero is known for Murky and Tyrael, think about that one. Tyrael is even very successful in Korea. And solo Tassadar is a think in EU and has been for a while.
We are seeing so many cool plays, hero picks and synergies in the team comps. Every game is different, every team has it's style and every region has its own meta. And that combined with all the action is what makes HOTS so interesting to watch for me.
For those of you who have seen both HOTS and LOL/DOTA2 tournaments. How do they compare? | As the title says I'm about to start my first, blind playthrough of Solasta and was wondering which difficulty to choose. I'm no stranger to cRPGs and I typically play them on the highest difficulty setting unless it's Perma-Death or so absurd that it's not much fun (Pathfinder: Kingmaker's Unfair difficulty, Hard was perfect for me though).
I don't like to min-max and prefer sticking to thematic builds so this is where my second question comes in, are there any difficulties in this game that require a fully optimized party or can I get away with making, for example, a party of three differently-specced Paladins (Tank, DPS, Ranged) and a Cleric or something untraditional like that?
I know you can fully customize each difficulty, but I'd rather stick to whatever the Devs laid out for me and pick the one that fits my preference. Any input would be appreciated, thanks.
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**EDIT:** After reading through your responses and looking up some Class progression I think I'll settle for a double Paladin (Protection and Great Weapon), a Ranger (Archer, wanted a Paladin Archer, but Paladins don't appear to have Archery as a Fighting Style in this edition) and a Cleric (not sure what kind of Archetype yet) party setup. I'll start on Cataclysm and lower the difficulty if I find it too challenging.
Thanks for all the help! | Long term FM player, from the red box Championship Manager days. Is it me, or have the last 2-3 versions of FM gotten too easy?
I remember clearly with older FM’s that I’d regularly end up sacked or failing to hit my goals but, in the recent the versions it seems real easy to build a strong squad and win in auto-pilot. Even with lower league it’s easy to loan in players and move up quickly and with the big teams or if you play in a weaker league there isn’t really a challenge.
Couple points in why I feel the game is too easy in its current state:
- Buying a great squad is too easy, the way finances work (instalments) and how static stats are mean you can sign good players with little to no risk.
- Moral. So once you get your players moral high going on long winning runs is really easy. It’s really easy to boost players by moral via praising them for training.
- March Engine - 4-2-3-1 gegenpress type tactics still work too well even with lesser sides. It should be a lot harder to get your side to play successful expansive football.
I get the game needs to cater for the casuals as well who are the vast majority of players, but the inclusion of a hard mode would help cater for the longer term players too. This is the first FM where I’ve stopped playing as it doesn’t really offer a challenge. And before someone says it, I’m not playing with Liverpool, Barcelona etc and I haven’t downloaded any tactics nor looked up players to sign. | Pretty self explanatory, in London which team / faction (I'm new, sorry :/ ) is the least popular? | So I was talking with my friends about who we though the most powerful and useful operators were. I have a lot of offensive ops but i need to even out my defensive ones. Who do you guys think are the best operators that really give your team the best advantage to win?
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I found this interesting article that answers this issue.
| They are against DIG, who are in struggle town, and NME who are a fellow new entry into the LCS. With no subs and their full lineup next week, is it worth taking the risk in picking up, say, Emperor as flex pick?
Or any TDK members for that matter? | 204 | Who do you all find harder between Failed Champion and Traitor Lord. For me personally I found them relatively the same difficulty which is probably why I beat Traitor Lord third try as I had beaten Failed Champion just before that | Try out different champions, you'll be surprised what you thought was needlessly hard and weak turns out to be easy and useful. | Mentally difficult champions? | what's the toughest warrior in tribal trouble | What's the hardest boss in Bloodborne? (In your opinion) | Give me a strong champion and another that's broken | Strongest champs in All for One | Why people say Garen isn't a strong champ? | I am convinced that Veteran is harder than Legend in conquest |
205 | DAE think guys calling their guy friends "the boys" is obnoxious | Boys should have friends that are boys, and girls should have friends that are girls. It’s disgusting when boys and girls are friends. | Why are boys so mean and sarcastic with girls? | Personally, I hate it. I'd rather you not call me anything than "babe". It just makes me cringe
View Poll | I read how simply calling females "woman" or "girl" can be disrespectful to women who have names, but I couldn't find opinions explaining why.
If my male friend say things like "peace out girl" or say "come on, girl", is that disrespectful? I don't like it when guys say things like "woman, make up your mind", "woman this, woman that, etc." because it generalizes that all women can't make up their mind, etc.
Does using the word "girl" have the same connotation? I'm the same age as my male friend (we're both 18) if it makes any difference. Is it the same thing when people say, "come on, man" or "peace out, man"? How is "hey guys" different from saying "hey boys" or "hey girls". I replied one time "peace out...boy", instead of with the general enthusiasm I usually do. He doesn't say it with a negative connotation, but being called "girl" felt kinda weird to me.
Brought up in my mind when I saw the Demi Lovato video responding to being called woman recently. | Sometimes I see it on youtube videos and whatnot and I just don't like it.I would call my girl honey or baby but IDK something about babe is just cringey to me. Even if my girl said it IDK just isn't what I like hearing. IDK if many relate to this and agree but just don't like corny shit like that. | I wouldn't like being called a boy since it's too patronising so I am guessing women don't like to be called girls.
Woman would be to formal if I were to use it in the same way you use guy, or at least I think so.
I thought "gal" was the perfect word until I realised it's just another word for girl. | wrong – jealous, and maybe a little scared for their well-being," and added that the opening newspaper headline warning was reminiscent of another ""femme fatale"" collaboration, Lady Gaga and Beyoncé's "Telephone." The music video was nominated for Best Art Direction at the 2013 MVPA Awards. Credits adapted from the liner notes of "Pink Friday: Roman Reloaded – The Re-Up". The Boys (Nicki Minaj and Cassie song) "The Boys" is a song recorded by American rapper and singer Nicki Minaj and American singer Cassie Ventura. It was written by Minaj, Anjulie Persaud, Jonas Jeberg and Jean Baptiste, and produced by the | i didnt think it was until a black coworker mentioned it kinda is. like how slave owners referred to slaves i guess? i just like to goof around and say boy in a southern accent.
edit: i am now a changed man. i shall replace the word boy from my southern vocabulary and replace it with fella. also not sure why im being downvoted because the comments are still pretty torn | 205 | I dont know a better way to describe it but when my boyfriend says hes with the boys it makes me cringe. I think it might be part of the whole "Saturday is for the boyz" bro memes but it just grates at me for no real reason. On a related note I've always found the whole overly bro thing some guys do to be equally annoying. | Thare is a boy he is annoying? | Why do guys bother girls? | The boys in Montana think it's quite funny to call me griz | what does it mean when a guy says he likes your laugh? | Does Anybody Else cringe at women who unironically use the term "fuckboy?" | Do boys like girls that are hard to get? | Stop glorifying "bitchy" attitude.(for male and females) | I think my boyfriend is a misogynist |
206 | Probably the best consumer compound | Delish. Recommended by my UK co-worker. Bought 1 bottle to try out last year. Then bought 2 double bottles. Another 2 double bottles and now bought a SIX pack. Kids love the taste. We use it for waffles and crepes in lieu of maple syrup and other store pancake syrups. Nice warm caramel taste. I need to make a pecan pie with this next and will return with a review. We use this bottle at least 3x/wk. When the bottle gets sticky, I just run it under warm sink water and wipe dry. | What type of protien powders are the best? | Ive seen a couple of companies that offer synthesis of small batches of any organic compound for research (mostly based in china)... I was wondering if anyone has used such a service? Recommendations? | Best, gives me energy all day long, no joke, it is also much redder in color then the other brands that I have tried......and thrown out because they did absolutely nothing for my energy level, only wish it came in a larger size. | This is a must have product. It keeps my Koi healthy and is easy to use. | Best brand, good value, long time until it expires. Of all condensed milk brands this one is by far my favorite. Highly recommendable to buy this 3 pack | Not worth its price. What do they mean by better ingredients | What is the best selling soft drink? | 206 | I have to admit, this is probably the best compound one could purchase as a consumer. It's a little on the milder side but that's a good thing since you want to achieve results using the least aggressive method possible. My other favorite compound besides Meguiar's would probably be by 3M.
I did a complete pain restoration on my neglected paint by first claying it (you will be socked how much crud comes off your paint with clay). I then wet sanded some fine scratches with 2500 grit then followed with 3000 and used UC to buff out the sanded spots individually. UC was able to easily buff out 3000 grit, even by hand (if you feel like getting a workout) but I used the drill mount buffer which worked great. It will probably buff out 2500 grit as well with multiple applications but don't expect it to be very effective buffing out 2000 grit easily. After I fixed the paint defects, I hit the whole car with UC using a terry bonnet. I then followed with Swirl X (I like this because it's a very fine polish) then followed by wax. The paint looks and feels better the new.
You can use this to polish plastic headlights as well. Forget PlastX, save your money and just use this as it works just a well (I tested them both). My headlights were pretty bad so I sanded them with 2000, 2500 and finally 3000 then used a drill mounted buffer to buff them clear. They came out superb!
Keep in mind that this product has abrasives that *do not* break down as you work them into the clear coat. This means that the cutting is more or less consistent as you're buffing. However, I felt the cutting was fairly mild compared to professional products I've used in the past. I think this has partly to do with the oils in the product. Anyway, highly recommended!
Update:
I noticed that Ultimate Compound contains quite a bit of oil. This is good for lubrication and workability but it's a doubled edged sword as it hids scratches that were not removed. Once the oil dries up, he scratches will come back. To look at my work right after buffing, what I did was fill a spray bottle with water with some dishwashing liquid and sprayed and wiped the area. This removes the oils and reveals the true finish. You can then work more into the finish if you find it's not satisfactory.
Another note. I found out that SwirlX was too mild to polish after UC. I used some Meguiar's Fine Cut Cleaner which removed most of the heavier swirls then hit it with SwirlX to remove the very fine swirls. Going from UC to SwirlX is like going from 1000 grit to 4000 grit... It's not going to work that well. You need to step the cutting level to get a good final finish before wax. Again, keep a bottle of water and dish liquid handly to spray down your work to see what the true finish is. | Polishing 304 Stainless Steel, Help Needed | Use 1,000/2000 grit sandpaper to make smooth-top ovens and stainless steel frying pans shine | Fixing exterior paint sheen lapping | Buffing compound vs tinned metal polish | Hey all! Im newish to the 3d pen world. I was wondering what tool i would need to smooth off the surfaces? And also in the mean time what sandpaper grit is reccomended? | IWTL How to repair scratches in car paint like the pros | I removed too much paint from compounding. Best way to fix this? | Need some advice on patching floors that I'm going to painting |
207 | Abstract We have determined the primary structure of a 3500 base-pair part of the silkmoth chorion locus mapping in a region containing genes of late developmental specificity. This part of the locus was found to harbour a pseudogene related to one of the families of chorion genes encoding high cysteine proteins, HcB. The pseudogene exhibits an overall sequence identity of 84 % to the consensus coding region of HcB chorion genes. A 95 % identity was observed over a length of 190 base-pairs of its immediate 5′ upstream sequences and the corresponding part of the consensus 5′-intergenic sequences of Hc gene pairs, normally encompassing 270 base-pairs. Thus, the pseudogene has retained part of the promoter region that includes sequence elements whose presence is thought to be necessary for transcriptional competence of HcB genes. The pseudogene is also characterized by the elimination of part of its first exon containing most of the 5′ untranslated region, the ATG translation initiation codon and part of the signal peptide sequences. Its intron is longer than that of other HcB genes due to the insertion of a copy of a repetitive element that appears to be transcribed by RNA polymerase III. A previously characterized chorion cDNA clone, m2282, representing a rare mRNA sequence of late developmental specificity, was found to be identical to the pseudogene over its entirety spanning 65% of the pseudogene's second exon. Hybridizations of clones spanning a 260,000 base-pair domain of the chorion locus of Bombyx mori and of total genomic DNA to a subfragment of the cDNA clone containing relatively unique sequences, coupled to primer extension experiments, have demonstrated that m2282 mRNA originated from the pseudogene and that the pseudogene transcripts are initiated at the chorion cap site consensus sequence. We conclude that the 5′-flanking sequences retained by the pseudogene encompass elements necessary and adequate for correct transcriptional activation, but may not include those required for quantitative expression of the promoter. Possible reasons for the observed lack of random drift in the 5′-upstream sequences of the pseudogene and the maintenance of a functional promoter in a non-functional gene are discussed on the basis of the observation that elements resembling scaffold attachment sites are present in these sequences. | Abstract Choriogenesis in silkmoths has been used as a model for relating developmental processes and evolutionary change. We now describe parallel studies in a nonsilkmoth lepidopteran species, the gypsy moth. Choriogenesis is described at the levels of ultrastructure, protein composition and synthesis, and specific mRNA accumulation. One complete chorion cDNA sequence is presented and features of its primary structure are discussed. This sequence is shown to be homologous to those of silkmoths. | Fragile sites are reproducibly expressed and chemically induced decondensations on mitotic chromosomes observed under cytological conditions. They are classified both on the basis of the frequency with which they occur (rare and common) and in terms of the chemical agent used to induce expression in tissue culture cells. Aphidicolinsensitive common fragile sites appear to be ubiquitous in humans and other mammals and have been considered as candidates of pathological importance. Recently DNA from FRA3B, the most highly expressed constitutive fragile site in the human genome, has been cloned although as yet the cause of the underlying fragility has not been identified. In this study we describe the isolation, using a direct cloning approach, of DNA from a region of the Chinese hamster genome associated with aphidicolin-inducible fragility. Cells of a human-hamster somatic cell hybrid were transfected with a pSV2HPRT vector while exposed to aphidicolin, an inhibitor of DNA polymerases α, δ and e. FISH analysis of stable transfectant clones revealed that the ingoing plasmid DNA had preferentially integrated into fragile site-containing chromosomal bands. Plasmid rescue was used to recover DNA sequences flanking one such integration site in the hamster genome. We demonstrate by FISH analysis of metaphase cells induced with aphidicolin that the rescued DNA is from a region of fragility on Chinese hamster chromosome 2, distal to the DHFR locus. Analysis of the DNA sequences flanking the integration site revealed the overall A+T content of the 3,725 bp region sequenced to be 63.3%, with a highly [A]•[T]-rich 156 bp region (86.5%) almost adjacent to the integration site. Computational analyses have identified strong homologies to Saccharomyces cerevisiae autonomous replicating sequences (ARS), polypyrimidine tracts, scaffold attachment site consensus sequences and a 24 bp consensus sequence highly conserved in eukaryotic replication origins, all of which appear to cluster around the [A]•[T]rich sequences. This domain also possesses structural characteristics which are common to both prokaryotic and eukaryotic origins of replications, in particular an unusually straight conformation of low thermal stability flanked either side by highly bent DNA segments. Further isolation and characterisation of DNA sequences from common fragile sites will facilitate studies into the underlying nature of these enigmatic regions of the mammalian genome, leading to a greater understanding of chromatin structure. SUMMARY |
INTRODUCTION
The centromere is the assembly site for the proteinaceous kinetochore complex, which enables the proper segregation of sister chromatids and their transmission to the daughter cells during mitosis and meiosis. Despite the conserved function of the centromere, the primary constriction of monocentric species is generally enriched in highly diverged gene-free repetitive sequences. These repeats include satellite DNAs and retrotransposons (Barra and Fachinetti, 2018;Talbert and Henikoff, 2020). The centromeric DNA sequence is not sufficient to maintain the centromere position and function. The precise assembly of the kinetochore complex at the centromere is epigenetically determined by substituting a centromere-specific histone H3 variant CENH3 for histone H3 in centromeric nucleosomes (Henikoff and Dalal, 2005;Allshire and Karpen, 2008). Besides some diploid species encoding multiple functional CENH3 variants, e.g., barley (Sanei et al., 2011;Ishii et al., 2015), rye (Evtushenko et al., 2017(Evtushenko et al., , 2021, Fabeae species (Neumann et al., 2015), and cowpea (Ishii et al., 2020), most diploid eukaryotes encode only one variant of CENH3. In contrast, in allopolyploids species like wheat (Yuan et al., 2015), each parental subgenome possesses at least one CENH3 variant operating in the context of multiple speciesspecific centromeric sequences.
Defects in the pathways that regulate centromere assembly and function affect the proper chromosome segregation and lead to chromosome instability and lethality in various organisms (Maheshwari et al., 2015;Britt and Kuppu, 2016;Barra and Fachinetti, 2018). Also, the alteration of CENH3 that impairs its loading and maintenance results in chromosome missegregation (Au et al., 2008;Pidoux et al., 2009;Ravi and Chan, 2010;Karimi-Ashtiyani et al., 2015;Kuppu et al., 2015Kuppu et al., , 2020Shrestha et al., 2017;Karimi-Ashtiyani, 2021).
Due to the high density of repetitive sequences and high similarity to non-homologous centromeres within a species, the primary constriction is vulnerable to breakage and recombination (Sullivan et al., 1996;Friebe et al., 2005;Barra and Fachinetti, 2018). Therefore, chromosome rearrangements and breaks often involve (peri)centromeric regions (Friebe et al., 2005;Lukaszewski, 2010;Barra and Fachinetti, 2018). Centric misdivisions, followed by the fusion of the broken arms from different chromosomes, result in whole-arm Robertsonian translocations (Robertson, 1961), which usually possess centromeric sequences of both chromosomes (Zhang et al., 2001;Song et al., 2016). However, to ensure mitotic stability, these chromosomes having a "hybrid (dicentric)centromere" convert to functionally monocentric chromosomes where only one centromere part remains active (Friebe et al., 2005;Han et al., 2006). It is suggested that centromere inactivation involves genomic and/or epigenomic reprogramming (Stimpson et al., 2012). Chromosome breaks and fusions occurred at centromeric and pericentromeric regions in wheat-rye translocation lines (Lukaszewski, 1997;Zhang et al., 2001;Friebe et al., 2005). The most common centric translocation is the 1BL/1RS translocation, in which the short arm of wheat chromosome 1B is replaced by the short arm of rye chromosome 1R (Lukaszewski, 2010;Moskal et al., 2021). Various 1BL/1RS translocations have served as valuable stocks in wheat breeding programs as chromosome 1R contains insect and disease resistance genes
1 .
To address whether both or only one part of the 1BL/1RS hybrid centromere is active Wang et al. (2017) applied a combination of immuno-FISH, chromatin immunoprecipitation (ChIP)-qPCR, and RT-PCR. They concluded that all analyzed 1BL/1RS translocations contain hybrid centromeres and that the wheat-derived CENH3 is incorporated into both, the wheatand rye-derived components of the hybrid centromere. The application of wheat and rye centromere-specific repeats, like the CRW clone 6C6 (Wang et al., 2017) and pAWRC.1/Bilby (Francki, 2001), respectively, allowed the visualization of the 1BL/1RS hybrid centromere. Both repeats are part of the CENH3positive chromatin in either wheat (Liu et al., 2008;Li et al., 2013) or rye . None of the rye CENH3 variants is encoded by the short arm chromosome 1R (Evtushenko et al., 2021;Rabanus-Wallace et al., 2021). Hence, the 1BL/1RS-located CENH3 derives from wheat.
We extended the analysis and applied ultrastructural superresolution microscopy to analyze the arrangement of the 1BL/1RS centromere at a resolution of ∼120 nm. Surprisingly, our findings demonstrate that only the rye-derived centromere incorporates CENH3 of wheat into the hybrid centromere of 1BL/1RS.
MATERIALS AND METHODS
Plant Material and Cultivation
The 1B rec -1 line of cv. Pavon 76 carrying a reconstructed chromosome 1B (Lukaszewski, 1993(Lukaszewski, , 1997 was grown in a greenhouse at 16 h light, 22 • C day/16 • C night conditions. Chromosome 1B rec -1 was reconstructed by centric misdivision 1 https://www.rye-gene-map.de/rye-introgression/html/preface.html from two centric wheat-rye translocations, 1RS.1BL and 1BS.1RL. In essence, the chromosome itself is a centric translocation, composed of a wheat chromosome arm 1BS from cv. Pavon 76 and 1BL arm from the translocation 1RS.1BL from the Aurora/Kavkaz source (Lukaszewski, 1993(Lukaszewski, , 1997. As demonstrated by Zhang et al. (2001) this chromosome carries a hybrid centromere, composed in part of a wheat centromere and in part of a rye centromere.
Fluorescence in situ Hybridization and Indirect Immunostaining
Root tips and anthers of five individual plants of line 1BS PVN .1BL VEE were used for the preparation of mitotic and meiotic chromosomes, according to Gernand et al. (2003). Immunostaining followed by FISH was done as described by Ma et al. (2010). The rye centromere-specific repeat Bilby (Francki, 2001), and the wheat centromere-specific repeat CRW2 (Liu et al., 2008) labeled by nick translation with Alexa 488-dUTP (Invitrogen), and Cy5-dUTP (GE Healthcare Life Sciences), respectively, were used as FISH probes. The primary antibodies, rabbit anti-Os-CENH3 (Nagaki et al., 2004), and the secondary antibodies, rhodamine-conjugated anti-rabbit IgG (Dianova) were used for indirect immunostaining. Finally, the slides were mounted in antifade (Vectashield) containing 4,6-diamidino2phenylindole (DAPI) as counterstain.
Microscopy
Imaging was performed by using an Olympus BX61 microscope and an ORCA-ER CCD camera (Hamamatsu). Deconvolution microscopy was employed for superior optical resolution of spherical structures. To investigate the centromeric chromatin ultrastructures at an optical resolution of ∼120 nm (superresolution achieved with a 488 nm laser excitation), we applied spatial structural illumination microscopy (3D-SIM) using a 63/1.40 objective of an Elyra PS.1 super-resolution microscope system (Carl Zeiss GmbH), (Weisshart et al., 2016). 3D-SIM image stacks were used to perform surface rendering and to produce the movies via the Imaris 9.7 (Bitplane) software.
RESULTS AND DISCUSSION
Fluorescence in situ hybridization with the rye-and wheatspecific centromere repeats pAWRC.1/Bilby (Francki, 2001) and CRW2 (Liu et al., 2008), respectively, demonstrated the hybrid structure of the 1BL/1RS centromere of the translocation line 1BS PVN .1BL VEE at somatic metaphase chromosomes ( Figure 1A and Supplementary Figure 1). In line with previous publications (Lukaszewski, 1997;Zhang et al., 2001) one half of the hybrid centromere displayed rye and the other half wheat centromerespecific signals.
As CENH3 is a mark for centromere activity (Talbert and Henikoff, 2020), the hybrid 1BL/1RS centromere activity was determined by immunostaining using antibodies that crossreacts with the CENH3 proteins of cereals (Nagaki et al., 2004;Liu et al., 2008;Houben et al., 2011). Subsequent FISH with differentially labeled centromeric repeats Bilby (Francki, 2001) FIGURE 1 | Wheat CENH3 incorporates exclusively into rye centromere repeats containing chromatin of the 1BL/1RS hybrid centromere during mitosis (A) and meiosis (B) as revealed by 3D-SIM. (A) Somatic wheat metaphase cell containing two 1BL/1RS homologs labeled by rye-specific Bilby repeats (arrows). All wheat chromosomes incorporate wheat CENH3 into the wheat-specific centromeric CRW2 repeat-positive chromatin (*). Instead, wheat CENH3 loads only into the rye-specific Bilby repeat-positive chromatin of the translocated 1BL/1RS chromosomes (**). Surface rendering of the centromeric components (below) show clearly the different co-localizations (see also Supplementary Movies 1, 2). (B) Early meiotic metaphase I showing in addition to all labeled wheat centromeres both 1BL/1RS homologs labeled specifically by Bilby (asterisks). During meiosis wheat CENH3 places also exclusively into the rye derived centromeric chromatin as shown enlarged below. The co-localization of CENH3 and Bilby induces the yellow color. (C) Schematic representation of the reconstructed wheat chromosome 1B with a hybrid wheat-rye centromere. This centromere is composed of wheat and rye centromeric repeats. The wheat-derived CENH3 co-localized only with the rye-derived centromeric chromatin creating a functional chromosome. and CRW2 (Liu et al., 2008) was performed to address whether the entire hybrid centromere or only the wheat-or rye-derived centromere component is active. In all analyzed dividing cells (about 80) of five plants, CENH3 signals consistently co-localized with the wheat centromeric repeat CRW2 in all non-translocation chromosomes. In contrast, only the rye-derived centromere of 1BL/1RS co-localized with the CENH3 signals ( Figure 1A and Supplementary Figure 1). To confirm this observation, naturally extended meiotic prophase I chromosomes were labeled and analyzed by super-resolution microscopy ( Figure 1B). Again, the rye derived centromere component co-localized with CENH3 signals. The CRW2-positive wheat centromeric region of 1BL/1RS was free of CENH3. The results are summarized in Figure 1C.
Our observation differs from the findings described by Wang et al. (2017) who described that CENH3 binds to both components of the 1BL/1RS hybrid centromere. What might be the reason for this difference? The apparent difference between both studies might be caused by the different 1BL/1RS genotypes analyzed and the different microscopical resolution achieved (diffraction-limited versus super-resolution microscopy). In addition, the ChIP-qPCR experiment performed by Wang et al. (2017) confirmed the interaction of the rye centromeric repeat pAWRC.1/Bilby with CENH3-containing nucleosomes. Still, it could not address whether the wheat component of the 1BL/1RS hybrid centromere interacts with CENH3 too. Besides, in their colocalization study of centromeric repeats with CENH3, they solely used a rye centromeric-specific probe without including any wheat centromere-specific probe. As only a fraction of CENH3 signals co-localized with the rye-specific probe, the authors concluded that CENH3 interacts with wheat centromeric sequences as well. In our study, we differentially labeled both centromeric repeats of rye and wheat (Bilby and CRW2) together with CENH3 in a single immuno-FISH experiment.
Although the centromere position is epigenetically determined and does not depend on its underlying sequences, studies in maize (Zhong et al., 2002), rice (Nagaki et al., 2005), wheat-rye B addition lines (Banaei-Moghaddam et al., 2012) and many other species have shown that CENH3 containing nucleosomes bind differentially to the repeats of the centromeres. Why the rye-and not the wheat-derived centromere component of the 1BL/1RS chromosome is epigenetically marked by CENH3 is unknown. However, it is tempting to speculate that fusion of the chromosome arm 1BL with 1RS triggered centromere sequence changes and, therefore CENH3 preference. The centromeric sequences of hybrids between distantly related or translocated chromosomes may undergo rearrangements like expansion and reduction. For example, centromeric retrotransposons were strongly reduced or eliminated in wheat aneuploids and addition lines from wide hybrids (Guo et al., 2016). The presence of CENH3 signals at novel positions suggests a de novo centromere formation. In contrast, rye-specific centromeric sequences in wheat-rye hybrids expanded towards the chromosome arms, possibly causing centromere expansion (Guo et al., 2016).
It is also possible that differential methylation of centromeric repeats may underlay the inactivation of wheat centromeric repeats in the hybrid centromere of 1BL/1RS. Investigations of the epigenetic landscape for the centromeres in Arabidopsis and maize showed that the centromere repeats associated with CENH3 are hypomethylated compared to flanking centromere repeats (Zhang et al., 2008).
In summary, our analysis of a 1BL/1RS centromere provides an additional example that one component of a hybrid (dicentric)centromere undergoes inactivation creating functional monocentric chromosomes to maintain their stability. Further investigations are needed to determine whether the fusion of 1BL with 1RS triggered centromere sequence changes and or epigenetic modifications and consequently CENH3 preference.
DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.
AUTHOR CONTRIBUTIONS
AH designed the study and provided editorial input to the manuscript. RK-A and VS performed the research and interpreted the results. RK-A wrote the first draft of the manuscript. All authors contributed to manuscript revision and approved the submitted version.
ACKNOWLEDGMENTS
We would like to thank Adam Lukaszewski (UC, Riverside, CA, United States) for providing the translocation 1BS PVN .1BL VEE line and Jianyong Chen (IPK, Germany) for sequence analysis.
SUPPLEMENTARY MATERIAL
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpls.2021. 802222/full#supplementary-material Supplementary Movie 1 | Wheat CENH3 (red) co-localizes the wheat-specific CRW2 repeats (white) of a wheat centromere.
Supplementary Movie 2 | Wheat CENH3 (red) co-localizes with the rye-specific centromeric Bilby repeats (green), but not with the wheat-specific CRW2 repeats (white) of a hybrid centromere of a translocated 1BL/1RS chromosome.
Frontiers in Plant Science | www.frontiersin.org
Supplementary Figure 1 |
1Wheat CENH3 incorporates exclusively into rye centromere repeats containing chromatin of the 1BL/1RS hybrid centromere during mitosis (A-F) and meiosis (G-L) revealed by standard fluorescence microscopy. (A-F) Wheat metaphase cells containing 1BL/1RS translocations (arrows) after CENH3-immunostaining and FISH with rye (Bilby, in green) and wheat (CRW2, in white) centromere-specific repeats. CENH3 signals co-localized with Bilby (centromeric repeat of rye) and not with the centromeric repeats of wheat in 1BL/1RS. (G-L) Meiotic metaphase I showing in addition to all labeled wheat centromeres a 1BL/1RS bivalent (arrow). (C,I) Co-localization of CENH3 and CRW2. (D,J) Co-localization of CENH3 and Bilby. (E,K) FISH with rye and wheat centromere-specific repeats (Bilby and CRW2, respectively). (F,L) Further enlarged views of 1RS/1BL. Selected chromosomes are labeled by * .
Frontiers in Plant Science | www.frontiersin.org
December 2021 | Volume 12 | Article 802222
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Altered dosage and mislocalization of histone H3 and Cse4p lead to chromosome loss in Saccharomyces cerevisiae. W.-C Au, M J Crisp, S Z Deluca, O J Rando, M A Basrai, 10.1534/genetics.108.088518Genetics. 179Au, W.-C., Crisp, M. J., Deluca, S. Z., Rando, O. J., and Basrai, M. A. (2008). Altered dosage and mislocalization of histone H3 and Cse4p lead to chromosome loss in Saccharomyces cerevisiae. Genetics 179, 263-275. doi: 10.1534/genetics.108. 088518
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The temporal and spatial pattern of histone H3 phosphorylation at serine 28 and serine 10 is similar in plants but differs between mono-and polycentric chromosomes. D Gernand, D Demidov, A Houben, CytogenetGernand, D., Demidov, D., and Houben, A. (2003). The temporal and spatial pattern of histone H3 phosphorylation at serine 28 and serine 10 is similar in plants but differs between mono-and polycentric chromosomes. Cytogenet.
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Chromosome-scale genome assembly provides insights into rye biology, evolution and agronomic potential. M T Rabanus-Wallace, B Hackauf, M Mascher, T Lux, T Wicker, H Gundlach, 10.1038/s41588-021-00807-0Nat. Genet. 53Rabanus-Wallace, M. T., Hackauf, B., Mascher, M., Lux, T., Wicker, T., Gundlach, H., et al. (2021). Chromosome-scale genome assembly provides insights into rye biology, evolution and agronomic potential. Nat. Genet. 53, 564-573. doi: 10.1038/s41588-021-00807-0
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Conflict of Interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Conflict of Interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
| The Polo family of serine/threonine kinases have been implicated in cell cycle control in a number of diverse organisms. Their localization and biochemical activity suggest that they play an important role in centro-some maturation, G2—to-M phase progression, the promotion of anaphase, and cytokinesis. The Polo family of kinases is distinct from other serine/threonine kinases in that they all contain a polo-box sequence motif in their non-catalytic C-terminal domain. Recently, it was reported that two Polo-related kinases, Plcl and Plc2, are present in C. elegans. Plc2 has diverged from Plcl with poor homology within the polo-box sequence and only had 40% amino acid identity with Plcl. We report here the full-length cDNA sequence of another Polo-related kinase from C. elegans. The predicted protein product has greater than 70% amino acid identity with PLK-1/Plc1, and has a highly conserved polo-box domain. |
INTRODUCTION
Originally termed interchromatin granule clusters (IGCs) due to the observation of 20-25 nm nuclear granules in electron microscopy micrographs (1), nuclear speckles are dynamic nuclear bodies (∼20-30 per nucleus) that are enriched in RNA binding proteins (RBPs) (2,3). Prominent examples include the SR proteins with roles in pre-mRNA splicing, mRNA export, RNA stability and translation (4)(5)(6)(7). The reasons for RBP accumulation in nuclear speckles and the role these structures play in cells are not completely understood. Most pre-mRNA splicing takes place co-transcriptionally, leading to the proposal that nuclear speckles are sites of assembly and/or storage of the pre-mRNA splicing machinery. Because RBPs are not retained in speckles, they are able to diffuse to active sites of transcription, where they participate in splicing. Alternatively, they may be recruited from nuclear speckles to pre-mRNA in the nucleoplasm during post-transcriptional splicing, mRNP formation and/or mRNA export (2,8,9).
While nuclear speckles contain a large variety of splicing factors, they are also enriched in poly(A)+ RNAs comprised of both and long non-coding RNAs (lncRNAs) and mRNAs (10,11). Whether these RNA components participate in the formation of nuclear speckles and their maintenance remains unclear. For instance, the localization of several SR splicing factors to nuclear speckles in cancer cells required interactions with MALAT1 (metastasis-associated lung adenocarcinoma transcript 1), a lncRNA that specifically localizes to nuclear speckles (12); however, MALAT1 did not seem to influence the localization of nuclear speckle components in mouse tissues (13). Thus, MALAT1 is not thought to be necessary for nuclear speckle formation or maintenance (10).
Recently, a library of natural compounds was screened in search of molecules that affect nuclear speckle structure and gene expression (14). Nuclear speckles were identified in the screen using poly(A)+ RNA fluorescence in situ hybridization (FISH) with a fluorescent oligo-dT probe that hybridized with the poly(A) tails. Tubercidin, an adenosine analogue in which the N-7 position of adenosine is replaced with C-H (7-deaza-adenosine), caused the complete delocalization of poly(A)+ RNA from nuclear speckles after 1 hr of treatment in HeLa cells. This was accompanied by the dispersal of the splicing factor SRSF1 from nuclear speckles. However, nuclear speckles were not disassembled, and Nucleic Acids Research, 2019, Vol. 47, No. 9 4779 the splicing factor SRSF2 remained within them, accompanied by changes in their overall structure.
Tubercidin was reported initially as having antibiotic and anti-cancer effects (15). This analogue of adenosine was identified from culture filtrates of Streptomyces tubercidicus, and held promise for treatment in the clinic. Tubercidin is incorporated into DNA and RNA and was shown to negatively affect protein synthesis (16). The cytotoxic effects of tubercidin on cancer cells drove experiments that tested its safety in animals (mice, rats, dogs and monkeys) (17) and later in humans. Altogether, phase I trials concluded that treating humans with tubercidin is inadequate due to severe toxicity (18)(19)(20).
The mechanistic explanation(s) for the high levels of tubercidin toxicity on normal cells was not explored. Its ability to incorporate into DNA, RNA and affect protein synthesis have been briefly documented and does not explain why this compound had such extreme effects in comparison to other adenosine analogues. With respect to nuclear speckles, it was suggested that tubercidin's incorporation into RNA may lead to the dispersal of RNA from nuclear speckles and perhaps to reduced mRNA stability (14). In our study, we set out to investigate the formation and composition of nuclear speckles and the fate of the RNAs and proteins within them, using tubercidin as a tool that compromises nuclear speckle structure. However, we discovered that tubercidin effects were much broader than anticipated, generating a cellular stress response. Although transcription and splicing continued to transpire, the stress conditions inhibited mRNP formation and mRNA export in multiple cell types. We found that many nuclear proteins and RNAs were mislocalized under these stress conditions, particularly components of the nuclear pore complex (NPC) and RNA processing factors that are necessary for mRNA export. All these defects hindered the nucleo-cytoplasmic flow required for the gene expression pathway. Moreover, this analysis has enabled us to examine the structural aspects of RNA-protein granules in cells during their assembly and disassembly. Finally, the induction of this stress response by tubercidin in normal and cancer cells can explain why this compound failed as a chemotherapeutic agent.
MATERIALS AND METHODS
Plasmids
IGF2BP3-GFP was received from S. Hüttelmaier (21) and GFP-CF I m 68 and GFP-CF I m 25 were received from S. Barabino (22). GFP-Dbp5 was received from S. Wente (23). For the plasmid encoding HIST1H2BA, the gene was amplified by RT-PCR (GoTaq Green Mix, Biological Industries) from genomic DNA (TIANamp Genomic DNA kit, TIANGEN) of U2OS cells, and subcloned into peGFP-C1 using primers containing the restriction enzyme sites of BsrGI and HindIII:
Forward-ATATGTACATTCCCTCGTCCAGACATCT CCT. Reverse-TATAAGCTTTGGGATTACAGGCGAGTCA CGG.
Cells and transfections
Human U2OS cells were maintained in low glucose Dulbecco's modified Eagle's medium (DMEM, Biological Industries, Israel) containing 10% fetal bovine serum (FBS, HyClone). The cell lines HeLa, mouse embryonic fibroblasts (MEF) (24), human foreskin fibroblasts (hFF), HCT116, PANC1, SW620 and MCF7 were maintained in high glucose DMEM containing 10% FBS. Transgenic U2OS E3 and E6 cell lines (25) with stable integration of BACs carrying C-terminally tagged SRSF2, SRSF4, SRSF5, SRSF6, SRSF7, U1-70K, U2AF65 and Prp8, were generated as described (26,27). The U2OS cell line expressing CFP-actin and the MEF -actin-MS2 cells were previously described (24,28).
Stress granules were formed by adding arsenite (1 Mm, Sigma) to the medium for up to 45 min or sorbitol (600 mM, Sigma) for 1.5 hr. Tubercidin (10 M, Sigma), toyocamycin (10 M, Sigma) and adenosine (10 M, Sigma) were added to the medium for different times. For inhibition of SG assembly, cells were treated for 3 hrs with GSK2606414 (10 M, Cayman) before tubercidin addition. Cells were induced to express the -globin-MS2 by the addition of 1 g/ml doxycycline (Sigma). For splicing inhibition, cells were treated for 6 hrs with Pladienolide B (10 M, Santa Cruz). For transcription inhibition, cells were treated for 2 h with actinomycin D (ActD) (5 g/ml, Sigma).
The Click-iT ® RNA Alexa Fluor ® 488 Imaging Kit (Invitrogen) was used for global RNA visualization. Cells were treated with the uridine analog 5-ethynyluridine (1 mM EU) only or together with tubercidin for 3 h. Then the EU was washed and fresh medium with or without tubercidin was added to the cells for another 3 h. After fixation, the Click-iT reaction cocktail was added to the cells for 30 min and washed with the Click-iT reaction rinse buffer.
For transient transfections, cells were transfected with 1-5 g of plasmid DNA and 40 g of sheared salmon sperm DNA (Sigma) when using electroporation (Gene Pulser Xcell, Bio-Rad). Stable expression of IGF2BP3-GFP was obtained by co-transfection of the cells with IGF2BP3-GFP (10 g) and puromycin resistance (300 ng) plasmids using electroporation (Gene Pulser Xcell, Bio-Rad) and selection with puromycin (1 g/ml; Invivogen, San Diego, CA). An E6 stable cell line expressing YFP-MS2 was created as described in (29).
Western blotting
Cells were washed with cold PBS and placed on ice for 15 min after resuspending in immunoprecipitation (IP) lysis buffer (Pierce) containing 10 mM Na-fluoride, 1 mM Na-orthovanadate, protease inhibitor cocktail (Sigma) and 1 mM phenylmethylsulfonyl fluoride (PMSF). The resulting lysate was centrifuged at 10,000 rpm for 10 min at 4 • C. 30 g of protein was run on SDS-polyacrylamide gels and transferred to a nitrocellulose membrane (0.45 m). The membrane was blocked with 5% BSA and then probed with a primary antibody for 2 h at room temperature (RT), followed by incubation with HRP-conjugated goat antirabbit/mouse IgG (Sigma) for 1 h at RT. Immunoreactive bands were detected by the Enhanced Chemiluminescence kit (ECL, Pierce). Primary antibodies used were rab-bit anti-eIF2␣ (Abcam), rabbit anti-P-eIF2␣, mouse anti-GFP and rabbit anti-tubulin. Experiments were performed three times and quantified. The quantification of the blots was performed in ImageJ. After the selection of the bands, the values of the intensities were obtained. The intensities of the eIF2␣ and P-eIF2␣ bands were divided by the corresponding tubulin band intensities.
Immunofluorescence
Cells were grown on coverslips, washed with PBS and fixed for 20 min in 4% PFA. Cells were then permeabilized in 0.5% Triton X-100 for 2.5 min. Cells were washed twice with PBS and blocked with 5% BSA for 20 min cells and immunostained for 1 h with a primary antibody. After three washes with PBS, the cells were incubated for 1 h with secondary fluorescent antibodies. Primary antibodies: mouse anti-G3BP1 (Abcam), rabbit anti-hnRNP A1, rabbit anti-eIF2␣, rabbit anti-eIF4B, rabbit anti-CBP80, rabbit anti-U2AF65, rabbit anti-eIF4A3, mouse anti-Y14, mouse anti-Aly, mouse anti-UAP56, rabbit anti-Dbp5, rabbit anti-Nup153, mouse anti-NXF1, rabbit anti-Nup214, rabbit anti-Nup358, mouse anti-Nup62, rat anti-Nup98, rabbit anti-TPR, rabbit anti-THOC5, goat anti-TIA1 (Santa Cruz), mouse anti-CBP20, mouse anti-THOC6, mouse anti-SC35 (Sigma), mouse anti-RACK1 (BD Biosciences). Secondary antibodies: Alexa488-labeled goat anti-mouse/rabbit/rat IgG (Abcam), Alexa488-labeled donkey anti-goat IgG, Alexa594labeled goat anti-mouse/rabbit. Nuclei were counterstained with Hoechst 33342 (Sigma) and coverslips were mounted in mounting medium. For colocalization analysis, the coloc2 ImageJ plugin was used to calculate Pearson's correlation coefficient (R r ) to measure the colocalization degree. One sample t-test was performed.
Fluorescence in situ hybridization
Cells were grown on coverslips and fixed for 20 min in 4% paraformaldehyde, and overnight with 70% ethanol at 4 • C. The next day cells were washed with 1× PBS and treated for 2.5 min with 0.5% Triton X-100. Cells were washed with 1× PBS and incubated for 10 min in 40% formamide (4% SSC; Sigma). Cells were hybridized overnight at 37 • C in 40% formamide with a specific fluorescentlylabeled Cy3 or Cy5 DNA probe (∼10 ng probe, 50 mer). The next day, cells were washed twice with 40% formamide for 15 min and then washed for two hours with 1× PBS. For oligo-dT labeling, 15% formamide was used. Nuclei were counterstained with Hoechst 33342 and coverslips were mounted in mounting medium. The probe for the MS2 binding site was: CTAGGCAATTAGGTACCTTAGGAT CTAATGAACCCGGGAATACTGCAGAC. PolyA: an oligo(dT) probe. The intron probe was from (25). In some cases, immunofluorescence was performed after the RNA FISH using the standard protocol.
FISH experiments with Stellaris (Biosearch Technologies) probes were performed according to the manufacturer's adherent cell protocol. Probes used were: CCND1, ANLN, HIST1H2BA, MALAT1 and NEAT1. To reduce photobleaching, the slides were mounted in GLOX buffer (pH 8,10 mM, 2× SSC, 0.4% glucose), supplemented with 3.7 ng of glucose oxidase (Sigma G2133-10KU) and 1 l Catalase (Sigma 3515) prior to imaging.
Fluorescence microscopy and live-cell imaging
Wide-field fluorescence images were obtained using the Cell ∧ R system based on an Olympus IX81 fully motorized inverted microscope (60× PlanApo objective, 1.42 NA) fitted with an Orca-AG CCD camera (Hamamatsu) driven by the Cell ® software. Live-cell imaging was carried out using the Cell ∧ R system. For time-lapse imaging, cells were plated on glass-bottomed tissue culture plates (Greiner Bio-One GmbH, Germany) in medium containing 10% FBS at 37 • C. The microscope is equipped with an incubator that includes temperature and CO 2 control (Life Imaging Services, Reinach, Switzerland). For long-term imaging, several cell positions were chosen and recorded by a motorized stage (Scan IM, Märzhäuser, Wetzlar-Steindorf, Germany). Cells were imaged immediately after the treatment with tubercidin or arsenite in 3D every 15 min, at 1 m steps for 6 h. For the presentation of the movies, the 4D image sequences were transformed into a time sequence using the maximum or sum projection options or manually selecting the in-focus plane using the ImageJ software.
RT-PCR
Total RNA was extracted using Tri-Reagent (Sigma) and DNA removed using a Turbo-DNase free kit (Ambion). cDNA (1 g RNA) was synthesized using the ReverseAid First Strand cDNA Synthesis Kit (Fermentase) and PCR was performed using GoTaq green mix (Promega) with the following primers:
E6 forward: TCTGACACAACTGTGTTCAC E6 reverse: TCCACGTGCAGCTTGTCACA p27 forward: CAGCTTGCCCGAGTTCTACT p27 reverse: GTCCATTCCATGAAGTCAGCG DXO forward: TGGGGAGGTTAACACCAACG DXO reverse: GCTCTGGGAAAGCTA AGGA MCL1 forward: GAGGAGGAGGAGGACGAGTT MCL1 reverse: ACCAGCTCCTACTCCAGCAA NOP56 forward: GCATCCACAGTGCAGATCCT NOP56 reverse: GCAATCGATTCGTGAGGCAA HSP40 forward: GAACCAAAATCACTTTCCCCAAGG AAGG HSP40 reverse: AATGAGGTCCCCACGTTTCTCGGG TGT
Statistical analysis
The intensities of P-eIF2␣ and eIF2␣ in the western blots were log 2 -transformed and the effect of tubercidin, arsenite, toyocamycin and adenosine treatments for different time points was compared to the control with a one-sample t-test against a mean of 0. All the experiments were repeated at least three times. The results are presented as mean values ± SEM of three independent experiments.
RESULTS
Differential effect of tubercidin on RNAs and nuclear speckle proteins
To examine the effect of tubercidin treatment over time on poly(A)+ RNAs as well as on nuclear speckle proteins, we treated U2OS cells with tubercidin for several hours. The distribution of the splicing factor SRSF2 that localizes to nuclear speckles was examined using immunofluorescence whereas poly(A)+ RNA, also normally accumulating in nuclear speckles, was detected by RNA fluorescence in situ hybridization (FISH) with a fluorescent oligo-dT probe. Although the continued presence of nuclear speckles was observed, as seen by SRSF2 staining, the poly(A)+ RNA population redistributed from the nucleus and accumulated in cytoplasmic structures ( Figure 1). Since tubercidin is a toxic adenosine analogue that interferes with translation, we considered the possibility that it may be lead to stress granule (SG) formation, cytoplasmic structures that are induced upon several cellular stresses and contain untranslated mR-NAs and various RBPs (30,31).
To determine whether mRNAs accumulated in SGs under tubercidin treatment, we examined whether the poly(A)+ RNA structures colocalized with SGs markers. Indeed, the strong RNA signal was found to accumulate in SGs after tubercidin treatment (6 h; Figure 2A). Tubercidin caused SG formation in different cancer cell lines (HeLa, MCF7), in normal human foreskin fibroblast cells (hFFs) and in mouse embryonic fibroblasts (MEFs) (data not shown). Since the composition of SGs can vary, we examined the presence of several SG protein markers -G3BP1 (GAP SH3 Domain-Binding Protein 1), TIA1 (T-Cell-Restricted Intracellular Antigen-1), hnRNP A1 (Heterogeneous Nuclear Ribonucleoprotein A1), eIF2␣ (Eukaryotic Translation Initiation Factor 2A), eIF4B (Eukaryotic Translation Initiation Factor 4B). All these proteins accumulated in SGs (Figure 2A and data not shown). Since the classic stress pathway usually includes the phosphorylation of eIF2␣ as part of the translation inhibition taking place during stress, we examined whether tubercidin also activated this pathway. Indeed, increased detection of phosphorylated eIF2␣ was observed upon either arsenite, the classical inducer of SGs, or tubercidin treatment ( Figure 2B). However, the effect occurred within minutes of arsenite treatment, whereas eIF2␣ phosphorylation was seen only after several hours of tubercidin treatment. To independently address differences in the time course of the tubercidin stress response, time-lapse imaging of U2OS cells stably expressing GFP-IGF2BP3 was performed. Visible SGs were detected after 15 min in arsenite, while SG formation took ∼90 min in tubercidin treated cells (Supplementary Movies S1 and S2). Interestingly, the adenosine analogue toyocamycin, a close relative of tubercidin, did not have any of the above effects, nor did adenosine itself (Supplementary Figure S1).
Tubercidin induces RNA accumulation in stress granules
RNA FISH experiments with a fluorescent oligo-dT probe can be used to detect both coding and non-coding RNA molecules. In order to examine the localization of spe-cific RNAs during tubercidin treatment, we used specific probes to several endogenous RNAs. The endogenous anillin (ANLN) and cyclin D1 (CCND1) mRNAs were partially localized to SGs ( Figure 3A), as previously shown (32). Two nuclear-retained lncRNAs--MALAT1 normally located in nuclear speckles and NEAT1 located in the paraspeckles--were not detected in cytoplasmic SGs and were dispersed in the nucleoplasm upon tubercidin treatment ( Figure 3A, B). Nevertheless, three fluorescent foci, which we postulated were the transcribing alleles of MALAT1 and NEAT1, remained detectable in the nucleus.
U2OS cells are expected to have three copies of chromosome 11 (33) and therefore three MALAT1 alleles. Since the MALAT1 gene is situated 50 kb from the gene to NEAT1 (34), we assumed that a probe to the NEAT1 lncRNA should colocalize with the transcribing loci of MALAT1. Indeed, three NEAT1 foci were found in partial colocalization with the three MALAT1 foci ( Figure 3B), suggesting that both genes continued to transcribe under tubercidin treatment. To further validate that the foci represented the active genes transcribing MALAT1 and NEAT1, we used additional cell types harboring different copy numbers of chromosome 11. Two foci were detected in normal human foreskin fibroblast cells (hFFs) and in human colon cancer cells HCT116, three foci in human breast cancer MCF7 and human colon cancer SW620 cells, and four in human pancreatic cancer PANC1 cells ( Supplementary Figure S2). Finally, transcription inhibition by actinomycin D eliminated the three foci, and MALAT1 distributed in the nucleoplasm while nuclear speckles remained (Supplementary Figure S3A). This suggests that MALAT1 and NEAT1 lncRNAs are not essential for nuclear speckle formation and maintenance, and that tubercidin does not inhibit transcription.
Tubercidin does not inhibit transcription but impairs nuclear mRNA export
To examine which points in the gene expression pathway are targeted during stress, we monitored the entire gene expression pathway for a single expressed gene, employing an inducible reporter gene termed E6 (25). The E6 gene is based on a Tet-inducible -globin mini-gene and contains six exons and five introns. The coding region is Nterminally fused to a cyan fluorescent protein (CFP) containing a SKL tri-peptide that targets the protein to cytoplasmic peroxisomes upon doxycycline (dox) induction. The E6 mRNA also contains a series of MS2 sequence repeats in its 3 UTR (35). A probe complementary to the MS2 sequence repeats allows robust detection of the E6 mRNA by RNA FISH (Supplementary Figures S3 and S4A). Upon tubercidin treatment, the E6 mRNA was detected in SGs as well as in the nucleus (Supplementary Figure S4A). The CFP protein product was not detected ( Supplementary Figure S4B, C), confirming stress-induced translation inhibition (36).
The E6 mRNA is usually predominantly cytoplasmic. Interestingly, E6 mRNA accumulated in the nucleus upon tubercidin treatment (Supplementary Figure S3). Since the E6 gene is transcriptionally inducible, we could determine the effect of tubercidin on E6 mRNA fate by varying the timing of dox and tubercidin treatments, and then examine whether tubercidin has an effect on nucleo-cytoplasmic mRNA transport. After overnight dox induction during which the E6 transcripts are transcribed, tubercidin was added for 6 h. The E6 mRNA was abundantly detected at the sites of transcription, which also persisted after subsequent tubercidin treatment, and the mRNAs were observed in the cytoplasm but also accumulated in the nucleus (Figure 4A). These results suggested that tubercidin did not inhibit transcription, in comparison to actinomycin D transcriptional inhibition that eliminated the site of the active gene (Supplementary Figure S3).
The nuclear accumulation of the E6 mRNA suggested a possible obstruction of mRNA export. To test this, tubercidin was administered to the cells together with dox induction ( Figure 4B). This form of the experiment allowed us to discriminate between the transcripts that were transcribed before or during tubercidin treatment. At the early time points, E6 mRNAs were detectable in the cytoplasm; however, at later time points, the cytoplasmic levels of the E6 mRNA were very low and the mRNAs accumulated in nuclear puncta. This implied impaired mRNA export. Namely, the cytoplasmic transcripts in stress granules had probably been transcribed prior to the tubercidin treatment, while the nuclear retained mRNAs apparently represent transcripts transcribed during the tubercidin treatment.
To examine whether the mRNA export impairment affects other transcripts, we used two additional inducible mRNA systems that contain MS2 repeats and allow control of gene expression timing relative to tubercidin administration. The two mRNAs contain MS2 sequences in their 3 UTR and were detected by RNA FISH with a probe to this region. Both a dox-inducible CFP--actin mRNA (28) ( Figure 5A) and endogenous -actin mRNAs in MEFs (24) (Figure 5B), the latter induced to transcribe by serum induction (37), demonstrated that the mRNAs remained stuck in the nucleus after tubercidin treatment. In addition, we demonstrated that histone H2B mRNAs, which have a different 3 -end processing mechanism (38), were also stuck in the nucleus upon tubercidin treatment ( Figure 5C).
Finally, to examine if tubercidin has a global effect on mRNA export, we used the modified nucleotide 5ethynyluridine (EU) that stains RNA in cells (39), in order to follow global RNA export ( Figure 6). The experiment was conducted in two ways in order to discriminate between new and old transcripts: (i) EU was added to the cells and allowed to incorporate into RNA for 3 h. This allows enough time for mRNAs to be exported into the cytoplasm (Fig-Figure 3. Accumulation of different RNAs in SGs following tubercidin treatment. (A) The localization of ANLN and CCND1 mRNAs, and NEAT1 and MALAT1 lncRNAs under tubercidin treatment (6 h) detected using RNA FISH with specific probes to these endogenous RNAs (green). SGs were detected by expression of GFP-IGF2BP3 (pseudo-colored red). The grey image is an inverted version of the RNA FISH images (green), emphasizing the localization of mRNAs (black) in SGs (SG periphery is marked in red in the boxed SGs). Bar = 10 m. (B) Tubericidin does not interfere with MALAT1 and NEAT1 transcription. RNA FISH with probes to MALAT1 (red) and NEAT1 (green) show that these lncRNAs disperse in the nucleoplasm during tubercidin treatment, and do not localize to nuclear speckles (anti-SRSF2, magenta). Three MALAT1 and NEAT1 active transcription sites overlap (merge). Bar = 10 m. ure 6A). Three hours later tubercidin was added and the accumulation of EU-tagged RNA in stress granules was observed, as was mRNA accumulation in the nucleus ( Figure 6B). (ii) EU was added together with tubercidin ( Figure 6C) and most of the EU-tagged transcripts were not able to exit the nucleus (increase in the nuclear stain), and were not seen in the cytoplasmic stress granules. The significant nuclear accumulation of mRNA that was observed implies that the export impairment is quite severe causing a global defect in mRNA export.
Stress redistributes nucleoporins and mRNA export factors into SGs
We examined whether tubercidin-induced stress might be interfering with components of the mRNA export machinery. First, we examined whether nuclear pore complex (NPC) proteins might be affected. Indeed, the nucleoporins (Nups) Nup62, Nup98 and Nup153 substantially accumulated in the stress granules (Figure 7). Nup153 is located in the nuclear basket and has an important role in the first steps of mRNA export (40)(41)(42). Similar redistribution of Nup62 and Nup98 was found also under arsenite stress, whereas Nup153 was not found in SGs (Supplementary Figure S5), suggesting that each stress affects different sets of proteins.
Since the Nups on the cytoplasmic side of the NPC that are important for mRNA export did not seem to be mislocalized to SGs, we examined whether the Dbp5/DDX19 helicase, situated on the cytoplasmic side at Nup214, and that acts in mRNA release into the cytoplasm, might be mislocalized. Indeed, Dbp5/DDX19 was found in SGs under tubercidin and arsenite conditions (Figure 8A). Dbp5/DDX19 releases the mRNA export factor NXF1/Tap from the mRNA thus allowing the return of NXF1/Tap into the nucleus (23,43,44). Therefore, we examined if NXF1/Tap and other mRNA export factors might be ending up in SGs. The TREX (TRanscription-EXport) complex (45) recruits the export factor NXF1/Tap to capproximal sites and SR proteins recruit NXF1/Tap in downstream regions of the mRNA (4,46,47). NXF1/Tap and the TREX factors THOC5 and THOC6 were found in SGs ( Figure 8B and Supplementary Figure S6).
We next wanted to explore whether the process of SG formation might be the reason for the impairment of mRNA export caused by the stresses. During this study, we found that the overexpression of Dbp5 causes the disassembly of SGs even when the cells were stressed. In this case NXF1 Tubercidin has a negative effect on global mRNA export. Cells were treated with the modified nucleotide ethynyl uridine (EU, 1 mM) for 3 h together with and without tubercidin, in order to label cellular RNAs. Then the EU washed and regular medium (A) or tubercidin (B and C) were added for 3 h. In B tubercidin was added after the EU labeling (stress granules are marked with arrowheads) and in C tubercidin was added together with the EU and an increase in the nuclear stain was observed. Enlarged sections are shown in the right hand column. Hoechst DNA stain is in blue. Bar = 10 m.
(and THOC6, not shown) were not mislocalized ( Figure 9A). However, when we examined the distribution of the E6 mRNA under these conditions, the mRNA was still retained in the nucleus even though SGs had not formed (Figure 9B). Another approach to prevent SGs assembly is inhibition of the kinase PERK that phosphorylates eIF2␣ using GSK2606414 (48). Cells that were treated with GSK 3 hrs before tubercidin addition together with dox induction for 6 hrs, did not exhibit SG formation and the E6 mRNAs were still stuck in the nucleus ( Figure 10). Moreover, proteins involved in nuclear export such as Nup153, NXF1 and THOC5, did not accumulate in the stress granules under those conditions (Supplementary Figure S7). These data demonstrate that the formation of SGs is not the sole reason for the mRNA export impairment, and suggests that stress might cause the relocalization of a variety of factors involved in several mRNA-related processes, such that stress leads to a widespread mislocalization of proteins both in the nucleus and in the cytoplasm, bringing the flow of gene expression to a halt. We therefore examined whether other nuclear processes related to mRNA might be affected.
Tubericidin interferes with the recruitment of EJC proteins to transcripts and affects nuclear speckle composition
As mentioned above, previous work has shown that tubercidin leads to the dispersal of SRSF1 from nuclear speck-les while SRSF2 remains in them (14), implying that the each component of nuclear speckles may behave uniquely with respect to nuclear speckle localization. To broadly examine the fate of RBP localization in nuclear speckles under tubercidin conditions, we used GFP-fused splicing factors expressed from stably integrated bacterial artificial chromosomes (BACs) containing the full gene-body of several splicing factors. The genes were expressed at near physiological levels under the control of their endogenous promoters with an in-frame, C-terminal GFP-tag (26,27). In untreated cells, each of these splicing factors accumulated in nuclear speckles with differing efficiencies ( Figure 11 and Supplementary Figure S8). After tubercidin treatment, SRSF2, SRSF4, SRSF5, SRSF6, SRSF7 and Prp8 remained in nuclear speckles, whereas SRSF1, SRSF3, U1-70K and U2AF65 were mostly nucleoplasmic ( Figure 11 and Supplementary Figure S8). This suggests that the affinity of different splicing factors for nuclear speckle binding sites varies, and that nuclear speckle structure can be maintained even though several protein components are missing.
Next, we reasoned that tubercidin stress might negatively affect the recruitment of other RNA-binding proteins to the mRNA to determine the fate of the mRNAs already at the stage transcription. This was tested using a protein factor recruitment assay performed on the E6 inducible gene (25,(49)(50)(51). Since the E6 gene was stably integrated as a tandem gene array in U2OS cells, the transcribing array recruits many RNA-binding proteins involved in mRNA processing that can be easily identified over the nucleoplasmic background. Under these conditions, recruitment of the cap binding proteins (CBP20 and CBP80) that are important for mRNA export persisted ( Figure 12A, B). Splicing factors were also recruited ( Figure 12C, D). Despite the fact that tubercidin is an adenosine analogue, we found that the proteins related to poly(A) processing of mRNA, such as mam-malian cleavage factor I subunits CF I m 68 and CF I m 25 (22) and the nuclear poly(A) binding protein (PABPN), were recruited to the mRNAs (Supplementary Figure S9).
In light of the changes in the splicing factors nuclear distribution under tubercidin treatment (Figure 11), we next examined if RNA splicing patterns might be changing upon tubercidin stress. When RNA FISH for the E6 mRNA was performed using the MS2 probe and compared to a probe that detects the E6 intron, the intronic signal was found only at the transcription site ( Figure 13A), suggesting that splicing is not inhibited by tubercidin. This was in contrast to treatment with Pladienolide B, a splicing inhibitor (52), which caused unspliced E6 mRNAs (detected with the intron probe) to accumulate in nuclear speckles during the export impairment ( Figure 13B). It is known that nonspliced mRNAs accumulate in the nuclear speckles when pre-mRNA splicing is inhibited (25,(53)(54)(55)(56). Interestingly, Pladienolide B did not induce SG formation, demonstrating that the two drugs act on different pathways. More-over, examining the patterns of alternative splicing of several genes, as performed in (57), showed that tubercidin did not change splicing patterns whereas the Pladienolide B splicing inhibitor did ( Figure 13C).
In contrast to the above RBPs that were cotranscriptionally recruited to the active transcription sites under tubercidin stress ( Figure 12A-D), accumulation of the export factor ALYREF at the E6 transcription site was significantly reduced ( Figure 12E). ALYREF is also part of the TREX complex but this factor did not Nucleic Acids Research, 2019, Vol. 47, No. 9 4791 Figure 10. Tubercidin causes an mRNA export impairment even when SGs cannot assemble due to a GSK inhibitor. U2OS cells treated with a GSK inhibitor for 3 h before dox induction for 6 h with or without tubercidin addition. The export of the E6 mRNA, detected by RNA FISH (black), is impaired in tubercidin cells even when SGs (magenta) do not form due to GSK. SGs are labeled with antibodies to G3BP1. Bar = 10 m. accumulate in SGs upon stress. Additionally, there was reduced recruitment of the exon junction complex (EJC) proteins eIF4A3, Y14 and UAP65 to the active genes ( Figure 12F-H). These factors function in nuclear mRNP metabolism with connections to splicing, mRNP packaging and perhaps to export of some mRNA species (58). We noticed that the EJC proteins that were not recruited to the mRNAs transcribed on the E6 transcription sites were nucleoplasmically dispersed rather than being present in nuclear speckles, in contrast to some of the splicing factors that remained in the speckles under tubercidin treatment (Figure 12), and in contrast to the E6 mRNAs that significantly accumulated in the nuclear speckles (Supplementary Figure S3). This meant that a) the E6 transcripts are not coated by these EJC proteins, and b) nuclear speckles still formed even though some components such as EJC factors were lacking within them. This complements the information obtained above on differential splicing factor interactions with nuclear speckles (Figure 11), and the nucleoplasmic dispersal of MALAT1 lncRNA ( Figure 3). Altogether, we find that stress leads to the severing of the nucleo-cytoplasmic distribution of RBPs such that key factors are mislocalized, thereby ending up in an obstruction to mRNA export.
DISCUSSION
The stress pathway induced by tubercidin uncouples nuclear RNA metabolism from cytoplasmic RNA metabolism, thereby separating the compartments. The normal flow of the gene expression pathway is blocked during this stress response even though transcription persists, leading to the mislocalization of RNAs. Hence, tubercidin is toxic to all cell types. It failed as a chemotherapeutic agent even though it is one of several adenosine analogues, many of which are used to target cancer cells (59,60). A phase I trial in which tubercidin was administered to cancer patients showed that it caused severe effects in some human tissues, as well as venous thrombosis and necrosis of the tissue at the site of injection. Taking these effects into consideration, another phase I trial was conducted but concluded that nephrotoxicity and local irritation of the veins were too severe, and the overall effect on tumor progression was limited (19,20). Therefore, tubercidin is not administered to patients for the treatment of cancer. Our study shows why tubercidin could not be used systemically on humans. Tubercidin does not preferentially target cancer cells as anticipated, rather, it negatively affects RNA metabolism processes in both normal and cancer cells, and its effects are irreversible (not shown). Global changes to the cells are not observed after a few hours of treatment as seen in the DIC images. In the nucleus, even though transcription persists, tubercidin hampers the co-transcriptional recruitment of TREX and EJC proteins to spliced mRNAs, disrupts nuclear speckle structure and the balance of protein distribution in the nucleoplasm, mislocalizes the lncRNA from speckles, and impairs nucleo-cytoplasmic mRNA export. Future studies will be required to examine if the export of other types of RNAs such as rRNAs in pre-ribosomal subunits are also affected. In the cytoplasm, tubercidin induces a protein translation stress pathway that induces stress granule formation. These granules accumulate several proteins that are crucial in the mRNA export pathway -nucleoporins and mRNA export adaptors -such that altogether the balance between the compartments is toppled.
We found a redistribution of RNAs with respect to nuclear speckles, namely, the lncRNA MALAT1 usually found in nuclear speckles was dispersed in the nucleoplasm whereas spliced mRNAs accumulated in nuclear speckles. This exemplifies the incorrect balance within the nuclear compartment. Possibly, the entry of these mRNAs into nuclear speckles causes the displacement of MALAT1. It is known that mRNAs can pass through nuclear speckles at diffusion rates that are similar to the nucleoplasm but normally mRNAs do not amass within nuclear speckles (61)(62)(63)(64). The accumulation of export-deficient mRNAs in nuclear speckles has been demonstrated in several studies (25,54,55,(65)(66)(67), but notably, this was observed for unspliced intron-containing pre-mRNAs. Also, it was shown that EJC proteins are not recruited to transcription sites of splicing defective mRNAs (53). Here we show that spliced RNAs that do not contain EJC proteins can also accumu- Figure 12. Tubericidin interferes with the recruitment of EJC proteins to transcripts. The recruitment of various RNA processing factors to the transcribing E6 gene was examined by immunofluorescence with antibodies to: CBP20, CBP80, SRSF2, U2AF65, ALYREF, eIF4A3, Y14 and UAP56 (green). The active E6 transcription site was detected by RNA FISH with a Cy5-labeled probe to the MS2 region of the E6 mRNA (red). Arrowheads point to the factors recruited to the actively transcribing genes. Bar = 5 m. late in nuclear speckles, and that EJC proteins that usually reside within nuclear speckles (68), are dispersed in the nucleoplasm. The observations that export defective mRNAs, either intron-containing mRNAs or spliced mRNA without EJC, accumulate in nuclear speckles, strengthen the suggestion that mRNAs can pass through the nuclear speckles as they travel in the nucleoplasm and prior to mRNA export (55,69), and their interactions with nuclear speckles might be enhanced under defective conditions. Hence, one speculation could be that nuclear speckles can serve as a quality check station for mRNAs before export.
The outcome of tubercidin stress allows us to come to several conclusions regarding the composition and fidelity of nuclear speckles. First, nuclear speckle structures can persist even when the following nuclear speckle factors became mostly nucleoplasmic: splicing factors--SRSF1, SRSF3, U1-70K and U2AF65; the ALYREF TREX factor; EJC factors--eIFA3, Y14 and UAP65; and 3 -end factors CF I m 68, CF I m 25 and PABPN. The splicing factors that remained in nuclear speckles and therefore might be considered 'core' nuclear speckle factors were SRSF2, SRSF4, SRSF5, SRSF6, SRSF7 and Prp8. Indeed, it was recently Figure 13. Tubercidin causes an mRNA export defect. (A) RNA FISH experiment to detect the distribution of the E6 mRNA in U2OS cells treated with tubercidin and Pladienolide B (PlaB) using a Cy5 labeled probe that detects the MS2 region of the E6 mRNA (yellow), and a Cy3-labeled probe that detects the intron of the E6 mini-gene (red). SGs were detected using an anti-G3BP1 antibody (magenta). Hoechst DNA stain is in blue. (B) Splicing inhibition causes RNA retention in nuclear speckles. The localization of E6 transcripts under splicing inhibition by Pladienolide B treatment in U2OS cell was followed by RNA FISH using a Cy5-labeled MS2 probe (green). Nuclear speckles were detected using anti-SRSF2 (red). Hoechst DNA stain is in blue. Bar = 5 m. (C) Semi-quantitative RT-PCR analysis of cells treated with Pladienolide B (10 M) or tubercidin (10 M) together with dox induction for 6 h. Cells were examined for intron inclusion of HSP40 and DXO pre-mRNAs and for exon skipping of E6, MCL1, NOP56 and p27 pre-mRNAs. The positions of different cDNA products are noted on the right of the gel images.
shown that different proteins occupy different sub-regions within nuclear speckles (70). Second, the MALAT1 and NEAT1 lncRNAs were not required for nuclear speckle maintenance. A previous study has demonstrated that SRSF1 and MALAT1 are important for nuclear speckle assembly, as seen by depleting these components (71). Altogether, these studies suggest that nuclear speckle assembly and nuclear speckle maintenance utilize different core factors. The uniqueness of tubercidin treatment compared to studies where one or two factors were depleted, is that tubercidin treatment shows that the nuclear speckle structure can persist even though 13 protein and RNA components that we tested were simultaneously lacking or dramatically reduced in nuclear speckles.
The results also suggest that tubercidin as an adenosine analogue does not stop transcription. It probably does not obstruct the capping of the mRNA as seen by the recruitment of capping protein, possibly because guanosine is the capping nucleotide. The splicing reaction also continued as observed in an RNA FISH experiment with a probe to an intron showing that the nucleoplasmic mRNA did not contain the intron, by RT-PCR and by the continued recruitment of splicing factors to the induced gene. It seems therefore that this stress pathway which does not drastically disrupt transcription and splicing, is targeted by the cell at the mRNA export level and also involves the redistribution of nuclear proteins into cytoplasmic stress granules.
Stress granules form in the cytoplasm of eukaryotic cells upon a variety of stresses including include oxidative stress, heat-shock, viral infection, and proteosome inhibition. SGs contain untranslating mRNPs stalled at the stage of translation initiation (31,72), and many proteins, in particular RNA-binding proteins (73). SGs can form through a pathway that requires the phosphorylation of the ␣-subunit of the translation initiation factor eIF2 (eIF2␣) at residue Ser51, which reduces the levels of the eIF2.GTP.Met-
Figure 1 .
1Tubercidin affects the sub-cellular distribution of poly(A)+ RNA. The distribution of poly(A)+ RNA was examined in U2OS cells treated with tubercidin for several hours. Poly(A)+ RNA was detected using RNA FISH with an oligo-dT probe (gray), while nuclear speckles were detected by immunofluorescence using an antibody to SRSF2 (green). Enlarged areas are shown on the right. Bar = 5 m.
Figure 2 .
2mRNAs accumulate in SGs during tubercidin treatment. (A) U2OS cells treated with tubercidin (6 hrs) show the translocation of poly(A)+ RNAs detected by RNA FISH (oligo-dT probe, green) into SGs labeled with anti-G3BP1 and eIF2␣ antibodies (red). Boxed regions in the images are shown in enlarged boxes. Bar = 5 m. (B) Tubercidin increases phosphorylated eIF2␣ levels. Western blot analysis of eIF2␣ and phosphorylated eIF2␣ protein levels in U2OS cells after tubercidin or arsenite treatments for different times. Tubulin was used as a loading control. Blots are representative of three independent experiments. The average quantification of three repeated experiments is presented in the plots (mean ± SEM). There were significant differences in the relative levels of phosphorylated eIF2␣ between the times point 0 h and 6 h in cells treated with tubercidin (one sample t-test, P = 0.03141) and between 0 h and 15, 30 and 45 min in cells treated with arsenite (one sample t-test, P = 0.033, P = 0.007246, P = 0.0004958). ***P < 0.001, **P < 0.01, *P < 0.05.
Figure 4 .
4Tubercidin does not inhibit transcription but inhibits nuclear mRNA export. E6 mRNA was detected after tubercidin treatment for different times, using RNA FISH with a probe to the MS2 region in the E6 mRNA (yellow). Tubercidin was added either (A) after overnight (o/n) induction of the E6 gene with doxycycline, or (B) together with the dox induction for 6 h. Hoechst DNA stain is in blue. Bar = 5 m.
Figure 5 .
5Tubercidin impairs mRNA export of endogenous and exogenous -actin mRNAs and histone non-polyadenylated mRNAs. (A) Dox-induced -actin mRNAs were detected in U2OS cells after tubercidin treatment for 6 h and (B) endogenous -actin mRNAs were detected in MEFs after tubercidin treatment for 3 h using RNA FISH with a probe to the MS2 region in the 3 UTR of the mRNAs (yellow). Big yellow dot in A and strong dots in B are transcription sites. Hoechst DNA stain is in blue. Boxed regions are shown in the merge. Bar = 5 m. (C) Histone H2B mRNAs were detected in U2OS cells after tubercidin treatment for 6 h using RNA FISH with a probe to the coding region (yellow). Hoechst DNA stain is in blue. Bar = 5 m.
Figure 6 .
6Figure 6. Tubercidin has a negative effect on global mRNA export. Cells were treated with the modified nucleotide ethynyl uridine (EU, 1 mM) for 3 h together with and without tubercidin, in order to label cellular RNAs. Then the EU washed and regular medium (A) or tubercidin (B and C) were added for 3 h. In B tubercidin was added after the EU labeling (stress granules are marked with arrowheads) and in C tubercidin was added together with the EU and an increase in the nuclear stain was observed. Enlarged sections are shown in the right hand column. Hoechst DNA stain is in blue. Bar = 10 m.
Figure 7 .
7Nucleoporins accumulate in SGs during tubercidin stress. Tubercidin stress (6 h) causes the accumulation of some nucleoporins in SGs. POM121 nucleoporin that does not change during stress was used as a control to demarcate the NPCs. SGs were identified with an antibody to TIA-1. Bar = 5 m.
Figure 8 .
8Factors involved in mRNA export accumulate in SGs during tubercidin stress. (A) The Dbp5/DDX19 helicase and (B) NXF1/TAP and THOC5 are found in SGs during tubercidin stress. This is seen also for NXF1/TAP and THOC5 with arsenite treatment. SGs are labeled with antibodies to G3BP1 and TIA-1. Boxed areas in the images are shown as enlarged boxes. Bar = 10 m.
Figure 9 .
9Tubercidin causes an mRNA export impairment even when SGs cannot assemble. (A) Overexpression of GFP-Dbp5 (cyan) in cells stops SG formation and NXF1/TAP does not accumulate in the cytoplasm. Boxed areas in the images are shown as enlarged boxes. (B) The export of the E6 mRNA, detected by RNA FISH (yellow), is impaired in tubercidin treated cells even when SGs (magenta) do not form due to GFP-Dbp5 overexpression. SGs are labeled with antibodies to G3BP1. Bar = 10 m.
Figure 11 .
11The distribution of splicing factors in nuclear speckles during tubercidin treatment and in untreated cells. The distribution of various GFPtagged splicing factors stably expressed from BACs under tubercidin treated (6 h) conditions and in untreated cells. Merge: BAC-expressed splicing factors in green and SRSF2 in red. Bar = 5 m.
Nucleic AcidsResearch, 2019, Vol. 47, No. 9
Nucleic AcidsResearch, 2019, Vol. 47, No. 9 4787
ACKNOWLEDGEMENTSWe thank Stefan Hüttelmaier (Martin Luther University) for the IGF2BP3-GFP plasmid, Susan Wente (Vanderbilt University) for the GFP-Dbp5 plasmid and Silvia M. Barabino (University of Milan-Bicocca) for the GFP-CF I m 68 & GFP-CF I m 25 plasmids. We thank Uri Nir and Ron Goldstein (BIU) for providing cell lines. We thank Jennifer I.C. Benichou (BIU) for the assistance with the statistical analysis.Nucleic AcidsResearch, 2019, Vol. 47, No. 9 4795tRNAi Met ternary complex that is required for translation initiation. We found that tubercidin leads to the phosphorylation of eIF2␣, but with slower kinetics in comparison to arsenite that is commonly used to induce SG formation. While the presence of RBPs in SGs is integral to SG formation, the localization of NPC subunits and mRNA export factors within SGs was unexpected. Recently, two studies have found that nucleoporins and transport factors are targeted to SGs during arsenite-or sorbitol-mediated stress(74,75). One study showed that arsenite and sorbitol disrupt protein import and export by causing the accumulation of Ran, karyopherins, and Nups in SGs. We however, found that tubercidin stress affects mRNA export(75). Yet, the accumulation of export factors in SGs is not necessarily the direct reason for the mRNA export impairment, since inhibiting the formation of SGs did not release the obstruction. Also, the NPC structures still existed even though some fraction of Nups accumulated in SGs under tubercidin treatment. The Dbp5/DDX19 helicase that assists in releasing mRNA from the NPC is also in SGs, as are the major mRNA export factor NXF1/Tap and some TREX components. It therefore seems reasonable that the many changes occurring in the nucleus in RNP formation are together rendering the mRNA export-incompetent. Taken together, this study shows that when imposed with stress that does not stop mRNA transcription, the cell ensures by a variety of means that the mRNA does not reach the translation machinery.SUPPLEMENTARY DATASupplementary Data are available at NAR Online.
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Drosophila) [5], and functions in the repression of alternative intragenic promoters [7,8]. The majority of DNA methylation in the genome of the urochordate, ascidian, Ciona intestinalis [9,10] is gene body DNA methylation and is found only at a subset of genes, where it is positively correlated with gene expression level [9,10]. How this subset is selected for methylation, and whether core promoter elements play a role in this, has so far remained unknown.
The identification of core promoter elements, and mapping of transcription start sites (TSSs), at singlenucleotide resolution, has been facilitated by Cap Analysis of Gene Expression (CAGE) [11]. This has led to the discovery of two main modes for specifying sites of transcription initiation [2,12]. Sequence motifs bound by the pre-initiation complex result in transcription initiation within a narrow region and lead to "sharp" promoter architectures. Conversely, the positioning of nucleosomes defines a wider catchment area for the pre-initiation complex and leads to "broad" promoter architectures [4]. Promoter architectures can also show associations to downstream translational events. For example, promoters of ribosomal protein genes are usually sharp with a highly conserved TCT Initiator (Inr) sequence [2,13,14], which forms the beginning of a Terminal OligoPyrimidine (TOP) motif critical for nutrient-dependent translational control [15]. In mammals, these promoters, unusually, have both a TATA-box and CpG islands. In C. intestinalis they are sharp with a TCT initiator, but lack a TATA-box [13]. Recently, it has been shown that a genome-wide switch occurs in the mode of TSS selection during zebrafish embryogenesis [4]. Maternal promoters in zebrafish are sharp, or multiple sharp, with TATA-like, AT-rich (W-box) upstream elements guiding TSS selection. During the maternal to zygotic transition, nucleosomes with H3K4me3 are positioned at zygotic promoters that lack a W-box, leading to broad promoter architectures. The extent to which these, or similar, features are evolutionarily conserved is unknown.
Oikopleura dioica is a marine, larvacean, chordate in the sister group to vertebrates and is well positioned to examine the evolution of TSS features and the dynamics of TSS selection. The O. dioica genome is the most compact of any animal genome sequenced so far and 27.8% of its genes are organised into operons [16]. Each operon contains two or more genes that are transcribed from a single promoter located upstream of the first gene. The resulting polycistronic mRNA is resolved via the trans-splicing [17,18] of a spliced-leader (SL) sequence to unpaired acceptor sites at the 5' ends of each resulting monocistron. Trans-splicing in O. dioica [19] also occurs at monocistronic genes; 39% of all annotated genes give rise to mRNAs that are trans-spliced [20]. During trans-splicing a portion of the original 5' sequence upstream of the trans-splicing acceptor site is removed. Here, we mapped TSSs at single-nucleotide resolution, using CAGE, in six key stages of O. dioica development, covering the entire 6-day life cycle. In order to maximise the mapping of original TSSs (rather than trans-splice sites) we sequenced only mRNAs without the SL sequence. We used our TSS maps, together with previously generated genome-wide maps of trans-splice sites [20], E2F1 binding sites, key histone modifications and DNA methylation [21], to derive TSSselection criteria at major developmental transitions and identify novel modes of regulation. Our data show that O. dioica has some promoter features in common with vertebrates, including evidence of nucleosome positioning at broad promoters and tissue-specific expression of TATA-dependent promoters, but it differs markedly in its mode of maternal transcription initiation, which is characterized by the ordering of nucleosomes and the binding of the cell cycle regulator E2F1. O. dioica also employs a remarkable genome-wide shift in mode of TSS-selection during spermatogenesis, associated with a distinct, tissuespecific, TCTAGA core promoter motif, that has not been previously identified.
Results
Promoter usage across development
We extracted RNA for CAGE from O. dioica at six stages of development across the 6-day life cycle of the animal (Fig. 1a). Illumina sequencing generated > 39 M reads, of which 2.4-5.9 M (54-64%) for each stage mapped uniquely to the genome (Additional file 1: Table S1). Summing tags that mapped to unique positions gave the abundance of transcripts originating from each TSS. We normalized these counts to tags per million reads (tpm) and clustered neighbouring TSSs (allowing up to 20 bp between TSSs) to generate tag clusters (TCs), which revealed the set of promoter regions that are active within each stage. TCs (supported by at least 1 tpm in at least one stage) mapped to 6241 annotated genes, 4,937 of which were defined as expressed using previously generated tiling array data [22] across equivalent developmental stages (Additional file 1: Figure S1). Multiple genes within an operon are transcribed from a common TSS. In line with this we captured TCs for only 538 downstream operon genes, out of 2832 (19%) that were defined as expressed based on tiling array data (Additional file 1: Figure S1). TCs for these 538 genes include previously unidentified stage-specific use of cryptic internal promoters within operons. Previously, we generated a bp-resolution, genome-wide map of trans-splice sites in O. dioica [20] using pooled animals collected at the same developmental stages we used here. As previously, we define a gene as trans-spliced if it is associated with a mapped trans-splice site. Our newly generated CAGE dataset captures the original TSSs . Changes in the proportion of mRNAs that are trans-spliced (blue) and nontrans-spliced (pink) are shown schematically in the upper panel, above a colour bar indicating major promoter categories (colours corresponding to clusters in (b)). Developmental stages are shown schematically below this bar. b Expression profiles obtained from self-organising map clustering of CAGE TSSs (CTSSs). Each beanplot shows the distribution of relative expression (y-axis) originating at CTSSs (number of CTSSs above each plot) within each cluster at each developmental stage (x-axis) labelled only in the bottom right plot. Coloured boxes and associated labels indicate groups of clusters with similar expression profiles. c Beanplots showing the distribution of interquantile widths of tag clusters (TCs) within each stage and assigned to the expression cluster of the dominant CTSS (plots are ordered and coloured as in (b)) revealing an increase in the use of sharp promoters in adult(tissue)-specific genes. d Heatmap showing the number of promoters that shift up-or down-stream in location between all possible pairs of developmental stages. The highest number of shifting promoters occurs between pre-metamorphic (tailbud) and post-metamorphic (day 2 and day 6) stages. e Distribution of the interquartile widths of consensus promoter regions of trans-spliced (SL) and non-trans-spliced (Non-SL) genes of 51% (1341/2643) of all monocistronic (non-operon) trans-spliced genes allowing us to analyse promoter features of trans-spliced genes. Since trans-splicing is thought to occur co-transcriptionally, and some monocistronic genes can be both trans-spliced and non-transspliced depending on the developmental stage, we did not expect to capture a larger proportion of the promoters of all potentially trans-spliced monocistronic genes. We defined 13,771 consensus promoter regions in the genome by clustering TCs, with > 5 tpm, across stages [4,23]. Expression profiles of individual TSSs were clustered using a self-organizing map [4,23] (SOM) in order to assess the dynamics of TSS selection across development ( Fig. 1b). Distinct ubiquitous, maternal and zygotic expression TSS clusters were present as well as a large cluster of male-specific TSSs. SOM clustering of consensus promoter region expression profiles revealed similar patterns (Additional file 1: Figure S2).
A genome-wide shift in mode of TSS selection during spermatogenesis
Maternal and ubiquitously expressed TSSs (identified by SOM clustering; Fig. 1b), and TSSs associated with transspliced genes, were found predominantly within broad TCs (Fig. 1c,e and Additional file 1: Figure S2) whereas TSSs used specifically in adult stages, particularly male-specific TSSs, were predominantly found in sharp TCs (median width of male-specific promoters in day 6 male was 4 bp compared to 25 bp in maternal promoters in oocytes and 23 bp in ubiquitous promoters in day 2 animals); Fig. 1c, Additional file 1: Figure S2). The presence of sharp TCs suggests sequence motifs in these core promoters determine the selection of TSSs at a fixed distance downstream. We therefore examined all promoter sequences and identified a core promoter element (TCTAGA), embedded in a TT-rich sequence context, which was remarkably specific to male-specific TSSs ( Fig. 2; see also Additional file 1: Figure S3 for frequencies of other motifs and dinucleotides, across the genome and around different classes of promoters). This element was present in 71.6% (1391/1943) of male-specific TCs in the male and was strictly positioned 40-50 nt upstream of the dominant TSS (with a strong preference for 45-48 bp; Fig. 2b). Given that the majority of the animal's mass at this stage is found in the gonad our data strongly suggests the use of a unique mode of gene regulation that is linked to spermatogenesis. Indeed, when we examined existing array data from dissected testes, ovaries and trunks of day 6 animals we found that 369/502 (73.5%) of genes that are specifically expressed in the testis (and represented in our CAGE data set) are associated with a TCTAGA promoter element, compared to 100/906 (11.0%) that are specific to the ovary and 7/275 (2.5%) that are specific to the trunk (Additional file 1: Figure S4).
In order to determine whether or not this mode of regulation is found in mammals we re-analyzed existing CAGE data [23,24] from a time course of 8 testis samples across mouse development from embryogenesis to adult tissues. We found no enrichment for a position-specific TCTAGA motif in promoter regions of any stage, nor of promoters with spermatogenesis-associated expression patterns (data not shown). In order to determine if this mode of regulation is present in other urochordate genomes we searched the promoter regions of 16,671 annotated genes in the C. intestinalis genome and found only 226 (1.3%) with a TCTAGA within 100 bp upstream of the annotated start site compared to 2088 (12.5%) that had a consensus TATA-box motif. This suggests a larvacean, lineage-specific evolution of this mode of TSS-selection for the activation of the spermatogenesis transcriptional program.
A single gene may have several alternative TSSs selected at different developmental stages. We identified all promoter regions with a shift in TSS usage [4,23] between Promoters were categorized according to promoter type as in d. Error bars show 95% confidence intervals for the mean obtained by bootstrapping any pair of developmental stages. We observed the highest number (124/519) of single promoter regions for which the TSS location changed (< 40% TC overlap) when comparing the embryo versus adult male stages ( Fig. 1d; Additional file 1: Figure S5). In 43/124 of these cases there was a shift from promoters lacking a TCTAGA in the embryo to a TCTAGA-associated promoter in the male. This suggests that the TCTAGA promoter element may play a role in selecting alternative TSSs during spermatogenesis.
The O. dioica genome contains 1765 operons that comprise multiple genes that are transcribed from a single promoter into polycistronic mRNA. Cryptic internal promoters within operons, which drive tissue-specific expression of downstream genes, have been described in C. elegans [25] but the prevalence of these in the O. dioica genome is unknown. We identified 693 internal promoters within operons in O. dioica: male-specific promoters (208) were over-represented and the TCTAGA element was found more frequently (25.5%; 177 promoters) than expected (χ 2 = 142.98, df = 1, p < 2.2 × 10 −16 ). This suggests that during spermatogenesis the TCTAGA element plays a role in selecting TSSs at internal promoters within operons that are otherwise transcribed from a single upstream promoter in other stages. We therefore analyzed patterns of enrichment of the H3K4me3 promoter mark from ChIP-chip data [21] in the ovary and testis of animals at the same developmental stage as the day 6 male and female animals used to generate our CAGE dataset. In support of the presence of male-specific cryptic internal promoters within operons, we only found enrichment of H3K4me3 at the start sites of internal genes within operons in the testis, whereas the start sites of operons were enriched for this mark in both the ovary and testis (Additional file 1: Figure S6).
Sites for trans-splicing are determined by the presence of an unpaired AG acceptor site, which is usually followed by an adenine [20]. Remarkably, we found that 89 male-specific promoters in males (associated with 87 genes) had a TCTAGA motif with its AGA mapping to a trans-splice site (representing 16.4% of all TCTAGA male-specific genes that were annotated as trans-spliced). Transcription downstream of these TCTAGA elements during spermatogenesis therefore results in mRNAs that lack a trans-splice acceptor site and are therefore not trans-spliced with the SL sequence. Transcription driven by alternative upstream promoters during other stages of development leads to mRNAs with the trans-splice site intact and are therefore trans-spliced with the SL. This finding reveals a novel mechanism for the developmental regulation of trans-splicing.
Male-specific TCTAGA promoters had significantly higher expression levels compared to other promoter types in males (all p < 0.05; Fig. 2d). We analyzed the profiles of a range of histone modifications as well as RNA pol II occupancy using ChIP-chip in the testis and ovaries of day 6 stage-matched animals [21]. We found that malespecific TCTAGA promoters were associated with higher RNA pol II occupancy and higher enrichment of histone modifications associated with active transcription (and depletion of repressive marks) in the testis, including specific marking by H3K18ac (Fig. 2e). Several of these marks were independent of expression level (Additional file 1: Figure S7). Together, our data revealed a unique transcription initiation code that was specific to male-specific core promoters. This code is associated with a chromatin state primed for high levels of transcription in the testis and directs both a genome-wide shift in promoter usage, and the developmental regulation of operon transcription and trans-splicing.
Maternal modes of TSS selection in endocycling nurse nuclei
Maternal promoters in zebrafish tend to be sharp, or multiple sharp, with a degenerate TATA-like motif (Wbox) determining TSSs [4]. In contrast, we found that maternal promoters in O. dioica were broad (Fig. 1c) and lacked a W-box at the expected TATA-box position or any other enrichment of dinucleotides (Additional file 1: Figure S3). Broad promoters in zebrafish are associated with ordered nucleosomes, as shown by the precise positioning of histone H3K4me3 enrichment at the first nucleosome downstream from the dominant TSS [4]. Here, we used ChIP-chip data [21] from the ovaries of day 6 (stage-matched) O. dioica and analyzed the profiles of H3 and H3K4 histone modifications around dominant TSSs of maternal promoters. Distinct peaks of histone H3 enrichment flanked the dominant TSSs at broad promoters in the ovary (Fig. 3a) with a peak in H3K4me3 enrichment immediately downstream (Fig. 3a) as seen in vertebrate broad promoters. These data show that TSS-selection in O. dioica broad promoters has similar features to those in vertebrate broad promoters, indicating that this may be the main mode of TSS selection in (predominantly broad) maternal promoters in O. dioica.
We also found that the nucleosome-free region at the TSS of broad promoters in the day 6 female corresponds to an enrichment of the activating transcription factor E2F1 (Fig. 3a), a key regulator of the cell cycle [26]: 27.7% (1075/3882) of genes with strong CAGE support (≥ 5 tpm) had promoters bound by E2F1 in the ovary. These genes were enriched for, though not limited to, known E2F1-regulated functions (Additional File 1: Figure S8). These results suggest that E2F1 has a role in regulating maternal transcription in O. dioica.
Maternal promoters in O. dioica were located on the X-chromosome more frequently than expected, compared , revealing a female-bias of X-linked genes [27] in O. dioica.
Regulation of zygotic promoters
Zygotic promoters in O. dioica (TSS clusters with low maternal and high embryonic expression; Fig. 1b) contained an upstream GC-rich region, characteristic of broad promoters, and a downstream poly(T)-tract (Additional file 1: Figure S3). An E-box [28] motif with a significant match to the binding site of TFAP4 (activating enhancer binding protein 4), a regulator of cell proliferation, was over-represented in the region immediately upstream of 259 zygotic-specific TSSs in the embryonic tailbud stage (Fig. 3b-d; Additional file 1: Figure S9). Genes associated with these TSSs were enriched for GO terms related to muscle development (Additional file 1: Figure S10).
TSS selection in ubiquitous and ribosomal protein gene promoters
Most O. dioica promoters used to drive ubiquitous expression throughout the life cycle (Fig. 1b) had a broad architecture with a strong GC-rich band immediately upstream of the TSS, as seen in zygotic promoters, and a clear GAAA signal at the expected +1 nucleosome position (Additional file 1: Figure S3). We also found a position-specific (median distance 56 bp upstream; Fig. 3e) ACCATAA sequence element associated with TSS-selection in sharp ubiquitous promoter regions ( Fig. 3b and Additional file 1: Figure S3), as well as in sharp promoters specific to day 2 animals (juvenile animals; pregametogenesis). This motif was present in 215 consensus promoter regions. Whereas a typical Initiator (Inr) CA dinucleotide was present in 53% of consensus promoter regions in O. dioica, the TCT initiator, which is highly conserved at ribosomal protein genes in other species, including C. intestinalis, was absent from all CAGE-detected ribosomal protein genes in O. dioica (29 detected out of 129 annotated; the majority being located within operons [20]). Unlike the sharp promoters of these genes in other species, TCs of these ribosomal protein genes in O. dioica were predominantly broad (only 6/51 were sharp; 2/6 contained a TATA-element), in line with other trans-spliced gene promoters in this animal (Fig. 1e), and we found a higher average CpG content than non-ribosomal protein genes (Welch Two Sample t-test: t = 3.22, df = 35.164, p = 1.379 × 10 −3 ). This indicates that these promoters have lost the specific transcriptional regulation conferred by the TCT initiator in other species and provides further evidence that the trans-spliced SL replaces the role of the TOP motif [20], which starts at this initiator sequence.
Conserved tissue-specific TATA-dependent TSS-selection is associated with higher levels of DNA methylation in gene bodies
We next searched all our CAGE-defined promoters for the ancient TATA-box promoter element in order to assess the usage of this promoter motif in O. dioica development. A TATAW element was present in 10.7% of Figure S2A) containing TATA-elements as labelled (TATAW = core TATA motif; TATA-box = consensus TATA-box). Percentage of promoters that contain TATA-elements within each expression cluster is also shown (right): the majority of TATA-dependent promoters are adult-specific. Expression clusters are grouped and coloured according to colours in Fig. 1b. b-c Plots show the mean log 2 ratio of methyl-DNA IP/input (b) or ChIP/input (c) (y-axis) at each probe position (x-axis) in a 1000 bp window centred on the dominant TSS, in ovaries, testes and embryos (tailbud) as labelled. Error bars show 95% confidence intervals for the mean obtained by bootstrapping. Promoters were divided into broad and sharp with sharp subdivided into those with a TATAW-element and those without and, in the testis, those with the position-specific TCTAGA motif. DNA methylation was enriched in the downstream of TATA-dependent promoters (b) and H3K4me2 and H3K4me3 were depleted in the same regions (c) consensus promoter regions, in line with the percentages of TATA-dependent promoters in mammals [29]. A lower percentage (3.8%) of promoters had a longer consensus TATA-box motif (TATAWAWR). The use of promoters with this consensus motif was specific to sharp promoters in adult stages (Fig. 4a and Additional file 1: Figure S3), indicating that this mode of TSS-selection at tissue-specific promoters is conserved between O. dioica and vertebrates. As in other species, the preferred location of the TATA box was 28-31 bp upstream.
We then analysed profiles of methylated DNA enrichment around promoters using meDIP-chip (methylated DNA immunoprecipitation followed by chip) data [21] from ovaries, testes and tailbud stage embryos, in order to uncover any associations with core promoter elements. Interestingly, we found that TATA-dependent sharp promoters had a higher average enrichment of DNA methylation in downstream gene bodies than TATAless sharp promoters in embryos, ovaries and testes (Fig. 4b). This trend was not explained by expression level (Additional file 1: Figure S11A) or proximity to the promoter (Additional file 1: Figure S11B) but did correspond to a higher frequency of CpGs (Additional file 1: Figure S11C). A regression analysis showed that despite accounting for expression level (B = 0.06, p = 2.04 × 10 −8 ), promoter width (B = -0.04, p = 2.47 × 10 −4 ) and downstream CpG content (B = 0.26, p < 2 × 10 −16 ) the presence of the most common core TATAA motif was a significant, independent, positive predictor (B = 0.27, p = 1.32 × 10 −12 ) of downstream DNA-methylation levels in ovary, testis and tailbud, (the stage of development was not a significant predictor, overall fit of the model, R 2 = 0.08). H3K4me3, which inhibits the interaction of DNA methyltransferases with histone proteins [30], was depleted (as was H3K4me2) at the TSS and in the downstream regions of TATA-dependent promoters, compared to TATA-less sharp promoters, in both the ovary and testis (Fig. 4c). Together our findings reveal a specific association of gene body DNA methylation, and H3K4me3 depletion, with a TATA-dependent mode of TSS selection in O. dioica. We found a similar association in zebrafish, although the increase in DNA methylation compared to TATA-independent promoters was at the TSS rather than the gene body (Additional file 1: Results and Figure S12).
Discussion and conslusions
Here, we mapped sites of transcription initiation genomewide at single nucleotide resolution across the life cycle of a marine chordate belonging to the sister group to vertebrates. Our data revealed a suite of of TSS-selection criteria in O. dioica (Fig. 5) with features that are both shared with vertebrates and markedly different, particularly among maternal and spermatogenesis promoters (Additional file 1: Table S2). A recent study in zebrafish found that maternal promoters are sharp (or multiple sharp) with a TATA-like upstream element whereas zygotic promoters are broad with transcription initiation guided by ordered nucleosome positioning [4]. In comparison, we found that in O. dioica, both maternal and zygotic promoters are broad. Moreover, we found evidence of nucleosome positioning as well as an enrichment for the binding of E2F1 at broad maternal promoters. These differences in maternal TSSselection between zebrafish and O. dioica may be due to different modes of oogenesis and different sources of maternal transcripts. In zebrafish maternal transcripts originate from oocyte nuclei whereas in O. dioica the majority of maternal transcripts originate from terminally differentiated polyploid nurse nuclei within the single-cell coenocyst and are transported to oocytes through ring canals [31,32].
Most maternal transcripts are trans-spliced in O. dioica [20] and this may have influenced the evolution of maternal promoter architectures. Since trans-splicing removes the 5' end of a pre-mRNA (the "outron") it follows that this sequence has little, if any, role in the post-transcriptional regulation of its mRNA. Indeed, one hypothesis for the function of trans-splicing in monocistrons is that it removes deleterious sequences at the 5' end of an mRNA (e.g. premature start codons). There is mounting evidence that the SL sequence itself plays an important role in translational control, particularly for TOP mRNAs, which are trans-spliced in O. dioica [20]. We have shown here that the conserved TCT initiator sequence, which constitutes the first two nucleotides of the TOP motif, is absent at O. dioica ribosomal protein TSSs. We hypothesize that there is no requirement for a strict site of transcription initiation for trans-spliced genes since the spliced leader provides any necessary 5' post-transcriptional regulatory motifs. Promoters of trans-spliced genes are then permitted to adopt a broad architecture governed by chromatin state rather than sequence motifs.
Our data also revealed a remarkable genome-wide shift in mode of TSS-selection during spermatogenesis to one associated with a position-specific core promoter motif (TCTAGA). This shift is likely regulated by a basal transcription factor that is specifically expressed in the male. With a distance (44 bp) from the TSS similar to that of the TATA-box (36 bp) it is tempting to speculate that a TFIID complex containing a male-specific variant of the TATA-binding protein (TBP) is the factor binding TCTAGA and driving expression of male-specific genes. Indeed, variants of the basal transcription factor (TF) machinery are known to play roles in development and gametogenesis across metazoans [33]. One consequence of this shift is the developmental regulation of trans-splicing during spermatogenesis: many mRNAs that are trans-spliced in other stages (often in operons) are transcribed during spermatogenesis from an alternative TSS, driven by a TCTAGA promoter located downstream of the trans-splice acceptor site. This trans-splice acceptor site is thereby excluded from resulting mRNAs, which are no longer trans-spliced with the SL sequence. This may lead to a switch in the translational control of these transcripts to one that is independent of nutrient levels [20]. We hypothesise that this translational control is not required during the non-vitellogenic process of spermatogenesis. Nutrient-dependent control over initiation of meiosis has, however, been described in both sexes of O. dioica [34]. The TCTAGA promoter motif may play a role in this regulation in males if its binding by a transcription factor is nutrient-dependent.
A recent study found that genes with transcriptionassociated gene body methylation encode more highly conserved proteins with typical "housekeeping" functions [9]. We discovered a strong association of gene body DNA methylation with TATA-dependent promoters in O. dioica. This relationship is present during early development as well as in both the male and female germ lines, despite these differing substantially in their chromatin landscapes [21]. Promoters with the malespecific TCTAGA motif did not exhibit this downstream DNA methylation enrichment, despite this motif being position-specific and located in the expected TATA-box position. This indicates that gene body methylation in a subset of O. dioica genes is driven by core promoter features, specifically the TATA-box. A study in C. intestinalis found that gene bodies in near identical sets of genes are methylated in different cellular contexts [35], which is similar to our observations in O. dioica. This study also showed, however, that features within two ubiquitously expressed promoters are not the primary determinant of gene body DNA methylation. Analysis of additional C. intestinalis promoters may nevertheless reveal a relationship with the TATA-box similar to what we observe in O. dioica. Further exploration of sequence context in both species may also reveal a role for additional factors.
Given that DNA methylation in gene bodies suppresses transcription from alternative downstream promoters [7,8] it is tempting to speculate that TATA-dependent sharp promoters employ DNA methylation as additional insurance for the strict positioning of transcription initiation. We also observed a depletion of H3K4me3 at, and downstream of, TATA-dependent promoters, in line with the inhibitory effect of H3K4me3 on DNA methyltransferases. Since TFIID is anchored at H3K4me3 on the +1 nucleosome [36] this indicates that TATA-dependent promoters are bound by TBP as part of an alternative complex. In yeast, TATAdependent promoters are depleted of both TFIID and a nucleosome positioned downstream of the TSS and TBP is instead directed to the TATA-box by the SAGA complex [37]. Further investigation is required to establish whether or not a similar situation exists in metazoans.
Our results support previous findings of overlapping promoter codes [4], while revealing additional diversity and differential usage during complex developmental transitions. We provide the first links between acquisition of trans-splicing and the reorganization of promoter architectures for a conserved set of core metabolic genes, probably arising at least in part, because of regulatory sequences encoded in the SL. We also show shifts in TSS selection associated with a previously unidentified core promoter motif during the spermatogenic program. Further work on a range of additional models would provide a better framework in understanding the evolution of core promoter architectures, particularly with respect to innovations within major lineages.
Methods
Modified cap analysis of gene expression (CAGE)
Total RNA from each stage of development was isolated using RNAqueous Micro (Ambion) and treated by Terminator TM 5'-Phosphate-Dependent Exonuclease to deplete excess small RNAs. A modified CAGEscan protocol [11] was carried out at DNAFORM, Yokohama City, Japan. The standard CAGEscan protocol was modified in order to separate trans-spliced from non-trans-spliced transcripts by first using a custom designed 5' linker, specific to the 5' spliced leader sequence, before using standard linkers for non-trans-spliced mRNAs. Sequenced libraries for each stage therefore included only non-transspliced transcripts.
Mapping reads
Illumina sequencing generated a total of 39,124,333 reads, 37 nt in length. We mapped these to the O. dioica reference genome [16] using Bowtie [38] with default parameters (allowing 2 mismatches per read). The 5' coordinates of all uniquely mapping read (CAGE tag) alignments were extracted from the Bowtie output to give positions of CAGE transcription start sites (CTSSes), and the number of tags at each position was computed to give a tag count for each CTSS. We normalized tag counts to tags per million reads (tpm).
Promoter types
We used the R package "CAGEr" [23] to cluster CTSSes into CAGE tag clusters, excluding those with < 1 tpm and singletons < 5 tpm, using a maximum distance of 20 bp between CTSSes within a cluster. We calculated the interquantile range (q 0.1 − q 0.9 ) of promoter widths (a measure of how broad/dispersed or peaked/focused a promoter's TSS usage is that is more robust to expression level than using the full promoter width). We used this to group promoters into four classes using the mean and upper and lower quartiles as thresholds. We defined the upper and lower quartiles as "broad" and "sharp" respectively. We categorized promoters by CpG frequency in a 200 bp window centered on the dominant CTSS. Promoters with a CpG frequency in the upper quartile of CpG frequencies were classed as high CpG (HCG) and promoters with a CpG frequency in the lower quartile classed as low CpG (LCG). Using CAGEr we grouped all tag clusters with > 5 tpm across all stages into consensus promoter regions, using the interquantile range (q 0.1 − q 0.9 ) of tag cluster widths and a distance of 100 bp to merge clusters into one region. We used SOM clustering both at the level of individual CTSSes and consensus promoter regions to generate 25 expression profiles in each case.
Shifting promoters
We calculated a shifting score and p-value of Kolmogorov-Smirnov test for all consensus promoters for all pairwise comparisons. We used a score > 0.6 and FDR < 0.01 to define a promoter shift -identifying promoters that have at least 60% of transcription initiation in the sample with lower expression occurring either upstream or downstream of transcription initiation in the compared sample.
Assigning CTSSes to gene models and operons
We used Genoscope gene model predictions and annotations of polycistrons (www.genoscope.fr) to classify genes into operons and non-operons. A CTSS was associated with a gene model if it overlapped a gene body or its 500 bp upstream region. Using previously published CAGE data for trans-spliced transcripts [20], we classed a gene as SL trans-spliced if there was a SL CTSS within the gene body or within a 500 bp upstream region, if it was supported by > 1 tag count and if it had an ' AG' acceptor site motif immediately upstream.
GO analysis
We used O. dioica GO annotations [22]. We used the Bioconductor GOstats package in R to compute hypergeometric p-values for over-representation of GO terms in different sets of genes.
Motif analyses
Over-represented motifs in core promoter regions were identified using MEME with default parameters on sequences in a 200 bp window, centred on the dominant CTSS within each tag cluster, for groups of CTSSes of interest. We also identified position-specific motifs (including initiator trinucleotides) by scanning core promoter regions for the occurrence of all possible k-mers (for k=1-6). We used TOMTOM to match positionweight matrices of motifs identified by MEME to known transcription factor binding sites [39]. We plotted the dinucleotide content of promoters using the R package "seq-Pattern". We searched for TATA elements in the region 37-22 bp upstream of the dominant CTSS in each TC. We searched for TCTAGA motifs in the 22-52 bp and 52-101 bp upstream regions. We searched for ACCATAA motifs in the 32-72 bp upstream region. We used zygotic (CTSS SOM cluster 0_0) promoter sequences (200 bp centred on the dominant CTSS) from the tailbud stage to identify over-represented zygotic motifs. We used the "Biostrings" R package to scan (using a minimum score of 85%) the 101 bp upstream region with the position weight matrix discovered by MEME that matched the binding site for human TFAP4.
ChIP-chip analysis
We analysed previously published meDIP-chip data and ChIP-chip data for E2F1, H3 and histone modifications H3K4me1, H3K4me2, H3K4me3 and H3K27me3 from mature O. dioica ovaries and testes [21]. We used the Bioconductor R package Ringo [40] for pre-processing all ChIP-chip data. Briefly, we normalized raw probe intensities from each sample (Cy5 channel) to corresponding input DNA probe intensities (Cy3 channel) by computing log 2 (Cy5/Cy3). We used the NimbleGen normalization method, which adjusts for systematic dye and labeling biases by subtracting from individual log 2 ratios the Tukey's biweight mean, computed across each sample's log 2 ratios. To reduce noise in the data we smoothened the normalized log 2 ratios using a running median across a 150 bp window (the approximate size of a single nucleosome) with a minimum threshold of 3 non-zero probes. For each group of promoters we plotted the mean log 2 ratio at each probe position for all probes in a 1000 bp window centred on the dominant CTSSes of promoter regions of interest. We excluded promoters with flanking regions that overlap. We defined regions of ChIPenrichment genome-wide as previously described [21].
Operon transcription analysis
We used tiling array data generated from O. dioica testes and ovaries [22] to categorize genes within operons as expressed or silent. We then defined an operon as expressed if any of its genes are classed as expressed. We intersected H3K4me3 ChIP-enriched regions with operon promoters, as well as potential promoters of internal operon genes, using the region 500 bp upstream and 100 bp downstream of annotated start sites. Any overlap was defined as a presence of H3K4me3 in a candidate promoter region.
5' RACE
RACE was performed using SMARTER RACE kit from Clontech according to manual.
Re-analysis of mouse testis CAGE data
Analysis of TSS data followed that found in [23] using data downloaded from http://promshift.genereg.net/CAGEr/ InputData/ consisting of TSSs from 8 stages of mouse testis development. Briefly, we used the CAGEr [23] package to normalize tag counts and cluster TSSs into TCs for each stage. We plotted the frequency of TCTAGA motif around TSSs from each stage, sorted by the width of TCs and saw no enrichment. We then used a self organizing map (SOM) to cluster the expression profiles of each TSS and identified a cluster with expression specific to later development which was previously annotated as being enriched for TSSs associated with spermatogenesis genes [23]. We plotted the TCTAGA frequency around the TSSs of this cluster and also saw no enrichment.
Search for TCTAGA and TATA-box motifs in C. intestinalis promoters
We searched the 100 bp region upstream of all annotated Ensembl 87 KH C. intestinalis genes for "TCTAGA" motif and the consensus TATA-box motif "TATAWAR" using the "Biostrings" R package.
Additional file
O
Fig. 2
2Features of spermatogenic promoters in O. dioica. a Heatmap shows the density of TCTAGA at each position (x-axis) in a -500 to +500 bp region centred on the male dominant TSS for spermatogenic promoter sequences (rows) ordered by promoter width (top to bottom = broad to sharp). Darker blue indicates higher enrichment. b Distribution of distances (median = 44 bp) to the TCTAGA motif relative to the dominant TSS in male day 6 animals. c The TCTAGA motif is specific to transcription in the adult male (final bar in each plot = male-specific (4_4) cluster): of all promoters with a TCTAGA motif the majority have a male-specific expression profile (top). Moreover, the majority of spermatogenic transcription is associated with a TCTAGA motif: of all promoters with a male-specific expression profile the majority contain a TCTAGA, whereas very few promoters in other expression classes contain this motif (bottom). d Distribution of tag counts (tpm) for different promoter classes (see colour key code in e) in the male: TATA = TSS with upstream TATAW element; TCTAGA = TSS with upstream TCTAGA; Sharp = all other promoters with narrow region of TSSs; Broad = dispersed region of TSSs. e ChIP-chip data for day 6 testes are shown for RNAPII, H3K18ac, H3K27ac, H3K4me3, H3K4me2, H3K36me1 and H3K9me1. Each plot shows the mean log 2 ratio of ChIP/input at each probe position in a 1000 bp window centered on the dominant TSS.
Fig. 3
3Features of maternal, zygotic and ubiquitous promoters in O. dioica. a Ordered nucleosome positioning at broad promoters in the ovary. Data are shown for H3, H3K4me1, H3K4me2, H3K4me3 and E2F1 ChIP-chip experiments. Each plot shows the mean log 2 ratio of ChIP/input at each probe position in a 1000 bp window centred on the dominant TSS. Promoters were categorized into sharp (blue) and broad (pink) using lower and upper quartiles of widths across all stages. Error bars show 95% confidence intervals for the mean obtained by bootstrapping. b Percentage of all consensus promoters (left) within each expression cluster (x-axis) (profiles shown in Additional file 1:Figure S2A) containing sequence elements as labelled (O. dioica TFAP4-like motif, ACCATAA motif). Percentage of promoters that contain each motif falling within each expression cluster is also shown (right). Expression clusters are grouped and coloured as coded inFig. 1b.c Sequence logo for an over-represented motif (E-value and number of sites as indicated) in zygotic promoters (tailbud sequences from TCs with dominant CTSS in cluster 0_0) in O. dioica (top), and its alignment to a significant match (E-value and p as indicated) for the binding site motif of human TFAP4. d Heatmap shows the density of the zygotic promoter motif matching TFAP4 at each position (x-axis) in a -500 to +500 bp region centred on the tailbud dominant TSS for zygotic promoter sequences (rows) ordered by promoter width (top to bottom = broad to sharp). Darker blue indicates higher enrichment. e Distance relative to the dominant TSS in day 2 animals for the ACCATAA motif found in sharp promoters that have ubiquitous and day 2-specific expression profiles to zygotic promoters (χ 2 = 43.34, df = 1, p = 4.61 × 10 −11 )
Fig. 4
4Features of TATA-dependent promoters in O. dioica. a Percentage of all consensus promoters within each expression cluster (left) (profiles shown in Additional file 1:
Fig. 5
5Promoter types in O. dioica. Schematic shows representative features of maternal, zygotic, ubiquitous (and ribosomal protein), tissue-specific and spermatogenic promoters with the key stages of the O. dioica life cycle. Horizontal lines represent positions of CAGE tags to indicate broad (staggered) or sharp (end-aligned) promoter architectures; green ovals represent pre-initiation complex sub-units. Motifs and dinucleotide enrichments are indicated. Brown circles represent positions of nucleosomes: no overlap indicates ordered positioning; question marks indicate lack of data. Trans-splicing with the spliced-leader (SL) at an AG acceptor site is also shown at promoter types where this is common. Boxes represent enrichments of histone modifications across maternal, spermatogenesis and adult promoters: red = enrichment; white = depletion
Abbreviations 5mC: 5-methylcytosine; CAGE: Cap analysis of gene expression; ChIP: chromatin immunoprecipitation; CTSS: CAGE transcription start site; GO: Gene ontology; Inr: Initiator; meDIP: Methylated DNA immunoprecipitation; RACE: Rapid amplification of cDNA ends; SL: Spliced leader; SOM: Self-organizing map; TC: Tag cluster; TF: Transcription factor; TOP: Terminal OligoPyrimidine; tpm: Tags per million; TSS: Transcription start site
Fig. 1 Promoter usage across the O. dioica life cycle. a The 6-day life cycle with stages used for single-nucleotide resolution of TSS-mapping by CAGE are labelled (oocyte, tailbud, tadpole, day 2, female day 6 and male day 6)o c y te
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Additional file 1: Supplementary Material. Supplemental Results, Supplemental Methods, Table S1, Table S2, Figures S1 -S12 and Supplemental References. (PDF 13 464 kb)
AcknowledgementsWe thank Matthias Harbers and his staff at DNAFORM (Yokohama, Japan) for their assistance in the development of the modified CAGE protocol. We thank Jean-Marie Bouquet, Magnus Reeve and Anne Aasjord for supplying animals as part of the animal culture facility.FundingThis work was supported by grants 183690/S10 and 133335/V40 from the Norwegian Research Council.Availability of data and materialsThe datasets generated and/or analysed during the current study are available in the NCBI Gene Expression Omnibus under accession number GSE78794 and GSE78915. Ethics approval and consent to participate Not applicable.Authors' contributionsConsent for publicationNot applicable.Competing interestsThe authors declare that they have no competing interests.Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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| BackgroundAnnelids and arthropods each possess a segmented body. Whether this similarity represents an evolutionary convergence or inheritance from a common segmented ancestor is the subject of ongoing investigation.MethodsTo investigate whether annelids and arthropods share molecular components that control segmentation, we isolated orthologs of the Drosophila melanogaster pair-rule genes, runt, paired (Pax3/7) and eve, from the polychaete annelid Capitella teleta and used whole mount in situ hybridization to characterize their expression patterns.ResultsWhen segments first appear, expression of the single C. teleta runt ortholog is only detected in the brain. Later, Ct-runt is expressed in the ventral nerve cord, foregut and hindgut. Analysis of Pax genes in the C. teleta genome reveals the presence of a single Pax3/7 ortholog. Ct-Pax3/7 is initially detected in the mid-body prior to segmentation, but is restricted to two longitudinal bands in the ventral ectoderm. Each of the two C. teleta eve orthologs has a unique and complex expression pattern, although there is partial overlap in several tissues. Prior to and during segment formation, Ct-eve1 and Ct-eve2 are both expressed in the bilaterial pair of mesoteloblasts, while Ct-eve1 is expressed in the descendant mesodermal band cells. At later stages, Ct-eve2 is expressed in the central and peripheral nervous system, and in mesoderm along the dorsal midline. In late stage larvae and adults, Ct-eve1 and Ct-eve2 are expressed in the posterior growth zone.ConclusionsC. teleta eve, Pax3/7 and runt homologs all have distinct expression patterns and share expression domains with homologs from other bilaterians. None of the pair-rule orthologs examined in C. teleta exhibit segmental or pair-rule stripes of expression in the ectoderm or mesoderm, consistent with an independent origin of segmentation between annelids and arthropods. |
Introduction
During meiosis, the germline nucleus undergoes extensive reorganization to accurately align homologous chromosomes along their entire length, enabling them to recombine and ultimately segregate from one another. Outside of the germline, however, homolog pairing, if it occurs at all, is usually transient and localized to a particular chromosomal region [1][2][3][4][5][6][7]. Indeed, the individual somatic chromosomes of many eukaryotes occupy distinct territories in the nucleus [8][9][10], which would be expected to minimize interactions between homologous chromosomes and thus pairing-mediated changes in gene expression, chromosome entanglements, and loss-ofheterozygosity due to mitotic recombination [11][12][13][14][15][16][17]. Consequently, extensive homolog pairing is generally considered a germline-specific phenomenon that is restricted to the early stages of meiosis.
One striking exception is found in Dipteran insects, such as Drosophila, where there is widespread homolog pairing in somatic cells. Such pairing has been documented in embryonic, larval, and adult tissues, with pairing frequencies at individual loci reaching 80% or more [18][19][20][21][22][23]. These observations have led researchers to speculate that Drosophila represents a major departure from other organisms in terms of nuclear organization. The implications are especially profound with respect to the germline, where it has been widely presumed that the homolog pairing observed during Drosophila meiosis is an extension of the pairing established during embryogenesis [24][25][26][27][28][29][30]. Notably, there is evidence for homolog pairing being in place during the mitotic divisions immediately preceding meiosis, consistent with it having been established much earlier in development [27,29,31]. Indeed, such pre-meiotic pairing has been reported to continue uninterrupted into meiosis [27,29,31], which may explain the ability of Drosophila females to maintain interactions associated with meiotic pairing and form the synaptonemal complex (SC) between homologs in the absence of double-strand breaks (DSBs) [32], induction of which is essential for pairing and SC formation in yeast and mammals.
This early pairing in the Drosophila germline is in stark contrast to meiotic pairing in nonDipteran organisms consisting of distinct soma and germline tissues [30,[33][34][35]; while a recent study showed pairing as early as the final round of pre-meiotic replication in mice, there was no demonstration of pairing earlier to this time point [36]. Here we clarify the origin of germline pairing in Drosophila, refuting a long-held hypothesis that it derives from pairing established during embryogenesis and arguing, instead, for a program of germline pairing that is not initiated until the five mitotic cell cycles just prior to meiosis.
Results and Discussion
Homologous chromosomes enter the germline unpaired
To determine whether chromosomes are paired prior to meiosis in Drosophila, we first analyzed adult germline stem cells (GSCs), focusing on the female germline, as meiosis in male Drosophila does not follow ''the standard meiotic script'' [26,37]. The GSC of the Drosophila female are found in its two ovaries, the very tip of which consists of ,16-20 germaria, each of which harbors just one or two GSCs positioned adjacent to the somatic niche [38]. During oogenesis, each GSC divides asymmetrically to produce a renewed stem cell and a differentiating cystoblast (CB), which is positioned distal from the niche and destined to undergo four more rounds of replication and division before entering meiotic prophase ( Figure 1A). In order to identify the GSCs and distinguish them from subsequent pre-meiotic stages, we took advantage of an antibody to the cytoplasmic protein SXL, levels of which increase in GSCs and then decrease as differentiation proceeds [39].
Chromosome positioning in individual GSC nuclei was assessed by fluorescent in situ hybridization (FISH) in whole-mounted tissues, using techniques that preserve the nuclear architecture followed by high-resolution microscopy and 3D-image reconstruction. Within each nucleus, a single FISH signal or two signals separated by #0.8 mm were considered to represent the paired state of the targeted locus. To evaluate the extent of genome-wide pairing, we used nine FISH probes ( Figure 1B and Table S1). Three probes targeted highly repeated sequences of the centromeric heterochromatin, including that of the X chromosome (359), chromosome 2 (AACAC), and chromosome 3 (dodeca). The remaining six probes were generated with Oligopaint technology [40] and targeted single copy euchromatic loci, including two loci (5A and 16E) on the X chromosome, loci on the left (24D) and right (50D) arms of chromosome 2 and the left (69C) and right (100B) arms of chromosome 3. Importantly, these probes were extremely efficient, with 100% of nuclei displaying at least one focus for each probe.
In stark contrast to the assumption that meiotic pairing is an extension of pre-existing somatic pairing and that chromosomes therefore enter the germline in the paired state, we observed extensive separation of homologs in GSCs. Eight out of the nine loci produced two distinct FISH signals in the majority of, if not all, nuclei and were considered unpaired in 75-100% of GSC nuclei ( Figure 1C-D) in experiments representing 15-30 ovaries. In fact, the average inter-allelic distances for these loci was equivalent to the radius of the nucleus (2.29 mm; p.0.05, unpaired t test; Table S1), consistent with a random positioning of the maternal and paternal chromosomes relative to each other. The dramatic deficiency of pairing at these eight loci argues that the genome-wide homolog pairing and subsequent SC formation during meiosis does not derive from a paired state that is extant in the GSC.
The one exception was the X-linked 359 repeat, which was paired in 80% of GSC nuclei ( Figure 1D). While this may be indicative of some homolog alignment in GSCs, it may also reflect the proximity of this locus to the rDNA gene cluster, which is spatially confined to the nucleolus, and/or the large size of this repeated region [20,28,41], estimated to be 11 Mb in size [42]. Importantly, two other euchromatic loci proximal (16E) and distal (5A) to the 359 repeat were mostly (75%) and completely (100%), respectively, unpaired, indicating that the X-chromosome is not exceptional in its capacity to pair in GSCs. We have also found the 359 repeat to exhibit atypical pairing dynamics in somatic cells [43].
Homolog pairing is established during the mitotic cell cycles prior to meiosis
The largely unpaired state of GSCs shifted our focus to determining whether, outside of the 359 repeat, pre-meiotic pairing occurs in the female germline to any significant extent. To this end, we looked directly downstream of the GSCs to the differentiating CBs, which number between one and two per germarium and, relative to the GSCs, are positioned downstream of the niche. Here, we targeted the euchromatic loci of 5A, 16E, 24D, 50D, 69C, and 100B ( Figure 1D and Table S1) and found unambiguous levels (11-35%) of pairing at all but 5A. These findings establish that Drosophila does, indeed, support at least some degree of pairing well before meiosis initiates.
Despite significant levels of euchromatic pairing in CBs, no pairing was detected at the centromeric repeats AACAC and dodeca, suggesting the partial nature of homolog pairing at this stage. In fact, when we performed two-color FISH targeting two loci across a single arm of chromosome 2 in CB nuclei, we did not detect any pairing of the centromeric locus despite 33% (n = 21) pairing of the chromosome arm ( Figure 1E).
The partial pairing observed in CBs raised the possibility that complete pairing can be achieved in cells progressing through mitotic divisions prior to the initiation of meiosis. In Drosophila, this program includes four rounds of divisions in which the CB becomes a 2-, 4-, 8-, and ultimately 16-cell cyst of interconnected cystocytes, one of which completes meiosis. Importantly, these stages precede the pachytene stage of meiosis, in which homologous chromosomes are fully synapsed (Figure 2A). In order to evaluate the progression of pre-meiotic pairing, we used the P[bamP-GFP] transgene, a transcriptional reporter that is not expressed in GSCs or pachytene, but is expressed in each of the intervening pre-meiotic stages [39,44], along with an antibody against Spectrin, a cytoskeletal protein that forms a spherical structure called the spectrosome in GSCs and CBs, and an antibody against C(3)G, which identifies the SC in meiotic nuclei [45] (Figure 2A-C). Developing cysts were staged based on the number of BAM-positive cells and by Spectrin staining, which, in cysts, localizes to a branched structure called the fusome. We found that homolog pairing levels rapidly increased through the divisions, with each of six FISH targets reaching maximum levels of pairing (87-95%) by the 8-cell cyst ( Figure 2D). Once maximum levels of pairing were achieved, they were maintained throughout the remaining pre-meiotic divisions and into the pachytene stage of meiosis ( Figure 2C-D), suggesting that homologous chromo-
Author Summary
Meiosis is a specialized cell division that permits the transmission of genetic material to following generations. A pivotal step for this process is the pairing and recombination between homologous chromosomes. In the case of Drosophila, which supports organismal-wide homolog pairing throughout development, it has been widely assumed that the homolog alignment occurring during meiosis in the adult gonad is an extension of the pairing established during embryogenesis. Here, we show that, contrary to this model, homologous chromosomes are unpaired in germline progenitors from embryogenesis to adulthood. This discovery refutes the presumption that homologous chromosomes are paired in Drosophila in all cell types and demonstrates that a specific form of chromosome organization, namely, homolog pairing, is a signature feature that distinguishes cells destined to be the soma from cells destined to be the germline.
somes initiate pairing up to four mitotic divisions prior to meiosis and enter meiosis fully aligned. Importantly, we were able to assess pairing in all four cells of twenty-seven 4-cell cysts, where 87%, 90%, 100%, and 95% of cells showed pairing at dodeca, 24D, 69C, and 100B, respectively. Because the oocyte derives from one cell of a 4-cell cyst, these observations demonstrate that pairing . Each GSC divides asymmetrically to produce a renewed stem cell and a differentiating cystoblast (CB, blue nucleus surrounded by green cytoplasm), which is positioned distal to the niche. The CB will undergo four more rounds of mitotic divisions to form a 16-cell cyst. Following these pre-meiotic stages, the 16-cell cyst will enter meiotic prophase, as defined by the initiation (zygotene) and complete formation (pachytene) of the synaptonemal complex (SC, red) between the paired homologs in two of the sixteen cells. Only a single cell will complete meiosis within each 16-cell cyst to form a mature egg (not shown) Arrow, direction of maturation. Right: Wild-type germarium stained for DNA (blue) and SXL (green). A GSC and CB are indicated by arrows and identified by SXL staining and relative position to somatic niche. Approximately 1-2 GSCs and 1-2 CBs are present in each germarium. Scale bar represents 10 mm. B, Drosophila chromosomes and targets of FISH probes (red). Heterochromatin is denoted in grey and rDNA cluster on the X-chromosome is in purple. C, Image of a GSC nucleus (dashed circle) at the tip of a germarium identified by DAPI (blue) surrounded by cytoplasmic SXL (green) staining and combined with FISH targeting AACAC (red) and dodeca (grey). Two signals for each FISH target represent separated homologous loci. Scale bar represents 5 mm. D, Percentage of nuclei exhibiting paired and unpaired loci in GSCs (left panel) and CBs (right panel). 15-30 ovaries were scored for each stage with a combined total of 242 GSC nuclei and 262 CB nuclei (approximately 30 nuclei for each locus at each stage). E, CB nuclei identified with SXL staining in combination with two-color FISH targeting AACAC (grey) and 24D (red) on Chromosome 2. Cartoon depicts hypothetical arrangement of homologous chromosomes as either unpaired or partially paired. Scale bars represents 5 mm. doi:10.1371/journal.pgen.1004013.g001
can be observed well before the initiation of meiosis. Analogous data were obtained for the 8-cell and 16-cell cysts.
Interestingly, not all chromosome loci achieved pre-meiotic pairing at the same rate; the 359, 24D, and 100B loci reached maximum levels of pairing prior to the 5A, AACAC, dodeca, and 69C loci by one to four divisions ( Figure 1D and Figure 2D). This observation is consistent with the higher level of euchromatic as versus centromeric pairing we observed for autosomes in CBs and suggests that, rather than strictly initiating at the centromeres, where SC formation is first observed [46,47], germline pairing may initiate at different rates or times across the genome.
Chromosomes maintain an unpaired state throughout germline development
The results described above refute the long held belief that homolog pairing in Drosophila meiosis is an extension of pairing events established within the embryo and maintained throughout development in all tissues, including the germline. Hence, they encouraged us to assess whether germline cells ever support somatic levels of homolog pairing during development or, alternatively, whether unpairing represents a global nuclear reorganization specifically in the GSCs. We, therefore, evaluated pairing levels during embryogenesis, as this 24-hour phase of development marks both the onset of somatic homolog pairing as well as the separation of germline and somatic lineages. The germline distinguishes itself ,2 hours after egg lay (AEL), with the primordial germ cells (PGCs), from which adult GSCs are derived, forming at the posterior pole of the embryo and becoming identifiable with the germline-specific protein marker VASA [48] ( Figure 3A-B). Examination of homologous pairing during embryogenesis has indicated that some sites attain pairing as early as 2 hours AEL [21]. In fact, the ,500 Kb histone locus on chromosome 2 has been reported to pair ,2.5 hours AEL in the soma and PGCs [21], providing reason to believe that PGCs do not differ from somatic cells in their capacity to pair. However, it is unclear if pairing of this locus reflects genome-wide levels or specific features of this locus, such as its transcriptional activity [17,20,21,28,49,50]. Here, we distinguish these alternatives by examining the behavior of four other loci across the genome -two centromeric (AACAC and dodeca) and two single-copy euchromatic loci (24D and 50D).
Confirming our ability to detect the onset of pairing in somatic cells, we examined embryos 2.5 hours AEL and observed, respectively, 12% and 10% pairing at the centromeric AACAC and dodeca repeats and 22% and 29% pairing at the euchromatic 24D and 50D loci ( Figure 3C). In contrast, the PGCs at the posterior pole of the embryos consistently exhibited lower levels of pairing at this stage for all four loci, ranging from 3% to 5% ( Figure 3C). We next analyzed embryonic nuclei 14 hours AEL and found 80-100% of somatic nuclei were paired for each of the four loci ( Figure 3D), levels consistent with full attainment of somatic homolog pairing [21]. Strikingly, however, homologous chromosomes in the PGCs, which at 14 hours AEL are in contact with somatic cells, remained essentially unpaired, attaining only 0-7% pairing at any of the four loci (p,0.0001; Figure 3D). In these cells, the inter-allelic distances were extensive, averaging 2.5-3.5 mm and, in some cases, reaching as much as 5-6 mm ( Figure S1). Additionally, sex-specific differences were not observed, suggesting that, regardless of sex, germline progenitors do not support genome-wide homolog pairing ( Figure S2). Thus, PGCs maintain a predominantly unpaired state of homologous chromosomes throughout embryogenesis. These observations argue that germ cells are never exposed to the widespread pairing observed in somatic cells and thus, represent the only Drosophila tissue identified so far that escapes this phenomenon.
Germline progenitors have large nuclear volumes with chromosomes juxtaposed to the nuclear envelope
To better understand how germline progenitors maintain an unpaired state, we determined whether they might exhibit other distinctive features of nuclear organization. Notably, we observed that the nuclear volumes of PGCs 14 hours AEL (172.5 mm 3 ) were ,3.3 fold greater than that of neighboring somatic cells (52.3 mm 3 , p,0.0001; Figure 4A) and reasoned that larger nuclear volumes could cause increased distances between homologs and thus account for the lower levels of pairing in PGCs. Consistent with this hypothesis, the nuclear volumes of GSCs and CBs (50.5-52.7 mm 3 ) were greater than two times larger than that of the surrounding somatic follicle cells (21.3 mm 3 , p = 0.0027; Figure 4B), while those of the 8-cell cysts and cells in pachytene were approximately the same or smaller in size ( Figure 4B). To test the potential of larger nuclear volumes to explain lower levels of pairing, we normalized inter-allelic distances to the nuclear radius. This analysis revealed that, even when inter-allelic distances were normalized, the level of pairing in PGCs remained less than that observed in somatic cells by six to nineteen fold ( Figure S3). This outcome suggests that the separation of homologous chromosomes cannot be fully explained by nuclear volume alone.
We next analyzed the global distribution of DNA within the larger GSC nuclei and found a distinct nuclear 49,6-diamidino-2phenylindole (DAPI) staining pattern compared to somatic follicle cells, indicating a change in chromatin structure. As shown in Figure 4C, surface plots of DAPI fluorescence intensity revealed a non-uniform peripheral staining pattern in GSC nuclei. In contrast, the DAPI fluorescence intensity in adjacent somatic follicle cell nuclei typically displayed a relatively uniform and diffuse staining pattern ( Figure 4C). To assess whether this DNA distribution could result from the juxtaposition of chromosomes to the nuclear envelope, we used FISH in combination with an antibody against lamin to measure the distance between the nuclear envelope and each of three loci across chromosome 2: the AACAC centromeric repeat and the 24D and 50D loci in the middle of each arm. As predicted, all three loci were equally close to the nuclear envelope in GSCs, with average distances of only 15-20% of the total nuclear radius ( Figure 4D). Similar results were found for the nuclei of CB, 8-cell cysts, pachytene cells, as well as embryonic PGCs ( Figure 4D and Figure S4), indicating that the peripheral localization of chromosomes is adopted early in germline development and maintained into meiosis. In contrast, the same three loci in somatic cells exhibited greater distances from the nuclear envelope, averaging of 25-47% of the radius, with the centromeric locus closest to the nuclear envelope ( Figure 4D and Figure S4). This arrangement, in which centromeres are located in the periphery with chromosome arms displaced across the nuclear space, is consistent with the Rabl configuration of chromosomes frequently found in Drosophila somatic cells [51,52]. We conclude that germline cells may adopt a distinct nuclear structure which, compared to somatic cells, involves placement of chromosomes in close proximity to the nuclear envelope along their entire length.
Conclusion
Our findings reveal extensive separation of homologous chromosomes in germline progenitors from early embryogenesis until the five mitotic cell cycles just prior to meiosis and, in this regard, align Drosophila with other organisms that establish homolog pairing de novo in the gonad. Importantly, our observa- should an organism ensure homologous chromosomes remain unpaired in germline progenitors, only to allow pairing beyond the stem cell divisions? One possibility is that, since germline progenitors generate the entire cell population responsible for transmitting the genome to subsequent generations, any negative outcome of that pairing could be propagated to a much greater extent as compared to undesired events occurring downstream of the GSCs and thus have a higher probability of multigenerational consequences.
Our discovery of unpaired homologs in germline progenitors also demonstrates that homolog pairing is not an inevitable feature of Drosophila chromosomes and is consistent with studies arguing that pairing is a controlled process reflecting genes that promote pairing as well as those that antagonize it [14,15,22,23,43,53]. Here, we further propose that potentially undesirable homologous interactions are precluded in Drosophila germline progenitors coordinately with, or due to, the separation of the progenitors from the soma in early embryogenesis. Pairing could also be precluded through a localization of chromosomes to the nuclear periphery. Such a configuration could lead to the formation of chromosome territories that separate homologs in the germline, as opposed to configurations that permit or even promote the pairing observed in the soma ( Figure 5). Note that our data do not clarify whether the mechanisms that pair homologous chromosomes in somatic cells are distinct from, or similar to, those that eventually pair homologous chromosomes in the pre-meiotic cells. Nevertheless, to the extent that the mechanisms may be different, our findings are consistent with the notion that germline nuclei may suppress or delay the mechanisms that support pairing in the soma, perhaps through nuclear organization, while, in the pre-meiotic cells, simultaneously permit a separate mechanism that promotes pairing. Indeed, Christophorou et al. (also in this issue) show that pre-meiotic pairing is perturbed in the absence of meiosis-specific proteins such as components of the SC, suggesting that the mechanisms of pre-meiotic pairing cannot be entirely similar to that of somatic pairing.
Interestingly, we found that chromosomes maintain their peripheral localization even during the pre-meiotic 8-cell stage when homologs are fully aligned and continue to maintain this configuration into meiosis. Whether this localization is a significant aspect of pre-meiotic pairing will be of interest, as chromosome interactions with the nuclear envelope have been proposed to promote meiotic pairing in several organisms [54][55][56][57], as well as influence polytene pairing in Drosophila [58]. Regardless, our observations establish a distinction between the organization of paired chromosomes in pre-meiotic nuclei (peripheral localization) and that in somatic nuclei (internal localization) in Drosophila. In closing, we return to the extraordinary degree of pairing that Drosophila and other Dipteran insects support in their soma. If homologous interactions can lead to negative outcomes, why do these organisms permit a near-organismal wide level of such interactions? One explanation is that somatic homolog interactions may, under some circumstances, confer advantages [12,28,34,[59][60][61][62][63] and, consistent with this, transient and localized instances of somatic homolog interactions have been documented or at least implicated in a wide variety of organisms, including mammals [1][2][3][4][5][6][7]12,[63][64][65]. Indeed, in light of our discovery that the different tissues of Drosophila can have dramatically different levels of pairing it is possible that greater scrutiny of nonDipteran species will reveal many more instances of somatic pairing and, hence, evidence that somatic pairing is a widespread potential of genomes in general [12,14,43].
Materials and Methods
Drosophila strains
Drosophila stocks and crosses were maintained on a standard medium at 25uC. For wild-type, we used the y 1 w 1118 strain. To identify the BAM protein that was used to distinguish the premeiotic cyst stages, we crossed y 1 w 1118 to a strain carrying the transgene P(bamP-GFP) [44], a kind gift from Michael Buszcak (The University of Texas Southwestern Medical Center at Dallas).
Generation of FISH probes
Oligo probes for the 359, AACAC, and dodeca heterochromatic repeats [42,66] were synthesized with either a 59 Cy5 or Tye3 fluorescent dye by Integrated DNA Technologies (IDT). The design of the probe sequences were previously described [43] and are as follows: 359: GGGATCGTTAGCACTGGTAAT-TAGCTGC, AACAC: AACACAACACAACACAACACAACA-CAACACAACAC, and dodeca: ACGGGACCAGTACGG. Oligo probes were resuspended in 16TE at 100 mM concentration and stored at 220uC.
Euchromatic probes 5A (4E2-5C10), 16E (16B3-17A2), 24D (24D1-24F1), 50D (50D1-53C7), 69C (69A1-69E6), and 100B (100B9-100D1) were designed and generated using the Oligopaint technology [40]. Briefly, a library of 7500 (24D and 100B), 10000 (5A, 16E, and 69C), and 25000 (50D) unique oligos (MYcroarray) were designed for amplification. Each library was amplified using a common 59 Cy3-conjugated forward primer (59-CGCTCGGTCTCCGTTCGTCTC) and unlabeled reverse primer (59-GGGCTAGGTACAGGGTTCAGCgcaatg).
Antibodies
The antibodies and dilutions used were mouse anti-SXL (m18, Developmental Studies Hybridoma Bank [DSHB], 1:10), rat anti-VASA (DSHB, 1:300), mouse anti-Spectrin (DSHB 3A9, 1:50), mouse anti-lamin (DSHB ADL84.12, 1:100) and rabbit anti-GFP (Molecular Probes, 1:300). The mouse anti-C(3)G (1A8-1G2, single nuclei. D, Left: GSC nucleus with FISH targeting 24D (red) and lamin staining (nuclear envelope, green). Scale bar represents 5 mm. Right: Average distance between FISH signals and the nuclear envelope (NE) 6 SEM, normalized to the nuclear radius, in germline and somatic follicle cells of the adult ovary. Asterisks denote significant differences in the normalized distances between somatic and GSCs (*p,0.05, **p,0.0001). For each data point, a minimum number of 30 nuclei were scored (see Materials and Methods). doi:10.1371/journal.pgen.1004013.g004 Figure 5. Model for germline nuclear organization. Once a germline cell fate is established in early embryogenesis, homologous chromosomes remain unpaired and localize to the nuclear periphery, creating non-overlapping chromosome territories that may block ectopic pairing. This organization is maintained through development and into the adult GSCs. Germline pairing initiates coincident with germline differentiation (time point denoted as 'D' during the pre-meiotic mitotic divisions, ultimately leading to complete homolog alignment and the initiation of meiosis and SC formation. In somatic cells, homologous chromosomes instead adopt a configuration that permits, or even promotes, pairing. Such a configuration might be the Rabl organization, which occurs in early embryogenesis and positions centromeres and telomeres at opposite nuclear poles [21]. doi:10.1371/journal.pgen.1004013.g005 1:200) antibody was a gift from Scott Hawley (Stowers Institute, Kansas City, Missouri).
The secondary antibodies were DyLight 488 goat anti-rabbit (Jackson Labs) used at 1:165, Cy3 labeled goat anti-rat (Jackson Labs) used at 1:100 and DyLight 488 goat anti-mouse (Jackson Labs) used at 1:100.
Immunofluorescence and FISH of Drosophila ovaries
Immunostaining was performed prior to FISH, using a modified protocol of [45]. Females (,10-15 per experiment) were aged 3-4 days in the presence of males and were fed yeast paste overnight prior to dissection. Ovaries were isolated in PBS and immediately fixed for 10 min in 200 ml of PBS containing 4% formaldehyde and 0.5% Nonidet P-40, plus 600 ml Heptane. Fixed ovaries were then rinsed three times in PBT (PBS plus 0.2% Tween-20), and washed three times for 5 min in PBT. Prior to immunostaining, the ovaries were teased apart and blocked by incubating in PBT plus 1.5% BSA at room temperature for 1 hour. Primary antibodies were incubated at 4uC overnight in PBT. Three 20min washes in PBT were performed prior to incubation with secondary antibodies at room temperature for 2 hours, followed by two 20-min washes in PBT and one 10-min wash in PBS.
For FISH, PBS buffer was replaced with 26SSCT (0.3 M NaCl, 0.03 M NaCitrate, 0.1% Tween-20) by three quick washes. After washing, the ovaries were then gradually exchanged into 26SSCT/50% formamide with 10-min washes in 26SSCT/20% formamide, then in 26SSCT/40% formamide, and then two washes in 26SSCT/50% formamide. Ovaries were then allowed to settle and the 26SSCT/50% formamide was removed prior to the addition of 36 ml of hybridization solution (26SSCT, 50% formamide, 10% (w/v) dextran sulfate, RNase) and up to 4 ml of probe. For heterochromatic targets, 100 pmol of probe was added to the hybridization. For single-copy euchromatic targets, 200-400 pmol of Oligopaint probes were added to the hybridization. To preserve the nuclear structure, chromosomes were denatured at 78uC in a thermal cycler for 30 min followed by incubation overnight at 37uC in the dark. Following hybridization, we performed two 30-min washes of 26SSCT/50% formamide at 37uC, followed by a 10-min wash in 26SSCT/20% formamide at room temperature and three quick washes in 26SSCT. After settling, excess 26SSCT was removed and the ovaries were mounted in Slowfade mounting media with DAPI (Invitrogen).
Collection and fixation of Drosophila embryos
We collected 2.5 hour-and 14 hour-old embryos for 1 hour on apple juice plates and then aged them an additional 1.5 or 13 hours, respectively. 2.5 hours after egg lay (AEL) should capture embryos in the final 10 min of cell cycle 13 and the first 50 min of cell cycle 14. Due to the time spent manipulating embryos during the dechorionation step (see below), most embryos were aged ,5-10 min longer before development was stopped during fixation. During imaging, embryos were also staged by the number and position of primordial germ cells, which are separated from the soma at the pole 2.5 hours AEL and encapsulated within the embryonic gonad 14 hours AEL ( Figure 3B).
After collection, we dechorionated the embryos by submerging them in 50% bleach for 90 seconds, followed by a thorough wash in ddH 2 O. For fixation, embryos were placed in PBS containing 4% formaldehyde, 0.5% Nonidet P-40, and 50 mM EGTA, plus 500 ml Heptane for 30 min. The aqueous phase was removed and replaced with 500 ml MeOH and mixed vigorously for 2 min. The embryos were allowed to settle and were washed two times in 100% MeOH and stored for up to a week at 220uC. Prior to immunostaining, the embryos were rehydrated in PBT. Immuno-staining and FISH were then performed as described above for ovaries.
Microscopy and image analysis
All images were collected using a Zeiss LSM780 laser scanning confocal microscope with a 636, N.A. 1.40 lens. We imaged whole germaria by collecting 200 nm optical sections through the entire tissue at 102461024 or 5126512 resolutions with a digital zoom of 3.0. The analysis of the images was performed by both 3D-image reconstruction and examining one section at a time using the Zeiss ZEN 2011 software. FISH foci were counted manually within each nucleus and the distance between the centers of allelic signals was measured using the Ortho -distance function, which permits length measurements in 3D space. 100% of nuclei examined in this study exhibited at least a single FISH signal, indicating high hybridization efficiency. Therefore, a single signal was considered two foci with an inter-signal distance of 0 mm. In some cases where noted, we normalized the inter-signal distances by the radius of the nucleus. In these cases, p values were determined by an unpaired t test.
Two homologs were considered paired if the distance between their focus centers was #0.8 mm or FISH produced a single signal.
To determine the significance between paired states, p values were calculated by a two-tailed Fisher's exact test.
To image the pre-meiotic 2-, 4-, 8-, and 16-cell cysts, we focused on that region of the germarium identified by P[bamP-GFP] expression, set the upper and lower limits of the scanned region to capture the entirety of the cysts, and then scored those nuclei that were fully contained within the scanned region and were also unambiguously distinguished from other cell types. This strategy enabled us to score 93-100% of the cells in any chosen cyst.
To image germline cells in the embryo, we focused on that region identified by VASA expression, set the upper and lower limits of the scanned region to capture the majority of the germline cells, and then scored only those nuclei that were fully contained within the scanned region and were also unambiguously distinguished from somatic cells. This strategy enabled us to score the majority of germline cells in any chosen embryo. The somatic embryonic cells that were scored were those that were within the scanned region containing the scored germline cells.
Measuring nuclear volume
Nuclear envelopes were labeled with an anti-lamin antibody. Nuclear volumes were calculated based on the nuclear diameter using the equation V = 4/3pr 3 .
Measuring distance between nuclear envelope and FISH signals
Nuclear envelopes were labeled with an anti-lamin antibody. The ZEN software package was then used to measure the shortest distance between FISH signals and the nuclear envelope in 3D space. When two FISH signals were present in the nucleus, only the shortest distance of the two was scored. p values were determined by an unpaired t test. Figure S1 Extensive separation of homologs in primordial germ cells. Relative frequencies of inter-allelic distances in embryonic PGCs and somatic cells 14 hours AEL based on FISH targeting AACAC (upper-left), dodeca (upper-right), 24D (lower-left), and 50D (lower-right). The percentage of nuclei exhibiting paired loci for this data set is presented in Fig. 3. (TIF) Figure S2 Male and female germline progenitors do not support genome-wide homolog pairing. A, Primordial germ cells (PGCs, VASA, red) in female embryos 14 hours AEL were distinguished from male embryos based on their expression of the femalespecific cytoplasmic protein SXL (green). B, Percentage of nuclei paired at AACAC (left-most graph) and 24D (right-most graph) in male and female PGCs as compared to somatic cells in embryos 14 hours AEL. No significant difference in pairing levels were observed between the sexes. For each data point, a minimum number of 20 PGCs and 50 somatic nuclei were scored from a total of 6-7 independent embryos (see Materials and Methods). (TIF) Figure S3 Homolog separation in primordial germ cells is not dependent on nuclear size. Distances between allelic signals by FISH ( Figure S1) were normalized to the radius of the nucleus to account for the larger nuclear volumes in PGCs as compared to that in somatic cells in embryos 14 h AEL. Despite this normalization, there was 6-(AACAC), 7-(dodeca), 16-(24D), and 19-(50D) times less pairing in PGCs than in somatic cells (**p,0.0001). (TIF) Figure S4 Chromosomes from primordial germ cells are in close proximity to the nuclear envelope. A, PGC nucleus with FISH targeting 24D (red, arrowheads) and lamin staining (nuclear envelope, green). Scale bar represents 5 mm. B, Average distance between 24D FISH signals and the nuclear envelope (NE) normalized to the nuclear radius 6 SEM in embryonic PGCs as compared to somatic cells 14 hours AEL. (TIF)
Supporting Information
Figure 1 .
1Homologous chromosomes enter the germline unpaired. A, Left: Schematic of a germarium showing pre-meiotic mitotic cell divisions as well as maturation of the meiotic cysts. The GSCs (purple nuclei) are positioned adjacent to the somatic niche (brown) and express high levels of SXL (green cytoplasm)
Figure 2 .
2Homolog pairing is established during the mitotic cell cycles prior to meiosis. A, Left: Schematic of a germarium identifying the pre-meiotic stages with BAM (red) and Spectrin (white) and meiotic stages with C(3)G (green). Right: Wild-type germarium in which GSCs are identified by the position near the niche, absence of BAM staining, and presence of a spectrosome (white). Developing cysts are identified by the presence of BAM staining and a branched fusome (white). DAPI, blue. Approximately 1-2 germline cysts are present in each germarium, with equal occurrence of the 2-, 4-, 8-, and 16-cell stages. Scale bar represents 10 mm. B, FISH targeting dodeca (grey). 2-cell and 4-cell cysts (the 4 th cell is out of focus) identified with BAM:GFP (pseudo-colored red). Scale bars represent 10 mm. C, FISH targeting 24D (red) and AACAC (grey) in a germarium identifying pachytene nuclei in meiosis with an antibody against the SC protein C(3)G (green). Scale bar represents 10 mm in upper panel and 5 mm in lower panel. D, Percentage of nuclei exhibiting paired and unpaired loci in pre-meiotic stages as well as in meiotic pachytene with FISH targeting AACAC, dodeca, 5A, 24D, 69C, and 100B. Pre-meiotic cysts were identified using BAM:GFP and Spectrin. Pachytene nuclei were identified in a separate experiment using an antibody against C(3)G. 15-30 ovaries were scored for each stage with a minimum of 20 nuclei counted for 2-and 4-cell stages, 40 nuclei for the 8-cell stage, and 80 nuclei for the 16-cell stage (*P,0.01, **P,0.0001). doi:10.1371/journal.pgen.1004013.g002 tions are in agreement with Christophorou et al. (also in this issue), who also found a deficiency of homolog pairing in the GSCs of the Drosophila adult female. The lack of pairing in germline progenitors is especially noteworthy, considering the widespread prevalence of pairing in the somatic tissues of Drosophila. Why
Figure 3 .
3Homolog separation is maintained in primordial germ cells throughout embryogenesis. A, Drosophila life-cycle. The Drosophila embryo develops through a series of synchronized, rapid divisions for the first 2.5 hours (h) after egg lay (AEL). Approximately 8-10 nuclei separate from the somatic divisions, migrate to the posterior pole of the embryo, and, following up to two further divisions, give rise to ,15-30 primordial germ cells[38]. These cells will eventually produce the adult GSCs, from which haploid gametes are derived. B, Using DAPI (blue) and an antibody to the germline-specific protein VASA (red), primordial germ cells (PGCs) are identified at the posterior pole of embryos 2.5 h AEL and within the embryonic gonad 14 h AEL. Right-most column are magnified images of PGCs and somatic cells at the respective embryonic stages with FISH targeting AACAC (green). White arrowheads denote PGC loci and orange arrowheads denote somatic loci. Scale bars represent 10 mm. C-D, Percentage of pairing in embryos 2.5 h (C) and 14 h (D) AEL within somatic and PGC nuclei (n.s. not significant, *p,0.05, **p,0.0001). The chromatin state (Het, heterochromatin, or Eu, euchromatin), and chromosome are noted below each FISH target. For each data point, 46-98 nuclei were scored from a total of 6-7 embryos (see Materials and Methods). doi:10.1371/journal.pgen.1004013.g003
Figure 4 .
4Germline progenitors contain large nuclear volumes with chromosomes juxtaposed to the nuclear envelope. A, PGC nuclei (VASA, red) are larger than surrounding somatic nuclei in embryonic gonads 14 h AEL. DAPI, blue. Dashed circles denote nuclear periphery. Scale bar represents 10 mm. Right: Average nuclear volume of PGCs and surrounding somatic cells 6 SEM. B, Average nuclear volume of germline and somatic follicle cells of the adult ovary 6 SEM (**p,0.0001). C, Wild-type germarium stained for DNA (grey) and SXL (green). Shown on right are crosssections of representative GSC and somatic nuclei with 3D and 2D (insets) surface plots displaying increased peripheral intensity in the nucleus of the GSC and more uniform intensity in the nucleus of the somatic cell. Scale bar represents 10 mm in the image of the germarium and 5 mm in images of
Table S1
S1Homolog pairing frequencies in GSCs and CBs. (DOCX)
PLOS Genetics | www.plosgenetics.org
December 2013 | Volume 9 | Issue 12 | e1004013
AcknowledgmentsWe are grateful to Mohammed Hannan and Chamith Fonseka for technical assistance and members of the Wu lab and Jean-René Huynh for critical reading of the manuscript. We also thank Jean-René Huynh for sharing unpublished information.Author ContributionsConceived and designed the experiments: EFJ CtW. Performed the experiments: EFJ. Analyzed the data: EFJ. Contributed reagents/ materials/analysis tools: EFJ NA BJB. Wrote the paper: EFJ CtW.
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| 207 | The part of the genetic locus of the domesticated silk moth, Bombyx mori, in which high cysteine (Hc) chorion genes of late developmental specificity reside contains regions encompassing gene-like sequences which exhibit properties distinct from those of functional Hc genes. One of these regions has been characterized and shown to contain a chorion pseudogene, psi HcB.15, which shares pronounced similarities with a transcribed chorion pseudogene, psi HcB.12/13, which was characterized previously. Both pseudogenes are homologous to HcB chorion genes but bear multiple single nucleotide substitutions and short segmental mutations (insertions and deletions) which introduce translational frame shifts and termination codons in the coding regions. Structural characteristics unique to the two pseudogenes suggest that psi HcB.15 was generated first from a functional HcB gene and gave rise subsequently to psi HcB 12/13 as a result of a sequence duplication event. The two pseudogenes can be distinguished from each other by the presence of distinct regions of similarity to the consensus sequence of functional HcB genes which appear to have arisen from gene-conversion-mediated correctional events. These findings lend support to the hypothesis that chorion pseudogene sequences represent reservoirs of genetic information that participates in the evolution of the chorion locus rather than relics of inactivated genes passively awaiting extinction. | The larval color patterns in Lepidoptera exhibit splendid diversity, and identifying the genes responsible for pigment distribution is essential to understanding color-pattern evolution. The swallowtail butterfly, Papilio xuthus, is a good candidate for analyzing marking-associated genes because its body markings change dramatically at the final molt. Moreover, the silkworm Bombyx mori is most suitable for identification of lab-generated color mutants because genome information and many color mutants are available. Here, we analyzed the expression pattern of 10 melanin-related genes in P. xuthus, and analyzed whether these genes were responsible for Bombyx larval color mutants. We found that seven genes correlated strongly with the stage-specific larval cuticular markings of P. xuthus, suggesting that, compared with Drosophila, more genes showed marking specificity in lepidopteran larvae. We newly found that the expression of both tan and laccase2 is strongly correlated with the larval black markings in both P. xuthus and B. mori. The results of F2 linkage analysis and mutant analysis strongly suggest that tan is the responsible gene for Bombyx larval color mutant rouge, and that tan is important in emphasizing black markings of lepidopteran larvae. Detailed comparison of temporal and spatial expression patterns showed that larval cuticular markings were regulated at two different phases. Marking-specific expression of oxidizing enzymes preceded the marking-specific expression of melanin synthesis enzymes at mRNA level, which is the reverse of the melanin synthesis step. | The silkworm (Bombyx mori) is an economically-important insect that can secrete silk. Carboxypeptidases have been found in various metazoan species and play important roles in physiological and biochemical reactions. Here, we analyzed the silkworm genome database and characterized 48 carboxypeptidases, including 34 metal carboxypeptidases (BmMCP1-BmMCP34) and 14 serine carboxypeptidases (BmSCP1-BmSCP14), to better understand their diverse functions. Compared to other insects, our results indicated that carboxypeptidases from silkworm have more family members. These silkworm carboxypeptidases could be divided into four families: Peptidase_M2 carboxypeptidases, Peptidase_M14 carboxypeptidases, Peptidase_S10 carboxypeptidases and Peptidase_S28 carboxypeptidases. Microarray analysis showed that the carboxypeptidases had distinct expression patterns, whereas quantitative real-time PCR demonstrated that the expression level of 13 carboxypeptidases significantly decreased after starvation and restored after re-feeding. Overall, our study provides new insights into the functional and evolutionary features of silkworm carboxypeptidases. | Colour patterns in butterflies and moths are crucial traits for adaptation. Previous investigations have highlighted genes responsible for pigmentation (ie yellow and ebony ). However, the mechanisms by which these genes are regulated in lepidopteran insects remain poorly understood. To elucidate this, molecular studies involving dipterans have largely analysed the cis -regulatory regions of pigmentation genes and have revealed cis -regulatory modularity. Here, we used well-developed transgenic techniques in Bombyx mori and demonstrated that cis -regulatory modularity controls tissue-specific expression of the yellow gene. We first identified which body parts are regulated by the yellow gene via black pigmentation. We then isolated three discrete regulatory elements driving tissue-specific gene expression in three regions of B. mori larvae. Finally, we found that there is no apparent sequence conservation of cis -regulatory regions between B. mori and Drosophila melanogaster , and no expression driven by the regulatory regions of one species when introduced into the other species. Therefore, the trans -regulatory landscapes of the yellow gene differ significantly between the two taxa. The results of this study confirm that lepidopteran species use cis -regulatory modules to control gene expression related to pigmentation, and represent a powerful cadre of transgenic tools for studying evolutionary developmental mechanisms. | Samia cynthia versus Bombyx mori : Comparative gene mapping between a species with a low-number karyotype and the model species of Lepidoptera | Insect molting and metamorphosis are intricately governed by two hormones, ecdysteroids and juvenile hormones (JHs). JHs prevent precocious metamorphosis and allow the larva to undergo multiple rounds of molting until it attains the proper size for metamorphosis. In the silkworm, Bombyx mori, several ''moltinism'' mutations have been identified that exhibit variations in the number of larval molts; however, none of them have been characterized molecularly. Here we report the identification and characterization of the gene responsible for the dimolting (mod) mutant that undergoes precocious metamorphosis with fewer larval-larval molts. We show that the mod mutation results in complete loss of JHs in the larval hemolymph and that the mutant phenotype can be rescued by topical application of a JH analog. We performed positional cloning of mod and found a null mutation in the cytochrome P450 gene CYP15C1 in the mod allele. We also demonstrated that CYP15C1 is specifically expressed in the corpus allatum, an endocrine organ that synthesizes and secretes JHs. Furthermore, a biochemical experiment showed that CYP15C1 epoxidizes farnesoic acid to JH acid in a highly stereospecific manner. Precocious metamorphosis of mod larvae was rescued when the wild-type allele of CYP15C1 was expressed in transgenic mod larvae using the GAL4/UAS system. Our data therefore reveal that CYP15C1 is the gene responsible for the mod mutation and is essential for JH biosynthesis. Remarkably, precocious larval-pupal transition in mod larvae does not occur in the first or second instar, suggesting that authentic epoxidized JHs are not essential in very young larvae of B. mori. Our identification of a JH-deficient mutant in this model insect will lead to a greater understanding of the molecular basis of the hormonal control of development and metamorphosis. | Modified fiber qualities of the transgenic cotton expressing a silkworm fibroin gene | Choriogenesis in the Lepidoptera: Morphogenesis, Protein Synthesis, Specific mRNA Accumulation, and Primary Structure of a Chorion cDNA from the Gypsy Moth | DNA degradation of Anopheles darlingi collected at high relative humidity and preserved in isopropanol |
208 | Double helix of the journal Cytology and Genetics: 50 years later | Non-helical models of DNA structure the top of this article, or there could be an equal number of right-handed and left-handed twists, as in the Rodley structure below. The abbreviation "TN", to be used to refer to any DNA structure whose strands are topologically non-linked, has been proposed. The double-helix model of DNA structure was first published in the journal "Nature" by James D. Watson and Francis Crick in 1953 with further details in 1954.) Their work was based upon the crucial X-ray diffraction image of DNA - labeled as "Photo 51" - from Rosalind Franklin in 1952, followed by her more highly clarified DNA | Who came up with the double helix model? | The Double Helix The Double Helix: A Personal Account of the Discovery of the Structure of DNA is an autobiographical account of the discovery of the double helix structure of DNA written by James D. Watson and published in 1968. Watson is a U.S. molecular biologist, geneticist and zoologist, best known as one of the co-discoverers of the structure of DNA in 1953 with Francis Crick. In 1998, the Modern Library placed "The Double Helix" at number 7 on its list of the 100 best nonfiction books of the 20th century. In 2012, "The Double Helix" was named as one | M Marteau, M P M Richards Cambridge University Press, £35, pp 355 ISBN 0 521 46288 6 ::: ::: Books about the “new genetics” continue to pour into medical book-sellers. Never, it seems, has any advance in human biology brought with it such high hopes for the future mixed with so many dire concerns about its misuse. When The Troubled Helix arrived on my desk I wondered how there possibly could be anything new to be said about the past, present, or future of medical genetics. ::: ::: Despite its title, however, The Troubled Helix is not yet another compendium of doom and gloom. Rather, it is a serious attempt to present both the … | Nucleic acid double helix common double helical structure found in nature, the double helix is right-handed with about 10–10.5 base pairs per turn. The double helix structure of DNA contains a "major groove" and "minor groove". In B-DNA the major groove is wider than the minor groove. Given the difference in widths of the major groove and minor groove, many proteins which bind to B-DNA do so through the wider major groove. The double-helix model of DNA structure was first published in the journal "Nature" by James Watson and Francis Crick in 1953, (X,Y,Z coordinates in 1954) based upon the crucial X-ray diffraction image | Nucleic acid double helix common double helical structure found in nature, the double helix is right-handed with about 10–10.5 base pairs per turn. The double helix structure of DNA contains a "major groove" and "minor groove". In B-DNA the major groove is wider than the minor groove. Given the difference in widths of the major groove and minor groove, many proteins which bind to B-DNA do so through the wider major groove. The double-helix model of DNA structure was first published in the journal "Nature" by James Watson and Francis Crick in 1953, (X,Y,Z coordinates in 1954) based upon the crucial X-ray diffraction image | How many different nucleotides are found in the DNA double helix? | The linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled DNA. Defined as double integrals over the shape of the double-helix, these numbers are not always straightforward to compute, though a simplified formula exists. We examine the range of applicability of this widely-used simplified formula, and show that it cannot be employed for plectonemic DNA. We show that inapplicability is due to a hypothesis of Fuller theorem that is not met. The hypothesis seems to have been overlooked in many works. | 208 | This survey paper contains a brief analysis of publications included in the current issue of the scientific journal Cytology and Genetics dedicated to its 50th anniversary. These papers reflect scientific achievements of their authors in the field of genetics and cell biology and underline the potential of these two biological disciplines, forming the double helix of the journal. | who was the first author of the cyc gene | which newspaper reported on the discovery of cell division in cell | Sides of the double helix dna? | the green curve of duplex circular dna is formed by | Oncologists partner with Watson on genomics. | What is known of a double helix? | why is dna called double helix? | who is listed in the first edition of the cyclopedia |
209 | who sings from a chevy to a lincoln song | The Lincoln was an automobile built in Detroit, Michigan by the Lincoln Motor Car Company in 1914. The Lincoln was an unsuccessful light two-seater. It weighed , and sold for $595. This vehicle make was not associated with the Lincoln division of Ford.
References
Defunct motor vehicle manufacturers of the United States
Motor vehicle manufacturers based in Michigan
Defunct manufacturing companies based in Michigan | Who sings drivers seat in lincoln mercury commercials? | Lincoln (film) Gordon-Levitt on September 13, 2012. Then, on September 10, 2012, a teaser for the trailer was released. "Lincoln" was released by Touchstone Home Entertainment on Blu-ray, DVD, and digital download in North America on March 26, 2013. The film debuted at No. 1 in Blu-ray and DVD sales in its first week of release. Disney Educational Productions donated DVD copies of the film and a teaching guide titled "Stand Tall: Live Like Lincoln" to more than 37,100 secondary schools in the United States, after Spielberg received letters from educators requesting to incorporate the film into their curriculum. "Lincoln" earned $182,207,973 | Lincoln Motor Company Lincoln, formally the Lincoln Motor Company, is a luxury vehicle brand of the American manufacturer Ford Motor Company. Marketed among the top luxury brands in the United States, Lincoln has competed closely against Cadillac for nearly its entire existence. Lincoln has the distinction of establishing the personal luxury car segment, with the entry of the Lincoln Continental into mass production in 1940. Lincoln Motor Company was founded in 1917 by Henry M. Leland, naming it after Abraham Lincoln; in 1922, Lincoln was acquired by Ford. Following World War II, Ford formed the Lincoln-Mercury Division, pairing Lincoln with | "fish tail" design. The '51 Lincoln's modified C pillar actually increased rearward vision. Lincoln EL-series The Lincoln EL-Series is a full-size luxury car that was marketed and sold by the Lincoln division of Ford Motor Company from the 1949 to 1951 model years. For the 1949 model year, Ford introduced redesigned model lines for all three of its divisions. To share development costs, Ford combined its separate Lincoln and Mercury divisions into the Lincoln-Mercury Division following World War II. As a result, the redesigned postwar Lincoln shared much of its design with the redesigned 1949 Mercury Eight. As with its | These mats are not representative of the Lincoln brand. They look like they belong in a farm pick up truck. | Lincoln Navigator area which, significantly, was not shared with the Expedition. Inspired by the symmetrical, "dual-cockpit" layout of the 1961 Lincoln Continental, the instrument panel and dashboard area was adorned with real walnut burl wood inserts and panels and switches painted with a low-luster satin nickel color. Adding to the upscale interior design further were white LEDs, 120 in all, which provided backlighting for controls and switches. Additionally, to direct attention to the high-quality satin nickel-faced analog clock mounted in the dashboard, an articulating door is present to conceal the radio head unit and optional satellite navigation system when they are not | Lincoln Motor Company Plant his association with Cadillac until the mid-1910s, when he resigned because of the company's unwillingness to transition to World War I wartime production needs. In 1917, Leland established the Lincoln Motor Company to build Liberty engines for fighter planes using Ford Motor Company-supplied cylinders. Leland immediately purchased a small factory on Detroit's west side. However, he quickly realized the facilities were not sufficient to house the engine production envisioned, so he purchased a 50-acre plot of land at Warren and Livernois. The company immediately broke ground for a factory complex of over , hiring architect George Mason to design the | 209 | Roland called "Golden Tears" a "highly coindental release." Dave & Sugar frontman Dave Rowland, it seemed, had driven Chevrolets for most of his life, including the early period of Dave & Sugar's national success. However, Rowland had just purchased a new Lincoln when he heard the demo tape for the song. The song's first line in the refrain: "From a Chevy to a Lincoln ... ." The song is about a woman who marries a rich man for his money, but quickly realizes that money does not necessarily buy happiness. In one sense, it is also about life in the | 70s soft rock song Chevy Van is about a serial killer | what was the song by gary and dave | when was somebody's crying by tom petty made | Who sings the chevy cruze jingle? | which band released the 1988 album 'lincoln' | craig mabbitt is the lead singer of which band | what was the name of motor ace's first album | when did chevy start racing in le mans |
210 | who did the canadian forces fight in the war | Canada and the Iraq War to sanction the invasion rested on two elements: a discussion of international law, including the Nuremberg Principles on preemptive war; and the UN inspections for Iraq's alleged possession of Weapons of Mass Destruction. Though the leader of the Canadian Alliance Party, Stephen Harper, objected to the Prime Minister's position on Iraq, stating that Canada should be fighting alongside the US, Chrétien's decision may have reflected the view of the general Canadian public: In March 2003, a poll conducted by EKOS Research Associates for the "Toronto Star" and has contrary views to the conservative party Stephen Harper led at the time | Canadian Army The Canadian Army (French: "Armée canadienne") is the command responsible for the operational readiness of the conventional ground forces of the Canadian Armed Forces. the Army has 23,000 regular soldiers, about 17,000 reserve soldiers, including 5,000 rangers, for a total of 40,000 soldiers. The Army is supported by 3,000 civilian employees. It maintains regular forces units at bases across Canada, and is also responsible for the Army Reserve, the largest component of the Primary Reserve. The Commander of the Canadian Army and Chief of the Army Staff is Lieutenant-General Jean-Marc Lanthier. The name "Canadian Army" came into official | Blue Army (Poland) Canada" composed of three battalions. This time there was considerable interest and the Canadians sought and were given permission by British high command to start setting up a Polish Army Camp in Niagara-on-the-Lake. With permission granted the Polish army-in-exile called its camp "Camp Tadeusz Kosciuszko", honouring Tadeusz Kościuszko (a Polish patriot who led the 1794 Kościuszko Uprising aimed at freeing the country from Imperial Russia and the Kingdom of Prussia). Over 20,000 men trained in Canada, equipped and paid by France. Yet even though the camp was in Canada and supported financially by the French, the Americans viewed it as | History of Canada and its self-confidence, as it played a major role in the Atlantic and in Europe. During the war, Canada became more closely linked to the U.S. The Americans took virtual control of Yukon in order to build the Alaska Highway, and were a major presence in the British colony of Newfoundland with major airbases. Mackenzie King — and Canada — were largely ignored by Winston Churchill and the British government despite Canada's major role in supplying food, raw materials, munitions and money to the hard-pressed British economy, training airmen for the Commonwealth, guarding the western half of the North Atlantic | Colonial militia in Canada and Acadian militias continued to fight in Nova Scotia throughout the French and Indian War. The success of the Canadiens was underscored during the French and Indian War by George Washington's defeat at Great Meadows and Edward Braddock's embarrassment at the Monongahela River. The British response was to create new "ranger" and "light infantry" units adept at woodland warfare. When France conceded Canada to Great Britain in 1763, defence of the territory remained a duty shared by Canadien and British colonists, Indian nations, and the regular forces of Britain. As the colonies advanced to nationhood, its people would be called | Canada in the Cold War several bases in Germany – including long tenures at CFB Baden-Soellingen and CFB Lahr, in the Black Forest region of West Germany. Also Canadian military facilities were maintained in Bermuda, France and the United Kingdom. From the early 1960s until the 1980s, Canada maintained weapon platforms armed with nuclear weapons – including nuclear-tipped air-to-air rockets, surface-to-air missiles, and high-yield gravity bombs principally deployed in the Western European theatre of operations as well as in Canada. Canada emerged from the Second World War as a world power, radically transforming a principally agricultural and rural dominion of a dying empire into a | Canada in the Cold War several bases in Germany – including long tenures at CFB Baden-Soellingen and CFB Lahr, in the Black Forest region of West Germany. Also Canadian military facilities were maintained in Bermuda, France and the United Kingdom. From the early 1960s until the 1980s, Canada maintained weapon platforms armed with nuclear weapons – including nuclear-tipped air-to-air rockets, surface-to-air missiles, and high-yield gravity bombs principally deployed in the Western European theatre of operations as well as in Canada. Canada emerged from the Second World War as a world power, radically transforming a principally agricultural and rural dominion of a dying empire into a | Canada in the Cold War several bases in Germany – including long tenures at CFB Baden-Soellingen and CFB Lahr, in the Black Forest region of West Germany. Also Canadian military facilities were maintained in Bermuda, France and the United Kingdom. From the early 1960s until the 1980s, Canada maintained weapon platforms armed with nuclear weapons – including nuclear-tipped air-to-air rockets, surface-to-air missiles, and high-yield gravity bombs principally deployed in the Western European theatre of operations as well as in Canada. Canada emerged from the Second World War as a world power, radically transforming a principally agricultural and rural dominion of a dying empire into a | 210 | Canadian War Museum the way in which armed conflict affected the evolution of the country and its peoples. It includes First Peoples warfare, the alliances and conflicts that marked the relationship between First Peoples and Europeans, and the imperial rivalries that marked most of North America's early history. Content includes the Seven Years' War, the American Revolution, the War of 1812, and conflicts in the Canadian West in 1870 and 1885. Canadian forces went abroad in 1899 and again in 1914 to fight in wars as part of the British Empire. This gallery covers the South African War and the First World War, | what war did canada and australia fight in | what war did black canadians mobilize to fight | Why didn't/don't historians refer to the Seven Year War as the first world war? | which canadian historian said that memories of the war of 1812 make everybody happy | which war did canada join in ww2 | A novel of Canadians in the Civil War | where did canada participate in the war in afghanistan | which battle of the first world war was the site of the canadian national memorial |
211 | how much range will the hwasong-10 reduce | So ive completed GB10, DB10 (not 100%) though and TOA 100 and i plan on starting to climb NB10, i know i should focus db10 and yes i wil to try make it more accurate but i just want to know what kind of builds should i use with my hwa and ran for db (hwa) and nb (hwa and ran)!
Thanks in advance
PS: HWA IS 6* MAX and i have double ran if anyuse
Other mons i have for nb10 could be colleen, fire nine tail, chilling , water lich. | M110 Semi-Automatic Sniper System 12, 2008, the M110 was ranked #2 on the U.S. Army's top ten inventions of 2007. According to performance specification (MIL-PRF-32316 (AR) w/AMENDMENT 1, 5 October 2009): 3.4.1.1.1 Accuracy. The distance between the mean point of impact of each shot group, both unsuppressed and suppressed, shall be not greater than 1.1 inches at 300 feet. 3.4.1.1.2 Dispersion. The average mean radius (AMR) (see 6.11), of each shot group shall be not greater than to 0.68 inches at 300 feet. All targets shall be fired on using M118LR ammunition or equivalent, using five (5) round groups. In April 2011, the U.S. | We present two epochs of observations of TW Hya from the high-dispersion near-IR spectrograph ARIES at the MMT. We detect strong emission from the Brackett gamma transition of hydrogen, indicating an accretion rate substantially larger than previously estimated using hydrogen line emission. The Brackett gamma line-strength varies across our two observed epochs. We also measure circumstellar-to-stellar flux ratios (i.e., veilings) that appear close to zero in both epochs. These findings suggest that TW Hya experiences episodes of enhanced accretion while the inner disk remains largely devoid of dust. We discuss several physical mechanisms that may explain these observations. | What is the best range damage/accuary/gear i can get with 97m
Or within the range of 90-120m?
for like most bosses | Just shipped up into a Cobra with trading in mind. Upgraded a few systems to reduce weight and removed hardpoints. Then I upgraded my FSD from E4 to A3, and it dropped my jump range to 6.9 ly unladen. This was odd, since I was at 11+ unladen with the stock E4. Every other FSD I can buy is now giving me a worse jump range, though I can't purchase an E4 here.
Am I misunderstanding how fitting works or is this a bug? | Sorry if this question has already been asked and answered.
I am going to buy a 10/22 soon. My two alternatives is a standard version and the take down. I've heard the takedown has worse groups than the standard version. Could any of ypu guys confirm that this is in fact a fact, and if so what kind of difference in accuracy are we talking about, for instance on a 50 yard range? | I made **this picture here** to give people a rough idea of Point Blank's damage fall off range.
Based on an old forum post I found **here**.
>Mark_GGG wrote:
>Damage bonus/penalty is as follows:
>Distance 0 to 10: 50%
>Distance 10 to 35: scales linearly from 50% down to 0%
>Distance 35 to 120: scales linearly from 0% down to -100%
>
>For reference, The greatest melee weapon range is 5, cold snap has a base range of 15, and 120 is the maximum distance it's possible to shoot an arrow (it's impossible to reach this usually except sometimes when firing at the upper corners of the screen).
Hope this helps! | The range could be better, but I did my homework and knew what to expect. This did meet those expectations and was worth the sale price I paid! | 211 | which will reduce its range by about half, after the experts acknowledged that the June 22 twin test range could be at 3,150 km if the missile was not launched in the lofted trajectory. North Korea sold a version of this missile to Iran under the designation BM-25. The number 25 represents the missile range (2500 km). The Iranian designation is Khorramshahr, and it was unveiled and test-fired in September 2017. Earlier test firing occurred in January 2017. According to IISS expert Dempsey, the missile looks very similar to Hwasong-10. It carries 1800 kg payload over 2000 km (Iran claims | how many missiles did north korea test in 2017 | Can the North Korean Nuclear test be confirmed by now? | how much did north korea ship missiles to iran in 1986 | Iran tests long-range missile as UN watchdog reviews nuclear ... | US warns N. Korea against missile tests | The 12 February 2013 North Korean Underground Nuclear Test | what is the altitudes of the a135 missile | how many b-25s were picked up by the 38th bombardment group |
212 | The seller clearly didn't describe this book as well used ... | Book is what I expected; it looks a little 'used,' but it is readable with no marks inside on the pages. | It said it is a new book, but when I got it, it looks used. I don't like it, so disappointed... | Book is used and had a little more shelf wear than described.. Its still readable, and they shipped it very fast. I'm happy with the purchase. | I don;t remember all this stuff. Book went to Half Price Books a really long time ago | The book came damaged. Poor packaging. I bought a new book and it looked very used. This is an art book, so condition is very important. I am returning it. | It's ok! We got this because you can't buy it in a store anymore since it was from 2008 or something like that. It is used and I can't complain since I knew it was something that was used. However some of the items in the book were missing and this was not in the description of the book. No biggie we still read it and it is still being loved. | I have purchase many used books through amazon seller and have never been dissapointed. Again-good condition | This was a 3rd party book and they advertised it as being the more recent Guidebook so when it was received it was NOT helpful at all | 212 | The seller clearly didn't describe this book as well used. As for the text and material covered it served it's purpose. | Despite the seller's disclaimer that the book might contain underlining/highlighting ... | This book came with an inscription on the opening page ... | I think the writer has some good material but has not presented it clearly | This delivered an outline for a novel that was sold ... | The book shown on the look inside, is not the book that was delivered | The Treatment of an 1855 British Paper Specimen Book | Not the expected content, most of the book talks ... | The book is such a display of literary talent used ... |
213 | Is queen beatrix of holland related to elizabeth 2nd? | Was Queen Elizabeth the 1st related to Queen Elizabeth II? | Who is Queen Elizabeth II's sister? | Does Elizabeth 2nd have any siblings? | What are queen elizabeth sons name? | Pets of queen elizabeth the 2nd? | Is Anne Boleyn related to Queen Elizabeth II? | Queen Elizabeth I family? | Was mary queen of scots elizabeth sister? | 213 | Which is better queen elizabeth ii or queen beatrix? | Queen Elizabeth II Useless? | What are the 2 middle names of queen elizabeth II? | The queen elizabeth II's job? | Was queen elizabeth you related to Elizabeth II? | Was queen elizabeths q good queen? | Who was queen elizabeth 2's sister? | What is the queen of england's position of power? | What is the current queen elizabeth's last name? |
214 | BlackBerry Q1 Expectations | **écraser la mûre**
* 1) to have an abundance of something, such as money; 2) to have a lot of choice in a situation (literally, *to crush the blackberry*)
The idea is that a very fruitful blackberry bush will also have dropped many on the ground, and you'll be stepping on as many as you're picking. | BlackBerry Limited celebrities. On September 28, 2013, media reports confirmed that BlackBerry lost US$1.049 billion during the second fiscal quarter of 2013. In the wake of the loss, Heins stated: "We are very disappointed with our operational and financial results this quarter and have announced a series of major changes to address the competitive hardware environment and our cost structure." Between 2010 and 2013, the stock price of the company dropped by 87 percent due to the widespread popularity of the iPhone. Goldman Sachs estimated that, in June 2014, BlackBerry accounted for 1 percent share of smartphone sales, compared to a peak | BlackBerry Q10 has been launched on 6 June 2013 and will be available in 20 cities, 1000 retail outlets from 7 June 2013. In Slovenia, the BlackBerry Q10 has been released by Telekom Slovenije. In Serbia, the BlackBerry Q10 has been released by Telenor Serbia. In Bulgaria, the BlackBerry Q10 has been released by Vivacom and Mobiltel. In Poland, the BlackBerry Q10 has been released by T-Mobile and Orange. Amosu has made 25 diamond encrusted BlackBerry Q10s available. In Russian Federation, BlackBerry Q10 is readily available from several retailers for use with any GSM services provider by the usual procedure | BlackBerry Q10 has been launched on 6 June 2013 and will be available in 20 cities, 1000 retail outlets from 7 June 2013. In Slovenia, the BlackBerry Q10 has been released by Telekom Slovenije. In Serbia, the BlackBerry Q10 has been released by Telenor Serbia. In Bulgaria, the BlackBerry Q10 has been released by Vivacom and Mobiltel. In Poland, the BlackBerry Q10 has been released by T-Mobile and Orange. Amosu has made 25 diamond encrusted BlackBerry Q10s available. In Russian Federation, BlackBerry Q10 is readily available from several retailers for use with any GSM services provider by the usual procedure | BlackBerry Q10 has been launched on 6 June 2013 and will be available in 20 cities, 1000 retail outlets from 7 June 2013. In Slovenia, the BlackBerry Q10 has been released by Telekom Slovenije. In Serbia, the BlackBerry Q10 has been released by Telenor Serbia. In Bulgaria, the BlackBerry Q10 has been released by Vivacom and Mobiltel. In Poland, the BlackBerry Q10 has been released by T-Mobile and Orange. Amosu has made 25 diamond encrusted BlackBerry Q10s available. In Russian Federation, BlackBerry Q10 is readily available from several retailers for use with any GSM services provider by the usual procedure | BlackBerry Classic The BlackBerry Classic, originally known as the BlackBerry Q20, is a touchscreen-based smartphone with a physical QWERTY keyboard developed by BlackBerry, previously known as RIM (Research In Motion). The BlackBerry Classic was unveiled in December 17, 2014 and it runs BlackBerry 10 operating system. Its design is similar to the BlackBerry Q10 in form and feel and especially to the BlackBerry Bold 9900 and related lines in that they feature an optical trackpad which can compliment or be used as primary means of navigation instead of or with the device's touch-screen. The BlackBerry Classic has a 3.5-inch IPS | said that approximately 700,000 handsets had been sold, down from 1.9 million in the same quarter in 2014, and down from 800,000 in Q2 of 2015. The average sale price per unit was up from $240 to $315, however. This should continue to increase with sales of the new Android Priv device which was selling at a premium price ($800 in Canada, for example). In Q3 of 2015, BlackBerry had a net loss of $89 million U.S. or 17 cents per share, but only a $15 million net loss, or three cents per share, when excluding restructuring charges and other | I'm a power email users and, for me, there are 11 reasons why the Peek is a far better alternative than a Blackberry. [...].
Folks, the Peek does what they say it will do. Reading the comments of people who do not give the Peek a Five Star rating, in most cases the writer simply is expecting the Peek to do things that it was not intended to do. Read my post. If your needs are the same as mine, I'm sure you'll be very happy with your Peek. | 214 | What's everyone's thoughts on BB going into tomorrow Q1?
I've been holding for about a year now and have seen a number of these roller coaster quarterly results. I know Cylance is not yet profitable, but I'm wondering what the forecast will do for the stock price and if I should sell if/when the stock rallies tomorrow. | Advice on next black market | What good news do we have today? Why we down 3% premarket | Likelihood of Zaza and McGee returning next year? | As we get ready to greet in the new year, let's work to continue decentralizing the Bitcoin network. We are at 11.8K nodes, let's push it to 20K! | Next Double Starcoin Weekend? | Curious what everyone’s prediction is for the upcoming presidential election, how will trading be? | I have stock in Micrel inc. and i was wondering if you think it will continue going up in the next month or if i should sell now | Guesses on what the big announcement is gonna be? |
215 | Very entertaning and enlightening Slap at the Christ myth | Thank you for reading how hysterical identification and resistance in the bible and film. Maybe you have knowledge that, people have look numerous times for their chosen novels like this how hysterical identification and resistance in the bible and film, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they cope with some harmful virus inside their desktop computer. | The author described incidents in American history that where attributed to the divine hand in part due to how improbable they seemed. He looked at the period from the Pilgrims to the Civil War. At the beginning, he mostly focused on specific events. As the book went on, he focused people who had a series of "divine incidents" happen in their life. The book ends with Abraham Lincoln, and that section read more like a biography. The more biographical portions are on George Washington, Andrew Jackson, Sam Houston, Nicholas Trist, and Abraham Lincoln.
When describing an incident, he often quoted people who actually witnessed these events. I'd previously heard of many of these events. However, I did learn some interesting new details about those events and learned about some events I was unaware of. If you're not familiar with this theme, I think a person would find it very interesting and well-researched.
Incidentally, his point is not that we have the right to be arrogant or feel faultless because God has intervened in our history but rather that we should be grateful and are obligated to act more nobly because of it. | Gibson offers his spectacle of Christ suffering as a reel sacrament. To do so, he writes the Hollywood passion hero and the legalistic Western Christian myth over Jesus, or lifts the sign of Jesus’ suffering into those mythic orders. In the West, as Gibson’s success shows, this myth often masquerades as the nature of things. This myth transforms us into bastards who consume the suffering of others at a safe distance. We can confess this myth, as if it were a hierophany, or we can wrestle with it, exposing it as an interpretation. | in benediction, in the heavens thou dost behold the Lord and Creator of all most splendidly, and helpest men who suffer amid all manner of trials. Thou dost strengthen soldiers in battle, rescuing them from capture by the enemy, from wounds, sudden death and cruel misfortunes. Wherefore, entreat Christ the Master, O ever-memorable one, that He deal mercifully with us in every circumstance, that He lead us not into temptations, but save our souls, for He is a lover of mankind. </poem> Source: John the Warrior is usually depicted with an uncovered head. His face is framed by dark hair | The theory of universal restoration (apokatastasis), the eventual eviction of evil and the purification, conversion and salvation of all rational creatures, was prominent in early Christian thinkers and present in more Patristic theologians than is commonly assumed. But, besides having philosophical, Biblical, and Jewish roots, may it have stemmed from another religion? The only suitable candidate would be Zoroastrianism. An analysis of the available sources concerning Zoroastrian eschatology shows that it is improbable that this may have influenced the Christian apokatastasis doctrine. At least, it is impossible to prove anything like this, mainly for chronological reasons. Fruitful interactions may, however, have occurred at the time of Bardaisan. This essays shows the importance of comparative religio-historical studies, and the reconceptualizing of theological doctrines into social discourse, for research into early Christianity. | It will touch you to the core of your being and stir within you a greater hunger for God in the depths of your heart, mind and soul. | Excellent.
Clearly demonstrates that the Christian assumption that legends/rumors cannot develop in a short period of time is blatantly false. There is a twenty to twenty-five year gap between Jesus' death and the first epistle of Paul. We have no idea how much the "Jesus Story" changed due to legends and myth during this "black hole". | Turning and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.
&#x200B;
Surely some revelation is at hand;
Surely the Second Coming is at hand.
The Second Coming! Hardly are those words out
When a vast image out of Spiritus Mundi
Troubles my sight: somewhere in sands of the desert
A shape with lion body and the head of a man,
A gaze blank and pitiless as the sun,
Is moving its slow thighs, while all about it
Reel shadows of the indignant desert birds.
The darkness drops again; but now I know
That twenty centuries of stony sleep
Were vexed to nightmare by a rocking cradle,
And what rough beast, its hour come round at last,
Slouches towards Bethlehem to be born? | 215 | The author uses very good evidence to prove that Chist was simply one of many "christs" from mythology. It would be a tough read for the faithful. | Questions about the Chimera Mystery | Core of Christian Chivalry | Chapter 139: Chitoge discussion | regarding chitoge's actions in the past chapters | who gave bellerophon advice about the chimera | who was the first person to describe chitonids | which movement is the narrator of charles dickens' 'the chimes' a | An Aetheist Investigative Reporter dissects the Christ Story |
216 | At what a ge do maost boys voices change? | Do girl's voices change? | The pronunciation of Middle Chinese voiced initials as l- is a characteristic of Yiyang dialect. The circumstances of the change are classified into three types: Cong (從), Xie (邪), Cheng (澄), Chong (崇), Chuan (船) and Chan (禪) followed the pathway dz- > z- > ɹ- > l-, Ding (定) followed the pathway d- > l-, and Ri (日) became pronounced as l- due to the influence of literary readings. The sound change of voiced affricates weakening to voiced fricatives, voiced fricatives changing to approximants and then to the lateral approximant, and voiced stops changing to the lateral approximant are unusual devoicing developments among Chinese dialects | Why do peoples voices change as they get older? | Men have deeper voices than women because boys experience a rise in testosterone during puberty that makes their vocal cords grow longer and thicker, causing their voices to drop as much as one full octave. Girls experience vocal cord changes during puberty as well, but their voices only deepen slightly compared to boys | Back in Xenoverse when him and hit were put in, hit has a completely different voice compared to the dub, and I'm assuming Black will have a totally different dub too compared to Xenoverse. My question is, since this game comes out so close to when the Black arc is set to premiere in english, do you think the voices will be the same? | The Voice of China (season 4) losing artist from their respective team, and they had to decide on the spot if they would like to exercise the power on the artist once he or she was announced as the loser of a battle. If the losing coach decides not to, the artist would be immediately eliminated. The two artists that were saved by the coaches (one from each team) would then perform again in the "coach's save" round, with the one receiving the most media votes moving on to the Top 10. In the event when there was only one saved contestant as the opposing coach | What dose vocal cords mean? | What dose voice mean? | 216 | What age does a boy voice change? | What age does a boy's voice change? | Hoarseness and voice change in male adolescents. | How will my voice be after adolescence | how old do you have to be to be on the voice | Good age to start vocal lessons. | Is there any way for Young Lando’s voice to be changed or redone in the future? | Why have boys stopped singing? | What age do most boys mature at? |
217 | The emerging field of vibro-polaritonic chemistry studies the impact of light-matter hybrid states known as vibrational polaritons on chemical reactivity and molecular properties. Here, we discuss vibro-polaritonic chemistry from a quantum chemical perspective, go beyond the cavity Born-Oppenheimer (CBO) approximation and examine the role of electron-photon correlation under vibrational strong coupling (VSC). We first quantitatively review ab initio vibro-polaritonic chemistry based on the molecular Pauli-Fierz Hamiltonian in dipole approximation and a VSC Born-Huang expansion. We then derive cavity and nuclear non-adiabatic coupling elements from the generalized Hellmann-Feynman theorem, provide a detailed discussion of their properties and reevaluate the CBO approximation. In the second part, we introduce a crude VSC Born-Huang expansion based on adiabatic electronic states, which provides a foundation for widely employed effective Pauli-Fierz Hamiltonians in ground state vibro-polaritonic chemistry. The latter do not strictly respect the CBO approximation but an alternative scheme, which we name crude CBO approximation. We argue that the crude CBO ground state misses electron-photon entanglement relative to the CBO ground state due to neglected cavity-induced non-adiabatic transition dipole couplings to exited states. A perturbative connection between both ground state approximations is proposed, which identifies the crude CBO ground state as first-order approximation to its CBO counterpart. We provide an illustrative numerical analysis of the cavity Shin-Metiu model, which reveals the nature of non-adiabatic coupling under VSC, addresses the effect of electron-photon correlation on classical activation barriers and illustrates potential shortcomings of the electron-polariton Hamiltonian when employed in the VSC regime. |
I. INTRODUCTION
The interesting fact that simply confining a quantum system increases its coupling to vacuum fluctuations of the radiation field so much as to change the system's properties has been known since the early days of quantum mechanics. A key realization was that spontaneous emission rates of a two-level system can be increased by placing it in a resonant cavity due to the enhanced lightmatter coupling strength [1]. The recent burst of activity in cavity quantum electrodynamics is largely due to impressive experimental advances in manipulating matter at the meso-and nano-scales, that have driven the investigations towards exploring the possibilities of new cavity-mediated phenomena. The playing field is rich when considering enhanced light-matter interaction on top of the already complex interactions of real matter, as opposed to the simple two-level-like systems that were considered earlier [2][3][4][5][6][7][8][9][10].
Polaritonic phenomena involve a complex interplay of photonic, electronic, and nuclear degrees of freedom, but often we are particularly interested in the dynamics of one particular subsystem. In polaritonic chemistry applications, it is typically the nuclear (or ionic) system we are interested in, for example in investigating changes in chemical reactivity when molecules are confined. The exact factorization (EF) approach [11][12][13][14][15][16] offers a natural context in which to study this problem since it provides a rigorous and unique definition of potentials acting on a subsystem that exactly incorporate the effects of coupling to the other subsystems.
In particular, one obtains a time-dependent Schrödinger equation (TDSE) for the nuclear wavefunction χ(R, t), in which the potentials contain the complete effect of coupling to the photonic and electronic systems. The full, exact wavefunction of the system has the form of a single correlated product, χ(R, t)Φ R (r, q, t), where r, q represent electronic and photonic coordinates respectively. This is quite in contrast to another exact representation for the full wavefunction, the Born-Huang expansion generalized to include photon degrees of freedom, which contains an infinite number of terms of correlated products, j χ j (R, t)Φ j R (r, q); here the Φ j R (r, q) are the polaritonic eigenstates. Instead of the single TDSE for the nuclear system that appears in EF, one has a set of coupled equations to solve, and it is not possible to identify a potential that drives the nuclear motion. The concept of a single equation for the nuclear wavefunction, as arises in EF, is especially useful when turning to mixed quantum-classical methods where being able to unambiguously define a force acting on a classical nuclear trajectory at each point is desirable.
The EF was originally derived with the static coupled electron-nuclear problem in mind [11,12,17], while the time-dependent problem was introduced later [13,14]. Extensions of the EF idea to a variety of different settings have been made: e.g. the static purely electronic problem [18] with connections to density functional theory [19], the time-dependent electronic problem with connections to the single-active electron approach [20], and recently electronic Fock space to derive a new quantum embedding method [21][22][23]. A reverse factorization for electron-nuclear problems has also been explored where the nuclear wavefunction is conditionally dependent on the electronic coordinate, which has an advantage when one is most interested in the electronic sys-tem [24].
Refs. [15,16,25] extended the EF approach to polaritonic systems, focussing on phenomena which are either primarily interesting for the photonic system [15], the electronic system [25], or the nuclear system [16]. The present work expands on the latter. Ref. [16] studied the exact potential driving a model of cavity-induced suppression of proton coupled electron-transfer. The model molecule was photo-excited into the first excited Born-Oppenheimer state, and, when outside the cavity, the nuclear wavepacket evolves towards a narrow avoided crossing where there is some transfer of population to the ground-electronic state. Since in this state the electronic dipole is localized on the opposite side to where it was localized initially, the process is known as proton-coupled electron transfer. The enhanced spontaneous emission rate from the excited molecule when placed in an optical cavity led to a significant partial photon emission when the cavity resonance was tuned to the initial excitation frequency. The interplay between the partial photon emission, the partial electronic deexcitation, and coupling to nuclear motion led to less of the nuclear wavepacket evolving to the narrow avoided crossing, and hence a suppression of the proton-coupled electron-transfer. While the shape of the polaritonic surfaces suggest that such a phenomenon could occur, they alone could not predict the suppression, as a weaker light-matter coupling strength led to practically identical surfaces but with no suppression dynamics. What would be needed to determine the dynamics would be coupling matrix elements between the surfaces. On the other hand, the exact potential arising from the EF approach could distinguish clearly the suppression phenomenon.
In this paper, we present two further examples of the EF approach applied to polaritonic chemistry. In the first, we revisit the same model of Ref. [16] but begin now in an excited polaritonic state instead of an electronically excited state. The dependence of cavityaltered phenomena on how the initial state of polaritonic system has not been widely explored. In particular, when there is an initial excitation in the system, a question is whether this excitation is done in the presence of the cavity such that the initial excitation is a polaritonic one, or whether it is done effectively outside the cavity and then the molecule is inserted into the cavity, in which case the initial excitation is a purely electronic one. For our model of proton-coupled electrontransfer, we find suppression is observed when beginning in a polaritonic state, although not as much as for the initial purely electronically excited state, and we compare the exact potential from EF in the two cases and with the cavity-free case. The second example we consider is one of cavity-induced electronic excitation, where a photo-excited molecule is placed in a cavity whose fundamental frequency is resonant with a molecular frequency at two different geometries: at one nuclear configuration the mode frequency coincides with the ground and first electronic states while at the other nuclear configuration it coincides with the ground and second. Thus as an excited nuclear wavepacket on the first electronic state evolves through the first nuclear configuration into the second, an electronic excitation into the second excited Born-Oppenheimer state occurs, which is absent in the cavity-free case. With an eye to developing mixed quantum-classical approximations, we plot the force on the proton at different time snap-shots due to different components of this exact surface, especially since somewhat localized large step features appear in one of the components which may exaggerate its effect on the dynamics. A quasiclassical Wigner propagation of nuclear trajectories shows that dynamics on the exact potential reproduces the exact quantum dynamics accurately. We begin in Sec. II with a brief review of the EF approach.
II. EXACT FACTORIZATION APPROACH
The essential statement of the exact factorization approach is very general: the complete wavefunction for a system of coupled quantum subsystems can be factorized into a marginal wavefunction depending on one (or some) of the subsystem coordinates, and a conditional wavefunction of the other coordinates, parametrically dependent on the marginal degrees of freedom. The equations for the two parts depend on the choice of the marginal and conditional and how the Hamiltonian depends on them. For example, consider a system of interacting electrons only. In Ref. [20], the factorization is done in real-space with a chosen number of electronic coordinates associated with the marginal, and the resulting equation for the marginal has a TDSE form. This is not the case in Ref. [22] where instead the factorization is done in Fock space with a chosen set of orbitals included in the marginal; instead, there an effective embedding Hamiltonian matrix is deduced which is of interest to problems in strong correlation.
Consider now any situation for which the components of the Hamiltonian associated with the chosen marginal degrees of freedom have the form of a kinetic term,T = − I ∇ 2 I /(2M I ), plus potential terms that are multiplicative operators in the marginal coordinate. Then the EF equations take the same form as in the original electron-nuclear case [13,14]. In particular, the equation for the marginal factor is a Schrödinger equation, containing scalar and vector potentials that incorporate exactly the effect of couplings to the other subsystems. Indeed, this is the case for a molecule in a cavity, when we take the non-relativistic photon-matter Hamiltonian in the dipole approximation in the length gauge [5,[26][27][28]. The full Hamiltonian has the form
H =T n +Ĥ BO +Ĥ p +V pm +V SP ,(1)
whereT n = − I ∇ 2 I /(2M I ) is the nuclear kinetic energy,Ĥ BO is the Born-Oppenheimer Hamiltonian of the molecule, and the other terms are arise from the photonic degrees of freedom. Note that we use atomic units (e 2 = = m e = 1) throughout this paper.Ĥ p is the "free" photonic Hamiltonian, which, has the harmonic formĤ
p = α 1 2 (p 2 α + ω 2 αq 2 α ) .(2)
Here the sum goes over all the modes α in the cavity, but in our examples we consider only a single mode of frequency ω α = ω c , resonant with an electronic excitation frequency at a particular molecular geometry;q α is the displacement field coordinate, andp α = −i∂ α . Recent work has shown that the dynamics can change significantly as more cavity modes are accounted for [29] but here we assume that the harmonics of this fundamental mode are high enough that they do not couple strongly with the molecule. The matter-photon coupling is represented by the term
V pm = 2Np α ω αqα λ α · Nn I Z IRI − Ne ir i ,(3)
where N p is the number of photon modes, N n,e the number of nuclei and electrons respectively, and λ α the matter-photon coupling vector. Finally the selfpolarization term iŝ
V SP = 1 2 2Np α λ α · Nn I Z IRI − Ne ir i 2 .(4)
This has a negligible effect in our examples, due to the small value of λ α that we use, so we will later safely neglect it. We note that the importance of this term grows as more modes are considered [29], and its necessity in obtaining a consistent ground-state and maintaining gauge-invariance has been pointed out [30,31]. It should be borne in mind that the Hamiltonian above completely neglects any losses at the cavity boundaries, so the phenomena that we will observe will in reality be dampened somewhat.
In the following we let R represent all nuclear coordinates (three degrees of freedom for each nucleus), r represent all electronic coordinates, and q all the displacement field coordinates for the photons (one degree of freedom for each mode). Taking the marginal as the nuclear degrees of freedom,
Ψ(r, R, q, t) = χ(R, t)Φ R (r, q, t)(5)
yields [13-16, 32, 33] Ĥ BO +Ĥ p +V pm +V SP +Û ep−n − (R, t) Φ R (r, q, t)
= i∂ t Φ R (r, q, t)(6)
and Nn I=1 (−i∇ I + A I (R, t)) 2 /2M I + (R, t) χ(R, t)
= i∂ t χ(R, t) (7)
with the following coupling terms: (i) the coupling operator between the electron-photon system and the nucleî
U ep−n = Nn I=1 1 M J (−i∇ I − A I (R, t)) 2 2 + −i∇ I χ(R, t) χ(R, t) + A I (R, t) · −i∇ I − A I (R, t) ,(8)
(ii) the time-dependent potential energy surface (TD-PES)
(R, t) = wpol (R, t) + kin (R, t) + GD (R, t) (9)
which has the three components: the (self-polarizationincluded) weighted-polaritonic component,
wpol (R, t) = Φ R |Ĥ pol +V SP |Φ R r,q ,(10)
whereĤ
pol =Ĥ BO +Ĥ p +V pm(11)
the kinetic-like term
kin = Nn I=1 1 2M I Φ R | −∇ I − A I (R, t) 2 |Φ R r,q ,(12)
and the gauge-dependent term
GD (R, t) = Φ R | − i∂ t |Φ R r,q ,(13)
and (iii) the time-dependent vector potential
A I (R, t) = Φ R | − i∇ I Φ R r,q(14)
Since the marginal factor χ(R, t) in Eq. (5) can be multiplied by a phase e iθ(R,t) while the conditional factor Φ R (r, q, t) is multiplied by the inverse phase e −iθ(R,t) , without changing the product χΦ R , there is a gaugelike dependence to these equations [13,14]. One can choose different gauges in which A I (R, t) is changed by the addition of ∇ I θ(R, t) while GD (R, t) is changed by the addition of ∂ t θ(R, t). The relation of the coupling terms that appear in the EF to the couplings that appear in a Born-Huang expansion may be found in Ref. [13] for the electron-nuclear case. We now note three simplifications to these general equations that are relevant for the case studies we will consider. First, our models here have only one nuclear degree of freedom, which means that we can always choose a gauge in which the vector potential A(R, t) = A(R, t) = 0. With this gauge-choice, then the exact nuclear wavefunction satisfies a Schrödinger equation Eq. (7) with a purely scalar potential of Eq. (9), composed of the three components, Eq. (10)-Eq. (13). Second, the kinetic component kin (R, t) is negligible compared to the other two terms, due to the factor of 1/M where M is the nuclear mass. Our models consider a proton of mass 1836 times the mass of an electron. This is in contrast to the cases where the electronic [24,34] or photonic [15] systems are chosen to be the marginal, where it certainly cannot be neglected. Third, we note that the self-polarization contribution to wpol (R, t) is negligible for the single-mode cases and coupling strengths we are considering here; this term becomes important on the other hand when many cavity-modes are considered [29]. Thus, the nuclear dynamics is driven by the Schrödinger equation (7) taking
A(R, t) = 0 and (R, t) = wpol (R, t) + GD (R, t).
A. Interpreting the TDPES
The TDPES is composed then of two potentials wpol (R, t) and GD (R, t) that completely govern the nuclear motion. Their dependence on the conditional electronic-photonic wavefunction Φ R (r, q, t) embodies the correlation between the nuclear and electronicphotonic systems. It is instructive to expand Φ R (r, q, t) in terms of the polaritonic eigenstates:
Φ R (r, q, t) = k C k (R, t)Φ k R (r, q) (15) whereĤ pol Φ k R (r, q) = pol,k (R)Φ k R (r, q)(16)
defines the polaritonic surfaces pol,k (R) and polaritonic eigenstates Φ k R (r, q) [35,36]. Then, due to orthonormality of the polaritonic eigenstates, one can decompose wpol in terms of the polaritonic projections:
wpol (R, t) = k |C k (R, t)| 2 pol,k (R)(17)
The physical meaning of wpol is then clear as a weighted average of the polaritonic surfaces, with the weights given by the projections of the conditional electronicphotonic wavefunction on the polaritonic surfaces. With mixed quantum-classical methods in mind, this is somewhat reminiscent of the form of the effective potential the classical nuclei experience in Ehrenfest dynamics, however with the crucial difference in that the coefficients are here spatially-dependent. Terms in the electronic equation yield gradients of these terms (with respect to the nuclear coordinate) which allow different trajectories making up the nuclear wavepacket in a multi-trajectory approach to go in different directions. This results in the possibility of wavepacket splitting when there is partial occupation of different electronic surfaces, which does not happen in a multi-trajectory Ehrenfest approach [37][38][39][40]. As in Ref. [38], we will see in Secs. III A and III B that although wavepacket splitting occurs to some extent when wpol is used to propagate, GD greatly increases this effect and is needed to get accurate dynamics. Similarly, expanding the gauge-dependent term in terms of polaritonic components,
GD (R, t) = − k C * k (R, t)i∂ t C k (R, t).(18)
The meaning and role of GD is less directly clear from its definition. Instead, some insight is gained from comparing the total energy of the system Ĥ with the "marginal energy" defined via Ĥ nuc where H nuc is the Hamiltonian in the nuclear Schrödinger equation, governing the motion of the nuclear wavepacket. We have
Ĥ = Ĥ pol + T n (19) = |χ| 2 wpol dR + T marg n + |χ| 2 Û ep−n r,q dR whereT marg n = − χ * (R, t) ∇ 2 2M χ(R, t)dR
is the kinetic energy of the marginal system, that differs from the nuclear kinetic energy
T n = − drdqΨ * (r, R, q, t) ∇ 2 R
2M Ψ(r, R, q, t) by the last term in Eq. (20) [14]. The expectation value ofÛ ep−n however is very small compared with the other terms when the marginal is chosen as the nuclear system, due to the 1/M factor in Eq. (8) [37]. (Note that only the first term of Eq. (8) contributes to its expectation value). This means, that the total energy is essentially
Ĥ = |χ(R, t)| 2 wpol (R, t) dR + T marg n(20)
On the other hand, the "marginal energy", Ĥ nuc , defined as that associated with the Hamiltonian driving the marginal motion,
Ĥ nuc = |χ(R, t)| 2 (R, t) dR + T marg n (21) = Ĥ + |χ(R, t)| 2 GD (R, t) dR(22)
That is, GD (R, t) does not contribute to the total energy but instead redistributes energy between the electronphoton system and the nuclear system. To get a qualitative sense of its structure, we allow ourselves to extend the ideas above to the energy density rather than the total integrated energy. We distinguish two cases. First, when the polaritonic character is distinct in a piecewise localized way, i.e. one polaritonic character dominates the wavefunction in one region of space, while another dominates it in a neighboring region. For definiteness, let us say the polaritonic energy is locally larger on the left than on the right. Then we expect T marg n would be smaller on the left than on the right, and this is enabled by a step up in GD from left to right in the transition region. This has been observed in the electron-nuclear case [38,41], and we will observe it again here in our polaritonic examples in the next section. In the second case, where there is a mixed polaritonic character, the expected structure of GD (R, t) is generally less clear. Here different parts of the nuclear wavepacket are associated with different polaritonic surfaces in the same region of space. In the cases where the mean-field nature of wpol (R, t) "washes out" distinct structures, we have found GD (R, t) can be of paramount importance. For example, when part of the nuclear wavepacket associated with a polaritonic surface begins to reflect from this surface, while the other parts do not, a dynamical step appears in GD (R, t) to enable the reflection of the part. Because of the average nature of wpol (R, t) the different curvatures of different polaritonic surfaces "under" the nuclear wavepacket are not always evident.
The equations of the exact factorization approach are no easier to solve than the original full Schrödinger equation; on the contrary, practical numerical schemes to solve them are currently elusive [42,43]. Rather, the practical power of the approach is due to providing rigorous definitions of coupling potentials, which then offer a clear and well-founded starting point for approximation schemes, as in Refs. [37,[44][45][46][47][48][49]. Studies of the exact potentials in cases where they could be found [38,41] were very instructive for these developments. Like in those works, we here obtain the exact potentials for the polaritonic case by inversion. That is, we first compute the full matter-photon wavefunction, which is possible for the systems of one nuclear, one electronic, and one photonic degree of freedom that we study. We then obtain the nuclear wavefunction χ(R, t) = |χ(R, t)|e iS(R,t) , which corresponds to the square root of the nuclear density times a phase. The nuclear density is obtained by integration, |χ(R, t)| 2 = drdq|Ψ(r, R, q, t)| 2 . The phase is fixed by the gauge choice, which for A(R, t) = 0 gives S(R, t) = R dR ( Ψ|∂ R |Ψ )/|χ(R, t)| 2 [38]. Once χ(R, t) is obtained, the rest is straightforward as Φ R (r, q, t) = Ψ(r, R, q, t)/χ(R, t) and we simply use Eqs. (9)-(13) with a simple two-point stencil finite difference in time to compute the gauge-dependent part of the potential.
III. MODEL HAMILTONIAN
The Hamiltonian for the matter part of our model systems has the Shin-Metiu [50][51][52] form:
H m =T n +Ĥ BO =T n +T e +V m(23)whereT n = − 1 2M ∂ 2 ∂R 2 ,T e = − 1 2 ∂ 2 ∂r 2 , and V m = σ=±1 1 |R + σL 2 | − erf |r+ σL 2 | aσ |r + σL 2 | − erf |R−r| a f |R − r|(24)
which describes one electron and one proton moving along the axis between two fixed heavy ions separated by a distance L.
We consider two sets of parameters, which will be used to illustrate two effects. The first effect (Sec. III A) is cavity-induced suppression of proton-coupled electrontransfer (PCET), and the parameters of the model are L = 19.0 a.u., a + = 3.1 a.u., a − = 4.0 a.u., a f = 5.0 a.u., and M = 1836 a.u., the proton mass, which was the set of parameters chosen in Ref. [16]. The cavity frequency is chosen as ω c = 0.1a.u. and the photonmatter coupling strength as λ = 0.005a.u. The second effect (Sec. III B) is cavity-induced electronic excitation (ELEX), and the parameters chosen here are L = 19.0 a.u., a + = 4.0 a.u., a − = 4.0 a.u., a f = 5.0 a.u., and M = 1836 a.u, with the cavity frequency ω c = 0.049a.u. and again λ = 0.005a.u. (These parameters would correspond to a one-dimensional cavity of length L = 50µm, with a mode function λ α = 2 L 0 sin(k α X) where the molecule is at a position X near the center of the cavity). The first few BO and polaritonic surfaces are shown in Fig. 1. In all our examples the initial nuclear wavepacket is a Gaussian centered at −4a.u.
A. Cavity-induced suppression of PCET
Ref. [16] showed that when the Shin-Metiu molecule is placed in a cavity resonant with the initial BO energy difference, the PCET process is suppressed. Part of the nuclear wavepacket never makes it to the electronnuclear avoided crossing region as it is associated with the emission of a photon. This behavior of the nuclear wavepacket was shown to be directly correlated with the curvature of the exact TDPES as it evolves in time, and impossible to predict from the shape of the static polaritonic surfaces alone. In Ref. [16] the initial state was a Gaussian nuclear wavepacket placed on the second BO surface with no photon in the cavity, which would be the case if the excited molecule was prepared outside the cavity and then placed inside it. Instead, if the molecule is placed inside the cavity before the excitation is done, beginning in a polaritonic state would be more appropriate than the purely electronically excited one. This is the case we consider in the present paper. That is, the initial state has the form Ψ(r, R, q, 0) =
N e −2.85(R+4) 2 Φ k=1 R (r, q), where Φ k=1 R (r, q)
is the first excited polaritonic state (see Eq. 16). Fig. 2 shows the electronic and nuclear dipoles (i.e. the expectation values of the electronic and nuclear coordinates respectively) when beginning in the first polaritonic state, compared with beginning in the 0photon, first-excited electronic state which we will henceforth call the factorized state, and the cavity-free dipoles. We observe that PCET is suppressed also in the case of beginning in the polaritonic state, although not as much as in the factorized state. Snapshots of the TDPES are plotted in Fig. 3 along with the nuclear density, in comparison with the cavityfree case, and the factorized initial state case. Initially, the exact TDPES coincides with the polaritonic surface in the case of the polaritonic initial state, and along the BO excited surface in the case of the factorized state.
Here we note that a global shift to the TDPES has no effect on the dynamics. As we do not set a zero of the potential at any particular R, when we say the TDPES coincides with a polaritonic surface, we really mean it is parallel to it. For R near -4, the polaritonic surface has the character of the 1-photon ground electronic BO state to the left and the character of the 0-photon electronically excited BO state to the right. The gentler slope of the polaritonic surface on the left at early times slows the nuclear wavepacket relative to both the dynamics of the factorized state and the cavity-free dynamics. The soft kink in the exact TDPES in the factorized initial-state case which separates a region where the surface slopes down to the left on the left and down to the right on the right (R ≈ −2 at t = 17.42 fs), develops at somewhat later times in the case of the polaritonic initial state (visible in this case at 21.29 fs). This results in the density splitting into two parts later than for the initially factorized case, and ultimately less of the wavepacket is trapped in the well on the left, compared to the factorized case. As in Ref. [16], we point out that this behavior cannot be predicted from the polaritonic surfaces alone; the polaritonic surfaces are independent of the choice of the initial state, and alone could not predict the distinct behavior resulting from different initial states. On the other hand, the distinct shapes of the TDPES for these two states does correlate with the different nuclear wavepacket dynamics, and their differences with the cavity-free TDPES also correlates with the different dynamics seen for the cavity-free nuclear wavepacket. Similar to the factorized case, the part of the nuclear wavepacket to the left of the soft kink is unable to overcome the energy barrier in the TDPES to reach the region of electron-nuclear avoided crossing (≈ 2a.u.) that leads to the electron transfer, thus resulting in suppression of PCET. Since less of the nuclear wavepacket is trapped on the left in the case of the initially polaritonic state because of the shape of the TDPES at the earlier times (gentler slope and later development of the soft kink), the suppression of PCET is less than in the factorized initial state case.
Underlying the shapes of the TDPES are the absorption and emission of a photon and electronic transitions between BO states which, through the conditional wavefunction dependence of the TDPES, control its structure. It can be instructive to consider these conditional quantities when interpreting the dynamics. Movies of the TDPES and its components along with the density are given in the Supplemental information, as well as the R-resolved BO electronic populations |C i (R, t)| 2 defined through
|C i (R, t)| 2 = | Φ BO,i R |Ψ r | 2 dq(25)
Movies of the n-photon resolved nuclear densities, χ n−ph (R, t) = ξ n |Ψ(t) r,q where ξ n (q) are the harmonic oscillator eigenstates of the photonic Hamiltonian are also provided. For the factorized initial state at early times partial photon emission occurs throughout the wavepacket, while for the polaritonic initial state only the right part of the wavepacket becomes correlated with photon emission and electronic de-excitation while the left part becomes correlated with photon absorption and electronic excitation. As the wavepacket moves towards the right, leaving the resonant region, there has been less time for the part of wavepacket originally on the left to re-emit the photon it absorbed, so more remains on the excited electronic surface compared to the factorized case, and less ends up being trapped. We have found that the essential features of the surface are similar to what was found for the factorized case but details and timings are different. The gradients of the two dominant contributions to the TDPES, wpol (Eq. (10)) and GD (Eq. (13)) are shown in Fig. 4. At the first time shown, 3.39fs, the force from the TDPES coincides with the slope of the second polaritonic surface as expected, with only the wpol component contributing, but after very short times, both components begin to come into play. Where different parts of the nuclear wavepacket show a single polaritonic character that differs in different spatial regions, the gradient of wpol follows the gradient of the relevant polaritonic surfaces in a piecewise manner, with a peak in the region where they change character, e.g. at times 17.42, 21.29, and 25.56 fs. The gradient of wpol is not simply a weighted average of the gradients of the polaritonic surfaces because the coefficients C i (R, t) in Eq. (15) vary with R, and in particular, these can vary significantly when the nuclear wavepacket correlated with one surface in one region switches to being correlated with another surface. The step-like transition in the coefficient leads to a peak-like structure in its gradient that affects the force the nuclei feel in this region. This structure tends to be partially compensated by a countering step in GD , whose gradient is zero in regions where the nuclear wavepacket is dominated by one surface; the total force from both terms becomes more a step-like feature in the transition region. Typically though, both components need to be considered through most of the nuclear wavepacket. For example, at 21.29fs, the transition region is quite large, and the GD correction to wpol results in quite a different force throughout the nuclear density except for the right-most part, even reversing the sign of the force. As the nuclear wavepacket separates into two distinct parts evolving on different surfaces the opposing peaks in GD and wpol , albeit large, have little effect when located in regions of low density in between the parts of the wavepacket (e.g. between R ≈ 0 and 2 at time 35.80 fs). At this time we see the gradient of the total surface coincides with the 4th polaritonic surface (parallel to the lowest polaritonic surface, with character 1 photon and ground electronic state) in the extreme left part of the wavepacket, and is coming entirely from wpol there. On the other hand the right-part of the wavepacket has a more mixed character, and really only on its extreme right is it dominated by a force from one polaritonic surface(the lowest surface). At later times, GD plays a more complex role. For example, consider a situation where there is mixed character of the nuclear wavepacket such that part is correlated with one polaritonic surface, while another part in the same region is correlated with a different polaritonic surface. These two surfaces could have quite different slopes, and wpol typically resembles neither of them. This is particularly noticeable at the later times shown, where for R > 0 reflections from the right-hand-side of the polaritonic surfaces yield complex overlaps of the component densities, and GD can dominate the force in some regions. It sometimes ensures a reflection which would not happen from purely wpol . To further demonstrate the importance of GD , and with a view to the development of mixed quantumclassical methods based on the TDPES, we run quasiclassical dynamics on the exact TDPES and compare with such dynamics on just the weighted-polaritonic component. That is, we first sample the initial Wigner phase-space distribution corresponding to the initial Gaussian wavepacket to find 3000 initial positions and momenta [53]. (In fact the results were well-converged with just 2000 trajectories). We then propagate each of these using classical Hamilton's equations,Ṙ = P,Ṗ = −∇ (R, t)/M and make a histogram of the resulting positions. Snapshots of the results are plotted in Fig. 5, and a movie is provided in the Supplemental Information. On the left are the histograms when the trajectories are classically propagated using the exact TDPES, and we observe the results are remarkably accurate. There appears to be two small differences: the "trapped" part of the quasiclassical evolution appears to travel just a little further to the right, and at later times, the reflection is somewhat too enthusiastic. Still, given that such an evolution lacks adiabatic interference effects, quantum reflection and tunneling, and incurs errors when potentials are far from harmonic [53], the results here are very good. (We note that non-adiabatic interference has been shown to be captured by such an evolution [54] but this is not a feature of the dynamics considered here). In contrast, on the right are the histograms when instead only the gauge-invariant wpol is used for the force on the classical trajectories. The agreement is much worse, not surprising from the discussion of Fig. 4; without the structures of GD the wavepacket splitting is hardly captured, nor is the detailed reflection at later times. The wavepacket propagates more or less in one piece to the right until it reaches the sharp rise of all the surfaces when the trajectories slow down before turning around.
B. Cavity-induced ELEX
We now turn to the second set of parameters for our model.
Our initial state is again Gaussian in the nuclear variables, centered at R = −4a.u., and placed on the upper electronic surface, with zero photons in the cavity: Ψ(r, R, q, t) = N e −2.85(R+4) 2 Φ BO R (r)ξ (0) (q) where ξ (0) = (ω c /π) 1/4 e −ωcq 2 /2 is the zero-photon state in the cavity. We choose our cavity-resonance at ω c = 0.049a.u., resonant with the BO frequency between the ground and first excited electronic states at R = ±2.2a.u., and also resonant between the ground and 2nd excited BO states at R = 0a.u (see right-hand panel of Fig. 1).
The dynamics outside the cavity is relatively simple: the nuclear wavepacket slides down the first excited BO surface, meeting a weak avoided crossing at the origin, where a little population is transferred to the groundstate. A second transfer occurs later upon reflection back to this region. Figure 6 shows the BO populations, (25). There is a very small transfer from the first to the second excited state, only just discernible in the figure. Now when the molecule is placed in the cavity, we see a more rapid and larger transfer to the ground-state surfaces along with a much greater rise in the population of the second excited BO state. Thus, this is an example of cavity-induced electronic excitation.
|C i (t)| 2 , where |C i (t)| 2 = dR|C i (R, t)| 2 with C i (R, t) defined in Eq.
The phenomena can be only partially understood from the polaritonic surfaces shown in Fig. 1 because these surfaces look practically identical to the eye for much smaller coupling strengths where the dynamics is almost the same as outside the cavity. Still, the fact that both the ground-state population and the 2nd excited population are enhanced at some times in the wavepacket evolution can be anticipated from the avoided crossings in the polaritonic surfaces and the nature of these surfaces: the wavepacket starts on the 2nd Born-Oppenheimer surface coinciding with the 3rd polaritonic surface at R = −4a.u., approaches the narrow avoided crossing with the 2nd polaritonic surface around R = −2.2a.u. suggesting a partial transfer to this surface. The part remaining on the 3rd surface is associated with a 1-photon ground-electronic character to the right of the crossing, as is evident from the shape of that surface, aligning with the ground-state surface shifted up by the energy of one photon in that region. This transfer is consistent with the earlier transfer of population from the electronically excited to the ground electronic state compared with the cavity-free case. The enhancement of the 3rd electronic state population then arises when the part of the wavepacket on the third polaritonic surface (that has the 1-photon ground electronic state character) approaches the narrow avoided crossing with the 4th polaritonic state at R = 0. Moving away from the crossing this 4th surface has the character of the 3rd electronic state.
|C 1 (t)| 2 |C 2 (t)| 2 |C 3 (t)| 2 |C 1 (t)| 2 |C 2 (t)| 2 |C 3 (t)| 2
FIG. 6. Cavity-induced ELEX: BO populations, |Ci(t)| 2 as a function of time, for the lowest three states, in the in-cavity (solid) and cavity-free (dashed) cases.
We now turn to the exact TDPES for this problem, shown at time-snapshots in Fig. 7 along with the cavityfree surface. The effect of the cavity on the nuclear wavepacket dynamics is much smaller than in the PCET example except at later times, but to highlight the electronic character, we plot here also the R-resolved electronic populations, defined in Eq. (25). These are plotted as the thin lines on the split scale shown at the bottom of each panel. We see the growth of the coefficient of the 3rd electronic state (red) beginning as the wavepacket goes through R = 0 as expected, and this coefficient is carried along in the tail of the wavepacket as it evolves to the right and then reflects. We see a very complex character develop by the end, especially in the left hand tail of the wavepacket which has a complex and oscillatory electronic structure. Again, the TDPES shows a piecewise polaritonic character when there are distinct single-surface dominated regions, but again in regions of mixed character, the polaritonic surface structure does not help to predict the correct force as given by the TDPES. Similar observations as for the PCET case can be made for the force plots in Fig. 8, with the salient point being that the force from the wpol is, more often than not, countered by an opposing force from GD in the mixed regions, and does not resemble a weighted average of forces from polaritonic surfaces. Once again the quasiclassical propagation on the exact TDPES in Figure 9 performs remarkable well, while the importance of including the force from GD is evident in its poorer prediction of the dynamics in the right-hand panel of the figure.
IV. CONCLUSIONS AND OUTLOOK
The exact potentials of the EF studied here provide the complete information to propagate the nuclei in cavity-QED problems. Our examples show how their structure correlates directly with the dynamics of the nuclear wavepacket, for two different cavity-altered phenomena. Unlike polaritonic surfaces, these exact potentials distinguish initial states of different polaritonic character, and reflect, for example, the different degrees of suppression achieved when an initially polaritonic state is used compared with an initially pure electronic excitation. We note that other possible factorizations may lead to interesting insights, for example, taking the marginal factor to include both the photonic and nuclear degrees of freedom, with the conditional electronic wavefunc-tion parametrically dependent on both degrees of freedom, χ(R, q, t)Φ R,q (r, t). The resulting surfaces would provide corrections to the sometimes used "cavity-BO" surfaces [55]. For real molecules of interest, finding the exact potentials of the EF method is as hard as solving the full TDSE exactly, so instead approximations need to be made. By studying the exact features in models where they can be found, such as the ones presented here, insight is gained into the effect that the various terms have on the nuclear dynamics and the results provide guidance for building approximate propagation methods. Similar features have been found in the exact surfaces driving the nuclei when coupled to electrons in the absence of cavities or external fields [38,41] which have then motivated and justified the mixed quantumclassical propagation methods of Ref. [37,44,45,56] and Ref [46][47][48][49]. This suggests that mixed quantum-classical methods along these lines can be generalized to include photons. The polaritonic surfaces play the role that the underlying Born-Oppenheimer surfaces would in that situation.
In such mixed quantum-classical methods, a key issue is to determine the force on the classical nuclei. While the Ehrenfest method takes a weighted-average over the Born-Oppenheimer surfaces, trajectory surface-hopping uses the gradient of a single surface at any time, switching between surfaces according to a stochastic algorithm. If applied now to problems in polaritonic chemistry, our results here stress that within an Ehrenfest-like approach, a weighted-average of polaritonic surfaces would lead to significantly incorrect dynamics, while if the gauge-dependent term was included to form the total TDPES, the results would improve significantly. However it is important to realize that the results shown here for the quasiclassical propagation on the weighted polaritonic surfaces are at a higher level than a traditional Ehrenfest calculation, since the latter involves an expansion of the conditional electronic wavefunction with nuclear-coordinate-independent coefficients, while the weights used in our calculations include coordinate dependence. The coordinate-dependence of the weights affects the forces obtained from the gradients as we explicitly showed. That is, the forces in a traditional Ehrenfest calculation differ from those from the exact weighted-polaritonic surface even if the populations of the polaritonic states averaged over the system are the same.
A traditional surface-hopping scheme, on the other hand, would be even more dogged by the problems of coherence than in the usual cavity-free case, due to the increased number of avoided amd trivial crossings between the polaritonic surfaces compared to the Born-Oppenheimer ones [57]. Both decoherence and recoherence effects would need to be captured for an accurate determination of the dynamics. The EF-based surfacehopping approach of Ref. [46][47][48][49] can be generalized to the polaritonic case. Here, an additional term, derived from the EF, appears in the electronic equation of motion and how well it captures these effects will be explored in future work, as will other methods of developing EFbased mixed quantum-classical methods for polaritonic chemistry.
V. DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.
FIG. 1 .
1Lower panels: BO (dashed) and polaritonic (solid) surfaces: cavity-induced suppression of PCET model (left) and cavity-induced electronic transition (right). The upper panels show the ground and first excited electronic BO wavefunctions, Φ BO,i R , i = 1, 2, for each case.
FIG. 2 .
2Cavity-induced PCET suppression: Electronic and nuclear dipoles: cavity-free, in-cavity with the 0-photon excited electronic initial state, in-cavity with the polaritonic initial state.
FIG. 4 .
4Cavity-induced PCET suppression: Snapshots of the components of the force −∇ (black) and its components coming from the weighted-polaritonic −∇ wpol (red) and the gauge-dependent −∇ GD (green) components along with the density, when starting in the initial polaritonic state. The gradients of the four lowest static polaritonic surfaces are shown for reference in orange.
8 FIG. 5 .
85Cavity-induced PCET suppression: Snapshots of the density resulting from quasiclassical propagation on the exact TDPES (left) and on the weighted polaritonic surface (right), when starting in the initial polaritonic state.
-
FIG. 8 .
8Cavity-induced ELEX: Snapshots of the components of the force −∇ and its components coming from the weighted-polaritonic (−∇ wpol ) and the gauge-dependent (−∇ GD) components, along with the density. The orange lines in the backdrop are the gradients of the four lowest polaritonic surfaces.
t=58.56[fs] ε[a.u.] |C(R,t)| 2 R[a.u.]FIG. 7. Cavity-induced ELEX: Snapshots of the TDPES and nuclear density for the case of the induced electronic excitation: cavity-free (pink), in-cavity with the factorized initial state (black), against the background of polaritonic surfaces (pale blue)In Cavity
Cavity Free
|C 1 (R,t)| 2
|C 2 (R,t)| 2
|C 3 (R,t)| 2
t=48.86[fs] −∇Є [a.u.] t=58.54[fs] −∇Є [a.u.] R[a.u.]0.06
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The backdrop of static polaritonic surfaces are shown in light blue for reference (as in Fig. 3). Lower row from left to right: 0-photon resolved density and 1-photon resolved density in the same color code as upper row, and the R-resolved Born-Oppenheimer population for (a) in-cavity with the polaritonic initial state (b) in-cavity with the 0-photon excited electronic initial state (c) cavity-free with |C 1 (R, t)| 2 (green). Movie Fig3.mp4 Upper row from left to right: (R, t), wpol (R, t). GD (R, t) for cavity free (pink), in-cavity with the 0-photon excited electronic initial state (dark blue), in-cavity with the polaritonic initial state (black). |C 2 (R, t)| 2 (orange) and |C 3 (R, t)| 2 (redMovie Fig3.mp4 Upper row from left to right: (R, t), wpol (R, t), GD (R, t) for cavity free (pink), in-cavity with the 0-photon excited electronic ini- tial state (dark blue), in-cavity with the polaritonic initial state (black). The backdrop of static po- laritonic surfaces are shown in light blue for ref- erence (as in Fig. 3). Lower row from left to right: 0-photon resolved density and 1-photon re- solved density in the same color code as upper row, and the R-resolved Born-Oppenheimer pop- ulation for (a) in-cavity with the polaritonic initial state (b) in-cavity with the 0-photon excited elec- tronic initial state (c) cavity-free with |C 1 (R, t)| 2 (green), |C 2 (R, t)| 2 (orange) and |C 3 (R, t)| 2 (red)
These are plotted as a function of R(a.u.) against exact solution (blue), Born-Oppenheimer ground state population (red) and Born-Oppenheimer first-excited state population (green). Right Panel: Same as above. Movie Fig5.mp4 Left Panel: Quasiclassical propagation of 3000 trajectories (orange) on the total TDPES. R, t) for the cavity-induced suppression of PCET (case IIIA). propagated using the weighted-polaritonic PES wpol (R, tMovie Fig5.mp4 Left Panel: Quasiclassical prop- agation of 3000 trajectories (orange) on the total TDPES (R, t) for the cavity-induced suppression of PCET (case IIIA). These are plotted as a func- tion of R(a.u.) against exact solution (blue), Born- Oppenheimer ground state population (red) and Born-Oppenheimer first-excited state population (green). Right Panel: Same as above, propagated using the weighted-polaritonic PES wpol (R, t).
The backdrop of static polaritonic surfaces are shown in light blue for reference (as in Fig. 7) Lower row from left to right: 0-photon resolved density and 1-photon resolved density in the same color code as upper row, and the R-resolved Born-Oppenheimer Population for (a) with the 0-photon excited electronic initial state and (b) cavity-free with |C 1 (R, t)| 2 (green). Movie Fig7.mp4 Upper row from left to right: (R, t), wpol (R, t). GD (R, t) for cavity free (pink), in-cavity with the 0-photon excited electronic initial state (black). |C 2 (R, t)| 2 (orange) and |C 3 (R, t)| 2 (red) (same color code as figure 7Movie Fig7.mp4 Upper row from left to right: (R, t), wpol (R, t), GD (R, t) for cavity free (pink), in-cavity with the 0-photon excited electronic ini- tial state (black). The backdrop of static polari- tonic surfaces are shown in light blue for refer- ence (as in Fig. 7) Lower row from left to right: 0-photon resolved density and 1-photon resolved density in the same color code as upper row, and the R-resolved Born-Oppenheimer Popula- tion for (a) with the 0-photon excited electronic initial state and (b) cavity-free with |C 1 (R, t)| 2 (green), |C 2 (R, t)| 2 (orange) and |C 3 (R, t)| 2 (red) (same color code as figure 7).
Plotted as a function of R(a.u.) against exact solution (blue), Born-Oppenheimer ground state population (red) and Born-Oppenheimer first-excited state population (green). Right Panel: Same as above. Movie Fig9.mp4 Left Panel: Quasiclassical propagation of 3000 trajectories (orange) on the total TDPES. R, t) for the cavity-induced electronic excitation (case IIIB). propagated using the weighted-polaritonic PES wpol (R, tMovie Fig9.mp4 Left Panel: Quasiclassical prop- agation of 3000 trajectories (orange) on the to- tal TDPES (R, t) for the cavity-induced elec- tronic excitation (case IIIB). Plotted as a func- tion of R(a.u.) against exact solution (blue), Born- Oppenheimer ground state population (red) and Born-Oppenheimer first-excited state population (green). Right Panel: Same as above, propagated using the weighted-polaritonic PES wpol (R, t).
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I. INTRODUCTION
The interaction of infrared-active molecular vibrations with quantized electromagnetic field modes of optical Fabry-Pérot-type cavities has been experimentally shown to have a peculiar impact on chemical ground state reactivity and molecular properties [1][2][3][4][5]. The origin of this impact is attributed to the formation of vibrational light-matter hybrid states, known as vibrational polaritons [2]. Linear [3,4,6] and nonlinear [7,8] infrared spectroscopic techniques have been the experimental methods of choice to characterize these vibrational light-matter hybrid states. Consequently, there has been a decent amount of theoretical effort to address the calculation of infrared spectra for vibro-polaritonic systems [9][10][11][12][13][14][15]. There, one or more molecular vibrations interact with a single or multiple quantized cavity modes and the composite system is commonly described by an effective vibrational Pauli-Fierz Hamiltonian in the length-gauge representation of non-relativistic cavity quantum electrodynamics (cQED) [16][17][18][19]. In the latter, the light-matter interaction is mediated by the molecular ground state dipole moment and its orientation relative to the cavity mode polarization directions. Often, the dipole moment * [email protected] † [email protected] is assumed to be either exactly aligned with the polarization direction of a cavity mode or fixed at a certain orientation with respect to a single cavity mode polarization. The impact of molecular rotations on vibrational polaritons, which naturally influences the light-matter coupling due to the orientation dependent nature of the interaction, has been addressed only recently in a few works [20][21][22][23]. There, the orientation of the dipole moment was allowed to vary with respect to the polarization direction of a single cavity mode and rotation related cavity-induced conical intersections have been studied in comparison to the role of classical laser fields [23]. However, the quantization of the cavity radiation field naturally leads to doubly degenerate optical modes with two orthogonal polarization directions [24], which both should be relevant for the light-matter interaction of rovibrating molecules.
Here, we consider a rovibrating diatomic molecule in an optical cavity, which interacts with a pair of degenerate and orthogonally polarized cavity modes. Inspired by recent work of Vibók and coworkers [22], we treat the rovibro-polaritonic problem from a non-adiabatic perspective by energetically separating the rotational and vibro-polaritonic dynamics. As a result, we observe non-adiabatic effects that manifest as three-state vibropolaritonic conical intersections (VPCIs) between vibropolaritonic surfaces. We discuss the three-state VPCIs in detail from a topological, a dynamical and a spectroscopical perspective. Further, we examine the effect of experimentally ubiquitous dissipation on the infrared spectra of rovibrating molecules in an optical cavity due to spontaneous emission from excited states. We note the model character of our study, as gas phase experiments in optical cavities have not yet been performed due to issues in reaching the vibrational strong coupling regime. This paper is structured as follows: In Sec.II, we introduce the effective rovibrational Pauli-Fierz Hamiltonian (II A), our ab initio molecular model (II B) and discuss the adiabatic separation of rotational and vibropolaritonic degrees of freedom (II C). In Sec.III, we present and discuss our results. First, we examine the formation of three-state vibro-polaritonic conical intersections and their topological properties (III A). Second, we discuss vibro-polaritonic population dynamics and the time-evolution of reduced vibro-polaritonic rotational densities (III B). Third, we characterize the light-matter hybrid system by means of infrared spectra (III C) and discuss the spectroscopic manifestations of non-adiabatic features in comparison to purely vibro-polaritonic systems (III C 1). Finally, we study the influence of dissipation on the infrared spectra due to spontaneous emission effects(III C 2). Sec.IV summarizes our work and connects our findings to other branches of molecular polaritonics.
II. THEORY AND MODEL
A. Rovibrational Pauli-Fierz Hamiltonian
We consider a diatomic molecule in a two-mode optical cavity (cf. Fig.1(a)) described by an effective lengthgauge, rovibrational Pauli-Fierz Hamiltonian in dipole and cavity Born-Oppenheimer type approximation [15][16][17][18], as given bŷ
H =Ĥ S +Ĥ C +Ĥ SC +Ĥ DSE .(1)
In the specific example chosen in this work,Ĥ S is the Hamiltonian of a single rovibrating CO moleculê
H S =ĵ 2 2I − 2 2µ ∂ 2 ∂r 2 + V (r) =Ĥ vib ,(2)
with moment of inertia, I = µr 2 , where r is the COstretching coordinate and µ the reduced mass, and angular momentum operator
j 2 = − 2 1 sin θ ∂ ∂θ sin θ ∂ ∂θ + 1 sin 2 θ ∂ 2 ∂φ 2 ,(3)
with polar angle, θ ∈ [0, π], and azimuthal angle, φ ∈ [0, 2π), respectively. The vibrational Hamiltonian, H vib , is determined by the molecular Born-Oppenheimer ground state potential energy surface, V (r). Further, we consider a Fabry-Pérot type cavity with two energetically degenerate and orthogonally polarized, transverse cavity modeŝ
H C = λ=z,y ω c â † λâ λ + 1 2 ,(4)
with polarization index λ, harmonic cavity frequency ω c and photon creation/annihilation operatorsâ † λ /â λ , respectively. Here, we chose the cavity modes to be polarized along the z-and y-axis of the molecular space-fixed frame (perpendicular to the wave vector, k), as shown in Fig.1(a). Further, the orientation dependent light-matter interaction is mediated by the molecular dipole moment
d(r, θ, φ) = d(r) sin θ cos φ sin θ sin φ cos θ ,(5)
where d(r) is the molecular dipole moment along the CObonding axis. The light-matter interaction is given by the projection of d(r, θ, φ) on the cavity mode polarization directions, (ǫ λ · d(r, θ, φ)), with λ = z, y. Accordingly, the bare cavity-molecule interaction Hamiltonian readŝ
H SC = g λ=z,y ǫ λ · d(r, θ, φ) â † λ +â λ ,(6)
= g d(r) â † z +â z cos θ + â † y +â y sin θ sin φ , and the dipole self-energy, which has been thoroughly studied in Refs. [25] and [26], is given bŷ
H DSE = g 2 ω c λ=z,y ǫ λ · d(r, θ, φ) 2 ,(7)
= g 2 ω c d 2 (r) cos 2 θ + sin 2 θ sin 2 φ .
Note, there are two independent contributions to the DSE term related to independent z-and y-polarized cavity modes without any cross terms coupling modes along different polarization directions. The light-matter interaction strength, g, in Eqs.(6) and (7), carrying the dimension of an electric field strength (V/m), is related to a dimensionless parameter η via [27]
g = ω c |d f i | η .(8)
Here, d f i is a vibrational transition dipole matrix element between selected initial and final molecular states (see below), to which we choose the cavity mode frequency ω c to be resonant. Generally, the coupling parameter g (or η) is a function of the cavity volume, the dielectric constant inside the cavity and the number of molecules in the cavity. [15] Here we treat g (and η) as an adjustable parameter. Further, η specifies the lightmatter interaction regime: Vibrational strong coupling (VSC) for 0.0 < η < 0.1 and vibrational ultrastrong coupling (VUSC) for η ≥ 0.1, respectively. In what follows, by assuming that the center of mass of the rovibrating CO is fixed in the cavity, the full Hamiltonian is five-dimensional (three molecular coordinates, r, θ and φ, and two cavity modes). Below we shall work in a mixed basis to representĤ, namely a grid basis for the angular coordinates and a state-representation for the vibro-polaritonic modes as characterized by quantum numbers v r (for the CO-vibration) and (n z , n y ) for the cavity modes. Further, we emphasize the CO molecule's free rotation is described by two angular coordinates θ, φ, i.e., the CO molecule is allowed to take arbitrary orientations with respect to the cavity polarization plane spanned by vectors, ǫ z and ǫ y . Moreover, we do not take into account the molecule's center of mass motion as cavity boundary effects are assumed to play no role under the long-wavelength approximation and the neutral CO's center of mass motion does not directly couple to the cavity modes, which would require a net molecular charge [21].
The dynamics as generated by the rovibrational Pauli-Fierz Hamiltonian in Eq.(1), is governed by a timedependent Schrödinger equation
i ∂ ∂t Ψ(v r , n z , n y , θ, φ, t) =Ĥ Ψ(v r , n z , n y , θ, φ, t) , (9) with a five-dimensional rovibro-polaritonic wave packet, Ψ(v r , n z , n y , θ, φ, t). We will discuss two different initial states to solve Eq.(9), as specified below, given by an isolated rovibrational excitation of the molecule and a light-matter superposition state, respectively.
B. Molecular Model
We study a single carbon monoxide molecule with reduced mass, µ = m C m O /m CO = 12506 m e (electron mass m e ). The molecular ab initio PES, V (r), and molecular dipole function, d(r), were calculated as function of the CO-bond-length r (cf. Fig.1(b)) on the CCSD(T)/aug-cc-pV5Z level of theory via the software package Gaussian16 [28]. We find a ground state equilibrium bond length of r e = 2.145 a 0 and a rotational constant of B = 4πcµr 2 e = 1.91 cm −1 , which is in close agreement with the experimental value of B exp = 1.92 cm −1 [29].
Further, we numerically obtained the two lowest vibrational eigenvalues/eigenstates (cf. Fig.1(b)) of the vibrational Hamiltonian,Ĥ vib , in Eq.(2) based on a Colbert-Miller discrete variable representation [30] with N r = 1501 grid points. The fundamental anharmonic transition frequency, ω 10 = 2137 cm −1 , between the two lowest lying vibrational eigenstates of the CO stretching mode compares well to an experimental value of 2143 cm −1 [31]. The corresponding vibrational transition dipole moment takes d 10 = 0.066 ea 0 , which is in agreement with Ref. [32]. The molecular dipole function d(r) changes roughly linearly in the r-range shown in Fig.1(b) and takes an absolute equilibrium value of |d(r e )| = 0.12 Db, which is in close agreement with literature [33]. In the following, we set the cavity mode frequency ω c = ω 10 and the transition dipole moment d f i = d 10 .
C. Diabatic Vibro-Polaritonic Basis
The rotational constant, B, and the fundamental vibrational transition energy, ω 10 , set two different excitation energy scales, which allow for adiabatic separation of vibrational ("fast") and rotational ("slow") degrees of freedom [22]. Accordingly, we consider a restricted basis of zero-order "vibro-polaritonic" states, |v r , n z , n y , which constitute eigenstates toĤ vib +Ĥ C , and is given by
X 0 : |0 r , 0 z , 0 y X 1 : |1 r , 0 z , 0 y , |0 r , 1 z , 0 y , |0 r , 0 z , 1 y ,(10)
with one-dimensional ground state manifold, X 0 , and three-dimensional singly-excited state manifold, X 1 . The X 1 -manifold allows for the description of the lowest lying excited vibro-polaritonic states in the VSC regime. Higher-lying excited states are neglected here.
In the following, we denote the four basis states in Eq.(10) generically as |D k and expand a rovibro-polaritonic wave packet as
Ψ(v r , n z , n y , θ, φ, t) = k ϕ k (θ, φ, t) |D k ,(11)
with time-dependent, rotational wave packets, ϕ k (θ, φ, t). Further, the matrix representation of the rovibrational Pauli-Fierz Hamiltonian in the zero-order basis, which constitutes a matrix operator in (θ, φ)-space, is given by
H = T (θ, φ) + V (θ, φ) ,(12)
with (4 × 4)-blocked potential energy, V (θ, φ), and rotational kinetic energy operator matrices, T (θ, φ), respectively. The latter is given by
T (θ, φ) =ĵ 2 2µ 0 r | 1 r 2 |0 r 0 r | 1 r 2 |1 r 0 0 1 r | 1 r 2 |0 r 1 r | 1 r 2 |1 r 0 0 0 0 0 r | 1 r 2 |0 r 0 0 0 0 0 r | 1 r 2 |0 r (13)
where . . . indicates integration with respect to the r-coordinate. The zero-point energy shifted potential energy matrix is given by
V (θ, φ) = g 2 ω c f θφ d 2 00 g 2 ω c f θφ d 2 10 g d 00 cos θ g d 00 sin θ sin φ g 2 ω c f θφ d 2 10 ω 10 + g 2 ω c f θφ d 2 11 g d 10 cos θ g d 10 sin θ sin φ g d 00 cos θ g d 10 cos θ ω c + g 2 ω c f θφ d 2 00 0 g d 00 sin θ sin φ g d 10 sin θ sin φ 0 ω c + g 2 ω c f θφ d 2 00 ,(14)
with dipole self-energy matrix elements,
d 2 vrv ′ r = v r |d 2 (r)|v ′ r , and f θφ = cos 2 θ + sin 2 θ sin 2 φ .(15)
In V (θ, φ), the first diagonal entry corresponds to the zero-order ground state and the diagonal elements of the lower 3×3-block resemble states forming the X 1 -manifold in the order given by Eq.(10). (The same assignment can be made for the kinetic-energy matrix elements in Eq. (13).) The X 0 -and X 1 -manifolds are energetically well separated by ω 10 = ω c and subject to a weak anharmonic coupling (g 2 d 2 10 ) induced by the dipole self-energy and comparatively strong light-matter coupling (g d 00 ). Further, the DSE constitutes a potential in angular coordinates on the diagonal (g 2 d 2 vrvr f θφ ) and the singly-excited molecular state couples to the two singly-excited cavity mode states (g d 10 ).
There is only a weak kinetic coupling in the kineticenergy matrix, by the termĵ 2 2µ 0 r | 1 r 2 |1 r . Hence, the Pauli-Fierz Hamiltonian takes a diabatic-like representation in the zero-order basis Eq.(10). Following arguments given in Ref. [22], we interpret the eigenstates of V (θ, φ) as vibro-polaritonic states, which are given by the vibro-polaritonic ground state |G , the lower |L 1 , the middle |M 1 and the upper |U 1 vibro-polaritonic states, respectively. Note, the latter take the role of adiabatic states here. Further, the corresponding eigenvalues ε G (θ, φ), ε L1 (θ, φ), ε M1 (θ, φ) and ε U1 (θ, φ), are functions of the angular coordinates, θ and φ, and constitute vibropolaritonic potential energy surfaces (PES) for the rotational dynamics of the molecule.
III. RESULTS AND DISCUSSION
A. Vibro-Polaritonic Conical Intersections
We first discuss cavity-mode induced non-adiabatic effects in the manifold of singly-excited vibro-polaritonic states. Under vibrational strong coupling, we identify three-state vibro-polaritonic conical intersections (VPCIs) between vibro-polaritonic surfaces ε L1 (θ, φ), ε M1 (θ, φ) and ε U1 (θ, φ) under the conditions
ω 10 = ω c , θ = π 2 , φ = 0, π .(16)
The three-state VPCIs, as shown in Figs.2(a) and (b) for η = 0.05 and η = 0.1, respectively, are located in a two-dimensional angular coordinate branching space. Two distinct intersections are identified with intersection coordinates (θ, φ) = ( π 2 , 0) and ( π 2 , π), due to the periodicity of the azimuthal angle, φ.
The three-state VPCIs exhibit a characteristic doublecone topology formed by the L 1 -and U 1 -surfaces. They are triply degenerate at the intersection point due to an additional crossing with the middle vibro-polaritonic surface, ε M1 (θ, φ), which exhibits a local minimum here. In the VSC regime (η = 0.05), the splitting of the L 1 -and U 1 -surfaces is slightly asymmetric with respect to the M 1 -surface as can be seen in Figs.2(a) and (c). At the onset of the VUSC regime (η = 0.1), the L 1 /U 1 -splitting turns out to be strongly asymmetric (cf. Figs.2(b) and (d)), with a dominant inverse cone in ε U1 (θ, φ). The M 1surface forms more pronounced minima at the intersection points for stronger light-matter interaction and the L 1 -surface is subject to a mild "Mexican-hat"-type topology close to the intersection coordinate.
To reveal detailed characteristics of the VPCI close to the intersection coordinate, we expand V (θ, φ) in θ, φ around the intersection point at (θ, φ) = ( π 2 , 0) (cf. Appendix B for details) in analogy to vibronic problems. In Figs.2(c) and (d), we show cuts through the VPCIs along θ and φ, with exact surfaces (bold) besides linear (dotteddashed) and quadratic (dotted) approximations. We observe three characteristic features of the VPCI: (i) the degeneracy is lifted linearly along both angular coordinates in ε L1 (θ, φ) and ε U1 (θ, φ) in analogy to linear vibronic coupling theory [34], (ii) ε M1 (θ, φ) exhibits a harmonic character at the intersection point, which results from the potential character of the dipole self-energy and (iii) the mild local "Mexican-hat"-type topology of ε L1 (θ, φ) at η = 0.1 also stems from the DSE.
We close by noting, that the topological motive of a three-state VPCI is similar to accidental threestate conical intersections in molecular vibronic coupling theory. [35][36][37][38] B. Rovibro-Polaritonic Dynamics
We now turn to the dynamics of different zero-order rovibro-polaritonic wave packets, which mimic a lightmatter hybrid system initially excited by an external classical, z-polarized laser field. The additional action of a laser could be included in the Pauli-Fierz Hamiltonian by adding a term, −µ · E(t) (with classical laser field E(t) and where µ is a "dipole" function depending on molecular and cavity degrees of freedom [11]), but here we simply assume that such an excitation already took place and appropriate initial rovibrational(-polaritonic) states have been prepared. In order to represent different laser-polariton coupling scenarios, or, implicitly, molecule-cavity dipole functions, we consider two different initial states, namely
Ψ (r) 0 = |1 r , 0 z , 0 y Y 1 0 (θ, φ) and(17)Ψ (r,z) 0 = 1 √ 2 |1 r , 0 z , 0 y + |0 r , 1 z , 0 y Y 1 0 (θ, φ) ,(18)
with first excited rotational state Y 1 0 (θ, φ), where we adopt the notation, Y j mj (θ, φ), for spherical harmonics. Here, Ψ (r) 0 resembles a purely molecular rovibrational excitation and Ψ (r,z) 0 constitutes a superposition of a singlyexcited molecular and a singly-excited cavity mode state, respectively. The first case resembles a scenario, where an external laser field had coupled exclusively to the molecule, whereas the latter considers additionally a coupling of the laser-field to the z-polarized cavity mode. [39] Using these initital states, we discuss the timeevolution of the light-matter hybrid system in terms of zero-order (diabatic) populations
P (k) dia (t) = 2π 0 π 0 |ϕ k (θ, φ, t)| 2 sin θ dθ dφ ,(19)
with ϕ k given in Eq. (11), and their vibro-polaritonic (adiabatic) counterparts, P
ad (t), with l = G, L 1 , M 1 , U 1 . The latter arise from adiabatic wave packets, ϕ ad l (θ, φ, t), by using an expansion analogous to Eq.(11 but with adiabatic basis states |G , |L 1 , |M 1 and |U 1 . Further, we study the adiabatic rotational dynamics by means of reduced rotational densities
ρ ad l (θ, t) = 2π 0 |ϕ ad l (θ, φ, t)| 2 dφ ,(20)
which resemble the reduced dynamics of rotational wave packets, ϕ ad l (θ, φ, t), on the vibro-polaritonic surfaces as depicted in Fig.2. We note, that dynamics along the θcoordinate turns out to be particularly illustrative compared to the φ-coordinate.
We solve the TDSE (9) with the multiconfigurational time-dependent Hartree (MCTDH) method in its multiset formulation [40] as implemented in the Heidelberg MCTDH package [41]. Numerical details on the MCTDH method as well as on evaluation of above mentioned populations and reduced densities are provided in Appendix A.
Vibro-Polaritonic Population Dynamics
Before we discuss the time-evolution of populations, we examine zero-order state contributions to stationary vibro-polaritonic states at t = 0. For the rovibrationally excited initial state, Ψ (r) 0 , we find only |L 1 and |U 1 equally populated for both light-matter interaction scenarios with η = 0.05 and η = 0.1 (cf. Figs.3(a) and (b)). In particular, we find no population in the middle vibropolaritonic state |M 1 , i.e., no molecular vibrationally excited state is contributing here, which identifies |M 1 as purely photonic in character. Further, for the superposition state, Ψ (r,z) 0 , we observe contributions from all three vibro-polaritonic states, with equally populated |L 1 and |U 1 constituting the dominant contribution opposed to |M 1 (cf. Figs.3(c) and (d)). Accordingly, |L 1 and |U 1 are identified as "true" light-matter hybrid states containing both molecular and photonic contributions.
Turning to the dynamics, we consider a total propagation time of t f = 3000 fs for zero-order ("diabatic") populations, P dia (t), and their vibro-polaritonic ("adiabatic") counterparts, P ad (t). We find the dynamics up to t f to be mainly dominated by states spanning the X 1 -manifold as shown in the left and right columns of Fig.3, which results from the relatively large energetic separation of X 0and X 1 -manifolds.
For the zero-order ("diabatic") dynamics initiated by Ψ (r) 0 and depicted in Figs.3(a) and (b) (left column), we observe a fast initial population transfer to both singlyexcited cavity mode states followed by coherent exchange dynamics. The latter are dominated by the molecular and the z-polarized excited states and subject to quantum beats with a period of roughly 1000 fs. For an increased light-matter interaction strength (η = 0.1), the quantum beat period shortens to roughly 600 fs and the frequency of coherent zero-order population transfer is strongly enhanced. In contrast, vibro-polaritonic ("adiabatic") dynamics (cf. Figs.3(a) and (b), right column) are dominated by slow population transfer from |U 1 to |L 1 , accompanied by a gradual population of |M 1 . For η = 0.05 we observe a characteristic maximum in the |L 1 -population at around 700 fs, which is shifted to roughly 500 fs for η = 0.1. Later times are characterized by several decaying recurrences in |U 1 . a slight population increase in |M 1 . The first maximum in |L 1 appears at same times as observed above and for longer times, the population dynamics is less structured here. We note, for both Ψ (r) 0 and Ψ (r,z) 0 the zero-order ground state is weakly contributing at η = 0.1 and exhibits a strongly oscillatory dynamics, which is especially pronounced for Ψ (r,z) 0 . Finally, from this population-based perspective, we conclude that (i) only |L 1 and |U 1 are light-matter hybrid states opposed to the purely photonic |M 1 state and (ii) the inclusion of rotational degrees of freedom provides a cavity-induced transfer channel between vibropolaritonic excited states. Notably, the latter is absent in purely vibrational problems, where an additional bath is required to mediate population transfer between vibropolaritonic states.
Reduced Rotational Dynamics
We now turn to rotational dynamics of the CO molecule based on vibro-polaritonic ("adiabatic") reduced rotational densities, ρ ad l (θ, t) (cf. Eq. (20)), for different vibro-polaritonic surfaces. In order to distinguish reduced densities for different initial states, we introduce the notation ρ In the VSC regime with η = 0.05 (cf. Fig.4, left column), density on the U 1 -surface symmetrically approaches the VPCI and is transferred to the L 1 -surface with minor contributions on M 1 . In parallel, ρ (r) L1 (θ, t) tends away from the intersection point and develops a rich interference pattern as time evolves. This pattern can be rationalized in terms of rotational wave packet interference, where non-adiabatic transfer between U 1and L 1 -surfaces induces interference between wave packets initially located on different surfaces. At later times, several recurrences at the U 1 -surface are observed due to ρ (r) L1 (θ, t) reentering the intersection region. Notably, significant density on ε M1 is mainly found in the harmonic region close to the VPCI. For VUSC with η = 0.1, the density transfer between L 1 -and U 1 -surfaces is enhanced but qualitatively equivalent to the VSC regime.
Turning to the initial superposition state, Ψ (r,z) 0 , we find the reduced vibro-polaritonic rotational density to be initially distributed over all three vibro-polaritonic surfaces (cf. Fig.5) in line with the population analysis. Further at t = 0, densities ρ (r,z) L1 (θ, t) and ρ (r,z) U1 (θ, t) show a highly asymmetric distribution with respect to the VPCI, in contrast to the symmetric character of ρ (r,z) M1 (θ, t). As time-evolves, we again observe a non-adiabatic density transfer via the VPCI between U 1 -and L 1 -surfaces for both interaction regimes (cf. Fig.5, left and right col- umn). The transfer is enhanced for VUSC in line with the population analysis given above and characterized by a rich interference pattern. Further, the asymmetric character of the reduced densities on the U 1 -and L 1 -surfaces is clearly observable for the whole time-interval studied and the M 1 -surface is substantially stronger explored for both coupling regimes. We attribute the latter effect to a finite initial population of |M 1 , as the non-adiabatic population transfer to ε M1 is rather inefficient as seen before.
In summary, rotational densities allow to reveal the non-adiabatic character of vibro-polaritonic population transfer, which is dominated by (i) a funneling effect of the VPCI and (ii) interference of rotational wave packets initially located on different vibro-polaritonic surfaces.
C. Rovibro-Polaritonic Infrared Spectra
We now consider the spectroscopic characterization of the rovibro-polaritonic system with an emphasis on nonadiabatic signatures of the three-state VPCI. Infrared (IR) spectra, σ(ω), are calculated as
σ(ω) = A ∞ 0 C(t) e iω t dt ,(21)
with an autocorrelation function, C(t), and a constant here chosen asA = 1. The autocorrelation function C(t) is defined as the overlap between the initial states Ψ(0) = Ψ (r) 0 and Ψ (r,z) 0 as defined in Eqs. (17) and (18) and the propagated state, Ψ(t), under the influence of the coupled Pauli-Fierz Hamiltonian. (Note that this is an approximation/variant to the "usual" procedure in which an eigenstate of the Hamiltonian is multiplied by the dipole function and then propagated in time. [42]) We ob-tain two different spectra due to the two initial states, or implicitly, molecule-cavity dipole functions µ (see above). Further details on the evaluation of C(t) and σ(ω) can be found in Appendix A.
All spectra shown below have been obtained for a total propagation time, t f = 6000 fs. In order to reveal rotational effects and effects of a second cavity mode, we consider IR spectra obtained for a purely vibropolaritonic system in the single-cavity-mode limit as a reference, i.e., a CO molecule solely interacting with the z-polarized cavity-mode. Here, we take into account initial states Ψ(0) =ψ 1 z ). In order to interpret spectroscopic signatures, we also consider contributions of eigenstates, φ i , of the effective Hamiltonian H (cf. Eq.(12)), to initial states, as given by intensities I (r) ∝ | Ψ (r) 0 |φ i | 2 and I (r,z) ∝ | Ψ (r,z) 0 |φ i | 2 , respectively (details are provided in Appendix A).
(r) 0 = |1 r , 0 z and Ψ(0) =ψ (r,z) 0 = 1 √ 2 (|1 r , 0 z + |0 r ,
Infrared Spectra
We first consider spectra in the VSC regime with η = 0.05 and initial states Ψ as shown in Fig.6(a) and (b). For both initial states, we observe a series of transitions with a dominant L 1 -peak at 2076 cm −1 below the intersection point energy of 2137 cm −1 . In the region of the U 1 -surface, we find a progression of five peaks between 2207 cm −1 and 2309 cm −1 depending on the initial state with spacing 17 − 33 cm −1 , which decreases for increasing peak energy. The peak intensity increases with energy with a significantly less intense high-energy peak terminating the progression. Notably, the latter transitions do not reflect purely rovibrational states, but as discussed below correspond to rovibro-polaritonic hybrid states. Moreover, for Ψ (r,z) 0 a prominent peak is found at 2171 cm −1 , which resembles an excitation of the purely photonic intermediate polariton state and is absent for Ψ (r) 0 . Further, the single-cavity-mode limit reveals the wellknown L 1 -and U 1 -peaks forψ (r) 0 with Rabi-splitting Ω R = 214 cm −1 , respectively (grey curves). Forψ (r,z) 0 , the chosen linear combination exactly captures the U 1state such that only a single peak is observed here. Accordingly, the inclusion of rotational effects leads to a much richer excitation spectrum (colored curves) than accessible in the single-mode limit (grey curves). Explicitly, non-adiabatic effects show up as multi-peak progression in the spectral region of the upper vibro-polaritonic state, which is characterized by the inverse cone topology of the ε U1 -surface.
From an analysis of intensities, I (r) and I (r,z) , we are able to reveal the detailed character of observed excitations, which are hidden in spectra due to finite peak widths resulting from finite propagation times of rovibropolaritonic wave functions. Both, I (r) and I (r,z) exhibit similar dominant contributions to the light-matter hybrid L 1 -and U 1 -peaks, whereas only I (r,z) exhibits the purely photonic M 1 -peak as expected. Notably, I (r,z) shows additional contributions from several energetically close lying states with lower intensity to individual spectroscopically resolved peaks. We attribute a dominant rotational light-matter hybrid character to the latter as they are absent for the rovibrationally excited initial state, i.e., seem to be dominated by a photonic contribution.
Turning to IR spectra at the onset of the VUSC regime with η = 0.1, we observe a broadening of the spectrum and additional peaks emerge as shown in Fig.6(c) and (d). In the single-mode limit, we find a large Rabisplitting of Ω R = 433 cm −1 . Further, the progression in the U 1 -spectral region related to rovibro-polaritonic states is now more pronounced with seven peaks showing slightly increased spacing of 29−49 cm −1 , which again decreases for increasing peak energy. The middle-polariton peak at 2171 cm −1 for the light-matter excited initials state splits into three peaks at 2116, 2239 and 2258 cm −1 , respectively. As previously for VSC, we observe a number of (potentially energetically close) rovibro-polaritonic hybrid states with lower intensity, which contribute to peaks in the spectrum obtained from Ψ (r,z) 0 as indicated by I (r,z) and I (r) .
In conclusion, IR spectra reveal the formation of lightmatter hybrid states with contributions from both molecular rotations and vibrations as well as cavity mode excitations, i.e., rovibro-polaritonic states, with nonadiabatic signatures prominently manifesting as rovibropolaritonic progression in the spectral region of the U 1inverse cone.
Cavity Loss Effects
Finally, we consider the impact of experimentally ubiquitous spontaneous emission effects from cavity modes on rovibro-polaritonic infrared spectra. Spontaneous emission manifests in finite excited cavity mode lifetimes (Finite lifetimes of molecular rovibrational states are neglected in what follows). These are considered here by a phenomenological approach recently employed in electronic strong coupling studies [43][44][45]. There, the cavity mode Hamiltonian,Ĥ C , is replaced by a non-Hermitian operatorĤ
(κ) C = λ=z,y ω c − i κ 2 â † λâ λ .(22)
The imaginary contribution accounts for an effective cavity decay rate, κ, which we here set to κ = 43 cm −1 to model an infrared cavity with quality factor Q = ωc κ = 50, being slightly lower as in Ref. [46]. Note that the zeropoint energy contribution is neglected in Eq.22 to avoid artificial ground state decay [43].
In Fig.7, we compare infrared spectra subject to spontaneous emission (dissipation) with non-dissipative re-FIG. 6. Vibro-polaritonic infrared spectra for different initial states and light-matter interaction parameters η with single-mode limit initial states,ψ sults as presented in Fig.6. Most prominently, cavityloss effects manifest themselves in a significant intensity reduction and peak broadening, especially for the M 1 -peak themselves . The latter again supports the purely photonic nature of the |M 1 -state. For the coupling scenario η = 0.05, spectra resulting from Ψ 0 . Further, the rovibro-polaritonic progression induced by the VPCI is only weakly observable and resembles several shoulders in the U 1 -spectra region. For increased light-matter interaction strength (cf. Figs.7(d)-(f)), the progression is clearly visible for both initial state although it suffers from the peak broadening effects.
IV. SUMMARY AND OUTLOOK
We studied a model system composed of a single rovibrating diatomic molecule (carbon monoxide), which interacts with two energetically degenerate and orthogonally polarized optical modes of a Fabry-Pérot-type cavity. The cavity modes were tuned resonant to the fundamental vibrational transition of the CO stretching FIG. 7. Vibro-polaritonic infrared spectra subject to dissipation (colored) with cavity decay rate, κ, for different initial states and light-matter interaction regimes with non-dissipative reference (grey) and VPCI energy (vertical line). Top row: Infraredspectra for the vibrational strong coupling (VSC) regime with η = 0.05 for (a) molecular rovibrationally excited initial state mode and we discussed the vibrational strong coupling regime up to the onset of the vibrational ultrastrong coupling regime. Based on an energetically motivated adiabatic separation of rotational and vibro-polaritonic degrees of freedom, we identified a three dimensional singleexcitation manifold of vibro-polaritonic surfaces, which is subject to two distinct three-state vibro-polaritonic conical intersections in a two-dimensional angular coordinate branching space. The lower and the upper vibropolaritonic states are of mixed light-matter hybrid character and the middle polaritonic state is purely photonic in nature. In the VSC regime, the lower and upper vibro-polaritonic surfaces exhibit a symmetric doublecone topology with respect to a harmonic middle polaritonic surface at the triply degenerate intersection point. For increasing light-matter interaction, the symmetric splitting of upper and lower vibro-polaritonic surfaces becomes strongly asymmetric, with the inverse cone of the upper vibro-polaritonic surface dominating the VPCI topology and a mild "Mexican-hat"-type topology in the lower vibro-polaritonic surface.
From a dynamical perspective, we studied the timeevolution of vibro-polaritonic populations and reduced vibro-polaritonic rotational densities. The population dynamics reveal, that the presence of rotational degrees of freedom induces an efficient transfer channel between vibro-polaritonic states in terms of the VPCI. Moreover, the rotational density shows a rich interference pattern throughout the dynamics, due to interfering rotational wave packets initially located on different vibropolaritonic surfaces.
Further, we studied infrared spectra of the rovibrating light-matter hybrid system with respect to different initial conditions, which mimicked classical laser-field excitations of a (i) molecular rovibrational excited state and (ii) a light-matter superposition state. We observe bright transitions to all three vibro-polaritonic states, only when the laser field is allowed to initially excite a light-matter superposition state. The non-trivial topology of the VPCI manifest as a pronounced progression in the spectral region of the upper vibro-polaritonic surface, which we find to correspond to rovibro-polaritonic states containing contributions of molecular rotational, vibrational and cavity degrees of freedom. Further, we considered finite lifetimes of cavity mode excitations due to spontaneous emission effects, which manifest in a significant reduction of the purely photonic middle polariton peak and broadening of the rovibro-polaritonic progression.
Possible extensions of the present study refer to in-creasing the reduced diabatic "vibro-polaritonic" basis to go beyond the (effective) single-molecule picture and aim at the study of collective effects. In particular, it would be instructive to investigate how the orientation dependent light-matter interaction effects the nature of "dark states" in rovibro-polaritonic problems. Further, we did not consider the nature of the vibro-polaritonic ground state here, which renders central for purely rotational dynamics of molecules in infrared Fabry-Pérot cavities. Moreover, we note that for electronic strong coupling (ESC) problems, it had already been suggested in Refs. [47,48] that (single-mode) cavity induced CIs could be formed, how one could detect them and what is the influence of molecular rotation on them [48]. This work is complemented by Ref. [49], where a similar problem has been studied with respect to Berry Phase effects in a polaritonic CI setting. Here, differences to "classical" light-induced conical intersections [50], which emerge from a linearly polarized, classical laser field with a single polarization direction, could be expected in the fully quantized cQED setting of ESC scenarios featuring (at least) two degenerate, orthogonally polarized cavity modes. Finally, the study of rovibro-polaritonic effects on cavity-altered chemical reactions and on polaritonic infrared spectra might be rewarding for a deeper understanding of molecular cQED.
B. 3-State-VPCI Details
We expand trigonometric functions in V (θ, φ) up to first order in θ and φ around the intersection point at (θ, φ) = ( π 2 , 0), as
cos θ ≈ θ − π 2 , sin θ sin φ ≈ φ ,(B1)
and
f (θ, φ) ≈ φ 2 + θ − π 2 2 = f (1) (θ, φ) . (B2)
The resulting approximate potential energy matrix is given by
V (1) (θ, φ) = G 00 f (1) (θ, φ) G 10 f (1) (θ, φ) −g 00 θ − π 2 g 00 φ G 10 f (1) (θ, φ) ω 10 + G 11 f (1) (θ, φ) −g 10 θ − π 2 g 10 φ −g 00 θ − π 2 −g 10 θ − π 2 ω c + G 00 f (1) (θ, φ) 0 g 00 φ g 10 φ 0 ω c + G 00 f (1) (θ, φ) .(B3)
with ω 10 = ω c , G ij = g 2 ωc d 2 ij as well as g ij = g d ij where i, j = 0, 1. The linear approximation, holds for small deviations from the intersection coordinate where f (1) (θ, φ) ≈ 0. For larger values of θ and φ, the quadratic approximation then takes into account the DSE-related term, f (1) (θ, φ). The corresponding eigenvalues of V (1) (θ, φ) correspond to the different approximations of vibro-polaritonic surfaces with cuts shown in Fig.2, bottom-row.
[ 27 ]
27
FIG. 1 .
1(a) Schematic sketch of diatomic molecule with vibrational coordinate, r, and angular coordinates θ, φ in optical two-mode cavity with polarization vectors ǫ z , ǫ y , wavevector, k, and molecular space-fixed frame with axes, x, y, z. A zpolarized cavity mode is indicated in yellow. (b) Anharmonic potential, V (r), and dipole function, d(r), of CO stretching mode (interpolated CCSD(T)/aug-cc-pV5Z results) with vibrational ground state, |0r , and first excited state, |1r . d(r) is given in units of Debye (Db).
FIG. 2 .
2Top: Three-state vibro-polaritonic conical intersections (VPCIs) between lower vibro-polaritonic, εL 1 (θ, φ), middle vibro-polaritonic, εM 1 (θ, φ), and upper vibro-polaritonic surfaces, εU 1 (θ, φ), for (a) VSC regime with η = 0.05 and (b) onset of VUSC regime with η = 0.1. Bottom: One dimensional cuts through vibro-polaritonic surfaces (bold), linear (dotted-dashed) and quadratic approximations (dotted) with ε l (θ, φ = 0) and ε l (θ = π 2 , φ) for (c) η = 0.05 and (d) η = 0.1 with l = L1, M1, U1.
zero-order population transfer between the molecular and the z-polarized excited mode states for both coupling scenarios (cf. Figs.3(c) and (d), left column). From the vibro-polaritonic perspective, as depicted in the right column of Figs.3(c) and (d), |U 1 is initially again depopulated in favor of |L 1 , accompanied by FIG. 3. Population dynamics for different initial states under VSC. Zero-order (diabatic), P dia (t), (left) and vibropolaritonic (adiabatic), P ad (t), (right) population dynamics for rovibrational singly-excited initial state, Ψ
for (a) η = 0.05 and (b) η = 0.1. Zero-order (left column) and vibropolaritonic (right column) population dynamics for singlyexcited superposition state, Ψ
l
(θ, t) is shown for excited-state surfaces ε U1 (top row), ε M1 (middle row) and ε L1 (bottom row), respectively, with η = 0.05 (left column) and η = 0.1 (right column). The horizontal θ-axis runs from π to 0 (left to right) and the vertical time-axis runs from 0 fs to 3000 fs (top to bottom). The position of the intersection point at θ = π 2 is marked by a vertical blue line. At t = 0, both L 1 -and U 1 -surfaces are nearly equivalently populated (in line with Figs.3(a) and (b)), and ρ (r) L1 (θ, t) and ρ (r) U1 (θ, t) show two symmetric maxima along θ with respect to the intersection point.
FIG. 4 .
4Time-evolution of adiabatic reduced rotational densities, ρ (r) l (θ, t), for rovibrational singly-excited initial state, Ψ (r) 0 , with vertical time-axis and horizontal θ-axis on upper, εU 1 (θ, φ) (top row), middle, εM 1 (θ, φ) (middle row) and lower, εL 1 (θ, φ) (bottom row), vibro-polaritonic potential energy surfaces for η = 0.05 (left column) and η = 0.1 (right column). Intersection at θ = π 2 indicated by blue vertical line. Total density, ρ (r) (θ, t) = l ρ (r) l (θ, t), with l = G, L1, M1, U1 normalized for fixed time t.
FIG. 5 .
5Time-evolution of adiabatic reduced rotational densities, ρ (r,z) l (θ, t), for singly-excited superposition state, Ψ (r,z) 0 , with vertical time-axis and horizontal θ-axis on upper, εU 1 (θ, φ) (top row), middle, εM 1 (θ, φ) (middle row) and lower, εL 1 (θ, φ) (bottom row), vibro-polaritonic potential energy surfaces for η = 0.05 (left column) and η = 0.1 (right column). Intersection at θ = π 2 indicated by blue vertical line. Total density, ρ (r,z) (θ, t) = l ρ (r,z) l (θ, t), with l = G, L1, M1, U1 normalized for fixed time t.
.
|1r, 0z + |0r, 1z ), (grey curves), VPCI energy (grey vertical lines) and intensities, I (r) ∝ | Ψ(r) 0 |φi | 2 , and, I (r,z) ∝ | Ψ (r,z) 0 |φi | 2 . Top row: Infrared-spectra for the vibrational strong coupling (VSC) regime with η = 0.05 for (a) molecular rovibrationally excited initial state, Ψ Bottom row: (c) and (d) analogous to (a) and (b) in top row for onset of vibrational ultrastrong strong coupling (VUSC) regime at η = 0.1.
slightly in their intensity as depicted in Figs.7(a)-(c), with slightly more intense L 1 -/U 1 -transitions for Ψ (r)
c) comparison of both dissipative spectra. Bottom row: (d)-(f) analogous to (a)-(c) in top row for onset of vibrational ultrastrong strong coupling (VUSC) regime at η = 0.1.
ACKNOWLEDGEMENTSWe acknowledge fruitful discussions with Shreya Sinha, Foudhil Bouakline, David Picconi and Tillmann Klamroth (all from Potsdam).The authors thank the Deutsche Forschungsgemeinschaft (DFG) for financial support through project Sa 547/18. E.W. Fischer also acknowledges support by the International Max Planck Research School for Elementary Processes in Physical Chemistry.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.CONFLICT OF INTERESTThe authors have no conflicts to disclose.APPENDIXA. Numerical DetailsWe employ the MCTDH approach[40,[51][52][53][54]as implemented in the Heidelberg MCTDH package, version 8.6.0[41]. The state-specific rotational wave packets ϕ k (θ, φ, t) in Eq.(11)are here expanded aswith time-dependent coefficients, A ki (t), and stateand time-dependent rotational single-particle functions (SPFs), ϕ (k)i (θ, φ, t), respectively. For all calculations, we chose n = 3 SPFs for each diabatic state and represented the states-specific rotational wave packets in a two-dimensional Legendre discrete variable representation (PLeg) with N θ = 51 and N φ = 37 grid points.Vibro-polaritonic (adiabatic) populations P (l) ad (t) are obtained from Eq.(19)by taking into account the adiabatic representation of the zero-order rotational wave packets, ϕ k (θ, φ, t), given aswhere u lk (θ, φ) are elements of a unitary matrix U (θ, φ), which diagonalizes the potential in Eq.(14). The vibro-polaritonic (adiabatic) rotational wave packets, ϕ ad l (θ, φ, t), evolve on the surfaces as depicted inFig.2. Further, infrared spectra are calculated as (setting a possible prefactor to 1)with autocorrelation function C(t) and window functionFor the Hermitian, non-dissipative case, we propagate a given initial wave packet Ψ(0) under the influence of the Pauli-Fierz Hamiltonian in Eq.(1), to a time t f = 3000 fs and the spectrum is obtained with T = 2 t f = 6000 fs since the autocorrelation function is evaluated as[53]In the non-Hermitian scenario,ĤC as defined in Eq.(22) is used instead for the cavity modes, and the autocorrelation function is computed aswhere we propagate up to T = t f = 6000 fs. Finally, for analysis, intensities (stick spectra) are obtained aswith eigenvalues ε i and eigenstates φ i of H calculated by means of a Lanczos algorithm as implemented in the Heidelberg MCTDH package. All converged results have been obtained based on a two-dimensional Legendre discrete variable representation (PLeg) with N θ = 51 and N φ = 37 grid points as above, with 9000 iteration steps.(r) 10 |1r, 0z, 0y 0r, 0z, 0y| cos θ, with, µ (r) |0r, 0z, 0y Y 0 0 = Ψ (r) 0 , and, µ (r,z) = d (r,z) 10 (|1r, 0z, 0y 0r, 0z, 0y| + |0r, 1z, 0y 0r, 0z, 0y|) cos θ, such that, µ (r,z) |0r, 0z, 0y Y 0 0 = Ψ (r,z) 0. For both, we set, d (r) 10 = d (r,z) 10
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I. INTRODUCTION
The quantum Rabi model (QRM) provides the simplest full quantum description of light-matter interaction. It is also one of the most well studied models in quantum optics, and a cornerstone of cavity quantum electrodynamics (cavity QED). The quantum Rabi Hamiltonian describes the dipolar interaction of a two-level system (TLS) or qubit with a single quantized mode of an electromagnetic resonator. It was first introduced by Jaynes and Cummings [1], in order to compare the semiclassical model, previously introduced by Rabi [2], with a full quantum model. To solve the model, the rotating wave approximation (RWA) is commonly introduced. In this approximation, known as the Jaynes-Cummings model (JCM), the counter-rotating terms are neglected. This is a valid approximation for the near resonance case and when the light-matter coupling rate is much smaller than the resonance frequency of the TLS, or equivalently of the quantized cavity mode. These conditions are fulfilled in several experimental settings [3,4]. The RWA may also fail for describing the optical pumping, when the excitation field is sufficiently strong or for a nonlinear short pulse excitations with several carrier cycles [5].
Despite its simplicity, the QRM is able to describe a wide variety of light-matter quantum systems and gives * [email protected] † [email protected] rise to a great diversity of behaviors and effects, depending on the relative magnitude of the light-matter coupling strength. However, the description and the analysis of experiments on systems which can be potentially modeled by the quantum Rabi Hamiltonian require additional theoretical tools. For example, it is necessary to take into account the interaction of both the TLS and cavity photons with the external environment (thermal reservoirs) [6]. Of course, in the absence of such interactions, basic features such as the excitation of the system components, dissipation and decoherence effects, and the detection of photons outside the cavity cannot be described properly. Even the definition of the different light-matter interaction regimes requires one to include the interaction of the system components with their reservoirs.
In weak coupling regime of cavity QED, dissipation is stronger than the intrinsic coherent coupling between matter and the light. Such a regime has lead to various applications, e.g., exploiting the well known Purcell effect [7] has allowed for breakthroughs in quantum technologies such as low-threshold solid-state lasers [8] and single-photon emitters [9,10]. These effects allow for the engineering of the spontaneous emission rate of an emitter, by tailoring its photonic environment. Indeed, resonant electromagnetic resonators with a narrow density of states can greatly enhance the efficiency of photonic devices. Going beyond weak coupling, the strong-coupling regime is characterized by lower losses in the system, allowing for the observation of effects such as vacuum Rabi oscillations [11], manifested by the coherent oscillatory exchange of energy between light and matter. Such effects are already being exploited in second generation quantum technologies [12,13]. In this strong-coupling regime, however, the light-matter coupling rate, remains much lower than the bare resonance frequencies, so that both the weak and the strong coupling regime can be adequately described by the JCM.
If the quantum light-matter interaction strength reaches a non-negligible fraction of the transition frequency of the components, the system enters the so-called ultrastrong coupling (USC) regime. In this regime, the interaction can significantly change the system properties. For example, the ground state of the system contains non-negligible virtual photons and virtual matter excitations. In the past decade, USC effects between light and matter has transitioned from a theoretical idea to an experimental reality. Nowadays, this regime has been achieved in a great variety of systems and settings [3,4]. The experimental progress in USC physics has motivated many theoretical studies showing interesting new effects enabled or boosted by this regime . Several studies explore higher-order processes in the USC regime, where the number of excitations is not conserved [43][44][45][46][47][48], such as multiphoton Rabi oscillations [49] and a single photon exciting multiple atoms [50,51].
When the light-matter interaction strength increases even further, a regime where the coupling strength exceeds the resonant frequencies of the material and/or of the quantized light modes can be achieved [52]-the deep strong coupling (DSC) regime. One of the most interesting effects predicted in this regime is the effective decoupling between light and matter [53]. A striking consequence of such a counterintuitive phenomenon is that the Purcell effect is reversed and the spontaneous emission rate, usually thought to increase with the lightmatter coupling strength, tends to vanish for sufficiently large couplings. Such a result has been predicted considering bosonic matter excitations interacting with a multimode optical resonator (generalized Hopfield model), and using the Coulomb gauge. Recently, a first confirmation of this prediction has been obtained using threedimensional crystals of plasmonic nanoparticles [54].
In subsequent work [55], this effect has also been studied considering a single superconducting qubit interacting with a multi-mode electromagnetic resonator. In circuit QED, for a qubit interacting with a superconducting waveguide, a microscopic treatment of the lightmatter coupling gives rise to a diamagnetic term, analogous to the A 2 term of the minimal coupling Hamiltonian. Using this spin-boson Hamiltonian, it has been shown that the spontaneous emission rate of the twolevel system decreases with the intensity of the A 2 term, without the need to be in the DSC regimes. The results in Refs. [53,55] suggest that the diamagnetic term plays a key role in determining the light-matter decoupling effect. However, some questions remains open. Indeed, the presence of the diamagnetic term is gauge relative (e.g., it disappears in the dipole gauge); moreover, the validity of the Coulomb gauge when describing truncated atomic systems has been questioned [56][57][58].
Recently, some gauge issues have been solved. In particular, it has been shown how to obtain the correct quantum Rabi and Dicke Hamiltonians in the Coulomb gauge [59][60][61][62]. It has also been shown how to derive a gauge-invariant master equation and obtain gaugeinvariant emission spectra [63]. Throughout this article, we will use these recent developments. Specifically, we provide a unified picture of light emission under incoherent pumping of the QRM, from the weak to the deep strong light-matter interaction. When the light-matter coupling strength spans from the very weak to the deep strong coupling regimes, the spectrum of the QRM, while initially quasi-harmonic, becomes strongly anharmonic at higher couplings. Then, after reaching the deep strong limit, its behavior tends back towards harmonicity.
While in the weak coupling regime, neglecting the counter-rotating terms and using the standard quantum optics master equation typically provides accurate results, in the USC regime this master equation fails to describe correctly the emission spectra. This problem can be partly solved by introducing the master equation in the dressed basis [64], an approach which includes the interaction between the system components in the derivation of the dissipators. However, this powerful approach can also fail in describing the emission of the QRM in both the weak and deep strong coupling regimes. To solve these problems, we study the incoherent emission of the system at any coupling strength, using a dressed-state generalized master equation (GME) working for systems displaying both harmonic, quasi-harmonic, and anharmonic spectra [65]. Moreover, we take particular care to derive a gauge-invariant GME, to ensure the gauge invariance of the obtained emission rates and spectra [63].
In Sec. II, we first provide a description of the QRM in both the Coulomb and multipolar gauges, and then present the GME approach which we will use for all the calculations. A detailed description of the derivation is provided in the Appendices (see also Ref. [63]). The numerical calculations and their analysis are presented in Sec. III. There, we show numerically-calculated cavity and qubit photon flux emission rates and spectra as a function of the normalized light-matter coupling strength, obtained for different effective temperatures and cavity-qubit detunings. In order to highlight the differences between our results based on a gauge-consistent GME, and some other standard methods, in Sec. IV, we present (i) results obtained using the JC model and the standard quantum optics master equation, and (ii) results obtained using a dressed master equation with post-trace rotating wave approximation [64]. Finally, in Sec. V, we give our conclusions.
In addition, the main theoretical framework used to develop all the results is fully explained in the Appendices. In Appendix A we model the cavity-and qubitbath interaction by using the gauge principle, while in Appendix B we provide a demonstration of the gauge in-variance of the GME.
II. DISSIPATIVE QUANTUM RABI MODEL
In this section, we describe the open QRM, thus including the interaction of the light and matter components with their respective reservoirs. We consider models in both the Coulomb and the multipolar gauge (within the dipole approximation), to show equivalence and verify gauge-invariant observables.
A. Quantum Rabi model in the Coulomb gauge
The quantum Rabi Hamiltonian in the Coulomb gauge can be written as ( = 1) [59]
H R = ω câ †â + ω q 2 σ z cos 2η(â +â † ) +σ y sin 2η(â +â † ) .(1)
whereâ (â † ) is the photon annihilation (creation) operator andσ x,y,z are Pauli matrices. The parameters ω c and ω q represent the cavity and the qubit resonance frequencies, respectively, while η = g/ω c is the normalized light matter coupling strength.
The HamiltonianĤ R can be obtained starting from the light-matter Hamiltonian in the absence of inter-actionĤ 0 =Ĥ q +Ĥ ph , whereĤ q = ω qσz /2 and H ph = ω câ †â , by applying a suitable unitary transformation (generalized minimal coupling transformation) tô H q only [59,61]. Specifically,
H R =ÛĤ qÛ † +Ĥ ph ,(2)whereÛ = exp iη(â +â † )σ x .(3)
We observe that in the Coulomb gauge, the canonical field momentum is not modified by the interaction with the matter component, i.e., Π = −ε 0Ê (ε 0 vacuum permittivity), such that, in this framework, the electric field operator can be written aŝ
E = iω c A 0 (â −â † ) ,(4)
where A 0 is the zero-point-fluctuation amplitude of the field coordinate. For simplicity we assume a simple one dimensional model, but the formalism can be easily generalized to three dimensions. Regardless of the chosen gauge, when the normalized coupling strength becomes significantly large, all the eigenstates become dressed by virtual excitations (owing to the presence of the counter-rotating terms) [66], and complications arise in the theoretical description [3]. Consequently, dissipation effects, input-output relationships, and photodetection rates [67,68] cannot be introduced adequately by using the standard tools of quantum optics in the usual fashion. For example, considering a given quantum state of the systemρ(t) (i.e., the density operator of the light-matter system at time t), the photon rate measured by a broadband point-like detector in the resonator is different from â †â t ≡ Tr[â †âρ (t)]. Instead, it is proportional to the expectation value W c (t) = Ê −Ê + t ≡ Tr[Ê −Ê +ρ (t)]. Here,Ê + [Ê − = (Ê + ) † ] is proportional to the positive (negative)-frequency electric field operator, and the expectation value is taken considering quantum states calculated in the Coulomb gauge (dressed-state representation).
Specifically, the positive-frequency electric field operator is obtained from
E + = i k>j j|(â −â † )|k |j k| ,(5)
where |j are the energy eigenstates of the Hamiltonian in Eq. (1) with eigenvalues ω j ordered so that k > j for ω k > ω j . Using the following relationship [69]
ω c j|(â −â † )|k = ω kj j|(â +â † )|k ,(6)
where (ω kj = ω k − ω j ), it is also possible to rewrite Eq. (5) asÊ
+ = i k>j ω kj ω c j|(â +â † )|k |j k| .(7)
Note that Eq. (6) remains valid even in the presence of very strong light-matter interactions and/or optical nonlinearities. By using the simple input-output theory [70], results analogous to W c (t) can be obtained for the rate W out c (t) of emitted photons detected by a detector placed outside the cavity [71,72]. However, the output field operators can display a different dependence on ω kj , arising from the density of states of the output modes and from the frequency dependence of the coupling coefficient, which (for example) depends on the mirror reflectivity in a standard microcavity. More generally, the output field operator, in the Coulomb gauge, can be written aŝ
E + out = i k>j α(ω kj ) j|(â +â † )|k |j k| ,(8)
where the function α(ω) encodes the specific, modeldependent dependence on the frequency. A more rigorous input-output theory can be formulated in terms of quantized quasinormal modes [73][74][75]. Analogously, it is possible to define the field operators describing the qubit emission W q (t) = Ŝ −Ŝ + t , wherê
S + = i k>j α q (ω kj ) j|σ x |k |j k| .(9)
In the following, we will assume both α c (ω kj ) = ω kj /ω c (corresponding toÊ + out =Ê + ) and α q (ω kj ) = ω kj /ω q , to be linearly dependent on the transition frequencies.
A different choice will give rise to similar spectra with different relative heights of the spectral lines. Notice that photodetection is an energy absorption process, thus it is reasonable to assume photon detection rates which tend to zero with frequencies ω → 0. Naturally, any realistic analysis covering a very large frequency range should also include dispersion in the material model. Including the latter, however, would make the study system dependent going beyond the aim of the present general framework.
B. Quantum Rabi model in the dipole gauge
The quantum Rabi Hamiltonian can also be expressed in the dipole gauge, which yields the form
H R = ω câ †â + ω q 2σ z − iηω c â −â † σ x + ω c η 2 .(10)
To be clear, by dipole gauge, we mean the multipolar gauge after the dipole approximation [76,77]. Light-matter Hamiltonians in the multipolar or dipole gauge can be obtained from the Coulomb gauge (minimal coupling replacement), after a unitary Power-Zienau-Woolley (PZW) transformation [78].
The last term in Eq. (10) is often disregarded, since it has no dynamical consequences. In the following, when needed, as for the Hamiltonian in the dipole gaugeĤ R , we will use primed symbols to indicate gauge-relative quantities in the dipole gauge. By considering a fixed polarization in the single-mode approximation, the field coordinate corresponding to the vector potential can be expressed as = A 0 (â +â † ). In the dipole gauge, the field conjugate momentum is modified by the interaction with the matter system, and it is proportional to the electric displacement (induction) field
Π = −D = −iε 0 ω c A 0 (â −â † ) .(11)
Thus, the electric field operator cannot be expanded in terms of photon operators only. Indeed, due to the fact thatD = ε 0Ê +P (for a dipole in free space), whereP is the electric polarization, the electric field operator in the dipole gauge has to be expanded aŝ
E = iω c A 0 (â −â † ) ,(12)
where (see Ref. [62])
a =RâR † =â + iησ x ,(13)
andR
=Û † = exp −iη(â +â † )σ x .(14)
This unitary operator essentially implements the PZW transformation for a truncated TLS model and in the dipole approximation [61]. Of course, the different representations provide the same energy levels for the lightmatter system. They also provide identical expectation values if operators and quantum states are both properly transformed [62]. We observe that the operatorsâ and a † satisfy the same commutation relations of the bosonic operatorsâ andâ † . Moreover, sinceâ +â † =â +â † , the vector potential can also be expressed as = A 0 (â +â † ). We observe that, in the dipole gauge,â andâ † (instead ofâ andâ † ) describe the creation and annihilation of the field quanta, as it is clear from Eq. (12).
The quantum Rabi Hamiltonians in Eq. (1) and Eq. (10) are related by a gauge transformation, implemented by the unitary operator in Eq. (14):
H R =RĤ RR † .(15)
The photon rate measured by a broadband point-like detector in the resonator can be expressed also in the dipole gauge as W c (t) = Ê −Ê + t , where the expectation values are calculated using the eigenstates |j of Eq. (10). Therefore,Ê + is now proportional to the positive-frequency electric field operator in the dipole gauge,Ê
+ = i k>j j |(â −â † )|k |j k | .(16)
From Eq. (13), clearly we see that the photon operators are not gauge invariant. Thus, in order to obtain correct results in the dipole gauge [62], it is essential to properly take into account how these operators change under thê U -transformation [see Eq. (13)].
Choosing the dipole gauge, without transforming the photonic operators accordingly, can lead to an erroneous evaluation of the emitted photon rate, as shown in Sec. III. Specifically, an incorrect photon rate is obtained by usingâ (â † ) instead ofâ (â † ) in the dipole gauge. In this case, the photon rate becomes
W c = Ê − wÊ + w ,(17)whereÊ + w = i k>j j |(â −â † )|k |j k | .(18)
Also note, W c = W c = W c (see Sec. III). The useful relationship shown by Eq. (6) can be appropriately transformed in the dipole gauge as
ω c j |(â −â † )|k = ω kj j |(â +â † )|k ,(19)
such that,
E + = i k>j ω kj ω c j |(â +â † )|k |j k | ,(20)
and we also have:
j |(â +â † )|k = j|(â +â † )|k .(21)
C. Theoretical description of losses and quantum noise
In order to calculate emission rates and emission spectra of the QRM, from the weak to the DSC regime, we describe the dissipative system dynamics considering a GME in the dressed basis [65],
ρ = −i Ĥ R ,ρ + L gρ ,(22)
where the dissipator L g contains two contributions L g = L c g + L q g , arising from the cavity-bath (c) and the qubitbath (q) interaction [see Appendix B and in particular Eq. (B2)]. It remains valid at any light-matter coupling strength. By using this approach, we also include the interaction of the matter and light components of the system with individual reservoirs that can be at different
temperatures [see Eq. (B3)].
Starting from a gauge-invariant approach (see Appendix B), the obtained photonic and atomic decay rates associated to given system transitions can be written as
Γ c kj = κ ω kj ω c | j|â +â † |k | 2 , Γ q kj = γ ω kj ω q | j|σ x |k | 2 ,(23)
where κ and γ are the bare (in the absence of cavityatom coupling) loss rates for the photon and the atom, and Ohmic reservoirs have been considered (i.e., the rates scale linearly with frequency). Since the matrix elements in Eq. (23) are gauge-invariant, then Γ c(q) kj = Γ c(q) k j . As done before, we label the quantum states and operators in the dipole gauge with the prime superscript.
These gauge invariant decay rates have been derived starting from cavity and qubit reservoir interactions obtained by invoking the gauge principle (see Appendix A). This also gives rise to a gauge-invariant GME (see Appendix B), which, in turns, provides gauge-invariant emission rates and spectra (see Sec. II D).
D. Formulas for cavity and qubit emission spectra
In addition to cavity and qubit emission rates, we also present emission spectra, which allows one to obtain information on the frequency of the emitted photons and, indirectly, on the system dynamics under incoherent excitation (for example). The steady-state cavity and qubit emission spectra (obtained from the steady-state density operatorρ ss by applying the quantum regression theorem [70,79]) can be defined as
S c (ω) = Re ∞ 0 dτ e −iωτ Ê − (t + τ )Ê + (t) ss S q (ω) = Re ∞ 0 dτ e −iωτ Ŝ − (t + τ )Ŝ + (t) ss . (24)
Note that, the above definition is valid only when considering steady-state (ss). In the USC regime, true steady-state is achieved only under incoherent pumping. Under coherent drive, the counter-rotating terms often determine the presence of oscillations in the signals, even for times much longer than coherence times. In this case the spectra have to be defined introducing an additional time integration [63].
Instead of Eq. (24), we will adopt a slightly different formulas for the spectra. Actually, the frequency of photons detected after a spectrum analyzer tuned at a frequency ω is just ω and not ω kj , even if they originate from a specific downward transition |k → |j (which, however, is broadened by the interaction of the system with the reservoirs). Hence, it is somewhat more accurate to replace ω kj with ω in the emission spectra formulas. In this way, in the low-frequency limit, the spectra goes to zero as expected. However, this replacement can affect the high-frequency behavior of the spectra, especially when some cut-off mechanism is not introduced.
By making use of Eqs. (6,19), and by applying the replacement ω kj → ω, we obtain
S c (ω) = ω 2 ω 2 c Re ∞ 0 dτ e −iωτ Ê − (t + τ )Ê + (t) ss S q (ω) = ω 2 ω 2 q Re ∞ 0 dτ e −iωτ Ŝ − (t + τ )Ŝ + (t) ss , (25) whereÊ − = −i k>j k|(â † +â)|j |k j| S − = −i k>j k|σ x |j |k j| .(26)
The results obtained using Eq. (24) and Eq. (25) are very similar, and small differences can emerge only on a logarithmic scale.
III. NUMERICAL RESULTS
In this section, we present numerical calculations for the photon emission rates and spectra for both the cavity and the qubit, under qubit incoherent pumping, as a function of the normalized coupling strength η. The incoherent excitation of the qubit is described by coupling it with a thermal reservoir at a given effective temperature T q ≡ K B T /ω q = 0 (here K B is the Boltzmann constant). All the results have been obtained assuming a zero temperature (T c = 0) cavity-reservoir, so that the cavity emission originates from the interaction with the qubit.
The eigenstates of the quantum Rabi Hamiltonian are obtained by standard numerical diagonalization in a truncated, but sufficiently large finite-dimensiona, Hilbert space. Specifically, we consider the Hilbert space resulting from the tensor product of the qubit basis {|g , |e }, and the basis constituted by the N +1 photonic Fock states up to the N -photon state |N . The truncation number N is chosen in order to ensure that the lowest M energy eigenvalues and corresponding eigenvectors of interest are not appreciably modified when increasing N . All the results are obtained solving the GME in Eq. (22), for the density matrix of the cavity-qubit in the dressed basis, including the lowest M energy levels. The truncation number M is chosen to reach convergence. Specifically, we check that the results (emission rates and spectra) do not notably change when increasing M .
In the following, where more convenient, we use a different notation for the eigenstates of the QRM, in analogy with the notation used to label the eigenstates of the JCM. At zero detuning [∆ ≡ (ω c − ω q )/ω q = 0], the excited eigenstates of the JC Hamiltonian can be written as |n ± = (|n, g ± |n − 1, e )/ √ 2. The eigenstates of the QRM, beyond the strong coupling regime do not display the same simple structure. Here, when useful, we indicate them by generalizing the above JC notation by introducing a tilde. With this notation, the state |0 denotes the ground state, and |ñ ± describes an eigenstate of the quantum Rabi Hamiltonian. Note that |ñ ± tends to the corresponding JC state |n ± for η 1. With this notation, the energy eigenstates maintain their parity (corresponding to the parity of the integer numberñ) independently of the value of η.
All the numerical calculations involving the master equation have been obtained using γ/ω q = 10 −4 and κ/ω q = 10 −3 and using QuTiP under Python [80,81].
A. Zero cavity-qubit detuning
Here, we present the results obtained analyzing emission rates and spectra at zero cavity-qubit detuning ∆ ≡ (ω c − ω q )/ω q = 0 1. Cavity and qubit emission rates Figure 1 shows the numerically calculated cavity and qubit steady-state photon emission flux rates (normalized with respect to the qubit emission rate W 0 q for
η = 0) W c = W c /W 0 q (blue-continuous curve), and W q = W q /W 0 q (red-dashed)
versus the light-matter normalized coupling strength η, calculated at two different effective temperatures of the qubit reservoir. The black-point-dashed curve indicates the cavity emission rates W c = W c /W 0 q calculated in the dipole gauge, using the wrong positive-frequency electric field operator in Eq. (18). We first observe that, the methods discussed in Sec. II allow to calculate emission rates for very different values of η, within a unified theoretical framework from the weak to the DSC regimes. Figure 1 clearly shows that, at low coupling strengths (i.e., weak coupling regime), a continuous increase of the cavity-emission rate with increasing η occurs for both, very low and higher effective temperatures (Purcell effect). When the system approaches the SC regime [ω q η (κ + γ)/4] a plateau is reached, in which the emission rate is equally shared between the atom and the cavity. By increasing further the coupling beyond the onset of USC (η > 0.1), a strong enhancement of both the cavity and qubit emission can be observed at low temperature T q = 5 × 10 −2 [ Fig. 1(a)]. It originates from the decrease of the transition frequency ω1 −,0 between the lowest excited state and the ground state for increasing values of η [see Fig. 2
(b)]. The strong decrease of ω1 −,0
enables the increase of the occupancy of the state |1 − at very low effective temperatures. Such a population growth determines an increase in the emission rate (of photons at frequency ω1 −,0 ), which can be observed in Fig. 1(a). The same behavior is not observed at a significantly higher temperature [ Fig. 1(b)]. In this case, the state |1 − can already be populated at small values of η. When increasing η to values beyond the DSC regime (η > 1), then both W c and W q decrease rapidly. This behavior can be understood by looking at the energy eigenvalues in Fig. 2(a) in the large η limit. Indeed, in this regime, all the transition frequencies tend to become flat, equally spaced, and two-by-two quasi-degenerate. Theoretical analysis [62] shows that, beyond the DSC regime, the quasi-degenerate light-matter eigenstates tend to factorize as |n, g and |n, e , so that the system tends to decouple from the qubit reservoir (Γ q kj → 0) and cannot be significantly excited. Specifically, the matrix elements j|σ x |k are different from zero only for states such that ω kj → 0. As a consequence, Γ q kj → 0. We also notice that in the large η limit, especially at low temperatures [see Fig. 1(a)], the cavity emission rate W c goes to zero more rapidly than W q . This feature is shown more clearly in Fig. 3(a), where the ratio W c /W q is displayed (blue-continuous curve). The figure shows the standard Purcell-like dependence in the weak-coupling regime, while W c saturates to 0.5 in the strong coupling and up to the onset of the USC regime. Still increasing η, the ratio W c /W q then decreases dramatically: the Purcell effect is reversed. A similar be-
(1 + ,0) (2 − ,0) (2 + ,0) (3 − ,0) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ω/ω q 0.0 0.5 1.0 1.5 2.0 2.5 η (b) (1 − ,0) (1 + ,0) (2 − ,1 − ) (2 − ,1 + ) (2 + ,1 − ) (2 + ,1 + ) (3 − ,2 − ) (3 − ,0)10 −5 10 −3 10 −1 (a) T q = 0.05 W c /W q (| 1 − |â +â † |0 |/| 1 − |σ x |0 |) 2 10 −6 10 −4 10 −2 10 0 η 10 −5 10 −3 10 −1 (b) | 1 − |â +â † |0 | 2 | 1 − |σ x |0 | 2 FIG. 3. (a)
Ratio of the cavity to the qubit emission rates Wc/Wq, for detuning ∆ = 0, Tq = 5 × 10 −2 , as a function of the normalized coupling strength η. The blue continuous curve describes the numerically calculated ratio, while the red-dashed one is the corresponding analytical approximated result
Wc/Wq | 1 −|(â +â † )|0 | 2 /| 1 −|σx|0 | 2 [see Eq. (27)].
The two curves tend to coincide for η > 5 × 10 −3 . In (b) the square modules of the matrix elements that determine the approximate ratio in (a) are shown.
havior has been predicted in a polariton system arising from the interaction of photons in a multi-mode cavity with collective electronic (bosonic) excitations [53], and experimentally confirmed in three-dimensional crystals of plasmonic nanoparticles interacting with light in the DSC regime [54]. It is interesting to explore the impact on the photon emission rate of not taking into account the proper transformation of the photon operators, when adopting the dipole gauge ( W c ). The dot-dashed black curves in Fig. 1 displays such a wrong result. The differences with respect to the correct results W c become evident at the onset of the USC regime (η ∼ 0.1). In the DSC regime, the impact of this mistake becomes very relevant: W c does not go to zero and becomes orders of magnitudes larger than the qubit emission rate W q .
In Fig. 3(a) it is also displayed an approximate analytical derivation of the ratio W c /W q . When the coupling rate η is strong enough to split sufficiently the two lowest energy excited levels (so that, at very low effec- Cavity Sc(ω) and qubit Sq(ω) emission spectra in the weak and strong coupling regimes, calculated for 2 × 10 −5 < η < 4 × 10 −2 , and for ∆ = 0. The spectra have been obtained under weak incoherent excitation of the qubit. We used an effective qubit temperature Tq = 5 × 10 −2 . The spectra have been normalized, so that the highest peak in each density plot is set at 1. The signal above the horizontal line in the lower panel (qubit emission spectra) has been magnified by a factor 10.
tive temperatures, only the system ground state and the first excited level are populated) the higher energy levels can be neglected (effective dressed two-level system). For these values of η, the cavity and emission rates can be simplified to
W c ω 2 1−,0 ω 2 c | 1 − |(â +â † )|0 | 2 ρ ss 1−,1− , W q ω 2 1−,0 ω 2 q | 1 − |σ x |0 | 2 ρ ss 1−,1− ,(27)
where ρ ss indicates the steady state density operator. It is interesting to note that the ratio W c /W q in Eq. (27) is independent of the density matrix. This approximate value of the ratio (red-dashed curve), shown in Fig. 3(a), is able to reproduce accurately the numerically calculated values of W c /W q for η > 10 −3 . In Fig. 3(b) it is shown the square modules of the transition matrix elements | 1 − |(â +â † )|0 | 2 and | 1 − |σ x |0 | 2 as a function of the normalized coupling η. In the high η limit, the first one goes to 0 and the second to 1.
In summary, the scenario in the high η and low qubittemperature limit is the following: the qubit spontaneous emission rate W q goes to zero because Γ q 1−,0 → 0 (qubit decoupling from its reservoir) and the cavity emission rate W c goes to zero even more rapidly (at increasing
η) because | 1 − |(â +â † )|0 | 2 → 0 and | 1 − |σ x |0 | 2 → 1 (light-matter decoupling).
2. Cavity and qubit emission spectra Figure 4 shows the cavity and qubit emission spectra under incoherent weak excitation of the qubit (T q = 5 × 10 −2 ) in the weak and strong coupling regimes (2 × 10 −5 < η < 4 × 10 −2 ). All the presented spectra are individually normalized, so that, in each spectral image the highest value is set to one. The transition from the weak (a single spectral line) to the strong (split lines) is clearly visible in the upper panel of Fig. 4. The two lines correspond to the transitions |1 ± → |0 indicated as (1 − ,0) and (1 + ,0) in Fig. 2. In the weak coupling regime, the emission line becomes brighter at increasing values of η. In the strong coupling regime, when the two lines are sufficiently split, an asymmetry in their relative intensity can be observed. This is a direct consequence of the higher population of the lower-energy excited state |1 − with respect to the higher-energy state |1 + at T q = 5 × 10 −2 . This behavior cannot be reproduced using the standard quantum-optics master equation where the reservoir occupations are calculated at the bare (in the absence of light-matter interaction) transition frequencies (see Sect. IV). Across the transition from the weak to the strong coupling regime, the qubit emission (lower panel) decreases approximately by an order of magnitude (see also Fig. 1), hence, to visualize the split lines, the signal above the horizontal line in the lower panel has been magnified by a factor 10. Figure 5 displays logarithmic cavity emission spectra ln [S c (ω)] as a function of the normalized coupling strength η, calculated for four different temperatures, showing the evolution of the emission spectra from the strong to the DSC regimes. In contrast to the case of light-matter systems described by a harmonic Hamiltonian (see, e.g., Ref. [82]), in the present highly anharmonic case, the spectra become very rich, if the system is adequately excited. On this scale, the weak coupling regime (already shown in Fig. 4) is confined to a negligible portion of the y axis and is not visible. At very low temperature (T q = 5 × 10 −2 ), only two spectral lines emerge, corresponding to the transitions (1 ± ,0) [see Fig. 2
(b)].
Notice that the transition (1 + ,1 − ) is forbidden owing to parity symmetry [3]. As expected, at such a low temperature, the emission from the lowest excited level at frequency ω1 −,0 dominates. Moreover, the line at ω1 + ,0 is visible only for η 0.3. When η increases (up to η 1), the intensity of the line ω1 − ,0 increases, due to the lowering of the ratio ω1 −,0 /(ω q T q ) which causes an increase of the excited state population ρ1 − ,1− . Then, for η 1, the population starts decreasing as a consequence of both light-matter and qubit-reservoir decoupling. This behavior is in agreement with the corresponding emission rate in Fig. 1(b).
At T = 0.1, the transition at frequency ω1 + ,0 becomes visible for all the values of η in the plot, although in the DSC regime, it tends to dissolve, owing to the qubitreservoir decoupling which prevents the excitation of the excited energy levels. We also notice that a new resonance line at frequency ω2 − ,1− appears [see Fig. 2(b)].
When further increasing the temperature (T q = 0.2), additional energy levels get populated and additional spectral lines appear. Most of these correspond to transitions indicated in Fig. 2(b). In the low-frequency range, in addition to the transition (1 − ,0), a new spectral line at |ω2 − ,1− | appears. This transition is forbidden in the JCM, since 1 + |(â +â † )|2 − = 0, at ∆ = 0. The crossing between the energy levels ω2 − and ω1 − , occurring at η ∼η = 0.43, manifests as a low spectral line approaching ω = 0 as η →η, and then (after the crossing), moving away from ω = 0. At higher frequencies (ω/ω q ∼ 1), other two crossing spectral lines become clearly visible. As shown in Fig. 2(b), they correspond to the transitions (2 + ,1 + ) and (3 − ,1 − ), both forbidden in the JCM at zero detuning. Still at higher frequencies, other two lines are observable for η 0.4: they correspond to the transitions (2 + ,1 − ) and (3 − ,0) [see Fig. 2(b)]. In the latter, the involved states differ by a number of excitations ∆ñ = 3. This transition is enabled by the presence of the counter-rotating terms in the QRM Eq. (10) and represents a clear example of USC physics [3], beyond the JCM. The spectra obtained at T q = 0.5 display still richer structures with the appearance of additional lines originated by higher energy levels that get populated at this effective temperature. The qubit emission spectra S q (ω) calculated at T q = 0.2 are shown in Fig. 6. As expected, emission lines corresponding to those observed for S c (ω) at the same temperature are shown. However, several differences emerge. In particular the spectral lines as a function of η display different relative intensities. For example, (i) two of the four lines around ω ∼ 1 in S c (ω) are not visible in S q (ω); (ii) the line corresponding to the transition (2 − ,1 + ) is more visible at small values of η; (iii) at increasing values of η, S q (ω), in contrast to S c (ω), exhibits an increasing background emission and a faster dissolving of the spectral lines at increasing values of η. All these differences originate from the different matrix elements in Eq. (26) [ j|(â +â † )|k and j|σ x |k ] entering S c (ω) and S q (ω), respectively. In particular, the most peculiar feature (iii) is a direct consequence of the fact that, for η 1.5, the matrix elements j|σ x |k → 0 for transitions with ω kj which are significantly different from zero. Therefore, for large values of η, the qubit spectra S q (ω) [see Eq. (25)] can be approximated by a Lorentzian line-shape (times ω 2 ) centered at ω ∼ 0:
S q (ω) ∝ ω 2 γ 2 ω 2 + γ 2 ,(28)
which, for ω γ, provides an almost constant background. Such behavior can be clearly observed in Fig. 7(h). Notice that this high-frequency behavior can be an artifact originating from the assumption in Eq. (25) and from the absence of any cut-off mechanism. Of course, a realistic behaviour in a so wide spectral range should include the specific frequency dispersion of the res-onator materials, which in general is system dependent, and goes beyond the present general treatment. Figure 7 displays cavity and qubit emission spectra S c(q) (ω) for four values of the normalized coupling strength η, calculated at T q = 0.5. The plots on the left correspond to horizontal line-cuts of the bottom-right density plot in Fig. 5. For a more accurate comparison, the spectra in Fig. 7 are reported all on the same x and y scale and have been normalized by the same amount, so that the highest peak in the figure is set to 1. Each spectral line in Fig. 7 originates from a specific transition between pairs of energy levels of the QRM [see Fig. 2].
These spectra show more in detail several features already present in the density plots. In particular, the six peaks in Fig. 7(a,b), originate from the following transitions (from the left): Fig. 7(e,f) at η = 1, the highest peak for both the cavity and qubit spectrum is the one at the lowest frequency and corresponds to the transition (1 − ,0). Moreover, at this coupling strength, higher energy peaks around ω/ω q ∼ 2, due to transitions from states differing by two excitations ∆ñ = 2, can be observed. At η = 2, well in the DSC regime, the intensity of the emission spectra decreases. Now S c (ω) shows bunches of peaks centered at ω ∼ 0, 1, 2, due to the tendency of the energy levels of the system towards an harmonic spectrum in the large η limit (see Fig. 2). In Fig. 7(h) it is displayed a very different behavior consisting of the constant emission background explained above [see Eq. (28)].
(2 − ,1 + ), (1 − ,0), (2 − ,1 − ), (2 + ,1 + ), (1 + ,0), (2 + ,1 − ). In
B. Cavity-qubit interaction in the presence of detuning
We now present numerically calculated emission rates and spectra obtained in the case of significant qubitcavity detuning ∆ ≡ (ω c − ω q )/ω q , in normalized units. In particular, we consider the cases of ∆ = ± 0.3.
Cavity and qubit emission rates and spectra at negative detuning (∆ = −0.3)
We start from a detuning value of ∆ = −0.3. Figure 8 shows the normalized cavity and qubit emission rates, obtained with the same parameters used to calculate the results in Fig. 1, except the finite detuning. At very low effective temperature T q = 5 × 10 −2 , and at low coupling strengths, the cavity emission rate W c increases linearly (on this log-log scale) as the zero-detuning case, but it is some order of magnitude smaller. As expected, the large detuning significantly reduces the energy transfer from the qubit to the cavity for ω q η ∆. However, the cavity emission rate becomes of the same order of magnitude of the qubit emission at η ∼ 0.05, when ω q η < ∆.
Moreover, the plateau in the strong coupling regime is no longer present, hence the standard Purcell be- havior continues in the USC regime. In the η region 5 × 10 −2 η 0.5, the cavity emission rate exceeds that of the qubit (W c > W q ). The qubit emission rate is almost constant from the weak coupling regime to the onset of the USC, where it reaches values which are more than five orders of magnitude greater than the qubit emission rate at zero coupling W 0 q . As in the zero detuning case, the strong enhancement of both the emission rates in the USC regime and at low effective temperature originates from the decrease of the transition frequency ω1 − ,0 , and as stated above, it is not present at higher effective temperatures. Moreover, beyond the DSC regime onset (η > 1), both W c and W q decrease rapidly because of the light-matter and qubit-reservoir decoupling. Figure 10 shows the low-temperature (T q = 5 × 10 −2 ) cavity and qubit emission spectra in the weak and strong coupling regimes (10 −5 ≤ η ≤ 3 × 10 −2 ), in analogy with the zero-detuning case in Fig. 4. As can be seen in Fig. 9, in the weak coupling regime ω1 − ,0 ≈ ω c and ω1 +,0 ≈ ω q . Moreover, at low values of the coupling strength and at low incoherent excitation rates (low temperature), the cavity cannot emit at the qubit frequency ω q , and the qubit cannot emit at ω c . Thus, Fig. 10 shows only the (1 + ,0) transition, while the (1 − ,0) transition is absent. Another difference between Fig. 10 and Fig. 4 is the intensity of the Purcell effect, which is much more effective in the zero-detuned case. Here the cavity starts to emit at η ≈ 10 −2 , a value which is three orders of magnitude greater than the zero detuning case. Figure 11 shows a logarithmic plot of the cavity emission spectra S c (ω) as a function of the normalized coupling strength η ranging from the strong to the DSC regimes. As in the zero-detuning case, at very low effec- tive temperature (T q = 5 × 10 −2 ), the transition (1 − ,0) is the brightest, while the atom-like transition (1 + ,0) is visible only for η 0.4. We also notice that the line at frequency ω2 − ,1− becomes slightly visible only for 0.7 η 1.7.
η (b) (1 − ,0) (1 + ,0) (2 − ,1 − ) (2 − ,1 + ) (2 + ,1 − ) (2 + ,1 + ) (3 − ,2 − ) (3 − ,
At T q = 0.5, additional energy levels get populated and additional spectral lines appear. As in the zero-detuning case, most of these transitions can be found in Fig. 9(b). The line at frequency ω2 −,1+ becomes sufficiently intense only for η 0.35, which is when the (1 + ,0) frequency transition becomes greater than (2 − ,0). We also observe that, at the higher effective temperature and at low coupling strengths (but with η 0.05), the cavity can also emit significantly at the qubit frequency ω q . It is worth noting that at very high coupling strengths, all the spectral lines tend to be at frequencies which are multiple integer of the cavity frequency ω c . Figure 12 displays the logarithmic qubit emission spectra S q (ω), which present features similar to those in the cavity emission spectrum but with a background emission above the onset of the deep USC regime. The spectra have been normalized, so that the highest peak in each density plot is set at 1.
2.
Cavity and qubit emission rates and spectra at positive detuning (∆ = 0.
3)
The emission rates versus the normalized coupling strength η, for the positive-detuning case, for both the cavity and the qubit are shown in Fig. 13 at both low and higher effective temperatures. For both the considered temperatures, the cavity emission rate never exceeds the qubit one. At T q = 5 × 10 −2 , the peak qubit emission rate exceeds the cavity peak by more than two orders of magnitude. The increase of the cavity emission rate at increasing values of η (Purcell effect) continues until the onset of the USC regime, and the plateau in the strong coupling regime, observed at zero-detuning, is here absent. At T q = 5 × 10 −2 , the qubit emission rate reaches in the USC regime values which are about six orders of magnitude larger than W 0 q . Looking at Fig. 14 We used ∆ = −0.3 (ωc/ωq = 0.7). The spectra have been normalized, so that the highest peak in each density plot is set at 1. Increasing the temperature, additional lines originating from transitions involving higher energy levels appear, where the majority of these correspond to transition energies shown in Fig. 9.
most coincides with the resonance frequency of the cavity mode. Figure 15 shows the cavity emission spectrum, obtained at the effective temperature T q = 5 × 10 −2 , in the weak and strong coupling regimes. In the frequency region displayed in Fig. 15, the only visible emission line corresponds to the transition (1 − ,0). As in the negative-detuning case (see Fig. 10), in the weak coupling regime, the emission originates from the qubit-like transition (1 − , 0), which however, now is the lowest energy transition. Figure 16 shows the logarithmic cavity emission spectra S c (ω) as a function of the normalized coupling strength η, ranging from the strong to the DSC regimes. At very low effective temperatures, the emission originates almost only from the lowest energy transition (1 − , 0), because the photon-like transition (1 + , 0) is at higher energy and, owing to the detuning, is poorly hybridized with the qubit excited state, at least for moder-
IV. COMPARISON WITH OTHER MODELS
In this section, we present examples of calculations of cavity and qubit emission spectra, (using the same parameters adopted in the previous section) obtained using different models and/or dissipators for the master equation. In particular, we present (i) some spectra obtained by using the JCM and the standard master equation for cavity QED, with the dissipators obtained by neglecting the light-matter interaction [64]; (ii) we also present spectra obtained with the same model used in Sect. III, using a master equation where the dissipators have been obtained taking into account the light-matter interaction, but applying the post-trace RWA [64].
A. Jaynes-Cummings model
The JCM is the simplest model describing a two level system interacting with a quantized single-mode of an electromagnetic resonator. It is obtained applying the RWA to the QRM in the dipole gauge. Therefore, it is expected to be valid only for coupling strengths below the USC regime. The JC Hamiltonian iŝ
H JC = ω câ †â + ω q 2σ z + ηω c 2 âσ + +â †σ − .(29)
In addition, in order to describe the interaction of the qubit-cavity system with the environment, we used the standard quantum optical master equatioṅ
ρ = −i Ĥ JC ,ρ + L c bareρ + L q bareρ ,(30)
where L c bare and L q bare are the standard dissipators for the cavity and the qubit respectively:
L c bareρ = κ [1 + n c (T c )] D â ρ + κn c (T c )D â † ρ L q bareρ = γ [1 + n q (T q )] D σ − ρ + γn q (T q )D σ + ρ .(31)
The term n c(q) (T c(q) ) = [exp 1/T c(q) −1] −1 is the thermal population, and D[Ô] indicates the generic dissipator In this case, the cavity and qubit emission rates are simply proportional to W c (t) = â †â t and W q (t) = σ +σ− t , respectively. Analogously, the steady-state cavity and qubit emission spectra can be defined as Figure 18 describes the normalized emission spectra of the cavity in the weak-strong coupling range. As mentioned above, the JCM is a good approximation in this range of coupling strengths. The only difference with respect to the results obtained using the full QRM (see Fig. 4) is the lack of any intensity difference between the split lines originating from the transitions (1 − , 0) and (1 + , 0). Actually, the reason is not directly due to the use of the JCM, but is a consequence of using the standard master equation which does not include bath populations calculated at the system transition frequencies.
D Ô ρ = 1 2 2ÔρÔ † −ρÔ †Ô −Ô †Ôρ .(32)η (b) (1 − ,0) (1 + ,0) (2 − ,1 − ) (2 − ,1 + ) (2 + ,1 − ) (2 + ,1 + ) (3 − ,2 − ) (3 − ,S c (ω) = Re ∞ 0 dτ e −iωτ â † (t + τ )â(t) ss S q (ω) = Re ∞ 0 dτ e −iωτ σ + (t + τ )σ − (t) ss . (33)
Of course such a model cannot provide reliable results beyond the strong coupling regime (see Fig. 19). We used an effective qubit temperature Tq = 5 × 10 −2 . The spectra have been normalized, so that the highest peak in each density plot is set at 1.
B. Dressed master equation with post-trace RWA
The standard quantum-optics master equation has several weaknesses, and one of the most relevant is that the interaction between the subsystems is not considered when deriving the dissipators [83]. One of the main drawbacks is that, owing to the presence of counter-rotating terms in the Hamiltonian describing the interaction between the light and matter components of the system, unphysical excitations are generated into the system even by a zero-temperature reservoir. For this reason a dressed master equation was developed [64]. This model takes into account that transitions in the hybrid system occur between dressed eigenstates, and not between the eigenstates of the free Hamiltonians of the components.
The dressed-state master equation iṡ
ρ = −i Ĥ R ,ρ + L dressedρ ,(34)
where L dressed is of the form The spectra have been normalized, so that the highest peak in each density plot is set at 1. Increasing the temperature, additional lines originating from transitions involving higher energy levels appear. Most of them correspond to transition energies shown in Fig. 9.
L dressedρ = i=c,q k>j Γ i kj [1 + n kj (T i )] D [|j k|]ρ + Γ i kj n kj (T i )D [|k j|]ρ .(35)
The terms n kj (T i ) are the thermal reservoir populations [see Eq. (B3)], calculated at the system transition frequencies ω kj , and Γ c(q) kj are the cavity and qubit decay [see Eq. (B5) and Eq. (B7)].
As mentioned above, this dissipation model is valid only with anharmonic systems and, as can be noticed in Fig. 20, it returns incorrect results when the coupling is very weak and the system displays a quasi harmonic spectrum-that is a non zero cavity photon emission at negligible couplings [compare with Fig. 4(a)]. Figure 21 shows the normalized emission spectra of the cavity, using the dressed master equation in the USC-DSC range. Also at very large values of the coupling strength, when the energy spectrum of the QRM tends towards harmonicity, the obtained emission spectra
S(ω)
FIG. 18. Cavity emission spectra Sc(ω) in the weak and strong coupling regime for the JCM, calculated for 2×10 −5 < η < 4 × 10 −2 , and for ∆ = 0. The spectra have been obtained under weak incoherent excitation of the qubit. We used an effective qubit temperature Tq = 5 × 10 −2 . The spectra have been normalized, so that the highest peak in each density plot is set at 1.
shown in Fig. 21, differ significantly from the corresponding ones in Fig. 5. The main difference is the background emission which covers almost all the USC and DSC region. Moreover, the emission lines are not well defined in the DSC region.
S(ω)
FIG. 20. Cavity emission spectra Sc(ω) in the weak and strong coupling regime using the dressed master equation, calculated for 2 × 10 −5 < η < 4 × 10 −2 , and for ∆ = 0. The spectra have been obtained under weak incoherent excitation of the qubit. We used an effective qubit temperature Tq = 5 × 10 −2 . The spectra have been normalized, so that the highest peak in each density plot is set at 1.
V. CONCLUSIONS
We have investigated how the QRM emits light under incoherent excitation of the two-level atom, considering coupling strengths ranging from the weak coupling to the USC and DSC regimes. We analyzed both the cavity and We used ∆ = 0. The spectra have been normalized, so that the highest peak in each density plot is set at 1. In the DSC regime (when the system became harmonic) this model fails.
the qubit emission, for both the resonant and detuned cases, considering different effective qubit-temperatures. In particular, by using a GME approach, we were able to calculate numerically cavity and qubit emission rates and spectra versus the normalized light-matter coupling strength and for different incoherent qubit excitation strengths (effective temperature). Following the work in Ref. [63], the obtained results are gauge independent. The theoretical framework allows us to investigate the light-matter decoupling and the fate of the Purcell effect in the QRM when the normalized coupling strength η is significantly larger than one. In this case, we found that the cavity and qubit emission rates are affected both by light-matter decoupling and qubit-reservoir decoupling.
Reaching the USC and DSC regimes with individual quantum emitters, whose interaction with light is implemented via the minimal coupling replacement, is currently very difficult, though progress is being made, especially with plasmonic cavity systems [54]. However, this theoretical framework can be easily generalized to include N qubits (Dicke model) [60]. Moreover, coupling strengths ranging from the weak to the DSC regime can be achieved with individual qubits using superconducting circuits (see, e.g., [31,84]). In this case, however, the light-matter interaction is not described by the minimal coupling replacement and specific calculations for these systems would have to be carried out, where the general approach described here and these results can provide a precise guide. A simple and widely adopted way to model the interaction of a quantum system with its environment, consists in writing the interaction Hamiltonian as a quadratic form involving the product of system-and bath-degrees of freedomĤ
I = k λ kŜBk ,(A1)
where the coefficients λ k represent the coupling strengths (assumed real, one for any bath-degree of freedom), whilê S andB k are Hermitian system-and bath-operators.
The specific values of the coupling strengths and the choice of the system and bath operators in Eq. (A1) is model dependent. In the next subsections, we present arguments to guide and to make these choices consistent (taking care of gauge issues). Specifically, we present a consistent derivation for the QRM, describing the interaction of the cavity mode and the qubit with their respective baths.
The approach followed here is close to that recently developed in Ref. [63], and gives rise to analogous results. The only difference is that here we introduce the interaction of the photonic and matter components with their reservoirs by invoking the gauge principle. This approach provides a rather fundamental model of systems-baths interactions and connects more with quantum field theory.
Cavity-bath interaction in the Coulomb and dipole gauges
Here, we introduce the cavity-bath coupling by regarding the environment as collective bosonic excitations of matter, so that we can introduce such interaction by invoking the fundamental gauge principle, which determines the form of light-matter coupling.
a.
Cavity-bath interaction in the Coulomb gauge
As a consequence of the gauge principle (minimal coupling replacement), in the Coulomb gauge, the only degrees of freedom of the electromagnetic field interacting with matter are the field coordinates. For a single mode resonator, there is a single coordinatex, which can be expressed asx =â +â † . This fact not only leads to the useful relation in Eq. (6), but it also allows to obtain a Thomas-Reiche-Kuhn (TRK) sum rule for the electromagnetic field [69].
Usually, input-output frameworks, used to model the interaction of cavity modes with the external modes, adopt as bath operators a continuum of bosonic electromagnetic modes, rather than a collection of bosonic matter excitations. However, the field-bath coupling, ultimately, originates from the interaction of the cavity electromagnetic field with matter (e.g., cavity mirrors). Due to this fact, even if such matter degrees of freedom can be adiabatically eliminated, it is reasonable to require that the general relationship Eq. (6) and the TRK sum rule remain valid. To ensure this, it is sufficient to start from the free bosonic Hamiltonian for the bath,
H b = k ω kb †
kb k , and to apply the generalized minimal coupling replacement, corresponding to transforming each matter operator of the bath by a suitable unitary transformation (see Ref. [60]
): b k →Û cbbkÛ † cb =b k − iη c k (â +â † ) ,(A2)whereÛ cb = exp i(â +â † ) k η c k (b k +b † k ) .(A3)
Assuming a coupling constant (effective charge q) independent on the matter mode k,Û cb can be written aŝ
U cb = exp iqxQ b ,(A4)
where the coordinate of the reservoir field readŝ
Q b = k α √ ω k (b k +b † k ) . (A5)
Here α is a constant. The resulting adimensional coupling in Eq. (A3) can be expressed as
η c k = qα/ √ ω k .(A6)
Of course, depending on the specific model, the effective charge can be frequency dependent, implying a different frequency dependence of η c k than that in Eq. (A6). By neglecting the diamagnetic term [of the second order η c k 2 (ω k )], we obtain the interaction Hamiltonian for the cavity field and the reservoir
H cb = i(â +â † ) k ω k η c k (b k −b † k ) .(A7)
A comparison between Eq. (A1) and Eq. (A7) clearly shows that,Ŝ = (â +â † ) andB k = iω k (b k −b † k ). Equation (A7) represents a consistent starting point to study the interaction of the cavity mode with its bath. In order to derive the GME (see Appendix B), it is useful to expand the cavity-field coordinate in the dressed basiŝ
H cb = i l,m x lmPlm k ω k η c k (b k −b † k ) ,(A8)
whereP lm = |l m| are the transition operators and x lm = l|(â +â † )|m are the matrix elements for the cavity-field coordinate, being |l the energy eigenstates of the Hamiltonian in the Coulomb gauge [Eq. (1) in Sec. II A]. In terms of cavity-photon operators with positive and negative frequencies [71], Eq. (A8) can be written aŝ
H cb = i l>m x lmPlm + x * mlPml k ω k η c k (b k −b † k ) .
(A9) Note that, l>m x lmPlm = ( l<m x * mlP ml ) † . Since the system-bath interaction is assumed to be weak, it is reasonable to apply to Eq. (A9) the rotating wave approximation:
H cb = −i l>m x * mlPml k ω k η c kb † k + H.c. .(A10)
b. Cavity-bath interaction in the dipole gauge
The cavity-bath interaction Hamiltonian in the dipole gauge could be obtained by simply performing the gauge transformation of the cavity operators in Eq. (A7):â → RâR † =â + iη cσ x =â , wherê
R = exp −iη(â +â † )σ x .(A11)
Therefore,Ĥ cb in the dipole gauge is equivalent toĤ cb in the Coulomb gauge, becausex =RxR † . In doing so, we are neglecting the action of the gauge transformation on the reservoir operatorsb k (b † k ), which is possible because, as shown in Ref. [59], gauge transformations affect significantly ladder operators only when the coupling is rather strong. Nevertheless, it remains interesting and instructive to derive directly the cavity-bath reservoir in the dipole gauge.
In general, for a light-matter system whose light component (in the absence of interaction) is described by the HamiltonianĤ ph , and matter component byĤ m , the total Hamiltonian (in the dipole approximation) in the presence of interaction can be obtained in the Coulomb gauge by applying a suitable unitary transformationÛ to the matter Hamiltonian only:
H =ÛĤ mÛ † +Ĥ ph .(A12)
The dipole gauge Hamiltonian is obtained from the above asĤ
=Û †Ĥ CÛ =Ĥ m +Û †Ĥ phÛ ,(A13)
which corresponds to applying a unitary transformation to the bare photonic Hamiltonian only: a sort of generalized minimal coupling replacement for the photonic Hamiltonian. Of course, the dipole-gauge Hamiltonian can also be written using the unitary operatorR =Û † :
H =Ĥ m +RĤ phR † .(A14)
In the present case, the generalized minimal coupling replacement for a single-mode photonic system interacting with a two-level atom and with a bosonic matter field, can be implemented by the following unitary operator
R cqb = exp −i(â +â † )[ησ x + k η c k (b k +b † k )] .
(A15) The dipole-gauge Hamiltonian for the system constituted by a cavity-mode interacting with a qubit and with a bosonic matter reservoir can be directly obtained applying the generalized gauge transformation [see Eq. (A15)] to the photon operators in the bare cavity Hamiltonian
H ph = ω câ †â : a →R cqbâR † cqb =â + iησ x + i k η c k (b k +b † k ) . (A16)
The resulting cavity-bath interaction Hamiltonian in the dipole gauge becomeŝ
H cb = −iω c (â −â † + 2iησ x ) k η c k (b k +b † k ) + ω c k η c k (b k +b † k ) 2 ,(A17)
which includes an effective interaction of the bath with the qubit, and a bath self-interaction term. The result in Eq. (A17) differs from what has been obtained above adopting a less rigorous approach (Ĥ cb =Ĥ cb ). However, in Appendix B we show that the two approaches, after the Markov and Born approximations, give rise to the same dissipators in the master equation. Neglecting the bath self-interaction term [of second order η 2 k (ω k )], and using the dipole-gauge photon operators in Eq. (13) (see Sec. II B), the cavity-bath interaction Hamiltonian in Eq. (A17) can be written aŝ
H cb = −iω c (â −â † ) k η c k (b k +b † k ) .(A18)
A comparison between Eq. (A1) and Eq. (A18) clearly shows that,Ŝ = −iω c (â −â † ) andB k =b k +b † k . By expanding in Eq. (A18) the cavity operators in the dressed basis, we obtain
H cb = −iω c m,l p lmP lm k η c k (b k +b † k ) ,(A19)
where p lm = l |(â −â † )|m , andP lm = |l m |, being |l the energy eigenstates of the Rabi Hamiltonian in dipole gauge [Eq. (10) in Sec. II B]. Looking at Eq. (19) in the main text, the above matrix element can also be written as p lm = ω lm x lm /ω c , with x lm = l |(â +â † )|m . In terms of cavity-photon operators with positive and negative frequencies, we obtain
H cb = −i l>m ω lm x lmP lm − x * mlP ml k η c k (b k +b † k ) .
(A20) Note that, l>m ω lm x lmP lm = ( l<m ω ml x * mlP ml ) † . Finally, applying the RWA, Eq. (A20) becomeŝ
H cb = −i m>l ω lm x lmP lm k η c k b † k + H.c. .(A21)
Modeling the qubit-bath interaction in the Coulomb and dipole gauge
Due to the fact that atoms interact with the electromagnetic field, here we model (as usual) the qubit-bath interaction considering the environment field as a freespace electromagnetic field described by a collection of harmonic oscillators. We indicate withĉ k andĉ † k the bosonic photon destruction and creation operators for the k-th mode of the reservoir, so that the free reservoir Hamiltonian can be expressed asĤ c = k ω kĉ † kĉ k .
a. Qubit-bath interaction in the Coulomb gauge
In the Coulomb gauge, in contrast to the field momenta, the matter momenta are modified by the lightmatter interaction. In particular, the canonical momenta of the matter field differ from the kinetic momenta (see, e.g., Ref. [62]). Hence, this gauge is not the more convenient one to study the qubit properties.
The qubit-bath interaction Hamiltonian in the Coulomb gauge can be obtained by applying the generalized minimal coupling replacement including, in addition to the qubit interaction with the cavity field, also the interaction with the environment. Specifically, the interaction of the qubit with the cavity and the bath fields can be directly obtained by applying to the qubit bare Hamil-tonianĤ q = ω qσz /2 a unitary transformation defined by the following unitary operator
U qb = exp iσ x [η(â +â † ) + k η q k (ĉ k +ĉ † k )] . (A22)
Keeping only the linear terms in the qubit-bath coupling strength η q k , the resulting qubit-bath interaction Hamiltonian in the Coulomb gauge becomes (see Ref. [62])
H qb = ω qΣy k η q k (ĉ k +ĉ † k ) ,(A23)
wherê Σ y ≡R † qbσ yRqb =σ y cos 2η(â +â † ) −σ z sin 2η(â +â † ) (A24) is the Pauli y-operator in the dipole gauge, transformed in the Coulomb gauge, andR qb =Û † qb . Analogously, we havê Σ z ≡R † qbσ zRqb =σ z cos 2η(â +â † ) +σ y sin 2η(â +â † ) , (A25)
Σ x ≡R † qbσ xRqb =σ x .(A26)
A comparison between Eq. (A1) and Eq. (A23) clearly shows that,Ŝ = ω qΣy andB k =ĉ k +ĉ † k . By expanding the qubit operatorΣ y in Eq. (A23) in the dressed representation, we obtain
H qb = ω q m,l (Σ y ) lmPlm k η q k (ĉ k +ĉ † k ) ,(A27)
where (Σ y ) lm = l|Σ y |m are the matrix elements of the Pauli y-operator, being |l the energy eigenstates of the Rabi Hamiltonian in the Coulomb gauge [Eq. (1) in Sec. II A]. The matrix elements in Eq. (A27) satisfy the relation ω q (Σ y ) lm = iω ml (Σ x ) lm .
As done for the previously cavity-bath interaction Hamiltonian, we can expand the qubit dressed-operators in terms of positive and negative frequencies operators, such that, applying the RWA, Eq. (A27) can be written asĤ
qb = i m>l ω ml (Σ x ) lmPlm k η q kĉ † k + H.c. .(A29)
b. Qubit-bath interaction in the dipole gauge
In the dipole gauge, the qubit-bath interaction Hamiltonian can be obtained by applying the generalized minimal coupling replacement to the bosonic Hamiltonian for the bare field-bathĤ b = k ω kĉ † kĉ k . This corresponds to transforming the bath operators as follows
c k →R qbĉkR † qb =ĉ k + iη q kσ x ,(A30)
whereR qb =Û † qb . The resulting qubit-bath Hamiltonian in the dipole gauge becomeŝ
H qb = iσ x k ω k η q k (ĉ † k −ĉ k ) .(A31)
A comparison between Eq. (A1) and Eq. (A31) clearly shows that,Ŝ = −iΣ x andB k = ω k (ĉ k −ĉ † k ). By expandingσ x in the dressed representation, we ob-tainĤ The GME [65] for strongly interacting hybrid quantum systems is developed using the basis of the system eigenstates (dressed-states). Moreover, it does not makes use of the secular approximation (post-trace rotating wave approximation). Thus, unlike the dressed master equation in Ref. [64], suitable for anharmonic systems, it is also valid for systems displaying harmonic or quasiharmonic spectra. This feature is essential to describe the system dynamics and the resulting spectra both at small and at very large (deep strong) values of the normalized coupling strength η. Here, we provide a demonstration of the GME gauge-invariance. Within this approach, we guarantee the gauge invariance of matrix elements of the density matrix and expectation values, as well as the obtained emission rate and spectra.
qb = −i m,l (σ x ) lmP lm k ω k η q k (ĉ k −ĉ † k ) ,(A32)
We start considering the GME in the Coulomb gauge for the Rabi model, which can be written aṡ ρ = −i Ĥ R ,ρ + L gρ , (B1) where the dissipator L g contains two contributions L g = L c g + L q g , arising from the cavity-bath (c) and the qubitbath (q) interaction, respectively: L c(q) gρ = 1 2 j>k l>m Γ c(q) lm n ml (T c(q) ) P lmρPkj −P kjPlmρ + Γ c(q) kj n jk (T c(q) ) P lmρPkj −ρP kjPlm + Γ c(q) lm [n ml (T c(q) ) + 1] P kjρPlm −ρP lmPkj + Γ c(q) kj [n jk (T c(q) ) + 1] P kjρPlm −P lmPkjρ ,
with n kj (T c(q) ) = {exp ω kj /(ω c(q) T c(q) ) − 1} −1 ,
which is the thermal populations of the cavity and qubit reservoirs calculated at the transition frequencies ω kj . The cavity-and qubit-bath coupling rates determine both the losses and the incoherent pumping of the system. These rates depend on the specific interaction Hamiltonian (which describe the coupling between the system component and its bath) and on the density of the states of the relative bath.
For the cavity-bath rate, following the general derivation in Appendix A 1 a, and using Eq. (A10), we obtain Γ c kj = 2πd c (ω kj )|ω kj η c (ω kj )| 2 | k|(â +â † )|j | 2 , (B4)
where d c (ω kj ) is the density of states of the bath calculated at the transition frequency ω kj . For any numerical calculations in the main text, we assumed η c k ∝ 1/ √ ω k , and d c independent on ω. Taking these assumptions into account, and including all the constants in the rate κ, the cavity-bath coupling rate can be expressed as
Γ c kj = κ ω kj ω c j|(â +â † )|k 2 .(B5)
It is clear that the cavity-bath interaction rates in Eq. (B4) and Eq. (B5) are gauge invariant. Analogously, from the general derivation in Appendix A 2 a, and using Eq. (A29) we obtain Γ q kj = 2πd q (ω kj )|ω kj η q (ω kj )| 2 | k|σ x |j | 2 .
Assuming η q k ∝ 1/ √ ω k , d c to be independent on ω, and including all the constants in the rate γ, the qubit-bath coupling rate can be expressed as Γ q kj = γ ω kj ω q | j|σ x |k | 2 .
(B7)
Gauge invariance
In any coherent description of the light-matter interaction, the expectation value of any Hermitian operatorÔ that characterizes a property of the optical system, has to be gauge invariant. Since the correct gauge transformation is described by a unitary operatorÛ, if |ψ is a quantum state in the Coulomb gauge, it is trivial to see that
ψ|Ô|ψ = ψ |Ô |ψ ,(B8)
whereÔ =ÛÔÛ † and |ψ =Û|ψ are a generic Hermitian operator and a ket state in the dipole gauge, respectively. In particular, by considering the definition of the density operatorρ = m p m |ψ m ψ m | one can clearly see that, while the matrix elements Here, we show that the master equation in Eq. (B2) does not break gauge-invariance. As done so far, we are labeling quantum states and operators in the dipole gauge with a prime apex primed superscript.
Due to the Eq. (B8), we want to show that the timeevolution of any system operator is gauge-invariant, namely Let us next consider separately the two terms on the right hand side of Eq. (B11). By means of the unitary gauge transformationÛ , we obtain
j j|Ô(Ĥ Rρ −ρĤ R )|j = j j |[ÛÛ † (ÛÔÛ † )[(ÛĤ RÛ † )(ÛρÛ † ) − (ÛρÛ † )(ÛĤ RÛ † )ÛÛ † ]|j = j j |Ô (Ĥ Rρ −ρ Ĥ R )|j = Tr Ô [Ĥ R ,ρ ] .(B12)
To deal with the second term on the right hand side of Eq. (B11), we first observe that Γ c(q) ml = Γ c(q) m l and n ml (T c(q) ) = n m l (T c(q) ) in Eq. (B2) are gauge invariant. Thus, it is sufficient to show that the terms in the square brackets (involving the transition operatorŝ P lm ) in Eq. (B2), provide gauge invariant contributions in Eq. (B10). Considering the first of these terms, we have Tr ÔP lmρPkj = n j|ÔP lmρPkj |j = n j |ÛÛ † (ÛÔÛ † )(ÛP lmÛ † )(ÛρÛ † )(ÛP kjÛ † )ÛÛ † |j (B13) = n j |Ô P lmρ P kj |j = Tr Ô P lmρ P kj .
It is easy to see that the other similar terms transform exactly in the same way. This proves that Tr Ô L gρ = Tr Ô L gρ , and, as a consequence, Eq. (B10) is gauge invariant.
FIG. 1 .
1Numerically calculated cavity and qubit steady-state photon emission flux rates (normalized with respect to the qubit emission rate W 0 q calculated for η = 0) Wc = Wc/W 0 q (blue-continuous curves), and Wq = Wq/W 0 q (red-dashed) versus the light-matter normalized coupling strength η. We used ∆ = 0 (zero cavity-qubit detuning). Black-point-dashed curves indicate the cavity emission rates W c = W c /W 0 q calculated in the dipole gauge, using the wrong positive-frequency electric field operator in Eq.(18). The upper panel (a) has been obtained for Tq = 5 × 10 −2 , the lower one (b) for Tq = 5 × 10 −1 .
FIG. 2 .
2Normalized energy levels and transition energies versus η, for ∆ = 0. (a) Lowest normalized energy levels (with the ground state energy as reference) |ωj ± − ω0|/ωq of the QRM. (b) Normalized parity-allowed transition energies |ω k − ωj|/ωq for the lowest eigenstates of the QRM.
FIG. 4. Cavity Sc(ω) and qubit Sq(ω) emission spectra in the weak and strong coupling regimes, calculated for 2 × 10 −5 < η < 4 × 10 −2 , and for ∆ = 0. The spectra have been obtained under weak incoherent excitation of the qubit. We used an effective qubit temperature Tq = 5 × 10 −2 . The spectra have been normalized, so that the highest peak in each density plot is set at 1. The signal above the horizontal line in the lower panel (qubit emission spectra) has been magnified by a factor 10.
FIG. 5 .
5Logarithmic 2D plots of cavity emission spectra Sc(ω) for values of η reaching the USC and DSC regimes, obtained using four different effective qubit temperatures Tq, and ∆ = 0. The spectra have been normalized, so that the highest peak in each density plot is set at 1. Increasing the temperature, additional lines originating from transitions involving higher energy levels appear. Most of the emission lines correspond to transition energies shown inFig. 2.
FIG. 6 .
6Logarithmic 2D plots of qubit emission spectra Sq(ω) for values of η reaching the USC and DSC regimes, obtained at Tq = 0.2, and ∆ = 0. The spectra have been normalized, so that the highest peak is set at 1. The visible lines correspond to transition energies shown inFig. 2. The origin of the flat (red) signal background for η > 1.5 is explained in the text [see Eq.(28)].
FIG. 7 .
7Cavity Sc(ω) and qubit Sq(ω) emission spectra (logarithmic), obtained at four different values of η, increasing from the top to the bottom (detuning ∆ = 0). The cavity spectra are on the left, while the qubit ones on the right side. We used an effective temperature for the qubit reservoir Tq = 0.5. The cavity and qubit spectra have been normalized to the highest peak which appears in panel (c) and (d), respectively. The plots show the evolution of the cavity and qubit emission spectra when increasing the normalized coupling strength η. Panel (h) reveals the flat background appearing in the qubit emission spectra in the DSC regime.
FIG. 8 .
8Cavity and qubit emission rates (normalized with respect to the qubit emission rate W 0 q calculated for η = 0) Wc = Wc/W 0 q (blue-continuous curve), and Wq = Wq/W 0 q (red-dashed) versus the light-matter normalized coupling strength η. We used ∆ = −0.3, corresponding to ωc/ωq = 0.7. The upper panel has been obtained for Tq = 5 × 10 −2 , the lower one for Tq = 5 × 10 −1 .
0 )FIG. 9 .
09Normalized energy levels and transition energies versus η, for ∆ = −0.3 (ωc/ωq = 0.7). (a) lowest normalized energy levels (with the ground state energy as reference) (ωj ± − ω0)/ωq of the QRM. (b) Normalized parity-allowed transition energies |ωj ± − ωk ± |/ωq for the lowest eigenstates of the QRM.
FIG. 10 .
10Cavity Sc(ω) and qubit Sq(ω) emission spectra in the weak and strong coupling regime, calculated for 10 −3 < η < 10 −1 , and for ∆ = −0.3 (ωc/ωq = 0.7). The spectra have been obtained under weak incoherent excitation of the qubit. We used an effective qubit temperature Tq = 5 × 10 −2 .
FIG. 11 .
11, we observe that, at weak coupling strengths the (1 − , 0) transition almost coincides with the qubit transition frequency, while the (1 + , 0) al-Cavity emission spectra Sc(ω) on logarithmic scale for values of η reaching the USC and DSC regimes, obtained for two different effective qubit temperatures Tq = 0.05, 0.2.
FIG. 12 .
12Logarithmic qubit emission spectra Sq(ω) for values of η reaching the USC and DSC regimes, obtained at Tq = 0.2. We used ∆ = −0.3. The spectra have been normalized, so that the highest peak is set at 1. The visible lines correspond to transition energies shown inFig. 2. The origin of the flat (red) signal background for η > 1.5 is explained in the text [see Eq.(28)].ate coupling strengths. Increasing the effective temperature (T q = 0.2) higher energy levels start to get populated, thus determining the appearance of several additional emission lines [seeFig. 14(b)]. The qubit emission spectra versus η, at T q = 0.2 are shown inFig. 17. The line corresponding to the transition (1 + , 0) is the brightest at any coupling strength where emission lines are visibile. Also in this case the flat background qubit emission in the DSC regime dominates.
FIG. 13 .
13Cavity and qubit emission rates (normalized with respect to the qubit emission rate W 0 q calculated for η = 0) Wc = Wc/W 0 q (blue-continuous curve), and Wq = Wq/W 0 q (red-dashed) versus the light-matter normalized coupling strength η. We used ∆ = 0.3, corresponding to ωc/ωq = 1.3. The upper panel has been obtained for Tq = 5 × 10 −2 , the lower one for Tq = 5 × 10 −1 .
0 )
0FIG. 14. Normalized energy levels and transition energies versus η, for ∆ = 0.3 (ωc/ωq = 1.3). (a) lowest normalized energy levels (with the ground state energy as reference) ωj ± − ω0 of the QRM. (b) Normalized parity-allowed transition energies |ωj ± − ωk ± | for the lowest eigenstates of the QRM.
FIG. 15 .
15Cavity Sc(ω) and qubit Sq(ω) emission spectra in the weak and strong coupling regime, calculated for 10 −3 < η < 10 −1 , and for ∆ = 0.3 (ωc/ωq = 1.3). The spectra have been obtained under weak incoherent excitation of the qubit.
FIG. 16 .
16Cavity emission spectra Sc(ω) for values of η reaching the USC and DSC regimes, obtained for two different effective qubit temperatures Tq = 0.05, 0.2. We used ∆ = 0.3 (ωc/ωq = 1.3).
FIG. 17 .
17Qubit emission spectra Sq(ω) for values of η reaching the USC and DSC regimes, obtained at Tq = 0.2. We used ∆ = 0.3 (ωc/ωq = 1.3). The spectra have been normalized, so that the highest peak is set at 1. The visible lines correspond to transition energies shown inFig. 2. The origin of the flat (red) signal background for η > 1.5 is explained in the text [see Eq.(28)].
FIG. 19 .
19Cavity emission spectra Sc(ω) for values of η reaching the USC and DSC regimes with the JCM, obtained with an effective qubit temperature Tq = 0.5. We used ∆ = 0. The spectra have been normalized, so that the highest peak in each density plot is set at 1. As predicted, the model drastically fails above the USC regime.
FIG. 21 .
21Cavity emission spectra Sc(ω) for values of η reaching the USC and DSC regimes using the dressed master equation, obtained with an effective qubit temperature Tq = 0.5.
two authors (A.M. and V.M) equally contributed to this work. F.N. is supported in part by: Nippon Telegraph and Telephone Corporation (NTT) Research, the Japan Science and Technology Agency (JST) [via the Quantum Leap Flagship Program (Q-LEAP), the Moonshot R&D Grant Number JPMJMS2061, and the Centers of Research Excellence in Science and Technology (CREST) Grant No. JPMJCR1676], the Japan Society for the Promotion of Science (JSPS) [via the Grants-in-Aid for Scientific Research (KAKENHI) Grant No. JP20H00134 and the JSPS-RFBR Grant No. JPJSBP120194828], the Army Research Office (ARO) (Grant No. W911NF-18-1-0358), the Asian Office of Aerospace Research and Development (AOARD) (via Grant No. FA2386-20-1-4069), and the Foundational Questions Institute Fund (FQXi) via Grant No. FQXi-IAF19-06. S.S. acknowledges the Army Research Office (ARO) (Grant No. W911NF-19-1-0065). S.H. thanks the Natural Sciences and Engineering Research Council of Canada, the Canadian Foundation for Innovation, the National Research Council of Canada, and Queen's University. Appendix A: Cavity-and qubit-bath interactions from the gauge principle
where (σ x ) lm = l |σ x |m are the matrix elements of the Pauli x-operator, being |l the energy eigenstates of the Rabi Hamiltonian in dipole gauge [Eq. (10) in Sec. II B].Finally, in terms of positive and negative frequencies of the qubit dressed-operators and applying the RWA
p m are gauge-invariant probabilities the quantum states |ψ m are gauge-dependent. If |ψ m are obtained
of Eq. (B1), we can write Eq. (B10) in the Coulomb gauge as Tr Ôρ = −i Tr Ô [Ĥ R ,ρ] + Tr Ô L gρ (B11) = −i j j|Ô[Ĥ R ,ρ]|j + j j|ÔL gρ |j .
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Introduction
Through the discovery of Schrödinger the theoretical physics community attained a powerful tool for computing atomic spectra, either exactly or in perturbation expansion. Born and Oppenheimer [4] immediately strived for a more ambitious goal, namely to understand the excitation spectrum of molecules on the basis of the new wave mechanics. They accomplished to exploit the small electron/nucleus mass ratio as an expansion parameter, which then leads to the static Born-Oppenheimer approximation. Since then it has become a standard and widely used tool in quantum chemistry supported by a vast number of mathematical results, the classical ones being [6,12,18].
Beyond excitation spectra and stationary scattering, dynamical processes gain increasingly in interest. Examples are chemical reactions or the decay of an excited state of a molecule. Such problems are conveniently described within a time-dependent version of the Born-Oppenheimer approximation, which is the topic of this article. The starting point is the observation that the electronic energy at fixed position of the nuclei serves as an effective potential between the nuclei. We call this the zeroth order Born-Oppenheimer approximation. The resulting effective Schrödinger equation can be used for both static and dynamic purposes. Of course, the input is an electronic structure calculation, which for the purpose of our article we regard as given by other means.
While there are many physical and chemical properties of molecules explained by the zeroth order Born-Oppenheimer approximation, there are cases where higher order corrections are required. Famous examples are the dynamical Jahn-Teller effect and the tunneling of singled out nuclear degrees of freedom at a conical intersection of two Born-Oppenheimer energy surfaces. The first order Born-Oppenheimer approximation involves geometric phases, which are of great interest also in other domains of non-relativistic quantum mechanics [3].
Keywords and phrases: Schrödinger equation, Born-Oppenheimer approximation, adiabatic methods, almost-invariant subspace.
Our plan is to repeat in some detail the conventional argument for the first order Born-Oppenheimer approximation. Only then the reader will appreciate why a more systematic approach is in demand, which will be the focus of our contribution.
Let us start from the molecular Hamiltonian
H mol = − 2 2m n ∆ x − 2 2m e ∆ y + V (x, y) .(1)
Here x = {x 1 , . . . , x K } are the positions of the K nuclei and y = {y 1 , . . . , y N } the positions of the N electrons.
The electrons have mass m e and the nuclei have, for notational simplicity, all the same mass m n . V (x, y) is the interaction potential, i.e. the Coulomb potential for electrons and nuclei. For the mathematical results to be valid in the form we present them, one needs to slightly smear out the charge distribution of the nuclei. This is in line with the physical picture that nuclei are not pointlike but extended objects. We transform (1) to atomic coordinates such that = 1 = m e and ε = m e m n ,
which will be our small dimensionless expansion parameter. Then (1) becomes
H ε = − 1 2 ε 2 ∆ x + H e (x)(3)
with the electronic Hamiltonian H e (x) = − 1 2 ∆ y + V (x, y) , (4) which depends through V parametrically on x. For complex molecules, one is often forced to model only a carefully chosen subset of degrees of freedom. We assume here that the final form is still as in (3) at the expense of a suitable modification of H e (x). Implicitly with (3) it is required that the initial wave function has a kinetic (and hence also a total) energy which is bounded independently of ε. Thus the nuclei move slowly.
The electronic structure problem is the eigenvalue equation
H e (x)χ j (x) = E j (x)χ j (x)(5)
with χ j ∈ H f , the Hilbert space for the electronic degrees of freedom. Here "f" is supposed to remind of fast.
Since electrons are fermions, in our case H f = S a L 2 (R 3N ) with S a projecting onto the antisymmetric wave functions. The eigenvectors in (5) are normalized as χ j (x) , χ j ′ (x) H f = δ jj ′ with respect to the scalar product in H f . Note that the eigenvectors are determined only up to a phase ϑ j (x). Their smooth dependence on x will be addressed with more care below. Generically, in addition to the bound states, H e (x) has continuous spectrum. We label the eigenvalues in (5) as
E 1 (x) ≤ E 2 (x) ≤ . . . ,(6)
including multiplicity. The graph of E j is the j-th Born-Oppenheimer energy surface. As a rule they have a complex structure with many crossings and avoided crossings. Let ψ(x) be a nucleonic wave function, ψ ∈ H s , with "s" reminding of slow. For simplicity we take H s = L 2 (R 3K ), remembering that to impose the physically correct statistics for the nuclei requires extra considerations [23]. States with the property that the electrons are precisely in the j-th eigenstate are then of the form
ψ(x) χ j (x, y) ,(7)
which we can think of either as a wave function in the total Hilbert space H = H s ⊗ H f or as a wave function for the electrons depending parametrically on x. In the latter case we abbreviate as ψ(x)χ j (x) ∈ H f for each x.
With this notation the projection operator onto the states of the form (7) is given by
P j = |χ j (x) χ j (x)| .(8)
Since the χ j (x)'s are orthonormal, P j is indeed an orthogonal projection. In a molecular collision or in excitations through a laser pulse only a few energy surfaces take part in the subsequent dynamics. Thus we take a set I of adjacent Born-Oppenheimer surfaces and call
P = j∈I |χ j (x) χ j (x)|(9)
the projection onto the relevant subspace (or subspace of physical interest). To ensure that other bands are not involved, we assume them to have a spectral gap of size a gap > 0 away from the energy surfaces in I, i.e.
|E i (x) − E j (x)| ≥ a gap for all j ∈ I , i ∈ I c .(10)
Also the continuous spectrum is assumed to be at least a gap away from the relevant energy surfaces. If ε = 0, then
e −iH 0 t ψ(x)|χ j (x) = e −iEj(x)t ψ(x) |χ j (x) .(11)
However, the Laplacian −ε 2 ∆ x weakly couples the x-fibers and P H is a subspace which is not invariant under the true unitary propagator exp[−iH ε t]. Still, we take
P H ε P(12)
as an approximate Hamiltonian for the time evolution in the relevant subspace P H. To compute P H ε P we choose ϕ, ψ ∈ P H, to say ψ(x, y) = j∈I ψ j (x)χ j (x, y) with ψ j ∈ H s and similarly for ϕ, and sandwich to the right and left as
ϕ, Hψ = m,n∈I dx ϕ m (x) * χ m (x), H ε χ n (x) H f ψ n (x) (13) = m,n∈I dx ϕ m (x) * δ mn E m (x) + 1 2 ε 2 − δ mn ∆ − ∇ · χ m (x), ∇χ n (x) H f + ∇χ m (x), χ n (x) H f · ∇ + ∇χ m (x), ·∇χ n (x) H f ψ n (x) , = dxφ m (x) * (P H ε P ) mn ψ n (x) ,(14)
where all derivatives are with respect to x. It is thus natural to introduce the geometric phase, or Berry connection,
A mn (x) = i χ m (x) , ∇χ n (x) H f , A mn (x) * = A nm (x) .(15)
Here, for each x, χ j (x), j ∈ I, is completed to an orthonormal basis through χ j , j ∈ I c . We also define the nuclear momentum operator p = −iε∇. Noting that ∇χ m , χ n + χ m , ∇χ n = 0 and inserting in the last term of (13), one obtains
(P H ε P ) mn = E m (x)δ mn + 1 2 ℓ∈I p δ mℓ − εA mℓ (x) · p δ ℓn − εA ℓn (x) + 1 2 ε 2 ℓ∈I c A mℓ (x) · A ℓn (x) .(16)
P H ε P acts on wave functions of the form ψ n (x), n ∈ I, i.e. ψ ∈ H s ⊗ C |I| .
To make further progress we concentrate on two cases of physical interest. 1) Let |I| = 1, I = {j}, i.e., we consider a single nondegenerate energy band, which by assumption is isolated from the remaining energy bands. Then χ j (x) can chosen to be real and smooth, which implies
A jj (x) = 0 .(17)
In other words, by a suitable choice of the phase ϑ j (x), see below equation (5), i.e., by a suitable gauge, the geometric phase can be made to vanish. According to (13) this results in
(P H ε P ) jj = 1 2 p 2 + E j (x) + 1 2 ε 2 φ(x)(18)
with the Born-Huang potential
φ(x) = ∇χ j (x) , (1 − |χ j (x) χ j (x)|) · ∇χ j (x) H f .(19)
2) Let |I| = 2. For convenience we label as m, n = 0, 1. E 0 (x) and E 1 (x) are allowed to cross. To be very specific, and to link to Section 3, let us assume that x ∈ R 2 and E 0 (0) = E 1 (0), while E 0 (x) = E 1 (x) otherwise. As first pointed out by Mead and Truhlar [23], if one insists on smoothness of the eigenbasis away from x = 0, then χ 0 (x), χ 1 (x) are necessarily complex-valued. A mn (x), m, n = 0, 1, corresponds to a vector potential with a magnetic field which is concentrated at x = 0 and which cannot be gauged away. As to be explained in more detail in Section 3, in principle, there are then two choices. In the subspace P H one can work in the adiabatic basis, adopted here, at the expense of having singular coefficients at x = 0. The alternative choice is to pick some diabatic basis, which is not an eigenbasis of H e , but has the advantage that in this representation P H ε P depends smoothly on x.
The conventional derivation of the time-dependent Born-Oppenheimer approximation leaves two points in the dark.
(i) Since the total energy is fixed, the nuclei move slowly and thus one has to follow their dynamics over a sufficiently long time to see a nontrivial dynamics. In our units the velocities are of order ε, hence times have to be of order ε −1 . At the zeroth order Born-Oppenheimer approximation one neglects terms of order ε in the intra-band Hamiltonian P H ε P , which over times of order ε −1 add up to an error of order 1 in the wave function. Thus on this time-scale the first-order Born-Oppenheimer approximation, i.e. the inclusion of the Berry connection term, becomes mandatory. But there is a more subtle problem with the standard derivation. Since the commutator [P, H ε ] is of order ε, it is not clear a priori, cf. (20), if states of the form (7) remain even approximately of this form for the relevant times of order ε −1 , put differently, if P H is approximately invariant under the time evolution generated by H ε for sufficiently long times. Again, this is because naively the order ε error in the generator may add up to an error of order 1 during times of order ε −1 . Thus the substitution of H ε by P H ε P needs justification.
(ii) If one wants to have the motion of nuclei at higher precision, then the simple ansatz (7) becomes questionable. Rather one expects small corrections to the product form. From the way we have presented the computation it is not so clear how to include such effects.
In Section 2 we review mathematical results which settle the two issues raised. The justification of the first-order Born-Oppenheimer approximation as in [30] is based on generalizing the standard adiabatic theorem of quantum mechanics to a space-adiabatic theorem. The higher order corrections require a systematic scheme developed in [5,8,22,24,26,28] heavily based on pseudo-differential calculus with operator valued symbols, a method which traces back to the pioneering work of Sjöstrand [29]. We therefore refrain from explaining the general scheme in detail, but instead present the main ideas and a new elementary derivation of the correct second order Born-Oppenheimer Hamiltonian. Section 3 deals with applications where the higher order corrections are potentially of importance. In particular we discuss the motion near a conical intersection and the reactive scattering H 2 + H → H + H 2 .
Justification of the Born-Oppenheimer approximation and higher order corrections
In this section we explain several mathematical results concerning the validity of the Born-Oppenheimer approximation and higher order corrections to it. We do not restate precise mathematical theorems, which can be found in the quoted literature, but focus on structural aspects instead. To this end we first argue how the gap in the conventional derivation of the Born-Oppenheimer approximation, as discussed in the introduction, can be closed. This understanding will open up the way to systematically determine also the higher order corrections to the Born-Oppenheimer approximation. While the general theory describing higher order corrections is rather technical, in Section 2.2 we present an elementary computation which yields the second order in ε corrections to the Born-Oppenheimer approximation.
Justification of the time-dependent Born-Oppenheimer approximation
In the conventional derivation of the zeroth and first order Born-Oppenheimer approximation the effective Born-Oppenheimer Hamiltonian is obtained by expanding P H ε P in powers of ε, where P projects on wave functions of the form (7). As explained under point (i) above, there is left open an important point in this derivation. For P H ε P to be a valid effective Hamiltonian in the first place, the dynamics generated by P H ε P for initial states in P H must be close to the one generated by the true Hamiltonian H ε for sufficiently long times, i.e. the difference e −iH ε t/ε − e −iP H ε P t/ε P must be small in an appropriate sense. The Duhamel formula yields
e −iH ε t/ε − e −iP H ε P t/ε P = ie −iH ε t/ε t/ε 0 ds e iH ε s (P H ε P − H ε ) e −iP H ε P s P = ie −iH ε t/ε t/ε 0 ds e iH ε s (P H ε P − H ε ) P e −iP H ε P s = ie −iH ε t/ε t/ε 0 ds e iH ε s [P, H ε ] P e −iP H ε P s .(20)
When acting on wave functions with kintic energy of order 1, i.e. ε∇ψ ε 2 = O(1), the commutator
[P, H ε ]P = j∈I |χ j (x) χ j (x)|, − ε 2 2 ∆ x P = O(ε)
contains terms of order ε but not smaller, independently of the choice of χ j (x). Thus in (20) a naive estimate of the right hand side yields an error of order 1. This is because the smallness of the integrand is cancelled by the growing domain of integration. Hence it is not clear from a naive perturbation argument that the dynamics generated P H ε P and thus the Born-Oppenheimer approximation is close to the true dynamics for sufficiently long times. This is directly linked to the question, whether the subspace P H of wave functions of the form (7) is invariant under the true dynamics for sufficiently long times. We stress this point, because the question of invariance of subspaces on which one approximates the dynamics by an effective Hamiltonian is crucial for understanding the higher order corrections to the Born-Oppenheimer approximation.
For the case of the first order Born-Oppenheimer approximation it was shown in [30] how to use arguments similar to those used in the proof of the adiabatic theorem by Kato [17] in order to prove approximate invariance of P H. In such a space-adiabatic theorem, the positions x of the nuclei take the role played by time t in usual time-adiabatic theory. The mechanism is that the integrand in (20) is oscillatory and therefore the errors of order ε in the integrand cannot add up to an error of order 1 even for a domain of integration of size 1/ε. The statement proved in [30] (with some typos in the proof corrected in [31]) is the following: Let P E := 1 (−∞,E] (H ε ) be the spectral projection of H ε on energies below E. Then there exists a constant C < ∞ independent of ε such that
e −iH ε t/ε − e −iP H ε P t/ε P P E B(H) ≤ C ε (1 + |t|) (1 + |E|) ,(21)
where · B(H) is the norm of bounded operators. Thus on subspaces of finite total energy the adiabatic approximation holds with a uniform error of order ε. Note that (21) holds also with P E replaced by 1 (−∞,E] (− ε 2 2 ∆), i.e. for finite kinetic energies of the nuclei. For large kinetic energies the velocities of the nuclei are no longer small compared to those of the electrons and thus the adiabatic approximation breaks down.
Clearly the first order Born-Oppenheimer approximation now follows from (21) by expanding the adiabatic Hamiltonian P H ε P as in (13). If we define the first order Born-Oppenheimer Hamiltonian as
H (1) ε = m,n∈I |χ m (x) E m (x)δ mn + 1 2 ℓ∈I p δ mℓ − εA mℓ (x) · p δ ℓn − εA ℓn (x) χ n (x)| ,(22)
where we omit one term of order ε 2 in (13), then
e −iH ε t/ε − e −iH (1) ε t/ε P P E B(H) ≤C ε (1 + |t|) (1 + |E|) .(23)
By now it is obvious why we cannot improve the approximation simply by adding the ε 2 terms in the expansion of P H ε P to the effective Hamiltonian. Their contribution is of the same order as the error in the adiabatic approximation (21). One might hope that the order of the error in (21) can be improved by a more careful analysis. This is however not the case, as can be seen directly from the proof in [30] or, alternatively, from the scheme to be presented in the following. In particular there is no reason to expect that (13) is the correct second order Born-Oppenheimer Hamiltonian and indeed, it isn't.
Corrections to the time-dependent Born-Oppenheimer approximation
But then the question arises whether and in which sense is the first order time-dependent Born-Oppenheimer approximation the leading term in a systematic perturbation expansion? This problem was considered several times in the literature and the solutions differ not only with respect to the level of mathematical rigor but also the formulation of the result itself is not unique. In the following we explain the approach from [26] which heavily relies on methods developed by Martinez, Nenciu, and Sordoni [22,24]. The main idea is to replace the subspace P H by a so called almost invariant subspace P ε H, which is invariant under the full dynamics to higher accuracy than P H. Because of the very technical character of the general construction, we only sketch the main ideas and instead give an alternative derivation of the correct second order Born-Oppenheimer Hamiltonian not using the pseudo-differential operator machinery. We shortly comment on other approaches at the end of this section.
Since the range of P is invariant only up to an error of order ε, the form (7) is not adequate for higher order approximations. Instead one has to look for slightly tilted subspaces P ε H which are invariant under the dynamics generated by H ε with smaller errors. Indeed one can find an orthogonal projection P ε close to P such that for any n ∈ N there is a constant C n < ∞ independent of ε and t satisfying
e −iH ε t/ε − e −iP ε H ε P ε t/ε P ε P E B(H) ≤ C n ε n |t| .(24)
It turns out that the projected Hamiltonian P ε H ε P ε can be expanded in powers of ε as
P ε H ε P ε = n j=0 ε j H j + O(ε n+1 ) =: H ε (n) + O(ε n+1 ) ,
which together with (24) implies
e −iH ε t/ε − e −iH ε (n) t/ε P ε P E B(H) ≤C n ε n |t| .(25)
In the same fashion the projector P ε can be expanded in a Taylor series, which for the purpose of the estimates in (24) and (25) may be truncated at the appropriate order. Since the zeroth and first order Born-Oppenheimer Hamiltonians are just the leading terms in the expansion of H ε (n) , one could call H ε (n) the n-th order Born-Oppenheimer Hamiltonian. But H ε (n) is an effective Hamiltonian which acts on a ε-dependent subspace of the full Hilbert space H, while the usefulness of the standard Born-Oppenheimer approximation comes partly from the fact that the effective Hamiltonian acts on wave functions depending only on nuclear and possibly a few discrete electronic degrees of freedom. Before we explain how to remedy this shortcoming let us briefly explain how to construct the projector P ε .
The construction of the projection P ε follows a general scheme outlined by Emmerich and Weinstein [8], refined in [5] and [24], and finally applied to the Born-Oppenheimer approximation by Martinez and Sordoni [22]. The basic idea is to determine the coefficients P j in the expansion P ε (n) = P + n j=1 ε j P j order by order such that P ε (n) is approximately a projection and commutes with H ε up to terms of order ε n+1 . Writing P 0 = P it clearly holds that P 0 is a projection and that the commutator
[P 0 , H ε ] = P 0 , − ε 2 2 ∆ = iε(∇P 0 ) · (−iε∇) + ε 2 2 (∆P 0 )
is of order ε when acting on functions of bounded kinetic energy. One now determines P j inductively by requiring that
(P ε (n) ) 2 − P ε (n) = O(ε n+1 ) ,(26)P ε (n) , H ε = O(ε n+1 ) ,
and assuming the the analogous statement holds already for P ε (n−1) . While the general construction is most conveniently done using the theory of ε-pseudodifferential operators, let us explicitly determine P 1 from the above conditions. Because of
(P 0 + εP 1 ) 2 − (P 0 + εP 1 ) = ε(P 0 P 1 + P 1 P 0 − P 1 ) + O(ε 2 )
we must require that
P 1 = P 0 P 1 + P 1 P 0 + O(ε)(27)
in order to make the order ε term vanish. And the order ε term in
[P 0 + εP 1 , H ε ] = iε(∇P 0 ) · (−iε∇) + ε[P 1 , H e ] + O(ε 2 ) vanishes, if P 1 satisfies [P 1 , H e ] = i(∇P 0 ) · (iε∇) + O(ε) .(28)
To focus on the simplest case, from now on we assume that P 0 (x) projects onto the eigenspace of a single eigenvalue E j (x), i.e. that we are in the situation of item 1) in the introduction. In this special but most important case, the unique solution of (28) up to order ε is obtained by multiplying (28) from the left and from the right by P 0 resp. (1 − P 0 ). The block-diagonal terms are of order ε, since P 0 (∇P 0 )P 0 = (1 − P 0 )(∇P 0 )(1 − P 0 ) = 0. For the off-diagonal terms one can invert (H e − E j ) on the range of (1 − P 0 ) and finds that
P 1 = iP 0 (∇P 0 )(H e − E j ) −1 (1 − P 0 ) · (iε∇) + adj. = i(iε∇) · P 0 (∇P 0 )(H e − E j ) −1 (1 − P 0 ) + adj. + O(ε) ,
which also satisfies the requirement (27). The abbreviation + adj. means that the adjoint of everything to the left is added. Here and in the following we use the fact that the spectral projection P 0 (x) and the reduced resolvent (H e (x) − E j (x)) −1 (1 − P 0 (x)) are smooth function of x with values in the bounded operators on the electronic Hilbert space H f . This follows from the assumed smoothness of H e (x) and the gap condition. As a consequence the commutator of the momentum operator p = −iε∇ with any such operator yields only a lower order term in ε, a fact which will be used several times in the following computations.
In a next step the operator P ε (1) can be turned into a true orthogonal projection by adding a term of order ε 2 , see [24], which we denote again by P ε (1) . Now the question arises, whether the range of P ε (1) is invariant under the dynamics generated by H ε up to errors of order ε 2 . A naive perturbation argument as in (20) will only yield an error of order ε, which, however, could be improved using again the space-adiabatic approach of [30]. Alternatively the results of [22,26] show that instead of (21) we now have
e −iH ε t/ε − e −iP ε (1) H ε P ε (1) t/ε P ε (1) P E B(H) ≤ C ε 2 (1 + |t|)(1 + |E|) .(29)
With (29) we are in a position to determine an effective Hamiltonian on the range of P ε (1) by expanding P ε
(1) H ε P ε (1) in powers of ε and keeping terms up to order ε 2 . This improves the conventional first order Born-Oppenheimer approximation by one order. However, because of the momentum operator appearing in P 1 , the range of P ε (1) is not spanned by wave functions of the form ψ(x)χ ε j (x, y) as in (7). Therefore P ε ) can no longer be seen as an effective Hamiltonian acting on a nucleonic wave function ψ(x) alone. But this reduction in the degrees of freedom of the state space is the crucial feature which makes the first order Born-Oppenheimer approximation so useful. In order to retain this feature also for the higher order Born-Oppenheimer approximations we thus need to map the range of P ε (1) unitarily to the space L 2 (R 3K ) of nucleonic wave functions in the case of a simple electronic band or to L 2 (R 3K , C |I| ) in the case of a group of |I| bands. In [26] we construct a unitary operator U ε : P ε H → L 2 (R 3K , C |I| ) and define the effective Born-Oppenheimer Hamiltonian for the group of levels in I as
(1) H ε P ε(1H ε BO = U ε P ε H ε P ε U ε * ,(30)
i.e. the full Hamiltonian H ε is projected onto the almost invariant subspace associated with the levels in I and then unitarily mapped to the ε-independent space of nucleonic wave functions. Thus (24) becomes
e −iH ε t/ε − U ε * e −iH ε BO t/ε U ε P ε P E B(H) ≤ C n ε n |t| ,(31)
where e −iH ε BO t/ε is the effective Born-Oppenheimer propagator of the nuclei within the relevant group of bands up to any order in ε. The expansion of H ε BO in powers of ε yields at the leading orders the usual zeroth and first order Born-Oppenheimer Hamiltonian, i.e. the matrix in the brackets in (22), but in addition also the correct higher order terms.
In order to avoid the technicalities of the general construction, let us determine the correct second-order Born-Oppenheimer Hamiltonian for the special case of a singe simple level E j (x) by an elementary calculation. For this case we already computed P ε = P 0 + εP 1 + O(ε 2 ) with P 0 (x) = |χ j (x) χ j (x)| and
P 1 = −i(−iε∇) · P 0 (∇P 0 )(H e − E j ) −1 (1 − P 0 ) + adj. =: p · B + B * · p .
Here and in the following we abbreviate p = −iε∇ x for the momentum operator. Also for U ε we make the ansatz U ε = U 0 + εU 1 + O(ε 2 ) where clearly
U 0 (x) = χ j (x)|(32)
is unitary from P 0 H to L 2 (R 3K ). Note that at this point the construction of U ε is not unique since the choice of basis χ j (x) enters.
Without loss of generality we write U 1 = U 0 A for some operator A on H. Then the requirement that U ε * is unitary up to O(ε 2 ) yields
(U 0 + εU 1 )(U * 0 + εU * 1 ) = 1 + ε(U 0 A * U * 0 + U 0 AU * 0 ) + O(ε 2 ) ! = 1 + O(ε 2 ) .(33)
The requirement that the range of U ε * is the range of P ε up to O(ε 2 ) yields
(1 − P 0 − εP 1 )(U * 0 + εU * 1 ) = ε(A * − P 0 A * − P 1 )U * 0 + O(ε 2 ) ! = O(ε 2 ) ,
i.e. that
(1 − P 0 )A * = P 1 P 0 + O(ε) .
A solution of this equation is A * = B * · p, which also makes the O(ε) term in (33) vanish. Thus
U 1 = U 0 p · B
yields an almost unitary U ε (1) = U 0 + εU 1 that almost intertwines P ε (1) H and L 2 (R 3K ). It is important for the following that U ε (1) can be modified by a term ε 2 U ε 2 of order ε 2 (i.e. U ε 2 is O(1)) to make it a true unitary exactly intertwining P ε (1) H and L 2 (R 3K ). As in the case of P ε (1) we denote the modified operator U ε (1) = U 0 + εU 1 + ε 2 U ε 2 again by the same symbol. It is shown in [26] how to construct U ε 2 explicitly, but its exact form is not important for the following. We will only use that unitarity of the modified U ε (1) together with the fact that
U 1 U * 0 + U 0 U * 1 = U 0 P 1 U * 0 = 0 implies that U 1 U * 1 + U 0 U ε * 2 + U ε 2 U * 0 = O(ε) .(34)
We thus have that
e −iP ε (1) H ε P ε (1) t/ε P ε (1) = U ε * (1) U ε (1) e −iP ε (1) H ε P ε (1) t/ε U ε * (1) U ε (1) P ε (1) = U ε * (1) e −iU ε (1) P ε (1) H ε P ε (1) U ε * (1) t/ε U ε (1) P ε (1)(35)
and therefore with (29) that (35) approximates the true time evolution up to errors of order ε 2 ,
e −iH ε t/ε − U ε * (1) e −iU ε (1) P ε (1) H ε P ε (1) U ε * (1) t/ε U ε (1) P ε (1) P E B(H) ≤ C ε 2 (1 + |t|) .(36)
Hence we can now expand U ε (1) P ε (1) H ε P ε (1) U ε * (1) in powers of ε to obtain the second order Born-Oppenheimer Hamiltonian, which now acts on the ε-independent space L 2 (R 3K ) of nucleonic wave functions. The expansion yields
U ε (1) P ε (1) H ε P ε (1) U ε * (1) = U ε (1) H ε U ε * (1) = (U 0 + εU 1 + ε 2 U ε 2 ) p 2 2 + H e (U * 0 + εU * 1 + ε 2 U ε * 2 ) + O(ε 3 ) = U 0 p 2 2 + H e U * 0(37)+ ε U 0 p 2 2 + H e U * 1 + adj.(38)+ ε 2 U 1 p 2 2 + H e U * 1(39)+ ε 2 U 0 p 2 2 + H e U ε * 2 + U ε 2 p 2 2 + H e U * 0 + O(ε 3 ) .(40)
We evaluate the four terms (37)-(40) separately. Expanding (37) yields
U 0 p 2 2 + H e U * 0 = p 2 2 + E j + U 0 p 2 2 , U * 0 = p 2 2 + E j − iεU 0 (∇U * 0 ) · p − ε 2 2 U 0 (∆U * 0 ) = p 2 2 + E j − εA · p − ε 2 [p, A] + ε 2 2 ∇χ j , ·∇χ j = 1 2 (p − εA) 2 + E j + ε 2 2 φ ,(41)
where we abbreviated A(x) = iε χ j (x), ∇χ j (x) (42) for the Berry connection coefficient and
φ(x) = ∇χ j (x), ·(1 − P 0 )∇χ j (x)(43)
for the Born-Huang potential. This is, as expected, exactly the usual Born-Oppenheimer Hamiltonian (13). However, as explained before, in order to obtain the correct second order Born-Oppenheimer Hamiltonian, we also must take into account the terms (38)-(40) which stem from the fact, that not P H but P ε (1) H is the correct adiabatically invariant subspace at that order. Expanding (38) yields
U 0 p 2 2 + H e U * 1 + adj. = U 0 p 2 2 B * · p + p · B p 2 2 U * 0 + U 0 (H e B * · p + p · B H e ) U * 0 = U 0 [ p 2 2 , B * ] · p + p · [B, p 2 2 ] U * 0 = −iεU 0 (p · ∇B * · p − p · ∇B · p) U * 0 + O(ε 2 ) = −2ε U 0 p · P 0 (∇P 0 )(H e − E j ) −1 (∇P 0 )P 0 · p U * 0 + O(ε 2 ) =: −2εM(x, p) + O(ε 2 ) ,(44)
where we used that ∇BP 0 = iP 0 (∇P 0 )(H e − E j ) −1 (∇P 0 )P 0 and P 0 ∇B * = −iP 0 (∇P 0 )(H e − E j ) −1 (∇P 0 )P 0 . Recall that the differences in operator ordering between p = −iε∇ x and operators depending on x are of lower order in ε. So any other operator ordering for the quantization of M(x, p) than the one used in (38) works as well at the given order. Put differently, any quantization rule for the symbol (=function)
M(x, p) = U 0 p · P 0 (∇P 0 )(H e − E j ) −1 (∇P 0 )P 0 · p U * 0 = ∇χ j · p, (H e − E j ) −1 (1 − P 0 ) p · ∇χ j H f(45)
will do the job. The simplest symmetric choice for M is presumably
(Mψ)(x) = 3K ℓ,k=1 1 2 m ℓk (x)(−iε∂ x ℓ )(−iε∂ x k ) + (−iε∂ x ℓ )(−iε∂ x k )m ℓk (x) ψ(x) ,
where m is the x-dependent matrix
m ℓk (x) = ∂ ℓ χ j (x), (H e (x) − E j (x)) −1 (1 − P 0 (x)) ∂ k χ j (x) H f For (39) we find U 1 ( p 2 2 + H e )U * 1 = U 0 p · B( p 2 2 + H e )B * · p U * 0 = U 0 p · B(H e − E j )B * · p U * 0 + U 0 p · B( p 2 2 + E j )B * · p U * 0 = U 0 p · P 0 (∇P 0 )(H e − E j ) −1 (∇P 0 )P 0 · p U * 0 + U 0 p · BB * · p U * 0 ( p 2 2 + E j ) + O(ε) = M(x, p) + U 1 U * 1 ( p 2 2 + E j ) + O(ε) .(46)
Finally the term (40) cancels the second remaining term in (46):
U 0 p 2 2 + H e U ε * 2 + U ε 2 p 2 2 + H e U * 0 = U 0 p 2 2 + E j U ε * 2 + U ε 2 p 2 2 + E j U * 0 = (U 0 U ε * 2 + U ε 2 U * 0 ) p 2 2 + E j + O(ε) = −U 1 U * 1 ( p 2 2 + E j ) + O(ε) ,(47)
where we used (34). Collecting all the results we find for the second order Born-Oppenheimer Hamiltonian of a simple isolated eigenvalue band E j that
H ε BO = 1 2 (p − εA(x)) 2 + E j (x) + ε 2 2 φ(x) − ε 2 M(x, p) ,(48)
where we recall that p = −iε∇ x and that A(x), φ(x) and M(x, p) are defined in (42), (43) and (45). The relation between the dynamics generated by the Born-Oppenheimer Hamiltonian H ε BO and the true time evolution is now
e −iH ε t/ε − U ε * (1) e −iH ε BO t/ε U ε (1) P ε (1) P E B(H) ≤ C ε 2 (1 + |t|) .(49)
Put differently, one can construct approximate solutions Ψ BO (t) to the full molecular Schrödinger equation
iε∂ t Ψ(t, x, y) = H ε Ψ(t, x, y) , Ψ(t) ∈ L 2 (R 3K ) ⊗ H f (50)
by solving the effective Born-Oppenheimer Schrödinger equation for the nuclei only
iε∂ t ψ(t) = H ε BO ψ(t) , ψ(t) ∈ L 2 (R 3K ) ,(51)
and defining Ψ BO (t) = U ε * (1) ψ(t). The difference between Ψ BO (t) and the true solution of (51) with the same initial condition Ψ(0) = Ψ BO (0) ∈ P ε (1) P E H is of order ε 2 in the norm of H. However, there are many cases where it suffices to know ψ(t) and it is not necessary to map it back to a full molecular wave function Ψ BO (t). For example for the position distribution of the nuclei one has that
Ψ BO (t, x), Ψ BO (t, x) H f = U ε * (1) ψ(t, x), U ε * (1) ψ(t, x) H f = |ψ(t, x)| 2 + O(ε 2 ) .
We continue with several remarks on the second order Born-Oppenheimer Hamiltonian. The correct second order Born-Oppenheimer Hamiltonian (48) contains the additional term ε 2 M(x, p) as compared to the conventional expression containing terms of that order, see (18), (19). In contrast to the Born-Huang potential φ(x), M(x, p) introduces a velocity-dependent correction in the form of an x-dependent effective mass tensor m. In Section 3 we compute H ε BO explicitly near a conical intersection of electronic energy levels, where the corrections to the conventional first order Born-Oppenheimer approximation become important. A further issue is the gauge invariance of H ε BO . The Berry connection coefficient A(x) clearly depends on the choice of χ j (x) and, in our particular context, can be made to vanish by a suitable choice of phase. However, although defined through χ j (x), the terms of order ε 2 are gauge invariant, as can be seen from writing them only by means of the projection P 0 (x),
φ(x) = Tr H f ∇P 0 (x) · ∇P 0 (x) (1 − P 0 (x) ,(52)M(x, p) = Tr H f p · ∇P 0 (x) 2 H e (x) − E j (x) −1 1 − P 0 (x) .(53)
In general, the structure of H ε BO is that of a semiclassical Hamiltonian for the nuclei, since the momentum operator still carries the small parameter ε. Therefore it is natural to study in a second step the semiclassical limit of the nuclear Schrödinger equation (51). There is a variety of methods available for such a semiclassical analysis, most prominently the WKB approximation, semiclassical wave packets and Wigner functions. All these techniques have been applied to further study the standard Born-Oppenheimer approximation and can also be used to investigate the higher order Born-Oppenheimer approximations. But since the semiclassical limit is conceptually and mathematically different from the adiabatic approximation considered here, we do not further comment on it.
We conclude this section with a few remarks on the literature. In the physics literature the correct second order Born-Oppenheimer Hamiltonian (48) was first obtained by Weigert and Littlejohn in [32] for the case of matrix valued H e (x). They approximately diagonalize the Hamiltonian H ε on the full space H, while we first reduce to an appropriate adiabatic subspace corresponding to the electronic levels of interest and then approximate the Hamiltonian on that subspace. This has the advantage that we can allow for H e (x) having continuous spectrum or level crossings outside the spectral part of interest.
Another mathematical approach to the time-dependent Born-Oppenheimer approximation, historically the first one, is due to Hagedorn and later Hagedorn and Joye [11,13,14,16]. In their approach the goal is not to construct an approximate Born-Oppenheimer Hamiltonian but to find directly approximate solutions of the molecular Schrödinger equation. This is achieved by approximating the nucleonic wave function by localized semiclassical wave packets. Hence, in the Hagedorn/Joye approach the adiabatic and the semiclassical approximation are done in one package.
Dynamics near conical crossings
The aim of this section is twofold. In the first part we show how the previous scheme extends to a family of energy bands, yielding a multiband effective Hamiltonian. While this effective Hamiltonian is the starting point for an analysis of the propagation of the wavefunction through eigenvalue crossings, we will not address this interesting problem here and instead refer the reader to the literature [9,10,15,19], see also [7] for a related result in a time-independent setup.
In the second part, Section 3.2, we return to the one-band Born-Oppenheimer dynamics and study in a simple case the behavior of the Berry connection A and of the second-order corrections φ and M near a conical crossing. We argue that this behavior is, in a sense, universal and leads potentially to observable effects in chemical exchange reactions.
The multiband effective Hamiltonian
We consider a family of ℓ eigenvalue bands {E j } j∈I , | I | = ℓ, which may cross each other but which are separated by a gap from the rest of the spectrum, see (10). We denote as P 0 (x) the eigenprojector of H e (x) corresponding to such a family of bands, with dim Ran P 0 (x) = ℓ.
By the construction outlined in the previous section, to such a family of bands there corresponds an almostinvariant subspace. More precisely one constructs an orthogonal projector P ε = P 0 + Ø(ε) satisfying (24). In order to describe the dynamics inside the almost-invariant subspace in a physically transparent way, one constructs a unitary operator U ε which intertwines Ran P ε and a reference space, i.e.
U ε : Ran P ε → H ref := L 2 (R 3K , C ℓ ).(54)
To the lowest order U ε = U 0 + Ø(ε), with
U 0 (x) = ℓ a=1 |e a ϕ a (x)| ,(55)
where {e a } a=1,...,ℓ is the canonical basis in C m and {ϕ a (x)} a=1,...,ℓ is any orthonormal basis spanning Ran P 0 (x) and depending smoothly on x. The freedom in choosing such a basis is an additional feature with respect to the previous section. If {ϕ a } a=1,...,ℓ is any such basis, by the construction in [26] one obtains a self-adjoint operator H ε BO , such that (31) is satisfied. It has the asymptotic expansion
H ε BO := U ε P ε H ε P ε U ε * = 1 2 p 2 + W (q) + ε 2 (p · A(x) + A(x) · p) + Ø(ε 2 ),(56)
where we introduced the ℓ × ℓ matrices
W (x) ab = ϕ a (x), H e (x) ϕ b (x) H f , A(x) ab = i ϕ a (x), ∇ϕ b (x) H f , a, b = 1, . . . , ℓ.(57)
The eigenvalues of W (x) are the energies {E j (x)} j∈I of the electronic Hamiltonian H e (x). The expansion in the second line of (56) is the generalization of (22) to the case of an arbitrary basis.
Since H e , as defined in (4), satisfies time-reversal symmetry the eigenfunctions {ϕ a } a=1,...,ℓ can be chosen to be real valued. With this restriction W (x) becomes a real symmetric matrix and iA(x) becomes a real antisymmetric matrix, in particular with vanishing diagonal elements.
The effective Hamiltonian (56) is clearly not unique. Indeed, one can consider a different basis {φ a } a=1,...,ℓ , with
ϕ a (x) = ℓ b=1 G(x) ab ϕ b (x)
where G(x) is some orthogonal matrix depending smoothly on x. The elements of the effective Hamiltonian in these two basis are related by
W (x) = G(x) −1 W (x) G(x),(58)A(x) = G(x) −1 A(x) G(x) + G(x) −1 ∇G(x).(59)
Notice that, even with time-reversal symmetry, in general the Berry connection A cannot be removed by a change of basis (a non-abelian change of gauge). Indeed, by (59) this is possible if and only if there exist a smooth solution G(x) of the system of differential equations
∂ i G(x) = −A i (x) G(x), i = 1, . . . , 3K,
which as a necessary condition requires the vanishing of the corresponding matrix valued field
ω ij = −i (∂ i A j − ∂ j A i ) + A j A i − A i A j .
The non-uniqueness of the effective multiband Hamiltonian (56) is irrelevant as far as expectation values of physical observables are concerned, since a change of basis affects both the Hamiltonian operator and the operator representing the observable quantity. However, the dependence on the basis may be relevant if one considers H ε BO as a bona fide model Hamiltonian to investigate the dynamics of the wavefunction in a family of bands. We will comment on this point in the following.
Higher-order corrections near conical crossings
We come back to the one-band Born-Oppenheimer dynamics, i.e. I = {j}, but consider now the case when the relevant energy band E j crosses other bands, so that (10) does not hold. The dynamics of a wavepacket localized far away from the crossing points, and in the almost-invariant subspace corresponding to the relevant energy band E j , is approximately governed by the Born-Oppenheimer Hamiltonian (48). (While in Section 2 we discussed only the case of a globally isolated energy band, the more general case has been studied in [26,31]). Since the adiabatic approximation breaks down near conical crossings one expects that the higher order corrections A, φ and M diverge near such crossings. It has been pointed out by Berry and Lim [2] that the Born-Huang potential φ creates a diverging repulsive force at the crossing points, and some authors argued that the wavefunction must vanish at those points. While it is certainly true that φ leads to a repulsive force, we emphasize that a complete analysis should take into account all contributions coming from the second order corrections.
Since a crossing involves generically just two bands, we focus on a family of ℓ = 2 bands, E ± , separated by a gap from the rest of the spectrum. We also focus on the case of conical crossings [15], which are, in a sense, the simplest non-trivial kind of crossings. The set of conical crossing points M con ⊂ R 3K is generically a manifold of codimension 2, see [25]. Since we are interested in the dynamics in the transverse direction we immediately assume x ∈ R 2 , x = 0 being the only conical crossing point. The conical structure at crossing means that E ± (x) = ±C ± |x| as |x| → 0.
The dynamics for the family {E + , E − } is approximately described by an effective Hamiltonian in the form (56). The choice of the basis appearing in (55) requires particular care near conical crossing points. As pointed out already, away from the crossing manifold it is convenient to use the adiabatic basis, i.e. a basis {χ a } a=± consisting of eigenfunctions of the electronic Hamiltonian, see (5). Such a basis is uniquely defined, up to a choice of the phases, away from the crossing manifold. Clearly, with this choice, W (x) becomes a diagonal matrix. On the other hand, ∇χ(x) generically diverges as x approaches a conical crossing, and so does the Berry connection term, yielding an effective Hamiltonian with singular coefficients. Diverging quantities are unstable when numerical discretization schemes are employed. Thus, if one is mainly interested in the dynamics near the crossing points, it is advantageus to skip condition (5), and to work in a different basis, with the property that it depends smoothly on x. Such a basis is called diabatic.
The next step is a reasonable truncation of the ε-expansion appearing in (56). We are interested in the oneband Born-Oppenheimer dynamics near a conical crossing, where the functions A + , φ + and M + are singular. Thus in (56) we retain the terms of order O(1) and between the terms of O(ε) or higher we retain only the singular contributions. Therefore, if (56) is written in a diabatic basis, so that A(x) is a smooth function, we truncate the expansion in (56) at the leading order, obtaining the model Hamiltonian H dia = 1 2 p 2 + W (x) (in a suitable diabatic basis). Viceversa, if the adiabatic basis is used, the singular term p · A + A · p has to be included.
The singular behavior of A + at the conical crossing does not depend on the choice of the basis in (55). Indeed, in the adiabatic basis W (x) is diagonal, and the one-band Berry connection for the upper band is given by A adia, + = i χ + , ∇χ + H f . On the other side, in a generic basis {ϕ a } a=1,2 one has a non-diagonal W (x) with eigenvectors ξ ± (x) ∈ C 2 . In this basis the O(ε) term contains
A dia, + (x) = i ξ + (x), A(x) ξ + (x) C 2 + i ξ + (x), ∇ξ + (x) C 2 ,(60)
where A(x) ab = i ϕ a (x), ∇ x ϕ b (x) H f . The first term in (60) corresponds to the reduction from H e to the 2-band Hamiltonian (56), while the second term is due to the reduction to a specific energy band, namely E + . Note that in the diabatic representation the singular contributions come from the eigenvectors ofW , while the first term in (60) is smooth and can thus be neglected for our purposes. The two basis are related by χ a (x) = b G ab (x)ϕ b (x), with G(x) an orthogonal matrix smoothly depending on x outside the crossing point.
With the help of (58) and (59) one easily checks that A dia, + = A adia, + . A similar behavior is expected for the second order terms φ + and M + , although we are not in position to discuss this point here.
With the purpose of having an explicit example, we now focus on the model Hamiltonian H dia = − 1 2 p 2 +W (x), acting in L 2 (R 2 , C 2 ), with x = (x 1 , x 2 ) = (|x| cos ϕ, |x| sin ϕ) and
W (x) = C x 1 x 2 x 2 −x 1 = C |x| cos ϕ sin ϕ sin ϕ − cos ϕ , C > 0.(61)
We freely switch between polar and cartesian coordinates in the following. The eigenvalues of W (x) are E ± (x) = ±C |x| and a smooth family of eigenfunctions for x = 0 is given by
ξ + (x) = e iϕ/2 cos ϕ 2 sin ϕ 2 ξ − (x) = e iϕ/2 − sin ϕ 2 cos ϕ 2 .(62)
A direct computation yields
∇ξ + (x) = 1 2|x| (ξ − (x) + iξ + (x)) e ϕ , ∇ξ − (x) = 1 2|x| (−ξ + (x) + iξ − (x)) e ϕ ,(63)
where e ϕ = |x| −1 (x 2 , −x 1 ) in cartesian coordinates. The derivatives ∇ξ ± are divergent at the crossing point. One easily computes the higher order Born Oppenheimer approximation for the upper band, with the result
A + (x) = i ξ + (x), ∇ x ξ + (x) = − 1 2|x| e ϕ ,(64)φ + (x) = ∇ x ξ + , ·(1 − P + (x))∇ x ξ + = 1 4|x| 2 .(65)
Using (W (x) − E + (x)) −1 (1 − P + (x)) = − 1 2C|x|
(1 − P + (x)) one obtains
M + = 1 2C|x| 2 i,j=1 p i ∂ i ξ + (x), (1 − P + (x)) ∂ j ξ + (x) p j = L(x, p) 1 4C|x| 5 L(x, p),(66)
where L(x, p) = x 1 p 2 − x 2 p 1 is the angular momentum operator. Thus the effective Born-Oppenheimer Hamiltonian to second order reads
h + = 1 2 p + ε 2|x| e ϕ 2 + C |x| + ε 2 1 4|x| 2 + ε 2 L(x, p) 1 4C|x| 5 L(x, p) + O(ε 3 ).
For the Hamiltonian of the lower band only M − = −M + changes, while A − = A + and φ − = φ + . The inversesquare potential corresponds to the repulsive force of Berry and Lim. On the other side, M contributes to the effective Hamiltonian with a more singular term, whose sign depends on the electronic state: on the upper band it leads to a repulsive force, while on the lower band it is of the same order, but attractive. In both cases it may dominate the contribution coming from the Born-Huang potential.
It is instructive to reexpress H dia in the basis (62). Denoting by S the unitary operator corresponding to the change of basis, one gets
H adi := S H dia S −1 = 1 2 p 2 + E + (x) 0 0 E − (x) − ε |x| e ϕ · p 1 i −i 1 + ε 2 2|x| 2 1 i −i 1 .
Since the transformation is unitary, no information as compared to H dia has been discarded. If for the dynamics in the upper band one merely restricts H adi to a, b = +, one recovers the Born-Huang potential but misses the M correction. So far we focused on the specific model (61). One may ask wether the singularities computed in (64), (65) and (66) are independent from the specific Hamiltonian considered. As for the Berry connection A + , we already pointed out that the singularity does not depend on the choice of the diabatic basis used to compute W (x). Moreover, the sign of M does not depend on the specific model. Indeed if two bands come very close, with E n (x) < E n+1 (x), but themselves are well separated from the others bands, the main contribution to the reduced resolvent comes from the n-th band. Thus
− (W (x) − E n+1 (x)) −1 P ⊥ n+1 (x) = − m =n+1 (E m (x) − E n+1 (x)) −1 P ⊥ m (x) ≈ − (E n (x) − E n+1 (x)) −1 P ⊥ n (x) > 0.
Thus M n+1 is positive and, by the mirror argument, M n is negative.
Second order corrections in chemical reactions
The search for observable effects of the Berry phase has been a wide field of investigations [3]. In the same spirit, one may ask if there are observable effects related to the second order corrections φ and M. A good candidate is the chemical exchange reaction involving a system of three hydrogen atoms: H 2 + H → H + H 2 . Indeed, the intermediate transition molecule H 3 exhibits an interesting structure: two electronic energy bands form a family of conical intersections, corresponding to those highly-symmetric configurations where the nuclei are at the vertices of an equilateral triangle.
Experimental studies of H 2 + H (which are usually performed by using one of its isotopic analogues, as D + H 2 → DH + H, so that the reactants are labelled) have reached a very high level of precision. For example, in [1] the rates are measured for reactions in which both the initial and the final hydrogen molecules are in a specific vibrational and rotational state. In fact, one expects the state-to-state cross section to be more sensitive than the total cross section to phase interference of the Born-Oppenheimer wave function.
The basic interference mechanism is simple. The labelled reaction A + BC → AB + C may happen in two qualitatively different ways: either (i) the incoming atom A binds directly with B, or (ii) atom A first approaches atom C before finally binding with atom B. In the Born-Oppenheimer approximation, this two possibilities correspond to classical paths on opposite sides of the conical crossing. Thus quantum interference is expected.
On the theoretical side, Kupperman and Wu [33] computed state-to-state differential cross section for the H + H 2 reaction, showing significant difference with previous calculations, where the Berry phase was neglected. Comparison between theory and experiments was firstly done for D+H 2 → DH +H. In early computations, the inclusion of the Berry phase improved significantly the agreement between theory and experiments. However, it has been later pointed out, the agreement could be due to accidental cancellations of errors, one source of error being the inaccuracy of the electronic structure data in the high-energy region. The results are still controversial, and no general consensus has been reached [3].
While we do not enter in the controversy, we comment on the relevance of second-order Born-Oppenheimer corrections in this kind of reactions. First of all, some orders of magnitude: in the identical atoms system the conical intersection exists at E cross ≈ 2, 7 eV above the minimal energy of the H 2 molecule, and the minimal potential barrier is E 0 ≈ 0.43 eV , corresponding to the collinear H−H−H configuration. We focus on a situation in which the kinetic energy is smaller than E cross , so that diabatic transitions to the upper band are negligible, but sufficiently larger that E 0 , so that the probability that the wavefunction follows a path of kind (ii) is not negligible. In this energy interval the wavefunction is likely to explore regions of the nucleonic configuration space close to the crossing point. The second order corrections φ and M are singular at the crossing point, and thus certainly relevant in the nearby region. Although a careful analysis requires quantitative estimates, we conclude that the second-order terms might be relevant in this kind of reactions.
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Controlling matter-light interactions with cavities is of fundamental importance in modern science and technology [1]. It is exemplified in the strong-coupling regime, where matter-light hybrid modes form, with properties controllable via the photon component on the optical-wavelength scale [2,3]. In contrast, matter excitations on the nanometer scale are harder to access. In twodimensional van der Waals heterostructures, a tunable moiré lattice potential for electronic excitations may form [4], enabling correlated electron gases in lattice potentials [5][6][7][8][9]. Excitons confined in moiré lattices [10,11] have also been reported, but cooperative effects have been elusive and interactions with light have remained perturbative [12][13][14][15]. Here, integrating MoSe 2 -WS 2 heterobilayers in a microcavity, we establish cooperative coupling between moiré -lattice excitons and microcavity photons up to liquid-nitrogen temperature, thereby integrating into one platform versatile control over both matter and light. The density dependence of the moiré polaritons reveals strong nonlinearity due to exciton blockade, suppressed exciton energy shift, and suppressed excitation-induced dephasing, all of which are consistent with the quantum-confined nature of the moiré excitons.
Such a moiré polariton system combines strong nonlinearity and microscopic-scale tuning of matter excitations with the power of cavity engineering and long range coherence of light, providing a new platform for collective phenomena from tunable arrays of quantum emitters.
I. INTRODUCTION
Controlling matter-light interactions has mostly been implemented with either microscopic, individual quantum particles, or macroscopic ensembles of free particles that often can be modelled classically. Bridging the two limits to realize collective coupling among arrays of quantum particles ushers new paradigms in quantum many-body physics and quantum simulation research, such as been pursued using atomic optical lattices and cavities [16][17][18]. In solid state systems, however, such a pursuit has been exceedingly difficult, for nonlinearity is often too weak, due to screened Coulomb interactions, and inhomogeneity, too large. In this work, we show that moiré lattices formed in hetero-bilayer (hBL) transition metal dichalcogenides (TMDCs) crystals may provide a platform that overcomes these limitations of conventional solids.
When two monolayer (ML) crystals are placed together, a moiré lattice can form due to a slight mismatch in the lattice constants or crystal orientations of the MLs [4,10,11]. Its period is tunable by the twist angle between the ML crystals from a few to a few tens of nanometers -comparable to the range of Coulomb interactions in semiconductors. The natural formation of the moiré lattice promises the prospect of uniformity among different moiré cells across the lattice, thereby potentially enabling a new solid-state platform for cooperative phenomena between light and arrays of nonlinear quantum particles. While exciton states induced by the moiré lattice have been reported [12][13][14][15], the fundamental question remains whether a sufficiently uniform lattice of quantized excitations can be formed in a moiré system. Exciton-light interactions have remained in the perturbative regime, and cooperative phenomena have not been reported.
II. MOIRÉ POLARITONS IN WS 2 -MOSE 2 HETERO-BILAYERS
To enable cooperative coupling between moiré excitons and photons, we use WS 2 -MoSe 2 hBLs enclosed in a microcavity (Fig. 1a). The hBL is encapsulated in hexagon boron nitride (hBN) with a twist angle measured to be 56.5 • ± 0.9 • (Extended Data Fig.1). The WS 2 -MoSe 2 hBL is unique among commonly studied TMDCs hBLs in that the two lowest-energy moiré exciton modes have large oscillator strengths, inherited from that of the ML MoSe 2 A exciton. [15,19,20]. This not only allows ready identification of moiré excitons via the absorption spectra, but also suggests both of the moiré excitons may strongly couple with light and form stable moiré polaritons.
We first identify the existence of moiré lattice and moiré excitons before enclosing the hBL in a cavity. As shown by comparison of the hBL and ML reflection spectra in Fig. 1c, the ML MoSe 2 A exciton is split into two moiré excitons in the hBL, X 1 and X 2 , separated by about 40 meV, both with pronounced absorption, consistent with calculations ( Fig. 1b-c) and temperature dependence of the hBL (Extended Data Fig.2).
When the hBL is placed at the anti-node of a λ/2 microcavity (Fig. 1d, see Extended Data Fig.3 for more details of the cavity), in place of the moiré excitons or the bare cavity, three dispersive modes are observed up to 70 K, as shown in Fig. 2a
H = E X 1 0 Ω 1 0 E X 2 Ω 2 Ω 1 Ω 2 E c .
Here E c is the energy of the cavity mode, E X 1 ,X 2 are the energies of the two moiré excitons, and Ω 1,2 are their coupling strengths with the cavity photon. The three distinct dispersions measured correspond to the three new, light-matter hybrid eigen-modes of the Hamiltonian: the upper (UP), middle (MP) and lower (LP) polaritons. The fitted E X 1 ,X 2 agree with the independently measured moiré excitons energies (Fig. 1c) within 5 meV, where the difference is commonly observed as a result of strain due to deposition of the top mirror. The fitted Ω 1,2 = 10.1 ± 0.3 meV and 8.5 ± 0.3 meV at 4 K and change slightly to 9.6 ± 0.4 meV and 8.7 ± 0.4 meV at 70 K.
From independent measurement, the exciton half linewidths increase from γ X 1 ,X 2 = 7.5 meV and 8.4 meV at 4 K to 8.8 meV and 8.9 meV at 70 K (Extended Data Fig.5), which are mainly due to inhomogeneous broadening [21]. The strong coupling condition Ω 1,2 > (γ c + γ X 1,2 )/2 is satisfied up to 70 K.
In comparison, a similar cavity enclosing a ML MoSe 2 also exhibits clearly strong coupling of the ML MoSe 2 A-exciton and the cavity photon ( Fig. 2c and f). Fitting the dispersions of the polaritons yield Ω XA =17.1±0.1 meV, which is comparable to but slightly larger than Ω 2 1 + Ω 2 2 =13.2 meV.
This confirms that most of the oscillator strength of the ML MoSe 2 A-exciton is distributed to the moiré states X 1 and X 2 . The reduction may be due to additional, higher-energy moiré states [7,15] or additional disorder introduced into the bilayer during stacking of the MLs.
III. ZERO-DIMENSIONALITY OF MOIRÉ EXCITONS
With robust polariton modes formed with both moiré hBL and ML excitons, we study the effect of the underlying moiré lattice via their nonlinear response to the excitation density n. We focus on n < n M ott = 1/a 2 B ∼ 10 6 µm −2 , for n M ott the Mott density and a B ∼ 1 nm the Bohr radius [22], and vary n from 10 µm −2 up to 3 × 10 4 µm −2 using a resonant 150 fs pulsed laser (see Methods for details) [23][24][25][26]. A few representative reflectance spectra at different excitation densities are shown in Fig. 3a-b for the hBL-and ML-cavities, respectively. Fitting the absorption dips in the spectra with Lorentzian functions, we obtain the polariton energies as plotted in Fig. 3c-d.
With increasing excitation densities, the moiré LP and MP shift symmetrically toward the moiré exciton resonance E X 1 while their linewidths remain the same ( Fig. 3a and Fig. 3c). These suggest reduced exciton-photon coupling strength, yet constant exciton energy or dephasing, which are typical properties of 0D excitons. In sharp contrast, the ML LP and UP shift together to higher energies, accompanied by significant linewidth broadening. These suggest a much weaker saturation of the exciton-photon coupling strength but pronounced many-body effects, as expected of 2D excitons.
To analyze the density dependence quantitatively, we use the coupled-oscillator model to extract from the polariton spectra the three basic properties of excitons: the exciton energy E X (n), linewidth γ X (n), and photon coupling strength Ω(n) (see Methods for details). The results can be compared with well-established models for free 2D excitons:
E X (n) = E X (0) + β 1 n − β 2 n 2 ,(1)γ X,n = γ X (0) + αn,(2)Ω(n) = Ω(0)/ 1 + n n s .(3)
These equations describe the energy shift due to two and three-particle exchange interactions with coefficients β 1,2 [24], the linewidth broadening due to exciton-induced dephasing (EID) with coefficient α [27], and oscillator strength saturation due to Pauli blocking with a saturation density n s [22,28].
Pronounced differences between moiré and ML-excitons are clearly seen in all three properties [24,27]. The coupling strength decreases slightly by up to 5%; the corresponding n s,M L = (2.8 ± 0.4) × 10 5 µm −2 is comparable to 1/a 2 B ∼ 10 6 µm −2 . These results confirm that the ML excitons behave as 2D particles; they also provide a consistency check of our density calibration.
In contrast to the ML excitons, the moiré excitons show no measurable energy shift, a much smaller line-broadening of < 1 meV, and a much stronger saturation of the coupling strength by up to 20% (Fig. 4a-c, red circles). These can not be explained with the 2D exciton picture, but are expected of 0D excitons, as we discuss below.
In a moiré lattice, the exciton center-of-mass wavefunction is no longer a plane wave, but becomes localized near the potential minimum of each moiré cell, with a localization length On the other hand, the suppressed energy shift and linewidth broadening are characteristic of quantum dots with strong exciton blockade. Exciton blockade takes place when the interaction energy between two excitons in the same cell becomes greater than the exciton linewidth, so that multiple excitations correspond to distinct, quantized energy levels. In our hBL, the on-site
(a B < < a M /2,exchange interaction U exc,hBL = 1 2π ( a B w ) 2 E b ∼ 40
meV for binding energy E b ∼ 250 meV, and exciton wavefunction extension w ∼1 nm. The dipole interaction due to the inter-layer component is U dd,hBL ∼ d a B U exc,hBL ∼ 30 meV for dipole length d ∼0.7 nm [11]. These values agree with a more detailed calculation (Extended Data Fig.9) and are much larger than the exciton full linewidth of 2γ X 1 ∼ 15 meV. So we indeed expect exciton blockade in a moiré cell. At the same time, since both the exchange and dipole-dipole interactions decrease quickly with distance, they are both suppressed for excitons in different moiré cells (Extended data Fig.9). The intra-cell exciton blockade, together with suppressed inter-cell interactions, lead to suppressed many-body effects for the single-exciton resonance, which manifests as absence of energy shift or EID, in agreement with our observations. Consistent with exciton blockade, exciton-photon coupling saturates at one exciton per moiré cell, or, n s ∼ 1/a 2 M ∼ (πa 2 B /a 2 M )n s,M L ∼ 6 × 10 4 , in excellent agreement with the fitted n s,hBL = (6.5 ± 0.3) × 10 4 µm −2 for n ≥ 1000 µm −2 (bottom solid line in Fig. 4c). In contrast, if the moiré excitons are 2D band excitons, n s would have remained the same as n s,M L , since the total oscillator strength is conserved in the band across the lattice. We note that the fit does not explain the abnormally strong saturation at very low densities of n < 1000 µm −2 , which we will discuss more later.
IV. MOIRÉ LATTICE-INDUCED NONLINEARITY OF MOIRÉ POLARITONS
The distinctly different density dependence of the moiré polaritons shown above suggests the possibility of achieving a much higher polariton nonlinearity, even for polariton modes that are stable at high temperatures. Fig. 4e shows the measured g(n) =| dE(n)/dn | for both the moiré and ML LPs (symbols).
While the nonlinearity increases with decreasing density for both moiré and ML LPs, the moiré LPs show surprisingly a larger nonlinearity. The nonlinearity of ML LPs originates primarily from exciton exchange-interactions and g M L−LP saturates below n ∼ 1000 µm −2 to 0.02 µeV·µm 2 (0.04 µeV·µm 2 ) at the measured (zero) detuning, in agreement with reported values [24,26,29].
The nonlinearity of moiré LPs results primarily from exciton blockade. Based on the data at n > 1000 µm −2 , we obtain g hBL−LP about four times higher than g M L−LP .
At very low densities of n < 1000 µm −2 , while the ML polaritons or excitons show no measurable shift, the moiré polaritons show clearly saturation-induced shifts down to n ∼ 10 µm −2 ( Fig. 3c), corresponding to a stronger exciton saturation than expected from exciton blockade, exciton-interactions, or effects of trions and defect states (Fig. 4c) [30]. However, this abnormally large nonlinearity is repeatable over multiple measurements in multiple devices (see Extended (Fig. 4c).
The polariton nonlinearity is a key figure of merit that distinguishes polariton systems from pure photon systems. Together with the robust coherence enforced by the photon component, it gives rise to a wide range of novel nonlinear many-body and quantum phenomena [31][32][33][34][35][36].
For polaritons made of 2D excitons, however, larger g is obtained only at the compromise of Ω, or the stability of polariton modes. This is because the exciton-exchange interaction and the exciton-photon coupling strength saturation, the two main contributions to g, both decrease with the exciton reduced mass µ: g exc ∼ E b a 2 B ∝ 1/µ and g sat ∝ a 2 B ∝ 1/µ 2 . Yet the exciton-photon
coupling strength Ω ∝ √ f ∝ 1/a B ∝ µ.
The highest polariton nonlinearity is achieved in single or few quantum-well GaAs microcavities [34,35], with g ∼ 3 µeV·µm 2 and Ω only ∼3 meV.
Wide-bandgap semiconductors, organic crystals and ML TMDCs all feature greater Ω and high-temperature polaritons, yet a much weaker polariton nonlinearity [23,26,37,38]. Higher order excitations in TMDCs, such as trions with strong band-filling effect [24,29] and 2s excitons with a larger Bohr radius [25], have shown enhanced nonlinearity, but again at the compromise of stability.
The moiré polariton system uniquely combines strong nonlinearity, due to quantum confinement of excitons within each moiré cell, and a large total photon coupling strength, due to collective coupling among the cells. It thereby provides a new route to achieve strong nonlinearities simultaneously with robust exciton-photon coupling.
V. CONCLUSION
In summary, we have demonstrated the first polariton system formed via collective coupling of a 2D lattice of 0D excitons with light in a microcavity. The system therefore introduces quantum-dot like nonlinearity into cooperatively coupled solid state system, opening a door to novel quantum many-body physics and polariton devices [16][17][18]39]. for an example spectrum of the laser). For the ML, due to the larger energy separation of the LP and UP, they were measured separately with the laser centered at each, respectively. The signal was detected using a Princeton Instruments spectrometer with a cooled charge-coupled camera.
Theory of moiré excitons The Hamiltonian for the moiré excitons is
H = E G + 2 k 2 2M X w(1 + e −ib + ·r + e −ib − ·r ) w(1 + e ib + ·r + e ib − ·r ) E G + δ 0 + 2 (k−κ) 2 2M IX (4)
where E G is an energy constant, M X and M IX are respectively the effective masses for intralayer and interlayer excitons, κ = (0, 4π/(3a M )) accounts for the momentum mismatch between the two excitons, and δ 0 is an energy offset. The off-diagonal terms are derived from interlayer tunneling, Fig. 1b. For the lowest-energy exciton X 1 , its interlayer component is plotted in Fig. 4d, which shows spatial localization.
and b ± = 4π/( √ 3a M )(±1/2, √ 3/2). The moiré period is a M = a 0 / √ δ 2 + θ 2 , where a 0 = (a MoSe 2 + a WS 2 )/2 = 3.26Åand δ = |a MoSe 2 − a WS 2 |/a 0 ≈
Polariton density calibration In this section, we will use the bilayer device data as an example;
the same procedure applies to the monolayer device. To extract the polariton density: First, we fit the reflection spectra in Fig. 3 using :
R = 1 − Absor LP − Absor M P ,(5)
where Absor LP and Absor M P represent absorption by the lower polariton (LP ) and middle polari-ton (M P ) in the bilayer, respectively, and they are described by Lorentzian functions:
Absor LP,M P (E) = A LP,M P (E − E LP,M P ) 2 + γ 2 LP,M P ,(6)
Resonance energy E LP,M P , linewidth (HWHM) γ LP,M P , and absorption amplitude A LP,M P are fitting parameters with uncertainties δ E LP,M P , δ γ LP,M P and δ A LP,M P corresponding to 95% confidence intervals.
We use pulsed laser with pulse duration of 150 fs and repetition rate f of 80 MHz. We calculate the polariton density n injected per pulse. The average power of the laser is P . The laser profile can be fitted with Gaussian function:
G(E) = A laser γ laser π/2 e − 2(E−E laser ) 2 γ 2 laser (7)
where A laser is the area of the Gaussian function, and γ laser is the linewidth. The power absorbed by LP and MP, P LP,M P can be calculated using the convolution:
P LP,M P = P G(E)Absor LP,M P A laser = P G(E) A LP,M P 4(E−E LP,M P ) 2 +γ 2 LP,M P A laser (8)
The total carrier density including both LP and MP created per pulse and its error δ n can be calculated by:
n = (n LP + n M P )/A beam = ( P LP f E LP + P M P f E M P )/A beam .(9)
δ n = δ 2 n LP + δ 2 n M P /A beam (10) Where, A beam =1.5 µm, is the beam area, and δ n LP,M P = n LP,M P ( To analyze the results quantitatively, we extract the density dependence of the exciton properties from the measured polariton spectra. In the heterobilayer cavity, we focus on the MP and LP modes and neglect changes caused by the X 2 , since X 2 is at a much higher energy, and its change only negligibly affects MP and LP (see Extended Fig.10 for details). The cavity resonance energy E c and linewidth γ c are assumed to change negligibly with exciton density. Using the two coupled oscillator mode, the energies of the MP and LP of the heterobilayer cavity, as well as of the UP and LP of the ML-cavity can be extracted. In the following, we will use the bilayer device data as an example; the same procedure applies to the monolayer device.
E LP,MP (n) = 1 2 E X (n) + E C + i(γ C + γ X (n)) ± Ω(n) 2 + 1 4 E X (n) − E C + i(γ C − γ X (n)) 2(11)
Here the cavity resonance, E C , and cavity half-linewidth γ C , do not change with carrier density.
Therefore, from the measured polariton energies and half-linewidth, γ LP,M P , we obtain the density dependence of exciton energy, E X , half-linewidth, γ X , and exciton-photon coupling strength, Ω:
Exciton energy E X and its uncertainty δ E X :
E X (n) = E LP (n) + E M P (n) − E C (12) δ E X = δ 2 E LP + δ 2 E M P + δ 2 E C(13)
where, E C and δ E C are the cavity resonance and its uncertainty obtained by fitting the angle resolved reflection spectrum in Fig. 3, and they do not change with polariton densities.
Exciton linewidth γ X and its uncertainty δ γ X :
γ X (n) = γ LP (n) + γ M P (n) − γ C (14) δ γ X = δ 2 γ LP + δ 2 γ M P + δ 2 γ C(15)
where, γ C and δ γ C are the cavity linewidth and uncertainty obtained by fitting the reflection spectrum of the bare cavity in Fig. 1d, and they do not change with polariton densities.
Coupling strength Ω:
Ω(n) = 1 2 [E LP (n) − E M P (n) + i(γ LP (n) − γ M P (n))] 2 − [E X (n) − E C + i(γ X (n) − γ C )] 2 (16)
Dipole-dipole interaction The interlayer component of moiré excitons contributes to dipoledipole interactions. The wave function for interlayer component of a moiré exciton localized near the potential minimum around the origin can be described as
W (r 1 , r 2 ) = x IX Φ( r 1 + r 2 2 )φ(r 1 − r 2 ),(17)
where x IX is the interlayer component weight, Φ and φ are respectively the center-of-mass and relative-mass wave function. We approximate Φ by a Gaussian Φ(R) = 1 √ π e −R 2 /(2 2 ) , and φ(r) = 8/π(1/a B )e −2r/a B , where R = r 1 +r 2 2 , r = r 1 − r 2 , is the localization length that can be estimated using the exciton state shown in Fig. 4d, and a B is the Bohr radius.
The dipole-dipole interaction between two excitons localized at different moiré sites can be approximated as U dd (L) = dr 1 dr 2 dr 3 dr 4 |W (r 1 , r 2 )| 2 |W (r 3 − L, r 4 − L)| 2
[V S (r 1 − r 3 ) + V S (r 2 − r 4 ) − V D (r 1 − r 4 ) − V D (r 2 − r 3 )] =2x 2 IX d 2 q (2π) 2 V (q) exp(−q 2 2 /2) [1 + 1 64 a * 2 B q 2 ] 3 e −iq·L ,(18)
where L is a moiré lattice vector, V S (r) = e 2 /( r) is the intralayer Coulomb interaction, V D (r) = e 2 /( √ r 2 + d 2 ) is the interlayer Coulomb interaction with d the interlayer distance, and V (q) = 2πe 2 q (1 − e −qd ). To calculate U dd (L), we take x IX ≈ 1/ √ 2, d = 0.65 nm, = 5, and a B ≈ 1 nm.
Extended Fig.9 shows the onsite and nearest-neighbor dipole-dipole interactions as a function of twist angle. The onsite repulsion is sizable (∼ 24 meV for a twist angle of 56.5 • ), while the offsite repulsion is negligible.
Data availability Data are available on request from the authors.
Competing interests The authors declare that they have no competing financial interests. Extended Data Fig. 10: Effect on the nonlinearity from the moiré exciton X 2 .
Author Contributions
0 -1 -2 -3 1 2 3 k // (µm -1 ) 0 -1 -2 -3 1 2 3 k // (µm -1 ) 0 -1 -2 -3 1 2 3 k // (µm -
Energy shifts of E BL
LP and E BL M P from the saturation of upper moiré exciton X 2 . In the main test, we ignore the effects of moiré exciton X 2 on the nonlinearity of lower and middle polaritons. To quantitatively estimate the effects, we calculate the ∆E BL LP and ∆E BL M P as a function of coupling strength (Ω 2 ) of X 2 . When the Ω 2 changes by 10%, the E LP and E M P will shift within 0.16 meV, which is less than 8% of the shift observed from the experiments (2meV) (Fig. 3c in the main text). So the change of E LP and E M P induced by Ω 2 can be safely ignored for simplicity.
-b. The modes anti-cross at the two moiré exciton resonances, showing clearly strong coupling of both moiré excitons (X 1 and X 2 ) with the cavity photon. Emission, temperature dependence, and time resolved studies are provided in the Extended Data Fig. 4-6.The measured dispersions(Fig. 2d-e)are described very well by calculations based on a three coupled oscillator model with a Hamiltonian:
(
Fig. 4a-c). For the ML exciton, all three properties are described very well by Eqs. 1-3 for 2D excitons (blue diamonds and lines in Fig. 4a-c). The exciton energy blueshifts by 1.5 meV due to exchange interactions, the linewidth broadens significantly by 3 meV due to EID. The fitted coefficients, β 1,M L = (1.2 ± 0.1) × 10 −1 µeV·µm 2 , β 2,M L = (2.9 ± 0.4) × 10 −6 µeV·µm 4 , and α = 0.11 ± 0.01 µeV·µm 2 , all agree well with reported values
where a M is the moiré period), as illustrated inFig. 4d. Evaluating for our device of a M = 4.2 nm yields = 1.2 nm. Therefore the confinement leads to an increase of the effective local density n ef f by (a M /2 ) 2 ∼ 3 at the potential minima, and thus enhanced exchange and dipole-dipole interactions. If the moiré exciton are 2D-like band excitons, the enhanced interactions should lead to correspondingly an enhanced energy shift and enhanced EID. On the contrary, we observe no energy shift and a much smaller line-broadening. Therefore, our observations show the moiré excitons in our device are no longer 2D band excitons.
Data
Fig.7for another example), suggesting hidden mechanisms for large polariton nonlinearity in moiré lattices. Phenomenologically, Ω X1 (n) over the full density range can be described very well by Eq. 3 if n s is replaced by a density-dependent effective saturation density n ef f,s =ñ s (1 − Ae −n/B ), for fittedñ s = (4.4 ± 0.1) × 10 4 µm −2 , A = 0.98 ± 0.04 and B = (7.4 ± 0.5) µm −2
Polariton blockade and a strongly-correlated polariton gases may become possible with reduced inhomogeneous broadening of moiré excitons, improved cavity quality factors, and a better understanding of the abnormal enhancement of the polariton nonlinearity at very low excitation densities. Electrical gating and electrical field tuning of the heterobilayer can be implemented to further control the nonlinearity and many-body phenomena in the moiré polariton system. METHODS Sample fabrication. The ML MoSe 2 , WS 2 and few layer hBN flakes were obtained by mechanical exfoliation from bulk crystals. A polyethylene terephthalate (PET) stamp was used to pick up the top hBN, WS 2 ML, MoSe 2 ML, and the bottom hBN under microscope. The WS 2 and MoSe 2 monolayer MLs were rotationally aligned to about 0 • in the heterobilayer. The bottom half of the cavity consists of 16 pairs of SiO 2 /TiO 2 DBR with a λ/4 SiO 2 layer. The heterostructure on the PET stamp was stamped onto the bottom half of the cavity and the PET was dissolved in dichloromethane for six hours at room temperature. Then 67 nm PMMA film was spin coated on the top of heterobilayer to form the second half of the λ/2 cavity. Then a silver film of 40 nm thick was deposited using electron beam evaporation as the top mirror of the cavity.Optical measurements. For low temperature measurements, the sample was kept in a 4 K cryostat (Montana Instrument). The excitation and collection were carried out with a home-built confocal microscope with an objective lens with a numerical aperture (NA) of 0.42. To characterize the dispersion of the polariton device, we performed angle-resolved reflection measurement using white light from a tungsten halogen lamp. The white light was focused on the sample with a beam size of 10 µm in diameter. To perform power dependent reflection measurements, we used a 150 fs-pulse laser as the light source with a repetition rate of 80 MHz and focused beam size on the sample of around 1.5 µm in diameter. For the hBL, the laser was centered between LP and MP to simultaneously measure both modes, while the intensity at UP is negligible (Extended DataFig.8
4%. We use the following parameter values,E G = 1.61eV, δ 0 = −20 meV,w = 14 meV, M X = 0.82m 0 , M IX = 0.71m 0 ,where m 0 is the electron bare mass. The energy spectrum of the moiré excitons is obtained by diagonalizing the moiré Hamiltonian H using plane-wave expansion, and is shown in
E
LP,M P ) 2 Extraction of exciton energy, linewidth, and coupling strength at different densities
H.D., L.Z.conceived the experiment. L.Z. performed the measurements. F. W. provided theoretical inputs. L.Z. and Z.Z fabricated the device. L.Z. and H.D. performed data analysis. S.H deposited the silver mirror. Y.C grew the bottom DBR mirror. K.W. and T.T grew hBN single crystals. H.D. and S.F. supervised the projects. L.Z and H.D. wrote the paper with inputs from other authors. All authors discussed the results, data analysis and the paper.
FIG. 1 :
1Illustration of the moiré polariton system and the constituent moiré excitons and microcavity. a, Schematic of the moiré polariton system formed by excitons confined in moiré lattice and coupled with a planar cavity. b, moiré band structure for hBL excitons, where X 1 and X 2 are two bright moiré exciton states. See Method (Theory of moiré excitons) for details of the calculation. c, Top panel: theoretical optical absorption spectrum calculated from the moiré exciton band structure. Bottom panel: Reflection contrast spectra near the MoSe 2 A exciton resonance, from the WS 2 -MoSe 2 hBL (red), MoSe 2 ML (blue) and WS 2 ML (green). The spectra are displaced vertically for easier reading. The MoSe 2 ML A-exciton (X A ) splits into two well resolved moiré exciton (X 1 and X 2 ) in the hBN. d Angle resolved white light reflection spectrum of the bare cavity, measured in a region where there is no hBL, showing a single cavity dispersion with a half linewidth γ c = 2.7 meV.
FIG. 2 :
2Strong coupling and dispersions of moiré and ML polaritonss. a − c, Angle resolved white light reflection spectra, demonstrating strong coupling between moiré exciton and cavity photon at 5K in a and 70K in b, in comparison with strong coupling between ML exciton and cavity photon at 5K in c. The left/right panels show the measured/simulated results, respectively. d − f , The polariton energies vs. in-plane wavenumber k // obtained from a − c, respectively. The solid lines are fits to the polariton dispersions with the coupled harmonic oscillator model. The dashed lines are the fitted energies of the uncoupled cavity photon and excitons. The error bars on the energy data correspond to the 95% confidence interval of the Lorentzian fit.
FIG. 3 :
3Nonlinearity of the moiré hBL and ML polaritons. a, Reflection spectra of moiré LP and MP at zero detuning for different pumping densities. From bottom to top, the carrier density increases from 17 µm −2 to 1.8 × 10 4 µm −2 . b, Reflection spectra of MoSe 2 ML LP (left) and UP (right). The cavity is red detuned from the exciton by 42.5 meV. From bottom to top, the carrier density increases from 22 µm −2 to 1.5 × 10 4 µm −2 . In a, b, the colored solid lines are examples of Lorentzian fits. The arrows are guides for the eyes. c, d Shift of polariton energies vs. the carrier density (log scale) obtained from a and b, respectively. Insets show the density in the linear scale, plotted over the same ranges of the horizontal and vertical axes as the main figure. Solid lines are calculations using parameters obtained from fitting the data inFig. 4a − c. The error bars on the energy data correspond to the 95% confidence interval of the Lorentzian fit.
FIG. 4 :Fig. 9 :
49Enhanced nonlinearity by moiré lattice confinement. a − c, Shift of exciton energy ∆E, half-linewidth γ, and normalized coupling strength Ω/Ω 0 of the hBL-LP (red) and ML-LP (blue) as a function of carrier density, obtained from the data in Fig. 3. The hBL ∆E hBL−X and γ hBL−X (red circles in a and b) are approximately constant. The ML ∆E M L−X and γ M L−X (blue diamonds in a and b) are fitted by a second order polynomial and a linear line, respectively (black solid lines in a and b). In c, the black solid lines are fits with equation (3) with a constant n s for the moiré excitons at n>1000 µm −2 and for ML excitons. The black dashed line is a fit with a density-dependent effective saturation density n ef f,s , and is used for calculating the polariton energies in Fig. 3 c. d, Real-space distribution of the interlayer component of the X 1 state. The white lines mark a moiré unit cell. The scale bar is 1 nm. e, The measured (symbols) and fitted (lines) nonlinear coefficient g vs. carrier density for the moiré hBL-LP (red) and ML-LP (blue). The magenta dashed line and blue solid line are the calculations using the fitted polariton energies in Fig. 3 c and d. The hBL-LP is at zero detuing; the red solid line and magenta dashed lines correspond to fitted Ω hBL using a constant and effective saturation density, n s and n ef f,s , in Eq (3), respectively. For ML-LP, the blue solid and dashed lines correspond to the measured detuning and zero detuning, respectively. The error bars in a-c and density in e are explained in Methods. The error bars of g correspond to the 95% Extended Data Fig. 2: Temperature dependence of moiré exciton. Temperature dependence of the moiré exciton X 1 and X 2 measured from a separate heterobilayer prepared on sapphire substrate. The black dashed lines are guides for eyes. The two exciton states can be well resolved up to 200K, which can exclude the possibility of charged exciton or trapped exciton by defect. Extended Data Fig. 3: Schematic of the device. a Schematic of the device shows the different layers of the heterostructure embedded inside a microcavity that consists of a bottom DBR and a top silver mirror. b Microscope image of the hBL on the top of DBR mirror, taken before depositing the PMMA layer and the silver mirror. c Thickness of each layer for the device. Extended Data Fig. 5: Transition from strong coupling to weak coupling driven by thermal broadening. Strong coupling to weak-coupling transition measured by temperature dependence of Ω 1 (red open circles), (γ c + γ X1 )/2 (purple left-triangle) in a and Ω 2 (red square), (γ c + γ X2 )/2 (purple right-triangle) in b. γ c = 2.7meV is constant with temperature. γ X1 and γ X2 are measured independently from bare hBL. Ω 1 and Ω 2 drop below the average linewidth at about 100K, showing the transition to the weak-coupling regime. Dipole-Dipole interaction strength as a function of twist angle θ.
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Twist angle of hBL in the main text measured by second harmonic generation (SHG) spectroscopy. a The polarization-dependent SHG signal measured on the. Extended Data Fig. 1: Heterobilayer twist angle. 2Extended Data Fig. 1: Heterobilayer twist angle. Twist angle of hBL in the main text measured by second harmonic generation (SHG) spectroscopy. a The polarization-dependent SHG signal measured on the ML WS 2 (green open circles) and
measured with the same experimental configurations. The suppressed SHG signal from hBL as a result of destructive interference indicates the stacking order is H-stacking. The twist angle is determined to be 56.5 • ± 0.8 • Extended Data Fig. 4: Photoluminescence from the moiré polariton. Left panel: Angle resolved photoluminescence spectrum of hBL in cavity, excited by a continuous wave laser at the energy of 2.3 eV and power of 50 µW. To enhance the visibility of states at higher energy, emission intensity above 1.607 eV is magnified by 5 times. MoSe2 (blue filling squares) regions of the hBL, and the corresponding fits with the sinusoidal functions (green and blue solid lines). b, the SHG signal from ML WS2 , ML MoSe2 , and hBL regions. Right panel: simulated angle resolved absorption, which agrees well with the measurementMoSe2 (blue filling squares) regions of the hBL, and the corresponding fits with the sinusoidal functions (green and blue solid lines). b, the SHG signal from ML WS2 , ML MoSe2 , and hBL regions, measured with the same experimental configurations. The suppressed SHG signal from hBL as a result of destructive interference indicates the stacking order is H-stacking. The twist angle is determined to be 56.5 • ± 0.8 • Extended Data Fig. 4: Photoluminescence from the moiré polariton. Left panel: Angle resolved photoluminescence spectrum of hBL in cavity, excited by a continuous wave laser at the energy of 2.3 eV and power of 50 µW. To enhance the visibility of states at higher energy, emission intensity above 1.607 eV is magnified by 5 times. Right panel: simulated angle resolved absorption, which agrees well with the measurement.
TRPL spectra measured by streak camera for ML MoSe 2 (ML) a and hBL WS 2 /MoSe 2 (hBL) b. (The hBL data is collected from a different sample from the main text, which is not integrated with microcavity) The different resonances are labelled with white arrows including ML exciton (ML-X), ML trion (ML-T), moiré exciton at higher energy (hBL-X 2 ), moiré excion at lower energy (hBL-X 1 ), and moiré trion (hBL-T). c and d shows the time resolved decay of ML-X and hBL-X 1 respectively by integrating the spectrum in the range labeled by the red rectangles in a and b. The red solid lines in c and d are the fits with single exponential decay function. Time resolved photoluminescence (TRPL) of ML exciton, ML trion, hBL excitons, and hBL trion. 6Extended Data Fig. PL decay time for ML-X and hBL-X 1 are 6.7 ps and 8.0 ps respectivelyExtended Data Fig. 6: Time resolved photoluminescence (TRPL) of ML exciton, ML trion, hBL excitons, and hBL trion. TRPL spectra measured by streak camera for ML MoSe 2 (ML) a and hBL WS 2 /MoSe 2 (hBL) b. (The hBL data is collected from a different sample from the main text, which is not integrated with microcavity) The different resonances are labelled with white arrows including ML exciton (ML-X), ML trion (ML-T), moiré exciton at higher energy (hBL-X 2 ), moiré excion at lower energy (hBL-X 1 ), and moiré trion (hBL-T). c and d shows the time resolved decay of ML-X and hBL-X 1 respectively by integrating the spectrum in the range labeled by the red rectangles in a and b. The red solid lines in c and d are the fits with single exponential decay function. PL decay time for ML-X and hBL-X 1 are 6.7 ps and 8.0 ps respectively.
Strong nonlinearity measured in another device. fits using coupled oscillator model. The dashed white lines are the fitted energies of the uncoupled cavity photon and excitons. b Power dependent reflection spectra for the lower polariton (left panel) and middle polariton (right panel).c Shift of polariton energies vs. the carrier density (log scale) obtained from b. d Extracted nonlinear coefficients for lower polariton. Extended Data Fig. 7red circles) and the calculations using fitted polariton energies (solid lineExtended Data Fig. 7: Strong nonlinearity measured in another device. fits using coupled oscillator model. The dashed white lines are the fitted energies of the uncoupled cavity photon and excitons. b Power dependent reflection spectra for the lower polariton (left panel) and middle polariton (right panel).c Shift of polariton energies vs. the carrier density (log scale) obtained from b. d Extracted nonlinear coefficients for lower polariton (red circles) and the calculations using fitted polariton energies (solid line).
Profile of pulsed laser (red dot) used for the nonlinearity measurement of moiré polaritons, compared with the moiré exciton X 1 and X 2 (blue dots), and moiré polaritons (black dots). The laser has a negligibly small tail on X 2 and upper polariton. 8Profile of the laser used for nonlinearity characterizationExtended Data Fig. 8: Profile of the laser used for nonlinearity characterization. Profile of pulsed laser (red dot) used for the nonlinearity measurement of moiré polaritons, compared with the moiré exciton X 1 and X 2 (blue dots), and moiré polaritons (black dots). The laser has a negligibly small tail on X 2 and upper polariton.
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I. INTRODUCTION
The Rabi model, which was introduced over 70 years ago, describes the important interaction between a twolevel system and a quantized harmonic oscillator (bosonic mode) [1]. The corresponding Hamiltonian of this model is written as
H R = ωa † a + 1 2 Ωσ z + gσ x (a † + a),(1)
where a † and a are creation and annihilation operators for the quantized harmonic oscillator with frequency ω, σ i (i = x, y, z) are the Pauli spin operators, Ω is the resonant frequency between two levels, and g is the interaction strength. In modern physics ranging from quantum optics [2], condensed-matter physics [3] to quantum information [4], the Rabi model has been one of the simplest and most ubiquitous models. Despite its old age and central importance, the Rabi model has not been solved exactly because it is hard to find a second conserved quantity besides the energy. The well-known method to obtain the energy spectrums and the wavefunctions for the Rabi model is the numerical diagonalization in a truncated finite-dimensional Hilbert space [5]. However, these numerical results are difficult to extract the fundamental physics of the Rabi model [6][7][8][9][10][11][12] and to precisely control the experimental parameters to process quantum information [13].
To overcome the problem in the analytical considerations, the rotating-wave approximation, which is valid in the regime g ≪ ω, was proposed to rewrite Hamiltonian * Corresponding author: [email protected] (1) as [14] H JC = ωa † a + 1 2
Ωσ z + g(σ − a † + σ + a).(2)
Interestingly, the Jaynes-Cummings model with U (1) symmetry has a conserved quantity C = a † a + 1 2 (σ z + 1), and thus, it can be solved easily in the subspaces {|↑, n , |↓, n + 1 }. Meanwhile, the Jaynes-Cummings model can successfully describe quantum dynamics of optical cavity electrodynamics with strong coupling. However, in the recent investigations about the solid-state quantum electrodynamics with the ultrastrong coupling (g ∼ 0.1ω) [15][16][17][18][19][20][21][22][23][24], the rotating-wave approximation breaks down and the system's dynamics must be governed by the Rabi model. Irish put forward a generalized rotating-wave approximation to solve the Rabi model. This method can be used to derive the analytical energy spectrums of Hamiltonian (1) in the ultrastrong coupling successfully [25]. However, this method works reasonable only for the negative detuning (Ω < ω) [26][27][28]. Recently, Braak used the property of Z 2 symmetry of the Rabi model to obtain its analytical solutions, which are, however, dependent of the composite transcendental function defining through its power series in the interacting strength g and the frequency ω [29]. In our previous work, we put forward a generalized variational method to analytically obtain the ground-state energy of the Rabi model, which agrees well with the numerical simulation in all regions of the resonant frequency of the two-level system including the negative detuning (Ω < ω), the resonant case (Ω = ω), and especially the positive detuning (Ω > ω). Unfortunately, our introduced method cannot be used to consider the excited-state energy spectrum [30].
In this paper, we present a simple and straightforward method to solve the Rabi model in both ground and excited states. We first map the unsolvable Rabi model (1) into a solvable Jaynes-Cummings-like model by choosing a proper variation parameter, as shown in Section II. Thus, the analytical energy spectrums including the ground and the excited states are obtained in section III. These derived analytical results agree well with the direct numerical simulations in a wide range of the experimental parameters. Moreover, the recent experimental observation of Bloch-Siegert [20], which is just the energy shift of the level transition, in the circuit quantum electrodynamics with the ultrastrong coupling can be well explained. In section IV, the analytical wavefunctions and the corresponding experimentally-measurable physics quantities such as the mean photon number are derived. Also, the obtained mean photon number can agree well with the numerical simulation. Finally, some conclusions are remarked in Section V.
II. MAPPING INTO THE JAYNES-CUMMINGS-LIKE MODEL
When performing a rotation around the y axis, the Rabi model becomes
H R = ωa † a + Ω 2 σ x − g(a † + a)σ z .(3)
Under a unitary transformation
U = exp[λσ z (a † − a)](4)
with λ being the dimensionless parameter determined by the following calculations, an effective Hamiltonian is given by H E = U HU † , namely,
H E = H 1 + H 2 + H 3 ,(5)
where
H 1 = ωa † a − λωσ z (a † + a) + ωλ 2 ,(6)H 2 = −g[σ z (a † + a) − 2λ],(7)H 3 = Ω 2 {σ x cosh[2λ(a † − a)] + iσ y sinh[2λ(a † − a)]}. (8)
Since cosh(y) and sinh(y) are the even and odd functions respectively, the terms cosh[2λ(a † − a)] and sinh[2λ(a † − a)] can be expanded as
cosh[2λ(a † −a)]= G 0 (N ) + G 1 (N )a †2 + a 2 G 1 (N ) + . . . , (9) sinh[2λ(a † −a)]= F 1 (N )a † −aF 1 (N ) + F 2 (N )a †2 −a 2 F 2 (N ) +. . . ,(10)
where G i (N ) (i = 0, 1, 2, · · · ) and F j (N )(j = 1, 2, · · · ) with N = a † a are the coefficients that depend on the dimensionless parameter λ and the photon number n. In general, the multi-photon process is weak in the Rabi model [2]. It means that the terms of the high-order terms for a and a † in Eqs. (9) and (10) can be eliminated. As a result, the effective Hamiltonian (5) reduces to the form (11) In the eigenstates of σ x with σ x |±x = ± |±x , the Pauli spin operators become σ z → −(τ + + τ − ) and
H E = ωa † a − (λω + g)σ z (a † + a) + ωλ 2 + 2λg + 1 2 Ω{σ x G 0 (N ) + iσ y [F 1 (N )a † − aF 1 (N )]}.σ y → −i(τ + − τ − ), where τ z = |+x +x| − |−x −x|, τ + = |+x −x| and τ − = |−x +x|,H E = ωa † a + ωλ 2 + 2λg + 1 2 ΩG 0 (n)τ z + R r (τ + a + τ − a † ) + R ar (τ + a † + τ − a),(12)
where
G 0 (n) = n| cosh[2λ(a † − a)]|n ,(13)R r = λω + g − 1 2 Ωf 1 (m, n),(14)R ar = λω + g + 1 2 Ωf 1 (m, n) (15) with f 1 (m, n) = m| F 1 (N )a † |n / √ n + 1 = n + 1| F 1 (N )a † |n / √ n + 1. It is straightforward to cal- culate that G 0 (n) = n|e 2λ(a † −a) + e −2λ(a † −a) |n /2 = n|e 2λ(a † −a) ]|n = e −2λ 2 L n (4λ 2 ) and f 1 (m, n) = f 1 (n + 1, n) = n + 1| sinh[2λ(a † − a)|n = 2λe −2λ 2 L 1
n (4λ 2 )/(n + 1), where L n (y) is the Laguerre polynomial and L 1 n (y) is the associated Laguerre polynomial. Thus, if the dimensionless parameter λ is chosen as λω + g + 1 2 Ωf 1 (n + 1, n) = 0, namely,
(λω + g) + Ωλ n + 1 e −2λ 2 L 1 n (4λ 2 ) = 0,(16)
the effective Hamiltonian (12) becomes a Jaynes-Cummings-like model
H E = ωa † a + ωλ 2 + 2λg + 1 2 ΩG 0 (n)τ z + R r (τ + a + τ − a † ),(17)
where R r = 2(λω + g). By means of Hamiltonian (17), the analytical energy spectrums and wavefunctions for the Rabi model can be obtained easily in the subspaces {|+x, n , |−x, n + 1 } .
Before proceeding, the solution of the dimensionless parameter λ in Eq. (16) should be analyzed since it has a crucial role in obtaining the explicit energy spectrums and wavefunctions. In general, the nonlinear equation (16) cannot be solved analytically. However, in the current experimental setup with the ultrastrong coupling (g ≤ 0.5ω), the numerical result shows that the dimensionless parameter λ is small compared with the unit. Thus, the associated Laguerre polynomial is given by L 1 n (4λ 2 ) ≃ n + 1 since L 1 n (y) = n + 1 + j>0 c j y j , and Eq. (16) becomes (λω + g) + Ωλe −2λ 2 = 0, which leads to a solution
λ ≃ − g ω + Ω exp[−2( g ω+Ω ) 2 ] .(18)
For the weak interaction strength g, the dimensionless parameter becomes λ ≃ −g/(ω + Ω).
III. ANALYTICAL ENERGY SPECTRUMS
In terms of the Jaynes-Cummings-like Hamiltonian (17) and Eq. (18), the ground-state energy spectrum can be written as
E G = ωλ 2 + 2λg − 1 2 Ωe −2λ 2 ,(19)
and the excited-state energy spectrum can be given by
E ±,n = (n + 1 2 )ω + ωλ 2 + 2λg + Ω 4 e −2λ 2 [L n (4λ 2 ) − L n+1 (4λ 2 )](20)± 1 2 {ω − Ωe −2λ 2 2 [L n (4λ 2 ) + L n+1 (4λ 2 )]} 2 + 4[(λω + g) √ n + 1 − Ωλe −2λ 2 √ n + 1 L 1 n (4λ 2 )] 2 .
The ground-state energy spectrum in Eq. (19) is identical to the result derived from the generalized variational method [30], which is, however, invalid for calculating the excited-state energy spectrum. In addition, for the weak resonant frequency Ω, Eqs. (19) and (20) reduce to the results obtained by means of the generalized rotatingwave approximation [25]. In Fig. 1, the energy spectrums of the ground and excited states for the Rabi model as a function of the interaction strength g for Ω = 0.5ω (a), Ω = 1.0ω (b) and Ω = 1.5ω (c) are plotted, compared the explicit results in Eqs. (19) and (20) with the direct numerical simulation. This figure shows that our analytical energy spectrums including both the ground-and excited states agree perfectly with the direct numerical simulation in the current experimental setup with the ultrastrong coupling (g ≤ 0.5ω). Moreover, these results are valid for all parameter regimes with the negative detuning (Ω < ω), the resonant case (Ω = ω), and especially the positive detuning (Ω > ω). This conclusion can be also drawn from Fig. 2, in which the energy spectrums as a function of the resonant frequency Ω for g = 0.1ω (a) and g = 0.3ω (b) are plotted. For the generalized rotating-wave approximation, the derived energy spectrums can agree well with the numerical simulation in the case of the negative detuning (Ω < ω). However, with the increasing of the resonant frequency Ω, this method breaks down and the error is increased linearly. In addition, by means of Eqs. (19) and (20), the Bloch-Siegert shift, which is just the energy shift of the level transition, can be also obtained. In Fig. (3), the smallest Bloch-Siegert shift with the transition E −,0 → E G as a function of the interaction strength g is plotted. The other parameters are the same as those in the recent experiment of circuit quantum electrodynamics with the ultrastrong coupling [20], namely, ω/2π = 8.13 GHz and Ω/2π = 4.25 GHz. If g/ω = 0.1, the smallest Bloch-Siegert shift is 50 MHz, which agrees well with the experimental observation [20].
IV. ANALYTICAL WAVEFUNCTIONS AND MEAN PHOTON NUMBER
The wavefunctions of the Rabi model (1) for the ground and excited states also need to be discussed. For the ground state, the corresponding wavefunction can be evaluated immediately as
|ϕ 0 = e iπ 4 σy e −λσz (a † −a) |0, −x .(21)
For the excited state, the wavefunction for the Jaynes-Cummings-like Hamiltonian (17) is given by |+, n = cos θ n |n, +x + sin θ n |n + 1, −x |−, n = − sin θ n |n, +x + cos θ n |n + 1, −x ,
where where E ±,n are given by Eq. (20). Thus, the excitedstate wavefunction for the Rabi model is given by , (24) where m is the number of the excited state.
θ n = 1 2 tan −1 2R r E −,n − E +,n ,(23)|ϕ e = e
Based on the wavefunctions in Eqs. (21) and (24), the experimentally measurable physics quantities can be well derived. For example, the ground-state mean photon number can be given by a † a 0 = ϕ 0 | a † a |ϕ 0 = 0, −x| e λσz (a † −a) e −iπ 4 σy a † ae iπ 4 σy e −λσz (a † −a) |0, −x , namely,
a † a 0 = λ 2 .(25)
For the excited state, the mean photon number is given by
a † a e = µ + λ 2 + 1+2λ tan θµ √ m+1 1+tan 2 θµ , (m = 1, 3, · · · ) ν + λ 2 + tan 2 θν −2λ tan θν √ m+1 1+tan 2 θν , (m = 2, 4, · · · ) ,(26)
where µ = (m − 1)/2 and ν = (m − 2)/2. In Fig. 3, the mean photon numbers of the ground and excited states for the Rabi model as a function of the resonant frequency Ω for g = 0.1ω are plotted. This figure shows that the analytical results in Eqs. (25) and (26) agree well with the numerical simulation. It implies again that the effective Hamiltonian (17) can describe the current experimental setup with the ultrastrong coupling. Eq. (25) also shows that the ground-state mean photon number for the Rabi model depends on all parameters including the frequency ω of the quantized harmonic oscillator, the interaction strength g, and especially, the resonant frequency Ω. It is quite different from the result derived from the generalized rotating-wave approximation that the ground-state mean photon number is independent of the resonant frequency Ω [25].
V. CONCLUSIONS
In summary, we have presented a unitary transformation to map the unsolvable Rabi model into a solvable Jaynes-Cummings-like model in the dress-state representation. As a result, the analytical energy spectrums and wavefunctions including both the ground and the excited states can be obtained easily. Moreover, our results agree perfectly with the direct numerical simulations in a wide range of the experimental parameters and are valid for all regions of the resonant frequency of the two-level system including the negative detuning (Ω < ω), the resonant case (Ω = ω), and especially the positive detuning (Ω > ω). Our results can also explain the recent experimental observation in the circuit quantum electrodynamics with the ultrastrong coupling.
FIG. 1 :
1(Color online) The energy spectrums of the ground and excited states for the Rabi model as a function of the interaction strength g for Ω = 0.5ω (a), Ω = 1.0ω (b), and Ω = 1.5ω (c). The lowest line reflects the ground-state energy spectrum. In all figures, the black solid lines represent the exact numerical results, while the red open symbol corresponds to the analytical results obtained in the paper.
FIG. 2 :
2(Color online) The energy spectrums of the ground and excited states for the Rabi model as a function of the resonant frequency Ω for g = 0.1ω (a) and g = 0.3ω (b). The lowest line reflects the ground-state energy spectrum. In all figures, the black solid lines represent the exact numerical results, while the red open symbol corresponds to the analytical results obtained in the paper.
FIG. 3 :
3(Color online) The Bloch-Siegert (BS) shift as a function of the interaction strength g with ω/2π = 8.13 GHz and Ω/2π = 4.25 GHz. In this figure, the black solid lines represent the exact numerical results, while the red open symbol corresponds to the analytical results obtained in the paper.
FIG. 4 :
4(Color online) The mean photon numbers of the ground and excited states for the Rabi model as a function of the resonant frequency Ω for g = 0.1ω. The lowest line reflects the ground-state mean photon number. In this figure, the black solid lines represent the exact numerical results, while the red open symbol corresponds to the analytical results obtained in the paper.
4 σy e −λσz (a † −a) |−, m − 1 , (m = 1, 3, · · · ) e iπ 4 σy e −λσz (a † −a) |+, m − 1 , (m = 2, 4, · · · )
and the effective Hamiltonian (11) turns into
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I. INTRODUCTION
Profound changes in the physical and chemical properties of material systems can be produced in situations where the quantum nature of light plays an important role in the interaction with the system. 1-3 A few notable recent examples of such effects are few-photon coherent nonlinear optics with single molecules, 4 direct experimental sampling of electric-field vacuum fluctuations, 5,6 multiple Rabi splittings under ultra-strong vibrational coupling, 7 exciton-polariton condensates, 8,9 and frustrated polaritons. 10 These exciting developments have been strongly driven by experimental efforts, thus exposing the immediate need for the development and improvement of theoretical approaches that can bridge the gap between quantum optics and quantum chemistry. 11 Due to the similarity of the electron-photon and the electron-nuclear problems, simulation methods that have traditionally been of use in the quantum chemistry community, such as semiclassical and mixed quantumclassical methods, offer a potentially interesting avenue to bridge this gap. In particular, the family of trajectory-based quantum-classical methods has the advantage of providing a very intuitive, qualitative understanding of nonadiabatic molecular dynamics. Further, these techniques typically do not exhibit the pernicious exponential scaling of computational effort inherent in grid-based quantum calculations. 12 Available techniques in this family of exact and approximate approaches are Ehrenfest mean field dynamics, fully linearized and partially linearized path integral methods, a) [email protected] b) [email protected] forward-backward trajectory methods, [13][14][15] and trajectory surface-hopping algorithms. 16 All these techniques have some ability to describe essential quantum mechanical effects such as tunnelling, interference, zero-point energy conservation.
Recently, Subotnik and co-workers have performed investigations of light-matter interactions where an adjusted Ehrenfest theory based method is used to simulate spontaneous emission of classical light. [17][18][19] Here, in contrast with these works, we focus on the description of quantized light fields. We then generalize the well established multi-trajectory Ehrenfest method to treat quantum mechanical light-matter interactions. We highlight the possibilities and theoretical challenges of this method in comparison to the exact treatment of the quantum system, by applying this approach to investigate spontaneous emission for a model atom in an optical cavity.
The remainder of this work is divided into three sections: in Sec.II we briefly review general interacting lightmatter systems, and the multi-trajectory Ehrenfest dynamics method. In this framework, we then introduce a one-dimensional model system comprising a single (two or three level) atomic system coupled to a multi-mode quantum electrodynamical (QED) cavity. In Sec.III we investigate the performance of multi-trajectory Ehrenfest (MTEF) dynamics in describing the process of spontaneous emission. We conclude our results in Sec.IV and discuss some prospects for future work.
II. THEORY
A. Quantum Mechanical Light-Matter Interactions
To begin, we describe a general coupled fieldmatter system using Coulomb gauge and the dipole arXiv:1901.01889v2 [quant-ph] 28 Jan 2019 approximation. 20,21 The total Hamiltonian for the system is 22
-26Ĥ =Ĥ A +Ĥ F +Ĥ AF .
(1)
The first term,Ĥ A , is the atomic Hamiltonian, which may be generally expressed in the spectral representation,Ĥ
A = k ε k |k k|.(2)
Here {ε k , |k } are the atomic energies and stationary states of the atomic system in absence of coupling to the cavity. The second term is the Hamiltonian of the uncoupled cavity fieldĤ F ,
H F = 1 2 2N α=1 P 2 α + ω 2 αQ 2 α .(3)
The photon-field operators,Q α andP α , obey the canonical commutation relation, [Q α ,P α ] = ı δ α,α , and can be expressed using creation and annihilation operators for each mode of the cavity field,
Q α = 2ω α (â + α +â α ),(4)P α = i ω α 2 (â + α −â α ),(5)
whereâ † α andâ α denote the usual photon creation and annihilation operators for photon mode α. The coordinate-like operators,Q α , are directly proportional to the electric displacement operator, while the conjugate momenta-like operators,P α , are related to the magnetic field. 24,25 The upper limit of the sum in Eq.(3) is 2N , as there are (in principle) two independent polarization degrees of freedom for each photon mode, however in the 1D cavity models presented here only a single polarization will be considered.
The final term in Eq.(1) represents the coupling between the atom and the cavity field,
H AF = 2N α=1 ω αQα (λ α ·μ) + 1 2 λ α ·μ 2 ,(6)
where we denoteμ as the electronic dipole moment vector of the atomic system, and λ α as the electron-photon coupling vector. 22,25 In the case of a two-level electronic system the quadratic term in the atom-field coupling Hamiltonian simply results in a constant energy shift and hence has no effect on observables, 27 and we neglect this term in the case of the three level model system. Furthermore, we note that this Hamiltonian can easily be extended to include nuclear degrees of freedom, however this has been omitted in the present work.
B. Multi-Trajectory Ehrenfest Dynamics
In this section we apply the well-known multitrajectory Ehrenfest method, traditionally introduced to study electron-nuclear systems, [28][29][30] to coupled lightmatter systems. 21,30,31 A particularly simple and instructive route to derive the MTEF mean field theory is via the quantum-classical Liouville (QCL) equation. 32 This equation of motion for the density matrix is formally exact for an arbitrary quantum mechanical system that is bilinearly coupled to a harmonic environment, as is the case in the atomfield Hamiltonian studied here. The QCL equation can be written in a compact form as
∂ ∂tρ W (X, t) = −iLρ W (X, t).(7)
It describes the time evolution ofρ W (X, t), which is the partial Wigner transform of the density operator taken over the photon field coordinates, which are thus represented by continuous phase space variables X = (Q, P ) = (Q 1 , Q 2 , ..., Q 2N , P 1 , P 2 , ..., P 2N ). The partial Wigner transform of the density operator,ρ, is defined asρ
W (Q, P ) = 1 (2π ) 2N dZe iP ·Z Q − Z 2 |ρ|Q + Z 2 .(8)
The QCL operator is defined as
iL· = i [Ĥ W , ·] − 1 2 ({Ĥ W , ·} − {·,Ĥ W }),(9)
whereĤ W denotes the Wigner transform ofĤ, [·, ·] is the commutator, and {·, ·} is the Poisson bracket in the phase space of the environmental variables.
At this point, one may arrive at MTEF equations by assuming that the total density of the system can be written as an uncorrelated product of the atomic and photonic reduced densities at all times,
ρ W (X, t) =ρ A (t)ρ F,W (X, t),(10)
where the reduced density matrix of the atomic system isρ
A (t) = Tr F ρ(t) = dXρ W (X, t),(11)
and the Wigner function of the cavity field is ρ F,W (X, t) = T r A (ρ W (X, t)). If one seeks solutions to the QCL equation of this form, the Ehrenfest mean-field equations of motion for the atomic system are obtained:
d dtρ A (t) = −i Ĥ A +Ĥ AF,W (X(t)),ρ A (t) ,(12)
whereĤ AF,W denotes the Wigner transform ofĤ AF . The evolution of the Wigner function of the photon field can be represented as a statistical ensemble of independent trajectories, with weights w j ,
ρ F,W (X, t) = Ntraj j w j δ(X − X j (t))(13)
that evolve according to Hamilton's equations of motion,
∂Q α ∂t = ∂H Ef f F,W ∂P α , ∂P α ∂t = − ∂H Ef f F,W ∂Q α .(14)
The effective photon field Hamiltonian is,
H Ef f F,W = 1 2 α P 2 α + ω 2 α Q 2 α − 2ω α λ α Q α µ(t) ,(15)
where µ(t) = Tr A (ρ A (0)μ(t)). The exact expression for the average value of any observable, O(t) , can be written as
O(t) = Tr A dXÔ W (X, t)ρ W (X, t = 0). (16)
We note here that for this class of systems the Ehrenfest equations of motion for the photon field coordinates correspond to a mode resolved form of Maxwell's equations. In applying the MTEF dynamics method numerically, we use the above expressions in the following manner:
1. We first perform Monte Carlo sampling from the Wigner transform of the initial density operator of the photon fieldρ F,W (X, 0) to generate an ensemble of initial conditions, for the trajectory ensemble (Q j α (0), P j α (0)). In this work we used uniform weights w j = 1 Ntraj , however other importance sampling schemes could be employed as the only requirement is that the sum of the weights is normalized, j w j = 1.
2. We evolve each initial condition independently according to the Ehrenfest equations of motion, producing a trajectory. In the following we refer to such a solution as an ensemble of independent trajectories.
3. Average values are constructed by summing over the entire trajectory ensemble, and normalizing the result with respect to N traj , the total number of trajectories in the ensemble,
O(t) = Ntraj j Tr A Ô W (Q j , P j , t)ρ A (0) /N traj .
Here ρ F,W (X, 0) is Wigner transform of the zero temperature vacuum state
ρ F,W (X, 0) = α 1 π exp − P 2 α ω α − ω α Q 2 α .(17)
C. Observables and Normal Ordering
Before we proceed with a discussion of our simulation results, we must note that the Wick normal ordered form for operators (denoted :Ô : for some operatorÔ) is used when calculating average values in this study. The reason for using the normal ordered form, in practice, is to remove the effect of vacuum fluctuations from the results, which ensures that both E = 0 and I = 0, irrespective of the number of photon modes in the cavity field, when the field is in the vacuum state. The effect of this operator ordering is particularly evident for the photon number operator,
:N pt := 1 2 α P 2 α ω α + ω αQ 2 α − 1 ,(18)
where normal ordering produces a constant shift due to the zero-point energy term. The quantized electric field operator is defined aŝ
E(r, t) = α √ 2ω α ζ α (r)Q α (t)(19)
with
ζ α (r) = ω α 0 L sin απ L r .(20)
The corresponding normal-ordered electric field intensity operator is given by
:Ê 2 (r, t) :=:Î(r, t) := 2 α ω α ζ 2 α (r)Q 2 α (t) − α ζ 2 α (r).(21)
The effect of normal ordering on this quantity is shown in Fig. 2, where the intensity of the electric field is plotted in both its canonical and normal ordered forms. In addition to a constant shift with respect to the normal ordered quantity, which is identically zero, the canonical average field intensity also displays additional oscillations near the boundaries and the atomic position, corresponding to the vacuum fluctuations for this system.
We also consider the second order correlation function for the photon field, 33 : g 2 (r 1 , r 2 , t) := :Ê + (r 1 , t)Ê + (r 2 , t)Ê(r 2 , t)Ê(r 1 , t) :
:Î(r 1 , t) : :Î(r 2 , t) : . This function is frequently used in quantum optics to discriminate between classical light and non-classical states of the photon field that exhibit photon bunching (g 2 > 1) or photon anti-bunching (g 2 < 1). The normal-ordered form of the numerator in g 2 , also referred to G 2 (r 1 , r 2 , t), is
: G 2 (r 1 , r 2 , t) := 4 α ω 2 α ζ α (r 1 )ζ α (r 2 )ζ α (r 2 )ζ α (r 1 )Q 4 α (t) − αβ 4ζ β (r 1 )ζ β (r 2 )ζ α (r 1 )ζ α (r 2 ) + ζ 2 β (r 2 )ζ 2 α (r 1 ) + ζ 2 β (r 1 )ζ 2 α (r 2 ) · 2ω αQ 2 α (t).(23)
The partial Wigner transforms of the polynomial functions of the bath coordinate operators are simply polynomial functions of the continuous bath coordinates, Q n α (t) W = (Q α (t)) n . 34 The same is also true for the corresponding momenta, and thus the average values of the preceding operators can be easily calculated using mean-field trajectories.
D. Model System
Following previous work, 23,35 we investigate a model atomic system in a one-dimensional electromagnetic cavity, as depicted in
III. RESULTS AND DISCUSSION
We now investigate the performance of the MTEF method in the context of cavity-bound spontaneous emission. In all calculations shown below we use 400 photon modes to represent the cavity field. We choose the atom to be initially in the excited state, and the cavity field is in the vacuum state at zero temperature. In all simulations reported here we use an ensemble of N traj = 10 4 independent trajectories, sampled from the Wigner transform of the initial field density operator given in the previous section. This level of sampling is sufficient to converge the atomic observables to graphical accuracy, however observables and correlations functions of the photonfield would require a slightly larger trajectory ensemble for graphical convergence. All observables shown below correspond to their normal ordered forms. For our benchmark numerical treatment we solved the time-dependent Schrödinger equation by using a truncated Configuration Interaction (CI) expansion. More precisely, the photon field state-space is truncated at two excitations per photon mode, whereas for the atomic system a two and three state discrete variable representation is used in each case. Numerical convergence is checked to ensure that the CI basis that we employ is complete for the models and parameter regimes studied in this work.
A. Two Level Atom: One Photon Emission Process
In Fig. 3 we show the intensity of the cavity field along the axis of the cavity, at four different times. As the spontaneous emission process proceeds, a photon wavepacket with a sharp front is emitted from the atom and travels toward the boundaries where it is reflected, and then travels back to the atom (e.g. panel (c) of Fig. 3). The emitted photon is then absorbed and re-emitted by the atom, which results in the emergence of interference phenomena in the electric field. This produces a photonic wavepacket with a more complex shape (e.g. panel (d) of Fig. 3). We observe that the MTEF simulations capture the qualitative character of the spontaneous emission process extremely accurately, as well as the wavepacket propagation through the cavity. However, MTEF dynamics fails to reproduce the interference phenomena in the field due to re-emission. We do note, however, that the MTEF simulations are capable of describing the remaining field intensity at the atomic position (e.g panel (e) of Fig. 3). This feature corresponds to a bound electron-photon state, or polariton, which is an emergent hybrid state of the correlated light-matter system.
We also plot the excited state population of the atomic system, and the average value of the photon number for the field, in Fig. 4. Again, MTEF is able to capture the qualitative behaviour of both of these quantities very nicely. However, it fails to quantitatively reproduce the correct values for the emitted photon number and atomic population transfer, as these quantities are underestimated. Furthermore, as a result of this loss in accuracy, only a part of the subsequent re-excitation and re-emission processes are captured.
In Fig. 5 we investigate the normalized second order correlation function, g 2 (r 1 , r 2 , t) for the cavity photon field. The unperturbed vacuum state, which is coherent, corresponds to g 2 (r 1 , r 2 , t) = 1, given by the black background seen in Fig. 5. The vacuum state is disturbed by the emitted wavepacket, corresponding to anti-bunched light with g 2 (r 1 , r 2 , t) < 1. The simplicity of the one-FIG. 6. Associated one-dimensional diagonal cuts g 2 (r±, t) of the second order correlation function, exact (black) and MTEF (green), plotted at four time snapshots:(a) t = 100 a.u., (b) t = 600 a.u., (c) t = 1200 a.u., (d) t = 2100 a.u.. dimensional/one-photon process is quite clear in Fig. 6, where we show the associated one-dimensional cuts of g 2 , along with projections of g 2 (r 1 , r 2 , t) along the positive and negative diagonals, r ± = (r 1 ± r 2 )/ √ 2. Here we find similar to the intensity a nice qualitative agreement between MTEF and the exact result for the first three time snapshots. However for the last time-snap-shot the exact solution shows a broader correlation than MTEF, which corresponds to the fact that MTEF is not able to accurately capture re-emission. Furthermore, as we only consider a one-photon process in this case, the correlation is symmetric in r + and r − .
B. Three Level Atom: Two Photon Emission Process
We now investigate the three-level system, for the same observables as the previous section. The initial state for the atomic system is now the second excited state. The photonic initial state remains the zero temperature vacuum state. In Fig. 7 we show the intensity of the cavity field during the two-photon emission process. Similar dynamics are observed compared with the two-level case. However, due to the additional intermediate atomic state, we now observe a double-peak feature in the emitted photonic wavepacket. This feature corresponds to the emission of two photons, as the excited atom initially drops to the first excited state emitting one photon, and then further relaxes to the ground state, emitting a second photon. The polariton peak (the central feature in the field intensity profile) is overestimated in the MTEF simulations. This overestimation is due to the incomplete relaxation of the second excited state within the Ehrenfest description.
In Fig. 8, we show the time evolution of the atomic state populations and total photon number. Again, the emitted photonic wavepacket moves through the cavity, is reflected at the mirrors, and returns to the atom. The first and second excited state are then repopulated due to stimulated absorption. A second spontaneous emission process ensues, and the emitted field again takes on a more complex profile due to interference. For the intensity, as well as the atomic population and photon number, we observe that MTEF displays qualitatively correct short-time dynamics. However it fails to describe the correct spatial structure of the (re)emitted two photon wavepacket, as well as the correct amplitude for the observables, in accordance with what was observed previously in the two-level case.
In Fig. 9 we show g 2 (r 1 , r 2 , t) for the two-photon emission process. The energy level spacing in the three-level truncation of the 1D soft-Coulomb hydrogen atom is un- even, such that the two emitted photons are of different frequencies. Hence, in contrast to the one-photon process, we expect to observe asymmetric features in the second order correlation function. In the exact result we observe that the vacuum state is locally disturbed by a structured, anti-bunched photon wavepacket. The fine, multi-lobed, spatial structure of the photon wavepacket is blurred into a single, rather narrow, feature in the MTEF result. However, MTEF dynamics indeed show the correct spatial asymmetry that is expected in g 2 (r 1 , r 2 , t).
In the corresponding one-dimensional cuts of g 2 (r 1 , r 2 , t), shown in Fig. 10, we show in further detail the comparison of MTEF dynamics and the exact results in this more complex two-photon case.
IV. SUMMARY AND OUTLOOK
In this work we have adapted the multi-trajectory Ehrenfest method (MTEF) to simulate correlated quantum mechanical light-matter systems. We applied this mixed quantum-classical dynamics method, which is traditonally applied to electron-nuclear dynamics problems, to two and three level model QED cavity bound atomic systems, and in order to simulate observables and correlation functions for both the atomic system, and the photon field. We find that MTEF dynamics is able to qualitatively characterize the correct dynamics for one and two photon spontaneous emission processes in a QED cavity. However, MTEF dynamics does suffer from some quantitative drawbacks. Furthermore, we also observed that MTEF dynamics simulations can, in fact, capture FIG. 9. Second order correlation function for the photon field, g 2 (r1, r2, t) for the three-level model, plotted at four time snapshots: (a) t = 100 a.u., (b) t = 600 a.u., (c) t = 1200 a.u., (d) t = 2100 a.u.. Exact (left panels) and MTEF (right panels).
some quantum mechanical features such as bound polariton states and second order photon correlations. Moreover, as experimental advances drive the need for realistic descriptions of light-matter coupled systems, trajectorybased quantum-classical algorithms emerge as promising route towards treating more complex and realistic systems. In particular, combining the ab initio light-matter coupling methodology recently presented in Jestädt et. al. 37 with our multi-trajectory approach, provides a computationally feasible way to simulate photon-field fluctuations and correlations in realistic three-dimensional systems. Work along these lines is already in progress. Furthermore, an alternative to the independent trajectorybased approach employed here is the conditional wavefunction approach, which allows one address nonadiabatic dynamics problems in complex systems with higher accuracy than MTEF dynamics, 38 and opens up an interesting potential route for mixed quantum-classical methods in correlated light-matter systems.
FIG. 10. Associated one-dimensional diagonal cuts g 2 (r±, t) of the second order correlation function, exact (black) and MTEF (green), plotted at four time snapshots: (a) t = 100 a.u., (b) t = 600 a.u., (c) t = 1200 a.u., (d) t = 2100 a.u..
FIG. 1 .
1Model atomic system in an electromagnetic cavity: Atom (green) trapped between two mirror-like surfaces of the cavity, supporting 2N photon modes with frequencies ωα = 2π cα L , where α = {1, 2, ..., 2N } and L is the distance between the mirrors. The strength of the interactions between each mode of the cavity field and the atomic system is λα.
FIG. 2 .
2Average value of the cavity electric field intensity. Wick normal ordering has been applied to the operator in the case of the red dashed line, whereas the solid black line corresponds to the original operator. The cavity field is prepared in the vacuum state, at zero temperature.
Fig 1 .
1
l=1 µ kl ω α λ α (r A )Q α |k l| , where the upper limit of the first and last summation m denotes the number of atomic energy levels. In the case of a two-level atomic system, this corresponds to a special case of the spin-boson model. With the position of the atom fixed at r A = L 2 in this study, half of the 2N cavity modes decouple from the atomic system by symmetry. We adopt the same parameters as in Ref.,23,36 which are based on a 1D Hydrogen atom with a soft Coulomb potential (in atomic units):{ε 1 , ε 2 } = {−0.6738, −0.2798}, λ α ( L 2 ) = 0.0103 · (−1) α , L = 2.362 · 10 5 and µ 12 = 1.034. For the three-level atom, we adopt all the same parameters for the field and the atom-field coupling as for the two-level case. The atomic energies for the three level model are {ε 1 , ε 2 , ε 3 } = {−0.6738, −0.2798, −0.1547} and as before the numerical parameters are based on the 1D soft-Coulomb Hydrogen atom. The dipole moment operator only couples adjacent states, such that, the only nonzero matrix elements are {µ 12 , µ 23 } = {1.034, −2.536} and their conjugates.
FIG. 3 .
3Time-evolution of the average field intensity for the one-photon emission process, at four different time snapshots: (a) t = 100 a.u., (b) t = 600 a.u., (c) t = 1200 a.u., (d) t = 2100 a.u.. (e) Zoom-in of the polariton-peak at the atomic position. Exact simulation results (black) and MTEF dynamics (green).
of the atomic state populations (top panel), and the total photon number (bottom panel). Top panel: Solid lines represent the atomic ground state, and dashed lines represent the excited state. Both panels: Exact simulation results (black) and MTEF (green).
FIG. 5 .
5Second order correlation function for the photon field, g 2 (r1, r2, t) for the two-level model, plotted at four time snapshots: (a) t = 100 a.u., (b) t = 600 a.u., (c) t = 1200 a.u., (d) t = 2100 a.u.. Exact (left panels), and MTEF (right panels).
FIG. 7 .
7Time-evolution of the average field intensity for the two-photon emission process, at time four different snapshots: (a) t = 100 a.u., (b) t = 600 a.u., (c) t = 1200 a.u., (d) t = 2100 a.u.. (e) Zoom-in of the polariton-peak at the atomic position. Exact (black) and MTEF (green).
FIG. 8 .
8Top panel: Time evolution of the atomic state populations: Solid line (m = 3), dashed lines (m = 2), and dotted line (m = 1). Bottom panel: Total photon number as a function of time. Exact simulation results (black) and MTEF (green).
ACKNOWLEDGEMENTSWe would like to thank Niko Säkkinen and Johannes Flick for insightful discussions and acknowledge financial support from the European Research Council (ERC-2015-AdG-694097). AK acknowledges support from the National Sciences and Engineering Research Council (NSERC) of Canada.
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I. INTRODUCTION
The past few decades have witnessed enormous progress in the development of quantum devices in various physical systems, such as superconducting devices, trapped ions, and semiconductor photonic devices, with significant improvement in their controllability and coherent property. [1][2][3][4] Besides the goal of building scalable fault-tolerant quantum computers, 5 these devices have been exploited to emulate numerous many-body phenomena that are difficult to solve with conventional techniques 6-10 in condensed-matter physics, high-energy physics, and nonequilibrium systems. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] The construction of artificial many-body systems lead to the study of strongly-correlated photons and polaritons. 27,28 In the coupled cavity array (CCA) models, [29][30][31] photons can hop between adjacent cavities. The cavity modes are also coupled to nonlinear medium, such as qubits and defects, which adds nonlinearity to the spectrum of the polariton excitations. The nonlinearity can be viewed as an onsite Hubbard interaction, in comparison to the Bose-Hubbard (BH) model. [32][33][34][35] The competition between the hopping and the nonlinearity results in quantum phase transitions between the Mottinsulating (MI) phase with localized polariton excitations and the superfluid (SF) phase with long-range spatial correlation. In the past few years, the CCA has been studied extensively in theory and in experiments. [36][37][38][39][40][41][42][43][44] Photon blockade has been demonstrated in a recent experiment. 45 Dynamical quantum phase transition with driven and dissipative cavities has been investigated. 46,47 In recent works, 48-51 a multiconnected Jaynes-Cummings (MCJC) lattice was introduced, where qubits and cavities are connected alternatively. Both CCA and MCJC can be realized with the microwave modes in superconducting resonators coupled to superconducting qubits or with optical modes in nanocavities coupled to quantum dots or defects. 1,3 A specific realization of the MCJC lattice is to connect Xmon qubits to superconducting resonators, enabled by the rich connectivity of superconducting cir-cuits. 52,53 Different from the CCA, no direct coupling exists between cavities in the MCJC. Quantum phase transition in a MCJC lattice has been studied with exact diagonalization. 48,49 It was shown that at integer filling, transitions between the MI and SF phases occur due to the competition between the qubit-cavity couplings. These systems provide a promising platform to study correlations in interacting photons and polaritons.
In this paper, we study the quantum critical behavior of the one-dimensional (1D) MCJC model using the density-matrix renormalization group (DMRG). 54,55 This method has previously been used to study the BH and CCA models. [34][35][36]43 We calculate the polariton ground states at both integer and half fillings. The phase boundaries separating the MI and SF phases are obtained by calculating the chemical potentials. 56 The single-particle density matrix is utilized to obtain the correlation lengths and the Luttinger parameters of the qubits and the cavities. Using the Luttinger parameters extrapolated to the thermodynamic limit, the quantum critical points are determined accurately and compared with the previous results. 48,49 We also calculate the structure factors, and find no evidence for a crystalline or charge-density-wave (CDW) phase at half filling. Our result may shed light on the study of strongly-correlated photons and polaritons, especially stationary and out-ofequilibrium effects in the MCJC and related models.
The paper is organized as follows. In Sec. II, we introduce the MCJC model and analyze its phase diagrams at integer and half fillings. In Sec. III, we describe the DMRG method and discuss the results of entanglement entropy and local density. In Sec. IV, the DMRG results on the phase boundary, single-particle density matrix, correlation length, Luttinger parameter, and densitydensity correlation function are discussed. Conclusions are given in Sec. V.
II. MULTICONNECTED JAYNES-CUMMINGS LATTICE
A. The model
A MCJC lattice is composed of alternatively connected qubits and cavities. 48,49 A schematic of a one-dimensional (1D) MCJC lattice is shown in Fig. 1, where each qubit couples to two adjacent cavities. The Hamiltonian of this model reads ( = 1)
H t = H 0 + H l + H r ,(1)H 0 = i ω z 2 σ z 2i−1 + ω c a † 2i a 2i ,(2)H l = i g l σ + 2i−1 a 2i−2 + a † 2i−2 σ − 2i−1 ,(3)H r = i g r σ + 2i−1 a 2i + a † 2i σ − 2i−1 ,(4)
where ω z is the energy splitting of the qubits, ω c is the frequency of the cavity modes, σ z,+,− i are the Pauli matrices, a i is the annihilation operator of cavity modes, g l (g r ) is the coupling constant between a qubit and a cavity next to it from the left (right) hand side. In this paper, periodic boundary conditions are assumed.
Similar to the CCA model [ Fig. 1(c)], a unit cell contains one qubit and one cavity. But unlike in the CCA model, the cavities are not directly coupled to each other. The unique geometry of this model renders a symmetry between g l and g r , and the energy spectrum is unchanged under the exchange of these two coupling constants. This leads to the symmetry in the phase diagram discussed below.
The energy spectrum of a single unit cell in the MCJC lattice can be exactly solved. If we take a qubit with its right cavity as a unit cell [ Fig. 1(a)], the Hamiltonian of the ith unit cell is given by
H i = ω c a † 2i a 2i + ω z 2 σ z 2i−1 + g r a † 2i σ − 2i−1 + σ + 2i−1 a 2i ,(5)
which is nothing but the standard Jaynes-Cummings (JC) model between a qubit and a cavity. 57 It has been extensively studied in cavity and circuit quantum electrodynamic (QED) systems. [58][59][60] In the ground state, there is no photon excitation and the qubit is in the down-spin state. If we use |n, σ to denote the basis states, then the ground state is given by |0, ↓ , where n is the number of photons in the cavity and σ = (↑, ↓) corresponds to the two spin states of the qubit, with ground-state energy E 0 = −ω z /2. The higher excitation states appear in pairs and can be regarded as a doublet, resulting from the coupling between the basis states |n − 1, ↑ and |n, ↓ . In this doublet subspace, the Hamiltonian can be expressed as a 2×2 matrix
[H i ] n = (n − 1)ω c + ωz 2 √ ng r √ ng r nω c − ωz 2 .(6)
There is no coupling between different doublets. Diagonalizing this matrix, we obtain the eigenstates
|n, ± = γ n± |n, ↓ + ρ n± |n − 1, ↑ ,(7)
where γ n+ = −ρ n− = sin θ n , γ n− = ρ n+ = cos θ n , and
θ n = arctan 4ng 2 r + ∆ 2 − ∆ 2 √ ng r .(8)
In the notion |n, ± , n = σ + 2i−1 σ − 2i−1 + a † 2i a 2i refers to the total number of excitations in the unit cell. The corresponding eigenenergies are
E n,± = (n − 1 2 )ω c ± 1 2 4ng 2 r + ∆ 2 ,(9)
where ∆ = ω z − ω c is the detuning between the qubit and the cavity. At ∆ = 0, the doublets become
|n, ± = 1 √ 2 |n, ↓ ± 1 √ 2 |n − 1, ↑ ,(10)
and E n,± = (n − 1/2)ω c ± √ ng r .
The lowest energy to excite one polariton in the JC model is ∆E 1 = E 1,− − E 0 , and the energy to add the second polariton is
∆E 2 = E 2,− − E 1,− . At ∆ = 0, ∆E 1 = ω c − g r and ∆E 2 = ω c − ( √ 2 − 1)g r .
In contrast to the excitations in a bare cavity, the JC model has an intrinsic nonlinearity that can be compared to the onsite interaction in the BH model. 30 For the lower polariton states {|n− } at ∆ = 0, the effective on-site interaction U ∼ (2− √ 2)g r , determined by the qubit-cavity coupling. Similar result can be derived at finite detuning.
B. Quantum phases at integer filling
In the MCJC model with finite g l , the polariton excitations can tunnel between adjacent unit cells. The competition between the tunneling and the effective onsite repulsion strongly affects physical properties of this model. The total number of polaritons in the entire lattice
N t = i σ + 2i−1 σ − 2i−1 + a † 2i a 2i(11)
is a conserving operator. It commutes with the model Hamiltonian, [N t , H t ] = 0. We first consider the phase at an integer filling, where N = N t is an integer multiple of the number of unit cells L. In the limit g l = 0, the unit cells are decoupled, and the ground state is a product state with all the unit cells being in the lower polariton states |1, − and the corresponding energy is E = N E 1,− . It is in the MI phase, which has a finite energy gap for adding or removing one polariton excitation from the system.
To analyze the MCJC model at finite g l , we adopt the polariton mapping technique 31,40 and define a polariton operator at each unit cell
p i nα ≡ |0, − i n, α|.(12)
This is an operator to annihilate a n-polariton state at the ith unit cell.
When i = j, [p i nα , p j † mβ ] = 0. But p i nα
and p i † mβ in the same unit cell do not satisfy the bosonic commutation relation. Using these operators, the spin and photon operators can be expressed as
a i = n,α,α ′ t n αα ′ p i † (n−1)α ′ p i nα ,(13)σ − i = n,α,α ′ k n αα ′ p i † (n−1)α ′ p i nα ,(14)
where the coefficients are given by
t n ±+ = √ nγ n± γ (n−1)+ + √ n − 1ρ n± γ (n−1)− , (15) t n ±− = √ nγ n± ρ (n−1)+ + √ n − 1ρ n± ρ (n−1)− ,(16)
and k n αα ′ = ρ nα γ (n−1)α ′ . The Hamiltonian, H t , can be represented in terms of the polariton operators. For example, at ∆ = 0,
H t = iαn (n − 1/2)ω c + α √ ng r p i † nα p i nα +g l inm αα ′ ββ ′ k n αα ′ t m ββ ′ H i hop ,(17)
where
H i hop = p i † nα p (i−1) † (m−1)β ′ p i−1 mβ p i (n−1)α ′ + h.c..(18)
The first term in Eq. (17) describes the local polariton states with a nonlinear spectrum that resembles the effective onsite interactions. The second term in Eq. (17) can be viewed as the hopping of a polariton from site i−1 (reducing the number of polaritons from m to m − 1) to site i (increasing the number of polaritons from n − 1 to n). The competition between these two terms leads to a phase transition between the MI and SF phases. When g l = 0, the system is in the MI phase. Increasing g l , especially in the parameter range where g l becomes comparable to g r , the hopping can effectively lower the on-site interaction generated by double occupancy and drive the system into the SF phase at a critical point g l /g r = β 0 . This is similar to the phase transition in the BH model with the increase of the hopping integral. 35 By further increasing g l , another MI phase whose properties are similar to the first one by simply exchanging g l with g r emerges above a critical point g l /g r = 1/β 0 . This analysis agrees with the result obtained by an exact diagonalization calculation 48 .
C. Quantum phases at half filling
In the limit there is no coupling between different unit cells, i.e. g l = 0, at the integer filling with N = L, the ground state is in the MI phase with one occupation in the lower polariton state |1, − per site. We denote this state as |1111... and the empty site as |0 for simplicity. In the same limit but away from integer filling, the ground states become highly degenerate. For example, in a lattice of L = 4 at half filling, i.e., N = 2, the ground states are six-fold degenerate, with the following polariton configurations |1010 , |0101 , |1100 , |0110 , |0011 , and |1001 . In the weak intercell coupling limit, g l ≪ g r , we can treat H l as a perturbation. In the first order approximation, the perturbed Hamiltonian can be expressed in this six-fold degenerate subspace as
H l = − g l 2
By diagonalizaiton, we obtain the ground state
|g = √ 2 4 (|1100 + |0110 + |0011 + |1001 ) + 1 2 (|1010 + |0101 ) ,(20)
and the corresponding correction to the ground-state energy E (1) = − √ 2g l .
III. METHOD
We use the finite-lattice algorithm of the DMRG to characterize the critical behavior of the MCJC model. This method has already been used to study critical behavior and quantum dynamics of low-dimensional strongly-correlated systems, including the 1D BH and 1D CCA models. [34][35][36]43 In the calculation, we limit the number of photon excitations at each cavity to be less than or equal to five. For the cases we have examined, we find that this is a good approximation because the contribution from the states with more than five photons at one cavity to the ground-state energy is much smaller than the truncation error. In order to see how fast the DMRG calculations converge with the bond dimension, we calculate the entanglement entropy of the ground state, 61 defined by
S = −Tr (ρ L ln ρ L ) ,(21)
where ρ L is the reduced density matrix for the left half of the lattice. Fig. 2 shows the entanglement entropy as a function of the bond dimension D at both half and integer filling at the symmetric point g l = g r . After a rapid increase at small D, we find that the entanglement entropy becomes almost saturated, which suggests that the ground state wave function is converged, when D is larger than 500. To further ensure the convergence, we take D = 600 for all the calculations presented below. For all the cases we have studied, we find that the ground states are translation invariant, as revealed by the distribution functions of the local excitation densities of qubits and cavities, defined byn q i = σ + i σ − i andn r i = a † i a i , respectively. Our calculation indicates that the excitation densities are homogenous on the whole lattice with no obvious fluctuations. For example, for the system with L = 120 at the integer filling and ∆ = 0, we find thatn q i = 0.40 andn r i = 0.60 when g l = g r = 0.015, andn q i = 0.46 andn r i = 0.54 when g l = 0.0055 and g r = 0.0245, on all the lattice sites. One interesting observation is that the difference |n q i −n r i | between the qubit and cavity excitation densities in the limit of g l ≪ g r (and similarly, g r ≪ g l ) is smaller than that at g l = g r . This is because in the limit g l ≪ g r , the system behaves like a chain of uncoupled JC models where the excitation is equally splitted between the qubit and the cavity. Whereas at g l = g r , the polariton excitations can hop along the lattice, enlarging the splitting of local densities. Similar result is found at half filling.
IV. PHASE DIAGRAM
A. Phase boundaries
We calculate the ground-state energy, E L (N ), of the MCJC model with L unit cells and N polariton excitations using the DMRG. The chemical potential for adding or removing a polariton to the ground state is then determined by the formula
µ p (N, L) = E L (N + 1) − E L (N ), (22) µ h (N, L) = E L (N ) − E L (N − 1).(23)
µ p and µ h are the chemical potentials for adding and removing a polariton, respectively. 35 To obtain the chemical potentials in the thermodynamic limit, we first calculate these quantities at finite lattice systems with L up to 120, and then perform an extrapolation using the formula
µ γ (N, L) = µ γ + b γ /L, (γ = p, h),(24)
where µ γ is the extrapolated chemical potential in the thermodynamic limit. Fig. 3 shows the extrapolated chemical potentials, µ p and µ h , as functions of ln(g l /g r ). At the integer filling with N = L, we find that µ p = µ h in the regime g l ∼ g r (small | ln(g l /g r )|) within numerical errors. As the ratio | ln(g l /g r )| increases, a finite difference appears between µ p and µ h , corresponding to the opening of a finite energy gap for adding or removing a polariton. 35 Thus there is a transition from the SF phase in the small | ln(g l /g r )| regime to the MI phase in the large | ln(g l /g r )| regime. In the SF phase, there is no gap in the energy spectrum and µ p = µ h . However, in the MI phase, the energy to add or remove a polariton becomes different, and µ p > µ h . The extrapolated chemical potentials shown in Fig. 3 thus determine the phase boundaries that separate the MI and SF phases. If the chemical potential falls between µ p and µ h in the MI phase, the filling factor is fixed at N/L = 1, and the polariton density remains a constant within this phase with zero compressibility.
At the integer filling, there are two quantum critical points which are symmetric with respect to the point ln(g l /g r ) = 0. The transitions between the MI and SF phases in this 1D system is of the Kosterlitz-Thouless type 62,63 . It results from the competition between g l and g r . While in the BH and CCA models, the phase transitions are due to the competition between the hopping and the onsite interaction. [29][30][31][32] The inset of Fig. 3 shows the energy gap for exciting a polariton, E gp = µ p − µ h , as a function of ln(g l /g r ). It is clear that there is a finite regime in which E gp = 0. But we cannot accurately determine the positions of the critical points, where E gp begins to deviate from zero, just from the result of this energy gap.
At half filling, the results of chemical potentials indicate that there is no difference in the energy for adding or removing a polariton, i.e. µ p = µ h , in the whole parameter regime. Thus there is no MI-SF phase transition and the ground state is always in the SF phase.
B. Correlation functions
The single-particle density matrices for the qubits and cavities are defined respectively by,
Γ q (i − j) = σ + 2i−1 σ − 2j−1 ,(25)Γ r (i − j) = a † 2i a 2j .(26)
They measure the correlations of polariton excitations. 64,65 Fig. 4 shows the normalized single-particle density matrices Γ r (i − j)/Γ r (0) and Γ q (i − j)/Γ q (0) versus i − j for two sets of parameters. At the integer filling, N/L = 1, both density matrices drop exponentially to zero with the increase of the distance between the two unit cells in the MI phase, g l /g r ≪ 1. In the SF phase, however, the two density matrices remain finite even in the large distance limit, indicating the existence of superfluid off-diagonal long-range order. At half filling, N/L = 1/2, the ground state is in the SF phase, and the two density matrices behave qualitatively similar to the case of g l = g r at the integer filling: they decrease with the increase of the distance between the two unit cells and saturate to certain finite values in the large distance limit. The single-particle density matrices can be fitted using the formulae
Γ α (i − j) = y α + A q e − |i−j| ξα , (α = q, r),(27)
where ξ q (ξ r ) is the correlation length between two qubits (cavities). Fig. 5(a) shows the coefficients y q and y r as functions of ln(g l /g r ). As expected, both y q and y r are zero in the MI phase, but become finite in the SF phase around the regime ln(g l /g r ) close to 0. The correlation lengths, shown in Fig. 5(b), increase quickly around the critical points in the MI phases. But we do not see the divergence of the correlation lengths at the critical point, due to the finite lattice size effect. At the critical point, the entanglement entropy is expected to grow logarithmically with the system size. Thus in order to accurately determine the critical points from the divergent correlation lengths, we need to enlarge not just the lattice size, but also the number of states retained in the DMRG calculation.
From the density-density correlation functions, we calculate the structure factors of the qubits and cavities, defined by
S α π = 1 N 2 i,j (−1) |i−j| n α i n α j , (α = q, r),(28)
where n r i = a † i a i and n q i = σ + i σ − i . Fig. 6 shows S q π and S r π as functions of 1/L at half filling and g l = 0.0055, g r = 0.0245. Within numerical errors, the extrapolated structure factors are found to be approximately zero, indicating that there is no crystalline or CDW ordered phases in this system at half filling. 34
C. Luttinger parameters
In the 1D SF phase, the ground state is a Luttinger liquid, 62,63 and the correlation functions should decay algebraically with the distance between the unit cells
Γ α (i − j) ∝ |i − j| −Kα/2 , (α = q, r),(29)
where K α is the Luttinger parameter. Our calculation, as shown in Fig. 7, has indeed confirmed this power law dependence for the single-particle density matrices. The deviation from the power-law dependence at large distance results from the finite-size effect. The power-law behaviors have also been observed at half filling, where the ground state is always in the SF phase. In contrast, in the MI phase, the single-particle density matrices decay exponentially with the distance. K q and K r are important parameters for characterizing the critical behavior of the MCJC model. To obtain the Luttinger parameters in the thermodynamic limit, an extrapolation of the finite lattice results to the L → ∞ limit is needed. From the numerical results, we find that K α (α = q, r) can be well fitted by the formula (see the insets of Fig. 7)
K α = K 0 α + λ α /L,(30)
where K 0 α is the extrapolated Luttinger parameter in the limit L → ∞ and λ α is a coefficient.
The MI-SF phase transition at integer fillings is of the Kosterlitz-Thouless type, and K 0 q = K 0 r = 1/2 are expected at the critical points for N/L = 1. 34,62,63 In contrast, the corresponding commensurate-uncommensurate phase transitions satisfy K 0 q = K 0 r = 1. From the calculation of these Luttinger parameters, we can accurately determine the critical points. Fig. 8 shows K 0 q and K 0 r as functions of ln(g l /g r ) for the MCJC model at the integer filling N/L = 1. Within numerical accuracy, we find that K 0 q = K 0 r in the whole parameter range we have studied. Deep in the SF phase, g l ∼ g r , K 0 q,r < 1/2, indicating that the spatial correlation decreases slowly with the distance. As | ln(g l /g r )| is increased, K 0 q,r increase and cross the points K 0 q,r = 1/2 at β 0 = g l /g r ≈ 0.579 and 1/β 0 = g l /g r ≈ 1.727. The Luttinger parameters at half filling, as shown in the inset of Fig. 8, are found to be 1/2 < K 0 α < 2, indicating no phase transition in the whole parameter regime studied.
V. CONCLUSIONS
To conclude, we study the ground-state properties of the 1D MCJC model of qubits coupled with cavities us-ing the DMRG. The phase boundaries of this model yield symmetric Mott lobes separated by a SF phase due to the intrinsic symmetry between the left and right qubitcavity interactions. The correlation lengths and the Luttinger parameters at integer and half-integer fillings are determined. By extrapolating the Luttinger parameters to the thermodynamic limit, we accurately determine the critical points separating the MI and SF phases. The structure factors reveal no evidence of crystalline or CDW order at half filling. Our result sheds light on the understanding of the critical behavior of strongly correlated polaritons in the MCJC lattice and related models, such as the CCA, and may stimulate further studies on various stationary and nonequilibrium properties in these systems.
FIG. 1 :
1Schematic of a 1D MCJC lattice (a, b) and a CCA (c). The circles represent the qubits and the blocks represent the cavities. A unit cell of the MCJC consists of a qubit and a cavity adjacent to it coupled (a) by gr or (b) by g l .
FIG. 2 :
2Entanglement entropy S as a function of the bond dimension D for the MCJC model with g l = gr = 0.015, ωc = 1, and ∆ = 0, at (a) half-filling, N/L = 0.5, and (b) integer filling, N/L = 1.
FIG. 3 :
3Chemical potentials µp and µ h versus ln(g l /gr) for the MCJC model with gr + g l = 0.03, ωc = 1, and ∆ = 0 at the integer filling N/L = 1. Inset: Energy gap Egp versus ln(g l /gr) for N/L = 1.
FIG. 4 :
4Normalized single-particle density matrices Γr(i − j)/Γr(0) and Γq(i − j)/Γq(0) versus i − j for the MCJC model with L = 120 at the integer (a,b) and half (c,d) filling. Circles: g l = gr = 0.015; triangles: g l = 0.0055, gr = 0.0245. Other parameters are the same as forFig. 2.
FIG. 5 :
5(a) Coefficients yq and yr and (b) correlation lengthes ξq and ξr versus ln(g l /gr) for the MCJC model with L = 80, 100, 120. Circles: yr and ξr; triangles: yq and ξq. Other parameters are the same as for Fig. 2.
FIG. 6 :FIG. 7 :
67Structure factors S q π and S r π versus 1/L at half filling and g l = 0.0055, gr = 0.0245. Other parameters are the same as forFig. 2. Log-log plot of the single-particle density matrices Γq,r(i) versus the distance i for the MCJC model at the integer filling N/L = 1 with g l = gr = 0.015. Insets: Kq,r versus 1/L. The curves are for L = 80, 90, 100, 110, 120 from top to bottom. Other parameters are the same as forFig. 2.
FIG. 8 :
8K 0 q and K 0 r versus ln(g l /gr) at N/L = 1. The dashed horizontal line is K 0 α = 1/2. Inset: K 0 q,r at N/L = 1/2. g l + gr = 0.03. Other parameters are the same as forFig. 2.
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I. INTRODUCTION
Vibro-polaritonic chemistry is a rapidly evolving field at the intersection of chemistry and quantum optics, which studies the impact of vibrational polaritons on chemical reactivity and molecular properties. [1][2][3] Vibrational polaritons are light-matter hybrid states, which form when molecular vibrations interact strongly with quantized light modes of optical Fabry-Pérot cavities operating in the infrared regime. [4] The field of vibropolaritonic chemistry was sparked by a series of seminal experiments, which reported on spectroscopic signatures of light-matter hybrid states [5][6][7][8][9][10] and, in particular, significantly altered reactive properties of chemical systems under vibrational strong coupling (VSC) [11][12][13].
A quantum mechanical ab initio description of molecular light-matter hybrid systems is based on the molecular Pauli-Fierz Hamiltonian underlying non-relativistic cavity quantum electrodynamics (cQED). [14][15][16][17][18][19] The Pauli-Fierz Hamiltonian accounts for interactions of electrons and nuclei forming molecules with quantized transverse * [email protected] field modes of an optical cavity and is usually formulated in dipole approximation and length-gauge representation. In contrast to the bare molecular many-body problem, the presence of quantized cavity modes renders the fully interacting light-matter hybrid problem significantly more complex. Motivated by experimental findings [12,13], especially an electronic ground state theory for the VSC regime has been of significant interest in recent years. This circumstance stimulated the formulation of a cavity Born-Oppenheimer (CBO) approximation [15,16], which extends concepts from quantum chemistry to the realm of molecular cQED. Within the CBO framework, both low-frequency cavity modes (e.g., infrared radiation) and nuclei are interpreted as "slow" degrees of freedom contrasted by "fast" electrons. [16] The CBO approximation manifests as truncation of an extended VSC Born-Huang expansion employing a basis of adiabatic electron-photon states, which is equivalently understood as neglecting both cavity and nuclear non-adiabatic coupling elements. [16] Small cavity non-adiabatic coupling has been motivated qualitatively by inquiring small momenta for cavity modes, which translated into small magnetic contributions to cavity mode energies. [16] A quantitative understanding and justification of the CBO approximation, however, requires knowledge about the explicit nature of cavity and nuclear non-adiabatic coupling effects under VSC, which have not been discussed in detail so far. Motivated by those aspects, non-adiabatic coupling under VSC constitutes the first main topic of the present work. We explicitly derive analytic expressions for cavity and nuclear nonadiabatic derivative coupling elements from the generalized Hellmann-Feynman theorem [65,66], which allows us to access the detailed character of cavity and nuclear non-adiabatic effects under vibrational strong coupling.
In spirit of the CBO approximation, two distinct routes to ground state vibro-polaritonic chemistry emerged. The first one aims at solving an extended electronic structure problem, which is capable of accounting for correlations between electrons and cavity modes [16],i.e., electron-photon correlation, by extending well established ab initio methods from quantum chemistry to the realm of molecular cQED [21][22][23][24][25][26][27]. An alternative and especially popular approach relies in contrast on effective model Hamiltonians, which are obtained by projecting the molecular Pauli-Fierz Hamiltonian on the adiabatic electronic ground state subsequently giving rise to even more approximate Tavis-Cummings [53] or Dickemodels [54] and variants thereof [20]. Thus, "only" the correlated electronic ground state problem is solved ab initio, which provides access to molecular potential energy and dipole moment surfaces by means of well established quantum chemistry methods. While the fully correlated approach to ground state vibro-polaritonic chemistry, here named VSC theory, has been consistently introduced in terms of an extended VSC Born-Huang expansion in combination with the CBO approximation [15,16], effective approaches commonly lack a derivation and rely on ad hoc formulations.
The second aim of this paper is to close the gap between fully correlated and effective approaches to ground state vibro-polaritonic chemistry. For this purpose, we introduce a consistent formulation of effective approaches, denoted as crude VSC theory, which employs a crude VSC Born-Huang expansion in terms of adiabatic electronic states. We identify the CBO approximation to be invalid with respect to effective ground state problems due to the emergence of non-adiabatic transition dipole couplings between adiabatic electronic states, which are not per se small for large energetic separation. In consequence, we formulate a crude CBO approximation, which leads to widely employed effective model Hamiltonians in ground state vibro-polaritonic chemistry. We argue that the crude CBO ground state misses electron-photon entanglement relative to the adiabatic electron-photon CBO ground state due to neglected non-adiabatic transition dipole couplings. In order to connect both ground state formulations, we propose a perturbative framework, which extends ideas from Herzberg-Teller theory to vibro-polaritonic chemistry. This new perspective allows us to perturbatively identify the crude CBO ground state as first-order approximation to the adiabatic CBO ground state. Moreover, we discuss systematic correc-tions in the crude VSC framework, which account for electron-photon correlation.
The paper is structured as follows: In Sec.II, we provide a consistent quantitative discussion of ab initio VSC theory beyond the cavity Born-Oppenheimer approximation and derive analytic expressions for nuclear and cavity non-adiabatic derivative couplings. In Sec.III, we introduce crude VSC theory as foundation for effective ground state models in vibro-polaritonic chemistry based on a crude CBO approximation. In Sec.IV, we identify differences in electron-photon entanglement accounted for in approximate CBO and crude CBO ground state theories and introduce a Herzberg-Teller inspired perturbative scheme for ground state VSC theory connecting both approaches. Sec.V numerically illustrates selected concepts via the cavity Shin-Metiu model. In Sec.VI, we summarize and conclude this paper.
II. VIBRATIONAL STRONG COUPLING THEORY FOR MOLECULES IN CAVITIES
We begin with a quantitative review of VSC theory based on the molecular Pauli-Fierz Hamiltonian in length-gauge representation and dipole approximation. [15,16] Starting from an extended VSC Born-Huang expansion, we explicitly derive coupled time-independent Schrödinger equations (TISE) for both adiabatic electron-photon states and nuclear-photon states along with non-adiabatic coupling elements for nuclei and cavity modes.
A. The Molecular Pauli-Fierz Hamiltonian
We consider a molecular system composed of N e electrons and N n nuclei coupled to 2N c quantized transverse field modes of an infrared Fabry-Pérot cavity. This lightmatter hybrid system is described by the molecular Pauli-Fierz Hamiltonian in minimal-coupling form [14,15,17]
H PF = Ne i p i + eÂ(r i ) 2 2m e + Nn a P a − Q a (R a ) 2 2M a + V (r, R) + 2Nc λ,k ω k â † λkâ λk + 1 2 .(1)
In the first line, we have kinetic energy contributions with electronic and nuclear momentum operators,p i = −i ∇ i , and,P a = −i ∇ a , electronic and nuclear masses, m e and M a , elementary charge, e, as well as nuclear charges, Q a = Z a e, with charge number, Z a . The first term in the second line is the molecular Coulomb-interaction potential
V (r, R) = Ne i>j e 2 4πǫ 0 |r i − r j | =Vee(r) + Nn a>b Q a Q b 4πǫ 0 |R a − R b | =Vnn(R) − Ne i Nn a Q a e 4πǫ 0 |r i − R a | =Ven(r,R) ,(2)
with electron-electron, V ee (r), nuclear-nuclear, V nn (R), and electron-nuclear, V en (r, R), Coulomb interaction terms. Electronic, r i , and nuclear coordinates, R a , are collected in vectors, r = (r 1 , . . . , r Ne ), and, R = (R 1 , . . . , R Nn ). The last term in Eq.(1) constitutes 2N c quantized transverse field modes characterized by mode index, k, polarization index, λ, and harmonic mode frequency, ω k , respectively.
[55] Cavity modes are represented by photon creation and annihilation operators, a † λk andâ λk , which satisfy, [â λk ,â † λ ′ k ′ ] = δ λλ ′ δ kk ′ . We restrict our discussion here to ideal cavities and neglect dissipative channels inducing spontaneous emission.
The quantized vector potential,Â(r), in Eq.(1) is purely transverse (Coulomb gauge), i.e., ∇ ·Â(r) = 0, and given by [14]
A(r) = 2Nc λ,k e λk ω k ω k 2ǫ 0 V c â † λk e −ik k ·r +â λk e ik k ·r , (3) ≈ 2Nc λ,k e λk ω k g k â † λk +â λk ,(4)
with vacuum permittivity, ǫ 0 , and cavity quantization volume, V c . Every cavity mode is doubly degenerate with respect to two orthogonal polarization directions related to polarization vectors, e λk , which satisfy the orthonormality condition, e λk · e λ ′ k ′ = δ λλ ′ δ kk ′ . In the second line, we employed the dipole approximation, e ±ik k ·r = 1 ± O(i k k · r) ≈ 1, which approximates,Â(r) ≈Â, as spatially uniform motivated by different length scales of infrared wavelengths and molecular diameters. [18] Further, we introduced a mode-specific light-matter interaction constant
g k = ω k 2ǫ 0 V c .(5)
From a quantum chemical perspective, the length-gauge representation of the molecular Pauli-Fierz Hamiltonian in dipole approximation as obtained via [14,22,60]
UŜ = exp i  · d en exp i π 2 2Nc λ,kn λk ,(6)
exhibiting electronic, d e , and nuclear, d n , components. Further,Ŝ in Eq.(6) relates to a unitary rotation in the cavity mode subspace, which is generated by the collective photon number operator, λ,kn λk = λ,kâ † λkâ λk , and induces a real light-matter interaction term as discussed below. [19] In length-gauge representation, the molecular Pauli-Fierz Hamiltonian in dipole approximation readŝ
H PF =Ŝ †Û †Ĥ PFÛŜ =T n +Ĥ e + 2Nc λ,k ω k â † λkâ λk + 1 2 =Ĥc + 2Nc λ,k g k e λk · d en â † λk +â λk =Ĥsc + 2Nc λ,k g 2 k ω k e λk · d en 2 =Ĥ dse .(8)
In the second line, we recover the nuclear KEO,T n , the electronic Hamiltonian,Ĥ e =T e + V (r, R), and the bare cavity Hamiltonian,Ĥ c . The third line constitutes the length-gauge representation of the light-matter interaction,Ĥ sc , determined by the polarization-projected molecular dipole moment, e λk ·d en . Finally, the last term in Eq.(8) resembles the dipole self-energy (DSE),Ĥ dse , which provides translational invariance, a bound ground state and gauge invariance ofĤ PF . [61,62] In what follows, we aim at describing infrared cavity modes on the same footing as nuclear DoF, which is achieved via a cavity coordinate representation [16] x λk = 2ω k â † λk +â λk ,
p λk = i ω k 2 â † λk −â λk .(9)
Here, x λk is a cavity displacement coordinate with conjugate momentum operator,p λk = −i ∂ ∂x λk , satisfying, [x λk ,p λk ] = i . In coordinate presentation, the cavity Hamiltonian readŝ
H c = 2Nc λ,k p 2 λk 2 + ω 2 k 2 x 2 λk =Tc+Vc(x) ,(11)
with KEO,T c , and harmonic cavity potential, V c (x), where, x, is a vector collecting all 2N c displacement coordinates. The cavity coordinate representation ofĤ PF is given then bŷ
H PF =T n +T c +Ĥ e + 2Nc λ,k ω 2 k 2 x λk + 2 ω 3 k g k e λk · d en 2 =Vc+Ĥsc+Ĥ dse ,(12)
which relates to a collection of displaced cavity modes shifted with respect to the polarization-projected molecular dipole moment, e λk · d en . One now introduces an electron-photon Hamiltonian [16]
H ec =Ĥ e + V c +Ĥ sc +Ĥ dse ,(13)
where the third term constitutes the length-gauge lightmatter interaction in coordinate representation,
H sc = 2Nc λ,k 2ω k g k e λk · d en x λk .(14)
The DSE term,Ĥ dse , remains as given in Eq.(8), since it is independent of the cavity mode representation.Ĥ PF in Eq. (12) can now be compactly rewritten aŝ
H PF =T n +T c +Ĥ ec ,(15)
such that the corresponding light-matter timeindependent Schrödinger equation (TISE) reads
T n +T c +Ĥ ec |Ψ i (R, x) = E i |Ψ i (R, x) ,(16)
with energies, E i , and corresponding orthonormal lightmatter many-body states, |Ψ i (R, x) . The ket -notation is employed with respect to the electronic subspace. In the remainder of this work, we are interested in finding approximate bound state solutions of Eq.(16).
B. The VSC Born-Huang Expansion
Ab initio VSC theory is based on an extended Born-Huang expansion for light-matter many-body states, |Ψ i (R, x) , in the following denoted as VSC Born-Huang expansion, which is given by [16]
|Ψ i (R, x) = µ χ (nc) iµ (R, x) |ψ (ec) µ (R, x) .(17)
Here, |ψ (ec) µ (R, x) , are adiabatic electron-photon states, which parametrically depend on both nuclear and cavity coordinates, (R, x), and provide a complete, orthonormal basis spanning the electronic subspace for each fixed configuration, (R, x). Moreover, χ (nc) iµ (R, x), are coefficient functions resembling nuclear-photon states. In order to indicate the hybrid character of states, we employ combined superscripts for electronic (e), nuclear (n) and cavity (c) contributions. We now insert Eq.(17) into the full light-matter TISE (16) and project on adiabatic electronphoton states, ψ (ec) ν |, which leads to
µ ψ (ec) ν |Ĥ PF χ (nc) iµ |ψ (ec) µ = E i χ (nc) iν .(18)
|ψ (ec) ν are taken to be eigenstates ofĤ ec in Eq.(13) and satisfy [16]
Ĥ ec |ψ (ec) ν = E (ec) ν (R, x) |ψ (ec) ν ,(19)
with cavity potential energy surface (cPES), E (ec) ν (R, x), for the ν th -state at fixed configuration, (R, x). Further, KEOs,T n andT c , inĤ PF act on both factors of the product, χ (nc)
iµ (R, x) |ψ (ec) µ (R, x)
, which leads to nuclear and cavity non-adiabatic coupling (NAC) elements between adiabatic electron-photon states [63]
C (n) νµ = − Nn a 2 2M a G (n) a,νµ + 2 F (n) a,νµ · ∇ a ,(20)C (c) νµ = − 2 2 2Nc λ,k G (c) λk,νµ + 2 F (c) λk,νµ ∂ ∂x λk .(21)
Nuclear contributions are determined by
G (n) a,νµ (R, x) = ψ (ec) ν (R, x)|∇ 2 a |ψ (ec) µ (R, x) r , F (n) a,νµ (R, x) = ψ (ec) ν (R, x)|∇ a |ψ (ec) µ (R, x) r ,(22)
and cavity contributions decompose into [63,64]
G (c) λk,νµ (R, x) = ψ (ec) ν (R, x)| ∂ 2 ∂x 2 λk |ψ (ec) µ (R, x) r , F (c) λk,νµ (R, x) = ψ (ec) ν (R, x)| ∂ ∂x λk |ψ (ec) µ (R, x) r ,(23)
where integration with respect to electronic coordinates is indicated by . . . r . Note, both cavity NAC elements are scalar in nature, in contrast to the first-order nuclear derivative term, F (n) a,νµ , which is a vector. The lengthgauge nuclear-photon TISE is eventually obtained as
T n +T c + E (ec) ν (R, x) χ (nc) iν + µ =νK νµ χ (nc) iµ = E i χ (nc) iν ,(24)
with generalized NAC elements given bŷ
K νµ =Ĉ (n) νµ +Ĉ (c) νµ .(25)
In the following, we give a detailed characterization of K νµ , which lies at the heart of the CBO approximation.
C. Non-Adiabatic Coupling under VSC and the CBO Approximation
We evaluate first-order derivative NAC elements,
F (c)
λk,νµ and F (n) a,νµ , analytically by means of the generalized (alternatively off-diagonal) Hellmann-Feynman theorem [65,66]
F (c) λk,νµ = ψ (ec) ν | ∂ ∂x λkĤ ec |ψ (ec) µ r E (ec) µ − E (ec) ν ,(26)F (n) a,νµ = ψ (ec) ν |∇ aĤ ec |ψ (ec) µ r E (ec) µ − E (ec) ν ,(27)
where,Ĥ ec , is the electron-photon Hamiltonian in Eq. (13). For the cavity contribution, we obtain (cf. Appendix A for details)
F (c) λk,νµ = 2ω k g k e λk · D νµ E (ec) µ − E (ec) ν ,(28)
with transition dipole elements between adiabatic electron-photon states
D νµ (R, x) = ψ (ec) ν (R, x)|d en |ψ (ec) µ (R, x) r .(29)
Eq.(28) can be traced back to contributions from the light-matter interaction term,Ĥ sc . Further, since F λk,νµ , becomes particularly large for close lying adiabatic states.
For nuclear derivative NAC elements in Eq.(27), we find (cf. Appendix A)
F (n) a,νµ = ψ (ec) ν |∇ aV en |ψ (ec) µ r E (ec) µ − E (ec) ν + 2Nc λ,k 2 Q a g 2 k ω k e λk · D νµ e λk E (ec) µ − E (ec) ν ,(30)
where the first term resembles the vibronic non-adiabatic coupling in the subspace of adiabatic electron-photon states. The second term constitutes a cavity-induced matter contribution, which emerges from the dipole selfenergy as apparent from the quadratic dependence on the light-matter interaction constant, g 2 k . This term therefore depends also on transition dipole moments between adiabatic electron-photon states, D νµ , in analogy to the cavity NAC element and relates to the transverse polarization operator (cf. Appendix A). Thus, bright and dark adiabatic electron-photon states do not only behave differently with respect to cavity-induced non-adiabatic coupling but also with respect to nuclear contributions under VSC.
When the adiabatic electron-photon ground state is energetically well separated from the excited state manifold, i.e., |E (ec) µ − E (ec) 0 | ≫ 0, both cavity and nuclear NAC elements are small and the VSC Born-Huang expansion can be truncated to the first term [16] |Ψ (ec)
cbo (R, x) = χ (nc) 0 (R, x) |ψ (ec) 0 (R, x) .(31)
This approach resembles the cavity Born-Oppenheimer (CBO) approximation to the light-matter many-body ground state, |Ψ 0 (R, x) ≈ |Ψ
H ec |ψ (ec) 0 (R, x) = E (ec) 0 (R, x) |ψ (ec) 0 (R, x)
.
Two approximate schemes concerning NAC elements are now possible: The first one, here denoted as cavity adiabatic approximation in analogy to vibronic notation [69], neglects off-diagonal NAC elements and accounts for diagonal CBO ground state corrections. The corresponding approximate adiabatic ground state cPES reads λk,00 are defined in Eqs. (22) and (23). The second scheme is realized by additionally setting diagonal non-adiabatic contributions to zero, i.e.,K νµ = 0, for all ν, µ, such that, E (ec) 0 (R, x) ≈ E (ec) 0 (R, x), in Eq.(32) is the bare cPES. Note, our definition slightly differs from the original formulation in Ref. [16], where the CBO approximation took into account diagonal NAC contributions, G
E (ec) 0 (R, x) = E (ec) 0 (R, x) + G (n) 00 + G (c) 00 ,(33)
III. CRUDE VSC THEORY FOR MOLECULES IN CAVITIES
A. The Crude VSC Born-Huang Expansion VSC theory, as discussed in the last section, crucially relies on the knowledge of adiabatic electron-photon states obtained from TISE (19). We now introduce an alternative approach, denoted as crude VSC theory, which circumvents this issue by employing a basis of adiabatic electronic states. In crude VSC theory, we consider a crude VSC Born-Huang expansion
|Ψ i (R, x) = µχ (nc) iµ (R, x) |ψ (ec) µ (R, x 0 ) ,(35)
where adiabatic electron-photon states, |ψ (ec) µ (R, x 0 ) , are considered at a fixed cavity displacement coordinate reference value, x 0 . In order to make the difference to VSC theory explicit, we write nuclear-cavity states,
χ (nc)
iµ (R, x), augmented by a tilde sign. We now choose reference cavity displacement coordinates as
x 0,λk = − 2 ω 3 k g k e λk · d en ,(36)
such that the electron-photon Hamiltonian reduces to the bare electronic Hamiltonian,Ĥ ec (x 0 ) =Ĥ e , for the cavity reference configuration, x 0 . Hence, the electronphoton TISE (19) evaluated at x 0 reduces to the bare electronic TISÊ
H e |ψ (e) ν = E (e) ν (R) |ψ (e) ν ,(37)
which is solved by adiabatic electronic states, i.e.,
|ψ (ec) ν (R, x 0 ) = |ψ (e)
ν (R) , with molecular potential energy surfaces, E (e) ν (R). Accordingly, the crude VSC expansion in Eq. (35) can equivalently be formulated as
|Ψ i (R, x) = µχ (nc) iµ (R, x) |ψ (e) µ (R) ,(38)
where the adiabatic basis is spanned by conventional adiabatic electronic states, which only show a parametric dependence on nuclear coordinates.
B. Coupled TISE in Crude VSC Theory
We now derive coupled TISE in crude VSC theory by inserting Eq.(38) into the light-matter TISE (16), which leads after projection on ψ
(e) ν | to µ ψ (e) ν |Ĥ PF χ (nc) iµ |ψ (e) µ = E iχ (nc) iν .(39)
Evaluation of matrix elements, as shown in Appendix B, eventually provides the bare electronic TISE (37) and the crude nuclear-photon TISE
T n +T c + V ν (R, x) χ (nc) iν + µ =νK νµχ (nc) iµ = E iχ (nc) iν ,(40)
with crude cPES
V ν (R, x) = E (e) ν (R) + V c (x) + 2Nc λ,k 2ω k g k e λk · d νν x λk + 2Nc λ,k g 2 k ω k e λk · d 2 νν + α =ν e λk · d 2 να ,(41)
and dipole matrix elements
d νµ = ψ (e) ν |d en |ψ (e) µ r .(42)
The crude cPES is determined by bare molecular and cavity potentials in the first line, the light-matter interaction term in the second line and the DSE contribution in the third line. The latter contains a "virtual" interaction involving adiabatic states, |ψ
(e) ν
, and, |ψ
(e)
α , which is commonly neglected in ground state problems with ν = 0. Eventually, generalized NAC elements read
K νµ =Ĉ (n) νµ + 2Nc λ,k 2ω k g k e λk · d νµ x λk + 2Nc λ,k g 2 k ω k α e λk · d να e λk · d αµ ,(43)
where the bare nuclear derivative coupling element,
C (n)
νµ , is augmented by two non-adiabatic coupling terms related to polarization-projected transition dipole moments, e λk · d νµ . Those terms emerge as off-diagonal contributions of light-matter interaction and DSE terms in the adiabatic electronic basis.
C. Crude Non-Adiabatic Coupling and the Crude CBO Approximation
We shall now examine the detailed character of crude non-adiabatic coupling elements,K νµ , introduced in Eq. (43) and the notion of a CBO approximation in crude VSC theory. We first recall, that nuclear derivative NAC elements follow from the generalized Hellmann-Feynman theorem as [66]
F (n) a,νµ = ψ (e) ν |∇ aĤe |ψ (e) µ r E (e) µ − E (e) ν ,(44)
which become small for energetically well separated states. However, for cavity-induced NAC contributions in Eq.(43), we found expressions crucially different from Eq.(44): Those terms are proportional to transition dipole moments, d νµ , which are in general not necessarily small for energetically well separated states. Hence, energetic arguments valid for invoking the CBO approximation in VSC theory do not strictly hold in crude VSC theory.
In order to make progress, we introduce a truncation of the crude VSC expansion, Eq. (38), in analogy to Eq.(31) as
|Ψ (e) ccbo (R, x) =χ (nc) 0 (R, x) |ψ (e) 0 (R) ,(45)
which we denote as crude CBO (CCBO) approximation. The latter equivalently resembles, |Ψ 0 (R, x) ≈ |Ψ (e) ccbo (R, x) , where we in particular assume that,K νµ = 0, i.e., all transition dipole NAC elements are neglected. The relevance of the crude CBO approximation manifests in an appealing sum-of-products form of the ground state crude cPES, V 0 (R, x), in Eq.(41) with respect to molecular and cavity degrees of freedom. This representation lies at the heart of effective vibro-polaritonic model Hamiltonians. Thus, according to the arguments presented here, most studies on ground state vibropolaritonic chemistry do actually not rely on the CBO approximation as formulated in Ref. [15,16], but its crude version as introduced in this work.
IV. ELECTRON-PHOTON ENTANGLEMENT AND CRUDE VSC PERTURBATION THEORY
In previous sections, we have seen that approximate crude CBO and CBO ground state theories differ in certain aspects, which we will discuss now in closer detail. First, based on a reduced density matrix (RDM) analysis, we argue that the crude CBO ground state accounts only for a fraction of electron-photon entanglement relative to the CBO ground state. Second, we introduce a Herzberg-Teller inspired perturbative scheme, denoted as crude VSC perturbation theory (cVSC-PT), which allows us to identify the crude CBO ground state as firstorder approximation to the CBO ground state. Higherorder perturbative corrections are subsequently shown to account for non-adiabatic electron-photon correlation effects, which manifest as cavity-induced transition dipole type couplings between adiabatic electronic states.
A. Electron-Photon Entanglement in Approximate CBO Ground States
In absence of electron-photon entanglement, an approximate light-matter ground state, Ψ 0 , is separable in the electron-cavity subspace such that the corresponding electronic RDM,ρ (e) , does not contain any vibropolaritonic contributions. [67,68] Based on this notion, we examine RDM,ρ (i) , for electrons, nuclei and cavity modes with i = e, n, c, as shown in Tab.I for three approximate ground states: The CBO ground state, Ψ We first recall, that both factors in Ψ (ec) cbo , Eq.(31), depend on nuclear and cavity coordinates. We then realize that the adiabatic electron-photon ground state, ψ (ec) 0 , can be expanded in the adiabatic electronic basis, Eq.(C.2), which replaces cavity coordinate dependence of the adiabatic contribution to Ψ I. Reduced density matrices for electrons,ρ (e) (r, r ′ ), nuclei,ρ (n) (R, R ′ ), and cavity modes,ρ (c) (x, x ′ ), for CBO, Ψ
µν , are defined in Appendix C. ρ (e) (r, r ′ )ρ (n) (R, R ′ )ρ (c) (x, x ′ ) Ψ (ec) cbo (r, R, x) µνρ (e) µν µνS (n) µν O (n) µν µS (c) µµ Ψ (e) ccbo (r, R, x)ρ (e) 00S (n) 00 O (n) 00S (c) 00 Ψ ref (r, R, x) ρ (e) 00s (n) 00s (c) 00 traced back to overlap integrals,S (n) µν andS (c)
µµ , between nuclear-photon states,χ
(nc) µ (cf. Appendix C).
The crude CBO ground state, Ψ (ec) ccbo , and related crude CBO-RDM (Tab.I, second line) emerge now naturally by truncating adiabatic basis expansions after the first term. This procedure resembles the crude CBO approximation in the wave function picture, which is equivalent to neglecting cavity-induced non-adiabatic transition dipole type couplings as discussed in Subsec.III C. We thus argue that electron-photon entanglement in Ψ (ec) ccbo due to cavity-induced non-adiabatic contributions from excited electronic states is missing relative to Ψ ccbo , but "indirectly" entangled via nuclei.
Illustratively, the reference state's electronic RDM,
ρ (e)
00 , is independent of vibro-polaritonic contributions (Tab.I, third line), which reflects the fully separable product structure of Ψ ref , Eq. (C.5), in the electron-cavity subspace: Here, electrons are disentangled with respect to both nuclei and cavity modes (although the latter are entangled).
B. Ground State VSC Theory from a Perturbative Perspective
We propose to connect ground state CBO and ground state crude CBO theories via a perturbative scheme, which extends ideas from Herzberg-Teller theory [69] to molecular cQED in the VSC regime. This approach is intended to systematically capture non-adiabatic electronphoton correlation effects accounting for entanglement in the respectively corrected ground state and will be abbreviated as cVSC-PT(n) at n th -order of perturbation theory.
According to Sec.II, the adiabatic electron-photon ground state, |ψ
(ec) 0 (R, x) , satisfies the TISE (32) with cPES, E (ec) 0 (R, x) = E (ec) 0 (R, x)
, in the CBO approximation. We now rewrite the electron-photon Hamiltonian asĤ
ec =T e + V (r, R, x 0 ) + ∆V (r, R, x) ,(46)
with difference potential
∆V (r, R, x) = V (r, R, x) − V (r, R, x 0 ) ,(47)
and recall that the cavity reference configuration, x 0 , in Eq. (36) was chosen such that,Ĥ ec (x 0 ) =Ĥ e . Hence,
V (r, R, x 0 ) = V (r, R)
, is just the bare molecular potential in Eq. (2) and ∆V (r, R, x) contains all cavity contributions toĤ ec . Subsequently, we apply Rayleigh-Schrödinger perturbation theory to approximately solve Eq.(32) with zeroth-order electronic Hamiltonian
H 0 =T e + V (r, R, x 0 ) =Ĥ e ,(48)
and perturbation, ∆V (r, R, x). Perturbative expansions of the CBO ground state and cPES are given by well known expressions
|Ψ (ec) cbo (R, x) = |Ψ (0) 0 (R, x) + λ |Ψ (1) 0 (R, x) + O(λ 2 ) ,(49)
and
E (ec) 0 (R, x) = E (0) 0 (R, x) + λ E (1) 0 (R, x) + λ 2 E (2) 0 (R, x) + O(λ 3 ) . (50) At zeroth-order, we find H e |Ψ (0) 0 (R, x) = E (0) 0 (R, x) |Ψ (0) 0 (R, x) ,(51)
which identifies the bare adiabatic electronic ground state, |Ψ
(0) 0 (R, x) = |ψ (e) 0 (R) , as zeroth-order state with corresponding molecular PES, E (0) 0 (R, x) = E (e) 0 (R).
The first-order corrected cPES is then given by
V (1) 0 (R, x) = E (e) 0 (R) + ψ (e) 0 |∆V |ψ (e) 0 r =E (1) 0 (R,x) ,(52)
where the difference potential, ∆V , reads
∆V = V c +Ĥ sc +Ĥ dse ,(53)
such that we recover for, V
0 (R, x), the correspond- ing ground state crude cPES, Eq.(41). Since E (1) 0 (R, x)(1)
is fully determined by the zeroth-order wave function, i.e., the adiabatic electronic ground state, in line with the crude CBO ground state in Eq.(45), we can accordingly interpret ground state crude VSC theory as firstorder approximation to ground state VSC theory, denoted by cVSC-PT(1). Further, we recall from Subsec.IV A, that electrons and cavity modes in the crude CBO ground state are only indirectly entangled via nuclei since electron-photon correlation induced by nonadiabatic coupling terms involving electronic transition dipole moments, d 0µ , is absent in cVSC-PT(1).
Non-adiabatic corrections accounting for electronphoton correlation enter in cVSC-PT(2) as
V (2) 0 (R, x) = V (1) 0 (R, x) + µ =0 |∆V 0µ (R, x)| 2 ∆E (e) 0µ (R) =E (2) 0 (R,x) ,(54)with, ∆V 0µ = ψ (e) 0 |∆V |ψ (e) µ r , and, ∆E (e) 0µ = E (e) 0 −E (e) µ ,
as determined by the first-order corrected state
|Ψ (1) 0 (R, x) = µ =0 ∆V 0µ (R, x) ∆E (e) 0µ (R) |ψ (e) µ (R) .(55)
In order to illustrate how electron-photon correlation corrections manifest perturbatively, we discuss E (53), we recognize the second-order correction to be independent of the bare cavity potential, since matrix elements, ∆V 0µ , are strictly off-diagonal. Hence, we have explicitly
(2) 0 (R, x) in more detail. From Eq.E (2) 0 (R, x) = µ =0 |H sc 0µ | 2 + 2 H sc 0µ H dse 0µ + |H dse 0µ | 2 ∆E (e) 0µ (R) , (56) with matrix element, H sc 0µ = ψ (e) 0 |Ĥ sc |Ψ (e)
µ r (equivalently for, H dse 0µ ). Further, we recall scaling with respect to the light-matter interaction constant as,Ĥ sc ∝ g, and, H dse ∝ g 2 (we dropped mode indices for brevity), such that, |H sc 0µ | 2 ∝ g 2 , in Eq.(56) provides the leading-order contribution to E (2) 0 (R, x), which reads explicitly
|H sc 0µ | 2 = 2 λ,λ ′ Nc k,k ′ 2ω k 2ω k ′ g k g k ′ × e λk · d 0µ e λ ′ k ′ · d 0µ x λk x λ ′ k ′ . (57)
This term accounts for correlations between electrons and cavity modes via a cavity-induced transition-dipole type interaction between adiabatic electronic states, which in turn couples cavity modes with potentially distinct mode and polarization indices, k, k ′ , and, λ, λ ′ . Interestingly, a similar observation has been recently reported from a non-perturbative perspective. [27] V. NUMERICAL ANALYSIS
We now numerically analyze several aspects of VSC and crude VSC theory discussed above for the cavity Shin-Metiu (CSM) model [15]. The CSM model provides a numerically exactly solvable model, which has been proven versatile to capture the rich physics of nonadiabatic phenomena involving moving electrons and nuclei coupled to quantized cavity modes.
A. The Cavity Shin-Metiu Model
The cavity Shin-Metiu (CSM) model describes a "molecular" model system composed of a moving nucleus and a moving electron [71], which couple via their charges to a single quantized cavity mode [15] as schematically shown in Fig.(1). Both particles move along a molecular axis connecting two fixed nuclei at a given distance, L.
T n +T c = − 1 2M a ∂ 2 ∂R 2 − 1 2 ∂ 2 ∂x 2 ĉ H ec =Ĥ e + ω 2 c 2 x c + 2 ω 3 c g c d en (r, R) 2 H e = − 1 2 ∂ 2 ∂r 2 + V (r, R) ,(58)
with single-mode cavity displacement coordinate, x c , molecular dipole moment
d en (r, R) = −r + Q a R ,(59)
and Shin-Metiu potential [71] V (r, R) = V n (R) + V en (r, R) .
The first term relates to a purely repulsive Coulomb interaction between the moving and fixed nuclei positioned at ±L/2
V n (R) = Q a Q |L/2 − R| + Q a Q |L/2 + R| ,(61)
with nuclear coordinate, R, and nuclear charges, Q a = Q = 1, respectively. The attractive "softened" Coulomb interaction between the electron and all nuclei reads
V en (r, R) = − Q erf |L/2 − r| R f |L/2 − r| − Q erf |L/2 + r| R f |L/2 + r| − Q a erf |R − r| R c |R − r| ,(62)
with error function, erf(. . . ), besides screening lengths for fixed, R f , and moving nuclei, R c . The latter determines the nuclear non-adiabatic coupling strength. [71] Following earlier work [16], we consider a model with L = 10 Å and R f = 1.5 Å, where we set, R c = 1.5 Å, for weak and, R c = 2.0 Å, for strong non-adiabatic coupling. CSM model parameters, which determine the VSC scenario, are obtained by first solving the electronic TISE withĤ e given in Eq.(58)
H e ψ (e) 0 (r; R) = E (e) 0 (R) ψ (e) 0 (r; R) ,(63)
for the ground state molecular PES, E (e) 0 (R), and subsequently the corresponding nuclear TISE
T n + E (e) 0 (R) ϕ (n) v (R) = ε v ϕ (n) v (R) ,(64)
for vibrational eigenstates, ϕ
B. Adiabatic Electron-Photon States
We begin our discussion by examining the impact of vibrational strong coupling on adiabatic electron-photon states. We restrict ourselves to the ground and first excited adiabatic electron-photon states of the CSM model with quantum numbers, ν = 0, 1, and consider reduced densities in the molecular coordinate subspace
ρ (ec) ν (r, R) = dx c |ψ (ec) ν (r; R, x c )| 2 ,(65)ρ (e) ν (r, R) = |ψ (e) ν (r; R)| 2 ,(66)
where, ψ ν ), we introduce a state-dependent difference density [16]
∆ρ (ec) ν (r, R) = ρ (ec) ν (r, R) − ρ (e) ν (r, R) ,(67)
which vanishes in the non-interacting limit, i.e., ν (r, R) are shown for VSC with η = 0.04, and quantum numbers ν = 0, 1 for both the weak and strong non-adiabatic coupling regimes. We observe cavity-induced density redistribution in both the weakly and the strongly non-adiabatic CSM model for the ground and first excited electronphoton state: Red coloured regions in ∆ρ (ec) ν (r, R) indicate a density increase and blue coloured regions a density decrease. New maxima emerge along the electron coordinate, r, in the weakly non-adiabatic regime, while density is dominantly shifted along the nuclear coordinate, R, under strong non-adiabatic coupling.
Density variations with η indicate non-trivial electronphoton correlation effects in energetically low lying adi-abatic electron-photon states of the CSM model, despite the fact that cavity photon energies lie significantly below characteristic electronic excitation energies. Based on those observations, an approximation of the adiabatic electron-photon ground state by the bare electronic ground state, i.e., ρ (ec) 0 (r, R) ≈ ρ (e) 0 (r, R) (crude CBO approximation), does not necessarily seem to be an always well justified simplification. We will provide further arguments supporting this statement in Subsec.V D.
C. Nuclear and Cavity Non-Adiabatic Coupling
We now turn to non-adiabatic coupling under VSC at η = 0.04 and discuss both nuclear and cavity derivative NAC elements for weak and strong NAC regimes of the CSM model.
As observed before in the weak non-adiabatic coupling regime [16], both the ground and first excited state cPES, V 0 (R, x c ) and V 1 (R, x c ), are distorted in the (R, x c )plane under VSC (cf. Figs.3a and 3d). Both states are subject to nuclear (mass-weighted) and cavity derivative NAC elements, F (n) 10 and F (c) 10 , which are found to behave qualitatively similar. According to Figs.3b and 3e, two dominant minima are observed, where the distorted cPES are energetically close. Minima are located close to the nuclear coordinate's origin and take values of x c ≈ ±100 √ m e a 0 for the cavity displacement coordinate corresponding to roughly, n c = 13, photons as estimated from classical turning points of the harmonic cavity potential. The cavity NAC element for the CSM model
F (c) 10 (R, x c ) = 2 ω 3 c d 30 η D 10 (R, x c ) ∆E (ec) 10 (R, x c ) ,(68)
is observed to be two orders of magnitude larger compared to the nuclear derivative NAC, F
F (n) en (R, x c ) = ψ (ec) 1 (R, x c )| ∂ V en ∂R |ψ (ec) 0 (R, x c ) r ∆E (ec) 10 (R, x c ) ,(69)F (n) dse (R, x c ) = 2 Q a η 2 d 30 D (ec) 10 (R, x c ) ∆E (ec) 10 (R, x c ) .(70)
From Figs.3c and 3f, we observe the DSE-induced term,
F (n)
dse , to be roughly one order of magnitude larger compared to the vibronic contribution, F 10 (R, x c ). The difference in magnitude is explained through different scaling with respect to η. Consequently, nuclear derivative NAC elements turn out to be significantly influenced by light-matter interaction, when transitions between two adiabatic states have a strong bright component (cf. Subsec.II C). This finding contrasts the bare molecular picture, where optical properties of adiabatic states are not relevant for non-adiabatic coupling. Moreover, since cavity NAC contributions are here found to be larger in magnitude than their molecular counterparts, the notion of a weak NAC regime does interestingly not simply transfer from the molecular to the light-matter hybrid scenario, at least in the herein presented model.
For the strong NAC regime under VSC, cPES and derivative NAC elements are presented in Fig.4. The ground state cPES shows here a pronounced double minimum, whereas the energetically close lying first excited state exhibits a single minimum close to the ground state's transition state. [16] NAC elements exhibit a sharp maximum with evenly spaced, large amplitude peaks along a seam in the (R, x c )-plane, which is parallel to the separating surface between the two minima of the ground state cPES. A similar observation has been reported very recently. [64] The maximal amplitude is naturally larger compared to the weak NAC regime and the cavity contribution is again roughly two orders of magnitude larger than the vibronic coupling. This observation points at another difference in the notion of weak and strong NAC regimes compared between light-matter hybrid systems and the bare molecular picture: For the system studied here, cavity weak non-adiabatic coupling is characterized by relatively localized peaks in NAC elements, i.e., where cPESs come close, which only becomes relevant when the system is excited in the cavity subspace. In contrast, cavity strong non-adiabatic coupling exhibits substantially extended non-adiabatic interactions between ground and first excited state cPESs as soon as the hybrid system enters the transition state region, irrespective of the energy stored in the cavity mode.
D. Electron-Photon Correlation and Cavity PES
Cavity potential energy surfaces are conceptually appealing, since they directly generalize well established ideas from quantum chemistry to the realm of vibropolaritonic chemistry. Hence, common quantum chemical concepts of (classical) activation barriers [35,38,40,41] and minimum energy paths (MEP) [38,72,73] are naturally transferred to mechanistic arguments in thermal vibro-polaritonic chemistry. However, correlated CBO and crude CBO approaches are commonly not distinguished, which motivates us to discuss here how the different treatment of electron-photon correlation impacts those properties.
In Fig.5a, we show the energy difference between the ground state cPES and its crude counterpart introduced in Eq. (41) under VSC at η = 0.04
∆E 0 (R, x c ) = E (ec) 0 (R, x c ) − V 0 (R, x c )(71)
for the weakly non-adiabatic CSM model. We find pronounced maxima in ∆E 0 close to the transition state along the nuclear coordinate and negative regions along the cavity displacement coordinate. The transition state is determined by classical activation barriers, which are defined as the energy difference between the global min-imum and the transition state energy
∆E a cl = E (ec) 0 (R ‡ , x ‡ c ) − min E (ec) 0 (R, x c ) ∆E a cl = V 0 (R ‡ , x ‡ c ) − min V 0 (R, x c ) ,(72)
for both CBO and crude CBO ground state cPES. In Tab.II, classical activation barriers are shown for the ground state cPES of the CSM model for different lightmatter interaction strengths, η, as obtained under the crude CBO approximation, ∆E a cl , and the CBO approximation, ∆E a cl . We observe classical activation barriers in crude VSC theory, ∆E a cl , to be nearly independent of η for the values studied here, which is in line with results reported in literature, fully accounting for the DSE term. [33,35] In contrast, classical barriers obtained from fully correlated calculations, ∆E a cl , increase with η, here about 4 %. We note, this can be already qualitatively observed in Ref. [16]. Hence, electron-photon correlation can lead to cavityinduced changes in classical activation barriers on CBO cPES, which in turn will potentially influence the reactive system's kinetics. This observation is naturally assumed to be system dependent. Further, since crude cPES do not exhibit a light-matter interaction dependent classical activation barrier, a comparison to CBO cPES should be taken with care. However, crude cPES studied here are indeed able to capture some light-matter interaction effects, e.g., barrier broadening and transition state valley narrowing. [35,38] Thus, further research will be required to map out the strength and weakness of the two perspectives.
Eventually, we consider differences in the cavity minimum energy path (MEP), another concept related to reaction kinetics beyond transition state arguments only: Along the (cavity) MEP, the energy is minimized with respect to variations along all orthogonal valley coordinates. [72] In Fig.5b, we compare cavity MEPs obtained for both ground state crude and CBO cPES at η = 0.04 and observe a rather close match, i.e., the path's curvature is qualitatively similar on CBO and crude cPES: Both MEPs show a linear behavior close to the transition state, whereas the crude version is subject to a slightly stronger curvature, i.e., the valley coordinates couple slightly stronger to motion along the crude reaction coordinate. Accordingly, electron-photon correlation seems to be less important for the cavity MEP, although the corresponding reaction potential still suffers from drawbacks in the barrier's description.
E. Perturbatively Corrected Ground State Crude cPES
In order to improve the crude description, we now examine perturbative corrections to the ground state crude cPES based on the cVSC-PT formalism introduced in Subsec.IV B. We discuss second-and third-order corrected cPESs of the weakly non-adiabatic CSM model in the CBO approximation, as given by
V (2) 0 (R, x) = V (1) 0 (R, x) + E (2) 0 (R, x c ) ,(73)
and
V (3) 0 (R, x) = V (2) 0 (R, x) + E (3) 0 (R, x c ) ,(74)
where, E
0 , is explicitly given in Appendix E. According to Eq.(56), the second-order correction decomposes into three contributions, E
(2) 0 = 3 i=1 E (2) 0,i , which read for the CSM model E (2) 0,1 = µ =0 |H sc 0µ | 2 ∆E (e) 0µ = µ =0 2ω c g 2 d 2 0µ x 2 c ∆E (e) 0µ ,(75)E (2) 0,2 = µ =0 2 H sc 0µ H dse µ0 ∆E (e) 0µ , = µ =0 α 8 ω c g 3 d 0µ (d µα d α0 ) x c ∆E (e) 0µ ,(76)E (2) 0,3 = µ =0 |H dse 0µ | 2 ∆E (e) 0µ , = µ =0 α,β g 4 ω 2 c (d 0α d αµ ) (d µβ d β0 ) ∆E (e) 0µ ,(77)
where, g = ωc d30 η. We suppress nuclear and cavity coordinate dependence for brevity and indicate contributions from DSE expectation values by brackets, e.g., (d 0α d αµ ). Numerically converged results are obtained via inclusion of all neutral states of the weakly non-adiabatic CSM model at fixed η.
We illustratively discuss the sensitivity of classical activation barriers to electron-photon correlation effects due to their potential relevance in thermal vibro-polaritonic chemistry. In Tab.II, second-order, ∆E (2) cl , and thirdorder, ∆E (3) cl , corrected classical activation barriers of the CSM model are provided for selected values of η. We immediately recognize sizable differences with respect to the crude barrier energy, ∆E a cl , which points at the relevance of beyond-crude CBO electron-photon correlation in low-frequency cavity mode settings. While the secondorder correction leads to a reduction of the barrier, we recover the correct trend and a significant fraction of barrier energy increase relative to the fully correlated result at third-order.
Finally, we note a significantly corrected classical activation barrier, ∆E (2,1) cl , when accounting only for the leading order term of cVSC-PT(2) in Eq. (75). Such a result is very appealing since the numerical effort towards a good approximation is rather low. However, this correction has to be treated carefully, since it always leads to a barrier increase. This statement is rationalized by not-ing that E (2) 0,1 vanishes at the transition state located at x c = 0.0, since only there the cavity coordinate gradient tends to zero as required by the minimum energy path. Further, since the numerator is strictly positive, the denominator leads to a negative E (2) 0,1 , which indicates an energy decrease at the reactant configuration and therefore an effective barrier increase. In this context, it is an interesting open question, which we here leave for future studies, whether classical activation barriers on cPES can actually be lowered due to light-matter interaction and under which circumstance this scenario appears to happen.
F. The Electron-Polariton Hamiltonian in Vibro-Polaritonic Chemistry
In this last section, we discuss potential issues occurring when the electron-polariton Hamiltonian,Ĥ p = T c +Ĥ ec , is employed in the VSC regime (cf. Appendix F for details). InĤ p , the electron-photon Hamiltonian, H ec , is augmented by the cavity KEO,T c , which motivates its applicability in the electronic strong coupling regime [25], where both electrons and cavity modes are treated as "fast" degrees of freedom due to similar energy scales. Here, we shall analyze a VSC scenario for the CSM model, where we calculate cPES based on,Ĥ p , motivated by a recent study [26].
In Fig.6a, we show polaritonic cPES, E (p) µ (R), obtained fromĤ p for forty states of the weakly nonadiabatic CSM model under VSC with η = 0.04 (cf. Appendix F for numerical details). We find a dense manifold of surfaces (colored orange), which show an energetic separation of approximately ω c . At elevated energies several avoided crossings appear (colored red), which can be traced back to the first excited adiabatic electronic state becoming energetically dominant.
In Fig.6b, the two energetically lowest lying cPES (colored blue) and the corresponding mass-weighted, nuclear derivative NAC element, − 1 Ma F (p) 10 (R), are shown as functions of the nuclear coordinate. The NAC element is subject to two symmetric maxima at around
R ≈ ±1.5 a 0 , where − 1 Ma F (p)
en (R) = 0.0012 a.u. and cPES are separated by ∆E 10 = 0.0024 a.u. = 527 cm −1 . From the latter, we have, ∆E 10 < ω c , which indicates strong light-matter coupling effects, since the first excited state's cPES is not just shifted by the cavity frequency relative to the ground state cPES. Further, the nuclear derivative NAC element shows a significant magnitude compared to the energy gap. We find, F Based on the non-vanishing non-adiabatic coupling and the small energetic spacing of polaritonic cPES obained fromĤ p , the CBO approximation for the ground state cPES seems not to be well justified from this perspective. Furthermore, due to small energetic separation of polaritonic cPES, corresponding "vibrational" eigenstates are assumed to hybridize, such that the bare ground state polaritonic cPES does not contain all relevant information. From a dynamics perspective, a ground state truncation additionally implies that the light-matter hybrid system will dynamically evolve only on a single surface, which effectively relates to suppression of excitations in the cavity subspace. Consequently, the electron-polariton Hamiltonian,Ĥ p , seems not straightforwardly applicable to ground state problems under the CBO approximation as compared to VSC theory discussed in Sec.II.
We like to close by emphasizing that our arguments apply to cavities, which operate at low energies compared to electronic excitations, i.e., infrared or terahertz cavities with, ω c ≈ ∆ vib ≪ ∆ e . In particular, our arguments do not transfer to scenarios, where cavity mode frequencies acquire a significant fraction of electronic excitation energies, as recently studied computationally in context of cavity-altered ground state reactions [74][75][76].
VI. SUMMARY AND CONCLUSION
In this paper, we extended ab initio vibro-polaritonic chemistry beyond the cavity Born-Oppenheimer approximation [15,16] and discussed the role of electronphoton correlation in the vibrational strong coupling regime. In the first part, we quantitatively reviewed VSC theory by derivation of coupled TISE for adiabatic electron-photon states and nuclear-photon states. Electrons are here described by an extended electronic structure problem, which accounts for correlations between electrons and cavity modes. [16] We furthermore derived explicit expressions for nuclear and cavity non-adiabatic derivative coupling elements via the generalized Hellmann-Feynman theorem. In combination with a numerical analysis of non-adiabatic coupling in the cavity Shin-Metiu model under VSC, our findings can be formulated as:
1. Cavity-induced non-adiabatic coupling is characterized by transition dipole moments between adiabatic electron-photon states and therefore relies crucially on their optical character. Nuclear nonadiabatic coupling is altered in presence of cavity modes by acquiring a transition dipole mediated correction to the vibronic coupling of adiabatic electron-photon states. The additional term emerges from the dipole self-energy and can be understood in terms of the transverse polarization operator.
2. The CBO approximation is well justified, when both adiabatic electron-photon states are energetically well separated and light-matter non-adiabatic coupling is small. The latter relates in particular to vanishing transition dipole moments between electron-photon states. Numerically, we find cavity-induced non-adiabatic coupling relevant if the system is highly excited in the cavity mode, which can become relevant even at low energies, when the non-interacting molecular system is already subject to strong vibronic coupling.
3. Numerical investigation concerning the applicability of the electron-polariton Hamiltonian in the VSC regime revealed the emergence of many close lying polaritonic cPES, which can be locally subject to cavity-induced non-adiabatic coupling. Thus, the CBO approximation seems not simply applicable in this setting. We argue that a separation of electrons as "fast" and cavity modes in combination with nuclei as "slow" DoFs finds in VSC theory a more suitable theoretical approach to vibropolaritonic chemistry. In contrast,Ĥ p , applies well in scenarios, where both electrons and cavity modes resemble "fast" high-energy degrees of freedom and nuclei are "slowly" moving (electronic strong coupling).
In the second part of this paper, we introduced a consistent approach to effective ground state models in vibro-polaritonic chemistry, named crude VSC theory, which can be understood as an approximation to the CBO model. Our formulation relies on a crude VSC Born-Huang expansion that employs a basis of adiabatic electronic states and does not satisfy the CBO but a crude CBO approximation. Accordingly, in crude VSC theory, only the bare electronic structure problem is solved ab initio, which motivates our argument that crude CBO and CBO ground state theories differ in the way they account for electron-photon correlation. We identified correlations partially missing in the crude framework to stem from neglected non-adiabatic coupling terms related to transition dipole moments in the adiabatic subspace, which in turn leads to different electronphoton entanglement character in Ψ (ec) cbo and Ψ (ec) ccbo . We furthermore proposed a perturbative formulation of CBO ground state theory inspired by molecular Herzberg-Teller theory, denoted as crude VSC perturbation theory (cVSC-PT). In the cVSC-PT framework, we characterized the crude CBO ground state as first-order approximation to the CBO ground state, which accounts only for electron-photon entanglement arising indirectly from interactions of electrons and cavity modes with nuclei. Correlation corrections manifest then as cavityinduced, transition dipole-mediated non-adiabatic couplings between adiabatic electronic ground and excited states, which are shown to initially enter at second-order of cVSC-PT. Further characteristics of electron-photon correlation effects based on a numerical analysis of the CSM model summarize as follows:
4. Electron-photon correlation in low-lying adiabatic electron-photon states manifests in terms of density variations in the molecular subspace relative to light-matter uncorrelated adiabatic electronic states (non-interacting limit of light-matter hybrid system).
5. Classical activation barriers on CBO cPES are subject to electron-photon correlation effects, which are absent on crude cPES. In the CSM model, electron-photon correlation induces a barrier increase of 4 % relative to the crude cPES under VSC at η = 0.04. Minimum energy paths on cPES are in contrast well reproduced by effective ground state models concerning path curvature, despite shortcomings in related reaction potentials. From this perspective, a comparison between fully correlated and effective results should be handled carefully, since the relevance of electron-photon correlation effects under VSC is a priori not clear. 6. Perturbative electron-photon correlation corrections at second-and third-order of cVSC-PT were explicitly evaluated for the weakly non-adiabatic CSM model under VSC and illustrated the relevance of electron-photon correlation beyond the crude CBO approximation. Further, cVSC-PT corrections allowed us to obtain significantly improved classical activation barriers relative to the crude cPES of the CSM model.
We conclude by noting, that it remains an open question, when an effective ground state description in spirit of the crude CBO approximation can qualitatively capture trends of the fully correlated CBO approach. Since ab initio approaches to the extended electronic structure problem underlying fully correlated VSC theory are still in their infancy, it would be desirable to identify suitable scenarios, where one can benefit from the appealing nature of crude model approaches to vibro-polaritonic chemistry. Further, non-adiabatic effects under vibrational strong coupling will become relevant for reactive systems subject to energetically low-lying excited states like for example the thermal isomerization process of azobenzene [77,78]. Such "beyond CBO" scenarios would be furthermore conceptually interesting, since they point at a deeper understanding of strong interactions between electrons, nuclei and cavity modes. Eventually, collective effects in vibro-polaritonic chemistry and their inclusion in an ab initio description of light-matter hybrid systems under VSC pose a contemporary theoretical issue relevant for connecting theoretical predictions with experimental findings. In particular, potentially non-local, cavity-induced interactions [79,80], which are able to shape the local "making-and-breaking" of chemical bonds in the VSC regime as well as the relevance of electron-photon correlation effects in this context requires further research. The applicability of crude VSC theory relative to fully correlated approaches can also here constitute a beneficial first step towards collective strong coupling scenarios due to its inherently simpler character.
ACKNOWLEDGMENTS
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.
CONFLICT OF INTEREST
The authors have no conflicts to disclose.
APPENDIX
A. Details on Derivative NAC Elements
We analytically evaluate derivatives of electron-photon Hamiltonians with respect to cavity displacement and nuclear coordinates in VSC theory for derivative NAC elements as discussed in Sec. II C.
Cavity Derivative NAC Elements
For the cavity displacement coordinate derivative, we obtain
∂ ∂x λkĤ ec = ∂ ∂x λk Ĥ e + V c +Ĥ sc +Ĥ dse , (A.1) = ∂ ∂x λk 2Nc λ ′ ,k ′ ω 2 k ′ 2 x 2 λ ′ k ′ (A.2) + 2ω k ′ g k ′ e λ ′ k ′ · d en x λ ′ k ′ + g 2 k ′ ω k ′ e λk · d en 2 , = ω 2 k x λk + 2ω k g k e λk · d en , (A.3)
such that the corresponding matrix element evaluates to
ψ (ec) ν | ∂ ∂x λkĤ ec |ψ (ec) µ r = ω 2 k x λk δ νµ + 2ω k g k e λk · D νµ . (A.4)
Here, the diagonal term in the first line vanishes since, ν = µ.
Nuclear Derivative NAC Elements
For the nuclear coordinate derivative, we find
∇ aĤ ec = ∇ aĤ e + ∇ a V c + ∇ aĤ sc + ∇ aĤ dse , (A.5)
where we immediately recognize, ∇ a V c = 0. The interaction term's derivative gives
∇ aĤ sc = ∇ a 2Nc λ,k 2ω k g k e λk · d en x λk , (A.6) = 2Nc λ,k 2ω k g k ∇ a e λk · d n x λk , (A.7) = 2Nc λ,k 2ω k g k ∇ a b Q b e λk · R b x λk , (A.8)
where in the second line, ∇ a e λk · d e = 0. With,
d n = b Q b R b ,
in the third line and evaluation of nuclear gradients as
∇ a e λk · R b = e λk ∇ a · R b = e λk δ ab , (A. 9) it follows that
∇ aĤsc = 2Nc λ,k 2ω k g k Q a e λk x λk . (A.10)
Turning to the dipole self-energy term, the nuclear derivative follows as where the second term corresponding to the light-matter interaction contribution, ∇ aĤsc , is independent of electronic coordinates and vanishes therefore due to orthogonality of adiabatic electronic states.
∇ aĤ dse = ∇ a
B. Details on Crude VSC Theory
Starting from Eq.(39), the matrix element with respect toĤ ec is evaluated as
ψ (e) ν |Ĥ ecχ (nc) iµ |ψ (e) µ = E (e) ν (R) + V c (x) χ (nc) iν (B.1) + ψ (e) ν |Ĥ sc |ψ (e) µ rχ (nc) iµ + ψ (e) ν |Ĥ dse |ψ (e) µ rχ (nc) iµ ,
where the first term constitutes the diagonal contribution determined by the molecular PES, E (e) ν (R), and the cavity potential, V c (x). The second term resembles the matrix element for the light-matter interaction,Ĥ sc , which evaluates to
ψ (e) ν |Ĥ sc |ψ (e) µ rχ (nc) iµ = 2Nc λ,k 2ω k g k e λk · d νµ x λkχ (nc) iµ , (B.2)
and has in general both diagonal and off-diagonal contributions with dipole matrix elements as given in Eq. (42). The third term in Eq.(B.1) involves the dipole self-energy term,Ĥ dse , with matrix element
ψ (e) ν |Ĥ dseχ (nc) iµ |ψ (e) µ = 2Nc λ,k g 2 k ω k α e λk · d να e λk · d αµ χ (nc) iµ , (B.3)
where we inserted the resolution-of-the-identity in the adiabatic subspace, α |ψ which holds, when e λk projects out only a single element of the molecular transition dipole moment, d να . This can be always achieved for linearly polarized cavity modes as considered here: Vectors, {e λk , e λ ′ k , k}, span a cavity coordinate frame, which can be chosen parallel to the molecule fixed frame with molecular center of mass located at the origin. Then, only single elements of d να are addressed with respect to polarization vectors, e λk , and, e λ ′ k , parallel to the molecular frame's axis.
C. Details on Reduced Density Matrices
A beneficial connection between CBO and crude CBO ground states in Eqs. (31) and (45) can be introduced by realizing that the adiabatic electron-photon ground state, |ψ (ec) 0 (R, x) , at a fixed nuclear configuration, R, can be expanded in an orthonormal basis of adiabatic electronic states, |ψ (e) µ (R) . [68] Accordingly, the CBO ground state can be written as
|Ψ (ec) cbo (R, x) = χ (nc) 0 (R, x) c µ (x) |ψ (e) µ (R) (C.1) = µχ (nc) µ (R, x) |ψ (e) µ (R) , (C.2)
where we absorb expansion coefficients, c µ (x), which account for the cavity displacement coordinate dependence, in the second line into,χ where expansion coefficients, u i (R), now accounting for nuclear coordinate dependence, are absorbed into, x). By truncating the expansion in Eq.(C.4) after the first term, we obtain a zeroth-order reference (ref) state
(nc) µ (R, x) = c µ (x) χϕ (nc) i (R, x) = u i (R)χ (nc) 0 (R,|Ψ ref (R, x) =φ (nc) 0 (R, x) |ψ (e) 0 , (C.5)
which is a product state with respect to electronic and nuclear-cavity DoF, i.e., electrons are by definition disentangled from nuclei and cavity modes. In the following, electronic, nuclear and cavity reduced density matrices are derived for the CBO ground state, the crude CBO ground state and the partially disentangled reference state in Eqs.(C.2)-(C.5).
Electronic Reduced Density Matrices
Starting with electronic RDM, we obtain for the CBO ground statê
ρ (e) cbo (r, r ′ ) = dR dx Ψ (ec) cbo (r, R, x) Ψ (ec)⋆ cbo (r ′ , R, x) , = µν dR ψ µ (r; R) ψ ⋆ ν (r ′ ; R) × dxχ µ (R, x)χ ⋆ ν (R, x) , = µν dR ρ µν (r, r ′ ; R)S µν (R, R) , = µνρ µν (r, r ′ ) =ρ (e) µν , (C.6)
with vibro-polaritonic overlap integral
S µν (R, R) = dxχ µ (R, x)χ ⋆ ν (R, x) =S (n) µν , (C.7)
and
ρ µν (r, r ′ ) = dR ρ µν (r, r ′ ; R)S µν (R, R) =ρ (e) µν , (C.8) where ρ µν (r, r ′ ; R) = ψ µ (r; R) ψ ⋆ ν (r ′ ; R) . (C.9)
The crude CBO electronic RDM follows immediately by truncating the sum over adiabatic electronic states in Eq.(C.6) asρ For the reference state, one findŝ
ρ (e) ref (r, r ′ ) = dR dx Ψ ref (r, R, x) Ψ ⋆ ref (r ′ , R, x) , = ψ 0 (r) ψ ⋆ 0 (r ′ ) dR dx |φ 0 (R, x)| 2 =1 , = ψ 0 (r) ψ ⋆ 0 (r ′ ) =ρ (e) 00 , (C.11)
where normalization ofφ 0 (R, x) was employed in the second line. Note, the third line resembles a bare (crude adiabatic) electronic contribution.
Nuclear Reduced Density Matrices
The nuclear RDM for the CBO state follows aŝ .
ρ (n) cbo (R, R ′ ) = dr dx Ψ (ec) cbo (r, R, x) Ψ (ec)⋆ cbo (r, R ′ , x) , = µν dxχ µ (R, x)χ ⋆ ν (R ′ , x) × dr ψ µ (r; R) ψ ⋆ ν (r; R ′ ) , = µνS µν (R, R ′ ) O µν (R, R ′ ) =S (n) µν O (n) µν
(C.14)
Eventually, for the reference state, we havê
ρ (n) ref (R, R ′ ) = dr dx Ψ ref (r, R, x) Ψ ⋆ ref (r, R ′ , x) , = dxφ 0 (R, x)φ ⋆ 0 (R ′ , x) dr ψ 0 (r) ψ ⋆ 0 (r) =1 , =s 00 (R, R ′ ) =s (n) 00 , (C.15)
where normalization of ψ 0 (r) was employed in the second line. Note, in contrast to CBO and crude CBO nuclear RDM,ρ
ref is independent of adiabatic electronic contributions, which directly follows from the product nature of the reference state.
Cavity Reduced Density Matrices
Finally, the cavity RDM for the CBO ground state is obtained aŝ 16) and the crude CBO cavity RDM is straightforwardly found to beρ
ρ (c) cbo (x, x ′ ) = dr dR Ψ (ec) cbo (r, R, x) Ψ (ec)⋆ cbo (r, R, x ′ ) , = µν dRχ µ (R, x)χ ⋆ ν (R, x ′ ) × dr ψ µ (r; R) ψ ⋆ ν (r; R) =δνµ , = µ dRχ µ (R, x)χ ⋆ µ (R, x ′ ) , = µS µµ (x, x ′ ) =S (c) µµ , (C.(c) ccbo (x, x ′ ) =S (c) 00 . (C.17)
For the reference state, we find an expression similar to the nuclear RDM witĥ
ρ (n) ref (x, x ′ ) = dr dR Ψ ref (r, R, x) Ψ ⋆ ref (r, R, x ′ ) , = dRφ 0 (R, x)φ ⋆ 0 (R, x ′ ) dr ψ 0 (r) ψ ⋆ 0 (r) =1 , =s 00 (x, x ′ ) =s (c) 00 . (C.18)
As in the nuclear case, the latter is independent of adiabatic electronic contributions.
D. Numerical Details on the VSC-CSM Model
We follow earlier work and consider the two fixed nuclei in the CSM Hamiltonian separated by L = 10 Å = 18.9 a 0 with screening length, R f = 1.5 Å and nuclear charges, Q a = Q = 1 e. Further, we discuss weak (strong) nonadiabatic coupling regimes characterized by mobile nucleus screening lengths, R c = 1.5 Å (R c = 2.0 Å).
For the numerical solution of the length-gauge CSM model Hamiltonian, we employ a Colbert-Miller discrete variable representation (DVR) for all DoF, i.e., the electron, the moving nucleus and the cavity mode, with KEO matrix elements
T ij = 2 2∆s 2 (−1) i−j π 2 3 , i = j 2 (i − j) 2 , i = j , (D.1)
for coordinates, s = r, R, x c . Up to vibrational strong coupling with η = 0.04, we obtain converged results on grids r ∈ [−2L, 2L], R ∈ [− L 2 , + L 2 ], and, x c ∈ [−300, 300] √ m e a 0 . We employ grid points, M e = M n = M c = 201, for electrons, nucleus and cavity mode in both the weak and strong non-adiabatic coupling regimes.
E. Details on cVSC-PT(3)
We provide an explicit expression for the thirdorder energy correction in cVSC-PT(3) when applied to the CSM model. Following conventional Rayleigh-Schrödinger perturbation theory, the third-order energy correction is given by
E (3) 0 = µ,ν =0 ∆V 0µ ∆V µν ∆V ν0 ∆E (e) 0µ ∆E (e) 0ν − ∆V 00 µ =0 |∆V 0µ | 2 ∆E (e) 0µ 2 , (E.1)
where we suppress coordinate dependence for brevity. We first show, that contributions involving the cavity potential, V c , cancel. Taking into account the orthonormal character of adiabatic electronic states, the first term can be written as
0 is independent of V c and can be decomposed into eight contributions, E
0 = 8 i=1 E(3)
0,i , by grouping equivalent products of expectation values. The leading order term scales as g 3 and reads .
(E.7)
The quintic contribution scaling as g 5 is determined by three terms E F. Details on the Electron-Polariton Hamiltonian
Extended Born-Huang Expansion and TISEs
The electron-polariton Hamiltonian is given aŝ
H p =T c +Ĥ ec , (F.1)
and augments the length-gauge electron-photon Hamiltonian by the cavity KEO. A generalized Born-Huang expansion can be introduced as
Ψ i (r, R, x) = µ φ (n) iµ (R) ψ (p) µ (r, x; R) , (F.2)
with orthonormal, adiabatic electron-polariton states, ψ (p) µ (r, x; R), and nuclear states, φ (n) iµ (R), providing expansion coefficients. Adiabatic states treat electrons and cavity modes here on equal footing and only the nuclear coordinate dependence is understood to be parametric in nature. The molecular Pauli-Fierz Hamiltonian takes the form,Ĥ PF =T n +Ĥ p .
After projecting on adiabatic electron-polariton states, ψ (p) ν (R)|, we obtain a system of two coupled TISEs, where adiabatic states solvê
H p |ψ (p) ν (R) = E (p) ν (R) |ψ (p) ν (R) , (F.3)
with polaritonic cPES, E (p) ν (R), which only depends on nuclear coordinates, R, and provides a potential for a nuclear TISE Although F (p) a,νµ (R) is formally similar to F (n) a,νµ (R) in Eq.(30) (note different superscripts (p) and (n)), it differs in two relevant aspects: First, for infrared Fabry-Pérot cavities
T n + E (p) ν (R) φ (n) iν (R) + µ =νĈ (p) νµ φ (n) iµ (R) = E i φ|E (p) ν − E (p) ν+1 | ≈ ω c ≪ ∆ e , (F.7)
with characteristic fundamental electronic transition energy, ∆ e , and second, D (p) νν+1 , is not necessarily small for energetically close-lying cPES. We discuss those aspects in some detail in Subsec.V F.
Numerical Details
We solve the electron-polariton TISE (F.3) illustratively for the CSM model in the weak NAC regime with R c = 1.5 Å and η = 0.04. Convergence of the 40 energetically lowest lying polaritonic cPES is obtained with grids, r ∈ [−2L, 2L], x c ∈ [−300, 300] √ m e a 0 and R ∈ [− L 2 , + L 2 ], discretized by grid points, M e = 91, M c = 91 and M n = 101. Note, we restrict the electronic grid to the region where the electron-nuclear potential dominates and do not account for regions far from nuclei as determined by a harmonically-confining electronic DSE contribution. The latter may be relevant if the electron is driven far from the three nuclei due to an external driving field for example, which is beyond the scope of the present work.
proportional to polarization-projected transition dipole moments, e λk · D νµ , the optical character of adiabatic electron-photon states plays a central role: Cavity non-adiabatic coupling elements vanish for dark transitions characterized by, D νµ = 0, and are non-zero for bright transitions with D νµ = 0, where, F (c)
R, x) , where the corresponding electron-photon ground state satisfieŝ
and a partially disentangled reference state, Ψ ref (cf. Appendix C for details).
contributions from all adiabatic electronic states (cf. Appendix C). Thus, CBO-RDM (Tab.I, first line) are determined by all adiabatic electronic states and furthermore contain vibro-polaritonic contributions (indicated by tilde signs)
only apparently separable in the electron-cavity subspace, since both factors depend on nuclear coordinates, which in turn results in vibro-polaritonic contributions to the electronic crude CBO-RDM,ρ
cf. Appendix C). From this perspective, electrons and cavity modes are actually not disentangled in Ψ (ec)
FIG. 1 .
1Schematic representation of the cavity Shin Metiu model with a moving positively charged nucleus (blue) with coordinate, R, and a moving negatively charged electron (yellow) with coordinate, r, both interacting with a single cavity mode. Fixed positively charged nuclei are colored in red and located at a distance L from each other, while mobile particles move along the related molecular axis connecting fixed nuclei.The length-gauge Pauli-Fierz Hamiltonian, Eq.(15), reads for the CSM model (in atomic units)
v
(R), with energies, ε v . For the CSM model under VSC, we tune the cavity resonant to the fundamental vibrational transition, ω c = ε 3 − ε 0 . For the weak (strong) NAC regime, we have a cavity frequency, ω c = 585.16 cm −1 (516.74 cm −1 ), with vibrational transition dipole element, d 30 = 0.089 ea 0 (0.26 ea 0 ). The light-matter interaction constant, g = ωc d30 η, is furthermore characterized by a dimensionless parameter, η.[20] Further model parameters and numerical details on the CSM model are provided in Appendix D.
ν
(r; R, x c ), are eigenstates ofĤ ec in Eq.(58). In order to access cavity-induced changes in reduced light-matter hybrid densities, ρ(ec) ν , relative to the bare FIG. 2. Contour plots of reduced adiabatic electron-photon densities, ρ (ec) ν (r, R), (a1-d1), reduced adiabatic electron densities, ρ (e) ν (r, R), (a2-d2) and adiabatic difference densities, ∆ρ
, R), (a3-d3) in electron-nuclear coordinate space for adiabatic ground and first excited states (ν = 0, 1) in weak and strong non-adiabatic coupling (NAC) regime of the CSM model under vibrational strong coupling with η = 0.04.
ν (r, R) = 0 , for, η = 0
00
FIG. 3 .
3Weakly non-adiabatic CSM model under VSC with η = 0.04: a) Ground, V0(R, xc), and d) first excited state cPES, V1(R, xc), as function of nuclear, R, and cavity displacement, xc, coordinates with energies in atomic units (a.u.). b) Mass-weighted nuclear derivative NAC element, − 1 Ma F (n) 10 (R, xc), and e) cavity derivative NAC element, − F (c) 10 (R, xc), in a.u. as function of coordinates under VSC. c) Molecular, − 1 Ma F (n) en (R, xc), and f) DSE-induced nuclear NAC contributions, − 1 Ma F (n) dse (R, xc), to mass-weighted nuclear NAC element in b) with same parameters.
(n) 10 .
10Note, d 30 , is the vibrational transition dipole moment, whereas ∆E (ec) 10 relates to the energy difference between adiabatic electron-photon states. The nuclear term, F (n) 10 , has according to Eq.(30) a vibronic, F (n) en , and a cavity-induced contribution, F (n) dse , which explicitly read here
which can be traced back to the bright transition dipole moment, D
only quadratic corrections in η (cf. Subsec.V E). All energies are given in wave numbers for selected values of η.
FIG. 4 .
4Strongly non-adiabatic CSM model under VSC with η = 0.04: a) Ground, V0(R, xc), and c) first excited state cPES, V1(R, xc), as function of nuclear, R, and cavity displacement, xc, coordinates with energies in atomic units (a.u.). b) Massweighted nuclear derivative NAC element, − 1 Ma F (n) 10 (R, xc), and d) cavity derivative NAC element, − F (c) 10 (R, xc), in a.u. as function of coordinates under VSC as a) and d).
FIG. 5 .
5Differences between ground state cPES and ground state crude cPES for the weakly non-adiabatic CSM model under VSC with η = 0.04. (a) Energy difference, ∆E0(R, xc), in wave numbers (cm −1 ) and (b) numerical approximations to cavity minimum energy paths for E (ec) 0 (R, xc) in red and for V0(R, xc) in blue (contour plot shown in cm −1 ).
to be dominantly determined by the cavity-induced contribution to the nuclear derivative NAC, − 1 Ma F (p) dse (R) (cf. Appendix F), as shown in dashed-blue, i.e., non-adiabatic coupling is an effect of strong interaction between electrons and cavity modes. The molecular component, − 1 Ma F (p) en (R), is very small and not observable from Fig.6b. FIG. 6. a) 40 energetically lowest lying adiabatic polariton cPES, E (p) µ (R), as function of nuclear coordinate, R, obtained from, Hp, for the CSM model in the weak NAC regime under vibrational strong coupling with η = 0.04. Lowest two surfaces are colored in blue and high energy cPES manifold subject to avoided crossings is colored in red. b) Two energetically lowest lying polaritonic cPES, E (R), as function of nuclear coordinate, R.
e λk · d en ∇ a e λk · d en , e λk · d en Q a e λk , (A.13) where we employed the chain rule in the second line and took advantage of the result found for the interaction term in the third line. The nuclear derivative of the DSE term is related to the transverse polarization operatore λk · d en e λk , e λk · d en e λk , (A.16) where the second line follows with, α = (λ, k), for the summation index and, λ λk = λ k e λk , whereas in the thirdline, λ k = 2 ω k g k .For the corresponding matrix element, we find ψ (ec) ν |∇ aĤ ec |ψ (ec)
α
| = 1 (e) , between projected dipole moments. For diagonal matrix elements with ν = µ, it is instructive to rewrite the sum over adiabatic states as α e λk ·d να e λk ·d αν = α e λk ·d 2 να , (B.4)
(nc) 0 (
0R, x). Eq.(C.2) is formally appealing, since the crude CBO ground state, |Ψ
R, x) , introduced in Eq.(45) follows directly by truncating Eq.(C.2) after the first term.Further, one can similarly expand the crude CBO ground state in an orthonormal basis of crude adiabatic electronic states, |ψ
R 0 ) , with nuclear reference configuration, R 0 , leading to |Ψ (e) ccbo (R, x) =χ
(r, r ′ ) =ρ (e) 00 .(C.10)
O
µν (R, R ′ ) = dr ψ µ (r; R) ψ ⋆ ν (r; R ′ ) = O (n) µν . (C.13) Note, the adiabatic matrix element, O µν (R, R ′ ), is nonzero for R = R ′ . The crude CBO equivalent follows again by truncating the sum over adiabatic electronic states in Eq.(C.12) to the ground state contribution ρ
F
, are formally similar to Eq.(20), however, act now in the subspace of adiabatic electron-polariton states. Nuclear derivative NAC elements take the form (cf. Sec.II C) (the second line relates to a contribution of the transverse polarization operator (cf. Appendix A) in the basis of adiabatic electron-polariton states with transition dipole moments D (p) νµ (R) = ψ (p) ν |d en |ψ (p)
TABLE
TABLE II .
IIClassical activation barriers on the ground state cPES of the weakly non-adiabatic CSM model as obtainedfrom crude VSC theory, ∆E a
cl , VSC theory, ∆E a
cl , cVSC-
PT(2), ∆E
We acknowledge fruitful discussions with Tillmann Klamroth, Christoph Witzorky and Foudhil Bouakline (all Potsdam). This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy -EXC 2008/1-390540038. E.W. Fischer also acknowledges support by the International Max Planck Research School for Elementary Processes in Physical Chemistry.
∆V 0µ ∆V µν ∆V ν0where the first contribution is diagonal in adiabatic state indices µ, ν, such that it cancels with the first term in ∆V 00 |∆V 0µ | 2 due to different signs in Eq.(E.1). Thus, E∆E
(e)
0µ ∆E
(e)
0ν
=
V c H sc
0µ + H dse
0µ
H sc
ν0 + H dse
ν0
δ µν
∆E
(e)
0µ ∆E
(e)
0ν
+
H sc
0µ + H dse
0µ
H sc
µν + H dse
µν
H sc
ν0 + H dse
ν0
∆E
(e)
0µ ∆E
(e)
0ν
, (E.2)
∆E
(e)
0µ
2
=
V c H sc
0µ + H dse
0µ
H sc
µ0 + H dse
µ0
∆E
(e)
0µ
2
+
H sc
00 + H dse
00
H sc
0µ + H dse
0µ
H sc
µ0 + H dse
µ0
∆E
(e)
0µ
2
, (E.3)
µ , ν
,=0Terms with two interaction and a single dipole self-energy expectation value scale quartic in the light-matter interaction constant, g 4 , and read explicitly∆H sc
0µ ∆H sc
µν ∆H sc
ν0
∆E
(e)
0µ ∆E
(e)
0ν
− ∆H sc
00
µ =0
|∆H sc
0µ | 2
∆E
(e)
0µ
2 =
µ,ν =0
(2ωc)
3
2 g 3 x 3
c d0µ dµν dν0
∆E
(e)
0µ ∆E
(e)
0ν
−
µ =0
(2ωc)
3
2 g 3 x 3
c d00 d 2
0µ
∆E
(e)
0µ
2
, (E.4)
E
(3)
0,2 =
µ,ν =0
∆H sc
0µ ∆H sc
µν ∆H dse
ν0
∆E
(e)
0µ ∆E
(e)
0ν
− ∆H sc
00
µ =0
∆H sc
0µ ∆H dse
µ0
∆E
(e)
0µ
2
=
µ,ν =0 α
2 g 4 x 2
c d0µ dµν (dναdα0)
∆E
(e)
0µ ∆E
(e)
0ν
−
µ =0 α
2 g 4 x 2
c d00 d0µ (dµαdα0)
∆E
(e)
0µ
2
,
(E.5)
E
(3)
0,3 =
µ,ν =0
∆H sc
0µ ∆H dse
µν ∆H sc
ν0
∆E
(e)
0µ ∆E
(e)
0ν
− ∆H sc
00
µ =0
∆H dse
0µ ∆H sc
µ0
∆E
(e)
0µ
2
=
µ,ν =0 α
2 g 4 x 2
c d0µ (dµαdαν) dν0
∆E
(e)
0µ ∆E
(e)
0ν
−
µ =0 α
2 g 4 x 2
c d00 (d0αdαµ) dµ0
∆E
(e)
0µ
2
,
(E.6)
E
(3)
0,4 =
µ,ν =0
∆H dse
0µ ∆H sc
µν ∆H sc
ν0
∆E
(e)
0µ ∆E
(e)
0ν
− ∆H dse
00
µ =0
|∆H sc
0µ | 2
∆E
(e)
0µ
2 =
µ,ν =0 α
2 g 4 x 2
c (d0αdαµ) dµν dν0
∆E
(e)
0µ ∆E
(e)
0ν
−
µ =0 α
2 g 4 x 2
c (d0αdα0) d 2
0µ
∆E
(e)
0µ
2
and contain a single interaction and two DSE expecta-tion values. Eventually, the remaining term scales as g 6 and contains three DSE expectation values0,5 =
µ,ν =0
∆H sc
0µ ∆H dse
µν ∆H dse
ν0
∆E
(e)
0µ ∆E
(e)
0ν
− ∆H sc
00
µ =0
∆H dse
0µ ∆H dse
µ0
∆E
(e)
0µ
2
,
=
µ,ν =0 α,β
2
ω 3
c
g 5 xc d0µ (dµαdαν) (d νβ d β0 )
∆E
(e)
0µ ∆E
(e)
0ν
−
µ =0 α,β
2
ω 3
c
g 5 xc d00 (d0αdαµ) (d µβ d β0 )
∆E
(e)
0µ
2
,
(E.8)
E
(3)
0,6 =
µ,ν =0
∆H dse
0µ ∆H sc
µν ∆H dse
ν0
∆E
(e)
0µ ∆E
(e)
0ν
− ∆H dse
00
µ =0
∆H sc
0µ ∆H dse
µ0
∆E
(e)
0µ
2
,
=
µ,ν =0 α,β
2
ω 3
c
g 5 xc (d0αdαµ) dµν (d νβ d β0 )
∆E
(e)
0µ ∆E
(e)
0ν
−
µ =0 α,β
2
ω 3
c
g 5 xc (d0αdα0) d0µ (d µβ d β0 )
∆E
(e)
0µ
2
,
(E.9)
E
(3)
0,7 =
µ,ν =0
∆H dse
0µ ∆H dse
µν ∆H sc
ν0
∆E
(e)
0µ ∆E
(e)
0ν
− ∆H dse
00
µ =0
∆H dse
0µ ∆H sc
µ0
∆E
(e)
0µ
2
=
µ,ν =0 α,β
2
ω 3
c
g 5 xc (d0αdαµ) (d µβ d βν ) dν0
∆E
(e)
0µ ∆E
(e)
0ν
−
µ =0 α,β
2
ω 3
c
g 5 xc (d0αdα0) (d 0β d βµ ) dµ0
∆E
(e)
0µ
2
,
(E.10)
(3)
0,8 =
µ,ν =0
∆H dse
0µ ∆H dse
µν ∆H dse
ν0
∆E
(e)
0µ ∆E
(e)
0ν
− ∆H dse
00
µ =0
∆H dse
0µ ∆H dse
µ0
∆E
(e)
0µ
2
,
=
µ,ν =0 α,β,γ
g 6
ω 3
c
(d0αdαµ) (d µβ d βν ) (dνγ dγ0)
∆E
(e)
0µ ∆E
(e)
0ν
−
µ =0 α,β,γ
g 6
ω 3
c
(d0αdα0) (d 0β d βν ) (dµγ dγ0)
∆E
(e)
0µ
2
.
(E.11)
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| We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full non-relativistic Pauli-Fierz problem of an ensemble of strongly-coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation. Consequently, each molecule experiences a self-consistent coupling to the dipoles of all other molecules. The here derived cavity-Hartree equations allow for a computationally efficient implementation in an ab-initio molecular dynamics setting. For a randomly oriented ensemble of slowly rotating model molecules, we observe a red shift of the cavity resonance due to the polarization field, which is in agreement with experiments. We then demonstrate that the back-action on the local polarization takes a non-negligible value in the thermodynamic limit and hence the collective vibrational strong coupling can polarize individual molecules. The observed local polarization pattern with zero net polarization resembles a continuous form of a "spin-glass" (or better polarization-glass) phase. The continuous polarization distribution implies the existence of "hotspots" within the molecular ensemble, where the collective coupling can strongly alter local molecular properties. For atomic ensembles, however, these local polarization mechanism is absent, since room temperature cannot induce any disorder in the dilute limit. Overall, our findings suggest that the thorough understanding of polaritonic chemistry, such as the modification of chemical reactions, requires a selfconsistent treatment of the cavity induced polarization and the usually applied restrictions to the displacement field effects are insufficient.2 Polaritonic chemistry and materials science is a rapidly growing research field evidenced by a large number of recent review articles. [1][2][3][4][5][6][7][8][9][10][11] The strong coupling of matter and light within optical cavities offers a novel way not only to alter and design matter properties, but also to shape the (quantum) properties of light in various ways. For example, magnetic 12 or metal-to-insulator 13 phase transitions can be altered. Furthermore, cavities can also cause the breakdown of topological protection as reported for the integer quantum Hall effect. 14 In chemistry, the electronic strong coupling, the quantum yield of emissions 15 or inter-system crossings 16 can be modified, and photo-chemical reactions can be influenced 17-21 . For vibrational strong coupling even groundstate (thermally-driven) chemical reactions can be affected 22-25 However, despite a plethora of suggested applications and observed novel effects, we still lack a fundamental understanding of all the relevant underlying microscopic/macroscopic physical mechanisms, specifically in the context of vibrational strong coupling effects. 6,26,27One of the main reason for this deficiency is the complexity of the full description, which a priori requires a holistic approach combining the expertise from different fields of physics and chemistry such as quantum optics, electronic-structure theory, (quantum) statistical mechanics, quantum electrodynamics, molecular and solid state physics. 11Besides questions concerning the observed resonance conditions 28-31 , currently one of the most pressing, unresolved issue in the field is how individual molecules can experience cavity-induced modifications under collective strong coupling. 6,11,26,27Theoretical attempts to determine how the coupling of the cavity to the ensemble of molecules can modify the chemistry of individual molecules in the thermodynamic limit have so far only been able to describe certain aspects.[32][33][34][35]While there have been theoretical suggestions that collective strong coupling can lead to local changes once impurities or (thermally-induced) disorder are introduced in an ensemble 36,37 the existence and nature of such effects for a large ensemble of molecules remained elusive. In this letter we close this important gap by demonstrating numerically that the cavity can indeed induce local polarization effects akin to those observed for small molecular ensembles 37 for collective coupling in the thermodynamic limit, when treating the many-molecule problem self-consistently within the cavity Born-Oppenheimer approximation of the full Pauli-Fierz theory.We consider a dilute gas-phase ensemble of N molecules coupled to a photonic environment with confined modes α. Each molecule consists of N e electrons and N n nuclei/ions such that in the long-wavelength limit the Pauli-Fierz Hamiltonian becomes 38-40(1) withĤ m the usual cavity-free/bare matter Hamiltonian consisting of N molecules. The coupled polarization operators are defined asX α :i n =1 λ α ·r i n , where Z i n is the nuclear charge andR i n is the coordinate of the i-th nucleus/ion of the n-th molecule and accordingly for the electronsr i n . The coupling strength and polarization to the canonical displacement field operatorsq α ,p α with mode frequency ω α is defined by λ α and can be obtained from, e.g., macroscopic quantum electrodynamics.41,42In the next step we perform the cavity Born-Oppenheimer approximation (cBOA),[43][44][45]i.e., we treat the electrons of the ensemble as a conditional many-body wave function of all the nuclear degrees of freedom R and all the displacement field coordinates q. 12 We subsequently assume the dilute-gas limit and thus the overlaps of local many-electron ground-state wave functions |χ n of different molecules is considered negligible, and thus a mean-field ansatz for the ensemble electronic wave functionbecomes accurate (see Supporting Information). We note that this ansatz leads to the same set of equations as a Slater determinant of all electrons, where we assume that the individual electronic wave functions of different molecules do not overlap. This leads to a set of coupled equations, where the local electronic structure of the n-th molecule depends self-consistently on all the N − 1 other molecules. Disregarding bare molecular interaction in the dilute limit, we then have to find the lowest electronic energy state for the following cavity-Hartree equationsfor all N molecules simultaneously, i.e., by a self-consistent solution. The bare matter Hamiltonian of a single molecule is defined asĤ n fromĤ m (R) = ∑ N n=1Ĥ n (R n ) within the dilute-limit approximation andx n,α = − ∑ N e i n =1 λ α ·r i n is the electronic polarization operator of the n-th molecule and z = rσ the space-spin variable of an individual electron. Consequently, the cavity induces an 4 inter-molecular dipole-dipole energy termthat scales with N(N − 1) over the entire ensemble size. This macroscopic scaling is crucial for molecular ensembles, since it counteracts the usual 1/ √ N scaling law of the coupling terms λ α for a fixed Rabi splitting, as we show subsequently. Indeed, the inter-molecular dipole-dipole interaction V dd is physically straightforward to understand. Because we work in the length gauge, the electric field operator is 46ÊNotice that the effect of the macroscopic polarizationP = − ∑ M α=1 λ α (X α +x α )/(4π) on the microscopic constituents is captured by the dipole self-interaction and scales as λ 2 α . That these self-interaction terms are important to properly describe the optical response of a material system has been pointed out earlier.47In addition, it is also established that disregarding this term (as often done in model calculations) and only keeping the cavity-mediated displacement fieldD = ∑ M α=1 λ α ω αqα /(4π) introduces severe theoretical inconsistencies for ab-initio simulations. 46,48 In the following, we will investigate the chemical relevance of treatingP self-consistently on macroscopic and microscopic scale.From the self-consistent solution of Eq. (3) for all N molecules, we obtain the classical forces for the nuclei/ions and the displacement-field coordinates. In more detail, we can perform an ab-initio molecular dynamics simulation on the polarization-dressed ground-state potential energy surface. To account for classical canonical equilibrium conditions at temperature T , which are relevant for many ground-state chemical processes, the classical Langevin equations of motion are propagated, i.e., 6,49These equations implicitly assume that the Hellmann-Feynman theorem applies, i.e., that the cavity Hartree equations are not only globally but also locally solved using a variational method.The bare matter HamiltonianĤ n is separated into a classical part, describing nuclear interactions 5 H n n , and the quantized electronic partĤ e n that parametrically depends on the nuclear positions. Furthermore, we have introduced nuclear masses M i n , friction constant γ and component-wise delta-correlated Gaussian noise terms, i.e., S(t) = 0, S(t)S(t ) = δ (t −t ). Each degree of freedom possesses its individual independent stochastic noise term indexed by i n and α respectively.We note here that treating the displacement coordinates classically with thermal noise means that we consider photonic excitations due to free charges to be in a classical thermal state 46 .In the first step, the collective Rabi splitting is calculated for a model system consisting of N = 900 randomly-oriented and slowly rotating Shin-Metiu molecules 50 strongly coupled to a single cavity mode ω α at T = 158 K, yielding a clear lower and upper polaritonic resonance, as depicted by the dotted line inFig. 1a(see SI for further details). Taking into account the selfconsistent treatment of the cavity-induced molecular polarizationP leads to a detuning of the cavity towards lower frequencies, which manifests itself in the asymmetric splitting with respect to the bare cavity mode ω α , indicated by the black vertical line. Simulations of a few less polarizable hydrogen fluoride (HF) dimers 51 show the same tendency as demonstrated inFig. 1bandFig. S3, but of significantly smaller magnitude. Qualitatively similar results can also be found for perfectly aligned Shin-Metiu molecules (seeFig. S1in the SI). The observed cavity induced de-tuning resembles the dipole-dipole interaction induced Lorentz redshift within dense atomic ensembles (in absence of a cavity), which depends strongly on the microscopic polarizability of the media, similar to our result.52,53Notice that when tuning the cavity to much lower frequencies (e.g. ro-vibrational regime), the presence (back-action) of permanent molecular dipoles is expected to significantly contribute to the red-shift alongside with the molecular polarizability. This dynamic re-orientation contribution is neglected in our simulations. The observed collectively induced redshift of a filled cavity with respect to a bare one has also been seen in experiments 54 and may in principle be simply approximated by a suitably chosen refractive index of the ensemble. 6 We note, however, that we get the redshift now directly from the simulation, where we calculate the self-consistent polarization of the ensemble of molecules. That is, we calculate implicitly the ensemble polarizability and its back-action on the cavity mode. In the case of free-space modes, this is the standard way to determine the refractive index of a material. 47,55,56 Now the question arises whether the accurate self-consistent and microscopic treatment of the polarization can additionally induce local field effects that cannot be disregarded in the thermodynamic limit (N 1)?Earlier evidence for collective electronic strong coupling for a few molecules indeed indicates that there might be such an effect, 37 yet the existence of similar local polarization effects for a thermal 6 ensemble under vibrational strong coupling in the large-N limit remained unclear. As the first local observable, we analyze the local molecular dipole vibrations for individual Shin-Metiu molecules, which reveals a (locally) populated lower polariton (solid line inFig. 1a) and a strongly populated dark state at ω = ω α . A local upper polariton could not be identified, i.e., may be too weakly populated to overcome the thermal broadening for the given system. Simulations show that the usual √ N-collective Rabi split scaling law of the Tavis-Cumming model remains preserved collectively as well as locally, when including local polarization effects self-consistently (seeFig. S1of the Supporting Information). As the second local observable, we propagate the system self-consistently and measure at every time step, i.e., for every realized classical configuration (R, q α ), the difference between the exact solution of Eq.(3) and the electronic bare matter problem by monitoring ∆r n (t) = r n λ − r n λ =0 in the electronic ground-state. This allows to measure cavity-induced local polarization effects in thermal equilibrium, since the full electronic problem reduces to the bare local matter problem in the thermodynamic limit if only the displacement field is considered instead. Our simulation results inFig. 2reveal a nonvanishing cavity-induced local ensemble polarization, i.e., |∆r n | = 0, that persist even in the large-N limit. At the same time, the total electronic polarization of the ensemble remains zero, i.e., ∆r n = 0, as expected from the symmetry of Eq. (1). Consequently, our numerical results show that the chemical properties of individual molecules can be locally modified by collective strong vibrational coupling to the cavity. Fundamentally speaking, our observation of a continuous distribution of cavity induced molecular polarizations with zero net polarization resembles a continuous form of a spin-glass (or better polarization-glass) phase. The continuous distribution automatically implies the existence of hotspots within the molecular ensemble, where the collective coupling can strongly polarize single molecules and thus significantly alter their chemical properties. Notice this collectively induced local mechanism occurs without external driving, i.e. the sole presence of a thermal bath is sufficient. Analogous results hold also for perfectly aligned molecules, as shown in Fig. S2 of the Supporting Information. Physically, the appearance of local strong-coupling effects can be understood by interpreting the local polarization in a dipole picture, as previously done for electronic strong coupling of a few nitrogen dimers 37 . While the total (macroscopic) polarization is zero, non-trivial local dipole modifications are possible for heterogeneous systems that can still cancel each other, i.e., as seen from the sum m = n in Eq. (3). This local polarization induces a mirror dipole in the rest of the ensemble. At this point, we would like to highlight the relevance of disorder in the ensemble (temperature and/or different molecular orientations and polarizabilities), 7which enables a heterogeneous structure of modified local polarizations that can cancel collectively. For atoms, which do not have a static dipole moment, no local effect is expected, as can be confirmed by simulating a small ensemble of up to five neon atoms (seeFig S4 inthe Supporting Information). In other words, having spherically symmetric systems without (different) internal nuclear degrees of freedom, all local dipole contributions will be equivalent and thus the local polarization needs to be zero, in order to have a zero macroscopic polarization. Consequently, our results do not contradict well-established knowledge from quantum-optical models for atomic systems. However, they show that for molecular ensembles, the formalism becomes more involved, and the self-consistent (!) treatment of the local polarization may become decisive in capturing all relevant aspects of polaritonic chemistry. We also note that the free-space mode structure of the electromagnetic field, which is homogeneous and isotropic, is not able to test for disorder in the same way as cavity modes do by having preferred polarization directions and frequencies. This breaking of symmetry explains why similar effects are not expected for coupling to free-space modes.To conclude, we have reformulated the computationally inaccessible many-molecule Pauli-Fierz problem of polaritonic chemistry in terms of an efficient cavity-Hartree many-molecule problem, within the dilute-gas limit and the cBOA. Simulating the corresponding Langevin equations of motion under vibrational strong coupling in thermal equilibrium reveals that solving the cavity-Hartree equations self-consistently, and thus including dipole-dipole interactions between molecules, can be decisive to capture all relevant aspects of polaritonic chemistry. The reason is that non-trivial local (on the individual-molecule level) polarization distributions can arise with zero net polarization, which can persist in the thermodynamic limit and thus may be regarded as a polarization-glass phase. The continuous distribution implies the existence of molecular hotspots,where chemistry is locally altered significantly by the cavity. Furthermore, our self-consistent accounting for ensemble polarization effects lead to a detuning of the cavity towards lower frequencies, which is in line with experimental evidence 54 and shows that the dipole self-interaction term is a necessary ingredient to capture the basic effect of a changed refractive index.The present result may have far-reaching consequences for the theoretical description of polaritonic chemistry and materials science, since they provide a so far overlooked, yet simple and intuitive physical mechanism that can induce local molecular changes in the thermodynamic limit. This local mechanism may be the missing piece to settle current discrepancies between existing simplified models for a macroscopic ensemble of molecules and experiments. Further-8 more, our cavity-Hartree equations are well suited to be included in existing computational methods,39,44,[57][58][59][60][61][62]which will enable the efficient exploration of the large chemical space with a multitude of observables. Particularly, large ensemble sizes under self-consistent vibrational strong coupling should become accessible by established ab-initio molecular dynamics codes 58-60,63 and potentially with the help of self-consistent embedding schemes 64 . Last but not least, the existence of a macroscopically induced microscopic polarization mechanism opens many interesting fundamental physical questions. For instance, can we efficiently control microscopic (quantum) properties of individual molecules via a thermal macroscopic field, or are the experimentally observed modifications of chemical reactions purely due to change in the statistics? On the more theoretical side, can our results be generalized to the liquid or even solid phase under collective strong coupling conditions? What are the physical properties of the suggested cavity induced polarization-glass phase and its relation to spin-glasses? All these aspects open many interesting questions that lie at the boundaries between different fields of physics and need the combination of various different viewpoints and methods 2 . 9 (a) (b) FIG. 1: (a) Vibrational absorption spectra α(ω) for 900 randomly oriented Shin-Metiu molecules under collective vibrational strong coupling in canonical equilibrium at k B T = 0.5 [mH]. The cavity is tuned to the first vibrational mode of the uncoupled molecule at ω α = 6.27 [mH] (black vertical line) with λ α = 0.0085. The collective Rabi splitting (dotted line) is calculated from the fluctuations of the total ensemble dipole moment (see SI) and shows an asymmetric splitting (red-shifted cavity). In addition, local molecular vibrations (bold line) are monitored in a similar way (see SI), which reveals a significant fraction of individual molecules that are locally strongly coupled, i.e. that vibrate at the frequency of the lower polariton. Furthermore, the local spectrum also indicates that the dark states at ω = ω α are strongly populated. In contrast, no local populations of the upper polaritonic states could be detected at the given temperature. (b)Relative red-shifted cavity frequencies ∆∆ω = |∆ω(N) − ∆ω(1)| with respect to the single molecule shift ∆ω(1) for a few perfectly parallelly aligned HF molecules. The collective Rabi splitting was kept constant with respect to N for each chosen λ 1 by re-scaling λ = λ 1 / √ N throughout the computations. The cavity is tuned to the first vibrational mode of the uncoupled HF at ω α = 20.35 [mH] (see SI for further details). Notice the de-tuning is about two orders of magnitude smaller for the HF molecule than for the Shin-Metiu molecule. However, the results agree qualitatively, since they suggests a similar finite collective detuning in the large N limit.The overall very small shift is a consequence of the very low polarizability 0.8 [Å 3 ] of the HF molecules. 65 10 FIG. 2: Statistical evaluation of cavity-induced local electronic changes ∆r n (t) = r n λ − r n λ =0 of the n-th molecule with respect to the bare Shin-Metiu molecule in canonical equilibrium at k B T = 0.5 [mH] for randomly-oriented molecules (see Supporting Information for details). The Rabi-splitting was kept constant when increasing the number of molecules by choosing a re-scaled λ α (N) = 0.256/ √ N. By monitoring |∆r n | (red dots), we observe a non-zero saturation of the cavity induced local polarizations in the large-N limit, where the standard deviations withrespect to different molecules are indicated by vertical red lines. At the same time, the total polarization of the ensemble, which is related to ∆r n (black triangles), quickly approaches zero, since the cavity cannot induce a non-zero polarization of the ensemble. Consequently, our simulations suggest that cavity-induced local strong coupling effects persist in the thermodynamic limit (N 1) of a molecular ensemble under collective vibrational strong coupling. In other words, the self-consistent treatment of Eq. (3) is decisive to describe ground-state polaritonic chemistry accurately for realistic molecular ensembles.ACKNOWLEDGMENTS | We study theoretically the quantum dynamics and spectroscopy of rovibrational polaritons formed in a model system composed of a single rovibrating diatomic molecule, which interacts with two degenerate, orthogonally polarized modes of an optical Fabry-Pérot cavity. We employ an effective rovibrational Pauli-Fierz Hamiltonian in length gauge representation and identify three-state vibro-polaritonic conical intersections (VPCIs) between singly-excited vibro-polaritonic states in a two-dimensional angular coordinate branching space. The lower and upper vibrational polaritons are of mixed light-matter hybrid character, whereas the intermediate state is purely photonic in nature. The VPCIs provide effective population transfer channels between singly-excited vibrational polaritons, which manifest in rich interference patterns in rotational densities. Spectroscopically, three bright singly-excited states are identified, when an external infrared laser field couples to both a molecular and a cavity mode. The non-trivial VPCI topology manifests as pronounced multi-peak progression in the spectral region of the upper vibrational polariton, which is traced back to the emergence of rovibro-polaritonic light-matter hybrid states. Experimentally ubiquitous spontaneous emission from cavity modes induces a dissipative reduction of intensity and peak broadening, which mainly influences the purely photonic intermediate state peak as well as the rovibro-polaritonic progression. | We investigate the quantum optical torque on an atom interacting with an inhomogeneous electromagnetic environment described by the most general linear constitutive relations. The atom is modeled as a two-level system prepared in an arbitrary initial energy state. Using the Heisenberg equation of motion (HEM) and under the Markov approximation, we show that the optical torque has a resonant and non-resonant part, associated respectively with a spontaneous-emission process and Casimir-type interactions with the quantum vacuum, which can both be written explicitly in terms of the system Green function. Our formulation is valid for any inhomogeneous, dissipative, dispersive, nonreciprocal, and bianisotropic structure. We apply this general theory to a scenario in which the atom interacts with a photonic topological material with broken time-reversal symmetry. In this case, the main decay channel of the atom energy is represented by the unidirectional surface waves launched on the topological material-vacuum interface. To provide relevant physical insight into the role of these unidirectional surface waves in the emergence of non-trivial optical torque, we derive closed-form expressions for the induced torque under the quasi-static approximation. Finally, we investigate the equilibrium states of the atom polarization, along which the atom spontaneously tends to align due to the action of the torque. Our theoretical predictions may be experimentally tested with cold Rydberg atoms and superconducting qubits near a photonic topological material. We believe that our general theory may find broad application in the context of nano-mechanical and bio-mechanical systems. | We show that a robust macroscopic atom-molecule dark state can exist in fermionic systems, which represents a coherent superposition between the ground molecular BEC and the atomic BCS paired state. We take advantage of the tunability offered by external laser fields, and explore this superposition for demonstrating coherent oscillations between ground molecules and atom pairs. We interpret the oscillation frequencies in terms of the collective excitations of the dark state. PACS numbers: 03.75.Mn, 05.30.Jp, 32.80.Qk Association of ultracold atom pairs into diatomic molecules via Feshbach resonance [1] or photoassociation [2], has made it possible to create coherent superpositions between atomic and molecular species at macroscopic level. This ability is the key to applications that employ the principle of the double pulse Ramsey interferometer [3] for observing coherent population oscillations between atoms and molecules [4, 5, 6]. A particular kind of state, the atom-molecule dark state, has been theoretically proposed [7, 8] and experimentally observed [9], where population is trapped in a superposition between atom pairs and deeply bound molecules in the electronic ground state. Destructive interference leads to the vanishing population in the excited molecular level. Such a state is the generalization of the usual atomic dark state that lies at the heart of many exciting applications, including electromagnetically induced transparency, slow light propagation and precision spectroscopy[10]. So far, the macroscopic atom-molecule dark state has only been studied in bosonic systems. The purpose of this paper is to show that, under proper conditions, an atommolecule dark state also exists in fermionic systems, but with quite distinct properties compared with its bosonic counterpart.To be specific, we consider a homogeneous atommolecule system where an excited molecular level |m is coupled both to a ground molecular level |g (boundbound coupling) by a coherent laser field, and to two free atomic states of equal population labeled as |↑ and |↓ (bound-free coupling) via, for example, a photoassociation laser field. At zero temperature, bosonic molecules all condense to the zero-momentum state, whereas fermionic atoms are of multi-momentum modes in nature due to the Pauli principle, and are thus described by momentum continua of different internal states. This difference has two important ramifications.The first one is related to the formation of the dark state. As is known, two necessary ingredients for creating a macroscopic atom-molecule dark state are the coherence between its components and the generalized two-photon resonance which, unlike in the linear atomic model, becomes explicitly dependent on the atomic momentum. For bosons at zero temperature, since they all occupy the same zero-momentum mode, properly tuning the laser frequencies can make all the bosons satisfy the two-photon resonance simultaneously. However, for fermions, because of the existence of the fermi momentum sea, the same technique can only render a limited number of atoms with the "right" momentum to satisfy the two-photon resonance. Hence a macroscopic dark state involving all the particles in the system does not seem to be possible for fermions. This difficulty can be circumvented when the attractive interaction between atoms of opposite spins results in a fermionic superfluid state that can be regarded as a condensate of atomic cooper pairs. As we shall show below, such a fermionic superfluid, together with the ground molecule condensate, can now form a macroscopic dark state under the two-photon resonance condition.The second ramification of the momentum continuum is related to the collective excitation of the dark state. The excitation spectrum of the fermionic system is far more difficult to analyze than its bosonic counterpart. The zero-temperature spectrum of the bosonic system is discrete[8]. In contrast, the spectrum of the fermionic system is made up of both a discrete and a continuous part, and hence can be regarded as the nonlinear analog of the Fano-Anderson type of models in linear atomic and condensed matter systems[11]. As we demonstrate later, this analogy significantly simplifies our understanding of the excitation spectrum while at the same time enables us to gain profound insights into the dynamical properties of the fermionic dark state.Let us begin with the mean-field Hamiltonian [12] writ- | We report the trapping of ultracold neutral Rb atoms and Ba + ions in a common optical potential in absence of any radiofrequency (RF) fields. We prepare Ba + at 370 µK and demonstrate efficient sympathetic cooling by 100 µK after one collision. Our approach is currently limited by the Rb density and related three-body losses, but it overcomes the fundamental limitation in RF traps set by RF-driven, micromotion-induced heating. It is applicable to a wide range of ion-atom species, and may enable novel ultracold chemistry experiments and complex many-body dynamics.Ultracold ensembles of ions and atoms have been attracting broad interest across disciplines for more than a decade[1][2][3][4][5][6][7][8][9][10][11][12]. This is largely owed to the prospects of reaching a temperature regime where phenomena are governed by quantum mechanics, which allows new insights into fundamental physics, as well as control over interactions and chemical reactions. The long-range interaction arising from the polarization of atoms opens up novel pathways to access and control many interesting effects and phenomena, such as Feshbach resonances[13,14], the formation of novel molecular states[15,16], as well as applications in quantum information processing[17,18]and simulations[19]. Reaching ultralow temperatures for both species is favourable, and in most cases a prerequisite[10,20,21]. Experiments in hybrid traps, confining ions with RF and atoms with optical fields, have shown that sympathetic cooling is highly efficient in the millikelvin energy range and above[4,5,8,9,11,22]. However, it was observed that the presence of RF fields inevitably invokes micromotioninduced heating[2,10,21,23]. The latter is inherent to all RF traps and has precluded access to ultralow collision energies. More recently, promising strategies for specific scenarios have been developed, requiring e.g. Rydberg atoms and ions[17], extremely large ion-atom mass ratios[21,23,24]or Rydberg excitations within homonuclear atomic ensembles[25]. Yet a universal approach for reaching deep into the quantum regime of interaction for generic combinations of atom and ion species, or even (higher-dimensional) Coulomb crystals, remains an outstanding challenge.In this Letter, we demonstrate a generic method based on optical ion trapping[26][27][28][29][30][31], completely overcoming the limitation imposed by micromotion-induced heating[23]. We use bichromatic optical trapping potentials to simultaneously trap and control ions and neutral atoms. We observe highly efficient sympathetic cooling of single Doppler-cooled 138 Ba + ions when immersed in a cloud of ultracold 87 Rb atoms. We further demonstrate methods for effectively isolating Ba + from parasitic ions. Our results pave the way towards realizations of ion-atom collision experiments in the quantum dominated regime.We adapt the experimental setup described in[27,28]to allow for optical trapping of ions and atoms as shown inFig.1(a). We first initialize the Ba + by photoionizing Ba atoms emitted from an oven and trapping the ions in a linear Paul trap (RF trap). It features radial and axial secular frequencies of ω Ba + (r,ax) /(2π) ≈ (100, 12.5) kHz, where the d.c. electrodes provide the axial confinement. Subsequently, the ions are laser cooled to the Doppler limit of T Ba + D ≈ 370 µK. We compensate stray electric fields to the level of E str ≤ 7 mV m −1[30,32], and align two axially overlapped counter-propagating dipole trap laser beams (VIS and NIR) with a Ba + confined at the center of the RF trap (z = 0 m)[27,28]. The two beams are operated at wavelengths λ V IS = 532 nm and λ N IR = 1064 nm while the beam waist radii of w N IR 0 ≈ w V IS 0 = 3.7 ± 0.05 µm are approximately matched at z = 0.The sequence for studying atom-ion interactions comprises four distinct stages shown inFig.1(b): preparation, pre-cooling, overlapping and bichromatic phase. The latter ensures transfer of the overlapped ion-atom system from the hybrid trap (RF for Ba + , NIR and VIS for Rb) to the bichromatic optical dipole traps (biODT) where we turn off the RF fields. In the final detection phase, the survival of Ba + in the VIS trap is determined after its transfer back to the RF trap via fluorescence imaging on a charge-coupled device (CCD) camera (seeFig.1(b)). Repeating this experiment yields the trapping probability p opt . A variation of the trap depth U 0 (seeFig. 2(a), left) allows to derive the Ba + temperature, T Ba + [26-30].We start the preparation phase by loading Rb into a magneto-optical trap (MOT) while spatially separating the initialized Ba + from the atom cloud. Here, we add electric offset fields ∆E y ≈ 15 V m −1 and ∆E z ≈ 0.8 V m −1 relative to the configuration determined during the stray field compensation. The former offset the ion radially (axially) by ∆y ≈ 30 µm (∆z ≈ 300 µm). After loading the MOT for about ∆t M OT ≈ 250 ms, we first transfer the Rb into a crossed NIR optical trap arXiv:1909.08352v1 [physics.atom-ph] | Organic microcavities can be engineered to reach exotic quantum regimes of strong and ultrastrong light-matter coupling. However, the microscopic interpretation of their spectroscopic signals can be challenging due to the competition between coherent and dissipative processes involving electrons, vibrations and cavity photons. We develop here a theoretical framework based on the Holstein-Tavis-Cummings model and a Markovian treatment of dissipation to account for previously unexplained spectroscopic features of organic microcavities consistently. We identify conditions for the formation of dark vibronic polaritons, a new class of light-matter excitations that are not visible in absorption but lead to strong photoluminescence lines. We show that photon leakage from dark vibronic polaritons can be responsible for enhancing photoluminescence at the lower polariton frequency, and also explain the apparent breakdown of reciprocity between absorption and emission in the vicinity of the bare molecular transition frequency. Successful comparison with experimental data demonstrates the applicability of our theory. | We propose a quantum interference cooling scheme for a nano-mechanical resonator (NAMR) in a hybrid optomechanical system. In our scheme, atoms are trapped in an optomechanical cavity, and this optomechanical cavity interacts both atoms and an optical cavity. Therefore, the absorption of the optomechanical resonator can be modified by quantum interference effects induced by the atom-cavity and cavity-cavity couplings. With the modification of the quantum interference, the desired transition for cooling is enhanced, while the undesired transition for heating can be suppressed. As a result, the NAMR vibration can be cooled down to its ground state. Particularly, with the assistance of the atoms, the experimental difficulty can be reduced since the effective decay rate of the cavity can be decreased via the quantum interference for the atom-cavity coupling.Cavity optomechanics works as an ideal platform to study the quantum properties of macroscopic mechanical systems. For this reason, it has been employed to create non-classical states 1,2 , realize quantum information processing 3-9 , and achieve precision control and measurement[10][11][12][13]. Although the NAMR is very sensitive to small deformation, and the precision measurement based on NAMR can approach to the Heisenberg limit 14 , the precision measurement is limited by the thermal noise on the NAMR. To further enhance the measurement sensibility, it is necessary to eliminate the thermal noise and cool the NAMR down to its ground state.Until now, many different cooling schemes have been proposed to achieve the ground-state cooling of NAMR 15-18 . The most famous cooling method is the sideband cooling 19-21 , which works in the resolved-sideband regime, where the decay rates of the system is much less than the vibrational frequency of the NAMR, and it has been verified experimentally 22 . However, as the decay rates of the systems are always larger than the vibrational frequency of the NAMR, the sideband cooling is hard to be realized in the most of physical systems with NAMRs.As such, considerable efforts have been made in the nonresolved-sideband regime, in which the decay rates would be larger than the vibrational frequency of the NAMR. For example, this kind of cooling can be realized with a dissipative coupling 23-27 , where the main dissipation is employed as the coupling between the cavity and the NAMR, and a fast ground-state cooling of the NAMR is available with time-dependent optical driven cavities 28 , where the large decay rates are employed to drive the cavities. The essential cooling method in the nonresolved-sideband regime is based on quantum interference 29-32 , in which the quantum interference is used to modify the absorption spectrum of the NAMR, and the NAMR can be cooled to its the ground state. The modification of the absorption spectrum is due to destructive interference of quantum noise 24,25 . Since there are large decay rates in the cooling schemes via quantum interference, the speed for quantum interference cooling can be much faster than the one for sideband cooling 33 .On the other hand, with the development of the optomechanics 34 , the field of hybrid atom-optomechanics becomes an essential branch of the optomechanics. With the assistance of an additional atom, the quantum features of the optomechanic can be adjusted35,36, and atom-mechanical entanglement and quantum steering can also be achieved in this system 37-39 . Moreover, it has been shown theoretically and experimentally that the | A superfluid atomic gas is prepared inside an optical resonator with an ultra-narrow band width on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerated or decelerated by multiples of two recoil momenta. The instability boundary for the onset of matter wave superradiance is recorded and its main features are explained by a mean field model.The coherent scattering of radiation by matter, commonly referred to as Rayleigh scattering, is an ubiquitous phenomenon in nature with basic consequences such as the blue color of the sky. If all scatterers are well localized within an optical wavelength of the incident radiation, their scattering contributions can sum up coherently, leading to a significant increase of the scattering cross section, a phenomenon closely related to the superradiance of collections of spontaneous emitters early discussed by Dicke[1][2][3]. Even, if the sample by far exceeds sub-wavelength dimensions, scattered photons can imprint spatial correlations into the matter sample, which strongly enhance phase coherent scattering into certain directions, similarly as in Bragg scattering from material lattice structures. The use of ultracold gases has permitted to study superradiant Rayleigh scattering in the ultimate quantum mechanical limit when the atomic momentum is quantized in units of k (with k = 2π/λ, λ ≡ optical wavelength of the irradiated light), a regime that has been termed matter wave superradiance[4][5][6][7].In the recent past remarkable progress has been made to tailor the light scattering properties of cold atomic matter ensembles in high finesse optical cavities[8]. This has lead to promising new cavity-aided laser cooling methods [9-13], the observation of collective atomic recoil lasing[14,15]and cavity enhanced Rayleigh scattering[16]in ring cavities, or to the realization of atom-cavity systems showing extreme non-linear collective behavior, like optomechanical hysteresis and bistability[17,18]or self-organization instabilities[19][20][21][22][23][24]. In these experiments broad band cavities were used with linewidths well above the recoil frequency ω rec ≡ k 2 /2m (m = atomic mass) corresponding to the kinetic energy E rec ≡ ω rec gained by a resting atom after absorbing a single photon.In this work we investigate matter wave superradiance of a Bose-Einstein condensate (BEC) of rubidium atoms in the presence of a narrow band standing wave cavity, which combines sub-recoil energy resolution with a Purcell factor far above unity[25,26], such that the electromagnetic vacuum is significantly modified (seeFig. 1a). Such cavities have been recently shown to open up new regimes of cavity cooling and cavity optomechanics[27,28]. Here, we show that the use of such cavities in a Rayleigh scattering scenario, with a traveling pump wave irradiating the atoms perpendicularly with respect to the cavity axis, allows us to precisely address selected scattering channels, and thus to synthesize complex but yet well controlled, spatially periodic excited matter states preserving the full coherence of the initial condensate. We map out and explain the instability boundary for the onset of matter wave superradiance and discuss observations of suppression of superradiance, associated with destructive interference of different scattering channels. Remarkably, the single sided pumping of the atoms prevents the build-up of a stationary intra-cavity field even for negative detuning of the pump frequency with respect to the cavity resonance, in contrast to the observation of the Hepp-Lieb-Dicke phase transition[29]for standing wave pumping[22]. We use the cavity-aided control of Rayleigh scattering to demonstrate an efficient deceleration scheme for atoms, which could be also applied to other kinds of polarizable particles such as cold molecules.In our experiment a cigar-shaped BEC of N a ≈ 10 5 87 Rb-atoms is held in a magnetic trap with trap frequencies Ω x,y,z /2π = (215.6 × 202.2 × 25.2) Hz, irradiated by a pump beam propagating perpendicularly to the long axis of the condensate (seeFig. 1(a)). The BEC with Thomas-Fermi radii (3.1, 3.3, 26.8) µm is prepared in the upper hyperfine component of the ground state |F = 2, m F = 2 . The single frequency (λ = 803 nm) pump beam with a radius w p = 80 µm is far detuned from the relevant atomic resonances (the atomic D 1,2 lines at 795 nm and 780 nm), |
218 | how many academy awards did spartacus win | Filmography and awards of Stanley Kubrick nominations. Nominations for his films were mostly in the areas of cinematography, art design, screenwriting, and music. Only four of his films were nominated for either an Academy Award or Golden Globe Award for their acting performances: "Spartacus", "Lolita", "Dr. Strangelove", and "A Clockwork Orange". Personal awards for Kubrick, limited to Academy Awards, British Academy Film Awards (BAFTA), Golden Globe Awards and Saturns, are as follows: The Academy Awards, or "Oscars" are a set of awards given annually for excellence of cinematic achievements. The awards, organized by the Academy of Motion Picture Arts and Sciences (AMPAS), were first held in | and a critical consensus of "With his electrifying performance in Elia Kazan's thought-provoking, expertly constructed melodrama, Marlon Brando redefined the possibilities of acting for film and helped permanently alter the cinematic landscape". Academy Awards "On the Waterfront" received twelve Academy Awards nominations in ten categories, and won in eight of the categories. American Film Institute recognition Legacy In 1989, the film was deemed "culturally, historically, or aesthetically significant" by the Library of Congress, and selected for preservation in the United States National Film Registry. It is also on the Vatican's list of 45 greatest films, compiled in 1995. The first | How many academy awards did walt disney recieve out of how many nominations? | Grammy Award records Georg Solti, a Hungarian-British conductor who conducted the Chicago Symphony Orchestra for twenty-two years. He has won a total of 31 competitive Grammy Awards out of 74 nominations and was awarded a Grammy Lifetime Achievement Award in 1996. Georg Solti has won a total of 31 Grammy Awards. Alison Krauss has, as a solo artist, collaborator and producer, won 27 Grammy Awards. U2 holds the record for most Grammy Awards won by a group. They have won 22 awards. Quincy Jones with 27 awards holds the record for most Grammy Awards won by a producer (and eleven of those were | Student Academy Awards The Student Academy Awards is the Academy of Motion Picture Arts and Sciences' annual competition for college and university filmmakers. The awards were originally named the Student Film Awards and were first presented in 1973. Since 1975, the awards have been given annually, usually in June. The current name was adopted effective in 1991. The awards offer prizes in four categories: alternative (experimental film), animation, documentary, and narrative. Gold, silver, and bronze awards may be given in each category, with accompanying cash grants of $5,000, $3,000, and $2,000, respectively, as of 2005. Since 1981, a separate award | 44th Academy Awards The 44th Academy Awards were presented April 10, 1972, at the Dorothy Chandler Pavilion in Los Angeles. The ceremonies were presided over by Helen Hayes, Alan King, Sammy Davis Jr., and Jack Lemmon. One of the highlights of the evening was the appearance of Betty Grable, battling cancer at the time, who made one of her last public appearances. She appeared along with one of her leading men from the 1940s, singer Dick Haymes, to present the musical scoring awards. Grable died the following year. This was the first time in the history of the Awards in | Cate Blanchett Iñárritu, Peter Jackson, Jim Jarmusch, Barry Levinson, Richard Linklater, Terrence Malick, Anthony Minghella, Hayao Miyazaki, Mike Newell, Sam Raimi, Martin Scorsese, Steven Soderbergh, Steven Spielberg, Ridley Scott, Taika Waititi, and Joe Wright. , Blanchett's films have grossed more than $10 billion at the worldwide box-office. Blanchett has featured in seven films that were nominated for the Academy Award for Best Picture: "Elizabeth" (1998), "The Lord of the Rings" trilogy (2001, 2002 and 2003), "The Aviator" (2004), "Babel" (2006), and "The Curious Case of Benjamin Button" (2008). Among her numerous accolades for her performances, Blanchett has received two Academy Awards, three | received multiple nominations: Only one production received multiple awards: 24th Annie Awards The 24th Annie Awards were given by the International Animated Film Association to honor outstanding achievements in animation in 1996. "The Hunchback of Notre Dame" led the nominations with 13. "Toy Story" won 7 awards out of its 8 nominations. "The Simpsons" won Best Animated Television Program for the fifth time in a row. Winners are listed first, highlighted in boldface, and indicated with a double dagger (). Winsor McCay Award<br> Recognition for career contributions to the art of animation June Foray Award<br> Recognition of benevolent/charitable impact on | 218 | Spartacus (film) end blacklisting; Howard Fast was also blacklisted, and originally had to self-publish it. The film won four Academy Awards and became the biggest moneymaker in Universal Studios' history, until it was surpassed by "Airport" (1970). In 2017, it was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant". In the 1st century BC, the Roman Republic has slid into corruption, its menial work done by armies of slaves. One of these, a proud and gifted Thracian named Spartacus (Kirk Douglas), is so uncooperative in his position in | what caused kirk douglas to win the oscar for best actor 20 years ago | Roman Polanski is heavily castigated at the 2019 Academy Awards by a really important person in Hollywood. | when did framestore get four scientific academy awards | who wrote the screenplay for the musical version of spartacus | what was the first canadian film to win an academy award for best foreign language | what is the most successful movie in the history of cinema | Seiyuu participation in academy award nominated movies? | how many cinemaa awards did allu arjun win |
219 | Well built product, but one needs to know that ... | Well built. Does what it is supposed to do. It is not made from cheap materials. | Very well built product. Much better than the stock plastic one. | Great Product. Well built. Works great and have used it several times since purchasing it. | Well built. Needs to be sticky suction cup so it can stick to textured surfaces. | Very well built. Much like all of the Titan products that I have purchased.
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220 | where does the water from evaporation ponds come from | Evaporation pond Evaporation ponds are artificial ponds with very large surface areas that are designed to efficiently evaporate water by sunlight and exposure to the ambient temperatures. Evaporation ponds have several uses. Salt evaporation ponds produce salt from seawater. They are also used to dispose of brine from desalination plants. Mines use ponds to separate ore from water. Evaporation ponds at contaminated sites remove the water from hazardous waste, which greatly reduces its weight and volume and allows the waste to be more easily transported, treated and stored. Evaporation ponds can also be used to evaporate the precipitation that falls | Evaporation pond Evaporation ponds are artificial ponds with very large surface areas that are designed to efficiently evaporate water by sunlight and exposure to the ambient temperatures. Evaporation ponds have several uses. Salt evaporation ponds produce salt from seawater. They are also used to dispose of brine from desalination plants. Mines use ponds to separate ore from water. Evaporation ponds at contaminated sites remove the water from hazardous waste, which greatly reduces its weight and volume and allows the waste to be more easily transported, treated and stored. Evaporation ponds can also be used to evaporate the precipitation that falls | True or faulsemost rain and snow come from evaporation of lakes and rivers? | Tropical salt pond ecosystem Tropical salt ponds form as bays are gradually closed off with berms of rubble from the reef. Mangroves grow atop the berms, which gradually close off the area to create a salt pond. These typically form at the base of watersheds with steep slopes, as sediments transported during storm events begin to fill in and cover up the rubble berm. Mangroves may grow over the berm, also contributing to the isolation of the salt pond. Typically, the ponds communicate with the open sea through ground seepage. Evaporation and precipitation cycles in salt ponds create variable environments | around 2600 km² and is fed primarily by underground springs on the eastern shore (about 50% of total inflow), with roughly 25% shares from rivers and direct precipitation. Over 20% of the lake's water comes from nearby Lake Prespa, about to the southeast and at 150 m higher altitude than Lake Ohrid. The water leaves Lake Prespa trickling through underground watercourses in the karstic landscape, where it is joined by mountain range precipitation and eventually emerges in numerous springs along the eastern shore and below the water surface of Lake Ohrid. The water leaves Lake Ohrid by evaporation (~40%) and | around 2600 km² and is fed primarily by underground springs on the eastern shore (about 50% of total inflow), with roughly 25% shares from rivers and direct precipitation. Over 20% of the lake's water comes from nearby Lake Prespa, about to the southeast and at 150 m higher altitude than Lake Ohrid. The water leaves Lake Prespa trickling through underground watercourses in the karstic landscape, where it is joined by mountain range precipitation and eventually emerges in numerous springs along the eastern shore and below the water surface of Lake Ohrid. The water leaves Lake Ohrid by evaporation (~40%) and | How do deying industrial disturbs ponds? | Evaporites are layered crystalline sedimentary rocks that form from brines generated in areas where the amount of water lost by evaporation exceeds the total amount of water from rainfall and influx via rivers and streams. | 220 | Evaporation pond Evaporation ponds are artificial ponds with very large surface areas that are designed to efficiently evaporate water by sunlight and exposure to the ambient temperatures. Evaporation ponds have several uses. Salt evaporation ponds produce salt from seawater. They are also used to dispose of brine from desalination plants. Mines use ponds to separate ore from water. Evaporation ponds at contaminated sites remove the water from hazardous waste, which greatly reduces its weight and volume and allows the waste to be more easily transported, treated and stored. Evaporation ponds can also be used to evaporate the precipitation that falls | evaporation ponds are used to remove what from desalination plants | where does the water in a evaporation pond come from | Help with evaporating water | Evaporation source for use efficiency of the organic material | Use of waste stabilization ponds’ systems in Mediterranean Europe | what law explains the efficiency of a solar pond | what kind of agents are used in evaporators | Research on Waste Stabilization Ponds in the United Kingdom: Sludge Accumulation in Pilot-scale Primary Facultative Ponds |
221 | Does Investor-Ownership of Nursing Homes Compromise the Quality of Care? | This is an excellent book on helping to protect your assets from nursing home costs.....but you'll still need an attorney that specializes in elder care. Be sure to read the reviews that are posted with this book....it's too much to go into with this note. | We analyzed what happens to a nursing home chain when private equity takes over, with regard to strategy, financial performance, and resident well-being. We conducted a longitudinal (2000-2012) case study of a large nursing home chain that triangulated qualitative and quantitative data from 5 different data sources. Results show that private equity owners continued and reinforced several strategies that were already put in place before the takeover, including a focus on keeping staffing levels low; the new owners added restructuring, rebranding, and investment strategies such as establishing new companies, where the nursing home chain served as an essential “launch customer.” | About 10 percent of U.S. nursing homes were found to have consistently inadequate quality since the year 2000, Consumers Union said on Tuesday. | The Federal Housing Administration (FHA) deserves considerable credit for helping support the housing market during the recent financial crisis by increasing its own market share. However, as the recovery continues, the FHA can gradually return to its "traditional" role as an insurer of low-down-payment home mortgages for low-to-moderate-income and first-time homebuyers. A major concern going forward is susceptibility to increased adverse selection if it continues in nontraditional markets. Indeed, the modest market share of the FHA going into the housing collapse was important both in limiting its losses and in allowing it to maintain the market when other traditional secondary market makers failed. | We've been struggling with the home ownership decision for the past 6 months. We live in a HCOL city that is driven by a huge tech presence. With several big tech firms announcing plans to try out remote work options on a permanent basis, even after the pandemic situation improves, we're concerned that real estate prices in the area might take a tumble, since these tech companies contribute sizably to the jobs in the area.
I understand that nobody can predict what happens in the future, but I'm curious to hear the opinions of other people in this situation.
Microsoft:
Twitter: washingtonpost.com/technology/2020/10/01/twitter-work-from-home/?arc404=true
Facebook: #:\~:text=Facebook%20employees%20will%20continue%20working,within%20the%20next%2010%20years. | Patch notes state that only FC's can buy houses after the patch, but I just saw a single person buy a relinquished house. Guess it's only for the new plot coming in a few days. | Maybe I’m missing something here, but this kinda seems like the logical conclusion when everyone in society views home ownership as an investment. Because each time a particular house is bought and resold, over and over again, the price goes up each time because each owner wants to make a profit. And if you’re the latest inhabitant of a particular house and want to sell it, fewer and fewer people will be capable of buying it each time it gets resold. Now apply this to a nationwide scale, and we have a housing crisis filled with unaffordable homes that fewer and fewer people can afford over the long run. Is this what will happen eventually? | Housing Supply and Affordability: Do Affordable Housing Mandates Work? | 221 | Quality problems have long plagued the nursing home industry. While two-thirds of U.S. nursing homes are investor-owned, few studies have examined the impact of investor-ownership on the quality of care. The authors analyzed 1998 data from inspections of 13,693 nursing facilities representing virtually all U.S. nursing homes. They grouped deficiency citations issued by inspectors into three categories (“quality of care,” “quality of life,” and “other”) and compared deficiency rates in investor-owned, nonprofit, and public nursing homes. A multivariate model was used to control for case mix, percentage of residents covered by Medicaid, whether the facility was hospital-based, whether it was a skilled nursing facility for Medicare only, chain ownership, and location by state. The study also assessed nurse staffing. The authors found that investor-owned nursing homes provide worse care and less nursing care than nonprofit or public homes. Investor-owned facilities averaged 5.89 deficiencies per home, 46.5 pe... | This study explores the determinants of nursing home quality, providing a theoretical framework that takes into account structural, process, and environ- mental factors. It asks: Do structural, process, and environmental factors influence nursing home quality? If so, which is the strongest predictor of quality? And does market competition have a positive impact on nursing home quality? Based on relevant literature, this study developed hypotheses and tested them with multiple regression models. The models show that most (but not all) structural, process, and environmental variables have a statistically significant relationship with nursing home quality. The ratio of nursing assistant hours to total nursing hours has the strongest positive influence on quality of care. But market compe- tition does not have a positive effect on nursing home quality; this implies that competition may not a good way to improve the quality of nursing home care. | Nursing homes often receive unfavorable press,[1,2] and this trend has intensified because of their involvement in multiple horrific COVID outbreaks[3,4]. On the one hand, high morbidity and mortality in nursing homes during the pandemic, apart from being a serious problem in itself, exposed ongoing inadequacies in the provision of quality care, which external supervision addressed only partially[5]. Running an effective nursing home is an expensive enterprise, which, unfortunately, is frequently underfunded[6,7]. Even with adequate funding, it is a complex endeavor at which it is not easy to excel[8]. On the other hand, as nursing homes are repositories for people with high morbidities whose health will invariably worsen over time, we may conclude that unmet expectations and unfortunate outcomes are not always preventable or the result of poor care. Nursing home care is not a government priority in the U.S.,[9]and probably not in other Western countries either. This is unfortunate for many reasons, not least because of the likelihood that some of us will eventually end up in one. I believe that, while some criticism is justified, as nursing home care is sometimes suboptimal, in other cases there is inappropriate malignment. This paper will analyze how a nursing home works and attempt to distinguish between preventable and unpreventable poor outcomes. | Predictors of Quality in Rural Nursing Homes Using Standard and Novel Methods | "It Depends": Reasons Why Nursing Home Residents Change Their Minds About Care Preferences. | What Happens to a Nursing Home Chain When Private Equity Takes Over? A Longitudinal Case Study | GENDER DIFFERENCES IN THE FINANCING OF NURSING HOME CARE | Do Nursing Homes Reduce Hospital Use | Interorganizational Linkages and Service and Personnel Shortages in Rural Nursing Homes |
222 | Environmental Sensitivity Indexes in oil hydrocarbons: Its application in SIROCO | The exposure to polycyclic aromatic hydrocarbons (PAH) in different industries using cutting, hardening and extruding oils, was investigated determining their concentration in oils and in environmental samples. The following compounds: phenanthrene, anthracene, fluoranthene, pyrene, benzo-a-anthracene, chrysene, triphenylene, benzo-a-pyrene, benzo-e-pyrene and perylene were evaluated by means of gas-chromatography-mass spectrometry. PAH concentrations in oils ranged from 652 to 4461 ng/gr and environmental concentrations from 63.86 to 120.54 ng/mc. In particular the BaP concentrations varied from 0.73 to 1.9 ng/mc. These results, compared with those measured in other environmental surveys and with the limit values proposed in various countries, point out the existence of a very low inhalatory risk of PAH. | The embryonic and larval stages of the quahog clam Mercenaria sp. were exposed to the water-soluble fractions (WSFs) of 6 oils and the effects on survival and growth rate of the various stages were noted. Kuwait crude oil was the least toxic on initial exposure to both stages, having LC50 values in excess of 10 ppm after continuous exposure to the WSF for up to 6 days. However, at 10 days, Kuwait was slightly more toxic than southern Louisiana crude oil, with both oils having LC50 values near 2 ppm. Florida Jay crude oil was much more toxic, with an LC50 of less than 1 ppm at 48 h and less than 0.2 ppm at 10 days. Two refined oils, No. 2 fuel oil and Bunker “C”, had LC50 values of 1 to 2 ppm after 48 h, while used crankcase motor oil, the most toxic oil tested, had LC50 values of 0.10 ppm or less at all exposure times. Larvae surviving exposure to water-soluble fractions of the various oils often grew at slower rates than the controls. | How does oil spill pollution affect sea turtle? | Even though the ASTM V.I. is based on an arbitrary and inconsistent series of reference oils, the system still persists as an industry standard to rate the viscosity-temperature characteristics of lubricating oils. There is need for an industry wide reassessment of the value of the V.I., particularly to answer the question, ''What does the V.I. measure.''. Before defining an alternative classification system, it is important to clearly formulate the problem and to realize that both relative and nonrealtive indices suffer from inherent assumptions and limitations, and that the choice of no rating index may be better than the choice of a misleading one. | Which plants are oil spills affecting? |
Introduction
Petroleum hydrocarbons compounds i.e. aliphatic hydrocarbons and polyaromatic PAHs that known as toxic pollutants to the environment e.g.rivers, lagoons, and marine, and some of them have mutagenic and carcinogenic properties [1,2,6,7]. Those compounds may be derived from petroleum or oil spills rafinery product (petrogenic sources), incomplete combustion of organic matter, and biomass fossile fuels (pyrolytic source) [1,3,6,7,10]. For that reason, petroleum hydrocarbons analysis within the organims are important to monitoring activity of pollutant in environment as one integrative approach [14].This study used Mediteranean mussel (M.galloprovincialis) to monitor marine ecosystems quality. Hydrocarbons can absorb into sediment via particulate or colloid and potentially ingested by marine benthic organisms in marine environment [2,9] [2,4,5,8,9]. Bivalves such as Mussels had used as sentinel organisms of marine pollution and have the capability to reflect the environment quality which related to their habitat, food chains, and pollutant hydrophobicity properties that have the tendency to be absorbed into their living tissues [2,9]. Mytillus families widely used since 1990's and become one of the most successful model organisms for time-integrated responses to complex mixture of pollutants [14], also as bioindicator reference of hydrocarbons level [8,13]. This study focus on the hydrocarbons content in mussel from traditional market that have direct impact to human, because as we know that the traditional market sell unknown source of mussels which can be from pollutant site or propre site for human consumption.
The significance of this study related to the extraction, fractination, and analysis method using GC-QQQ/MS [1,2,6,7,10]. Quadropole can be used in scanning or filtering mode. Triple quadropole system contains of three quadropoles. Quadropole 1 and 3 as mass filter while quadropole 2 as collision cell [15].Several studies used heptane: dichloromethane (1:1 v/v) [1,6,7,9,10] and heptane:acetone (1:1, v/v) to extract the hydrocarbons [4,13]. Thematrice of mussels tissues are more complex than sediment and can influence the interference effect to separate the hydrocarbons content from their matrices.This study aimed to analyze the content of hydrocarbons in M.galloprovincialis mussel species that derived from traditional markets in Marseille, France, by using protocol analysis of hydrocarbon sediments and to compare the different extraction solution to extract hydrocarbons that can be optimized using GC-QQQ/MS.
Material and Methods
Sampling
Approximately 3 kg wet mussels, M. galloprovincialis have taken from Noailles traditional market, Marseille, France. Fresh seafood market is located about 300 meters from Mediteranean port. After purchased, the wet mussel stored in freezer -20 0 C.
Chemicals
Sampel Preparation
The tissues taken and placed in buchner. Water content in wet tissues removed by gravitation for 30 minutes [3], then wetmass weighed with microbalance (Perkin Elmer AD2Z, Marseille France, weighed approximately ± 250 gr). The tissues were freeze-dried under pressure 0.080 bar and freeze at -50 0 C for 48 h. Then it cutted and crashed by mortar to small size and the dry mass weighed and stored under temperature ambient before the extraction [8,13].
Extraction and Purification
Hydrocarbons extracted from mussel tissues by using protocole extraction of hydrocarbons for sediments [1,6,7,11,12]. 10 gram freeze-dried mussels tissues accurately weighed and placed into precleaned cellulose extraction thimble by soxhterm apparatus for 3.5 h with 150mL HEP:DCM (1:1 v.v) solvent extraction. Beside that, same extraction method has been done, with another solvent extraction, 150mL HEPT:ACE (1:1. v:v). 0.5 mL each internal surrogate deuterated standard solutions of hydrocarbons (n-alkane (nonadecane-d 40 (15 mg/L)) and PAH (anthracene-d 10 (20mg/L); chrysened 12 (20mg/L)) added into sample before the extraction. Then, the extract concentrated to 2 mL with
Quality Control
Calibration Curves have been performance with external standards methods at different concentrations levels usingdilluted individual labeled hydrocarbons standards (i.e. 0.05; 0.2; 0.5; 1.5; 2; 3;3.5 mg/L). In duplicate samples have been calculated that the mean recovery are 97% (HEP:ACE ; 1:1, v/v) and 93% (HEP:DCM, 1:1,v/v). For PAHs are anthracene-d 10 and chrysene-d 12 respectively (82%; 89%( HEP:DCM ; 1:1, v/v) and 90%; 101% HEP:ACE ; 1:1,v/v).The coefficient of correlation was 0.99 forall labeled standard compounds.
Result and discussion
Extractable Organic Matter (EOM) concentrations, Total Hydrocarbons Content (THC), quantities of F1 and F2, comparing between THC and MOE, F1 and F2 from two different solvant extraction are given gravimetrically in Table 1 Generally, n-alkanes are nonpolar compounds and semipolar for PAHs, that can extracted and separated using fractionation method with comparing different polarity of eluent. GC/MS analysis with Single Ion Monitoring (SIM)mode has found 20 peaks n-alkanes (n-C 15-34 ) and 8 peaks identic of PAHs (Figure 1 and Figure 2). According from chromatograms, both of chromatograms have similar profile. Besides n-alkanes derivatives, isomer found from n-alkanes such Pristane, Phytane which indicate the presence of crude oils that might be from natural (biogenic or diagenetic) and isomer from n-alkenes, squalene which derived from microbial degradation [1]. Figure 1 showed that there are two high peaks (n-C 29 and n-C 31 ) in the last chromatograms and n-C 17 , n-C 18 , n-C 19 and n-C 20 have high peaks in the beginning. Total of n-alkanes (n-C 15-34 ) and PAHs respectively were 27026 and 133μg.kg -1 tissues.dw for those extracted with HEP:DCM (1:1, v/v) and for HEP:ACE (1:1, v/v), ∑n-C 15-34 and ∑PAHs respectively have value 28335 and 202μg.kg -1 tissues.dw (see Table 2). The high level of n-alkanes content have the possibilities that originated from disrupting of lipid and metabolites, or these mussels have high contamination in mussels tissues from Mediteranean sea. The mixed solvents HEP:ACE (1:1, v/v) known to be more polar than HEP:DCM (1:1, v/v).From this result, hydrocarbons content from M.galloprovincialis were determined. The properties of mussels tissues are presumably more complex because of their macromolecules content such as lipid, protein, and other metabolite [4]. Such compounds are capable to interference while separating process and these metabolites macromolecules can affect the extraction yield since they have the same polarity with hydrocarbons compounds. For that reason, hydrocarbons can associated with this macromolecul and have the same ion fragmentation with ion target [4]. The method of fractionation need another method to separate these macromolecules before the hydrocarbons fractination process. One of method for macromolecules separation is permeable gel chromatography, which is the macromolecule can be removed from mussel tissues before the fractionation process. Our finding showed aliphatic and PAHs extraction yield within the same greater magnitude that compared to previous studies using sediment as environmental matrices. Partially concluded thatthe mussels from traditional market were potentially polluted by hydrocarbons [1,6,7 and 10]. Obviously, further research is needed to revalidate and to find out the effective method to separate another molecules prior for the environmental analysis. In addition, high concentration of the hydrocarbons in M. Galloprovincialis has been observed, compare to another previous studies concerning PAHsin Mytillus edulis (27,6-442 μg.kg -1 mussels dw ) [12]; M.galloprovincialis from coastal of Saronikos, Gulf, Greece, (17PAHs: 219-1487 μg.kg -1 mussels tissues dw) [13] and for n-alkanes in M.galloprovincialis from Galicia coast (n-C 8-35 : 89.46-5098.01 μg.kg -1 mussels tissues dw) [16]. 7 ratios for n-alkanes used to assess the potential sources of hydrocarbons contamination: CPI (Carbon Preference Index), NAR (Natural alkane ratio, nC18/phyt, nC17/phyt, prist/phyt,TAR (Terrigenous Aquatic Ratio), and LMW/HMW (Low Molecular Weight/High Molecular Weight), while PAHsindices are derived from comparison identical molecular weight such as (anthracene/∑m/z 178; Fluorene/∑m/z 202; Bz(a) anthracene/∑m/z 228; indeno (123 cd)pyrene/∑m/z 176). Generally, there are two main sources of hydrocarbons, origin from anthropogenic activities and from biogenic process (natural process) or biological activites. Concern tobiogenic source, it may be derived from plant or animal residualor both of them. Parameters index and their values of hydrocarbons are given at Table 3 for n-alkanes and Table 4 for PAHs. CPI: Carbon Preference Index = 2*(n-C 25 +n-C 27 +n-C 29 +n-C 31 )/(n-C 24 +2*(n-C 26 +n-C 28 +n-C 30 ) +n-C 32 ); NAR: Natural n-alkane ratio = ((∑n-C 19-32 )-2∑even n-C 20-32 )/(∑n-C 19-32 ); TAR: Terrigenous/Aquatic Ratios = (n-C 27 +n-C 29 +n-C 31 )/(n-C 15 +n-C 17 +n-C 19 ); Pris: Pristane; Phy: Phytane; LMW/HMW (Low Molecular Weight/High Molecular Weight) = (n-C 15-21 )/(n-C 22-34 ) [1,6,7,10,16] The results showed an apportionment of the n-alkanes level from biogenic sources, probable from aquatic organism or terrestrial environment with index (CPI, n-C17/Pr, n-C18/Phy, and TAR ) >1, for NAR is close to zero < 1, indicates for petroleum hydrocarbons, LMW/HMW< 1 usually represent nalkanes that are produced by higher plants, marine animals and sedimentary bacteria.there are found parameters ratio from oil which origin from n-alkanes isomer (Pristane/Phytane) < 2. The source nalkanes from this experiment are shown in Table 5. Source of PAHs Fluoranthene/ (Fluoranthene+pyrene) (Fl/∑202) is often used to discriminate PAH sources (1, 10). Ratio<0.5 is generally characteristic as petrogenic sources and ratio > 0.5 founded in kerosene, grass, coal, and wood combustion samples. The ratio of anthraceene/(Anthracene+Phenanthrene) ratio (An/∑178) < 0.1 indicates a petrogenic source while a ratio > 0.1 reflects a combustion source [1,2,6,10]. Benz (a) anthracene/chrysene (Benzo(a)Anthracene/Benzo(a) anthracene+Chrysene) ratio (BzA/∑228) < 0.2 indicates petroleum sources whileratio > 0.35 indicates combustion sources and values between 0.2-0.35 cannot used to discriminate petroleum and/or combustions sources [1,6].
The index indicates the source of PAHs in mussels from traditional market derived as natural or biogenic sources which origin from the burning of fossil or living creatures biosynthesis results with given indices < 0.5 (anthracene / Σm/z 178, benzo (a) anthracene / Σm/z 228; indeno (123cdi) pyrene / Σ m/z 176 and it also has the probability that those indices came from oil with indices > 0.5 (Fluorene / Σ m/z 202) parameters source of PAH resulting from the two solutions of different extracts that shown in Table 6. The profile of capillary column gas chromatograms of n-alkanes fraction in mussels extract between HEP:ACE (1:1, v/v) and HEP: DCM (1:1, v/v) as solvent extraction have same profile. n-C 15-34 were found with different yield.
Conclusion
The
a gentle nitrogen stream to obtain the total extractable organic matter (EOM). The extract (EOM) weighed on a microbalance (Perkin-Elmer AD2Z) and part of EOM dissolved in a minimum of HEP. The fractination of aliphatic and aromatic hydrocarbons using 1.0 x 3.0 cm borosilicate glass column with 8 gr of silica gel and 8 gr of alumina (bottom and top, respectively), both adsorbents activated with 5% H 2 O. Saturated hydrocarbon fraction or n-alkanes fractions eluted with 30 mL HEP and 20 mL HEP :DCM (90:10, v:v). For PAHs fraction or fraction 2 eluted with 40mL HEP:DCM (80:20, v/v). Both of fraction evaporated on rotary evaporator at 0.5mL. Then, dry fraction (F1 and F2) weighed and obtained the total hydrocarbon content. Fraction 1 dilluted with 300μL HEP and for fraction 2 dilluted in 300μL DCM.2.5. Analysis by capillary gas chromatography coupled to mass spectrometry(GC/MS) Both of fractions (F1 and F2) analyzed by GC-QQQ/MS (Autosystem XL GC and TurboMass triple quadropole mass spectrometer, Perkin Elmer, USA). Chromatographic conditions follows: splitless injection (30 s), Elite 5MS capillary column (30 m x 0.25 mm i.d. x 0.25 μm). The GC oven temperature-programmed from 40 0 C (isotherm 2 min) then raised to 120 0 C (45 0 C.min -1 ) and then raised to 310 0 C (5 0 C.min -1 ) and finally held isothermally for 20 min. Helium (1mL.min-1 ) used as carrier gas in constant flow mode. For injector temperature 50 0 C (isotherm 0.1 min) to 250 0 C (20 0 C/min) for reduce solvant peaks. The mass spectrometer operated in the electron ionization (EI) positive ion mode (70 eV) and simultaneously scanned in both Full Scan and Selected Ion Monitoring (SIFI mode). MS scanned with comparing with NB library reference to confirm and matching their retention times and fragmentation profiles againts corresponding standards. Detection of n-alcanes (m/z 71),), 8 PAH target ions (Acenaphtene, m/z 152; Acenaphtylene, m/z 154; Phenanthrene, m/z 178; Anthracene, m/z 178; Fluoranthene, m/z 202; Pyrene, m/z 202; Benzo(a)anthracene, m/z 228; Chrysene, m/z 228; Indeno(123cdi) pyrene, m/z 276; Benzo(ghi)perylene, m/z 276). internal labeled standard of PAHs (Anthracene-d 10 , m/z 188 and Chrysene-d 12 , m/z 240) and n-alkanes (nanodecane-d40, m/z 66) to evaluate hydrocarbons analysis.
.
The solvant extraction(HEP:ACE ; 1:1 ; v/v) solvant has a lot EOM, THC and fractions content then HEP:DCM (1:1, v/v). Total hydrocarbon content from both extract are < 1 mg.g -1 generally. The proportions of THC in EOM are 18 % for HEP:DCM (1:1),v/v) and 53% for (HEP:ACET (1:1), v/v). Fraction saturated (F1) has more quantity then F2. Comparing of F1/F2 with solvant extraction HEP :ACE (1:1), v/v) more abundance than HEPT :DCM (1:1), v/v).
Figure 1 .
1Capillary column gas chromatograms of the n-alkanes fraction with HEP:DCM (1:1, v/v) (under) and HEP:ACE (1:1,v/v) (above) as solvant extraction; Sq: Squalene; Pr: Pristane; Ph: Phytane.
Figure 2 .
2Capillary column gas chromatograms of the polycyclic aromatic hydrocarbon fraction with HEP:DCM (1:1, v/v) (above) and HEP:ACE (1:1, v/v) (under) as solvant extraction. Phe: Phenanthrene; An: Anthracene; Fl: Fluoranthene; Pyr: Pyrene; BzA: Benzo(a)Anthracene; Chry: Chrysene; IndP: Indeno (123 cdi) pyrene; BghiP: Benzo(ghi)Perylene.
n-heptane (HEP), acetone (ACE), and dichloromethane(DCM) for organic solvent (Suprasolve, GC analysis grade (Merck, Pessac, France)). Individual deuterated standards for PAHs ([ 2 H 10 ]Anthracene, m/z 188 [ 2 H 12 ] Chrysene, m/z 240 (CIL Cluzeau, Andover, MA, USA) and individual labeled standards of n-alkane ([ 2 H 40 ] n-nonadecane, m/z 66 (PESTANAL Sigma-Aldrich, St Quentin, Fallavier, France) and 1-eicosane (n-C 20 ) (Dr.Ehrenstrofer Laboratories, Augsburg, Germany). 16 PAHs US EPA (PAH mix 25) standar mix solutions(Dr. Ehrenstonfer Laboratories, Augsburg, Germany). Silice gel-60 and Alumine gel-60 (Merck, Darmstatd, Germany, size 200-300 mesh for each of them.
Table 1 .
1Gravimetric data (mg.g -1 tissuesdry weight) Conf. Series: Materials Science and Engineering 107 (2016) 012008 doi:10.1088/1757-899X/107/1/012008Extraction
MOE
(mg/g)
THC
(mg/g)
F1
(mg/g)
F2
(mg/g)
THC/MOE
%
F1/F2
(mg/g)
F1/TH
C %
F2/TH
C%
HEP:DCM
55.67
0.10
0.075
0.025
18
3
75
25
HEP:ACE
72.90
0.39
0.325
0.065
53
5
83
17
7.89
12.89
17.89
22.89
27.89
32.89
37.89
42.89
47.89
52.89
57.89
Temps (min)
MOULES -1
C 15
C 18
C 19
C 17
C 20
Pr
C 16
C 21 C 22
C 23
C 24
C 25 C 26
C 27
C 28
C 29
C 30
C 31
C 32
C 33
Ph
UCM
Sq
7.89
12.89
17.89
22.89
27.89
32.89
37.89
42.89
47.89
52.89
57.89
Temps (min)
MOULES -2
C 15
C 18
C 19
C 17
C 20
Pr
C 16
C 21 C 22
C 23
C 24
C 25 C 26
C 27
C 28
C 29
C 30
C 31
C 32
C 33
Ph
C 34
Sq
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Conf. Series: Materials Science and Engineering 107 (2016) 012008 doi:10.1088/1757-899X/107/1/01200817.31
19.31
21.31
23.31
25.31
27.31
29.31
31.31
33.31
35.31
37.31
Time
Phe
Ant
Fl
Pyr
BzA
Chry
IndP
BghiP
MOULES -1 Fraction aromatique ( HEPT / DCM)
Ion 178
Ion 202
Ion 228
Ion 276
M. galloprovincialis HEP:DCM (1:1, v/v)
16.46
18.46
20.46
22.46
24.46
26.46
28.46
30.46
32.46
34.46
36.46
38.46
40.46
Time
Phe
Ant
Fl
Pyr
BzA
Chry
IndP
BghiP
MOULES -2 Fraction aromatique ( HEPT / ACET)
Ion 178
Ion 202
Ion 228
Ion 276
Mytillus galloprovincialis heptana: aceton
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Table 2 .
2Concentrations of n-alkanes, pristane and phytane and PAHs in M.galloprovincialis from traditional market, Noailles,Marseille, France (μg.kg -1 tissues. dw)
Compounds
(HEP:ACE)
(HEP:DCM)
n-C 15
442
654
n-C 16
663
712
n-C 17
1775
1737
Pristane
940
1082
n-C 18
1794
1682
Phytane
2023
1541
n-C 19
2288
2244
n-C 20
2039
1885
n-C 21
1541
1412
n-C 22
1725
1568
n-C 23
1424
1289
n-C 24
1075
953
n-C 25
971
634
n-C 26
574
375
n-C 27
1103
1126
n-C 28
535
525
n-C 29
2009
2400
n-C 30
589
521
n-C 31
3332
3352
n-C 32
449
398
n-C 33
699
714
n-C 34
346
222
∑n-C 15-34
28335
27026
Phenanthrene
24
13
Anthracene
9
8
Fluoranthene
93
52
Pyrene
62
45
Benz(a)anthracene
3
4
Chrysene
8
9
Indeno(1233cdi)pyr
1
1
Benz(ghi)perylene
2
1
∑PAH
202
133
Table 3 .
3Characteristic of n-alkanes from different sources[1,6 and 7] Parameters
Origin
Oil
Aquatic
environment
Terrestrial
environment
CPI (24-32)
≈ 1
>1
n-C 29 /n-C 17
<1
<1
>1
n-C 17 /prist
>1
<1
>1
n-C 18 /Phyt
>1
≈ 1
≈ 1
Prist/Phyt
<2
>2
>2
NAR
≈ 0
>0.5-1
TAR
<1
>1
LMW/HMW
>2
≈ 1
<1
CPI: Carbon Preference index; TAR: Terrigenous/Aquatic Ratio; NAR:
Natural n-alkane ratio; LMW/HMW (Low Molecular Weight/High
Molecular Weight); Pr: Pristane; Phy: Phytane
Table 4 .
4Characteristics of PAH source from different source (μg.kg -1 mussels tissues dw) Series: Materials Science and Engineering 107 (2016) 012008 doi:10.1088/1757-899X/107/1/012008Origin from oil
Origin from mix
between oil
and combustion product
Origin from combustion
of fossil and plant
An/∑178
< 0.1
> 0.1
Fl/∑202
< 0.4
0.4 -0.5
Mixed source from
combustion of fossil
> 0.5
Cerosen combustion,
charbone or biomass
(herbal, wood…)
BzA/∑228
< 0.2
Mixed
> 0.35
IndP/∑276
< 0.2
0.2 -0.5
Combustion result or
flammable
fossil liquid
> 0.5
combustion of
charbone or from
biomass (wood, herbal)
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Table 5 .
5Selected n-alkanes ratios in M galloprovincialis (μg.kg -1 mussels tissues dw)Mussels
CPI n-C 17 /Pr
n-
C 18 /Ph
Pr/Ph n-C 29 /n-
C 17
NAR
TAR LMW/HMW
M.galloprovinsialis
(HEP:DCM)
3.0
1.6
1.1
0.7
1.4
0.4
1.5
0.7
M.galloprovincialis
(HEP:ACE)
2.6
1.9
0.9
0.5
1.1
0.3
1.4
0.8
Table 6 .
6Characteristic of PAH sources fromM. galloprovincialis (μg.kg -1 mussels tissues dw)An/∑178 a
Fl/∑202 b
BzA/∑228 c
IndP/∑276 d
M.galloprovincialis
(HEP:ACE)
0.27
0.53
0.32
0.29
M.galloprovincialis
(HEP:DCM)
0.38
0.54
0.31
0.31
a An/∑178 (Anthracene/ (Anthracene+ Phenanthrene)
b Fl/∑202 (Fluoranthene/(Fluoranthene+Pyrene)
c BzA/∑228 (Benzo(a)anthracene/Bz(a)anthracene+chrysene)
d IndP/∑276(Indeno(123cdi)pyrene/Indeno(123cdi)pyrene+Benzo(ghi)perylene)
extract solution of HEP:ACE (Σn-C15-34: 28 335 μg.kg -1 tissues dw and Σ PAHs: 202 μg.kg -1 tissues dw) better than HEP:DCM (Σn-C15-34: 27026 μg.kg -1 tissues dw and Σ PAHs: 133 μg.kg -10th Joint Conference on Chemistry IOP Publishing IOP Conf. Series: Materials Science and Engineering 107 (2016) 012008 doi:10.1088/1757-899X/107/1/0120088
1 tissues dw). High hydrocarbons extract yield might be come from two possibilities (i).direct disruption of lipids and metabolites during analysis; (ii). the apportionment as source of n-alkanes and PAHs from the use of diagnostic molecular indices that indicated pyrolytic and biogenic, also petrogenic sources.
Occurence and distribution of hydrocarbons in surface sediments from Marseille Bay (France). L Asia, S Mazouz, M Guiliano, P Doumenq, G Mille, Mar. Pollut.Bull. 58Asia L, Mazouz S, Guiliano M, Doumenq P and Mille G 2009 Occurence and distribution of hydrocarbons in surface sediments from Marseille Bay (France) Mar. Pollut.Bull. 58 443- 451
Polycyclic aromatic hydrocarbon (PAH) burden of mussel (Mytillus sp) in different marine environments in relation with sediment PAH contamination and bioavailability Mar. P Baumard, H Budzinski, Q Michon, P Garrigues, J F Narbonne, T Burgeot, Michel X Bellocq, T , Environ.Res. 47Baumard P, Budzinski H, Michon Q,Garrigues P, Narbonne J F, Burgeot T, Michel X and Bellocq T 1999 Polycyclic aromatic hydrocarbon (PAH) burden of mussel (Mytillus sp) in different marine environments in relation with sediment PAH contamination and bioavailability Mar.Environ.Res. 47 415-439
Unep/Ramoge, Manual on the Biomarkers Recommended for the MEDPOL Biomonitoring Programme UNEP Athens. UNEP/RAMOGE 1999 Manual on the Biomarkers Recommended for the MEDPOL Biomonitoring Programme UNEP Athens
Validation of an analytical procedure for polychlorinated biphenyls, coplanar polychlorinated biphenyls and polycyclic aromatic hydrocarbons in environmental samples. A Jaouen-Madoulet, A Abarnou, A Le-Guellec, V Loizeau, F Lebouleger, J.Chrom A. 886Jaouen-Madoulet A, Abarnou A, Le-Guellec A M Loizeau V and Lebouleger F 2000 Validation of an analytical procedure for polychlorinated biphenyls, coplanar polychlorinated biphenyls and polycyclic aromatic hydrocarbons in environmental samples J.Chrom A. 886 153-173
Biochemical responses of the marine mussel Mytillus galloprovincialis to petrochemical environmental contamination along the North-western coast of. I Lima, S M Moreira, J R V Osten, A M V M Soares, L Guilhermino, Portugal Chemosphere. 66Lima I, Moreira S M, Osten J R V, Soares A M V M and Guilhermino L 2007 Biochemical responses of the marine mussel Mytillus galloprovincialis to petrochemical environmental contamination along the North-western coast of Portugal Chemosphere 66 1230-1242
Hydrocarbons in coastal sediments from the Mediterranean sea (Gulf of Fos area, France). G Mille, Asia L Guiliano, M Malleret, L Doumenq, P , Mar.Pollut.Bull. 54Mille G, Asia L, Guiliano M, Malleret L and Doumenq P 2007 Hydrocarbons in coastal sediments from the Mediterranean sea (Gulf of Fos area, France) Mar.Pollut.Bull. 54 566- 575
Sources of hydocarbons in sediments of the Bay of Fort de France (Martinique) Chemomsphere. G Mille, M Guiliano, Asia L Malleret, L Jalaluddin, N , 64Mille G, Guiliano M, Asia L, Malleret L and Jalaluddin N 2006 Sources of hydocarbons in sediments of the Bay of Fort de France (Martinique) Chemomsphere 64 1062-1073
Bioaccumulation and biomarker responses of trace metals and micro-organic pollutants in mussels and fish from the Lagoonof Venice. N Nesto, S Romanon, M Moschino, M Mauri, L Da Ros, ItalyMar.Pollut.Bull. 55Nesto N, Romanon S, Moschino M, Mauri M and Da Ros L 2007 Bioaccumulation and biomarker responses of trace metals and micro-organic pollutants in mussels and fish from the Lagoonof Venice, ItalyMar.Pollut.Bull 55 469-489
Accumulation and distribution of petroleum hydrocarbons found in mussels (Mytilusgalloprovincialis) in the canals of Vence Italy Mar. D W Wetzel, Van Vleet, V , Pollut. Bull. 48Wetzel D W and Van Vleet V S 2004 Accumulation and distribution of petroleum hydrocarbons found in mussels (Mytilusgalloprovincialis) in the canals of Vence Italy Mar.Pollut. Bull 48 927-936
Source apportionment of sedimentary hydrocarbons in the Segara Anakan Nature Reserve IndonesiaMar. A D Syakti, N V Hidayati, Piram A Hilmie, P Doumenq, Pollut. Bull. 74Syakti A D, Hidayati N V, HilmiE, Piram A and Doumenq P 2013 Source apportionment of sedimentary hydrocarbons in the Segara Anakan Nature Reserve IndonesiaMar.Pollut. Bull 74 141-148
. A D Syakti, N Hidayati, A S Siregar, Agen Pencemar Laut IPB press Bogor. 1Syakti A D, Hidayati N V and Siregar A S 2012 Agen Pencemar Laut IPB press Bogor 1 100- 101
Certificat of Analysis Standard Reference Material 1974 C Organics in Mussel Tissue (Mytilus edulis) NIST MD. S Wise, Wise S A 2012 Certificat of Analysis Standard Reference Material 1974 C Organics in Mussel Tissue (Mytilus edulis) NIST MD 20899 USA 1-10
aromatic hydrocarbons in surface seawater and in indegenous mussels (Mytillus galloprovincialis) from coastal areas of the Saronikos Gulf (Greece). A Valvanidis, T Vlachogiann, S Triantafillaki, M Dassenaki, Androutsos F Scoullos, M , Estuar.Coast. Shelf Sci. 79Valvanidis A, Vlachogiann T, Triantafillaki S, Dassenaki M, Androutsos F and Scoullos M 2008Polycyclic aromatic hydrocarbons in surface seawater and in indegenous mussels (Mytillus galloprovincialis) from coastal areas of the Saronikos Gulf (Greece) Estuar.Coast. Shelf Sci. 79 733-739
PAH body burden and biomarker responses in mussels (Mytillus edulis) exposed to produced water from a North Sea oil field: Laboratory an field assessment Mar. R C Sundt, D M Pampanin, M Grung, J Barsiene, A Ruus, Pollut.Bull. 62Sundt R C, Pampanin D M, Grung M, Barsiene J and Ruus A 2011 PAH body burden and biomarker responses in mussels (Mytillus edulis) exposed to produced water from a North Sea oil field: Laboratory an field assessment Mar.Pollut.Bull. 62 1498-1505
Advantages of using triple quadropole over single quadropole mass spectrometry to quantify and identify the presence of pesticides in water and soil samples Food and. A Schreiber, Chemisrtry AB Sciex Concord Ontarion. 1Schreiber A 2010 Advantages of using triple quadropole over single quadropole mass spectrometry to quantify and identify the presence of pesticides in water and soil samples Food and Chemisrtry AB Sciex Concord Ontarion 1 1-6
10.1088/1757-899X/107/1/01200810th Joint Conference on Chemistry IOP Publishing IOP Conf. Series: Materials Science and Engineering. 1071200810th Joint Conference on Chemistry IOP Publishing IOP Conf. Series: Materials Science and Engineering 107 (2016) 012008 doi:10.1088/1757-899X/107/1/012008
| What is true about aromatic hydrocarbons? |
Introduction
Emissions of air contaminants as CO, sulfur dioxide, nitrogen oxides, unburned hydrocarbons and aerosols of vehicles increase tremendously every year. One of the reasons that cause air pollution and climate changes is distribution of these materials. In addition, efforts is also considered to reduce dependence on oil products due to rapid decrease in oil resource and price instability 1 .
Pure vegetable oils have been considered as an alternative for diesel fuel, but the high viscosity at room temperature made them unsuitable for diesel engines. However, Fatty Acid Methyl Ester (FAME) derived from them have lower viscosity than the pure oils. So research about the use of fatty acid ester as an alternative of diesel fuel is justifiable 2 .
Biodiesel is a non-toxic, renewable fuel and has no sulfur and aromatic compounds. It consist alkyl esters fatty acids with long chain that is prepared from renewable resources such vegetable oils or animal fats. It has the general chemical formula 3C19H35COOR. Also it is only used as a fuel in internal combustion engines and heating systems 3 .
The fuel properties of biodiesel are strongly influenced by the properties of the fatty acid esters that are formed. Identification of these acids can be very effective on obtaining the properties of biodiesel fuels. More Attempts have been performed by various researchers to determine the composition of biodiesel in order to improve the combustion process. It was observed that the fuel properties of biodiesel play a significant role in the combustion process. The fuel Cetane Number is one of the most important factors in the combustion process 4 .
The Cetane Number is expressed as a rate of Fuel Preparation for the auto-ignition temperature and pressure conditions inside the combustion chamber. Fuel Keywords: Biodiesel, Cetane Number, Fatty Acid Ethyl Ester injected into the cylinder should be ignited before reaching the maximum density and in the range of a few thousandths of a second. The Cetane Number indicates the natural tendency of the fuel to ignite. This means that higher Cetane Number causes the better performance of the engine and shorter ignition delay (the interval between injection and ignition) and finally the combustion performs quieter and more uniform. So the Cetane Number is an important parameter in the quality of biodiesel fuel 5 .
The use of vegetable oils directly in diesel engines, due to the high oil viscosity and inappropriate atomization, cause problems such as low quality ignition and incomplete combustion of fuel. On the other hand, the formation of a layer of non-combustible fuel on the cylinder wall disrupts lubrication system. Also low Cetane Number of Vegetable oils causes knock at low engine loads and low temperatures. In general, vegetable oils have high ignition delay and slower combustion than the diesel fuel. In result, maximum pressure in their combustion is also lower than diesel fuel. On the other hand, the engines that work with vegetable oils, due to blockage of the injector in high pressure, cannot have direct injection 6 .
It is necessary to extend the relationship between weight percent of biodiesel fuel components and the Cetane Number. It can be obtained as a regression analysis. Regression analysis includes the relationship between a dependent variable and one or more predictor variables (or independent variables). In this research, the independent variable is percentage of fatty acids and dependent variable is Cetane Number 7 .
Materials and Methods
In this research, the biodiesel fuel is produced with the trans-esterification method by using ethanol and sodium hydroxide as catalyst from seven types of vegetable oils (sunflower, soybeans, canola, olive, corn, grape seed and rice bran). Specific molar ratio of alcohol to oil (6 to 1) under certain temperature (70° C) and a certain specific weight of sodium hydroxide catalyst ratio (A percent weight of oil) was considered in accordance with optimum conditions for producing biodiesel fuel intensity mixer (600 rpm min). In this case, the fatty acids chain will be converted to impure fatty acid ethyl esters. But due to use of sodium hydroxide catalyst, pH of fuel got in the bases range that Chloride acid was used to neutralize it. Considering the fact that alcohol is evaporated and glycerin is solved in the water, in order to remove the existing glycerin and alcohol in fuel, water leaching process is performed by using distilled water in three stages. In this position the fuel is made pure. The determination of the weight rate percent (wt %) of the existing ethyl ester of fatty acids in these kinds of fuels is performed via GC-mass based on ASTM standard and using polar columns 8 .
Measurement of Cetane Number of unknown fuel is possible by two methods, chemical method or air throttling. At the chemical method of Cetane Number measurement, the volume percentage of normal Cetane of unknown fuel is measured. At air throttling method, Cetane Number of fuel is measured by the CFR engine and the ignition delay time according to ASTM-D613 or din 51773 standard. The CFR engine is shown at Figure 1 3 .
The Cetane Number has inverse relationship with the fuel ignition delay time. On the other hand, the ignition delay for a diesel engine is proportional with the Air to Fuel Ratio (AFR) or rate of fuel consumption to air 9 .
This relationship is used for calculate of the Cetane Number. In the CFR engine, fuel consumption rate is constant and air consumption rate is variable so Cetane Number can be determined by measurement of fuel consumption rate a standard diagram (Cetane-Air consumption rate) that provided by the CFR engine manufacture. For experiment performance, the CFR engine are calibrated by the normal Cetane base fuel. After engine calibration, the unknown fuel is poured into the engine. In CFR engine, fuel consumption rate is constant and for achieving a constant ignition delay time, only variable parameter is air consumption rate that ignition delay time remains the same as the previous standard by changing the air consumption. In the engine standard conditions, Cetane Number of fuel is determined from gage of air consumption measurement and diagram (Cetane -Air consumption) that is provided by the CFR manufacturer. In the study, regression analysis was used for establishing the relationship between the Cetane Number and compounds of biodiesel fuel. Regression analysis established simple model between fatty acids as independent variable and Cetane Number as dependent variable.
Results and Discussion
Compounds present in biodiesel fuels.
In the study, the GC-mass set was used for detecting the biodiesel fuel compound. The results are shown in Table 1.
The Cetane Number is Measured by CFR Engine
Air meter gage was obtained by CFR engine according to DIN51773 standard. The results are shown in Table 2.
The CFR engine has CN-Air meter reading standard diagram that determine CN at air meter gage data. The results are shown in Table 3.
Modeling to Predict Cetane Number
Five types of biodiesel fuel (soybean -sunflower -olive -grape seed -rice bran) was used to determine a relationship between the CN and FAAE compounds. A linear regression analysis was performed by SPSS 17 software. A five matrix was formed with CN as the dependent variable and the pure (FAAE) compounds as the independent variables. The results are shown as Equation (1).
Validation for CN Prediction Model
As mentioned five types of biodiesel fuel was used in this model. Data from two types of biodiesel fuel, corn and canola, was used to validate the model. The average measured values of CN obtained from CFR engine in compare to the predicted values from equation, showed that the regression model can predict the Cetane Number with maximum error of 5% (Table 4). The predicted values of CN in compared to the measured values from CFR engine is shown in Figure 2.
Presented regression model can predict Cetane Number of biodiesel fuel with an error of less than 5 percent and correlation coefficient of 9662/0.
Conclusions
In this study, an equation established that the Cetane Number can be predicted by the FAAE composition of ethyl ester with 96.62% accuracy. Experimental results showed that the Cetane Number depends on fatty acid mono-esters in biodiesel fuel. Stearate saturated fatty acid (C16 = 0) with short hydrocarbon chains decrease fuel Cetane Number but linoleate unsaturated fatty acid (c18=0) with long hydrocarbon chains increases the biodiesel Cetane Number. So, the production of biodiesel fuel from vegetable oils, which have a high degree of saturation, can increase the Cetane Number of the fuel.
Reference
Figure 1 .
1CFR engine in University of Tabriz.
Table 1 .Table 2 .
12The Fatty Acid Ethyl Ester (FAAE) composition Air meter gage data for biodiesel fuelsEthyl
linoleate
Ethyl
oleate
Ethyl
Palmitate
Ethyl
Stearate
Biodiesel
53.666
32.133
4.807
9.393
Soybean
51.32
27.93
11.63
9.12
Rice bran
54.694
25.873
5.112
12.395
Sunflower
15.78
68.537
11.033
4.644
Olive
54.826
30.88
5.681
8.613
grape seed
51.344
32.933
6.25
9.473
Canola
50.7
30.38
10.31
8.61
Corn
Average
Repeat 3
Repeat 2
Repeat 1
Biodiesel fuel
33
33
33
33.5
Soybean
33.5
33.5
33.5
33
Canola
28
28
28
29
Sunflower
29.5
29.5
29.5
29
Rice bran
26
26
26
27
Grape seed
25
25
25
25
Olive
27
27
26.5
26.5
Corn
Table 3 .Table 4 .
34CN measured Evaluation of ErrorCN measured
Biodiesel fuel
41.2
Soybean
44.25
Race bran
45.75
Sunflower
49.35
Olive
48.1
Grape seed
44.81
Canola
46.38
Corn
Corn
Canola
Biodiesel fuel
46.38
44.81
measured CN
46.98
47.09
Predicted CN
1.55%
5.08%
Error %
Figure 2. Relationship between measured and predicted values of Cetane number.
Artificial neural networks used for the rediction of the cetane number of biodiesel. A S Ramadhas, S Jayaraj, C Muraleedharan, K Padmakumari, Renewable Energy. 3115Ramadhas AS, Jayaraj S, Muraleedharan C, Padmakumari K. Artificial neural networks used for the rediction of the cetane number of biodiesel. Renewable Energy. 2005; 31(15):2524-33.
J A Van Gerpen, Cetane number testing of biodiesel. Proceedings on 3rd Conference ASAE Liquid Fuel. Van Gerpen JA. Cetane number testing of biodiesel. Proceedings on 3rd Conference ASAE Liquid Fuel;
. T N Nashville, Usa , Nashville, TN, USA. 1996 Sep 15-17.
Experimental investigation of performance and emission parameters of a small diesel engine using CNG and biodiesel. 13th Small Engine Technology Conference. B Najafi, V Pirozpanah, Najafi Gh, Y Talal, B Ghobadian, Toki MesseNiigata, JapanNajafi B, Pirozpanah V, Najafi Gh, Talal Y, Ghobadian B. Experimental investigation of performance and emission parameters of a small diesel engine using CNG and bio- diesel. 13th Small Engine Technology Conference; Toki Messe, Niigata, Japan. 2007 Oct 30-Nov 01. p. 40-76.
Dependence of biodiesel fuel properties on the structure of fatty acid alkyl esters. G Knothe, Fuel Proc Technol. 8610Knothe G. Dependence of biodiesel fuel properties on the structure of fatty acid alkyl esters. Fuel Proc Technol. 2005; 86(10):1059-70.
Knock rating for high-speed C. I. engine fuels. G D Boerlage, J J Broeze, World Petroleum Congress ProceedingBoerlage GD, Broeze JJ. Knock rating for high-speed C. I. engine fuels. World Petroleum Congress Proceeding;
. U K London, London, UK. 1933. p. 271-8.
Effects of specific fatty acid methyl esters on diesel fuel lubricity. D P Geller, J W Goodrum, Fuel. 83Geller DP, Goodrum JW. Effects of specific fatty acid methyl esters on diesel fuel lubricity. Fuel. 2004; 83(17- 18):2351-6.
Prediction of cetane number of biodiesel fuel from the Fatty Acid Methyl Ester (FAME) composition. A I Bamgboye, A C Hansen, Int Agrophysics. 221Bamgboye AI. Hansen AC. Prediction of cetane number of biodiesel fuel from the Fatty Acid Methyl Ester (FAME) composition. Int Agrophysics. 2008; 22(1):21-9.
Prediction of thermophysical properties of of biodiesel fuel using artificial neural network [Thesis submited to the graduate studies for the degree of master science. M Abbasifakhr, B Najafi, S H Jamali, IranUniversity of mohaghegh ArdabilAbbasifakhr M, Najafi B, Jamali SH. Prediction of ther- mophysical properties of of biodiesel fuel using artificial neural network [Thesis submited to the graduate studies for the degree of master science]. Iran: University of moha- ghegh Ardabil; 2010.
An experimental investigation of diesel engine ignition delay using biodiesel and diesel fuels. Fuel and Combustion. S M Neicharan, B Ghobadian, T Tavakoli, K R Saray, 2Spring-SummerNeicharan SM, Ghobadian B, Tavakoli T, Saray KR. An experimental investigation of diesel engine ignition delay using biodiesel and diesel fuels. Fuel and Combustion; 2009 Spring-Summer; 2(1);55-68.
| 222 | In this study, the Environmental Sensitivity Indexes (ESI) are analyzed through SIROCO (Island Response Systems and Operations against ocean pollutants), which allow us to determine the behavior of the substrates that constitute the coastal littoral in front of the polluting action originated by hypothetical accidental spills of hydrocarbons that may affect the islands of Lanzarote and Fuerteventura. | Sensitivity analysis is a powerful tool for understanding the response of an environmental system (e.g., air quality) or model of that system to both inputs and system parameters. A fast, formal sensitivity analysis method was developed for application to multidimensional, chemically-active environmental models. The technique was then implemented in a three-dimensional air quality model and applied to the South Coast Air Basin (SoCAB) of California. Using direct derivatives of the equations governing the evolu tion of species concentrations, the local sensitivities to a variety of model parameters (e.g., rate constants, dry deposition velocities, wind speed) and inputs (e.g., initial concentrations, ground-level emissions, wind speed) are computed simultaneously. Since the equations governing sensitivity coefficients have a structure similar to that of the pollutant concentrations, the implementation using this technique is straightforward and computationally efficient. | Sensitivity Analysis for Decision Making (Análisis De Sensibilidad Para La Toma De Decisiones. Slides) | ESO information guide: Environment Policy | Singular vector decomposition for sensitivity analyses of tropospheric chemical scenarios | Effectiveness of Environmental Impact Assessment (EIA) in addressing development-induced disasters: a comparison of the EIA processes of Sri Lanka and New Zealand | To effectively reduce the environmental compliance costs associated with meeting specific requirements under the Aerospace Manufacturing and Rework Facility's National Emission Standard for Hazardous Air Pollutants rule, the U.S. Environmental Protection Agency's (EPA) Data Quality Objective (DQO) process has been proposed as a suitable framework for developing a scientifically defensible surface compliance monitoring program. By estimating the variability associated with the air cap pressure of high- volume, low-pressure (HVLP) surface-coating spray equipment, the number of monitoring samples necessary for an affected facility to claim compliance with a desired statistical confidence level was established. Using data taken from the pilot test facility, the DQO process indicated that the mean of at least 21 HVLP air cap pressure samples taken over the compliance period must be < or = 10 pounds per square inch (psig) gauge for the facility to claim regulatory compliance with 99.99% statistical confidence. Fewer compliance samples could be taken, but that decision would lead to a commensurate reduction in the compliance confidence level. Implementation of the DQO-based compliance sampling plan eliminates the need for an affected facility to sample all regulated HVLP surface-coating processes while still maintaining a high level of compliance assurance. | what type of study is sensitivity analysis used in | Abstract : The report concerns the results of a 2-year study of the fouling species occurring in the northeastern Gulf of Mexico offshore from Panama City, Florida. Although the efficacy of one kind of antifoulant (organotin) was determined, the principal objective of the study was to follow the progressive development and reorganizations of potential fouling assemblages in this region. Differences both in species composition and diversity existing among the stations (located 2, 11, and 25 miles offshore) and at different depths at the same station (4 to 44 m) revealed that the water masses bathing the floats often had very different origins and histories. Moreover, the placement of the 25-mile fouling station in a region thought to be devoid of natural hard surfaces revealed the presence of pelagic larvae of epifaunal species that do not exist along the shore at Panama City. Oceanographic data indicate the possibility that some of these larvae may have been carried by currents from points as distant as Yucatan (about 400-500 nautical miles). The exposure-harvest schedule has permitted calculation of valuable data on the secondary productivity of various consumer species in this region. (Author) |
223 | I ended up choosing the one with the thicker stitches because I feel like the loosely-stitched one would fall apart a lot sooner | Mine is currently the puff stitch, but I'm looking for more interesting and fun stitches to try! | I bought this and another brand of the same cut and this is far better sewn and cut. Nice medium thickness of fabric. | New stitching on the side as compared to what I have. Not as comfortable and looked cheap. | Excellent seam ripper for those standard/larger stitch lengths, > 2.5mm. I use a smaller ripper for anything smaller. This particular ripper Ive had about a year and its still sharp. | You get what you pay for, although these feel soft to the touch, the sewing is incredibly sloppy. There are lots of holes along the edges as well. | This is a very helpful book. I like looking at all the different stitches. It is easy to follow | The stitching had long loose threads connected to segments of weak stitching. I used craft glue to hopefully prevent potential fraying when I trimmed the threads. Also, the plastic inside coating started peeling off immediately.
Update, after 9 months of mild use, at least none of the problems have gotten worse. | I love the shape/size, but after a couple months of use, some of the stitching on trim is coming undone. | 223 | I received two of these by mistake and was able to compare the two books. One was heavier, had a larger latch on the front, a loose stitching pattern, and had much thicker paper, while the other had a smaller latch, tighter stitching pattern, and thinner paper. I ended up choosing the one with the thicker stitches because I feel like the loosely-stitched one would fall apart a lot sooner. The thinner pages still hold ink from my Micron pen well without bleeding through, so that's a relief. If anything I HIGHLY recommend you buy one of these books JUST FOR THE SMELL! It smells HEAVENLY | The books appearance (it's very professional) It's thick (it promisses a lot of information) The letter size (it's easy to read) | Books that are better on paper? | what is the weight of a book when it is rebolded | The hardcover book is much better. | Any difference between the signature Disney Collection? | WHAT IS THE DIFFERENCE BETWEEN DIARY AND PAPERBACK? | Help on a comparison between two book series. | The illustration and print are fine, though the thickness of the pages are a ... |
224 | A comparison of fire-resistant hydraulic fluids for hazardous industrial environments. Part II. Stability, fluid life, and environment | This article covers the various types of fire-resistant hydraulic fluids available and the characteristics of each of the foreign categories of the fluid. Aspects of component selection, system design, material compatibility, and comparison of commercially available fluids are discussed. | A methodology is developed to predict the flammability of water-based hydraulic fluids. The methodology is based on the heat release rate of an atomized spray and the calculated adiabatic flame temperature of the fluid for cases where the fire point (ASTM D-92) cannot be measured, because of the presence of water. NASA equilibrium code yields the adiabatic flame temperature from the knowledge of elemental composition of the fluid as well as its gross heat of complete combustion (oxygen bomb calorimetry). A criterion has been developed to identify less flammable water-based hydraulic fluids. It is that for a fluid showing no fire point, have a chemical heat release rate less than or equal to 130 kW in FM Global’s standardized spray fire test and its adiabatic stoichiometric flame temperature is less than or equal to 2100 K. For fluids having fire points one would use the traditional spray flammability parameter (SFP) FM Approval Standard2. | A methodology is developed to predict the flammability of water-based hydraulic fluids. The methodology is based on the heat release rate of an atomized spray and the calculated adiabatic flame temperature of the fluid for cases where the fire point (ASTM D-92) cannot be measured, because of the presence of water. NASA equilibrium code yields the adiabatic flame temperature from the knowledge of elemental composition of the fluid as well as its gross heat of complete combustion (oxygen bomb calorimetry). A criterion has been developed to identify less flammable water-based hydraulic fluids. It is that for a fluid showing no fire point, have a chemical heat release rate less than or equal to 130 kW in FM Global’s standardized spray fire test and its adiabatic stoichiometric flame temperature is less than or equal to 2100 K. For fluids having fire points one would use the traditional spray flammability parameter (SFP) FM Approval Standard2. | The invention discloses a water-soluble fire retardant and application thereof. The water-soluble fire retardant is composed of the following ingredients (by weight): 4-30% of a water-soluble inorganic fire retardant, 10-40% of an aqueous inorganic binder, 10-30% of a water-molecular polymer emulsion, 1-3% of a thickening agent and 1-3% of an osmotic agent. The invention also discloses application of the water-soluble fire retardant to wood and/or fiber surface. The water-soluble fire retardant has a flame retardant effect. The disaster rescue and fireproof effects can be greatly raised. In addition, durability and waterproofness after material surface treatment can be solved. | This thesis discusses improved water supply control system with constant pressure in the fire fighting that is composed of transducer, pressure sensor, PLC as well as homemade controller. This system possesses the function that can automatically time examine whether the fire engine works normally, whether the system leakes water, whether the system is operated by anyone. Furthermore, the system possesses the function that can automatically start up fire engine when fire happens and overcome the status operated manually or depended on fire sensor formerly. | Protection Systems for Tanks Containing Hazardous Materials Exposed to Fire | Flamethrower A flamethrower is a mechanical incendiary device designed to project a long, controllable stream of fire. They were first used by the Greeks in the 1st century AD. In modern times, they were used during World War I, and more widely in World War II. Most military flamethrowers use flammable liquid thickened into a substance similar to napalm, but commercial flamethrowers tend to use high-pressure propane and gasoline, which is considered safer as they both die out faster and are easier to put out. Note that actual napalm was never used with flamethrowers. In comparison, a liquid flamethrower's fuel | The Jasper County Sheriff’s Department is asking for the public’s help in identifying who’s responsible for opening some fire hydrants in Reasnor and near Prairie City that led to the loss of thousands of gallons of water.
Sheriff John Halferty says someone tampered with four fire hydrants, and although there were fires in both Sulley Saturday at 11 p.m., and in Prarie City at 1:30 Sunday morning — he doesn’t think the fire and tampering are related.
He says they believe the water sources were tampered with during the same time frame as the fires, but he says the two things appear to be a coincidence. Three of the opened hydrants were in Reasnor, and one hydrant was near the Central Iowa Water Association Water Tower east of Prairie City. Central Iowa Water Association estimates approximately 300,000 gallons of water was lost due to the tampering. Sheriff Halferty also notes one of the tampered with hydrants was damaged and unusable.
“Because a hydrant wrench was not used, I suspect that’s why the one hydrant in Reasnor was damaged. You can break the part of the hydrant that actually opens up the water flow, and I believe what happened to the hydrant in Reasnor,” Halferty says. The Sheriff says the hydrant openings did not impact the water supply of local fire departments during the two structure fires. But he said it did create a dangerous situation if the water had been needed.
“It’s extremely dangerous, number one the fire departments usually have preplanning in place and know what water sources they are going to go to,” Halferty explains. “An if they arrive and they are not able to utilize that or it has been tampered with and they have to go to a backup plan…it delays their ability to fight the fire and protect not only the citizens, but their property as well.” Anyone with information pertaining to the person or persons responsible for tampering with these fire hydrants is asked to contact the sheriff’s office at 641-792-5912.
(By Randy Van, KCOB, Newton/Photo from Jasper County Sheriff’s Facebook page) | 224 | Fire-resistant hydraulic fluids have been developed since the Second World War. In addition to phosphate esters, there are various other fluids (e.g. oil-in-water emulsions, water glycols) available. This paper provides a technical comparison of the different fluid types, in terms of fire resistance, lubricating properties, and viscosity. The second part of the study examines the corrosion properties, thermal and oxidative stability, shear stability, materials compatibility, and other physical properties. | A comparison of fire‐resistant hydraulic fluids for hazardous industrial environments. Part I. Fire resistance and lubrication properties | Practical considerations for fire-resistant fluids | The combustion intensity of hydraulic fluids and mineral oil, methanol, ethanol, and heptane, ejected vertically up ward through a pressure-jet hollow cone nozzle and stabilized by a ring burner, has been characterized in terms of heat release rates. A relationship has been established between the chemical heat release rate, fluid exit velocity, and chemical heat of combustion. Mineral oil, along with some organic esters, has the highest combustion intensity as indicated by heat release rate, followed by esters (organic and phosphates), heptane, water-in-oil emulsion, ethanol, methanol, and polyglycol-in-water. Variations in combustion intensities in hydraulic fluids are found to be due to variations in the chemical structures and additives. | Fire contributes to aircraft accidents and many fatalities. The growing use of polymer composite materials in aircraft has the potential to increase the fire hazard due to the flammable nature of the organic matrix. This report assesses the fire hazard of current and next-generation polymer composites for aircraft, and identifies those materials with improved flammability resistance. A comprehensive review of the scientific literature was performed to develop a database on the fire properties of a large number of polymer composite materials. For both aircraft cabin materials and aircraft structural materials the following fire properties were considered in the determination of fire safety: time-to-ignition, limiting oxygen index, peak heat release rate, average heat release rate, total heat release, flame spread rate, smoke, and combustion gases. The data is presented as performance tables which rank the composite materials in order from best to worst. The composite most often used in pressurised aircraft cabins is glass/phenolic, and the database shows that this material has excellent fire reaction performance and that very few next-generation composites display superior properties. The most used structural composite is carbon/epoxy, and this material has poor fire resistance and can pose a serious fire hazard. A number of advanced structural composites with superior fire properties are identified, including materials with high temperature thermoset polymer, thermoplastic or inorganic polymer matrices. | Water-resistant flame retardants for preventing forest fires | Chemical and Mechanical Characteristics of a Deep-Dewaxed Mineral Oil Hydraulic Fluid | What fluid is used in a hydraulic jack? | Water-soluble fire retardant and application thereof |
225 | Bungie is working on a fix to solar based dot effects that were unintentional | Hey there Redditors! I have lurked on this sub for quite some time but never really posted anything. So while I was doing some testing on the ptr (It only took like 4 hours to get in lol) I noticed something weird about the new wizard source, "Etched Sigil". It's affix is "Your Arcane Torrent, Disintegrate, and Ray of Frost also cast your other damaging Arcane Power Spenders every second". For some reason the closer you get to the player with your cursor, the higher up this launches arcane orbs. here is a video demonstrating:
I may have had a bit too much fun throwing orbs at my screen at 2:30 in the morning...
P.S (I have not had a chance to test this, but I wonder if the shorter trail on scorch is just cut off early, or actually overlapping the damage... I sort of doubt this is the case, but the animation on the ground definitely does seem to be overlapping...) | Has there been any update from Bungie about the fixing of these two quests as of yet? | I can't aim LMGs. Not that I can't find the green laser dot or have problem spraying bullets in the enemies' general direction, it's just that ADS looks almost the same as look mode - so my muscle memory can't tell the difference and applies the wrong amount of force on my mouse when switching targets, undershooting every time. Frustrated, I downloaded the script to enable ironsight on machine guns. The one on KSP sucks and obstructs the view too much but at least I can actually aim properly with it now.
Do you think this is cheating? This is clearly something Overkill didn't want (considering that they removed the option to ADS with LMGs in the first place), but on the other hand I can't see how this is affecting other players' experience or giving me an unfair advantage (assuming there is such a thing in a game that's entirely co-op). I know that there's basically no repercussion for cheating in Payday 2, I just want to keep my game relatively clean (feature enhancements like HUDs are ok, but free of actual cheats etc). | I got the Chauchat via glitch in January and it was literally my favorite LMG in the whole game until they took it away from me, which at the time I was fine with, most glitches like this get corrected anyway and I thought since they’re taking it away that must mean it’s coming as a Tides Of War reward for Chapter 3, right?
apparently not.
Why are we getting some inconsequential face paint next week when there’s a completely finished gun JUST SITTING THERE? That’s fucking pathetic | I am trying to add an effect where there is no blur in the middle but the blur gets larger towards the corners like vignette
Are there any effects like this or should I just buy after effects | I know it used to only buff primary and energy weapons. I read a post awhile ago (before Shadowkeep came out) saying bungie was planning to apply it to power weapons. Did that ever happen? | This report discusses: long-term changes in the apparent solar diameter/limb-darkening functions; work on solar gravity modes; and development on inverse techniques. | I know Fusion always updates, so I'm wondering did they go away with editing features like revolve/extrude etc? You used to be able to use them and continue your design and then go double click and edit them and have the design update. Am I stupid or did they eliminate this? | 225 | The nerf to solar grenades and incendiary grenades seems to be unintentional. Bungie is working on it.
Check out @GrantGMackay's Tweet: | Please nerf sticky grenades | I'm Only Hoping for a Sticky Grenade Nerf | Does anyone else feel like certain enemy types in Pve/co-op need a nerf of some kind? and grenades ...why only 1? and why only 1 primary in Pve? | Fire grenades' armor penetration bug appeared a month ago and it is still not fixed. | Thoughts on nerf to Monument for Gathering storm? | Tempest changes buffs/nerf | Just what I expected works great for Nerf Wars for my 4 and 7 year ... | I know it's a dead horse, but: why the hell did fusion rifles get nerfed? |
226 | who called ivan ivanovich a goose in 1835 | Ivan Ivanovich (Vostok programme) the ground. His second space flight, Korabl-Sputnik 5, on 26 March 1961, was similar - he was again accompanied by a dog, Zvyozdochka, and other animals, he had a recording of a choir (and also a recipe for cabbage soup to confuse any listeners) inside him, and he safely returned to Earth. These flights paved the way for Vostok 1, the first manned flight into space on 12 April 1961. In 1993, Ivan was auctioned at Sotheby's, with the winning bid coming from a foundation belonging to US businessman Ross Perot. He fetched $189,500. Since 1997, he has been on | The name of Pavel Ivanovich Novgorodtsev (1866-1924) is not very widely known to the reader at large. It has only been in the last ten or twelve years that isolated studies of particular problems in his creative works have begun to appear.1 | http://en.wikipedia.org/wiki/Nikolai_Ivanovich_Lobachevsky | Shatov () is a Russian masculine surname, its feminine counterpart is Shatova. It may refer to
Edward Shatov (born 1973), Russian Catholic priest
Oleg Shatov (born 1990), Russian football player
Nikolay Shatov (1909–1992), Russian weightlifter
Panteleimon Shatov (born 1950), Russian Orthodox Bishop
Russian-language surnames | disease were caused by an extremely minuscule infectious agent, capable of permeating porcelain Chamberland filters, something which bacteria could never do. He described his findings in an article (1892) and a dissertation (1902). Then he worked in Warsaw and Rostov-on-Don. In 1898, the Dutch microbiologist Martinus Beijerinck independently replicated Ivanovsky's experiments and became convinced that the filtered solution contained a new form of infectious agent, which he named virus. Beijerinck subsequently acknowledged Ivanovsky's priority of discovery. Dmitri Ivanovsky Dmitri Iosifovich Ivanovsky (alternative spelling "Dmitrii" or "Dmitry Iwanowski"; ; 28 October 1864 – 20 June 1920) was a Russian botanist, the | Fyodor Ivanovich Tolstoy person was put ashore at Kamchatka and made his way across land back to Petersburg. What hasn't been said about him . . . ." Tolstoy's voyage concluded with his arrival in Petersburg at the beginning of August 1805. Thanks to his adventures, which gave rise to much gossip in high society, the count acquired an almost legendary celebrity, as well as the lifelong nickname "the American", referring his stay in Russian America. Immediately upon Tolstoy's arrival in Petersburg, he was greeted with new problems: he was arrested at the city gates and sent to the guardhouse. Moreover, a special | Fyodor Ivanovich Tolstoy person was put ashore at Kamchatka and made his way across land back to Petersburg. What hasn't been said about him . . . ." Tolstoy's voyage concluded with his arrival in Petersburg at the beginning of August 1805. Thanks to his adventures, which gave rise to much gossip in high society, the count acquired an almost legendary celebrity, as well as the lifelong nickname "the American", referring his stay in Russian America. Immediately upon Tolstoy's arrival in Petersburg, he was greeted with new problems: he was arrested at the city gates and sent to the guardhouse. Moreover, a special | The first russian ruler to adopt title czar was who? | 226 | Ivans agreeing to fight a duel. Ivan Ivanovich, as the challenged party, has the choice of weapons, so he chooses the Turkish rifle, but the duel degenerates into a struggle for the rifle. It goes off in the struggle, having been overloaded with gunpowder, and the two Ivans are killed. They both go to Heaven, but upon seeing Ivan Ivanovich's outspread wings Ivan Nikiforovich again calls him "a goose", which sets off the squabble all over again. The Tale of How Ivan Ivanovich Quarreled with Ivan Nikiforovich "The Tale of How Ivan Ivanovich Quarreled with Ivan Nikiforovich" (, 1835), also | what fruit does ivan eat in the one and only ivan | how many men did fyodor ivanovich tolstoy fight in a | when did nikolai linevich start his military career | who does ivan end up with in captain vorpatril alliance | during which war was ivan nikitich konev a major general | What ever happened to IvanG?: An answer. | in which battle did lazar of serbia die | who made the.44 russian bullet |
227 | what is the slogan of the kobo mini | for kids" and "those looking for a less expensive alternative to the Kindle." Kobo Mini The Kobo Mini is a miniature, touch-based e-book reader produced by Kobo Inc. Kobo Mini was introduced on 6 September 2012, with the Kobo Glo and Kobo Arc. Marketed with the slogan "Small is a Big Deal", it was targeted to those who wanted a pocket-sized device. Kobo Mini includes an E Ink screen for legibility in direct sunlight. It also included 2 GB of internal storage (although some units were shipped with 4 GB cards internally, which may be modified by the user, voiding | for kids" and "those looking for a less expensive alternative to the Kindle." Kobo Mini The Kobo Mini is a miniature, touch-based e-book reader produced by Kobo Inc. Kobo Mini was introduced on 6 September 2012, with the Kobo Glo and Kobo Arc. Marketed with the slogan "Small is a Big Deal", it was targeted to those who wanted a pocket-sized device. Kobo Mini includes an E Ink screen for legibility in direct sunlight. It also included 2 GB of internal storage (although some units were shipped with 4 GB cards internally, which may be modified by the user, voiding | Kobo Mini The Kobo Mini is a miniature, touch-based e-book reader produced by Kobo Inc. Kobo Mini was introduced on 6 September 2012, with the Kobo Glo and Kobo Arc. Marketed with the slogan "Small is a Big Deal", it was targeted to those who wanted a pocket-sized device. Kobo Mini includes an E Ink screen for legibility in direct sunlight. It also included 2 GB of internal storage (although some units were shipped with 4 GB cards internally, which may be modified by the user, voiding any warranty, to gain access to the unpartitioned space). A distinguishing feature included | Kobo Mini The Kobo Mini is a miniature, touch-based e-book reader produced by Kobo Inc. Kobo Mini was introduced on 6 September 2012, with the Kobo Glo and Kobo Arc. Marketed with the slogan "Small is a Big Deal", it was targeted to those who wanted a pocket-sized device. Kobo Mini includes an E Ink screen for legibility in direct sunlight. It also included 2 GB of internal storage (although some units were shipped with 4 GB cards internally, which may be modified by the user, voiding any warranty, to gain access to the unpartitioned space). A distinguishing feature included | I did not use it even once... the description does say "Mini" but I never thought it would be that tiny!! The construction and materials of the tote looked good, but I had to give it away to someone with a pre-K kid so he could take an apple and some crackers to his daycare, won't fit anything else! | It's the cutest thing ever! I know it said mini but I didn't expect it to be as small as it is. Super cute none the less. | Koogle Koogle was a flavored peanut spread marketed by Kraft, introduced in 1971. It was available in several flavors, including chocolate, cinnamon, vanilla and banana. The ingredient list for Koogle changed over its lifetime. Examples of ingredient lists include: Many of Koogle's TV commercials featured the product's mascot, an oversized puppet costume in the abstract form of a giant jar with spinning eyeballs, frog-like arms and legs, and a "jive" voice similar to that of then-popular radio disc jockey Wolfman Jack. In the premiere commercial the mascot danced to a jingle, "Pea-nutty-koogle with the koo-koo-koogly eyes," which was modeled on | Love this mini easy to by parts for runs great so far love the colors the design over all satisfied | 227 | Kobo Mini The Kobo Mini is a miniature, touch-based e-book reader produced by Kobo Inc. Kobo Mini was introduced on 6 September 2012, with the Kobo Glo and Kobo Arc. Marketed with the slogan "Small is a Big Deal", it was targeted to those who wanted a pocket-sized device. Kobo Mini includes an E Ink screen for legibility in direct sunlight. It also included 2 GB of internal storage (although some units were shipped with 4 GB cards internally, which may be modified by the user, voiding any warranty, to gain access to the unpartitioned space). A distinguishing feature included | what does the slogan on kobo mini mean | how much memory does a kobo touch have | when was the book small wonder published | when was the book small wonder written | what was the name of the mini that was discontinued in 1991 | The Technology of Small Satellites | why is the cfa 1.2 millimeter wave telescope nicknamed the mini | Used on MBP not to small |
228 | Plasmid Profile and Virulence Analysis of Salmonella Gallinarum Indian Isolates |
outbreaks associated with meat and poultry products over the last few years in the United States and other countries (1). In the United States alone, it is estimated that more than 1 million Salmonella infections occur annually, resulting in nearly 20,000 hospitalizations and 400 deaths (2). Some S. enterica serovars cause more invasive infections than others; for example, a previous study demonstrated that the Heidelberg and Typhimurium strains were more invasive, responsible for 13% and 6% of infections, respectively, compared to the other serovars (3). Many Salmonella strains carry plasmids that harbor genes that contribute to increased virulence and antimicrobial resistance (4,5). Previous studies in our laboratory characterized the impact of plasmids in S. enterica on antimicrobial resistance and virulence (4,5).
We sequenced four S. enterica strains designated SE163A, SE696A, SE710A, and SE819, isolated from turkey-associated sources. SE163A and SE696A are virulent strains that possess plasmids including incompatibility group (Inc) FIB, IncA/C, and IncX4 (VirB/D4 type 4 secretion system-encoding plasmid) that carry virulence and/or antimicrobial resistance-associated genetic factors (5,6). SE819 is a less virulent strain that lacks these virulence and antimicrobial resistance plasmids and has served as a recipient strain for studies evaluating the contribution of plasmids to antimicrobial resistance and virulence (4,6,7). Studies have demonstrated that genetic factors encoded by these transmissible SE163A-and SE696A-associated plasmids contribute to antibiotic resistance and the virulence in Salmonella species (6)(7)(8). SE710A also contains IncFIB, IncA/C, and IncX4 plasmids; however, con-tribution of these plasmids in virulence has not been examined for this isolate. Genome analysis of these particular S. enterica strains will be beneficial to our future understanding of the role of plasmid-encoded factors that contribute to virulence and antibiotic resistance.
Genomic DNA was extracted using a DNeasy blood and tissue kit (Qiagen, Valencia, CA, USA) and sequenced by the DNA Sequencing Core Facility at the University of Arkansas for Medical Sciences (UAMS; Little Rock, AR, USA). The DNA library was constructed with a Nextera XT DNA sample prep kit according to the manufacturer's protocol (Illumina, San Diego, CA, USA), and sequencing was performed using the Illumina MiSeq with 2 ϫ 250 paired-end reads. CLC Genomics Workbench version 8.5.1 (Qiagen, Germantown, MD, USA) was used for the trimming and de-novo assembly of the paired-end reads.
Draft genomes of these four S. enterica strains were annotated using the Rapid Annotation using Subsystem Technology (RAST) server (9), the Pathosystems Resource Integration Center (PATRIC) (10), and the NCBI Prokaryotic Genome Annotation Pipeline (PGAP) ( Table 1). The GϩC content for these strains is identical, with an estimate of 52.1%. Annotation using PATRIC (10) revealed that strain SE163A contains 5,448 coding sequences, in which 4,637 encode functional proteins, while 811 encode hypothetical proteins. Strain SE696A contains 5,296 coding sequences, in which 4,584 encode functional proteins and 712 encode hypothetical proteins. Strain SE710A possesses 5,337 coding sequences, in which 4,626 proteins have functional assignments and 711 encode as hypothetical. Strain SE819 contains 5,103 cod- ing regions, in which 4,450 encode functional proteins and 653 are assigned as hypothetical proteins. Accession number(s). The genome sequences of SE163A, SE696A, SE710A, and SE819 were deposited in GenBank under the accession numbers shown in Table 1.
ACKNOWLEDGMENTS
The research project and B.K.K. are supported by the FDA Commissioner's Fellowship Program. The Sequencing Facility is supported in part by grants from NIH to UAMS's Translational Research Institute (UL1TR000039) and the Center for Microbial Pathogenesis and Host Inflammatory Responses (P20GM103625). The opinions expressed in this manuscript are solely the responsibility of the authors and do not necessarily represent the official views and policy of the U.S. Food and Drug Administration or National Institutes of Health. Reference to any commercial materials, equipment, or process does not in any way constitute approval, endorsement, or recommendation by the Food and Drug Administration.
FUNDING INFORMATION
This work, including the efforts of Steven L. Foley, Bijay K. Khajanchi, Jing Han, Kuppan Gokulan, Shaohua Zhao, and Allen Gies, was funded by HHS | U.S. Food and Drug Administration (FDA) (E0759601).
TABLE 1
1Summary of the genome sequence analysis of four Salmonella enterica strains isolated from turkey-associated sourcesStrain
Location, yr
No. of contigs
Assembly size (bp)
GϩC content (%)
No. of rRNAs
No. of tRNAs
Accession no.
SE163A
Ohio, 2002
257
5,202,941
52.1
7
74
LSZD00000000
SE696A
Midwest United States, 2000
230
5,096,557
52.1
16
78
LXHA00000000
SE710A
North Dakota, 1992
318
5,100,225
52.1
8
78
LXGZ00000000
SE819
Maryland, 2002
233
4,914,824
52.1
11
82
LSZE00000000
September/October 2016 Volume 4 Issue 5 e01122-16
Characterization of multidrugresistant Salmonella enterica serovar Heidelberg from a ground turkeyassociated outbreak in the United States in 2011. J P Folster, G Pecic, R Rickert, J Taylor, S Zhao, P J Fedorka-Cray, J Whichard, P Mcdermott, 10.1128/AAC.00201-12Antimicrob Agents Chemother. 56Folster JP, Pecic G, Rickert R, Taylor J, Zhao S, Fedorka-Cray PJ, Whichard J, McDermott P. 2012. Characterization of multidrug- resistant Salmonella enterica serovar Heidelberg from a ground turkey- associated outbreak in the United States in 2011. Antimicrob Agents Che- mother 56:3465-3466. http://dx.doi.org/10.1128/AAC.00201-12.
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Salmonellosis outcomes differ substantially by serotype. T F Jones, L A Ingram, P R Cieslak, D J Vugia, -D' Tobin, M Angelo, S Hurd, C Medus, A Cronquist, F J Angulo, 10.1086/588823J Infect Dis. 198Jones TF, Ingram LA, Cieslak PR, Vugia DJ, Tobin-D'Angelo M, Hurd S, Medus C, Cronquist A, Angulo FJ. 2008. Salmonellosis outcomes differ substantially by serotype. J Infect Dis 198:109 -114. http:// dx.doi.org/10.1086/588823.
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Evaluation of virulence and antimicrobial resistance in Salmonella enterica serovar Enteritidis isolates from humans and chicken-and egg-associated sources. J Han, K Gokulan, D Barnette, S Khare, A W Rooney, J Deck, R Nayak, R Stefanova, M E Hart, S L Foley, 10.1089/fpd.2013.1518Foodborne Pathog Dis. 10Han J, Gokulan K, Barnette D, Khare S, Rooney AW, Deck J, Nayak R, Stefanova R, Hart ME, Foley SL. 2013. Evaluation of virulence and antimicrobial resistance in Salmonella enterica serovar Enteritidis isolates from humans and chicken-and egg-associated sources. Foodborne Pat- hog Dis 10:1008 -1015. http://dx.doi.org/10.1089/fpd.2013.1518.
Impact of plasmids, including those encodingVirB4/D4 type IV secretion systems, on Salmonella enterica serovar Heidelberg virulence in macrophages and epithelial cells. K Gokulan, S Khare, A W Rooney, J Han, A M Lynne, S L Foley, 10.1371/journal.pone.0077866PLoS One. 877866Gokulan K, Khare S, Rooney AW, Han J, Lynne AM, Foley SL. 2013. Impact of plasmids, including those encodingVirB4/D4 type IV secretion systems, on Salmonella enterica serovar Heidelberg virulence in macro- phages and epithelial cells. PLoS One 8:e77866. http://dx.doi.org/10.1371/ journal.pone.0077866.
Characterization of Salmonella enterica serovar Heidelberg from turkey-associated sources. P Kaldhone, R Nayak, A M Lynne, D E David, P F Mcdermott, C M Logue, S L Foley, 10.1128/AEM.00409-08Appl Environ Microbiol. 74Kaldhone P, Nayak R, Lynne AM, David DE, McDermott PF, Logue CM, Foley SL. 2008. Characterization of Salmonella enterica serovar Heidelberg from turkey-associated sources. Appl Environ Microbiol 74: 5038 -5046. http://dx.doi.org/10.1128/AEM.00409-08.
Horizontal gene transfer of a ColV plasmid has resulted in a dominant avian clonal type of Salmonella enterica serovar Kentucky. T J Johnson, J L Thorsness, C P Anderson, A M Lynne, S L Foley, J Han, W F Fricke, P F Mcdermott, D G White, M Khatri, A L Stell, C Flores, R S Singer, 10.1371/journal.pone.0015524PLoS One. 5Johnson TJ, Thorsness JL, Anderson CP, Lynne AM, Foley SL, Han J, Fricke WF, McDermott PF, White DG, Khatri M, Stell AL, Flores C, Singer RS. 2010. Horizontal gene transfer of a ColV plasmid has resulted in a dominant avian clonal type of Salmonella enterica serovar Kentucky. PLoS One 5:e15524. http://dx.doi.org/10.1371/journal.pone.0015524.
The RAST server: rapid annotations using subsystems technology. R K Aziz, D Bartels, A A Best, M Dejongh, T Disz, R A Edwards, K Formsma, S Gerdes, E M Glass, M Kubal, F Meyer, G J Olsen, R Olson, A L Osterman, R A Overbeek, L K Mcneil, D Paarmann, T Paczian, B Parrello, G D Pusch, C Reich, R Stevens, O Vassieva, V Vonstein, A Wilke, O Zagnitko, 10.1186/1471-2164-9-75BMC Genomics. 975Aziz RK, Bartels D, Best AA, DeJongh M, Disz T, Edwards RA, Formsma K, Gerdes S, Glass EM, Kubal M, Meyer F, Olsen GJ, Olson R, Osterman AL, Overbeek RA, McNeil LK, Paarmann D, Paczian T, Parrello B, Pusch GD, Reich C, Stevens R, Vassieva O, Vonstein V, Wilke A, Zagnitko O. 2008. The RAST server: rapid annotations using subsystems technology. BMC Genomics 9:75. http://dx.doi.org/10.1186/ 1471-2164-9-75.
PATRIC, the bacterial bioinformatics database and analysis resource. A R Wattam, D Abraham, O Dalay, T L Disz, T Driscoll, J L Gabbard, J J Gillespie, R Gough, D Hix, R Kenyon, D Machi, C Mao, E K Nordberg, R Olson, R Overbeek, G D Pusch, M Shukla, J Schulman, R L Stevens, D E Sullivan, V Vonstein, A Warren, R Will, M J Wilson, H S Yoo, C Zhang, Y Zhang, B W Sobral, 10.1093/nar/gkt1099Nucleic Acids Res. 42Wattam AR, Abraham D, Dalay O, Disz TL, Driscoll T, Gabbard JL, Gillespie JJ, Gough R, Hix D, Kenyon R, Machi D, Mao C, Nordberg EK, Olson R, Overbeek R, Pusch GD, Shukla M, Schulman J, Stevens RL, Sullivan DE, Vonstein V, Warren A, Will R, Wilson MJ, Yoo HS, Zhang C, Zhang Y, Sobral BW. 2014. PATRIC, the bacterial bioinfor- matics database and analysis resource. Nucleic Acids Res 42:D581-D591. http://dx.doi.org/10.1093/nar/gkt1099.
| Virulence plasmids and antibiotic resistance plasmids are usually maintained separately in Salmonella spp.; however, we report an instance of a hybrid plasmid (pN13-01125) in Salmonella enterica serovar Dublin. Review of the complete sequence of the 172,265-bp plasmid suggests that pN13-01125 is comprised of the previously described pSDVr and pSH696_135 plasmids and that the mechanism of hybridization likely involves IS6 (IS26) insertion sequence elements. The plasmid has a low conjugation frequency, confers resistance to six classes of antimicrobials, and contains a complete spv virulence operon. | Virulence plasmids, which are found in a small number of Salmonella serotypes, greatly enhance the extraintestinal growth of salmonellae and lower the LD50 by 2-5 logs in experimental murine infections. To determine if virulence plasmids are important in the pathogenesis of Salmonella bacteremia in humans, blood and fecal isolates of Salmonella typhimurium from California were examined for the presence of a virulence plasmid. Colony blots were done using a labeled probe made from the highly conserved EcoRI fragment of the Salmonella dublin virulence plasmid. A total of 42% of the fecal and 76% of the blood isolates hybridized with the probe. This is the first evidence that the virulence plasmid is important in the pathogenesis of Salmonella bacteremia in humans. | R-plasmid transfer in Salmonella spp. isolated from wastewater and sewage-contaminated surface waters. | Salmonella infections have been implicated in large-scale die-offs of wild birds in the United States. Although we know quite a bit about the epidemiology of Salmonella infection among domestic fowl, we know little about the incidence, epidemiology, and genetic relatedness of salmonellae in nondomestic birds. To gain further insight into salmonellae in these hosts, 22 Salmonella isolates from diseased nondomestic birds were screened for the presence of virulence and antibiotic resistance-associated genes and compared genetically using pulsed-field gel electrophoresis (PFGE) and random amplified polymorphic DNA analysis. Of the 22 Salmonella isolates examined, 15 were positive for the invasion gene invA and the virulence plasmid-associated genes spvC and pef. Most (15 of 22) were generally sensitive to antibiotics. However, two Salmonella isolates from pet birds were identified as Salmonella enterica serovar Typhimurium DT104. Despite the general susceptibility of these Salmonella isolates to most antimicrobial agents, antibiotic resistance-associated genes intI1, merA, and aadA1 were identified in a number of these isolates. Five distinct XbaI and nine distinct BlnI DNA patterns were observed for the 22 Salmonella isolates typed by PFGE. PFGE analysis determined that Salmonella isolates from passerines in Georgia and Wyoming were genetically related. | Summary ::: ::: The virulence properties of various non-typhoid Salmonella serotypes depend on the presence of large plasmids 60–100 kb in size. We have shown previously that the virulence region on the 80 kb plasmid pSDL2 of Salmonella dublinLane maps within a 14kb SalI fragment. In this report we show that an 8.2kb region within this fragment is sufficient to express lethal disease in BALB/c mice. Sequence analysis of this segment revealed six sequential open reading frames designated vsdA–F, which encode putative proteins of 13–65kDa. Deletion analysis and location of Tn5-oriT inserts which abolish virulence suggest that vsdA, vsdC, vsdD and vsdE are essential for virulence expression. Downstream of vsdF we discovered a locus involved in stable plasmid maintenance. Deletion of that region resulted in plasmid multimerization and instability. |
The wide usage of antibiotics contributes to the increase in the prevalence of antibioticresistant Salmonella. Plasmids play a critical role in horizontal transfer of antibiotic resistance markers in Salmonella. This study aimed to screen and characterize plasmid profiles responsible for antibiotic resistance in Salmonella and ultimately to clarify the molecular mechanism of transferable plasmid-mediated antibiotic resistance. A total of 226 Salmonella isolates were examined for antimicrobial susceptibility by a disk diffusion method. Thirty-two isolates (14.2%) were resistant to at least one antibiotic. The presence of plasmid-mediated quinolone resistance (PMQR) genes and β-lactamase genes were established by PCR amplification. PCR-based replicon typing revealed that these 32 isolates represented seven plasmid incompatibility groups (IncP, HI2, A/C, FIIs, FIA, FIB, and I1), and the IncHI2 (59.4%) was predominant. Antibiotic resistance markers located on plasmids were identified through plasmid curing. Fifteen phenotypic variants were obtained with the curing efficiency of 46.9% (15/32). The cured plasmids mainly belong to the HI2 incompatibility group. The elimination of IncHI2 plasmids correlated with the loss of β-lactamase genes (bla OXA and bla ) and PMQR genes (qnrA
INTRODUCTION
Salmonella is recognized as the predominant pathogen implicated in bacterial foodborne diseases worldwide (Yang et al., 2016). The emergence of multidrug-resistant (MDR) Salmonella strains due to the prolonged and extensive usage of antibiotics has become a public health issue. Such resistance toward medically significant antimicrobial agents including fluoroquinolones and extended-spectrum cephalosporins (ESCs) that are regarded as primary treatment options for bacterial infections will make it difficult for antibiotic therapy due to the reduced efficiency of empirical strategies as well as limited choice of treatment (Wong et al., 2014;Folster et al., 2015). The dissemination of undesirable antibiotic resistance in Gram-negative bacteria has been largely attributed to the acquisition of multiple plasmid-located antibiotic resistance genes by horizontal gene transfer (HGT; Carattoli, 2013;Wang et al., 2015). The emergence of plasmid-mediated quinolone resistance (PMQR) predominantly encoded by qnr variants, aac(6 )-Ib-cr, qepA, and oqxAB genes in Salmonella, has further facilitated selection of high-level chromosomal quinolone resistance via mutations in topoisomerase genes, as well as the wide spread of quinolone resistance via HGT (Jiang et al., 2014;Skov et al., 2015). In addition, the apparent correlation between the PMQR genes (such as qnr or aac(6 )-Ib-cr genes) and extended-spectrum β-lactamase (ESBL) genes or ampC genes on the same plasmid and their association with other antibiotic resistance genes have raised particular global concern, since their transmission could be driven by other mobile genetic elements located on plasmids among various bacterial species Jiang et al., 2014). Particular plasmid families associate with the emergence and dissemination of specific antibiotic resistance traits with differential prevalence and distribution (Johnson et al., 2007;Carattoli, 2013). Thus, characterization of plasmids based on PCR-based replicon typing (PBRT) is an indispensable part of plasmid epidemiological surveillance enhancing discrimination between Salmonella strains as well as tracing the spread and evolution of antibiotic resistance genes . Certain replicon types were found to be associated with MDR as well as with bacterial disease outbreaks (Huang et al., 2012). It has been reported that plasmids with IncA/C, B/O, HI1, HI2, I1, N, F, and P replicons are often associated with MDR in Salmonella, while many of them are found to be co-resident in some MDR Salmonella strains (Poole et al., 2009;Glenn et al., 2013).
Transmissible plasmids contain a full set of conjugationencoding genes facilitating their spread over large taxonomic distances, and they harbor drug-resistance determinants, virulence factors and addiction systems promoting their stability and maintenance in bacterial hosts under different environmental conditions. It is essential to clarify the roles of these genetic elements and the corresponding surrounding genetic structures by plasmid sequencing in order to trace the transmission and persistence of antibiotic resistance (Carattoli, 2013;Wang et al., 2015).
The aim of this study was to screen and characterize plasmid replicon profiles containing PMQR and β-lactamase genes in Salmonella so as to clarify molecular mechanism of transferable plasmid-mediated antibiotic resistance.
MATERIALS AND METHODS
Salmonella Isolates
A total of 226 Salmonella isolates were used in this study, and all the non-susceptible strains are listed in Supplementary Table S1, of which 39 were food isolates and 39 were clinical isolates. Among these Salmonella isolates, clinical isolates were collected by Shanghai Municipal Center for Disease Control and Prevention and Wuhan Municipal Center for Disease Control and Prevention, while food isolates were collected from beef, poultry, pork, shrimp, vegetables, fresh juice, and shellfish. PCR-based serotyping was performed as previously described (Ranieri et al., 2013). Two different primer pairs and an additional primer pair were used in this study (Supplementary Table S2). The detailed information of these isolates is listed in Supplementary Table S1.
Antimicrobial Susceptibility Testing
All 226 Salmonella isolates underwent antimicrobial susceptibility testing using the disk diffusion method against a panel of 18 antibiotics, according to the standards and guidelines recommended by the Clinical and Laboratory Standards Institute (CLSI; CLSI, 2013). A total of 18 antibiotic disks (Oxoid Ltd., Basingstoke, UK) that included ampicillin (AMP, 10 µg), piperacillin/tazobactam (TZP, 100/10 µg), ampicillin/sulbactam (SAM, 10/10 µg), ceftriaxone (CRO, 30 µg), ceftazidime (CAZ, 30 µg), cefepime (FEP, 30 µg), cefotetan (CTT, 30 µg), aztreonam (ATM, 30 µg), cephazolin (CZO, 30 µg), ciprofloxacin (CIP, 5 µg), imipenem (IPM, 10 µg), amikacin (AMK, 30 µg), gentamicin (GEN, 10 µg), tobramycin (TOB, 10 µg), ertapenem (ETP, 10 µg), levofloxacin (LEV, 5 µg), nitrofurantoin (NIT, 300 µg), and sulfamethoxazole/trimethoprim (SXT, 23.75/1.25 µg), were assessed. Escherichia coli ATCC 25922 was used as the control strain. Isolates were defined as MDR if they were resistant to at least three different classes of antibiotics.
Detection of PMQR and β-Lactamase Genes
Genomic DNA of Salmonella isolates was purified by the cetyltrimethylammonium bromide (CTAB) method as described elsewhere (Wilson, 2001). The antibiotic-resistant isolates identified by antimicrobial susceptibility testing were screened for the presence of PMQR determinants (qnrA, qnrB, qnrS, qnrC, qnrD, aac (6 )-Ib-cr) and β-lactamase genes (bla TEM−1 , bla OXA−1 , bla PSE−1 , and bla CMY−2 ) by simplex PCR amplification. Primers targeting above antibiotic resistance genes were listed in Supplementary Table S3.
Plasmid Replicon Typing
Plasmid incompatibility (Inc) groups were assigned by PBRT using genomic DNA of Salmonella isolates as template. Amplification by PCR was performed with eighteen specific primer pairs designed for FIA, FIB, FIC, HI1, HI2, I1, L/M, N, P, W, T, A/C, K, B/O, X, Y, F, and FIIA basic replicons, and the corresponding protocol was previously described . Resulting amplicons were sequenced by Shanghai Majorbio Bio-pharm Technology Co., Ltd. Comparative analysis of nucleotide sequences was performed using the BLAST program at the National Center for Biotechnology Information (NCBI) site 1 .
Plasmid Curing
To determine if the antibiotic resistance observed in this study was plasmid-mediated, the identified antibiotic-resistant Salmonella isolates were subjected to a curing treatment using sodium dodecyl sulphate (SDS), according to Tomoeda et al. (1968) with modifications. Briefly, the overnight culture in Luria-Bertani (LB) broth was inoculated (1:10 4 dilution) in LB broth containing 5% SDS and incubated for 48 h at 44.5 • C with constant agitation. Aliquots of the cultures were then appropriately diluted and spread on LB agar plates without antibiotics and incubated at 37 • C for 16-18 h. The resulting single clones were streaked onto two LB agar plates with or without ampicillin. Because ampicillin was the most prevalent among antibiotic-resistant isolates, for the screening convenience of those plasmid-loss mutants, ampicillin was used as the priority selective marker. The LB agar plates were incubated at 37 • C overnight, and ampicillin-susceptible clones were considered positive for loss of the incompatible plasmid. After treatment with the curing agent, the putative cured derivatives were examined for the antibiotic susceptibility profile using the same set of antibiotics, and for the presence of related antibiotic resistance genes as well as plasmid replicon type by PCR method as described above.
Plasmid Sequencing and Analysis
The Salmonella isolate SJTUF 10584 identified in this study was chosen as the plasmid donor for its complete loss of plasmids and MDR after one single trial of plasmid curing. The plasmid was obtained through conjugation experiments by the liquid mating assay using rifampin-resistant E. coli Nk5449 as the recipient strain as previously described (Zurfluh et al., 2014). Transconjugants were selected on LB agar plates containing ampicillin (100 µg/ml) and rifampin (200 µg/ml). Antimicrobial susceptibility tests and antibiotic resistance gene detection were performed to confirm the plasmid transfer, followed by PBRT to test which plasmid and antibiotic resistance markers were transferred.
Plasmid DNA was purified from the transconjugant by the Qiagen Plasmid Midi Kit (Qiagen, Germany) according to the manufacturer's protocol. Plasmid sequencing was performed on the IIIumina Hiseq sequencing platform at the Shanghai Biotechnology Corporation (Shanghai, China). The complete sequence was annotated using the NCBI Prokaryotic Genome Annotation Pipeline (PGAP), followed by manual inspection. Each predicted protein was further confirmed against the NCBI all-protein database using BLASTP 1 . Insertion sequences and repetitive elements were identified using IS finder 2 . DNA sequence comparisons and alignments were performed using BLAST 1 and Geneious software (version 9.1.2; Kearse et al., 2012), and a schematic plasmid map was constructed with WinPlas 2.7 software. 1 http://blast.ncbi.nlm.nih.gov/Blast.cgi 2 https://www-is.biotoul.fr//
Nucleotide Sequence Accession Number
The complete sequence of the plasmid pS10584 has been deposited in Genbank/EMBL/DDBJ with accession number KX058576.
RESULTS AND DISCUSSION
Antimicrobial Susceptibility
Among 226 Salmonella isolates, 14.2% (32/226) demonstrated resistance to at least one antibiotic and 11.1% (25/226) were resistant to ≥3 antibiotics. In addition, 4.9% (11/226) showed MDR phenotypes. It's noteworthy that the strain SJTUF 10702 isolated from chicken exhibited strong resistance to 11 antibiotics. In terms of 32 antibiotic-resistant isolates (Figure 1), 25.0% (8/32) presented the quinolone resistance phenotype (LEV or CIP) while 96.9% (31/32) were resistant to the five tested β-lactams (AMP, SAM, CZO, CRO, and CAZ) alone or in combination. Moreover, resistance to individual agents was most frequently observed to AMP (31/32, 96.9%) and SAM (26/32, 81.3%), followed by TOB (14/32, 43.8%) and SXT (11/32, 34.4%). No resistance was detected to CTT, FEP, IPM, and ETP.
Prevalence of PMQR and β-Lactamase Genes
Amongst the 32 antibiotic-resistant Salmonella isolates, the PMQR genes aac(6 )-Ib-cr and qnrA were present alone or in combination in 25 (78.1%) and 5 (15.6%) isolates, respectively; three isolates harbored both two determinants (Figure 1). The qnrB, qnrS, qnrC, and qnrD genes were not detected in any of the tested isolates. In terms of β-lactamase genes detected, 75.0% (24/32) were positive for bla OXA−1 , 37.5% (12/32) for bla TEM−1 and 9.4% (3/32) for bla CMY−2 . In addition, seven isolates simultaneously carried bla OXA−1 and bla TEM−1 , and two carried bla OXA−1 and bla CMY−2 , while one isolate harbored all these three determinants. No isolates contained bla PSE−1 . Of these 27 PMQR-bearing isolates, 23 isolates (85.2%) also carried at least one β-lactamase gene with the prevalent pattern of aac(6 )-Ib-crbla OXA−1 (12/23, 52.2%) and aac(6 )-Ib-cr-bla OXA−1 -bla TEM−1 (4/23, 17.4%).
Plasmid Replicon Typing
Plasmid replicons detected among 32 antibiotic-resistant Salmonella isolates are listed in Figure 1. Overall, seven different replicons of the 18 classic replicon types associated with Enterobacteriaceae were identified in all the isolates except SJTUF 10023 and SJTUF 10054. The two untypeable isolates may possess divergent or novel replicons (Carattoli, 2009). PBRT demonstrated that IncHI2 (19/32, 59.4%) was the predominant type while the other Inc groups such as P (7/32, 21.9%), A/C (4/32, 12.5%), I1 (3/32, 9.4%), FII S (2/32, 6.25%), FIA (1/32, 3.1%), and FIB (1/32, 3.1%) were just present in few isolates. Seven isolates were mixed of two replicon types, including the combinations of HI2 and I1 (3/7, 42.9%), HI2 and P (2/7, 28.6%), HI2 and A/C (1/7, 14.3%), and FIA and FIB (1/7, 14.3%). Inc groups HI2, I1, FIGURE 1 | A heat-map summary of the serovars, the sources, the antibiotic resistance phenotypes and genotypes, and the corresponding Inc plasmid type(s) for 32 drug-resistant Salmonella isolates. Black and white squares denotes the presence and absence of a particular feature, respectively. The antibiotics listed are abbreviated as follows: AMP, ampicillin; TZP, piperacillin/tazobactam; SAM, ampicillin/sulbactam; CRO, ceftriaxone; CAZ, ceftazidime; ATM, aztreonam; CZO, cephazolin; CIP, ciprofloxacin; AMK, amikacin; GEN, gentamicin; TOB, tobramycin; LEV, levofloxacin; NIT, nitrofurantoin; SXT, sulfamethoxazole/trimethoprim. A/C, P, FIA, and FIB were found to be associated with MDR isolates, in agreement with previous studies (Poole et al., 2009;Glenn et al., 2013). In addition, IncHI2 was the dominant replicon type both among MDR isolates (7/11, 63.6%) and Salmonella Typhimurium isolates (15/17, 88.24%). When comparing multiple antibiotic resistance genes with replicon types, 86.7% (19/22) of bla OXA−1 positive isolates as well as 81.8% (9/11) of bla OXA−1 -aac(6 )-Ib-cr positive isolates were carrying IncHI2 plasmids. And all the three bla CMY−2 positive isolates contained IncHI2 and IncI1 plasmids simultaneously. In addition, bla TEM−1 positive isolates tended to carry the IncHI2 (5/12, 41.7%) and IncP (6/12, 50.0%) plasmids while qnrA positive isolates were likely apt to carry IncA/C plasmids (4/5, 80.0%).
Plasmid Curing and Antibiotic Resistance Localization
All the 32 antibiotic-resistant Salmonella isolates underwent plasmid curing using 5% SDS as well as elevated temperature (44.5 • C) for 48 h to ensure that the antibiotic resistance profile was related to the plasmid. Fifteen phenotypic variants were obtained after up to 10 trials of curing (Figure 2), and the curing efficiency was 46.9% (15/32). The cured plasmids mainly belonged to IncHI2 group (7/8, 87.5%), followed by FIGURE 2 | A heat-map showing the changes of Salmonella isolates after plasmid curing based on antibiotic resistance profiles as well as plasmid replicon type(s). "C" denoted the cured variant. Black and white squares denotes the presence and absence of a particular feature, respectively. The antibiotics listed are abbreviated as follows: AMP, ampicillin; TZP, piperacillin/tazobactam; SAM, ampicillin/sulbactam; CRO, ceftriaxone; CAZ, ceftazidime; ATM, aztreonam; CZO, cephazolin; CIP, ciprofloxacin; AMK, amikacin; GEN, gentamicin; TOB, tobramycin; LEV, levofloxacin; SXT, sulfamethoxazole/trimethoprim. IncF group (3/3, 100%), and IncI1 group (1/1, 100%); however, no strain showed curing of IncP group plasmids (0/5, 0%). When attributing the loss of resistance phenotypes to the loss of plasmids, we could infer that the antibiotic resistant phenotypes AMP-SAM-TOB of SJTUF 10236, AMP-SAM-GEN-TOB-LEV-SXT of SJTUF 10476, AMP-SAM of SJTUF 10479, AMP-SAM-GEN-TOB-CZO of SJTUF 10565, AMP of SJTUF 10577, and AMP-SAM-TOB-SXT of SJTUF 10580 were all related to IncHI2 plasmids while AMP-SAM-CZO-CAZ-CRO-CIP-SXT of SJTUF 10584 was determined together by IncI1 and IncHI2 plasmids. And the resistant phenotype AMP-SAM-CZO-GEN-CIP-LEV of SJTUF 10713 and AMP-GEN-TOB of SJTUF 10718 were both determined by IncF plasmids. In addition, the elimination of IncHI2 plasmids correlated with the loss of β-lactamase genes (bla OXA−1 and bla TEM−1 ) as well as PMQR genes (qnrA and aac(6 )-Ib-cr), and the loss of IncFIA and FIB plasmids resulted in the absence of the aac(6 )-Ib-cr gene. Furthermore, four cured variants (SJTUF 10211 C , 10700 C , 10702 C and 10705 C ) lost antibiotic resistance genes as well as drug resistance phenotypes but still retained the identified plasmids (Figure 2). This may be due to the loss of divergent or novel replicons which were untypeable by the current PBRT scheme. The cured SJTUF 10577 C lost the AMP resistance phenotype, bla genes, and the IncHI2 plasmid simultaneously, even though it retained the IncP plasmid. The function of IncP plasmids in antibiotic resistance needs further study.
Particular plasmids belonging to the Inc families usually carry multiple physically linked genetic determinants, playing a major role in the diffusion of specific antibiotic resistance genes among different bacteria (Carattoli, 2013;Wang et al., 2013). In this study, we characterized IncHI2 plasmids as the main vehicle in horizontal transfer of β-lactamase genes (bla OXA−1 and bla TEM−1 ) as well as PMQR genes (qnrA and acc(6 )-ib-cr). The co-existence of aac(6 )-Ib-cr with bla OXA−1 , with or without bla TEM−1 was also identified. IncHI2 plasmids are known to play a significant role in the acquisition of antibiotic resistance, and they have recently been implicated in the dissemination of genes encoding extended-spectrum β-lactamase (Cain and Hall, 2012). In contrast, IncA/C plasmids are prevalent in several MDR Salmonella serovars and closely linked to the expansion of MDR in the United States (Folster et al., 2010(Folster et al., , 2015. We also discovered the high prevalence of IncHI2 plasmids in S. Typhimurium, similar to the report from Li et al. (2013). The identical genetic context of antibiotic resistance genes on IncHI2 plasmids was also detected in S. Indiana in China as well as S. Typhimurium in Europe (Campos et al., 2015), suggesting a similar evolutionary origin and highlighting the potentially global spread of IncHI2 plasmids among Salmonella. Furthermore, a similar genetic context of aac(6 )-Ib-cr with bla OXA−1 was also identified on an IncR plasmid of a K. oxytoca strain in Spain (Ruiz et al., 2011), and an IncN plasmid of an E. coli isolate in Hong Kong (Ho et al., 2013). The similar resistance gene module infers that the transfer of resistanceassociated module was driven by mobile genetic elements like integrons, insertion sequences or transposons between different plasmid replicons, and was probably mediated by IS26 in terms of the above cases (Miriagou et al., 2005;Li et al., 2013;He et al., 2015). Thus, further active surveillance is needed to minimize the spread of particular plasmids such as IncHI2 group to control the dissemination of antibiotic resistance. As mobile genetic elements play a major role in the acquisition and dissemination of antibiotic resistance genes, further study may be required to determine the distinct genetic environment of antibiotic resistance genes on plasmids.
Analysis of pS10584
The MDR Salmonella enterica serovar Indiana isolate SJTUF 10584 identified in this study was chosen as the plasmid donor. This isolate contains IncHI2 and IncI1 plasmids simultaneously, and these two types of plasmids were easily eliminated after one trial of curing. The plasmid designated as pS10584 was acquired through conjugation experiments recovered from ampicillin and rifampin resistance selection. Replicon typing showed that the only transferred plasmid pS10584 belonged to the IncI1 group and PCR analysis confirmed that it was positive for bla CMY−2 gene but not for bla OXA−1 or aac(6 )-Ib-cr genes. All of the transconjugants shared the same antibiotic resistance pattern of AMP-SAM-CZO-CAZ-CRO.
Complete DNA sequence of pS10584 revealed that it was a circular molecule of 94,697-bp with an average G+C content of 50.0% and 110 putative CDSs. In general, pS10584 possessed a plasmid scaffold typical for IncI1 plasmids, with important IncI1-associated genetic modules including traABCD regulatory cluster, traLMNOPQRSTUVWXY transfer region, nikB-trbABC region, ssb-psiAB region, and type IV thin pilus formation region pilIJKLMNOPQRSTUV (Figure 3). Besides the approximate 89,866-bp "core genome" region encoding characteristic IncI1 plasmid replication, transfer, maintenance and stability functions, a 4,831-bp accessory module encoding the antibiotic resistance gene as well as flanking insertion sequences was also discovered. BLASTN comparison revealed that the overall genetic organization of pS10584 was very similar to that of another fully sequenced IncI1 plasmid pJIE512b (GenBank accession no. HG970648; Tagg et al., 2014) with high sequence identity (>99% at nucleotide level) except an inversion within the pilV shufflon and a 2,307-bp deletion (nucleotide 6,685 th to 8,991 nd of pS10584, containing a truncated colicin gene cia and an intact putative DNA-binding transcriptional regulator gene yagA) in pJIE5112b.
In pS10584, the 4,831-bp antibiotic resistance-associated module comprised 161-bp of the right end of ISEcp1 truncated by IS1294 in the reverse orientation and a 2,823-bp region originating from the Citrobacter freundii chromosome including a bla CMY−2 gene, with blc (an outer membrane lipoprotein, lipocalin), sugE (a small MDR transporter), and ecnR (LuxR family transcriptional regulator) genes immediately downstream, followed by a 159-bp fragment of IncA/C ending in GTTC which matched the last 4-bp of terIS of IS1294 (Figure 4). In addition, the 4831-bp bla CMY−2 segment inserted within the cia gene at the 698-bp from the 5 end without causing adjacent deletion, followed by the remaining 1,184-bp segment of the cia gene.
A similar genetic context surrounding the bla CMY−2 gene was identified in an IncI1 plasmid p2735 (KP017243; Yassine et al., 2014) isolated from Klebsiella pneumoniae as well as six IncI1 plasmids isolated from E. coli including two completely sequenced plasmids pJIE512b (HG970648; Tagg et al., 2014), and pR7AC (KF434766; Minoia et al., 2012), and four partially sequenced plasmids pTN38148 (FM246883), pTN10, pTN13, and pTN386 (Verdet et al., 2009) (Figure 4). Compared to pS10584, the bla CMY−2 insertion was within the yagA gene 16-bp from the 5 end, removing the rest of the yagA gene, as well as a large part FIGURE 3 | An overview of the bla CMY−2 -carrying plasmid pS10584. Genes are color-coded as follows: dark brown, replication-associated genes; green, insertion sequences; red, antibiotic resistance gene; blackish green, partition-or stability-associated genes; army green, transfer-leading region associated genes; pink, tra locus; blue, type IV pilus region; purple, trb locus; and gray, hypothetical protein. of the cia gene, leaving the same part of the cia gene in the 3 end followed by the same 159-bp IncA/C backbone ending in GTTC in pJIE512b. Whereas, the flanking fragments of bla CMY−2 gene in other six IncI1 plasmids (pTN10, pTN13, pTN386, pTN38148, p2735, and pR7AC) were much more different from that in pS10584, including an IS1294-like element designated as IS1294b (Yassine et al., 2014), followed by a 372-bp truncated ISEcp1, the identical 2,823-bp region of the C. freundii chromosome that contained bla CMY−2 and the additional 1395-bp IncA/C backbone also ending in GTTC (Figure 4). This bla CMY−2 insertion was downstream of the repZ gene, removing a larger adjacent part and truncating the 3 end of yafA followed by yafB.
Although S. Indiana frequently exhibited MDR phenotypes, very little research has been done to clarify the molecular mechanisms conferring its MDR or the transferability of the resistance properties . Among ampC-like genes, the bla CMY−2 gene which probably originated from C. freundii, is the most prevalent gene worldwide conferring resistance to clinically important β-lactam-based compounds particularly the third-generation cephalosporins. (Verdet et al., 2009;Call et al., 2010;Karczmarczyk et al., 2014;Tagg et al., 2014). In this study, two bla CMY−2 -positive isolates both showed resistance phenotypes against the third-generation cephalosporins (CRO, CAZ, and CZO) while the other one was susceptible to them, probably due to the low-level expression or silence of this gene. In previous research, it was observed that resistance to a second generation cephalosporin, cefoxitin in Salmonella isolates harboring bla CMY−2 (Giles et al., 2004;Martin et al., 2012;Noda et al., 2015). However, none of the three bla CMY−2 -positive isolates was resistant to cefotetan, which is a second-generation cephalosporin like cefoxitin. This was also found in a previous study (Noda et al., 2015). This may also be attributed to the low-level expression or silence of bla CMY−2 gene.
Among various plasmid types associated with the carriage of the bla CMY−2 gene, IncI1 and IncA/C plasmids are often reported as the predominant carriers (Mata et al., 2012;Bortolaia et al., 2014). Additional research discovered that bla CMY−2 carrying IncA/C plasmids always conferred additional antimicrobial resistance phenotypes such as chloramphenicol and sulfisoxazole, whereas in this study, bla CMY−2 carrying IncI1 plasmids only conferred a bla CMY−2 -associated phenotype, which was also observed in Folster et al. (2011). The bla CMY−2 genetic context on the IncI1 plasmid identified in this study was IS1294-ISEcp1bla CMY−2 -blc-sugE-ecnR followed by 159-bp IncA/C backbone, which was identical to that of pJIE512b from an E. coli isolate (Tagg et al., 2014). The genetic arrangement ISEcp1-bla CMY−2blc-sugE-ecnR was conserved on IncA/C plasmids (Verdet et al., 2009;Ye et al., 2016). ISEcp1 was presumed to be responsible for the mobilization of bla CMY−2 (Verdet et al., 2009) or bla CTX−M−2 (Lartigue et al., 2006) as well as its adjacent region from the bacterial chromosome to the IncA/C plasmids by a one-ended mobilization mechanism. On the basis of sequence alignments, it was suggested that mobilization of bla CMY−2 from the IncA/C plasmid to the IncI1 replicon occurred through IS1294-mediated transposition activity (Tagg et al., 2014). The bla CMY−2 insertion region of pS10584 started in CTTG and ended in GTTC, both of which matched the last 4-bp of oriIS and terIS of IS1294 (Tavakoli et al., 2000;Yassine et al., 2014), implying that IS1294 inserted into ISEcp1 in an IncA/C plasmid and subsequently mobilized the adjacent region, including the bla CMY−2 segment plus a 159bp IncA/C backbone (Tagg et al., 2014). A similar bla CMY−2 context was also observed in six reported IncI1 plasmids p2735 (Yassine et al., 2014), pR7AC (Minoia et al., 2012), pTN38148, TN10, TN13, and TN386 (Verdet et al., 2009); however, in these plasmids the bla CMY−2 insertion segment varied in the length of IncA/C backbone and the position that ISEcp1 interrupted by an IS1294-like element designated as IS1294b. And the integration of the bla CMY−2 gene by IS1294b between IncA/C and IncI1 replicons was experimentally confirmed by Yassine et al. (2014). By comparing the integration sites of bla CMY−2 insertion segments on these reported IncI1 plasmids, we inferred that the downstream of repZ gene could represent a "hot spot" for the integration of IS1294b element in the IncI1 plasmid scaffold but determination of the "hot spot" for IS1294 may require further study.
Besides the resistance determinants IncI1 plasmids encode, additional factors may be responsible for their prevalent diffusion. The shufflon multiple inversion system on IncI1 plasmids involves four segments separated by seven inverted repeats and a shufflon-specific recombinase (Rci) which acts to catalyze recombination between these repeats (Sampei et al., 2010). This shufflon system is responsible for generating variation in the C terminus of the pilV tip adhesins of the pili, leading to the specificity of recipient cells in liquid mating (Tagg et al., 2014). The resulting type IV pilus is also a known virulence factor, contributing to adhesion and invasion of Shiga toxinproducing E. coli (Kim and Komano, 1997), which accounts for the prevalent existence of IncI1 plasmids in pathogenic E. coli (Johnson et al., 2007). Thus, the association of epidemic ability as well as resistance determinants may favor the wide dissemination of plasmids belonging to the IncI1 group (Carattoli, 2009;Folster et al., 2010).
CONCLUSION
We screened and characterized antibiotic resistance plasmids from clinical and food Salmonella isolates in this study and discovered that IncHI2 was the major plasmid lineage contributing to the dissemination of antibiotic resistance in Salmonella. We also reported the complete sequence of an IncI1 plasmid harboring an antibiotic resistance-encoding region with the genetic arrangement of IS1294-ISEcp1-bla CMY−2 -blc-sugE-ecnR, interrupting the cia gene from a MDR S. Indiana isolate. To our knowledge, this is the first report of this bla CMY−2 context on the IncI1 plasmid in Salmonella. These results revealed that plasmids represent a potential threat for the dissemination of antibiotic resistance since they carry relevant resistance determinants and complete transfer-associated genes. Thus, in addition to phenotypic monitoring of antimicrobial resistance in Salmonella, further active surveillance is needed to minimize the spread of particular plasmids such as those belonging to the IncHI2 group. In addition, investigations of mobile genetic elements that are located on plasmids, such as insertion sequences, integrons, and transposons, may aid in understanding the source and spread of antibiotic resistance.
AUTHOR CONTRIBUTIONS
WC completed the antimicrobial susceptibility test, PMQR and β-lactamase gene detection, plasmid replicon typing, plasmid curing, plasmid sequencing, and prepare the manuscript; TF completed the isolate collection, antimicrobial susceptibility test, PMQR and β-lactamase gene detection, plasmid replicon typing, and plasmid curing; XZ helped to finish the isolate collection and antimicrobial susceptibility test; DZ helped to finish the plasmid sequencing and analysis; XS helped to design the project and give some valuable suggestions; and CS designed the project, completed the data analysis, and prepared the manuscript.
FIGURE 4 |
4Genetic context of the bla CMY−2 gene in plasmid pS10584 of Salmonella Indiana isolate SJTUF 10584 and structure comparison with plasmids p2735 from Klebsiella oxytoca and pTN38148, pTN10, pTN13, pTN386, pR7AC, pJIE512b from Escherichia coli. Regions of >99% homology are marked by gray shading.
Frontiers in Microbiology | www.frontiersin.org
September 2016 | Volume 7 | Article 1566
ACKNOWLEDGMENTSSUPPLEMENTARY MATERIALThe Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fmicb.2016.01566Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.Copyright © 2016 Chen, Fang, Zhou, Zhang, Shi and Shi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
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Background
Salmonella enterica is one of the major foodborne pathogens leading to worldwide human gastroenteritis [1]. S. Enteritidis was considered the most frequent one followed by S. Typhimurium isolated from human worldwide [2]. Of note, poultry is usually incriminated in outbreaks of human salmonellosis [2]. Therefore, the detection of Salmonella species in poultry production chain especially at the farms level is an issue of large concern. Furthermore, the resistance of some Salmonella serotype to multiple antibiotics [3], makes the study of the antibiotic susceptibility profile and its ecology of this zoonotic pathogen has a great priority. Indeed, the widespread misapplication and overuse of antimicrobial agents in food animal production have contributed to the development of antimicrobial resistant pathogens such as Salmonella that has emerged as a major public health implication [2].
Virulence gene encodes products that aid the organisms to interact with the host cells [4]. To that end, numerous virulence genes are incriminated in the pathogenesis of salmonellosis [5]. These genes are clustered within Salmonella pathogenicity islands (SPIs)-1 and − 21 (SPI-1 to SPI-21) and participate in the adhesion and invasion of the pathogen to the host as inv gene or help in the pathogen survival within the host like mgtC5 gene [6]. Serovars like S. Typhimurium also harbor self-transmissible virulence plasmid-encoded fimbriae (pef) fimbrial operon [7]. The enterotoxin (stn) gene was demonstrated as a suitable PCR target for detection of Salmonella strains [8]. In fact, previous studies had demonstrated the molecular characterization and antibiotic resistance of Salmonella serovars isolated from chickens farms in Kafr El-Sheikh Province, Egypt during 2014-2015 [9] and Sharkia Province [5] during 2009-2010 in Northern Egypt. While these studies used only clinical samples collected from different organs of broiler flocks without highlighting the prevalence of the infection in the surrounding farm environment and workers hand. Additionally, El-Sharkawy et al. [9] and Ammar et al. [5] didn't investigate selected genes (csgD, hilC, bcfC, mgtC, avrA, ompf and pefA) and selected antimicrobial agents (cefaclor, cefotaxime, cefepime and imipenem). Therefore, this study was set out to determine the prevalence of various Salmonella serovars in broiler chickens, chicken carcasses, drinking water, feed, litter, fans swabs and workers hand collected from broiler chickens farms at El-Sharkia province in Egypt. Moreover, the present study highlighted the antimicrobial resistance profiles of Salmonella serotypes using 11-antimicrobial agents (amoxicillin-clavulanic acid (AMC), ampicillin (AMP), cefaclor (CEC), cefotaxime (CTX), cefepime (FEP), doxycycline (DO), ciprofloxacin (CIP), imipenem (IPM), streptomycin (S), chloramphenicol (C) and trimethoprim-sulfamethoxazole (SXT) commonly used in human and veterinary medicines. Additionally, the pathogenic potential of recovered Salmonella serovars was assessed in the present study using virulotyping PCR assay targeting the invA, csgD, hilC, bcfC, stn, avrA, mgtC, ompF, sopE1 and pefA gene sequences. To the best of our knowledge, this is the first study that determines the distribution of csgD, hilC and ompF genes in Salmonella isolates from chickens in Egypt.
Results
Prevalence and serotypes of isolated Salmonella enterica
The prevalence and serotypes of Salmonella enterica were screened in the present study in samples collected from chickens' cloacal swabs, farm environmental samples and freshly dressed whole chicken carcasses at El-Sharkia province in Egypt. Of 420 samples, the Salmonella species were identified in 120 (28.6%) samples ( Table 1). The Salmonella strains were observed in 32% (48/150) of cloacal swabs, 22% (22/100) of environmental samples (2-samples from the litter, 8-samples from the drinking water, 8-samples from the feed, 1-sample from the workers hand and 3-samples from the fans swabs) and 29.4% (50/170) of whole chicken carcasses (Table 1). In general, S. Enteritidis (11.4%) was the most common identified serotypes followed by S. Typhimurium (8.6%), S. Kentucky and S. Molade (2.85% each), S. Bargny (1.4%), S. Inganda (0.95%) and S. Infantis (0.48%) ( Table 1). The identified serovars from cloacal swabs were S. Enteritidis (20 isolates), S. Typhimurium (19 isolates), S. Kentucky (1 isolates), S. Molade (6 isolates) and S. Bargny (2 isolates). While, the isolated strains from whole chicken carcasses were S. Enteritidis (18 isolates), S. Typhimurium (11 isolates), S. Kentucky (8 isolates), S. Molade (6 isolates), S. Bargny (2 isolates), S. Inganda (4 isolates), S. Infantis (one isolate). The isolated serovars from environmental samples were S. Enteritidis (10 isolates), S. Typhimurium (6 isolates), S. Kentucky (3 isolates), S. Bargny (2 isolates) and S. Infantis (one isolate) ( Table 1). The results indicated that S. Enteritidis was the most dominant Salmonella serotype in chicken in El-Sharkia Province in Egypt.
Antimicrobial resistance and distribution among differently identified Salmonella serovars
Variable rates of resistance of Salmonella serotypes were observed against 11 different types of antimicrobials. The antimicrobial susceptibility testing revealed absolute resistance to SXT (100%), AMP, AMC (68.3% each), S (Table 2). Salmonella isolates were showed resistant to two and up to seven antimicrobial agents (Table 3). In addition, multidrug resistance (MDR) to three or more antimicrobial classes was detected in 92 out of 120 (76.7%) isolates with multidrug antibiotic resistance index (MARI) of 0.2-0.6 ( Table 3). Salmonella serovars in this study demonstrated 11 different MDR patterns (Table 3), reflecting the high prevalence of MDR among Salmonella isolates in the surveyed Province.
Distribution of virulence genes among Salmonella serovars PCR targeting 10 virulence genes (invA, csgD, hilC, bcfC, stn, avrA, mgtC, ompF, sopE1 and pefA) were performed in this study to detect the identified Salmonella serovars virulence (Additional file 1: Figures S1-S3). Generally speaking, all Salmonella isolates showed at least two virulence-associated genes ( Table 4). Of note, invA gene (genus specific gene) was detected in 100% (120/120) of the isolates. On the contrary, sopE1 and pefA genes were completely absent in all isolates (Table 4). csgD and hilC genes were investigated in 90% (108/120) and 60% (72/ 120) of the isolates, respectively. The genes bcfC and stn were simultaneously detected in 40% (48/120) of the isolates and 30% (36/120) of the isolates were positive for avrA (located on SPI-1) and mgtC (carried on SPIs) genes. Whilst, the ompF gene was present in 20% (24/120) of the isolates (Table 4). Different frequencies of virulence genes among various serovars were detected with the absence of stn, avrA, mgtC and ompF genes among the isolates; S. Molade, S. Bargny, S. Inganda and S. Infantis (Table 4). Based on the combination of present and absent virulence genes, the Salmonella isolates were divided into seven different genetic profiles that were devoid of SopE1 and pefA (Table 5). In order to facilitate the analysis, these profiles were named P1-P7. Regarding the profiles, among the 120-analyzed isolates, 10% (12/120) were categorized as P1 (positive for all genes except SopE1 and pefA), 10% as P2 (hilC absent), 10% as P3 (ompF absent), 10% as P4 (avrA, mgtC and ompF absent), 20% as P5 (invA, hilC and csgD genes only present), 10% as P6 (invA and hilC only present) and 30% as P7 (invA and csgD only present) ( Table 5).
Relationship between antimicrobial resistance pattern and virulence determinants
The presence of virulence determinants (invA, csgD, hilC, bcfC, stn, avrA, mgtC and ompF) in different Salmonella serovars recovered from cloacal swabs, farm environment and whole chicken carcasses samples exhibited various antimicrobial resistance patterns as shown in Additional file 2: Table S2. A detailed analysis displayed associations of resistance phenotypes with potential virulence genes.
Discussion
In the present study, seven Salmonella serovars were identified from examined samples with a notably high prevalence of S. Enteritidis (11.4%) and S. Typhimurium (8.6%). These results were in concordance with those observed in dead and diseased chickens by Rabie et al. [10], Ammar et al. [5] in Egypt and Borges et al. [11] in Brazil. Moreover, a higher isolation rate of Salmonella spp. was detected in broiler chickens' cloacal swabs followed by whole chicken carcasses and farm environmental samples. Both drinking water and feeding are considered the main sources of contamination inside the farms. In contrast to ours, the isolation rate of Salmonella spp. in chickens' wastewater (20%) was higher than those (9.2%) detected in the whole chicken carcass in a study performed by Nwiyi et al. [12]. Such higher prevalence of Salmonella spp. in the whole chicken carcasses might be attributed to low slaughter hygiene, cross-contamination of products at different stages of chicken dressing and preparation in the retail shops at El-Sharkia province, Egypt. Also, isolation of Salmonella enterica serovars with high percent from broiler chicken farms necessitated the application of biosecurity program inside the farms beside using alternatives to the antibiotics such as bacteriophages or herbal extracts. Such alternative therapeutic interventions may help in cutting the cycle of horizontal transmission of Salmonella to broiler carcasses. Increasing rates of antimicrobial resistance among Salmonella is a growing healthcare problem that needs to be monitored continuously. Our study indicated that all isolated Salmonella strains exhibited absolute resistance (100%) against trimethoprim-sulfamethoxazole, indicating the limited therapeutic value of this antibiotic to poultry. Higher rates of resistance were observed to extended spectrum penicillin [ampicillin and amoxicillin-clavulanic acid], streptomycin, cefaclor, and doxycycline. These antimicrobial resistances of Salmonella spp. to extended spectrum penicillin, streptomycin, cefaclor, and doxycycline were cited previously in Egypt [5,13], and in Turkey [14]. Interestingly, the resistance of Salmonella spp. to cefaclor, a second-generation cephalosporin antibiotic was detected in the present study (36.7%) which is higher than those (14.5%) recently detected in Saudi Arabia by Abo-Amer and Shobrak [15]. In the current study, 13.3% of Salmonella spp. isolated showed resistance to cefepime, a fourth-generation cephalosporin antibiotic, which was consistent to a previous observation by Mir et al. [16] in poultry in India. In an astonishing way, no resistance was detected from Salmonella serovars to imipenem. Such absence of resistance to imipenem might be attributed to the fact that there was no history of using this antimicrobial candidate for the prevention or treatment in commercial chickens farms in EI-Sharkia Province. Therefore, other In fact, MDR pathogens create a difficulty in the treatment of human and animal illnesses and MDR strains of Salmonella have been associated with high morbidity, compared to susceptible strains [17]. Unfortunately, results obtained in the current study revealed MDR against three or more antibiotics in 76.7% of isolates with MARI ranged from 0.2 to 0.6. MARI value lower than 0.2, is considered a low risk, while value higher than 0.2 indicates high risk [17]. This result was compatible with Chuanchuen et al. [18], who isolated 70% of multiresistant Salmonella from poultry and swine with the most resistant pattern to ampicillin, chloramphenicol, streptomycin, sulfamethoxazole, tetracycline, and trimethoprim. The higher MARI value that was observed in the present study might be attributed to the widespread use of antibiotics in the locality in Egypt, the indiscriminate use of antibiotics either at recommended doses or at sub-therapeutic doses as feed additives to promote the growth of the poultry in developing countries. Subsequently, multi-drug resistant Salmonellae constituted a public health hazard and potentially affected the efficacy of medications in humans [19]. The increasing occurrence of Salmonella serovars resistant to sulfonamides, β-lactam, and aminoglycosides is considered alarming, as they are used for the treatment of invasive salmonellosis [13].
2 2 0 0 0 0 0 S. Bargny (6) 6 4 2 4 0 0 0 0 0 0 0 S. Inganda (4) 4 4 0 4 0 0 0 0 0 0 0 S. Infantis (2) 2 2 0 2 0 0 0 0 0 0 0
In the present study, well-recognized 10-virulence genes (invA, csgD, hilC, bcfC, stn, avrA, mgtC, ompf, sopE1 and pefA) were screened using PCR assay. Considering the importance of their function, for the first time in Egypt, the prevalence of the csgD, hilC, and ompF genes were evaluated to find out whether these genes can be detected in Salmonella isolates or not. The investigated genes comprised invA, hilC, avrA and mgtC genes associated with SPIs, the biofilm-associated gene csgD, the fimbrial related gene bcfC, the stn gene involved in heat labile Salmonella enterotoxin production, the outer membrane porin F (ompF) gene as a major general diffusion porin, sopE1 gene encoding a translocate effector protein and pefA gene as plasmid-encoded fimbria were also investigated in this study.
The csgD gene is the master regulator of the biofilm matrix compounds of Salmonella to promote the survival of bacteria when they are exposed to unsuitable conditions and was widely distributed among Salmonella isolates (90%) in our study regardless of their serovars. The hilC gene is located on SPI-1 and modulates invasion gene expression [20]. Irrespective of their serovars, a hilC gene was detected in 60% of analyzed strains. Compared to previous investigations, a hilC gene was absent in all of the Salmonella isolates from poultry [21].
The outer membrane porin (ompF) allows substrates across the membrane in Gram-negative organisms and does a non-specific cation prefer porin [22]. In this study, ompF gene was detected only in 20% of Salmonella isolates. While, a previous study [23] detected ompF gene in all 218-Salmonella strains surveyed in the USA. Interestingly, the isolates for the sopE1 gene coded by SPI-5 were screened, and the results revealed its absence in all isolates as compared with 41.18% prevalence of sopB gene in the isolates obtained from the liver, heart, and spleen collected from freshly dead and diseased broiler chicken previously screened in Sharkia Province in Egypt during 2009-2010 [5]. Similar to our findings, Abd El-Tawab et al. [24] reported the absence of sopE gene in Salmonella isolates recovered from milk samples of cattle with clinical mastitis in Egypt. Additionally, a very low percentage (7.7%) of sopE gene was detected in the Salmonella isolates obtained from chicken hatchlings [25].
The ability of antimicrobial resistant Salmonella strains to produce invasive disease can be attributed to various virulence genes, and virulotyping rapidly allows the discrimination of isolates with diverse pathogenic potential [26]. Indeed, there are numerous factors incriminated in the antimicrobial resistance acquisition or dissemination in Salmonella species like the misuse of antibiotics, unregular sales and inappropriate prescription of antibiotics, the presence of mobile genetic elements in the organisms; plasmid DNA, transposons, integrons etc. [27]. The present study proved the spreading of antimicrobial resistance patterns and virulence determinants in the analyzed isolates. This finding is significant with respect to public health and had been previously reported in Egypt [5,25]. In general, acquisition of the antimicrobial resistance affects the virulence in the invading bacteria through two alternative scenarios; increased resistance is accompanied by increased virulence (a positive effect) or increased antimicrobial resistance reduces the bacteria virulence (apparently negative effect) [28]. For Salmonella virulence, the resistance to aminoglycosides is associated with fitness cost in the Salmonella spp. [28]. Similarly, the resistance to fluoroquinolones has an implication in the fitness cost of S. enterica [29], and a higher risk of invasive illness or death of S. Typhimurium [30]. The association between antibiotic resistance and virulence among Salmonella serovars happened due to the genetic determinants for the antibiotic resistance in addition to virulence genes could be harbored by the same transferable element [31,32]. Generally speaking, specific pathogenicity genes (SPIs) are the main feature differentiate the pathogenic Salmonella spp. from the non-pathogenic ones and contribute to both natural and acquired resistance in Salmonella spp. [33]. The invA, hilC, avrA and mgtC genes that screened in the present study are associated with SPIs and were detected previously in the resistant strains [33,34]. Additionally, the omps and stn genes are commonly distributed among the resistant Salmonella strains and have a global contribution for Salmonella-associated diseases in animal and human populations [34,35].
Limitations
It should be noted that there are some limitations to the present study. Although this is the first study addressing csgD, hilC and ompF genes in Salmonella enterica isolates using PCR in Egypt, it focused on chicken samples collected from only one province of Egypt and didn't elucidate the antimicrobial resistance profiles and virulence genotyping of Salmonella enterica in other provinces. Therefore, additional studies are warranted to explore such profiles in other provinces of Egypt. The present study reported no resistance from Salmonella serovars to imipenem. However, further studies are required to confirm the potential of imipenem in the treatment of salmonellosis in chickens by evaluating the inhibitory effect of this candidate against Salmonella serovars isolated from different localities in Egypt and estimating the resistance of these isolates to imipenem. Moreover, future in-depth studies are necessary for analyzing the synergistic or an antagonistic effect of imipenem when used in combination with commonly used anti-Salmonella drugs and to determine the best effective composition ratio for the growth inhibition of Salmonella for clinical application. These drugs might be more effective if used as a part of a combination therapy rather than a single therapy.
Conclusions
Multidrug resistance (MDR) and virulent Salmonella serovars is highly prevalent in broiler chickens, chicken carcass and farm environment in Egypt. Serotyping of recovered Salmonella, clarified predominance of S. Enteritidis and S. Typhimurium in examined sources, but other five serovars were also encountered. These findings clearly demonstrated the high prevalence of MDR Salmonella serovars that indicated alarming in the veterinarian therapeutic treatment. The virulotyping verified the variety in number and distribution of different virulence-associated genes among screened Salmonella serovars and provided additional evidence on the risk of virulent salmonellosis posted from chickens. Finally, the obtained data provide a more accurate profile for understanding the dangerous spread of virulence genotypes and antibiotic resistance in Salmonella serovars. Such data imposes planning and application of biosecurity programs in addition to the establishment of bio-control measures to control Salmonella infection inside broiler chicken farms.
Methods
Sample collection and preparation
A total of 420-broiler chickens' cloacal swabs, farm environmental samples and freshly dressed chicken carcasses (humanly euthanasia using physical method; cervical dislocation) were randomly collected from five small scale broiler chicken farms at 3 weeks of growing cycle and five retail shops at El-Sharkia Province, Egypt during summer 2017 and used in this study. In details, 100 samples were collected from the farm environment (20 samples per farm) including drinking water (25 ml), feed (25 g), litter (25 g), fans and workers hand (4 samples for each type), 150 cloacal swabs (30 samples per farm) and 170 freshly dressed whole chicken carcasses samples (34 samples per shop) from outer skin were obtained from retail shops. All collected samples were subjected separately into a sterile impermeable labeled polyethylene bag (Thomas Scientific, USA), and transferred within 1 h in an icebox at 4°C for bacteriological analysis. All collected samples (25 g or 25 ml) were aseptically placed into sterile Difco-buffered peptone water (BPW) (225 ml) tubes (Oxoid, UK) and pre-enriched at 37°C for 24 h [36].
Isolation and identification of Salmonella
Each pre-enriched homogenate (1 ml) was aseptically added to 10 ml of Rappaport-Vassiliadis (RV) broth and incubated at 42°C for 24 h. Then, the broths were subcultured on xylose-lysine-desoxycholate (XLD) agar (Oxoid) and incubated at 37°C for 24 h. Next, the presumptive colonies were picked and subjected to standard biochemical methods (urea hydrolysis, H2S production on triple sugar iron agar, lysine decarboxylation, indole, methyl red test, Voges-Proskauer test and citrate utilization test). Typical Salmonella isolates were serotyped by slide agglutination test based on O and H antigens using polyvalent and monovalent antisera (DENKA SEIKEN Co., Japan) following the White-Kauffmann-Le Minor scheme [37]. [39]. Also, the MARI index was calculated for all Salmonella isolates according to the protocol designated by Krumperman [40] using the formula a/b (where "a" is the number of antimicrobials to which an isolate was resistant and "b" is the total number of antimicrobials to which the isolate was exposed).
Molecular detection of Salmonella virulence-associated genes
The determination of Salmonella virulence factors was performed using the uniplex polymerase chain reaction assays targeting the invA, csgD, hilC, bcfC, stn, avrA, mgtC, ompF, sopE1 and pefA gene sequences. DNA was extracted from 200 μl bacterial sample using a commercial kit (QIAamp DNA Mini kit, Qiagen, Germany) following the manufacturer's instructions, and then stored at − 20°C until further use. DNA concentration was measured by using a NanoDropTMND-1000 Spectrophotometer (Erlangen, Germany). Primer sequences and the expected size of the PCR product are detailed in Additional file 2: Table S1. All PCR reactions were performed using EmeraldAmp Max PCR Master Mix (Takara, Japan) in a final volume of 25 μl containing 12.5 μl of EmeraldAmp Max PCR Master Mix, 1 μl of each primer of 20 pmol concentrations, 4.5 μl of water, and 6 μl of DNA template. The Applied biosystem 2720 thermal cycler was programmed with specific profiles (Additional file 2: Table S1). Gel electrophoresis of the PCR products was applied to 1.5% agarose gel (Applichem, Germany). Next, the products were stained with ethidium bromide (Sigma-Aldrich, U.S.A.) and visualized under ultraviolet light photographed by a gel documentation system (Alpha Innotech, Biometra). Consideration of the positive result was depending on detection of a band similar to that in size of the positive control for a particular gene. Bacterial strains of Salmonella Enteritidis (ATCC 13076) were used as positive control for all PCR reactions.
Statistical analysis
The obtained data were statistically analyzed using Pearson's chi-square exact test using the SPSS Statistics 17.0 software program. The results were considered to be significant at P < 0.05.
Additional files
Additional file 1: Figure S1. Additional file 2: Table S1. Primers sequences, target genes, amplicon sizes and cycling conditions for virulence factors [41][42][43][44]. Table S2.
are warranted to evaluate the inhibitory effect of imipenem against Salmonella spp. in vivo.
Amplification of (A) invA gene (651 bp) in Salmonella isolates. Lane L: DNA ladder (100 bp), lane Pos: Positive control, lane Neg: negative control, lanes 1-10: invA positive. (B) csgD gene (651 bp), lanes 1-5,7-10: csgD positive, lane 6: csgD negative. (C) hilC gene (241 bp) lanes 2,4-8: hilC positive, lanes 1,3,9,10: hilC negative. (D) Stn gene (617 bp) lanes 2,3,7,8: stn positive, lanes 1, 4-6,9,10: stn negative. Figure S2. Amplification of (A) bcfC gene (467 bp) in Salmonella isolates. Lane L: DNA ladder (100 bp), lane Pos: Positive control, lane Neg: negative control, lanes 2,3,7,8: bcfC positive, lanes 1,4-6,9,10: bcfC negative. (B) mgtC gene (677 bp) lanes 2,3,7: mgtC positive, lanes 1,4-6,8-10: mgtC negative. (C) avrA gene (422 bp) lanes 2,3,7: avrA positive, lanes 1,4-6,8-10: avrA negative. (D) ompF gene (519 bp) lanes 2,3: ompF positive, lanes 1,4-10: ompF negative. Figure S3. Amplification of (A) sopE1 gene (422 bp) in Salmonella isolates. Lane L: DNA ladder (100 bp), lane Pos: Positive control, lane Neg: negative control, lanes 1-10: sopE1 negative (B) pefA gene (700 bp), lanes 1-10: pefA negative. (PDF 856 kb)
Distribution of virulence genes combinations and antibiotic resistance patterns in the different Salmonella serovars. (PDF 143 kb) Abbreviations AMC: Amoxicillin-clavulanic acid; AMP: Ampicillin; ATCC: American Type Culture Collection; BPW: Difco-buffered peptone water; C: Chloramphenicol; CEC: Cefaclor; CIP: Ciprofloxacin; CTX: Cefotaxime; DO: Doxycycline; FEP: Cefepime; IPM: Imipenem; MARI: Multidrug antibiotic resistance index; MDR: Multidrug resistance; pef: Plasmid-encoded fimbriae; RV: Rappaport-Vassiliadis; S: Streptomycin; S.: Salmonella; SPIs: Salmonella pathogenicity islands; SXT: Trimethoprim sulfamethoxazole; XLD: Xylose-lysinedesoxycholate
Table 1
1Distribution of Salmonella serovars in study samples (n = 120)Serotypes
Antigenic formula
Sample type (n)
Table 2
2Antimicrobial resistance profiles of isolated Salmonella serovarsSerovars (n)
Antimicrobial resistance
SXT
AMP
AMC
S
DO
CEC
C
FEP
CTX
CIP
IPM
S. Enteritidis (48)
48
34
42
28
24
20
12
10
6
6
0
S. Typhimurium (36)
36
18
22
22
14
18
6
4
4
2
0
S. Kentucky (12)
12
12
10
10
8
4
2
2
6
4
0
S. Molade (12)
12
8
6
8
AMC Amoxicillin-clavulanic acid, AMP Ampicillin, CEC Cefaclor, CTX Cefotaxime, FEP Cefepime, DO Doxycycline, CIP Ciprofloxacin, IPM Imipenem, S Streptomycin, C Chloramphenicol and SXT Trimethoprim sulfamethoxazole a The percentage of the total number of isolates resistant, intermediate, or susceptible for a particular antimicrobial is indicated in the last three rows below each antimicrobialTotal (120)
120
82
82
78
48
44
20
16
16
12
0
a Resistant %
100%
68.%
68.%
65%
40%
36.7%
16.7%
13.3%
13.3%
10%
0
a Intermediate %
0
4.2%
0
8.3%
10.8%
12.5%
16.7%
0
5.8%
0
0
a Susceptible %
0
27.5%
36.7%
26.7%
49.2%
50.8%
66.7%
86.7%
80.8%
90%
100%
Table 3
3Distribution of antibiotic resistance rates of Salmonella isolates AMC Amoxicillin-clavulanic acid, AMP Ampicillin, CEC Cefaclor, CTX Cefotaxime, FEP Cefepime, DO Doxycycline, CIP Ciprofloxacin, IPM Imipenem, S Streptomycin, C Chloramphenicol, SXT Trimethoprim sulfamethoxazole, and MARI Multidrug antibiotic resistance indexAntibiotic pattern profile Antibiotics
No. of isolates Percentage of resistant isolates (%) No. of resistance antibiotics MARI (%)
1
SXT, AMP,AMC,S, DO,CEC,C 10
8.3
7
0.6
2
SXT,AMP,AMC,S,CEC,C,FEP
6
5
7
0.6
3
SXT,AMP,AMC,S,DO,CTX,CIP 6
5
7
0.6
4
SXT, AMP,AMC,S, DO,CEC
8
6.7
6
0.6
5
SXT,AMP,AMC,CEC,FEP,CTX 10
8.3
6
0.6
6
SXT, AMP,AMC,S,DO
10
8.3
5
0.5
7
SXT, AMP,S,DO,CIP
6
5
5
0.5
8
SXT,S, DO,CEC
10
8.3
4
0.4
9
SXT,AMP,AMC,C
4
3.3
4
0.4
10
SXT, AMP,S
22
18.3
3
0.3
11
SXT,AMC
28
23.3
2
0.2
Table 4
4Distribution of virulence genes among different Salmonella serovarsSerovars (n)
Virulence genes (n)
invA
csgD
hilC
bcfC
Stn
avrA
mgtC
ompF
SopE1
pefA
S. Enteritidis (48)
48
44
42
28
36
20
18
6
0
0
S. Typhimurium (36)
36
36
6
16
12
14
16
16
0
0
S. Kentucky (12)
Table 5
5Virulence profile of Salmonella serovars isolated in this studyGenetic profile
Virulence genes
No. of isolates (%)
P1
invA,csgD,hilC,bcfC,stn,avrA,mgtC,ompF
12 (10%)
P2
invA,csgD,bcfC,stn,avrA,mgtC,ompF
12 (10%)
P3
invA,csgD, hilC,bcfC,stn,avrA,mgtC
12 (10%)
P4
invA,csgD, hilC,bcfC,stn
12 (10%)
P5
invA,csgD, hilC
24 (20%)
P6
invA,hilC
12 (10%)
P7
invA,csgD
36 (30%)
The in vitro sensitivity of Salmonella isolates to antimicrobial agents Antibiograms of all identified Salmonella isolates were determined by the disc diffusion assay according to the guideline of Clinical and Laboratory Standards Institute[38] using Mueller-Hinton agar (Oxoid, Basingstoke, Hampshire, England, UK). Antimicrobial agents commonly used in either human or veterinary medicine was tested as follows: AMC (20/10 μg), AMP (10 μg), CEC (30 μg), CTX (30 μg), FEP (30 μg), DO (30 μg), CIP (5 μg), IPM (10 μg), S (10 μg), C (30 μg) and SXT (1.25/ 23.75 μg). All drugs were purchased from (Oxoid, England). Escherichia coli American Type Culture Collection (ATCC) 25922 were used as a reference strain. The isolates resistant to three or more separate classes of antimicrobials were defined as MDR
AcknowledgementsThe authors would like to thank owners and staff of the study animal in Egypt.FundingNo funding.Availability of data and materialsThe datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.Authors' contributionsConceived and designed the experiments: RME, MME, AIZ, SAESES. Performed the experiments: RME, MME, AIZ, SAESES, MAR. Analyzed the data: RME, MAR. Contributed reagents/materials/analysis tools: RME, MME, AIZ, SAESES, MAR. Wrote the paper: RME, MME, SAESES, MAR. All authors reviewed the manuscript. All authors read and approved the final manuscript.Ethics approval and consent to participate All used protocols and humanly euthanasia (physical method) were approved by the Committee on the Ethics of Animal Experiments of the Faculty of Veterinary Medicine, Mansoura University(Permit numbers 20-17).An informed verbal consent was obtained from the owner (for experimental studies involving client-owned animals).Consent for publicationNot applicable.Competing interestsThe authors declare that they have no competing interests.
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| 228 | Epidemiological Characterization of Avian Salmonella enterica Serovar Infections in India | Comparison of Salmonella enterica Serovar Heidelberg Isolates from Human Patients with Those from Animal and Food Sources | Serovars and antimicrobial resistance of non-typhoidal Salmonella from human patients in Shanghai, China, 2006–2010 | Experimental Pathogenesis of Pullorum Disease with the Local Isolate of Salmonella enterica serovar. enterica subspecies Pullorum in Pullets in Bangladesh | Prevalence and Antibiogram Studies of Salmonella from Foods of Animal Origin in Mumbai City | Prevalence of enterotoxin gene (stn) among different serovars of Salmonella. | Poultry-associated Salmonella enterica subsp. enterica serovar 4,12:d:- reveals high clonality and a distinct pathogenicity gene repertoire. | Detection of Virulence Genes in Salmonella Serovars Isolated from Broilers | The detection of Salmonella serovars from animal feed and raw chicken using a combined immunomagnetic separation and ELISA method |
229 | My left nipple has a slight bulge. | What is this new hell????? My right nipple feels like its being subjected to death of a thousand razors, or my straightening iron,... Nursing is almost impossible as I just want to cry or scream with pain, pumping is slightly less painful. It's not hot, I don't really see anything wrong... Help! | Yeah just read the title I have a hard spot under my right nipple. Why and is this normal? | Why are your nipples sore and swollen? | The past couple of days I’ve had pain in my right nipple (after having no pain for weeks) and when I’m breastfeeding part of my breast goes numb, has anyone else experienced this? It’s making me not want to feed on that side :( | So I got my nipples pierced about mid March of this year so it’s been 7 months. I haven’t had any problems with them what so ever since getting them pierced. Today I noticed my left one was a little sore when I put my seat belt on. And when I finally got to my destination I looked and it is swollen so much that there is no more room on the barbell. There is no puss or anything. It just slightly hurts and is very swollen. I do not have access to a bigger barbell right now. Do you guys have any suggestions because I really don’t want to remove it 😢 | Is it normal if one of your nipples are in a little but pops out when your horny? | I'm asking because I have a small, hard mass under one of my nipples without having enlarged breasts and my father thinks it's gyno. | Is having a third nipple rare? | 229 | Hi I am a 13 yo male, 5’ 1” and about 90lbs (small kid). Sometime in the past few weeks a little bulge appeared behind my left nipple, but not my right. Putting to much pressure against it produces pain (i would say it’s a dull pain, coming in at a four depending on where I push on it). It almost feels loose, like I can get my fingers under it or push it around slightly, but it’s stuck behind my nipple. The bulge itself is not very big, probably unnoticeable to the untrained eye, but I can see it and while I’m not looking at it right now, it may be about half a centimeter high and 2-3 cm across. I don’t really want to ask my mom but I want to know what it is. Thanks in advance! | Small lump - is this his nipple? | Odd lump in left breast after one month HRT | there is a lump under my breast? | Identify a Lump in a Breast | Painful lump feeling in right breast and Skipped Menstrual Cycle? | 12 M why is there a hard spot under my nipple?? | WHAT DOES A BREAST LUMP FEEL LIKE? I THINK I FOUND A LUMP. I am a man. I am confused. Help? | What is this new hell??? Terrible nipple pain, please help. |
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231 | where did ben stapleton serve as mayor of | John Emerson (mayor) John Emerson (June 4, 1859 – July 25, 1932) was the 15th mayor of Calgary, Alberta. He was the mayor at the time that Alberta became a province of Canada, which was on September 1, 1905. Born in England, Emerson emigrated to Calgary in 1885 and began farming on a homestead just outside the city limits. Soon he left farming and established a successful grocery business on Stephen Avenue. After spending three years on Calgary City Council, Emerson spent two years as mayor from January 2, 1905 to January 14, 1907. During his tenure as mayor, Calgary | Isidore B. Dockweiler Governor of California. Governor-Elect Lane and Lt. Governor-Elect Dockweiler won the electorate's plurality by 25,000 votes, but lost on a minor legal technicality decided by the California Supreme Court - a controversial event. Republican George Cooper Pardee became Governor of California as a result. Dockweiler helped secure California's vote for Woodrow Wilson, who would become President of the United States. Dockweiler was held in high esteem and confidence by Wilson. Lane served as U.S. Secretary of the Interior. When Lane resigned in 1920, Dockweiler was offered the position. Dockweiler declined due to family responsibilities of 11 children. Instead he was | Brockton, Massachusetts Balzotti defeated Harrington to become the city's first female mayor. Balzotti was defeated in 2013 by Bill Carpenter who won the election only by 44 votes. In 2009, community activist Jass Stewart was elected to councilor-at-large becoming the first African American to serve in Brockton's city council. The city council consists of 4 Councilors-at-Large and 7 ward Councilors, one for every ward in the city. Brockton has three hospitals, Signature Healthcare Brockton Hospital on the east side, Good Samaritan Medical Center - a Steward Family Hospital (formerly Caritas Good Samaritan, and before that Cardinal Cushing) Hospital to the northwest, and | Olivia Chow a statue dedicated to Layton; tributes to him were written in English, Chinese and French. The statue is located in Harbour Square Park at the Jack Layton Ferry Terminal. Chow is portrayed by Sook-Yin Lee in the 2013 CBC Television film "Jack". Lee won a Canadian Screen Award for her performance. Chow first became active in politics working with local NDP MP Dan Heap. With his support, she ran for school board trustee, and won in 1985. Popular on the school board, she was elected to Metropolitan Toronto Council in 1991 for the Downtown Ward in the riding of Trinity—Spadina. | Alexander Dalway was an Irish politician.
Dalway was born in Carrickfergus and educated at Trinity College, Dublin.
Dalway represented Carrickfergus from 1715 to 1719.
References
Irish MPs 1715–1727
Members of the Parliament of Ireland (pre-1801) for County Antrim constituencies
18th-century Irish people
People from Carrickfergus
Alumni of Trinity College Dublin | Mayoralty of Dianne Feinstein Dianne Feinstein became mayor pro-tem of the City and County of San Francisco, California on December 4, 1978, following the Moscone–Milk assassinations in which her predecessor in office, George Moscone and fellow member of the San Francisco Board of Supervisors, Harvey Milk, were assassinated by former supervisor Dan White. At the age of 45, Feinstein became the first female mayor of the municipality, and was formally elected to the position on November 4, 1979 and re-elected in 1983. She was prevented from seeking a third term in office and was succeeded in 1987 by Art Agnos. | Jimmie Smith is an American politician and member of the Democratic Party who has served as the mayor of Meridian, Mississippi since 2021. Previously, he served 20 years on the Lauderdale County Board of Supervisors.
Early life
Smith was born in Chicago on June 29, 1952. As a teenager, he moved to Meridian.
Career
Shortly after his arrival in Meridian, Smith worked in area hospitals. Later, he joined the Meridian Police Department where he worked in various divisions including the SWAT Team.
Community involvement
Smith served for 20 years on the Lauderdale County Board of Supervisors.
Mayor of Meridian
In 2005, while still serving on the Board of Supervisors, Smith was the Democratic nominee for mayor. He lost to the incumbent John Robert Smith in the general election by only 104 votes.
Sixteen years later, Jimmie Smith faced off against Mayor Percy Bland in the Democratic primary. After, beating Bland in the April 2021 run-off, he faced city council member Weston Lindemann, an independent, and Republican Robert Ray in the general election. In June 2021, Smith won that race decisively with over 60 percent of the vote.
When he assumed office in July 2021, he became only the second African American mayor of Meridian, a town with a population that is over 60 percent Black.
References
1952 births
African-American mayors in Mississippi
Living people
Mayors of Meridian, Mississippi
Mississippi Democrats
Politicians from Chicago
21st-century African-American people
20th-century African-American people | Rex Stratton Kirton is a local body politician in the Wellington Region. He was Mayor of Upper Hutt for 24 years until 2001, and then served three terms on the Greater Wellington Regional Council.
Biography
Kirton attended St. Patrick's College, Silverstream 1955–1959. He lives in Whitemans Valley RD1.
Local government
Kirton was first elected Mayor of Upper Hutt in 1977. When he retired from this role in 2001, he was the longest-serving mayor in New Zealand at that time. In 2001, Kirton stood as the Upper Hutt representative on the Wellington Regional Council. He served three terms until 2010, when he was beaten by Paul Swain. Swain and Kirton received 5,117 and 3,794 votes, respectively, with two other candidates contesting the election. In 2007, he had been returned unopposed. He was chairman of the regional council's parks, forests and utilities committee.
In the 1997 New Year Honours, Kirton was appointed a Companion of the Queen's Service Order, for public services. Kirton Drive, the main street in the suburb of Riverstone Terraces, is named after him.
References
Year of birth missing (living people)
Living people
Mayors of places in the Wellington Region
People from Upper Hutt
Companions of the Queen's Service Order
People educated at St. Patrick's College, Silverstream
Wellington regional councillors | 231 | Benjamin F. Stapleton Locke. Rumors of Stapleton's Klan membership circulated during the mayoral campaign. Stapleton responded by denying that he was a Klan member and condemning the Klan, "to appease his Jewish and Catholic supporters." Stapleton declared, "True Americanism needs no mask or disguise. Any attempt to stir up racial prejudices or religious intolerance is contrary to our constitution and is therefore un-American." The voters believed Stapleton's denial and he was elected, defeating an unpopular incumbent, Dewey Bailey. Stapleton then appointed fellow Klansmen to multiple positions in Denver government, though he initially resisted Klan pressure to appoint a Klansman as chief of police. | how long has the mayor of cedar grove been in office | who was the republican candidate who questioned obama about his patriotism | when did the patriot party become a criminal enterprise | who did robert hicks think should help the white protesters | in which state did us senator bernie sanders represent when edward snowden | how many people were arrested in dewey square during the occupy boston movement | where did james reeb go to protest for voting rights | who questioned anthony senecal about calling for the assassination of obama |
232 | How to Calculate the Value/Price of Monero? | Hey all.
I’ve got ~$1,000 invested in purchases in 2 cryptos so far (BTC and ETH). I’ve seen the prices of each move some I bought, but can’t tell how much I’ve made/lost. Any advice on how to calculate or figure that out?
I’m using Coinbase pro.
Thanks. | How do you calculated Consumer Price Index? | I made a simple spreadsheet detailing the total cost to buy all the stock of each item for reference's sake.
Available here:
Edit: If you want to use this as a calculator for only buying certain items, e.g. pendants and diamonds only, open the link and click File -> Make a Copy -> Ok and then edit the values in the max exchange amount column. Image guide for clarification:
kthxbai. | Multiply the original price by 0.2 to find the amount of a 20 percent markup, or multiply it by 1.2 to find the total price (including markup). If you have the final price (including markup) and want to know what the original price was, divide by 1.2. | I’m struggling to understand how to work out my cost base when calculating CGT. Say I buy 1 bitcoin for $1000 and then buy 2 bitcoin for $2000 each a month later. I understand if I then sold all 3 bitcoin together my cost base would be $5000. So would my cost base be $2000 if I only sold 1.5 bitcoin. | So I had to miss one of my accounting classes and in the notes my professor left there isn't much explanation for one type of problem. I'm confident I can figure out how to do it, but **I just can't figure out where a specific value is coming from. I will bold that part in the problem below**. If I can understand how to calculate this I believe I can easily solve the problem.
**"** Assume that the semi-annual cash payments have already been correctly computed to be $25,000. Given this number, and remembering that the face value of the bonds ($600,000) will be paid out at the end of the 20 years, what is the total issue price (present value) of the bonds if the market rate for bond issues of similar risk is 8%, compounded semi-annually?
25,000 x PVA,4%,40 = 25,000 x **19.793** = 494,825
600,000 x PVS,4%,40 = 600,000 X **.208** = 124,800 **"**
Technically I can already get the answer by adding the second result to the first, but in order to be able to do other problems I need to understand where the numbers 19.793 and .208 are coming from. I can tell that they are calculated based on PVA and PVS but nothing I have tried has worked. | How do you calculate cost price from selling items? | How do you find the original price of an item that is discounted? | 232 | I am wondering how the value/price of one Monero is determined. It probably is connected to a lot of factor and not just made up by a random person. I just can imagine how I could calculate the value myself. I would like to know a way to determine the price by myself if that is even possible. | How is market price of a share determined? | How do you determine market pricing? | who determines the present value of a given amount of money | What determines crypto prices? | Calculating a price based on nodes and discounts | Electronic price labeling system and its price data recovering method | Inverse mineral price calculation | Calculate price in underlying based off of options pricing |
233 | What explains why vote buying occurs in some elections but not others? The phenomenon of vote buying is under-studied in authoritarian, single-party-dominant regimes, especially in non-partisan elections in which competition is candidatecentered rather than party centered. Village elections in China provide a valuable window on the dynamics of vote buying in these conditions. Employing both an in-depth case study and an original, panel survey to provide new, systematic measures of rents and vote buying, we develop and test the following hypothesis: the availability of non-competitive rents accessible by winning candidates explains the variation in the incidence of vote buying in local elections. Our causal identification strategy exploits the timing of land takings and the exogenous nature of formal land takings authorized in state land-use plans at higher administrative levels to test the vote-buying-as-rent-seeking hypothesis. We find that the lure of rents, mainly from government takings of village land, is a key driver of vote buying by non-partisan candidates for the office of village leader. The evidence suggests that vote buying provides information to the authoritarian state about which local elites it should recruit into the rent-sharing coalition.Keywords Vote buying · Rent seeking · Village elections · China · Land What explains why vote buying occurs in some elections but not others? The existing literature most commonly analyzes vote buying as a strategy of political parties to mobilize electoral support(Bratton 2008;Corstange 2018;Hicken 2011;Mares and Young 2016;Stokes et al. 2013). Parties pursue vote buying to increase their tallies at the polls. Vote buying is less commonly studied in electoral contexts in which parties and political machines are weakly institutionalized or absent (e.g., | ABSTRACTDespite the burgeoning comparative literature on authoritarian elections, less is known about the dynamics of competition in authoritarian subnational elections where opposition is not allowed to organize into parties. Local elections without partisan competition in single-party authoritarian regimes provide considerable advantages to the incumbents and may well turn the incumbent advantage common in liberal democracies into incumbent dominance. What economic factors can break incumbent dominance in such competition without parties? With quantitative and qualitative evidence from grassroots elections in China, this article illustrates that economic growth and industrial economic structure offering more economic autonomy help to break incumbent dominance and increase the prospects of successful challenge to incumbency by non-party outsiders. The examination of the findings in a broad context in China and against the backdrop of local democratization in the developing world suggests that though we m... | Democratic governance is believed to improve government responsiveness to citizens' demand for public goods. In China, villagers' committee elections represent a major progress in China's development toward good governance. We develop a rational model to explain villagers' participation. Utilizing a national survey of rural residents in 2005, this paper tests the insights of the model. Two findings are of interest to the students of voting and elections. First, there is disagreement over the causal relationship between political trust and voting. This paper offers a rational interpretation of political trust by emphasizing the informational aspect of the concept. Second, voting is generally theorized as a process of overcoming various costs. The prospect of benefits figures more prominently in Chinese village elections. Our findings highlight the pivotal role of township governments in China's rural politics and reveal the inner dilemma of democratization in China. | Although the People's Republic of China attaches little importance to elections in parliamentary democracies, elections are seen as important in societies going through the transition between capitalism and communism. 1 Elections of local level leaders were carried out in the CCP-controlled base areas before 1949, and throughout the period after Liberation. The attention devoted to election propaganda and voter turn-out attest to the importance placed on mass electoral participation by the Chinese leadership. 2 * I wish to express my gratitude to Thomas Bernstein, Steven Butler, Victor Falkenheim, Andrew Nathan, Brian Shaw, and David Strand for reading earlier drafts of this paper and providing many useful suggestions for its revision. Needless to say, all errors are the responsibility of the author. | Accommodating “Democracy” in a One-Party State: Introducing Village Elections in China | How do politicians buy votes in secret ballot elections? I present a model of vote buying in which a broker sustains bribed voters’ compliance by conditioning future bribes on whether her candidate’s votes reach an optimally set threshold. Unlike previous explanations of compliance, the threshold mechanism does not require brokers to observe individual voters’ political preferences or even vote totals of the bribed voters. I show that when there is uncertainty about voters’ preferences, compliance can be sustained as long as electoral results of small groups are available. If preferences are observed however, vote buying is not deterred by higher aggregation of electoral results. I also find that vote buying is facilitated when voters care about the welfare of other voters. Using survey data from Nigeria, I provide evidence consistent with the model’s results. | Vote allocation Vote allocation is a system of tactical voting used in the Republic of China on Taiwan from the late-1990s, after which the voting system is to be changed from single non-transferable vote to a parallel voting system. In this system, voters are asked to vote for a party candidate based on items such as their day of birthday so as to evenly distribute votes. In districts where a party is running two candidates, males may be asked to vote for one candidate and females for another to insure even distribution. It was also practice in Japan and South | The democratic election of the head of the town in Longgang section, Shenzhen, which we name as the two vote system, is a great contribution to the democracy of grass roots units in China. The two vote system carries out the basic principles of democratic election, and it also embodies all the rules of democratic centralism from the lower level upward during the nomination of candidates. The universality of the two vote system is the measurement of the democratic election. It is a kind of pure democratic voting. |
Introduction
In parliamentary voting, a plurality voting system is a system where each voter can vote for one party, and the seats in parliament are allocated to the parties dependent on (usually proportional to) the cast votes. If one party received the majority of We are grateful to Francis Bloch and Anirban Kar for fruitful discussions, as well as to four anonymous referees for their helpful comments and suggestions. the votes, then it can be considered the winner of the election. However, very often there is no majority party, and two or more parties need to cooperate and make an agreement to form a (majority) government. Although in such situations there is no party that can guarantee for itself to be in the government, and thus it is not immediately clear who is the winner of the election, usually immediately after the elections there is at least one party that claims to be the winner of the election. For instance, the party with the most votes/seats often declares itself as the winner of the election. But if other, smaller, parties form a majority coalition, then the party with the most votes might eventually be the 'loser'. For example, if after election a right wing party received the most votes, but the left wing parties can form a majority coalition, then it might be that the largest, or most moderate, left wing party can be considered to be the winner of the election.
Typically, in such situations, whether a coalition is winning or losing might depend on the way how players outside the coalition are organized into coalitions. Therefore, in this paper, we frame debates about winners of an election in the setup of simple cooperative games in partition function form. We address the question if it is possible to assign weights to political parties that somehow measure who is the winner of an election. If that is possible, we say that the corresponding simple game supports a plurality voting democracy.
We introduce plurality games as a special type of simple games in partition function form. A classical simple game assigns to every coalition (i.e., subset of the player set) either a worth of one (if the coalition is winning) or zero (if the coalition is losing). In such a game, whether a coalition is winning or losing does not depend on the way how the players/parties outside the coalition are organized. This assumption is reasonable when we define a coalition to be winning if it has a majority, since in that case any coalition of the opposing parties is a minority coalition. However, in this paper we want to address the issue of determining the winner or strongest party in a coalitional configuration of parties, even when there is no majority coalition formed (yet). During the process of government formation, different potential compositions of government parties might be considered, and the parties trying to form a government use coalition formation with parties outside the current government negotiations in strengthening their arguments or bargaining positions.
Usually, in these cases, the strength of parties also depends on the way other parties form alliances, i.e., there are externalities of coalition formation in the sense that parties forming a coalition has impact on the strength of parties outside the coalition. Such situations can be modeled by simple games in partition function form, where a worth is assigned to every so-called embedded coalition being a pair consisting of a coalition and a partition that contains this coalition. The worth is one (respectively zero) if the corresponding coalition is winning (respectively losing) in the partition. We call such a game a plurality game, if in every partition there is at least one coalition that wins in the partition. So, winning does not necessarily mean that the coalition has a majority and can pass a bill, but simply that it is considered as the strongest in a given coalitional configuration as represented by the partition. For example, it is common practice that the party that got the most votes in an election is considered as a winner and takes the initiative to form a government. Although this does not imply that eventually this party will be in the government, it obviously gives the party an advantage as long as no coalitions are formed yet. On the other hand, it might be that a party that is not the largest, but has ideologically close parties that are big enough to form a majority coalition with, will eventually form a government, and thus can also be considered a winner after the elections. In that case there can be two (or even more) parties that are declared to be winner of the election.
In this paper, we assume plurality games to be monotonic, both with respect to a coalition as well as to a certain type of externalities regarding other coalitions. Specifically, we assume that (i) a winning coalition cannot become losing when it grows, and (ii) there are negative externalities of other coalitions growing in the sense that bigger outside coalitions give 'more resistance' and thus outside coalitions becoming bigger cannot turn a losing coalition into a winning one. 1 Within this model of (monotonic) plurality games, we study the possibility of assigning weights to players (parties) such that a winning coalition in a partition is always one that has the maximal sum of its players' weights over all coalitions in the partition. If this is possible for a given game, then we call the game weighted and refer to the corresponding weights as supporting weights. In that case, we can say that the game supports a plurality voting democracy. In the following, we sometimes shortly speak about the weight of a coalition as being the sum of the weights of the players in the coalition. Notice that a game being weighted does not imply that, when two coalitions in a partition have maximal weight, then both are winning. It only requires that the winner should be one of the coalitions with maximal weight.
In this paper, an important role is played by decisive plurality games being plurality games, where each partition contains exactly one winning coalition. In Sect. 2, we illustrate the problem of assigning supporting weights to plurality games by providing an example of a five-player decisive plurality game which is not weighted. We start our investigation of finding plurality games that are weighted in Sect. 3, by showing that all games with at most four players are weighted. In Sect. 4, we show that a majority game (i.e., a plurality game such that the winner in every partition is a coalition of maximal size in the partition) with more than four players is weighted. We also define a notion of symmetry, and show that such symmetric majority games can only be supported by assigning equal weights to all players. Notice that, intuitively, not all players can be symmetric in a decisive plurality game, because for such a game exactly one singleton is winning in the partition that consists of all singletons. We refer to this special partition into singletons as the atomistic partition. It describes, for example, the situation directly after elections when no coalitions or alliances are formed yet.
The closest we can get to symmetry in a decisive plurality game is to require that all players but one (the winner in the atomistic partition) are symmetric. We call such games (n − 1)-symmetric and show in Sect. 5 that (n − 1)-symmetric decisive plurality games with an arbitrary number of players are weighted. For this, we define the power of the winner in the atomistic partition in a specific way, show how it shapes the structure of the possible candidates for a winning coalition in a partition, and explicitly use it in the construction of supporting weights.
Section 6 concludes the main part of the paper and provides an overview of the related literature. All proofs are collected in Appendix A (proofs from Sect. 3), Appendix B (proofs from Sect. 4), and Appendix C (proofs from Sect. 5).
Plurality games
All games we consider will be defined on a fixed and finite player set N = {1, … , n} with n ≥ 2 , whose non-empty subsets are called coalitions. A collection of coalitions is called a coalition structure if is a partition of N, i.e., if all coalitions in are non-empty, pair-wise disjoint, and their union is N. We denote by P the set of all partitions (coalition structures) of N. For ∈ P and i ∈ N , the notation (i) stands for the coalition in containing player i. The partition a ∈ P with a (i) = {i} for each i ∈ N , is called the atomistic partition. A pair (S; ) consisting of a non-empty coalition S ⊆ N and a partition ∈ P with S ∈ is called an embedded coalition. The set of all embedded coalitions is E = (S; ) ∈ 2 N ⧵ � × P | S ∈ .
For partition ∈ P and set of players S ⊂ N , we denote by
S = T ∩ S | T ∈ ∶ T ∩ S ≠ � the partition of S induced by . Further, we will often write {T 1 , … , T k , S } for {T 1 , … , T k , S 1 , … , S p } if S = {S 1 , … , S p }.
Simple games in partition function form A simple game in partition function form is a pair (N, v) , where the partition function v ∶ E → {0, 1} is such that v(N;{N}) = 1 . An embedded coalition (S; ) ∈ E is winning in the game (N, v) if and only if v(S; ) = 1 . Otherwise, it is called losing. We sometimes say that coalition S is winning in partition when (S; ) is a winning embedded coalition. The set of all winning embedded coalitions in the game v is denoted by E W (v) . Notice that this game form allows to model externalities of coalition formation. For instance, it can be that a coalition contained in two partitions and ′ is winning in but losing in ′ . Since the player set N is fixed, we often write a simple game in partition function form (N, v) by its partition function v. We use the following notion of inclusion, borrowed from Alonso-Meijide et al. (2017): For S � ; � , (S; ) ∈ E , we say that S ′ ; ′ is weakly included in (S; ) , denoted by
S � ; � ⊆ (S; ) , if (i) S ′ ⊆ S , and (ii) for each T ∈ ⧵{S} , there exists T � ∈ � with T ⊆ T ′ . A game v is then defined as monotonic if S � ; � , (S; ) ∈ E with S � ; � ⊆ (S; ) implies v S � ; � ≤ v(S; ) .
This monotonicity notion reflects (i) a nonnegative effect when a coalition grows, and (ii) an idea of negative externalities when players outside a coalition form larger coalitions. In particular, it implies that when a coalition is winning in a partition, then it is winning in every finer partition that contains this coalition. In other words, the idea expressed here is that in a finer partition there is 'less resistance' against the winning coalition. Clearly, a winning coalition can become losing in a coarser partition since other players forming coalitions might give a 'stronger resistance' against the winning coalition, or make the winning coalition more likely to 'break down'.
Plurality games and supporting weights We call a simple game in partition function form v a plurality game if (i) it is monotonic, and (ii) for each ∈ P we 1 3
Winning coalitions in plurality voting democracies have v(S; ) = 1 for at least one S ∈ . A plurality game v is decisive, if for each ∈ P we have that v(S; ) = 1 for exactly one S ∈ . A plurality game v is weighted, if there exists a weight vector w ∈ X N
+ ∶= w ∈ ℝ N + | Σ i∈N w i = 1 such that for each (S; ) ∈ E , (S; ) ∈ E W (v) implies w(S) ∶= Σ i∈S w i ≥ Σ i∈T w i ∶= w(T) for each T ∈ .
We call w a supporting weight vector for the plurality game. In words, a plurality game is weighted if there exist nonnegative weights for the players, such that if an embedded coalition is winning, then the sum of the weights of the players in the winning coalition is maximal among the coalitions in the corresponding partition.
The example given below illustrates that a decisive plurality game need not be weighted.
Example 1 Consider the following five-player decisive plurality game, where we slightly abuse notation and write for instance 12, 34, 5 to denote the partition
{{1, 2}, {3, 4}, {5}} with the coalition {1, 2} being winning in it, i.e., 12, 34, 5 means that v({1, 2};{{1, 2}, {3, 4}, {5}}) = 1.
Suppose that the above game were weighted with w ∈ X N + . We should then have w 4 + w 5 ≥ w 1 (due to 45, 1, 2, 3 ) and w 1 ≥ w 2 + w 4 (due to 24, 1, 3, 5 ) and thus, (by adding these two inequalities) w 5 ≥ w 2 . On the other hand, from w 1 ≥ w 2 + w 4 and w 2 + w 3 ≥ w 1 (by 23, 1, 45 ) follows w 3 ≥ w 4 . Finally, from w 1 ≥ w 2 + w 4 and w 2 + w 5 ≥ w 1 (by 25, 1, 3, 4 ) we have w 5 ≥ w 4 .
We also have w 3 + w 4 ≥ w 1 (by 34, 1, 2, 5 ), and it follows with w 1 ≥ w 2 + w 4 (see above) that w 3 ≥ w 2 . We have w 1 ≥ w 3 + w 5 (by 24, 1, 35 ) and thus, with w 3 + w 4 ≥ w 1 (by 34, 1, 2, 5 ), we have w 4 ≥ w 5 . Summarizing, so far we have
w 1 ≥ w 3 ≥ w 4 = w 5 ≥ w 2 .
Further, we have w 2 + w 5 ≥ w 3 + w 4 (by 25, 34, 1 ) and thus, with w 4 = w 5 and w 3 ≥ w 2 (see above), this gives w 2 = w 3 . Hence, w 1 ≥ w 3 = w 4 = w 5 = w 2 should hold.
Moreover, from w 2 + w 3 ≥ w 1 + w 4 (by 14, 23, 5 ) and w 2 = w 4 , follows w 3 ≥ w 1 . We conclude then that all weights should be equal. However, w 1 ≥ w 2 + w 4 (by 24, 1, 35 ) then implies that w 1 = w 2 = w 4 = 0 , which results in all weights being equal to zero. Thus, we have a contradiction to w ∈ X N + . ◻ 1 3
In view of the above example, in what follows we first concentrate on decisive plurality games with at most four players (Sect. 3), and then consider additional restrictions on games with an arbitrary number of players guaranteeing that these games are weighted (Sects. 4 and 5).
Games with at most four players
We start our analysis by considering decisive plurality games with at most four players. A first reason to start by considering four player games, is that these are very illustrative, and hint to conditions for games with more than four players to be weighted.
A second reason to start with four player games is that, also for standard simple games (simple games without externalities), four player games received considerable attention. For instance, von Neumann and Morgenstern (1944) show that all simple games with less than four players, all proper or strong simple games with less than five players, and all constant sum games with less than six players have voting representations, i.e., they can be represented by weights assigned to the players. However, there are constant-sum games with six players for which representative weights do not exist. In their study of rough weightedness of small games, Gvozdeva and Slinko (2011) show that all games with at most four players, all strong or proper games with at most five players, and all constant-sum games with at most six players are roughly weighted. Finally, it is worth mentioning that Shapley (1962) also explicitly analyses games with four or less players when discussing several properties of weighted majority games. In particular, he studies homogeneous games where the weights can be assigned in such a way that all minimal winning coalitions have the same weight.
For decisive games with at most four players, it turns out that the winning coalition in a partition is either one of maximal size, or the one containing the winner in the atomistic partition. In our results, for convenience and without loss of generality, we will often assume that player 1 is the winner in the atomistic partition of a decisive plurality game.
Proposition 1 Let v be a decisive plurality game with at most four players and
v({1}; a ) = 1. Then for each (S; ) ∈ E, (S; ) ∈ E W (v) implies either |S| ≥ |T| for each T ∈ , or S = (1).
The above conclusion is very helpful for the proof of our main result in this section.
Theorem 1 Every decisive plurality game with at most four players is weighted.
The proofs of Proposition 1 and Theorem 1 can be found in Appendix A.
3
Winning coalitions in plurality voting democracies
Majority games and symmetric players
Proposition 1 suggests that, if the winning coalition does not contain the winner in the atomistic partition, then it is only the size of a coalition that matters. For an arbitrary number of players, this fact invites us to consider the following type of majority games.
A plurality game v is a majority game if for all (S; ) ∈ E , every winning coalition is one of maximal size in the partition, i.e., (S; ) ∈ E W (v) implies |S| ≥ |T| for each T ∈ . It is easy to verify that w = 1 n , 1 n , … , 1 n is a supporting weight vector for every majority game.
Theorem 2 Every majority game is weighted.
Of special interest are majority games where the players exhibit some kind of symmetry. For simple games in partition function form, several symmetry notions can be defined. Two possibilities are the following. Given a plurality game v, we say that two players i, j ∈ N are 2
• switch-symmetric in v, if for each ∈ P with j ∉ (i) , ( (i); ) ∈ E W (v) implies that (i)⧵{i} ∪ {j} is winning in the partition (i)⧵{i} ∪ {j}, (j)⧵{j} ∪ {i}, N⧵( (i)∪ (j)) ; • grow-symmetric in v, if for each ∈ P with S, T ∈ and i, j ∉ S ∪ T , (S; ) ∈ E W (v) implies that S ∪ {i} is winning in the partition S ∪ {i}, T ∪ {j}, (i)⧵{i}, (j)⧵{j}, N⧵(S∪T∪ (i)∪ (j)) .
Notice that in the definitions above, we can switch the roles of players i and j. A plurality game v is switch-symmetric (respectively grow-symmetric) if all players 3 are switch-symmetric (respectively grow-symmetric) in v.
Each of these symmetry notions expresses an independence idea. Two players being switch-symmetric in a game requires that a winning coalition that contains one of them but not the other player, remains winning in the partition obtained by exchanging the places of these two players. On the other hand, grow-symmetry requires that for a winning and a losing coalition not containing both players, the winning coalition should remain winning if we add either one of these players to the winning, and the other to the losing coalition.
Our next result provides a characterization of switch-symmetric majority games and shows that, on the class of majority games, switch-symmetry implies grow-symmetry. 4
Proposition 2 A majority game is switch-symmetric if and only if all coalitions of maximal size in a partition are winning in it. Moreover, any switch-symmetric majority game is also grow-symmetric.
The proofs of this section can be found in Appendix B. It is worth mentioning that not every grow-symmetric majority game is also switch-symmetric, as illustrated by the following example.
Example 2 Consider the four-player decisive majority game v defined below.
Notice first that all players from N⧵{1} are grow-symmetric in v. To see this, take, for example, players 2 and 3, and a partition with two coalitions, say S and T, that (i) do not contain these two players ( 2, 3 ∉ S ∪ T ), and (ii) are such that one coalition, say S, is winning, and the other coalition T is losing in the partition. In fact, the only partition of this type is the atomistic partition with ({1}; a ) ∈ E W (v) . Since the coalition (1) containing player 1 is winning in any partition consisting of two two-player coalitions, irrespective of which player joins player 1, players 2 and 3 are grow-symmetric in v. A similar argument for player 4 shows that all players in N⧵{1} are grow-symmetric in v. To see that player 1 is also grow-symmetric with the other players in v, take player 1 and, for example, player 2. Notice that there is no partition with at least two coalitions that do not contain players 1 and 2, such that one of these two coalitions is winning. Therefore, players 1 and 2, and thus all players, are obviously grow-symmetric in v. However, from the fact that {1} is the unique winning coalition in the atomistic partition, it immediately follows that the game is not switch-symmetric. ◻
If we require a majority game to be switch-symmetric, then the equal weight vector used to prove Theorem 2, is the only one making the game weighted.
Proposition 3 If a weight vector supports a switch-symmetric majority game, then all weights are equal in this weight vector.
As one can see, this result is clearly driven by the fact that, in a switch-symmetric majority game, all largest coalitions in a partition are winning in it.
1234
12, 34 14, 2, 3 123, 4 12, 3, 4 23, 1, 4 124, 3 13, 24 24, 1, 3 134, 2 13, 2, 4 34, 1, 2 234, 1 14, 23 1, 2, 3, 4
Footnote 4 (continued) is an implication only in one direction. Examples 3 and 4 (in Sect. 5) show that, on the class of (n − 1) -symmetric games, the above two statements are independent.
3
Winning coalitions in plurality voting democracies
(n − 1)-symmetric games
We have defined decisive plurality games as games where there is exactly one winning coalition in each partition. Since this implies that there is a unique winner in the atomistic partition, no decisive plurality game is switch-symmetric. The 'most symmetric' a game can be is if all other players are symmetric. Therefore, we call a decisive plurality game (n − 1)switch-symmetric if all players but one (the winner in the atomistic partition) are switch-symmetric in the game. We study the impact of this restriction on the game's support. Due to the decisiveness of v, the following result is immediate.
Proposition 4
Let v be a decisive plurality game with at least three players and v({1}; a ) = 1. If v is (n − 1) -switch-symmetric, then all players in N⧵{1} are switch-symmetric in v.
Recall from Proposition 2, that for the case of majority games, grow-symmetry is implied by switch-symmetry. We define a decisive plurality game v to be (n − 1) -grow-symmetric if all players but one (the winner in the atomistic partition) are grow-symmetric in v, and show that (n − 1)-switch-symmetry and (n − 1)-growsymmetry are independent properties.
For this, let us first show that (n − 1)-switch-symmetry does not imply (n − 1) -grow-symmetry.
Example 3 Consider the six-player (n − 1)-switch-symmetric decisive game v with player set N = {1, i, j, k, , m} and coalition (1) winning in every partition ∈ P , except in the partitions of type {{1}, {i, j, k}, { , m}} , {{1}, {i, j, k}, { }, {m}} , {{1}, {i, j, k, }, {m}} , and {{1}, {i, j, k, , m}} where it is always the largest coalition in the partition that wins. The game is indeed (n − 1)-switch-symmetric since exchanging any two players from N⧵{1} does not change the size of the (corresponding) winning coalition in a partition. Suppose now that the game v is (n − 1) -grow-symmetric and consider for instance players and m. Then 1, ijk, m should imply that 1m, ijk which is in contradiction to the fact that {1, m} wins in the partition {{1, m}, {i, j, k, }}. ◻ Our next example shows that (n − 1)-grow-symmetry does not imply (n − 1) -switch-symmetry.
Example 4 Consider the five-player decisive majority game v on N = {1, 2, 3, 4, 5} where, for every partition ∈ P containing exactly two coalitions S and T of maximal size, we have that 1 ∈ S ∪ T implies ( (1); ) ∈ E W (v) , while 1 ∉ S ∪ T implies ( (2); ) ∈ E W (v) . Assume additionally that ({1}; a ) ∈ E W (v) . Obviously, players 3, 4 and 5 are grow-symmetric in v. To show that players 2 and 3 are also growsymmetric in v, notice that the only partitions containing two coalitions that do not contain either of these two players, such that one of these coalitions is winning, are 1, 45, 2, 3 ; 4, 15, 23 ; 4, 15, 2, 3 ; 5, 14, 23 ; 5, 14, 2, 3 ; and the atomistic partition. By majority, the winning coalition in these partitions stays winning after either player 2 or player 3 joins, showing that players 2 and 3, and thus all players in N⧵{1} are grow-symmetric in v; thus, the game is (n − 1)-grow-symmetric. Notice, however, that the game is not (n − 1)-switch-symmetric since, considering players 2 and 4, we
have that {2, 5} wins in {{2, 5}, {3, 4}, {1}} but {4, 5} loses in {{2, 3}, {4, 5}, {1}}.
In what follows, we call a decisive plurality game v • (n − 1)-symmetric, if all players but the winner in the atomistic partition are both switch-and grow-symmetric in v.
(n − 1)-symmetric decisive plurality games turn out to be weighted (Theorem 3). We show this by proving important implications (stated in Propositions 4-6) on the winning embedded coalitions in such games. In these results, we also explicitly state the type of (n − 1)-symmetry (i.e., (n − 1)-symmetry, (n − 1)-switchsymmetry, or (n − 1)-grow-symmetry) which is used in the corresponding proofs. All proofs of this section are provided in Appendix C.
We start by showing that in (n − 1)-switch-symmetric games, a winning coalition in a partition either contains the winner in the atomistic partition, or has strictly more players than any other coalition in the partition.
Proposition 5 Let v be a decisive and (n − 1) -switch-symmetric plurality game with
v({1}; a ) = 1. Then (S; ) ∈ E W (v) implies either S = (1) or |S| > |T| for each T ∈ ⧵{S, (1)}.
This proposition gives as a corollary that in a partition having two or more coalitions of maximal size, the winning coalition should contain the winner in the atomistic partition.
Corollary 1
Let v be a decisive and (n − 1) -switch-symmetric plurality game with v({1}; a ) = 1, and let ∈ P. If ⧵{ (1)} contains at least two largest coalitions, then ( (1); ) ∈ E W (v).
Define P 1 = { ∈ P | {1} ∈ } as the collection of those partitions that contain singleton {1} . In what follows, we make use of the power p 1 (v) of player 1 in a decisive plurality game v with v({1}; a ) = 1 , and define it as that is, it is the size of a largest coalition that loses against {1} in some partition from P 1 . We denote by P * the set of all partitions in which there is only one largest coalition that does not contain player 1. For ∈ P * , S stands for the largest coalition in ⧵{ (1)}.
Our next result explains the crucial role of p 1 (v) in determining the winning coalitions in the partitions contained in P * .
p 1 (v) = max ∈P 1 {t | ∃T ∈ with |T| = t and ({1}; ) ∈ E W (v)},
Proposition 6
Let v be a decisive and (n − 1) -symmetric plurality game with at least five players and v({1}; a ) = 1, and let ∈ P * . Then,
1. | | S | | ≥ p 1 (v) + | (1)| implies S ; ∈ E W (v); 2. | | S | | < p 1 (v) + | (1)| implies ( (1); ) ∈ E W (v) .
Corollary 1 and Proposition 6 allow for a complete characterization of the winning embedded coalitions in (n − 1)-symmetric games. For ∈ P , the coalition (1) is winning in when either ⧵{ (1)} contains at least two largest coalitions, or the unique largest coalition in ⧵{ (1)} is smaller than the threshold level p 1 (v) + | (1)| . Otherwise, it is the unique largest coalition which wins in the partition . Notice that, in the two cases where (1) is winning in , a coalition S ∈ with |S| > | (1)| may exist; so, it is not necessarily that a largest coalition wins in a partition.
The value p 1 (v) also plays an important role in the following main result on (n − 1)-symmetric plurality games, which gives explicit supporting weights for a decisive (n − 1)-symmetric plurality game.
Theorem 3
Let v be a decisive and (n − 1) -symmetric plurality game with v({1}; a ) = 1. Then v is weighted. In particular, the weight vector w defined by
w 1 = p 1 (v) p 1 (v)+|N|−1 and w i = 1 p 1 (v)+|N|−1 for each i ∈ N⧵{1} supports v.
The following example sheds light on how the results in this section lead to a plurality game being weighted.
Example 5 Consider a five-player decisive and (n − 1)-symmetric game v with v({1}; a ) = 1 . Notice first that it is impossible for the power of player 1 in the game v to be p 1 (v) = 1 . The reason is that p 1 (v) = 1 would imply that in the partition {{1}, {2, 3}, {4, 5}} either {2, 3} or {4, 5} should be winning, which is a contradiction to Corollary 1. So, p 1 (v) ∈ {2, 3, 4}.
If p 1 (v) = 4 , then ({1};{{1}, {2, 3, 4, 5}}) ∈ E W (v) and thus, by monotonicity, the winning coalition in any partition contains player 1. Clearly then, the vector w = 1 2 , 1 8 , 1 8 , 1 8 , 1 8 supports the game v. Suppose next that p 1 (v) = 3 holds. Since p 1 (v) + | (1)| ≥ 4 , we have, by Corollary 1 and Proposition 6, that (1) is winning in all partitions except in {{1}, {2, 3, 4, 5}} (where {2, 3, 4, 5} is winning). It can be checked that the vector w = 3 7 , 1 7 , 1 7 , 1 7 , 1 7 supports the game v. Finally, consider the case of p 1 (v) = 2 . Due to p 1 (v) + | (1)| ≥ 3 , we have, by Corollary 1 and Proposition 6, that (1) is winning in all partitions except in {{1}, {i, j, k}, { }} (where {i, j, k} is winning) and {{1}, {i, j, k, }} (where {i, j, k, } is winning). Clearly then, the weight vector w = 1 3 , 1 6 , 1 6 , 1 6 , 1 6 supports the game v.
Let us finally remark that decisive plurality games are always weighted in case there are no externalities. We say that a plurality game v is externality-free if v(S; ) = v(S; � ) holds for all S ⊆ N and for all partitions , � ∈ P such that S ∈ ∩ � .
Proposition 7 Every externality-free, decisive plurality game is weighted.
This proposition makes clear that problems with decisive plurality games being not weighted arise from the existence of (negative) externalities.
Related literature
In our study about the possibility of assigning weights to players in simple partition function form games, we have presented classes of games which do allow for a weighted representation. Moreover, the support of the corresponding games was shown to crucially shape the set of possible winning coalitions in a partition and thus, to shed light on which coalitions are most powerful in the presence of (negative) externalities. This naturally places our work within the strands of literature devoted to the numerical representation of standard simple games as well as to the study of general partition function form games.
The first strand of literature is mainly concerned with the question whether it is (always) possible to represent a standard simple game as a weighted majority game, that is, to find non-negative weights and a positive real number (quota) such that a coalition is winning in the simple game if and only if the combined weights of its members weakly exceeds the quota. As shown by von Neumann and Morgenstern (1944), not all simple games do allow for such weighted majority representation. The question of finding properties that characterize weighted games within the class of simple games was then naturally posted by Isbell (1956Isbell ( , (1958, and answered by Elgot (1961) and Taylor and Zwicker (1992). More precisely, Taylor and Zwicker (1992) characterize weighted voting in terms of the ways in which coalitions can gain or lose by trading among themselves, while Hammet et al. (1981) and Einy and Lehrer (1989) answer the above question by using results about separating convex sets. Peleg (1968) and Sudhölter (1996) show for the case of (constant-sum) weighted majority games that, correspondingly, the nucleolus and the modified nucleolus induce a representation of the game.
If a standard simple game does not allow for a weighted representation, then one might consider rough weights (cf. Taylor and Zwicker 1999). A simple game is roughly weighted if there exist weights and a threshold such that every coalition with the sum of its players' weights being above (respectively below) the threshold is winning (respectively losing). Again, not all standard simple games turn out to be roughly weighted. Gvozdeva and Slinko (2011) give necessary and sufficient conditions for a simple game to have rough weights. Related to the issue of non-weightedness of games, Carreras and Freixas (1996) and Freixas and Molinero (2009) investigate complete simple games being simple games behaving in some respects as weighted simple games.
All the papers cited above deal with standard simple games, while the focus of our work is on the weighted representation of plurality games which we defined as special type of simple games in partition function form. To the best of our knowledge, we are the first to study and provide conditions assuring weighted representations of such games.
The second strand of related literature deals with general partition function form games as initiated by the seminal works of Thrall (1962) and Thrall and Lucas (1963), and recently surveyed by Koczy (2018). Besides the investigation of general properties of such games (e.g., Lucas and Marcelli 1978;Maskin 2003;Hafalir 2007), there are two main issues of simultaneous interest in the corresponding works: which coalitions will form (cf. Ray 2007), and how the coalitional worths will be allocated to their members. For instance, de Clippel and Serrano (2008) separate the intrinsic payoffs from those due to the externalities of coalition formation. However, the main focus in that literature has been on extending the Shapley value for games with externalities (e.g., Myerson 1977;Gilboa and Lehrer 1991;Albizuri et al. 2005;Macho-Stadler et al. 2007, de Clippel andSerrano (2008);McQuillin (2009);Dutta et al. (2010); Grabisch and Funaki (2012)) and on extending different power indices to the class of simple games with externalities (e.g., Bolger 1986;Alonso-Meijide et al. 2017;Alvarez Mozos et al. 2017).
Although the study of power indices for simple partition function form games was out of the scope of this paper, we nevertheless used a notion of power (for the winner in the atomistic partition) in order to derive our results with respect to (n − 1) -symmetric plurality games. In follow-up research, we intend to generalize this notion as to apply to each player, to investigate in detail its properties, and to axiomatically characterize it.
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Appendix: Proofs from Sect. 3
Proof of Proposition 1 Notice first that for |N| ≤ 3 the assertion follows by {1} being winning in the atomistic partition and the monotonicity of v. Suppose now that |N| = 4 , i.e., N = {i, j, k, } , and let there exist (S; ) ∈ E with (S; ) ∈ E W (v) , 1 ∉ S , and |S| < |T| for some T ∈ . We show that this leads to a contradiction. Since there are only four players, we have |S| = 1 . Assume, w.l.o.g., that Finally, if |N| = 4 let us take N = {1, j, k, } . Since player 1 is winning in the atomistic partition, we have that if supporting weights w do exist, it must hold that w 1 ≥ w j , w k , w . We distinguish the following cases with respect to bipartitions containing coalitions of size 2.
Case 1 (Player 1 is in no winning coalition in a bipartition of this type (v) . Take the weight vector w with w 1 = w j = w k = 1 3 > 0 = w . It can be checked that w is a suitable weight vector, also irrespective of the winning coalitions in the partitions {{j, }, {1}, {k}} and Table 3.
(4.2) ({1};{{1}, {j, k, }}) ∈ E W (v) . Then, by monotonicity, in every partition the winning coalition is the one containing player 1. Take the weight vector w with w 1 = 1 > 0 = w j = w k = w . It can be checked that w is a suitable weight vector by just applying the monotonicity of the game, see Table 4. ◻
Proof of Proposition 2
We first show that if in a majority game v all coalitions of maximal size in a partition are winning in it, then the game is switch-symmetric. Suppose that, on the contrary, there were two players, i and j, who are not switch-symmetric in v. In such a case, there should be S ⊂ N with i ∈ S and j ∉ S such that (S; ) ∈ E W (v), but S⧵{i} ∪ {j} is not winning in the partition S⧵{i} ∪ {j}, (j)⧵{j} ∪ {i}, N⧵(S∪ (j)) . Since S and S⧵{i} ∪ {j} are of the same size, by v being a majority game, S is a largest coalition in , and thus S⧵{i} ∪ {j} is a largest coalition in S⧵{i} ∪ {j}, (j)⧵{j} ∪ {i}, N⧵(S∪ (j)) . By supposition, (S⧵{i}) ∪ {j} should be winning in that partition, which gives a contradiction.
Let us show next that if a majority game v is switch-symmetric, then all coalitions of maximal size in a partition are winning in it. Notice first that, by the definition of a majority game, a winning coalition in a partition should be of maximal size. We are left to show that all coalitions of maximal size are winning. For this, take (S; ) ∈ E W (v) and suppose that there is T ∈ ⧵{S} with |T| = |S| . Since the game is switch-symmetric, we can (repeatedly) replace all players from S⧵T by those from T⧵S and conclude that (T; ) ∈ E W (v) should hold.
Finally, to show that every switch-symmetric majority game is also growsymmetric, consider a switch-symmetric majority game v and let us show that the game is also grow-symmetric. Take i, j ∈ N , and let ∈ P with S, T ∈ be such that (S; ) ∈ E W (v) and i, j ∉ S ∪ T . Consider then the partition � = S ∪ {i}, T ∪ {j}, N⧵(S∪T∪{i,j}) . If S is the unique largest coalition in , then S ∪ {i} will be the unique largest coalition also in ′ . By the definition of a majority game, S ∪ {i}; � ∈ E W (v) . Suppose now that S and T are two largest coalitions in . In such a case, S ∪ {i} and T ∪ {j} will be two largest coalitions also in ′ . Since the majority game v is switch-symmetric, it follows from the above characterization of such games that all largest coalitions in ′ are winning in it, i.e., S ∪ {i}; � ∈ E W (v) . We conclude that the game v is grow-symmetric as well. ◻
Proof of Proposition 3
Suppose that a switch-symmetric majority game v is supported by a weight vector w. Consider the atomistic partition a and notice that, by Proposition 2, ({i}; a ) ∈ E W (v) holds for each i ∈ N . Since the game v is weighted, we have that the inequalities w k ≥ w and w ≥ w k hold for all k, ∈ N . We conclude then that all weights should be equal. ◻ Appendix: Proofs from Sect. 5
Proof of Proposition 4
Since {1} is the unique winning coalition in the atomistic partition, player 1 cannot be switch-symmetric in v with any other player due to the decisiveness of the game. By definition of (n − 1)-switch-symmetry of v, all players in N⧵{1} are switch-symmetric in v. ◻
(S; ) = ({i};{{i}, {j}, {k, }}) with i ≠ 1 holds. Then, by monotonicity of v, ({i};{{i}, {j}, {k}, { }}) ∈ E W (v) should hold as well, giving a contradiction to v being decisive and {i} ≠ {1} . By a similar argument, it can be shown that (S; ) ∈ E W (v) cannot be of the form {{i};{{i}, {j, k, }}} with i ≠ 1 . ◻ Proof of Theorem 1 Let v be a decisive plurality game defined on the player set N and assume that, w.l.o.g., player 1 wins in the atomistic partition. For |N| = 2 , the vector w = ( 1 2 , 1 2 ) supports the game v. If |N| = 3 , let us take N = {1, j, k} . By monotonicity of v, ({1, j};{{1, j}, {k}}) ∈ E W (v) and ({1, k};{{1, k}, {j}}) ∈ E W (v) holds. Take the weight vector w with w 1 = 1 2 and w j = w k = 1 4 . Notice that it supports v independently of the fact whether coalition {1} or coalition {j, k} is winning in the partition {{1}, {j, k}}.
). Let v be such that ({k, };{{1, j}, {k, }}) ∈ E W (v) , ({j, };{{1, k}, {j, }}) ∈ E W (v) , and ({j, k};{{1, }, {j, k}}) ∈ E W (v) . Take the vector w = ( 1 ) . Notice that it supports v for the winning coalitions in the above partitions. Further, by monotonicity of v, ({k, };{{1}, {j}, {k, }}) ∈ E W (v) , ({j, };{{1}, {k}, {j, }}) ∈ E W (v) , and ({j, k};{{1}, { }, {j, k}}) ∈ E W (v) . Clearly, w is a suitable weight vector for these embedded coalitions as well. Again by monotonicity of v, ({j, k, };{{1}, {j, k, }}) ∈ E W (v) and weight vector w still works here. We conclude that weight vector w indeed supports game v. Case 2 (Player 1 is in the winning coalition of one bipartition of this type). Let v be such that ({1, j};{{1, j}, {k, }}) ∈ E W (v) , ({j, };{{1, k}, {j, }}) ∈ E W (v) , and ({j, k};{{1, }, {j, k}}) ∈ E W (v) . The vector w with w 1 = w j = 1 3 > 1 6 = w k = w works for these winning embedded coalitions. It can be checked that w is a suitable weight vector also in the embedded coalitions (S;{{k, }, {1}, {j}}) , irrespective of the winning coalition S ∈ {{k, }, {1}, {j}} . The winning coalitions in the other partitions are determined by monotonicity of the game as displayed inTable 1. In this table, the single underlined coalitions are winning in the corresponding partitions by assumption, and the double underlined coalitions are winning by monotonicity. A partition with no underlined coalition displays the fact that the assumptions do not exactly determine which coalition is winning.Case 3 (Player 1 is in the winning coalition of two bipartitions of this type). Let v be such that ({1, j};{{1, j}, {k, }}) ∈ E W (v) , ({1, k};{{1, k}, {j, }}) ∈ E W (v) , and ({j, k};{{1, }, {j, k}}) ∈ E W4 , 1
4 , 1
4 , 1
4
Table 1
1Proof of Theorem 1, Winning coalitions in plurality voting democracies {{k, }, {1}, {j}} . The winning coalitions in the other partitions are determined by monotonicity of the game, seeTable 2.Case 4 (Player 1 is in the winning coalition of all (three) bipartitions of this type).Let v be such that ({1, j};{{1, j}, {k, }}) ∈ E W (v) , ({1, k};{{1, k}, {j, }}) ∈ E W (v) , and ({1, };{{1, }, {j, k}}) ∈ E W (v). Two sub-cases have to be considered:(4.1) ({j, k, };{{1}, {j, k, }}) ∈ E W (v). Take the vector w with w 1 = 2 5 and w j = w k = w = 1 5 . It can be checked that w is a suitable weight vector, also in the embedded coalitions with partitions {{j, k}, {1}, { }} , {{j, }, {1}, {k}} , and {{k, }, {1}, {j}} , irrespective of the winning coalitions in these partitions; notice that, due to Proposition 1, there is no winning singleton in these partitions which differs from {1} . The winners in the other partitions are determined by monotonicity of the game, seeCase 2
1jk
1j, k
1, , jk
1k , j
1j, k,
1k, j,
1j , k
1k, j
1 , j, k
1jk,
1, k, j
1, j, k
jk , 1
1 , jk
1, j, k,
Table 2
2Proof of Theorem 1,Case 3
1jk
1j, k
1, , jk
1k , j
1j, k,
1k, j,
1j , k
1k, j
1 , j, k
1jk,
1, k, j
1, j, k
jk , 1
1 , jk
1, j, k,
Table 3 Proof
3of Theorem 1,
Case 4.1
1jk
1j, k
1, , jk
1k , j
1j, k,
1k, j,
1j , k
1k, j
1 , j, k
1jk,
1, k, j
1, j, k
jk , 1
1 , jk
1, j, k,
Table 4
4Proof of Theorem 1, Appendix: Proofs from Sect. 4Case 4.2
1jk
1j, k
1, , jk
1k , j
1j, k,
1k, j,
1j , k
1k, j
1 , j, k
1jk,
1, k, j
1, j, k
jk , 1
1 , jk
1, j, k,
In this paper, we focus on negative externalities for the reason explained in the text, but notice that there can also be situations of positive externalities, where coalition formation of other parties strengthens the position of a party. Such situations are not considered here.
For notational convenience, we are not quite precise here since, in case (i)⧵{i} or (j)⧵{j} is the empty set, then this set should be deleted from the partition. 3 This means that each pair of players is switch-symmetric (respectively grow-symmetric).4 We use symmetry among players in order to introduce classes of decisive plurality games, i.e., we impose these conditions on games. Although it is worthwhile to study properties of the symmetry relation itself, for example to see if these notions define equivalence classes, this is beyond the goal of this paper. Proposition 2, in combination with Example 2 shows that, on the class of majority games, there
Recall that, by Theorem 1, every decisive plurality game with at most four players is weighted. What we show in Case A is that every decisive and (n − 1)-symmetric plurality game with at most four players is supported by the weight vector w specified above.
Proof of Proposition 5Take (S; ) ∈ E W (v) and suppose that S ≠ (1) . Notice that |S| > 1 should hold; otherwise, by monotonicity, the single player in S should be winning in the atomistic partition, which is in contradiction to the decisiveness of v and {1} being the winner in the atomistic partition. We now have to show that |T| ≥ |S| for some T ∈ ⧵{S, (1)} , leads to a contradiction.Suppose that such a coalition T exists. Take T ′ ⊆ T with |T � | = |S| . Since the game is (n − 1)-switch-symmetric (and all players in S ∪ T are switch-symmetric in v since both coalitions do not contain player 1), we can (repeatedly) replace all players from S by those from T ′ and conclude that T � ; T � , S ∪ (T⧵T � ), N⧵(S∪T) ∈ E W (v) . By monotonicity, (T; T, S, N⧵(S∪T) ) = (T; ) ∈ E W (v) should hold as well, which is a contradiction to (S; ) ∈ E W (v) and the decisiveness of the game. ◻The following two lemmas will be used in the proofs of Proposition 6 and Theorem 3.Lemma 1Let v be a decisive and (n − 1) -switch-symmetric plurality game with at least five players and v({1}; a ) = 1. should hold. If |N| is even, one can take the partition � = {1}, S � , T � , {i} with |S � | = |T � | = |N|−2 2 as to conclude again from Corollary 1 that p v (1) ≥ |N|−2 2 must be the case. ◻Lemma 2Let v be a decisive and (n − 1) -switch-symmetric plurality game with at least five players and v({1}; a ) = 1, and let ∈ P * . Thenwhere the second inequality follows from Lemma 1. Since 1 ∉ S ∪ S , we have a contradiction. If |N| is even, then | | S | | + |S| > 2p 1 (v) ≥ |N| − 2 where the second inequality again follows from Lemma 1.holds with the first inequality following from ∈ P * and the second from |S| > p 1 (v) . We have then | | S | | + |S| > |N| , which leads to a contradiction. ◻Proof of Proposition 6We consider the two assertions separately.(we have a contradiction to the definition of p 1 (v) . So, ({1}; � ) ∉ E W (v) . By Lemma 2, each coalition in N⧵( (1)∪S ) is of size at most p 1 (v) , implying that S ′ is the unique largest coalition in ′ . We then have, by Proposition 5, that. In view of Proposition 5, it is sufficient to show that S ; ∈ E W (v) leads to a contradiction. For this, notice that, by the monotonicity of v, S would be winning in the, and let �� = {S} ∪ {{i}} i∈N⧵S be the partition containing S with all other players being single. By monotonicity of v, {1}; �� ∈ E W (v) since {1} is winning in ′ . Due to 1 ∉ T ⊇ S and 1 ∉ S , the players in S ∪ S are switch-symmetric in v, and we can exchange the players from S by those from S (in the partition * ) as to conclude that S should be the winning coalition in ′′ . This gives a contradiction to {1}; �� ∈ E W (v) and the decisiveness of v. Therefore, (S ; ) ∉ E W (v) , and by Proposition 5, ( (1); ) ∈ E W (v).(, and notice that, by Lemma 2, each coalition in N⧵( (1)∪S ) is of size at most p 1 (v) . The latter fact implies that the winning coalition in ′ is either {1} (if there is a coalition in N⧵( (1)∪S ) of size p 1 (v) and by Corollary 1) or S ′ (if the size of each coalition in N⧵( (1)∪S ) is less than p 1 (v) and by Proposition 5). Let us now show that S � ; � ∈ E W (v) leads to a contradiction and thus, {1}; � ∈ E W (v) should follow.To get to a contradiction, suppose that (S � ; � ) ∈ E W (v) . Consider the partition �� = {1}, S � ∪ {{r}} r∈N⧵({1}∪S � ) and notice that, by the monotonicity of v, S � ; �� ∈ E W (v) . Let ′′′ be a partition with respect to which p v (1) was calculated, that is, there exists T ∈ ��� with |T| = p v (1) and {1}; ��� ∈ E W (v) . By monotonicity of v, {1}; iv ∈ E W (v) , where iv is the partition containing T with everyone else being single. Since | | S � | | = |T| = p v (1) , and all players in S � ∪ T are switchsymmetric in v, in the partition ′′ , we can replace all players from S ′ by those from T as to conclude that T should be winning in the partition containing it with everyone else being single. Thus, we have a contradiction to {1}; iv ∈ E W (v) and henceit follows from monotonicity and applying grow-symmetry | | S ⧵S ′ | | -times that Q * is winning in the partition * = Q * , S , N⧵( (1)∪S ) ∪ {{r}} r∈ (1)⧵Q * , where Q * contains player 1 and | | S ⧵S ′ | | other members of (1) . By monotonicity of v, ( (1); ) ∈ E W (v) . ◻Proof of Theorem 3Let v be a decisive and (n − 1)-symmetric plurality game defined on the player set N, and let v({1}; a ) = 1 . Take the weight vector w ∈ X N + defined byIn order to show that w is supporting the game v, we explicitly consider the two cases in which N contains either at most four players (Case A) 5 or at least five players (Case B).Case. The corresponding weight vectors supporting the games are then 3 6 , 1 6 , 1 6 , 1 6 and 2 5 , 1 5 , 1 5 , 1 5 .Case B ( |N| ≥ 5 ): Take ∈ P and notice that in view of Proposition 5 and by the fact that each player in N⧵{1} has the same weight according to w, it suffices to compare the weights of the coalitions (1) and a largest coalition in ⧵{ (1)} . There are only two possible cases for the partition : either ∈ P * or ∈ P⧵P * .Case B.1 ( ∈ P * ): If p 1 (v) + | (1)| > | | S | | , then ( (1); ) ∈ E W (v) follows from Proposition 6. We have thenwhere the inequality holds due to Lemma 1.(B2.4) ( |N| is odd and |N⧵ (1)| is even): We have in this case |S| ≤ |N|−| (1)| 2 and thus, w(S) ≤ |N|−| (1)| 2(p 1 (v)+|N|−1) . On the other hand,where the inequality holds due to Lemma 1. In this case, |N| − 3 + 2| (1)| ≥ |N| − | (1)| holds, and thus, w( (1)) ≥ w(S) . ◻Proof of Proposition 7Consider an externality-free decisive plurality game v and suppose that, w.l.o.g., player 1 is the unique winner in the atomistic partition. Since there are no externalities, we have that {1} is the unique winning coalition in any partition containing {1} . But then, by monotonicity of v, (1) is winning in every partition ∈ P . Taking the vector w with w 1 = 1 and w i = 0 for each i ∈ N⧵{1} then shows that v is weighted. ◻ w( (1)) = p 1 (v) + | (1)| − 1 p 1 (v) + |N| − 1 ≥ |N|−2 2 + | (1)| − 1Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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1 3 Keefer and Khemani 2005;Muñoz 2014) and in which elections are implemented by authoritarian regimes (e.g., Blaydes 2011;Frye et al. 2019). Village elections in China provide a valuable window on the dynamics of vote buying in these contexts. 1 Employing both an in-depth case study and an original, panel survey to provide new, systematic measures of vote buying and rents, we develop and test the following hypothesis: the availability of non-competitive rents accessible by elected officials explains the variation in the incidence of vote buying in local elections. We find that the lure of rents, mainly from government takings of village land, is a key driver of vote buying by non-partisan candidates for the office of village leader. Our causal identification strategy exploits the timing of land takings and the exogenous nature of formal land takings authorized in state land-use plans at higher administrative levels to test the vote-buying-as-rent-seeking hypothesis.
Our findings build on and extend the existing literature on comparative vote buying. Scholars note that more personalized competition is less likely to be programmatic and more likely to rely on the exchange of individual benefits (Kitschelt and Wilkinson 2007). In non-partisan competition, individual candidates' promises to voters about future benefits lack the institutional commitment mechanisms that political parties provide, making pre-election vote buying an important electoral strategy (Hanusch and Keefer 2013). We examine rent-generating state interventions at the local level and make a theoretical contribution by showing that candidates invest personal resources to buy votes as an individual investment strategy repaid by the capture of rents once in office. Our study also makes an empirical contribution by providing novel and systematic evidence on how land takings-a common phenomenon in the developing world-generate rents and drive vote buying in grassroots elections, where parties do not structure or finance competition and where government intervention in the local economy varies across locales. In testing hypotheses involving rent seeking and vote buying, one challenge is measurement (Lehoucq 2003;Kramon 2016). Existing work examining the link between rent seeking and vote buying relies on anecdotal accounts or formal models. 2 Combining an in-depth case study with an original multi-wave survey that covers 1,240 household in 62 villages allows us to identify a scalable measure of rents and develop a unique measure of vote buying based on household reports.
While most studies of vote buying focus on multi-party elections, the prominence of vote buying in non-party elections has important implications for our understanding of authoritarianism. Existing studies demonstrate the informational value of vote buying to voters in democratic contexts (Kramon 2016;Muñoz 2014). This study highlights how successful vote-buying candidates reveal information to the state about their social and financial capacity to command support from the local community. Authoritarian regimes can use this information about local notables to decide whom to allow into the rent-sharing coalition and how to coopt these local elites for regime purposes (Blaydes 2011). Fieldwork evidence shows that the Chinese Communist Party (CCP) has tapped successful, non-partisan vote-buying candidates after their election to take on party roles within the village.
The paper proceeds as follows. The next section grounds the analysis in the comparative literature on vote buying. The following sections detail our argument that vote buying is best explained as a means of capturing rents and provide background on the institutional context in which rents are generated. We then present an in-depth case study, which allows us to identify a scalable measure of rent-seeking opportunities and to generate specific, testable hypotheses about vote buying. The remaining sections present the data and findings, discuss implications of the study, and conclude with an agenda for future research.
Vote Buying in the Comparative Literature
Vote buying is a particular form of clientelism, in which voters receive a non-programmatic benefit-like cash or gifts-in exchange for a future vote for a particular candidate (Hicken 2011,292). Vote buying is prevalent in elections across globe. Roughly half of respondents in the sixth wave (2010)(2011)(2012)(2013)(2014) of the World Values Survey report that "voters were bribed very or fairly often in their country's elections"; in light of its prevalence, the question of "why politicians undertake vote buying in the first place" has begun to receive more scholarly attention (Keefer and Vlaicu 2017,775). While vote buying is typically analyzed as a political strategy to mobilize voters in multi-party competition (e.g., Diaz-Cayeros et al. 2016;Greene 2010;Lust-Okar 2006;Magaloni 2008;Stokes et al. 2013), it is also a common phenomenon in contexts where electoral competitions do not develop along partisan lines, such as local elections in one-party regimes (e.g., Zhao 2018). Theoretical analyses suggest that vote buying is more likely to take place when competition is candidatecentered rather than party-centered (Hicken 2007) and when the role of parties is weak or absent (Keefer and Vlaicu 2017;Muñoz 2014). Voters are less likely to trust candidates' policy promises that yield benefits only after the election. When party organizations that could discipline candidates are not involved in the elections, individual candidates' policy promises are less credible. Candidates instead choose to deliver pre-election benefits (i.e., vote buying) to mitigate the commitment problem (Hanusch and Keefer 2013). In an empirical analysis, Heath and Tillin (2018) find that when governance institutions are weak and inefficient, voters prefer benefits from direct, clientelistic exchanges (e.g., vote buying) over promises of uncertain programmatic rewards.
Elections and vote buying, where it occurs, can distort citizens' wishes but provide useful information to autocrats. Focusing on China, Martinez-Bravo et al. (forthcoming) show that local, non-partisan elections in autocratic regimes delegate selection and monitoring of village officials to citizens. They argue that rulers introduce elections when they lack information about local officials. However, they do not address the existence of vote buying or how it distorts the information that 1 3 regimes receive from elections. In describing parliamentary elections in Mubarak's Egypt, Blaydes instead suggests that vote buying in elections "works as a kind of market mechanism for the selection of individuals who will be allowed to extract state rents (2011,49)." Local elites who enter and win in the electoral marketplace reveal information to the regime about whom to coopt. Thus, vote buying serves as a mechanism to select local elites to be drawn into the rent-sharing coalition. As important and prevalent as vote buying is, the empirical evidence on the relationship between rent seeking and vote buying in non-partisan, authoritarian elections remains scant.
Vote Buying as Rent Seeking
We hypothesize that the incidence of vote buying in non-partisan elections is patterned on the availability of rents. We build our argument on the comparative literature that highlights the prominence of rents in shaping vote buying (Diaz-Cayeros et al. 2016;Keefer and Vlaicu 2017;Kitschelt 2000). Chandra (2007), in her conceptual overview of vote buying, begins by establishing the existence of rents, which stem from the state's "monopolistic control" over valued resources. Officials can sell resources for artificially high prices, generating non-competitive rents (Bates 1987;Buchanan et al. 1980). Thus, where the state controls significant resources, political control of the state is a valuable prize.
Identifying rents presents both a theoretical and empirical challenge. In his study of clientelism, Kitschelt (2000,862) is critical of studies that conceptualize rentseeking opportunities in terms of macro-level trade policies or the overall size of the public sector, since they fail to specify micro foundations or allow for sub-national variation. Hellman associates the existence of rents and rent seeking with partial reform in post-Communist transitions. "Partial reforms were expected to generate rent-seeking opportunities arising from price differentials between the liberalized sectors of the economy and those still coordinated by nonmarket mechanisms … these arbitrage opportunities have generated rents to those in a position to take advantage of these market distortions (Hellman 1998,219)." In the next section on China's institutional context, we establish the existence of non-competitive rents associated with village leadership positions in China.
Having established the existence of rents, scholars analyze how political actors seek to access them. 3 While bribery of regulators is a paradigmatic example of rent seeking (Aidt 2016), this paper highlights buying votes as an important pathway to controlling lucrative rents. Posner describes how shifting monopoly profit to officials "draws real resources into the activity of becoming the official (1975,812)." Politicians' access to rents rewards election winners with personal benefits. According to Aidt, "Controlling these rents is a contestable prize (2016,150)," and individuals will seek positions in government in order to gain access to them. Elections in authoritarian regimes are widely understood as a mechanism for sharing rents or spoils with elites who have the potential to threaten regime survival (Gandhi 2008).
Recent literature suggestively links vote buying and rent seeking. Blaydes argues that Egypt's non-partisan "rent-seeking elite" buy votes with cash or goods in a quest to win seats in parliament in order to access rents-not policy influence or party representation (2011,8). As she notes, "parliamentary hopefuls spend millions to reap billions (10)." High spending on vote buying is a rational choice, since elections in Egypt are a "sorting mechanism" for "access to state largesse," and "those who spend the most on campaigning are most likely to prevail (54)." While this account reflects comments from Egyptian informants, the study offers no test of the intuition. Zhao (2018), in a case study of village elections in China, similarly relates the availability of rents to vote buying on the part of candidates for local office. Keefer and Vlaicu (2017) develop a formal voting model in which parties use various strategies to win votes. They suggest that the larger the available rents, the greater the incentive to buy votes in order to control those rents. These studies derive their conclusions from anecdotes (Blaydes 2011;Ahram 2012), case studies (Zhao 2018), and theoretical models (Keefer and Vlaicu 2017).
A direct challenge in systematically testing the vote-buying-as-rent-seeking hypothesis is the measurement of rent-seeking opportunities and vote-buying activities; both remain largely hidden in most electoral contexts. We use an in-depth case study to reveal the nature of rent seeking and vote buying. Then, employing original survey data, we provide a quantitative test of the relationship between rent seeking and vote buying in China's village elections. Our measures of rents address Kitschelt's (2000) call for specifying micro foundations and accounting for subnational variations in rents in the context of elections.
Institutional Context
This section introduces the relevant institutions in which rents are generated and elections are contested. In contemporary rural China, rent seeking occurs overwhelmingly in the context of formal land takings, in which the state exercises a statutory monopoly over the sale of rural land into the urban market, making available non-competitive rents to state authorities, including village leaders (Zhao 2018). 4 The county land management bureau requisitions land from village collectives at below-market value, calculated in terms of the agricultural use-value of the land, and sells it to commercial developers at higher, market prices, making the rents quite sizeable (Chen and Kung 2016). Indeed, land takings have become a significant source of revenue for county governments (Su and Tao 2017). The difference between the price received from developers and the compensation paid to farmers, minus any public investment in basic infrastructure, represents the rent the state captures. Village leaders, who manage compensation funds for the village, share in these land rents by under-compensating rural households and by controlling compensation paid for land collectively owned and operated by the village.
Land takings are part of a top-down planning process. Since the 1990s, the Ministry of Land and Resources has assigned "annual land requisition quotas to each locality in the country (Su et al. 2019,761)." As concerns about loss of arable land have mounted, the ministry has established even tighter guidelines on land takings (Brandt et al. 2017(Brandt et al. ,1041. Regulations protecting arable land place strict limits on the area of farmland that may be converted into construction land in any given year (World Bank and Development Research Center 2014,113). Land-use plans received by the county are highly detailed, and "alteration [is] very rare (Su et al. 2019,762)." Ma and Mu (2020, 4) and Su et al. (2019,762) conclude that village leaders have no influence on formal state decisions to requisition land. Only after a decision is made, officials from the county, township, and village hold joint meetings to announce the decision and to present information to villagers regarding the purpose and size of the taking as well as the basis on which households are to be compensated (Brandt et al. 2017). Compensation funds, to be paid by the developer (the state in the case of takings for rail and highway projects, e.g.), reach the village via the local government late in the course of the project, since funds are generated only after land is taken, cleared, and sold through auction or negotiation by the state to the developer.
A related source of rents for village officials comes from illegal, informal sales of farmland by the village. Informal sales occur outside the purview of local government agencies that regulate the taking of village land for lucrative non-agricultural uses. Such informal sales are one response to state limits on rural-to-urban land conversion intended to protect arable land. In a survey designed to enumerate all changes to rural land holdings in a two-province sample between 1996 and 2011, Brandt et al. (2017Brandt et al. ( ,1036 find that only 12 percent of land takings recorded at the village level were initiated informally, i.e., by the township or village.
Village-run enterprises have historically been a source of rents, stemming from privileged access to capital from local state-run banks and credit cooperatives and soft tax obligations (Hu 2005;Oi and Rozelle 2000;Takeuchi 2013). 5 However, Whiting (2001,289-295) shows that, following the banking and fiscal reforms of the 1990s, township-and village-run enterprises (TVEs) struggled to compete and survive. "TVEs, instead of being a tremendous asset, turned into a liability (Su and Tao 2017,240)."
Leaders tasked with governing villages in China are selected through popular election for three-year terms. Village elections take place under the auspices of the 1998 Organic Law of Villagers' Committees and select the village head and members of the village leadership committee. 6 The entire village constitutes the electoral district, and any adult whose household registration is in the village may stand for election and vote. Elections are directly managed by election steering committees, which are themselves selected by popular bodies, including village assemblies, village groups, or village representative assemblies. According to O'Brien and Han, election steering committees are quite "independent [from the Chinese Communist Party] and responsive [to villagers], even though committees in most locations continue to be presided over by village party secretaries (2009,." Moreover, under rules in force in most provinces of China, "[CCP] control over the nominating process has been gradually loosened," and every voter is entitled to nominate candidates (364). Electoral rules mandate that there must be at least two candidates for village leader. Elections are candidate-centered and self-funded; party affiliation does not appear on the ballot, and the party does not finance campaigns of candidates who are party members. Indeed, CCP members may compete against each other. Most candidates campaign by making personal appeals in speeches before village assemblies and during visits to voters' homes.
In an intensive study of one county in Yunnan, Landry et al. (2010) show that the ruling party does not structure competition in village elections. They "confidently conclude that in practice both party and nonparty members were allowed [to] run in the …village elections and that nonparty candidates emerged from strata of villagers that were unlikely to be incorporated in the formal, non-electoral political institutions that dominated village life before the introduction of elections (2010,(13)(14)." Kennedy further argues that vote buying is unlikely to occur in elections where competition is absent or manipulated by the local party-state. "[Vote buying] is a problem that exists only because of reduced township interference and a fairer election process (2009,394)," i.e., absence of direct interference by the CCP in the selection of candidates and electoral choices of voters.
Scholars highlight the ambiguity of the 1998 Organic Law with respect to the legality of vote buying (Kennedy,(620)(621). The law does not mention vote buying (贿选); it states that the occurrence of bribery (贿赂) may invalidate an election, without defining what bribery entails. A 2009 central party-state notice acknowledges this problem and calls for "further clarification of the bounds of vote buying ( 进一步明确贿选的界限)" without final resolution. 7
Case-Study Evidence on Village Elections
Working within this institutional context, we combine an in-depth case study with an original survey in order to identify scalable measures of key concepts-rents and vote buying-and to generate specific, testable hypotheses relating rent seeking and vote buying. 8 The experience of villages in one satellite county outside a metropolis in an eastern coastal province of China is illustrative. In 2013, one of the authors conducted more than seventy in-depth interviews, including elected village leaders, unsuccessful candidates, villagers (voters), and township officials as well as informal discussions with county officials, focusing on village governance in more than a dozen villages in the county. 9
Land Rents
Land development in Baijia Village (a pseudonym) was spurred in 2005 by the county's decision to site the new campus of a highly regarded secondary school on land near the village. The county government's economic development plan, designed to attract outside investment to the county, included mixed residential and commercial development of roughly 500 mu 10 of village land in the vicinity of the new school, which would be the anchor for a new, planned community. In the case of Baijia Village, urban-planning regulations necessitated dividing the entire 500-mu project into multiple, smaller sub-developments to be included in consecutive annual land-use plans in order to comply with the letter-if not the spirit-of provincial regulations limiting the pace of urbanization.
Three levels of local authorities-the county, township, and village 11 -shared in the lucrative rents generated by the series of land takings implemented over the following years. The county government controlled the lion's share of rent, while the township and village received smaller shares. Although the amount the developer actually paid to the county for the land was undisclosed, compensation to be paid to Baijia villagers was publicly announced and set at 18,000 yuan per mu. This amount reflects the average value of agricultural output on the land over the preceding three years (1,000 yuan), calculated over the number of years remaining on farm households' 30-year land-use contracts with the village (18 years, in this case). Interviews reveal that the village leadership received at least 21,000 yuan per mu, representing a direct rent to the village leadership of 3,000 yuan per mu. Thus, the village leader would have access to approximately 1.5 million yuan in rents at the village level over the course of the 500-mu project as a result of the lower compensation to villagers.
A related source of rent came from compensation paid directly to the village for collective land under village management, including land previously used for village offices, plazas, and roads as well as forest land managed directly by the village. Compensation for this land, roughly 50 mu at 21,000 yuan per mu, totaled approximately one million yuan and was paid to the village and managed by the village leader but not distributed among village households.
The village leader's role in negotiations between the government and real estate developers, on the one hand, and members of the village collective, on the other, presented further opportunities for generating rents in the process of the land takings. Villagers who lost housing in addition to arable land were slated to receive Studies in Comparative International Development (2022) 57:337-360 new housing provided by the developer based on a per-meter exchange negotiated between the developer and the village leader, acting on behalf of village households. For example, an exchange rate of 1:1.5 meant that 100 square meters of villagers' old housing could be exchanged in the future for 150 square meters of new housing in the new residential community. However, in return for side payments from the developer, the village leader reportedly lowered the negotiated rate. In 2009, he agreed with the developer to an exchange rate of 1:1.25, while other affected villages had settled on a rate of at least 1:1.3. Villagers believed that the leader was willing to accept a lower exchange rate because he had received more than two million yuan in side payments from the developer.
In sum, interviews suggest that the leader of Baijia Village could control nearly five million yuan from the development project from these three sources alone. Land takings represent the greatest opportunity for a village official to access rents.
Vote Buying as Rent Seeking
Prior to the advent of land takings, elections in Baijia Village had been a sleepy affair. However, the 2008 election for village leader saw unprecedented competition, with six candidates contesting the election, along with the introduction of vote buying to the village. Two leading candidates emerged. One was the incumbent village leader, who reportedly offered targeted voters 600 yuan (about 86 US dollars) each for their votes. The leader's wife's successful retail business in the township provided funds to buy votes. His main challenger was the local owner of a construction company who had never before stood for election. The owner operated his construction company out of the county seat, but because his household registration remained in the village, he was eligible to compete for the position of village leader. Through paid vote brokers, well-connected and respected members of the village, he offered 800 yuan (about 116 US dollars) to targeted voters in order to counter the appeal of the incumbent. This sum is equivalent to approximately ten percent of an individual's average annual income (8,000 yuan) at that time. 12 The remaining candidates, including a middle school teacher who reportedly borrowed money to buy votes, were quickly outbid and abandoned any attempt at vote buying. As one villager commented, "Nobody in our village would spend money on running for office in the past… But since we've had land takings, people have become crazy spending money on the election. They know that no matter how much money they invest, they can easily recoup it from the land takings if they win the election." 13 Another villager made a similar assessment: "What could make an owner of a construction company give up his comfortable life in the county and move back to our poor village? It can only be because he expected to earn more money from his position." 14
Vote-Buying Process
Vote-buying candidates took a number of steps to try to ensure electoral success. They targeted swing voters, recognizing that relatives and allies of competing candidates were unlikely to be swayed by payments of cash from other candidates. Swing voters targeted in the vote buying schemes reportedly cast their votes for the highest bidder. 15 Vote-buying candidates and their brokers used a variety of mechanisms to monitor vote choice. For example, brokers instructed recipients of cash for votes to include their own names as write-in candidates for the less important position of village committee member. These voters' names would be read in the public vote count but would not be elected with a single vote. In other cases, brokers instructed recipients of cash for votes to take pictures of their completed ballots with their cellphones and to send them to the brokers. 16 The construction company owner took other steps to try to ensure electoral success. He offered bribes of gift cards and expensive liquor to township officials overseeing the election to look the other way as vote buying occurred and to send cooperative officials to monitor the election itself. Interviews suggest that these actions inhibited township officials from reporting vote buying to the county civil affairs bureau, the government agency responsible for overseeing village elections. Rumors repeated by villagers in interviews suggested that the construction company owner also sought to curry favor with the deputy county leader overseeing elections by providing the finish work on his house for free. At the same time, these reports also indicate that township and county officials were aware of vote buying in the village election.
Aftermath of Vote Buying
In the aftermath of vote buying, competition in the 2008 village election dwindled to two effective candidates, and victory went to the highest bidder-the construction company owner. After his victory in the village-wide election, the new village head was recruited by the local party apparatus to serve concurrently as village party secretary. 17 Finally, once land was formally requisitioned for the mixed residential and commercial development, the new village leader controlled the rents from the taking of land. As chairman of the village committee, his signature was required to implement the land taking and to access compensation funds deposited in the village account. As detailed above, the village leader controlled up to five million yuan (three quarters of a million US dollars) in rents through the land taking. The new village head's actions were not without controversy. Rumors circulated among villagers about under-compensation for their lost land. A small group of villagers-initially 5-6 people, ultimately growing to 15-mobilized to protest the low compensation by petitioning township and county authorities. They sought both higher compensation for land lost to urban development and dismissal of the elected village leader. However, neither township nor county officials took any action against the village leader. In the conclusion, we return to the issue of accountability in the context of vote buying in the agenda for future research.
Hypothesis Generation
The case of Baijia Village provides the basis for the following testable hypothesis. Specifically, we hypothesize that availability of rents is associated with the occurrence of vote buying in non-partisan, village elections. Candidates buy votes in order to gain access to rents controlled by the state. The case study also highlights the political context: in the absence of parties to structure and finance political competition, vote buying by candidates is a calculated, individual investment to capture rents.
Data and Identification Strategy
Survey
We test this hypothesis with an original dataset. The dataset includes two waves of a multi-wave panel survey; the relevant waves were conducted in 2008 and 2014, in which two of the authors directly participated. The 2008 wave is based on a sample of 2,000 households in 100 villages selected from five provinces: Jilin, Hebei, Shaanxi, Sichuan, and Jiangsu. 18 Within each of the five provinces is a stratified random sample; five sample counties were randomly selected-one from each income quintile. Within each of the 25 counties, two townships were selected-one each from the top and bottom halves of the income distribution. Within each of the 50 townships, two villages were randomly selected for a total of 100 villages. In each village, 20 randomly selected households were interviewed, along with village and small group leaders. 19 The 2014 wave of the panel survey is based on a 60-village sub-sample of the original panel. To select the sub-sample, the counties from the high-and low-income quintiles were retained, and a third county was randomly selected from among the three remaining sample counties in each province. Two additional sample villages were included, bringing the total number of villages to 62. 20 The present study employs the 62-village sub-sample, with data from 1,240 households. Village leaders and household representatives were surveyed in faceto-face interviews. The 2008 wave included detailed batteries on village elections and other aspects of the household and village experience. The 2014 wave included extensive batteries on changes in household and village assets, including land. The unit of analysis for this study is the village election. Appendix I includes individuallevel analysis as a robustness check (Table A4); results are consistent with those reported, below. 21
Dependent Variable: Vote Buying
The dependent variable is operationalized through questions asked at the household level about the overall situation in the village's most recent election, specifically: Did anyone approach you [literally, go to your house] to buy your vote? (有人到 你家拉选票吗?) In the village-level analysis, the dependent variable is the share of households in each village responding affirmatively to the question about vote buying. The use of a common euphemism for vote buying (literally, "pulling votes" (O'Brien and Han 2009,365)) is intended to reduce its sensitivity for respondents. While official statements often use the more formal term "huixuan (贿选)" to refer to vote buying, "lapiao (拉票)" is the more colloquial term used by villagers in faceto-face interviews to refer to the payment of cash to influence vote choice. Lu (2011) reports that lapiao is a common usage by villagers in referring to material exchange for votes. A special feature on elections in the official People's Daily newspaper uses the combined term "lapiao huixuan" in analytical context but the more informal "lapiao" in providing specific accounts of vote buying in village elections (Yang and Li 2016). To check for sensitivity, we include an indirect measure of vote buying ("Did you hear about vote buying in the village?) (Appendix I, Tables A2, A3).
Independent Variables: Availability of Rents
The main independent variable of interest is availability of rents, measured in terms of whether there was a land taking within one term of a village election. 22 We use village responses to the following question: Since the second round of land contracting [in the mid-1990s], have there been any land takings in this village? Enumerators recorded all instances of land takings.
The identification strategy is two-fold. We are able to leverage multiple sources of variation, including formal and informal land takings and those preceding and following elections. Formal land takings involve decisions made at higher levels of government and are exogenous to the village. We contrast formal takings with all takings, including informal, illegal ones initiated by village leaders. We also exploit the timing of the land taking process, comparing takings initiated before and 21 Note that land takings and elections vary systematically at the village level. 22 Both village and household representatives were surveyed, and the data on land takings are mutually consistent. See Appendix I, Table A1. after the election. In order to influence the election, vote-buying candidates, who, we hypothesize, are motivated to control land rents that pass through the hands of village leadership, must know about land takings before the election. Moreover, delivery of compensation funds to the village comes late in the process. Thus, we test the relationship between land takings (available rents) and vote buying in three time periods: when land takings occur within one term before or after the election, three years before, and three years after the election. We also include other possible sources of rent, namely the number of enterprises in the village.
Control Variables
Scholars of clientelism identify a range of other factors, including income level, population size, and electoral rules that are conducive to vote buying. Comparative studies find that vote buying is more common among poorer communities (Stokes et al. 2013;Brusco et al. 2004), as these voters "discount the future, rely on short causal chains, and prize instant advantages (Kitschelt 2000,857)." By contrast, Kennedy notes with respect to the Chinese case "that vote buying is most prevalent in wealthier villages close to urban centers, such as large metropolitan areas (Beijing, Shanghai, or Shenzhen), provincial capitals, district cities, and even smaller county seats (Kennedy 2010,625)." However, the apparent association between wealthier, peri-urban communities and vote buying is also likely to be a reflection of the locus of land takings rather than the level of income. We address this debate by including an income measure in tests of our hypothesis.
Consistent with variants of clientelist theory that emphasize face-to-face interactions, smaller communities are also more likely to experience vote buying (Cox 1987). Candidates incur lower costs in smaller villages, because the number of votes to be bought is smaller in these villages (Takeuchi 2013). In what follows, we control for village population.
There is disagreement in the literature regarding the impact of the secret ballot on vote buying. Since the informational requirements of clientelist vote buying are high, secret ballot reforms are frequently associated with declines in vote buying (Schaffer 2007;Kam 2017). However, "many voters share the belief that their electoral choices can't be kept secret," even though they do not necessarily know how their votes are monitored (Stokes et al. 2013,101). Blaydes (2011,106) describes the ways that brokers in Egyptian parliamentary elections observe voters' choices on ostensibly secret ballots. To address this issue, we control for the use of secret ballots in the analysis. Other procedural factors arise in the case of village elections in China; some villages permit proxy voting, in which another person-often a husband or wife-may cast a ballot on behalf of another voter. Brandt and Turner indicate that "a village where looser proxy voting is permitted can engage in considerably more rent-seeking behavior than in a village where proxy voting is more restricted (Brandt and Turner 2007, 477)." Therefore, we control for proxy voting as well as the use of a secret ballot.
The intensity of competition is also commonly associated with vote buying (Golden and Chang 2001;Cox and Thies 1998). If candidates can easily win 1 3 elections or are not challenged by other candidates, they have less incentive to pursue vote buying. In studies of village elections in China, scholars use the number of candidates as an indicator to show that, in general, village elections have become more competitive over time (He 2007;O'Brien and Han 2009). We control for competitiveness using this measure.
Scholars have also noted the impact of higher-level interference on village elections (e.g., Fang and Hong 2020). To account for this possibility, we control for whether candidates are approved by local government officials and the numbers of official monitors on the day of election.
We also examine the effect on reports of vote buying when the winning candidate for village head is the CCP village party secretary. To the extent that the party influences electoral competition through vote buying, we would expect the election of the party secretary to be positively associated with vote buying.
Descriptive Statistics
The descriptive data (Table 1) allow us to paint a picture of both available rents and vote buying in the context of village elections. In 69 percent of the villages, one or more villagers reported vote buying. In the average village, 11 percent of respondents experienced vote buying. The highest percentage of respondents in any single village experiencing vote buying was 50 percent. 23 When asked less directly, 20 percent of villagers reported having heard of vote buying taking place. According to the case-study research, vote buying is limited by the fact that candidates believe their relatives and friends will vote for them without vote buying, while the relatives and friends of opposing candidates will behave the same way. 24 Over the period 1996-2013, 85 percent of the sample villages have reported at least one instance of land taking. These land takings affect more than 22 percent of all households in our sample. The average village experienced two takings during that period, and the average area of land lost was 133 mu. With compensation for arable land ranging in the tens of thousands of yuan per mu in sample villages, these takings presented clear opportunities to access rents.
The descriptive data also show that, in the period covered by the study, elections are meaningful contests for the selection of village leader. 25 For example, villages held between one and four rounds of nominations for candidates, with eight candidates on average coming from open nominations and at least 23 These percentages are not extreme by international norms. Keefer and Vlaicu (2017) note that, "Approximately 52 percent of respondents to Wave Six of the World Values Survey (2010)(2011)(2012)(2013)(2014) reported that voters were bribed very or fairly often in their country's elections." They also note significant cross-national variation: "The fraction of respondents who said that vote buying occurred often in their country ranged from 12 percent in the OECD to 56 percent in South Asia; and from 4.3 percent of Dutch respondents to 75.8 percent of Brazilian (773).". 24 Author's interviews. See also Nichter (2008) and Stokes (2005). Mattingly (2016) argues that lineage leaders, particularly those who become village leaders, exercise effective influence over their kinship group. 25 See full descriptive data in Appendix I Table A1. two candidates contesting the final election. Typically, not all candidates were members of the Chinese Communist Party. In 58 percent of sampled villages, candidates made campaign speeches. All elections were supervised by at least one representative of the township government. Seventy-five percent of villages employed secret ballots. Eight-five percent of villages allowed proxy voting; for voters using proxies, their proxy was a relative in the vast majority (85 percent) of cases. On average, turnout was over 80 percent of eligible voters. In all sample villages, the winner was decided by simple majority. The elected village head was concurrently party secretary in less than a third of villages.
Analysis and Findings: Vote Buying as a Form of Rent Seeking
In this section, we report tests of the hypothesis that the presence of one or more land taking within one term of a village election will be associated with a higher incidence of vote buying.
We estimate the following specification using ordinary least square to test our hypothesis:
where VB i is the proportion of voters reporting vote buying in a given village, land_taking i is the number of land takings within three years (one term) before and after the election in that village, X includes controls, and K denotes county dummies. Column 1 of Table 2 provides a baseline by examining the correlation between all land takings-formal and informal-within one term-both before and after an election-and vote buying. In the bivariate model, the number of rent-seeking opportunities in the three-year period both before and after the election is positively and significantly associated with the prevalence of vote buying. Each additional rent-seeking opportunity is associated with a 2.6 percent increase in the share of villagers reporting vote buying. 26 Columns 2-5 show that the number of firms in the village, hypothesized to be another possible source of rents to office holders, is negatively related to vote buying, substantively small, and not significant. This result is consistent with Su and Tao's (2017) assessment that village-run enterprises have become a liability. Moreover, in our dataset, the majority of firms registered in sample villages are privately owned and operated, meaning that village leaders cannot extract rents from the firms as easily. In case-study research, one of the authors finds that the presence of more private firms, especially ones that make significant contributions to the local tax base, is associated with closer monitoring of the village leader by the county and township governments. 27 This context makes it more difficult for village leaders to capture rents in regulating firms.
VB i = c + land_taking i + XB + K + i
Column 2 also introduces controls for village characteristics. As hypothesized in both the comparative and China-specific literature, the larger the population of the electoral district, the less likely the occurrence of vote buying. However, this factor is not significant when county fixed effects are included, while land takings remain significant. The results also show no significant relationship between income levels in the community and vote buying. While the finding that poorer communities are more likely to experience vote buying is well established in the literature (Stokes et al. 2013), it does not find support here. One possible reason is that income measures in surveys in rural China may be unreliable due to social desirability bias. Kennedy's (2010) suggestion that vote buying is prevalent in wealthier communities is not supported by the analysis; rather, his hypothesis likely reflects the role of land takings, which are more likely in peri-urban areas. In this dataset, land takings are significantly negatively correlated with distance from the village to the county seat. 28 The analysis also controls for multiple aspects of electoral rules and design (columns 3-5). None of these variables is consistently significant, while land takings are positive and significant and robust to all specifications. Although measures of electoral competitiveness-number of candidates and number of rounds of nominations-are positively associated with vote buying as expected, they do not attain statistical significance. Similarly, winning candidate vote share, a measure of (non) competitiveness, is negatively and significantly related to vote buying, as expected, but loses significance after controlling for county fixed effects. Two other variables, higher-level government approval of candidates and the number of government officials monitoring village elections, reflect local government intervention or oversight of the election, but neither is significant. Based on one author's interviews with township officials, monitors arrive in villages only on polling day to supervise elections, while candidates or their brokers usually make their deals with villagers at earlier times. 29 As a result, it is difficult for officials to know about the existence of these deals. The officials also point out that, even when they do know about vote buying, they may still prefer to not report it so as to avoid unnecessary trouble. In some situations, if the government receives complaints from villagers about vote buying prior to the election, it might send a higher number of officials to monitor elections to assure that the elections will not be disrupted by conflicts between villagers and candidates. 30 Among electoral rules, the positive (but insignificant) relationship between secret ballots and vote buying is most striking. This finding stands in contrast to much of the existing literature, which documents the importance of secret balloting in undermining the ability of candidates and their brokers to monitor vote choice (Lehoucq 2007). However, qualitative evidence produced by one author's fieldwork reveals strategies that candidates use to monitor votes even in the context of secret balloting. Blaydes (2011) describes similar techniques in Egyptian elections. Thus, candidates, motivated by the desire to capture large rents while in office, buy votes even when monitoring is difficult and devise new strategies to monitor votes. As Kam concludes, the secret ballot is "a powerful institutional force in improving… elections but not a decisive one (2017,626)." In columns 3 and 4, proxy voting is negatively and significantly related to vote buying. It remains negative but loses significance when controls for county fixed effects are introduced in column 5. Proxies reduce the number of targets for vote buying, since relatives cast ballots on behalf of their family members.
Finally, column 4 introduces a variable to assess whether the election of the party secretary as village head is associated with vote buying. When the party secretary runs in the election for village head, he must compete with other candidates (including, potentially, other party members) and may do so by buying votes. The relationship is positive, although after controlling for county fixed effects, the coefficient is not significant. This result is consistent with vote buying being an individual rather than institutional practice. Using the less sensitive measure of vote buying (Appendix I, Tables A2, A3), this variable remains positive and regains significance. This suggests that voters may hesitate to report having directly experienced vote buying in the election for village head when the party secretary participates in vote buying but are more willing to report having heard about vote buying in this situation.
Formal Land Takings as an Exogenous Source of Variation
The hypothesis-testing strategy employed here relies on the grounded assumption that land takings are exogenous to village electoral politics. If village leaders themselves can initiate informal land takings outside of official land-use plans, then the causality may be reversed: successful vote-buying candidates may drive land takings.
To further explore the hypothesized causal relationship between land rents and vote buying, Table 3 limits the analysis to only formal land takings, as measured in the survey by the presence of a permit accompanying the land taking. These takings are unambiguously initiated outside the village; formal land takings are approved and included in land-use plans at the county level and above and are implemented with the oversight of the county land bureau. Columns 1 and 2 of Table 3 present both simple bivariate results and control variables for all elections that occur within one electoral term of a land taking. In the first bivariate model, the number of formal land takings within one electoral term is positively and significantly associated with the prevalence of vote buying. Each additional formal land taking is associated with a 2.9 percent increase in the share of villagers reporting vote buying. In the fully specified model, each additional formal land taking is associated with a 3.1 percent increase in the share of villagers reporting vote buying. This effect appears to be driven by formal land takings that were initiated outside the village and not other factors.
Land-Taking Information Prior to an Election
The information environment in which electoral candidates operate is important. Our hypothesis-testing strategy also relies upon the logic that candidates for village office have information about the land rents available to office holders before they engage in vote buying. Columns 3-6 of Table 3 disaggregate rent-seeking opportunities into the electoral term immediately preceding and following an election. Column 3 reports the positive bivariate relationship between rent-seeking opportunities during the term before the election and the proportion of villagers reporting vote buying. Column 4 includes variables controlling for other possible causes of vote buying identified above and including county fixed effects. In this specification, only available rents through land takings, among all other relevant factors, is significant. Each additional formal land taking is associated with a 2.9 percent increase in the share of villagers reporting vote buying. This result reinforces the initial findings that the presence of land rents motivates vote buying on the part of individual candidates. The number of formal land takings in the three years after the election is not significantly correlated with vote buying. 31 Reliable information about land takings to be initiated in the future is not likely to be known or available to election candidates and therefore is unlikely to influence their electoral ambitions. This result is consistent with the information environment and the process of formal land takings described in the case study and supports the hypothesis that the lure of land rents drives vote buying.
Conclusion
This study makes an empirical contribution to the vote buying literature by introducing a new measure of available rents that captures sub-national variation and reflects the micro-foundations of vote buying. In theoretical terms, rent-seeking opportunities created by state intervention in the local economy shape vote-buying behavior by candidates. We find that the availability of rents-as reflected in the occurrence of lucrative state land takings-explains variation in vote buying in village elections in China. Furthermore, the Chinese case reveals the dynamics of elections in which competition is non-partisan and candidate-centered, rather than structured and financed by any political party. The evidence suggests how hegemonic political parties use authoritarian elections. The party as an institution does not use vote buying to elect its preferred candidate. Rather, vote buying provides information to the authoritarian state about local elites' economic capacity to buy votes and their socio-political standing to win elections. These distorted electoral contests provide information to the authoritarian state about whom it should recruit into the rent-sharing coalition. As reflected in the qualitative data, local economic elites who successfully buy their way into the office of village head may be recruited to the post of village party secretary. Similarly, village party secretaries may position themselves as individuals to try to win elections for village head in order to control the rents flowing through the village.
Recent policy changes since 2018 calling for village party secretaries to serve concurrently as the-presumably elected-heads of village committees raise new questions about the future of village elections. 32 One possible scenario is suggested by the findings of the present study. The lure of lucrative land rents may continue to drive vote buying as an individual strategy among competing village notables inside and outside the party. Non-party elites may seek to buy victory in competitive elections for the position of village head in the hopes of being tapped to join the party, undertaking the concurrent role of village party secretary, and thereby entering the rent-sharing coalition. Alternatively, vote buying may become a prominent phenomenon in intra-party elections for village party secretary.
The emergence of vote buying also has important implications for governance; comparative studies highlight the effect of vote buying on political accountability. Leight et al. (2019) find that voters who receive payment for their votes are more likely to tolerate takings by politicians and to tolerate expropriation in larger amounts. Moreover, politicians who pay for votes are likely to expropriate more resources than they would in the absence of vote buying.While multiple studies of village elections in China highlight their positive impact on accountability of leaders and on the quality of governance (e.g., Birney 2007; Kennedy et al. 2004;Manion 2006), the ways in which vote buying erodes local accountability remain an unexplored topic.
Further research is needed to assess the accountability of elected leaders who engage in both vote buying and rent appropriation. Two types of data will be useful in this regard. First, in future work, data on subsequent electoral contests involving incumbent leaders who previously bought votes, presided over the distribution of land takings compensation, and captured sizeable rents will shed light on the willingness and ability of voters to hold leaders accountable. Second, data on the presence or absence of villager protests following land takings will allow us to 32 See note 1.
3
test the results of laboratory experiments suggesting that voters who are paid for their votes are more likely to tolerate rent appropriation by the leaders they elect (Leight et al. 2019). Given the scale of land grabbing and rent appropriation under electoral authoritarianism as well as in electoral democracies in Asia, Africa, and Latin America (White et al. 2012), it is important to explain not only the causes of vote buying but also the relationship among rents, vote buying, and political accountability.
Supplementary Information
The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s12116-022-09355-y.
Table 1
1Descriptive statistics of variables in baseline analysis (unit: village)N
Mean
SD
Min
Max
Proportion of villagers experienced vote buying
62
0.11
0.12
0
0.5
Frequency of land takings from 1996 to 2013
62
2.29
2.22
0
12
Frequency of land takings within 3 years of election
62
1.13
1.32
0
7
Formal Land takings within 3 years of election
62
0.63
1.16
0
7
No. of enterprises
61
4.64
12.23
0
86
Total population (unit: persons)
62
1535
972
161
4800
Average annual income of villagers (unit: yuan)
62
3531
1865
350
8000
Secret ballot (0 = no, 1 = yes)
61
0.75
0.43
0
1
Proxy voting (0 = no, 1 = yes)
61
0.85
0.36
0
1
No. of higher level Monitoring Officials
61
4.41
3.2
1
16
Rounds of nomination
59
2
0.7
1
4
Election winner is concurrent party secretary
62
0.32
0.47
0
1
Winning candidate vote share
60
79.62
11.19
55
98
Candidates approved by government (yes = 1, no = 0)
60
0.9
0.3
0
1
Number of final candidates
59
2.2
0.91
1
6
Table 2
2Rent-seeking opportunities and vote buying*p < 0.1; **p < 0.05; ***p < 0.01
Table 3
3Formal rent-seeking opportunities (exogenous to village) and vote buying *p < 0.1; **p < 0.05; ***p < 0.01Independent variableDependent variable: proportion of households reporting vote buyingWithin one electoral
term
Term before election
Term after election
Availability of rents
Land taking(s) in village
0.029**
0.031**
0.039**
0.029*
0.007
0.035
(0.014)
(0.013)
(0.017)
(0.016)
(0.024)
(0.023)
Firm(s) in village
− 0.002
− 0.002
− 0.001
(0.001)
(0.001)
(0.001)
Village characteristics
Log (population)
0.034
0.041
0.019
(0.027)
(0.029)
(0.029)
Log (income)
− 0.042
− 0.020
− 0.038
(0.039)
(0.039)
(0.042)
Election characteristics
Number of candidates
0.008
0.004
0.009
(0.016)
(0.017)
(0.017)
Rounds of nominations
0.026
0.017
0.028
(0.026)
(0.027)
(0.028)
Candidates approved by gov
0.036
0.034
0.064
(0.051)
(0.054)
(0.053)
Number of official monitors
− 0.002
− 0.002
− 0.002
(0.006)
(0.006)
(0.006)
Secret ballot
0.067
0.060
0.064
(0.050)
(0.052)
(0.053)
Proxy voting
− 0.029
− 0.048
− 0.037
(0.049)
(0.050)
(0.052)
Party influence
Party secretary as candidate
0.007
0.014
0.007
(0.042)
(0.044)
(0.045)
Constant
0.089***
0.195
0.095***
− 0.036
0.104***
0.187
(0.018)
(0.349)
(0.016)
(0.346)
(0.018)
(0.388)
County fixed effects
No
Yes
No
Yes
No
Yes
Observations
62
57
62
57
62
57
R 2
0.067
0.791
0.083
0.773
0.002
0.766
Adjusted R 2
0.051
0.609
0.067
0.575
− 0.015
0.564
Prior to 2018, the ruling Chinese Communist Party (CCP) played little or no institutional role in structuring electoral competition among candidates for village leadership (Landry, Davis, and Wang 2010). For the new role for CCP secretaries in village elections beginning in 2018, see CCP Central Committee and State Council (2018; 2019) in Appendix II, Documents. 2 Ahram (2012, 158) notes the anecdotal nature of Blaydes' analysis of vote buying as rent seeking; Keefer and Vlaicu (2017) employ a formal model.
We define rent seeking as the expenditure of effort/resources to capture returns by seeking political advantage in an institutional setting characterized by political allocation. SeeBuchanan et al. (1980,4).
Land Management Law (see Appendix II, Documents).
Ang (2016) shows that material payoffs constitute an important incentive for grassroots officials in China. 6 See Appendix II, Documents. In 2018, the electoral term was extended to five years.
CCP Central Committee Office, State Council Office 2009 (see Appendix II, Documents). 8 This analysis echoesMuñoz's (2014, 95) call for multi-method studies of electoral clientelism.
The case study was conducted separately in a province and county not included in the survey sample. 10 One mu, the standard unit of land area in China, is equal to 0.067 hectares or 0.16 acres. 11 There was a clear division of work among the village leadership in Baijia Village. While the party secretary was responsible for party affairs, the village head was responsible for public affairs involving ordinary villagers. Land requisition fell within the bailiwick of the village head. Author's interviews.
The price of votes varies. Kennedy reports that the "amount can vary from 5 yuan (US $0.75) to 1500 yuan (US$220) for a single ballot (2010,621)."Zhao (2018,283) finds that the price that candidates paid to villagers for each ballot ranged from 400 to 1800 yuan, with an average of 880 yuan.13 Author's interview 2013. 14 Author's interview 2013.
Author's interview 2013.16 Author's interview 2013. 17 A single person serving as both village committee chairman and village party secretary is referred to as "carrying on a single set of shoulders (一肩挑).".
The provinces are broadly representative of all of China's major regions with the exception of the south-southeast.19 On average, sample villages have about four hundred households; the random sample includes approximately 5 percent of households in each village. 20 The two-village over-sample was included in case a village withdrew from the sample.
Using the less direct measure, each additional land taking leads to a 3.2 percent increase in proportion of villagers who heard about vote buying (Appendix I,Table A2).27 Author's interview 2013.28 When land takings and distance from the county are both controlled in the specification, only land takings register a statistically significant result.
Author's interview 2013. 30 Author's interview 2013.
Findings are robust to the less direct measure of vote buying (Appendix I,Table A3).
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.Authors and Affiliations
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| Practical Innovation of Village Election in Shaanxi,Gansu and Ningxia Border Region,Instance of election in 1941 | This article argues that post-conflict consociational arrangements in ethnically divided societies incentivize moderation by political parties, but not policy differentiation outside the main conflict. This results in little policy-driven voting. Analysing party manifestos and voter survey data, we examine the evolution of party policy and cleavage voting under power-sharing in Northern Ireland 1998-2016. We find a reduction in ethnonational policy differences between parties and that ethno-nationalism has become less important in predicting vote choice for Protestants, but not Catholics. We also find little party differentiation in other policy areas and show that vote choices are largely independent of people's policy stances on economic or social issues. Our findings are thus largely consistent with a 'top-down' interpretation of political dynamics.The Northern Ireland Assembly and power-sharing executive have now been in place, albeit not in continuous operation, for over 20 years. In the early years of power-sharing opinion was divided as to how the new consociational institutions would shape party politics and voter behaviour. Some argued that the new rules of the game would almost inevitably lead to increased 'ethnic outbidding'(Dixon 2002;Taylor 2001;Wilford 2001). This perspective emphasized that consociational power-sharing would incentivize party competition within the unionist and nationalist blocs, with competition focused on the underlying ethno-national dimension. This dynamic would polarize the parties and, ultimately, voters. Consociational power-sharing was thus a recipe for political instability.Others argued that the proportional electoral system used in Assembly elections and the incentivized collaboration of parties in government would lead to a moderation of party positions on the main ethno-national dimension and potentially | Despite global policy shift towards liberalization of the housing market, different forms of rent control have still remained in a number of countries. Most of these controls are currently uphold by the view that they are different from the old forms that involved complete freezing of the nominal rents. Generally, this view has been sustained by lack of in-depth studies on the remaining forms of rent control. This paper fills this gap by examining the effects of rent-controlled public housing sector on the supply of private rent housing and household mobility in Malawi. The findings from Malawi demonstrate that the effects of rent control are varied and depend on the nature of residential market as well as the political environment under which the rent controls are implemented. Under dictatorial regime, rent controlsin Malawi produced negative effects on both the supply of private rent housing and household mobility. This is consistent with existing studies from many other countries. However, after adoption of liberal democracy and economic policies, rent controlhas produces varied outcomes. While its effect on constraining household mobility remains undisputable, rent control in the public housing sector has insignificant effect on the supply of private rented housing. These differences may be explained by the fact that during dictatorial regime private housing sector in the country was also de facto under rent control. | Political Competition, Rent Seeking and the Choice of Environmental Policy Instruments: Comment | Students of rent seeking have erred in focusing their attention exclusively on the analysis of competitions for exogenously specified transfers. When redistributive policies are treated as endogenous choices, it is clear that there are both incentives and opportunities for policymakers to design them in ways that prevent the wasteful dissipation of a large proportion of the intended transfers. An analytical framework that treats policy design in this way is capable of explaining a variety of common attributes of redistributive policies that are apparent anomalies under the traditional approach to rent seeking. Furthermore, we predict, and find supporting evidence, that authoritarian regimes tend to be associated with higher ratios of government revenue to total income than do democracies. We attribute this tendency to the substantially greater potential for dissipative competition for revenues under democracy than under dictatorship. Finally, available estimates of lobbying expenditures and rents transferred under the recent federal crude oil controls contradict the hypothesis that rents are fully or almost fully disspated through political competition. | Village Elections: Democracy From The Bottom Up? | The Regressive Effects of Direct Democracy: Evidence from Property Tax Assessors | This essay aims to examine whether there is a partisan influence on local government spending using three different measures, ideology, fragmentation and constellations of government. The ideology measure examines the share of socialists (left-wing parties) in the council. Fragmentation consists of a Herfindahl index which uses information on number of parties in the council and their respective strength, and number of committees in the political organization. The third measure is political regimes and tries to capture the effects of constellations of government. Three hypotheses are introduced to examine partisan impact where it is assumed that a higher share of left-wing parties lead to increased spending. Because of the common pool problem, that groups that assert pressure on the budget only internalizes parts of the costs of increased spending, fragmentation and weak forms of government are expected to lead to increased spending. The essay also tries to account for the political setting in Sweden in order to evaluate the accuracy of the measures. Using a panel data analysis on data from a selection of 17 municipalities during 1983-1999, the results show that there is a partisan impact on municipal expenditure and it is inflicted by ideology. An increase in left-wing party share by 1 % increases total and current expenditure by 0,4-0,5% of mean per capita spending. None of the other two measures come out significant and indicates that neither fragmentation nor constellation of government matter for local government spending. However, there are some technical and data problems that make inference difficult. The results also show that level of debt is positively related to total expenditure and municipal income is positively related to current expenditure. The demographic parameter shows that there are scale economies in the selection of municipalities. |
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236 | where is the sangiovese grape grown in canada | clone to the vineyard site and controlling the vine's vigor. The high acidity and light body characteristics of the Sangiovese grape can present a problem for winemaking. The grape also lacks some of the color-creating phenolic compounds known as acylated anthocyanins. Modern winemakers have devised many techniques trying to find ways to add body and texture to Sangiovese — ranging from using grapes that come from extremely low yielding vines, to adjusting the temperature and length of fermentation and employing extensive oak treatment. One historical technique is the blending of other grape varieties with Sangiovese, in order to complement its | mm long x 17 mm wide, with an average weight of 3 grams. Soils with low fertility are ideal and help control some of the vigor of the vine. Planting vines in high densities in order to curb vigor may have the adverse effect of increasing foliage and limiting the amount of direct sunlight that can reach the ripening grapes. Advances in understanding the quality and characteristics of the different clones of Sangiovese has led to the identification and propagation of superior clones. While high-yielding clones have been favored in the past, more attention is being paid to matching the | was one of the leading "home winemaking" grapes in production. In 2010, there were of the grape planted in the state with American Viticultural Areas in Contra Costa, Mendocino, and Sonoma counties seeing a slight increase in interest while plantings the Central Valley have declined. Outside of California, plantings of the grape can be found in Washington State as well as in Missouri and Texas. In Mexico, plantings of Carignan are found in the states of Aguascalientes, Sonora, and Zacatecas. In Chile, old vines of plantings of Carignan are grown without irrigation in the Maule region which accounted for the | Blaufränkisch (German for blue Frankish) is a dark-skinned variety of grape used for red wine. Blaufränkisch, which is a late-ripening variety, produces red wines which are typically rich in tannin and may exhibit a pronounced spicy character.
The grape is grown across Central Europe, including Austria, Czech Republic (in particular southern Moravia where it is known as Frankovka), Germany, Slovakia (where it is known as Frankovka modrá), Croatia, Serbia (frankovka), Slovenia (known as modra frankinja), and Italy (Franconia). In Hungary the grape is called Kékfrankos (also lit. blue Frankish) and is grown in a number of wine regions including Sopron, Villány, Szekszárd, and Eger (where it is a major ingredient in the famous red wine blend known as Egri Bikavér (lit. Bull's Blood) having largely replaced the Kadarka grape). It has been called "the Pinot noir of the East" because of its spread and reputation in Eastern Europe. In America the grape is also known as Lemberger, Blauer Limberger or Blue Limberger and grown in Pennsylvania, Washington state, Michigan, New Jersey, Idaho, New York, Colorado, Ohio, Virginia. and California,
DNA profiling has shown that Blaufränkisch is a cross between Gouais blanc (Weißer Heunisch; male parent) and Blaue Zimmettraube (female parent; the offspring of Blauer Gänsfüsser). Historical sources of grapevine classification have provided very solid evidence that the geographic area of origin of the variety is Lower Styria (today Slovenian Styria). For a long time before the application of DNA analysis, Blaufränkisch was erroneously thought to be a clone of the Gamay grape variety, due to certain similarities in morphology and possibly due to its name Gamé in Bulgaria.
The German name Lemberger derives from the fact that it was imported to Germany in the 19th century from Lemberg in Lower Styria in present-day Slovenia and then in the Austro-Hungarian Empire. An 1877 export of Lembergerreben to Germany has been recorded. The almost identical name Limberger refers to Limburg at Maissau in Lower Austria, where in the late 19th century "ungrafted Limberg Blaufränkisch vines" (wurzelechte Limberger Blaufränkisch-Reben) were offered for sale.
History and origins
While the first officially documented appearance of Blaufränkisch did not occur until 1862 when the grape was included in a viticultural exposition in Vienna, Austria, it is likely that the grape is much older and has perhaps been around as long as the Middle Ages under a variety of Fränkisch synonyms. The term Fränkisch itself comes from Franconia, the German wine region that includes northwest Bavaria, the northeastern reaches of Baden-Württemberg around Heilbronn-Franken, and parts of southern Thuringia. During the Middle Ages, the wine from this region was highly praised, and grapes that were thought to be capable of producing superior wines were called Fränkisch to distinguish them from the less highly prized Hunnic grapes. It is likely that from sometime during this period up until the 1900s, Blaufränkisch (literally Blue Frankish) began to be grown in the region.
Despite the close association to Franconia, ampelographers believe that the grape likely originated somewhere in a swath of land stretching from Dalmatia through Austria and Hungary. They base this belief on the proliferation of synonyms originating from these areas as well as DNA evidence showing that the old Hungarian wine grape Kékfrankos was, in fact, Blaufränkisch, and that Gouais blanc (Weisser Heunisch) and an unknown grape variety are the parent varieties of Blaufränkisch. Despite its French name, it has been speculated that Gouais blanc has Eastern European origins, with the term "Heunisch" thought to derive from the Huns, and Gouais blanc being confirmed as a parent variety of another old Hungarian wine grape Furmint, but ultimately the exact birthplace of both Gouais blanc and Blaufränkisch are unknown.
The synonyms Lemberger and Limberger first appeared in literature near the end of the 19th century in relation to the grape's believed origins from the Austro-Hungarian cities of Lemberg (today in modern Slovenia) and Limberg (today known as Maissau) in Lower Austria. In 1875, the International Ampelographic Commission in Colmar, France adopted Blaufränkisch as an officially sanctioned name.
Viticulture
The Blaufränkisch vine is known as an early budding variety that can be susceptible to early spring frost. It is a late ripening variety, and tends to be planted in warmer vineyard sites. Among the viticultural hazards that Blaufränkisch is most prone to are powdery and downy mildews.
Blaufränkisch is considered a high productive vine capable of producing high yields fairly easily. In some parts of Europe it is not uncommon to see it harvested at . However over-cropping the vine has a tendency to produce thin wines with many green, weedy notes.
Wine regions
Today Blaufränkisch is planted across the globe from Japan, the United States and Australia to Germany, Hungary and Austria.
Austria
It is possible that Blaufränkisch or a similar forerunner of the grape was already cultivated in regions of present Austria (Lower Austria and Burgenland) in the 10th century. In his 1777 publication Beschreibung der in der Wiener Gegend gemeinen Weintrauben-Arten, ampelographer Sebastian Helbling accounted the variety as one of the best red grape varieties of Lower Austria, and used the name Schwarze Fränkische for it.
In present-day Austria Blaufränkisch is the second most important red grape variety after Zweigelt, with , representing 6% of all Austrian plantings in 2008. The vast majority of these plantings are in the Burgenland region of eastern Austria. It is particularly common in Mittelburgenland, with planted in 2008, an area sometimes given the nickname "Blaufränkischland". The Mittelburgenland is considered ideal for the grape due to the dry warm winds from the east across the Pannonian Plain, and the sheltering influence of the hill regions to the north, south and west of the region.
Outside the Burgenland, of Blaufränkisch were planted in the Neusiedlersee region, and were planted in the Neusiedlersee-Hügelland region in the hill country bordering the lake. The wines produced in this region, influenced by the warm moderating climate of the lake, tend to be, as described by wine expert and Master of Wine Jancis Robinson, "richer and more full bodied", while the clay vineyard soils south of the lake in the Südburgenland tend to produce wines with more spice notes.
In the Carnuntum area located between Vienna and the Neusiedlersee, the slate-based soils near the city of Spitzerberg are also home to some Blaufränkisch plantings.
Districtus Austriae Controllatus and wine styles
Within Austria Blaufränkisch is a permitted variety in several Districtus Austriae Controllatus (DAC) zones. Producers in the Burgenland tend to delineate light bodied, unoaked Blaufränkisch wines to the Mittleburgenland DAC Classic, while labeling more full bodied, oaked styles as Burgenland DAC Reserve.
In the Eisnberg DAC of the southern Südburgenland, the grape is grown in iron-rich soils and tends to produce a distinctive varietal style. In the Leithaberg DAC situated in the slate and limestone hills around the Leitha Mountains, Blaufränkisch must make up at least 85% of the blend, with St. Laurent, Zweigelt or Pinot noir permitted to round out the remaining portion. In this cooler climate wine region the Blaufränkisch tends to be, as described by Robinson, "nervy and elegant".
In Austria, Blaufränkisch tends to produce deeply colored wines with dark fruit aromas, peppery spice notes and moderate to high acidity. Depending on where it is produced the wine can be unoaked, or spend some time aging in the barrel. The unoaked styles tend to be lighter bodied while the oaked versions tend to be fuller bodied.
Other European wine regions
In Germany, there are of Blaufränkisch, grown primarily in the Württemberg wine region around the town of Stuttgart. Here, where the grape is often known as Blauer Lemberger or Blauer Limberger, the grape tends to make more light bodied wines with softer tannins than the style typically made in Austria.
Blaufränkisch, known here as Frankovka, is the second most widely grown red grape variety in the Czech Republic. It is grown only in the Moravian wine subregions due to its late-ripening nature. Almost 9% of the total vineyard area in Slovakia () is planted to Blaufränkisch, where the grape is more widely known as Frankovka modrá. In the city of Bratislava, specifically the suburb of Rača, local wine producers hold an annual wine festival that highlights Frankovka modrá wines from the region as well as examples of Blaufränkisch from around the globe.
In Hungary, the grape is known as Kékfrankos (literally "Blue Frankish") and Nagyburgundi. There are more than of the variety planted throughout the country, particularly around Sopron near the Austrian border of Burgenland, and Eger and Kunság in central Hungary. In the Eger region, Kékfrankos has displaced Kadarka in several modern incarnations of Egri Bikaver (Bull’s Blood).
In Slovenia, the grape is known as Modra Frankinja. At present, there are 2,759,316 reeds of Blue Frankish that are planted in Slovenia, which grow on almost 700 hectares of wine-growing areas. This represents 4.68 percent of all plantations in the country. The variety of Blue Frankish is spread in two wine-growing regions Podravje and Posavje. It's the fourth most common variety of red grapes in Slovenia.
Blaufränkisch goes by the name Burgund Mare in Romania, where most of the variety's are located in the southern wine regions of Ștefănești and Dealu Mare. In recent years, plantings of the grape have expanded eastward towards warmer vineyard sites near the Black Sea. In Bulgaria, for many years the Blaufränkisch plantings in the country, known as Gamé, were thought to be the Gamay noir grape grown in the Beaujolais wine region of France until DNA evidence proved that it was in fact Blaufränkisch.
In Croatia, the nearly of Blaufränkisch, known as Frankovka, represent around 2.7% of all Croatian vineyard plantings. This number is expected to rise, as many plantings previously thought to be a different variety, Borgonja, have now been proven by DNA testing to be Blaufränkisch. Most of the Croatian plantings are found in the Kontinentalna Hrvatska (Continental Croatia) region in the northwestern part of the country and on the Istrian peninsula along the Adriatic Sea. In Serbia, most of the plantings of Blaufränkisch are found in the province of Vojvodina.
In Italy, the grape is known as Franconia Nera, with planted mostly in the Friuli-Venezia Giulia wine regions of the Friuli Isonzo and Friuli Latisana Denominazione di origine controllata. In Spain, some experimental plantings of Blaufränkisch are found in the Spanish wine region of Málaga and Sierras de Málaga, where a German-descended winemaker is making varietal wines under the synonym Lemberger.
New World wine regions
In the New World Blaufränkisch is found in the Australian wine region of the Adelaide Hills, where a single grower, Hahndorf Hill, has been growing this variety for the past 20 years to make a full-bodied version of this wine. Other producers in Australia have recently planted Blaufränkisch and will soon be presenting their own versions. In Canada, there are some plantings of the variety in Ontario in the Niagara region, British Columbia wine regions of Vancouver Island, Nova Scotia, and the Okanagan Valley.
The grape can be found across the United States, from the Finger Lakes, Cayuga Lake, Hudson River Region and Long Island AVAs in New York, where it often blended with Cabernet franc, to California, (particularly the Lodi and Temecula Valley AVAs) and Washington State. In Pennsylvania, varietal and blended wines are produced in the Lake Erie (which also includes Ohio and New York) and Lehigh Valley AVAs. The Snake River Valley AVA in Idaho is home to a few hectares of the grape. Blaufränkisch has recently been making strides in New Jersey, specifically in the Outer Coastal Plain AVA, becoming a stand out grape for this region. Additional plantings are found in New Mexico, Virginia, Rhode Island, Maryland, Michigan, Montana, Colorado and the greater Southeastern New England AVA.
In Canada, Lemberger is found in several planting in the Niagara Peninsula DVA.
Washington Lemberger
The grape has a long history in Washington State, where it known mostly as Lemberger. Here the grape has been used to produce a variety of styles from light bodied claret-style blends, higher bodied more alcoholic "Zinfandel-like" wines to port style fortified wines. The grape was a favorite of Dr. Walter Clore, the "father of Washington wine". He encouraged the grape's planting throughout the Yakima Valley AVA in the 1960s and 1970s. In 1976, John Williams of Kiona Vineyard in what is now the Red Mountain AVA planted a few hectares that would be used in 1980 to make the first commercial Lemberger wine produced in Washington.<ref name="Seattle pi">Richard Kinssies "Wine Pick of the Week: 2001 Kiona Lemberger"' Seattle Post-Intelligencer June 17th, 2003</ref>
As of 2011 there were of the variety planted throughout the Columbia Valley AVA, including Red Willow Vineyard in the Yakima Valley AVA, Champoux Vineyard (which along with Kiona and Red Willow has some of the oldest Lemberger vines in the state) and Destiny Ridge Vineyard in the Horse Heaven Hills AVA, with additional plantings in the Rattlesnake Hills and Columbia Gorge AVAs.
Despite the grape's history, winemakers have had a difficult time marketing the grape due to consumers' association of the name Lemberger with the smelly cheese of a similar name. Some winemakers have taken the approach of California winemaker Jed Steele who, in partnership with Chateau Ste. Michelle, makes a Washington Blaufränkisch that he labels under the proprietary name "Blue Franc" to avoid using the names Lemberger or Blaufränkisch which have also not fared well among consumers.Frank Prial "WINE TALK; And Now for Something a Little Different" The New York Times April 25th, 2001
According to wine expert Paul Gregutt, Washington Lembergers are characterized by their "blood red" color, with light peppery spice aromas and flavors of ripe berry fruit.
Wines and food pairings
Blaufränkisch wines have aromas of dark ripe cherries and dark berries, are spicy, have medium tannin levels and sometimes very good acidity. Young wines are deeply fruity and become more velvety, supple and complex with age.
According to wine expert Oz Clarke, well made examples of Blaufränkisch will have notes of red currants and blackberry fruit. The grape does have the potential to have high tannins and acidity levels which can be moderated by harvest decisions and some oak aging. However, Clarke notes that wines from Blaufränkisch can take on too much oak flavoring and come across as excessively oaky. When blended with other varieties, Blaufränkisch often contributes acidity and structure to the blend.
In food and wine pairings, Blaufränkisch/Lemberger are often paired with lamb dishes and grilled meats.
Offspring and relationship to other varieties
At one time it was believed that Blaufränkisch was a clone of the Gamay grape of Beaujolais, due in part to the prevalence of the synonym Gamé used in Bulgaria, and perhaps because it was thought that there was a parent-offspring relationship between the two. However, in the 21st century DNA evidence showed that Blaufränkisch was an offspring of Gouais blanc and an unknown parent, making it a half-sibling to Gamay as well as other varieties of grapes which have Gouais blanc as a parent such as Chardonnay, Riesling, Elbling, Aramon noir, Grolleau noir, Muscadelle and Colombard.
Blaufränkisch is a parent to Zweigelt, the most widely planted red grape in Austria, from a crossing with St. Laurent (also known as Sankt Laurent'') done in 1922 by Dr. Fritz Zweigelt at the Klosterneuburg research facilities in Vienna. This same Blaufränkisch x Sankt Laurent pairing was used to produce the Czech/Slovak grape André. Dr. Zweigelt also crossed Blaufränkisch with Blauer Portugieser to produce Blauburger, with August Herold using the same pairing to produce Heroldrebe in 1929 at the Weinsberg research center in Baden-Württemberg. Also at Weinsberg, Blaufränkisch was crossed with Dornfelder to produce Acolon, and with Cabernet Sauvignon to produce both Cabernet Cubin and Cabernet Mitos in 1970.
In 1951 researchers at the Szent István University in Hungary crossed Blaufränkisch with Kadarka to produce Rubintos. Two years later they crossed the grape with Muscat Bouschet, (an offspring of Petit Bouschet), to produce Magyarfrankos.
In 1986 Blaufränkisch was crossed with Regent at a research facility at Geilweilerhof to produce Reberger.
Synonyms
Over the years Blaufränkisch has been known under a variety of synonyms including Blanc doux, Blau Fränkisch, Blau Fränkische, Blauer Limberger (Germany), Blaufränkische, Blaufranchis, Blaufranchisch, Blue French, Borgonja (Croatia), Burgund Mare (Romania), Cerne Skalicke, Cerne Starosvetske, Cerny Muskatel, Chirokolistny, Cierny Zierfandler, Crna Frankovka (Croatia), Crna Moravka, Fernon, Fränkische, Fränkische schwarz, Franconia (Italy), Franconia nera (Itay), Franconia nero, Franconien bleu, Franconien noir, Frankinja, Frankinja modra, Frankovka (Croatia, Serbia, Czech Republic), Modra Frankinja (Slovenia), Frankovka modra (Slovakia), Imbergher, Jubiläumsrebe, Gamay noire, Gamé (Bulgaria), Karmazin, Kék Frankos, Kékfrank, Kékfrankos (Hungary), Lampart, Lemberger (Germany and United States), Limberg, Limberger (Germany), Limberger blauer, Limberger noir, Limburske, Maehrische, Modra Frankija, Modra Frankinja, Modry hyblink, Moravka, Moravske, Muskateller schwarz, Nagy burgundi, Nagyburgundi (Hungary), Neskorak, Neskore, Neskore cierne, Noir de Franconie, Oporto (Slovakia), Orna Frankovka, Portugais lerouse, Portugais rouge, Portugieser rother, Pozdni, Pozdni skalicke cerne, Schwarz Limberger, Schwarze Fraenkische, Schwarzer Burgunder, Schwarzgrobe, Serina, Shirokolistnyi, Sirokolidtnyj, Sirokolstnii, Skalicke cerne, Starovetsky hrozen, Sura Liscina (Serbia), Szeleslevelü, Teltfürtü Kékfrankos, Vaghyburgundi, Velke bugundske and Vojvodin.
References
Red wine grape varieties
Austrian wine
Czech wine
Hungarian wine
Slovak wine
Slovenian wine | What is the place called where grapes are grown? | Bachet noir Bachet noir is a traditional French variety of red wine grape that is a sibling of Chardonnay. A little is still grown in the Aube, where it is used to add colour and body to Gamay wines. DNA fingerprinting has shown that it is one of many grapes to be the result of a cross between Gouais blanc (Heunisch) and Pinot noir, making it a sibling of famous varieties such as Chardonnay and Aligoté. Gouais blanc was widely grown by the French peasantry in the Medieval ages. This offered lots of opportunities for hybridization, and the offspring benefited | Are grapefruits grown in rich topsoil inside vineyards? | grapes. Museles is now being standardized by the wine producing industry in China and marketed under the brand-name of Merceles. Museles Museles is a wine produced in Xinjiang. It is commonly made for local consumption, but is now also produced commercially for export outside the region. China's Xinjiang Autonomous Region have an ancient history of viticulture going back to around the 4th century BC, when Greek settlers brought the vine and more advanced irrigation techniques. The area around Turfan was, and still is, particularly noted for its grape production, and its production of grape wines is mentioned in the historical | 236 | Sangiovese in Washington have declined in recent years to in 2011. Other areas in the United States with sizable plantings of Sangiovese include the Rogue Valley and Umpqua AVA in Oregon, the Monticello in Virginia, the Sonoita AVA with 45 acres planted in Arizona, and Texas Hill Country in Texas. In Canada, there are less than of Sangiovese planted, mostly in Ontario where some producers in Niagara-on-the-Lake are experimenting with ice wine versions of the grape. A small amount of the grape can also be found in British Columbia. Italian immigrants introduced the Sangiovese vine to Argentina in the late | how many clones of sangiovese are there in australia | what percentage of sangiovese is in rosso di montalcino | where did the movie sangaree take place | what area of florence is home to flavourful sangiovese-based red | where is sangchris lake located in the united states | who is sangaree's fiance in the movie | who lived along the mouth of the sangamon river | in which mountain range is the river sangone |
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238 | what was the original b-side for this is love | JohnsonJ it is the seen-it-so-many-times idea of love as the main motivation and inspiration in life. The black and white 60-sec video shows the everyday moments of tenderness, closeness and attention that we very… | Love Is... Love Is... is the name of a comic strip created by New Zealand cartoonist Kim Casali (née Grove) in the 1960s. The cartoons originated from a series of love notes that Grove drew for her future husband, Roberto Casali. They were published in booklets in the late 1960s before appearing in strip form in a newspaper in 1970, under the pen name "Kim". They were syndicated soon after and the strip is syndicated worldwide today by Tribune Content Agency. One of her most famous drawings, ""Love Is...being able to say you are sorry"", published on February 9, 1972, | Loving (2016 film) "Coverage Opinions", Hirschkop expressed his view on Jon Bass' portrayal of himself, with Hirschkop remarking that Bass was too mild mannered and nothing like himself, and while Hirschkop mentions that "Loving" served its purpose as a film, he also listed several discrepancies between the film and what actually occurred. Mark Loving, the grandson to Mildred Loving, said his grandma is not African American as portrayed by Ruth Negga with Ethiopian blood, but rather Native American as Rappahannock Indian. On October 23, 2015, "TheWrap" promoted "Loving" by releasing the first image of the film, featuring Edgerton's Richard Loving and Negga's Mildred | Love. A powerful and empowering song, actually. | Who owns the copyright for I can't help falling in love with you in blue Hawaii? | R&B Songs. A music video to accompany the release of "Love & Sex, Pt. 2" was directed by Billie Woodruff. Love & Sex, Pt. 2 "Love & Sex, Pt. 2" is a song by American recording artist Joe, featuring guest vocals from singer Kelly Rowland. Originally recorded by Joe and fellow R&B singer Fantasia Barrino for his tenth album "" (2013), a re-arranged version of the song, featuring a new instrumentation and vocals by Rowland, was included on Joe's follow-up album "Bridges" (2014). Written by Alvin Garrett, Gerald Isaac, and Derek "D.O.A." Allen, with production helmed by the latter, it | Love Is a Beautiful Thing (Phil Vassar song) version reached its peak of #2 on the "Billboard" Hot Country Songs charts in mid-2008. The song is a moderate up-tempo detailing the various events of a wedding. The verses primarily list off the actions by the various relatives who have gathered for the event, such as a young kids jumping in the pews, and an aunt who arrived because her "sister's girl" is getting married. In the chorus, the narrator observes that "love is a beautiful thing". The first version of this song was released as by Canadian singer Paul Brandt under the title "It's a Beautiful Thing". It | directed by Chris Robinson, who also directed Blige in a music video-styled Lady Foot Locker commercial in which "Love @ 1st Sight" is played in the background. Method Man appears in it, while Sean "Diddy" Combs makes a special cameo appearance. An iPod is featured prominently at the beginning of video, an instance of paid-for product placement on the part of Apple Inc.. Credits adapted from the "Love & Life" liner notes. Love @ 1st Sight "Love @ 1st Sight" is a song by American recording artist Mary J. Blige, performed along with rapper Method Man. It was written by | 238 | This Is Love (George Harrison song) "This Is Love" is a song by English rock musician George Harrison that was released on his 1987 album "Cloud Nine". Harrison co-wrote the song with Jeff Lynne, who also co-produced the track. In June 1988, it was issued as the third single from "Cloud Nine", peaking at number 55 on the UK Singles Chart. The original B-side for the single was going to be "Handle with Care", a collaboration between Harrison, Lynne, Roy Orbison and Tom Petty recorded at Bob Dylan's studio in Santa Monica, California. When executives at Harrison's distributor Warner Bros. | what album was i dig love on by george harrison | george michael love action i believe in love song | who produced my love is like wo harrison | when did the song you are love come out | when did the song we were in love come out | who wrote it's a love thing by keith urban | when did the love of richard nixon album come out | who wrote the song if this is love |
239 | A recent trend of research on direction-of-arrival (DOA) estimation is to localize more uncorrelated sources than sensors by using a proper sparse linear array (SLA) and the Toeplitz covariance structure, at a cost of robustness to source correlations. In this paper, we make an attempt to achieve the two goals simultaneously by using a single algorithm. In order to statistically efficiently localize a maximal number of uncorrelated sources, we propose an effective algorithm for the stochastic maximum likelihood (SML) method based on elegant problem reformulations and the alternating direction method of multipliers (ADMM). We prove that the SML is robust to source correlations though it is derived under the assumption of uncorrelated sources. The proposed algorithm is usable for arbitrary SLAs (e.g., minimum redundancy arrays, nested arrays and coprime arrays) and is named as maximumlikelihood estimation via sequential ADMM (MESA). Extensive numerical results are provided that collaborate our analysis and demonstrate the statistical efficiency and robustness of MESA among state-of-the-art algorithms. | The paper considers direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), leading to stochastic maximum likelihood (ML) DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots. Simulations demonstrate that taking the heteroscedastic noise into account improves DOA estimation. | The authors present an approach for reducing the threshold observation time required to achieve high-resolution localization of multiple broadband sources. The proposed techniques are based on a space-time statistic called the steered covariance matrix (STCM). The STCM, like the well-known cross-spectral density matrix (CSDM), has asymptotic properties which facilitate high-resolution source localization. In broadband settings, however, the STCM has the advantage that it can be estimated with much greater statistical stability than the CSDM. The STCM is used in conjunction with minimum variance and linear predictive spectral estimation to obtain the steered minimum variance (STMV) and steered linear prediction (STLP) methods. Analytical and simulation results are presented that indicate that the STMV and STLP methods exhibit lower threshold observation times than their CSDM-based counterparts. > |
Abstract-This letter studies the problem of Direction of Arrival (DoA) estimation from low-resolution few-bit quantized data collected by Sparse Linear Array (SLA). In such cases, contrary to the one-bit quantization case, the well known arcsine law cannot be employed to estimate the covaraince matrix of unquantized array data. Instead, we develop a novel optimizationbased framework for retrieving the covaraince matrix of unquantized array data from low-resolution few-bit measurements. The MUSIC algorithm is then applied to an augmented version of the recovered covariance matrix to find the source DoAs. The simulation results show that increasing the sampling resolution to 2 or 4 bits per samples could significantly increase the DoA estimation performance compared to the one-bit sampling regime while the power consumption and implementation costs is still much lower in comparison to the high-resolution sampling implementations.
Index Terms-Direction of arrival (DoA) estimation, lowresolution quantization, Sparse linear arrays, few-bit quantization.
I. INTRODUCTION
Direction of Arrival (DoA) estimation from Uniform Linear Array (ULA) measurements is extensively studied in the literature [1][2][3]. However, the number of identifiable sources with ULAs is limited to the number of array elements minus one [3,4]. Deployment of Sparse Linear Arrays (SLAs), e.g. Minimum Redundancy Arrays (MRAs) [5], co-prime arrays [6] and nested arrays [7], allows for transcending this limitation under the assumption of uncorrelated source signals such that the number of identifiable sources can go considerably beyond the number array elements. A detailed study on the performance of DoA estimation via SLAs has been conducted in [8] through an analysis of the Cramér-Rao Bound (CRB). Further, a variety of algorithms for estimating DoAs from SLA data have been presented in the literature [7,[9][10][11][12][13][14][15].
Most of the algorithms developed for estimating DoAs from SLA measurements are based on the assumption that quantization errors are negligible as a result of using high-resolution Analog-to-Digital Converters (ADCs). However, use of highresolution ADCs is typically expensive and power-hungry [16]. Hence, to reduce energy consumption and production costs, DoA estimation with binary measurements collected by onebit ADCs has been recently proposed and discussed in the literature [17][18][19][20][21][22][23][24][25][26][27]. One-bit ADCs represent each sample of the analog array observations with only a single bit offering, an exceedingly high sampling rate at a low production cost and very low power consumption [16]. The analytical performance bounds for DoA estimation from one-bit data have been studied in [28][29][30]. Further, a number of one-bit DoA estimators have been provided in [23][24][25]27], which rest on retrieving the covariance matrix of unquantized array observations using the well-known Bussgang theorem [31].
In this paper, as opposed to the previous works which have studied the problem of DoA estimation under two extreme scenarios for analog-to-digital conversion, i.e., infinite-bit quantization and one-bit quantization, we aim to investigate the problem of estimating DoAs from low-resolution few-bit SLA measurements. In such cases, contrary to the one-bit quantization case, the Bussgang theorem may not be directly employed to retrieve the covaraince matrix of array unquantized observations. Instead, we develop a novel optimization-based framework for retrieving the covaraince matrix of unquantized array observations from low-resolution multi-bit measurements. Then, we apply the Co-Array-Based MUSIC (CAB-MUSIC) [7,13] to the recovered covariance matrix to find the DoAs of interest. The simulation results show that increasing the sampling resolution with a few bits per samples could significantly improve the DoA estimation performance compared to the one-bit sampling case while the power consumption and implementation costs are still much lower than the highresolution scenario.
Paper organization: The system model is described in Section II. Section III presents the proposed algorithm for estimating DoAs from few-bit data. Simulation results are shown and discussed in Section IV. Finally, conclusions are drawn in Section V.
Notation: : Lightface, lower-and upper-case bold-face letters denote scalars, vectors and matrices, respectively. The conjugate, transpose and Hermitian (conjugate transpose) operations are referred to by the superscripts * , T , H, respectively. A F and rank(A) stand for the Frobenius norm and the rank of A, respectively. II. SYSTEM MODEL We consider an SLA with M elements located at positions
m 1 λ 2 , m 2 λ 2 , · · · , m M λ 2 with m i ∈ M.
Here λ denotes the wavelength of the incoming signals and M is a set of integers with a cardinality of M . It is assumed that K narrowband signals with distinct DoAs θ = [θ 1 , θ 2 , · · · , θ K ] T impinge on the SLA from far-field. The signal received by the array at time instance t can be modeled as
y(t) = A(θ)s(t) + n(t) ∈ C M ×1 , t = 0, · · · , N − 1,(1)
where
s(t) ∈ C K×1 denotes the vector of K source signals, n(t) ∈ C M ×1 is additive noise, and A(θ) = [a (θ 1 ) , a (θ 2 ) , · · · , a (θ K )] ∈ C M ×K represents the SLA steering matrix with a(θ k ) = [e jπ sin θ k m 1 , e jπ sin θ k m 2 , · · · , e jπ sin θ k m M ] T ,(2)
being the SLA manifold vector for the k th signal. Further, the following assumptions are made on source and noise signals: A1 n(t) follows a zero-mean circular complex Gaussian distribution with the covariance matrix E{n(t)n H (t)} = σ 2 I M . A2 The source signals are modeled as zero-mean uncorrelated circular complex Gaussian random variables with covariance matrix
E{s(t)s H (t)} = diag(p) where p = [p 1 , p 2 , · · · , p K ] T ∈ R K×1 >0
(i.e., p k > 0, ∀k). A3 No temporal correlation is assumed between the snapshots, i.e., E{n(t 1 )n H (t 2 )} = E{s(t 1 )s H (t 2 )} = 0 when t 1 = t 2 and 0 is an all-zero matrix of appropriate dimensions. Based on the above assumptions, the covariance matrix of y(t) is given by
R = E{y(t)y H (t)} = A(θ)diag(p)A H (θ)+σ 2 IM ∈ C M ×M . (3)
It is readily verified that R is a structured matrix with only
2D−1 free parameters where D = |D| with D = {|m p − m q | : m p , m q ∈ M}.
The set D is called the difference co-array [8,15]. Noticing the structure in R, it can be rewritten as follows
R(u) = u0L0 + D−1 n=1 unLn + D−1 n=1 u * n L T n ,(4)where u0 = σ 2 + K k=1 p k , un = K k=1 p k e jπ sin θ k n and [Ln]p,q = 1, if mp − mq = n, 0, otherwise,(5)
with n ∈ D, m p , m q ∈ M, 1 ≤ p, q ≤ M and 0 ≤ n ≤ D − 1. A proper design of SLA allows for identifying more uncorrelated source signals than the number of array elements by exploiting the resulting structure of R efficiently [6][7][8]15]. Fig. 1 illustrates an SLA along with its difference co-array.
In the classical mode, the received signals are sampled at Nyquist rate and processed assuming full-precision analog-todigital conversion. On the other hand, herein, we assume that each array sensor is equipped with a low-resolution multi-bit ADC converting the received analog signal into digital data using q bits per sample. A generic q-bit ADC has 2 q − 1 threshold levels where α1 < α2 < · · · < 0 < · · · < α2q < α2q−1. The q-bit ADC at the m th array element transforms the real and imaginary parts of [y(t)] m into one of the 2 q − 1 prescribed qunatization levels {γ1, γ2, · · · , γ2q−1} by comparing them individually with the threshold levels. Particularly, the q-bit quantized output signal at the m th array element is expressed as
[x(t)]m = Q([ {y(t)}]m) + jQ([ {y(t)}]m),(6)
where Q(.) denotes the q-bit quantization operation defined as
Q(a) = γ h if α h ≤ a < α h+1 .(7)
We are interested in estimating DoAs from qbit quantized output signals of the SLA, i.e., X = x(0), x(1), · · · , x(N − 1) .
III. MULTI-BIT DOA ESTIMATION WITH SPARSE ARRAYS
In this section, we first formulate an optimization problem whose solution provides us with an estimate of the covariance matrix of y(t), i.e., R, using q-bit quantized array measurements, i.e., X. Subsequently, we apply the CAB-MUSIC [7,13] to obtain DoA estimates from the estimate of R.
It follows from (4) that R is fully described by the complex vector u = [u 0 , u 1 , · · · , u D−1 ] T . Hence, for a given Y = y(0), y(1), · · · , y(N − 1) , R can be obtained from the solution of the following optimization problem
minimize u R(u) − YY H 2 subject to R(u) 0.(8)
However, Y is unknown here, and instead, we only have access to its q-bit quantized values, i.e., X. It follows from (6) and (7) that each element of the observation matrix X determines a lower and an upper bound for the real and imaginary parts of the corresponding element in Y. Putting these lower and upper bound into the matrices Γ l and Γ u , an optimization problem for joint estimation of u and Y can be cast as follows:
minimize u,Y R(u) − YY H 2 F subject to R(u) 0, vec( {Y} − {Γ l }) ≥ 0, vec( {Y} − {Γ l }) ≥ 0, − [vec( {Y} − {Γu})] ≥ 0, − [vec( {Y} − {Γu})] ≥ 0.(9)
where the last four constraints in (9) aim to enforce the consistency of Y with the q-bit measurements by ensuring that the elements of Y lie in the regions determined by the observation matrix X. The above optimization problem is nonconvex as its objective is a quartic function with respect to Y.
In what follows, we first present an equivalent reformulation for (9), which paves the way for iteratively solving this non-convex optimization problem.
where T = I N Y H Y W(10)
∈ C (M +N )×(M +N ) and η is a regularization parameter.
Proof. Consider the slack variables W = YY H . Then it is readily seen that the optimization problem (9) is equivalent to: (11) can be replaced with a rank constraint on a semi-definite matrix. Hence, the optimization problem (11), and equivalently (9), can be recast as follows:
minimize u,Y,W R(u) − W 2 F subject to R(u) 0, vec( {Y} − {Γ l }) ≥ 0, vec( {Y} − {Γ l }) ≥ 0, − [vec( {Y} − {Γ u })] ≥ 0, − [vec( {Y} − {Γ u })] ≥ 0, W = YY H .(11)minimize u,Y,W R(u) − W 2 subject to R(u) 0, vec( {Y} − {Γ l }) ≥ 0, vec( {Y} − {Γ l }) ≥ 0, − [vec( {Y} − {Γ u })] ≥ 0, − [vec( {Y} − {Γ u })] ≥ 0, T 0, rank(T) = N.(12)
The constraint rank(T) = N in (12) is equivalent to imposing the constraint that the M smallest eigenvalues of T are all zero. This constraint on the M smallest eigenvalues of T can be formulated by introducing the new slack variables G ∈ C (M+N )×M and ξ ∈ R with G H G = I M . Indeed, in what follows, we will show the M smallest eigenvalues of T are all zero if ξI M − G H TG 0 and ξ → 0. Let ρ 1 ≤ ρ 2 ≤ · · · ≤ ρ M +N and ν 1 ≤ ν 2 ≤ · · · ≤ ν M denote the eigenvalues of T and G H TG, respectively. From ξI M − G H TG 0, we have ν i ≤ ξ for i = 1, 2, · · · , M . Additionally, it follows from [33,Corollary 4.3.16] that 0 ≤ ρ i ≤ ν i for i = 1, 2, · · · , M . Hence, we observe that
0 diag([ρ1, ρ2, · · · , ρM ] T ) diag([ν1, ν2, · · · , νM ] T ) ξIM .(13)
It easily observed from (13) that ξ → 0 leads the M smallest eigenvalues of T to go to zero. Accordingly, we can deduce that, by properly selecting η in (13) such that the optimum value of ξ goes to zero, the constraints ξI M −G H TG 0 and G H G = I M in (13) will be equivalent to the rank constraint in (12). This implies that (13) is equivalent to (12) and thus to (9). This completes the proof.
The optimization problem (10) can be solved iteratively by alternating between G and the other parameters, i.e., u, Y, W and ξ. Let G (k) , u (k) , Y (k) , W (k) and ξ (k) be the values of the parameters G, u, Y, W and ξ at the k-th iteration, respectively. Given G (k−1) , the optimization problem with respect to u, Y, W and ξ at the k-th iteration becomes
minimize u (k) ,Y (k) ,W (k) ,ξ (k) R(u (k) ) − W (k) 2 F + ηξ (k) subject to R(u (k) ) 0, vec( {Y (k) } − {Γ l }) ≥ 0, vec( {Y (k) } − {Γ l }) ≥ 0, − vec( {Y (k) } − {Γu}) ≥ 0, − vec( {Y (k) } − {Γu}) ≥ 0, T (k) 0, ξ (k) IM −G (k−1) H T (k) G (k−1) 0, ξ (k) ≤ ξ (k−1) .(14)
Once T (k) , u (k) and ξ (k) are found by solving (14), G (k) can be obtained by seeking an (M+N )×M matrix with orthonormal columns such that
G (k) H T (k) G (k) ξ (k) I M . Choosing G (k)
to be equal to the matrix composed of the eigenvectors of T (k) corresponding to its M smallest eigenvalues, and following similar arguments provided after (12), we have
G (k) H T (k) G (k) = diag([ρ (k) 1 , ρ (k) 2 , · · · , ρ (k) M ] T ) diag([ν (k−1) 1 , ν (k−1) 2 , · · · , ν (k−1) M ] T ) ξ (k) IM ,(15)
where ρ
(k) 1 ≤ ρ (k) 2 ≤ · · · ≤ ρ (k) M +N and ν (k−1) 1 ≤ ν (k−1) 2 ≤ · · · ≤ ν (k−1) M
denote the eigenvalues of T (k) and G (k−1) H T (k) G (k−1) , respectively. It follows from (15) that the matrix composed of the eigenvectors of T (k) corresponding to its M smallest eigenvalue is a right choice of G (k) . Accordingly, at each iteration of the proposed algorithm, we need to solve a Semi-Definite Program (SDP), which can be solved efficiently, followed by an Eigenvalue Decomposition (ED). The alternating optimization procedure is repeated until either the objective or the optimization variables converge to a constant value. Algorithm 1 summarizes the steps of the aforementioned iterative approach to solving (9). Further, to initialize the algorithm, G (0) can be found through the ED of T (0) obtained from solving (12) without considering the rank constraint. We note that the proposed algorithm, which is based on alternating optimization method, is guaranteed to converge to at least a local minimum of (10) [34]. Once R is retrieved from Algorithm 1, the CAB-MUSIC [7,13] is applied to the retrieved R to estimate DoAs.
IV. SIMULATION RESULTS
In this section, numerical results are provided for assessing the performance of the proposed algorithm for estimating DoAs from low-resolution few-bit SLA output. In all experiments, each simulated point has been computed by 1000 Monte Carlo repetitions over noise realizations. In addition, the K independent sources with an equal power p are equispaced in the angular domain [−60°, 60°] with respect to a 8-sensor nested array with M : {1, 2, 3, 4, 5, 10, 15, 20} . The SNR is also defined as 10 log p σ 2 . Fig. 2 demonstrates that increasing the number of quantization bits from one to two and then to four leads to a considerable performance improvement. Further, it is observed that the RMSE of 4-bit Algorithm 1 Covarinace Matrix Estimatiton from Low-Resolution Few-Bit Data Input: The problem information Γ l , Γu, η, 1 , 2 , 3 and 4 . Output: The estimate of the covariance matrix of the fullprecision data. 1: initialization: Set k = 0 and obtain G (0) by dropping the rank constraint.
2: while u (k) −u (k−1) 2 ≥ 1 , W (k) −W (k−1) F ≥ 2 , Y (k) − Y (k−1) F ≥ 3 and ξ (k) ≥ 4 do 3:
Increase k by one. 4: Find u (k) , W (k) , Y (k) and ξ (k) by solving (14). 5: Compute the ED of T (k) . 6:
G (k) equals the matrix composed of the eigenvectors of T (k) corresponding to its M smallest eigenvalues. 7: end while DoA estimation is very close to that of DoA estimates obtained from the unquantized array observations. For instance, when K = 4, the performance loss arising from quantization, defined as 10 log(RMSE quantized /RMSE unquantized ), at SNR = 5 dB are about 3.33 and 1.39 dB in case of 1-bit and 2-bit quantization, respectively, while it is almost zero in case of 4-bit quantization. However, the implementation costs and power consumption of 4-bit and 2-bit ADCs are still much lower compared to high-resolution ADCs. For example, at sampling frequency of 10 MHz, a 14-bit ADC consumes roughly 10 3 times more power than 2-bit and 4-bit ADCs [35]. The gap between the power consumption of low-and high-resolution ADCs further increases with higher sampling frequencies, e.g. at sampling frequency of 1 GHz, a 14-bit ADC consumes roughly 10 5 times more power than 2-bit and 4-bit ADCs [35]. Further, it is relatively easy to implement 4-bit and 2-bit ADCs even at very high sampling frequencies while implementation feasibility of high-resolution ADCs moves from difficult at sampling frequencies of ∼ 1 MHz to infeasible beyond those sampling frequencies [35]. Moreover, it is seen that the proposed method in case of 1-bit quantization performs as well as the one-bit DoA estimator in [24], which relies on estimating the covariance matrix of unquantized array observations directly from one-bit data using the Bussgang theorem. Fig. 3 plots the RMSE for θ 2 in degree versus the number of snapshots for SNR = 0 dB and: (a) K = 4 < M , and (b) K = 10 > M . Fig. 3 shows that, to achieve an RMSE of 0.1 for example, infinite-bit, 4-bit, 2-bit and one-bit cases need 300, 300, 500 and 800 samples when K = 4, respectively. This indicates that the total number of bits required to achieve an RMSE of 0.1 is, respectively, 1200, 1000 and 800 bits for 4-bit, 2-bit and one-bit sampling scenarios.
V. CONCLUSION
The problem of DoA estimation from low-resolution fewbit SLA data was investigated. Firstly, the covariance matrix of unquantized array observations was retrieved from low-resolution few-bit SLA data by employing an iterative optimization-based algorithm. Then, DoAs were estimated by applying CAB-MUSIC to the recovered covariance matrix of unquantized array observations. The simulation results showed that increasing the sampling resolution to 2 or 4 bits per samples could significantly increase the DoA estimation performance compared to the one-bit sampling case while the power consumption and implementation costs are still much lower than the high-resolution sampling scenario.
[a] i indicates the i th entry of a. diag(a) is a diagonal matrix made out of entries of a. I M denotes an M × M identity matrix. {a} and {a} stand for the real and imaginary parts of a, respectively.
Figure 1 .
1(a) An SLA with M = {1, 2, 3, 4, 8, 12}; (b) corresponding difference co-array with D = {0, 1, · · · , 11}.
Theorem 1 .
1Consider slack variables G ∈ C (M+N )×M , W ∈ C M×M and ξ ∈ R. The optimization problem (9) is equivalent to minimize u,Y,W,G,ξ R(u) − W 2 F + ηξ subject to R(u) 0, vec( {Y} − {Γ l }) ≥ 0, vec( {Y} − {Γ l }) ≥ 0, − [vec( {Y} − {Γu})] ≥ 0, − [vec( {Y} − {Γu})] ≥ 0, T 0, ξIM − G H TG 0, G H G = IM ,
It is readily confirmed that W = YY H if and only if rank(W−YY H ) = 0. Further, rank(W−YY H ) = 0 can be equivalently expressed as rank(I N ) + rank(W − YY H ) = N . Since I N is positive definite, it follows from the Guttman rank additivity formula[32] that rank(I N ) + rank(W − YY H ) = rank(T). Moreover, it follows from W − YY H = 0 and I N 0 that T has to be positive semi-definite. These imply that the equality constraint in
Fig. 2 depicts the Root-Mean-Squares-Error (RMSE) for θ 2 in degree versus SNR for different bit-width when N = 300, M = 8 and: (a) K = 4 < M ; (b) K = 10 > M .
Figure 2 .
2RMSE in degree for θ 2 versus SNR for a nested array with M = 8 elements and configuration given in (IV), N = 300, and: (a) K = 4 < M ; (b) K = 10 > M .
Figure 3 .
3RMSE in degree for θ 2 versus the number of snapshots for a nested array with M = 8 elements and configuration given in (IV), SNR = 0 dB, and: (a) K = 4 < M ; (b) K = 10 > M .
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| Multiple signal classification (MUSIC) can be seen as one of the most popular solutions to the direction-of-arrival estimation problem in array signal processing. Traditionally, this method utilizes the whole array observations to construct the noise subspace. In this letter, based on the randomly chosen sensors outputs, we exploit the Nystrom method to approximate the noise subspace, and develop a low-complexity modified MUSIC version for far-field sources localization. Computer simulations confirm that the novel algorithm using only one-fourth sensors outputs provides almost the same estimation performance as its traditional version. | In this paper, a partitioned matrices products approach based on Gerschgorin disk estimation (PM-GDE) method is proposed in order to solve the problem of correlated source number estimation under spatially correlated noise background. This method is based on a uniform linear array. The improved partitioned matrices products of the array receiving data are computed by weighted summation of the rows and adjustment of the element sequence from partitioned matrices products matrix. The auto correlation matrix of the partitioned matrices products and its Gerschgorin radii are computed. A source number estimation criterion based on Gerschgorin radii is deduced by considering the second-order statistical property of the partitioned matrices products auto correlation matrix. Simulations results validate the efficiency and robustness of PM-GDE with correlated signals and spatially correlated noise background. PM-GDE performs better than its counterpart especially for close incident azimuth correlated sources. | Direction-of-arrival (DOA) estimation with spatially displaced electro-magnetic vector-sensors (SD-EMVS) is considered in this paper. Instead of the conventional single-set formulation of SD-EMVS outputs, the array signals here are interpreted as a multi-set problem. The steering vectors are identified via a newly proposed multi-set approach named generalized non-orthogonal joint diagonalization (GNJD). DOA estimates are then extracted from these steering vectors via vector cross-product based methods. Numerical simulations demonstrate that, compared with conventional single-set approaches, the proposed multi-set method provides more accurate DOA estimates. | Detection of the number of signals and estimation of their directions of arrival (DOAs) are fundamental problems in array processing. We present three main contributions to these problems, under the conditional model, where signal amplitudes are assumed deterministic unknown. First, we show that there is an explicit relation between model selection and the breakdown phenomena of the Maximum Likelihood estimator (MLE). Second, for the case of a single source, we provide a simple approximate formula for the location of the breakdown of the MLE, using tools from the maxima of stochastic processes. This gives an explicit formula for the source strength required for reliable detection. Third, we apply these results and propose a new joint detection-estimation algorithm with state-of-the-art performance. We demonstrate via simulations the improved detection performance of our algorithm, compared to other popular source enumeration methods. | The two-dimensional (2-D) direction-of-arrival (DOA) estimation for incoherently distributed (ID) sources always has a high computational complexity because it depends on multidimensional search. To reduce the complexity, we propose a new method based on three closely parallel unity linear arrays (ULAs). This method derives the approximation of three received ULA vectors under small angular extension from first-order Taylor approximation. The derived vector approximations are rotationally invariant, which enables one to estimate 2-D DOAs of ID sources via propagator. This procedure is more efficient because no multidimensional search or eigen-decomposition is needed. Simulation results testify to the performance of the proposed method. | 239 |
I. INTRODUCTION
Direction-of-arrival (DOA) estimation is a fundamental problem in statistical and array signal processing. It refers to the problem of estimating the directions of a number of sources impinging on a sensor array given a series of snapshots of the output of the sensor array [3]. In this paper, we consider DOA estimation for far-field narrowband sources using a uniform or sparse linear array (ULA or SLA), resulting in a DOA estimation problem equivalent to multiple-snapshot spectral analysis, a topic at the core of wireless channel estimation [4], radar signal processing [5], structural health monitoring [6] and fluorescence microscopy [7]. The SLA corresponds to the missing data case in the language of spectral analysis [8] or compressive data in the language of compressed sensing [9], [10] and brings new challenges to theoretical analysis and algorithm design.
The use of SLAs for DOA estimation dates back to [11] and has been extensively studied in the past two decades with an emphasis of localizing O(M 2 ) sources using M sensors only.
The key to achieving such a goal is that under the assumption of uncorrelated sources the data covariance matrix regarding a Part of this paper was presented in the 2021 CIE IEEE International Conference [1] and part will be presented in the 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) [2].
The authors are with the School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China (e-mail: [email protected]).
ULA becomes Toeplitz and thus can be determined by a few of its entries. With this in mind, different array geometries for SLAs, e.g. minimum redundancy arrays (MRAs) [11], nested arrays [12]- [14] and coprime arrays [15], [16], have been proposed that determine which entries (indexed by the coarray) are sampled to reconstruct the whole or a shrunk version of the Toeplitz covariance matrix. The assumption of uncorrelated sources is crucial to guarantee the Toeplitz covariance structure, however, it is not always satisfied. In fact, correlated and coherent (fully correlated) sources usually occur in practice due to multipath propagations and other effects, and dealing with them has always been a central topic in DOA estimation (see, e.g., [17]- [22]). Consequently, the goal of localizing more uncorrelated sources than sensors by using the Toeplitz covariance structure seemingly contradicts with the one of robust localization of highly correlated and coherent sources, making the practical use of previous methods questionable in correlated environments. In the present work, we make the first attempt to achieve the two goals simultaneously and resolve the above concern.
It is well-known that the maximum likelihood (ML) method, if solvable, provides benchmark performance for DOA estimation. Under the assumption of uncorrelated sources, the stochastic ML (SML) method can be used to localize the maximal number of sources with statistical efficiency. Its asymptotic performance, in terms of the Cramér-Rao bound (CRB), has been well understood [23], [24]. However, few algorithms have been proposed for the SML method since it resorts to a highly nonconvex optimization problem. The challenges arise due to the nonlinearity with respect to the DOAs, the nonconvex log-det term in the SML criterion function and the source number constraint, and it becomes even worse in the SLA case. In this work, in order to achieve the aforementioned two goals simultaneously, we present an effective algorithm for the SML and prove that the SML for uncorrelated sources is robust to source correlations. Our main contributions are summarized below. 1) We start with the specialized ULA case and formulate the SML optimization problem as a rank-constrained Toeplitz covariance estimation problem, which is further transformed as sequential rank-constrained semidefinite programs (SDPs) by applying a majorizationminimization (MM) technique [25]. An elegant reformulation of the rank-constrained SDP is derived to fit and solved using the alternating direction method of multipliers (ADMM) encouraged by its successes in solving nonconvex problems [26], [27]. The resulting algorithm is named as maximum-likelihood estimation via sequential ADMM (MESA) (see Section III). 2) In the general SLA case, we repeat the above derivations and show that the SML problem can be similarly solved, extending MESA to this case (see Section IV). 3) While the SML method concerned in the present paper is derived under the assumption of uncorrelated sources, we prove that it produces consistent estimates of the DOAs and the source powers (regardless of source correlations) as the noise vanishes, implying its robustness to correlated and coherent sources (see Section V). 4) Numerical results are provided confirming statistical efficiency of MESA for uncorrelated source localization, in cases when the source number is less than or greater than the sensor number, and its robustness to correlated and coherent sources (see Section VI).
A. Relations to Prior Art
The SML method is known also as unconditional ML and has a long history of research. Its asymptotic performance in the ULA case, in terms of the CRB, is well documented in literature [28], [29]. To solve the SML optimization problem, expectation maximization (EM) and Newton-type algorithms have been proposed in earlier works [30], [31] but their performance heavily depends on the initialization step. Instead of solving for an exact ML estimator, great efforts have been made to develop algorithms that have the same asymptotic performance as the SML. Such examples include multiple signal classification (MUSIC) [32], method of direction estimation (MODE) [33] and weighted subspace fitting (WSF) [34]. Good reviews can be found in [35], [36]. But it is worth noting that these algorithms usually consider the ULA and assume deterministic (as opposed to uncorrelated) sources and thus cannot be used to localize more sources than sensors with an SLA.
Sparse optimization and compressed sensing methods [37]- [39], which have become popular since early of this century, do not use explicitly the array geometry and fit into the SLA case. The recent atomic norm and gridless compressed sensing methods [40]- [44] are remedies of earlier compressed sensing methods by working with continuous (as opposed to on-grid) DOAs and providing theoretical guarantees. These methods do not make statistical assumptions on the sources and are robust to source correlations. But correspondingly, they cannot localize more sources than sensors. Readers are referred to [45] for a review.
To localize more uncorrelated sources than sensors, a coarray-based averaging/selection (CBA/S) step is usually adopted to explicitly use the Toeplitz covariance structure and transform the sample covariance matrix regarding the SLA as an output regarding an enlarged virtual ULA, followed by a DOA estimation method for ULAs; see such two-step estimation approaches in [46]- [51], to name just a few. It is shown in [23] that CBA combined with spatial-smoothing (SS) MUSIC results in strictly non-efficient solutions. A state-ofthe-art method is proposed in [52] that uses a weighted least square (WLS) criterion for the vectorized sample covariance and is shown to yield an asymptotically efficient estimator. An iterative algorithm is also proposed to solve the resulting nonconvex optimization problem. While these methods are tailored for uncorrelated sources, it is confirmed by numerical results in this paper that they are indeed sensitive to highly correlated sources. In contrast to this, MESA achieves statistical efficiency and robustness to source correlations simultaneously.
Several algorithms have been proposed to deal with a mixture of uncorrelated and coherent sources given the source coherence structure [20]- [22], [53]. Differently from these algorithms, MESA allows the sources to be correlated but noncoherent and needs only the total number of sources (as opposed to the detailed coherence structure).
The SML method in the ULA case is closely related to structured (to be specific, Toeplitz) covariance estimation (see e.g., [54]- [57]) because the data covariance matrix is the sum of a low-rank Toeplitz covariance and the noise covariance, where the rank is specified by the source number and the DOAs are uniquely determined by the Toeplitz covariance matrix. While the low-rank constraint is a major challenge for Toeplitz covariance estimation, it is explicitly considered in [58], [59]. In [58], the Toeplitz structure is relaxed initially and then used to obtain a Toeplitz approximation of an intermediate solution, which does not result in an exact SML estimator. In [59], the noise variance is assumed known and the Carathéodory-Fejér theorem [45,Theorem 11.5] is invoked to approximate the Toeplitz covariance by a Vandermonde decomposition in which the frequency nodes of the Vandermonde matrix are restricted on a fixed grid so that the original problem is transformed as one of nonnegative sparse vector recovery. In contrast to these methods, we make no approximations or relaxations and MESA solves the exact SML. Moreover, MESA is usable in the SLA case.
Since the difficulty in solving the SML problem partly comes from the source number constraint, which is known as signal sparsity in compressed sensing, it is relaxed in sparse Bayesian learning (SBL) methods [60]- [62]. Similar relaxation techniques are also used in covariance fitting methods [63]- [67], which are approximate versions of the SML method by using convex surrogates for its criterion function. Interestingly, it has been empirically observed in [60], [64], [65] that the resulting algorithms are robust to source correlations though they are derived by assuming uncorrelated sources. In the recent work [68], the case of two correlated sources is considered and it is shown that if the DOAs and the noise variance are known a priori, then the source powers can be stably estimated from the SML method. In contrast to this, our result on robustness is applicable to any source number and shows that the DOAs can be accurately estimated jointly with the source powers, at least in the high SNR regime. It also partially explains the observations in [60], [64], [65].
B. Notation
The sets of real and complex numbers are denoted by R and C respectively. For vector x, diag (x) denotes a diagonal matrix with x on the diagonal. The jth entry of vector x is x j . For matrix A, A T , A H , |A|, A −1 , rank (A), tr (A) and A F denote the matrix transpose, conjugate transpose, determinant, inverse, rank, trace and Frobenius norm of A, respectively. The complex conjugate of scale x is denoted by x. The notation A ≥ 0 means that A is Hermitian positive semidefinite. For index set Ω and matrix A, A Ω represents a submatrix of A obtained by keeping only the rows indexed by Ω unless otherwise stated. The inner product is represented by ·, · . For matrices Y and C ≥ 0, we define
tr Y H C −1 Y = min X tr (X) , subject to X Y H Y C ≥ 0
(1) whenever C is positive definite or not. The expectation of a random variable is denoted by E[·]. Assume that K far-field narrowband sources impinge on the ULA in which adjacent sensors are placed by half a wavelength apart. The output of the sensor array at each snapshot composes an N × 1 complex vector y that can be modeled as [3], [36]:
y(l) = K k=1 a (f k ) x k (l) + e(l), l = 1, . . . , L,(2)
where L is the number of snapshots, x k (l) is the kth (complex) source signal at the lth snapshot, f k ∈ [− 1 2 , 1 2 ) has a one-toone connection to the kth DOA θ
k ∈ [−90 • , 90 • ) by f k = 1 2 sin θ k , a (f k ) denotes an N × 1 steering vector given by a (f ) = [1, e i2πf , . . . , e i2(N −1)πf ] T ,(3)
and e(l) is the vector of complex noise. It is seen that all snapshots share the same parameters {θ k } and {f k }. By stacking {x k (l)} , {f k } into vectors x(l), f and defining the steering matrix (2) is written compactly as:
A (f ) = [a (f 1 ) , . . . , a (f K )] that is N × K Vandermonde, the data model iny(l) = A(f )x(l) + e(l), l = 1, . . . , L.(4)
In the general SLA case, the array output at one snapshot is a subvector of y(l), denoted by y Ω (l). The data model in (4) thus becomes
y Ω (l) = A Ω (f )x(l) + e Ω (l), l = 1, . . . , L,(5)
which encompasses (4) as a special case. Our objective is to estimate the DOAs {θ k } K k=1 , or equivalently {f k } K k=1 , given the multiple-snapshot data {y Ω (l)}
K l=1
under certain statistical assumptions on the source signals {x(l)} and noise {e(l)}. Since each f k is the frequency of a sinusoid, the DOA estimation problem that we concern is equivalent to multiple-snapshot spectral estimation with missing data. We focus on the estimation of {f k } K k=1 throughout this paper.
B. The SML Method for DOA Estimation
We make the following assumptions to derive the SML method for DOA estimation. A1: The sources {x(l)} are spatially and temporally independent and follow a complex Gaussian distribution with zero mean and covariance P = diag (p 1 , . . . , p K ), where p k > 0 denotes the kth sources power; A2: The noises {e(l)} are spatially and temporally independent and each entry follows a complex Gaussian distribution with zero mean and variance σ > 0; A3: The sources and noises are independent. It follows immediately that {y Ω (l)} are i.i.d. Gaussian with zero mean and covariance
R Ω = A Ω (f )P A H Ω (f ) + σI.(6)
By maximizing the likelihood criterion, or equivalently minimizing the negative log-likelihood function, we obtain the SML optimization problem as:
min f ,p,σ ln |R Ω | + tr R −1 Ω R Ω ,(7)
where
R Ω = 1 L L l=1 y Ω (l)y H Ω (l)(8)
is the sample covariance matrix.
The SML method has good statistical properties. But the SML problem in (7) is nonconvex and complicated to solve due to the log-det term and the nonlinearity of R Ω with respect to {f k } K k=1 . Moreover, the SML is derived under the assumption of uncorrelated sources and its performance is unclear in presence of source correlations.
C. The ADMM Algorithm
The ADMM algorithm solves the following optimization problem:
min x∈D1,q∈D2 g(x) + h(q), subject to Ax + Bq = c, (9)
where D 1 , D 2 defines the feasible domain of x, q respectively. Write the augmented Lagrangian function as:
L µ (x, q, λ) = g(x) + h(q) + Ax + Bq − c, λ + µ 2 Ax + Bq − c 2 2 = g(x) + h(q) + µ 2 Ax + Bq − c + µ −1 λ 2 2 + C,(10)
where λ is a Lagrangian multiplier, µ > 0 is a penalty coefficient and C is a constant independent of x, q. ADMM consists of the iterations:
x ← arg min
x∈D1 L µ (x, q, λ) ,(11)q ← arg min q∈D2 L µ (x, q, λ) ,(12)λ ← λ + µ (Ax + Bq − c) ,(13)
where the latest values of the other variables are always used. The ADMM algorithm has been extensively studied and practically used due to its global optimality in solving convex problems, simplicity in dealing with nonsmooth functions, and good scalability for solving high-dimensional problems [26]. Good performance has also been frequently achieved for nonconvex problems; see [27] and references therein. See also [69]- [71] for theoretical progresses on this topic. It is worth noting that the key to using ADMM to solve a specific problem is to provide an elegant problem formulation within the ADMM framework so that the two subproblems in (11) and (12) can be simply and efficiently solved.
III. MESA IN THE ULA CASE
In this section, we derive the MESA algorithm for the SML optimization problem in (14) in the specialized ULA case. In this case, we write the data and sample covariance matrices R Ω , R Ω into R, R for simplicity and the problem to solve becomes: min
f ,p,σ ln |R| + tr R −1 R ,(14)
where
R = A(f )P A H (f ) + σI.(15)
The MESA algorithm consists of re-parameterization, majorization-minimization, problem reformulation and ADMM steps which are detailed below.
A. Re-parameterization
The data covariance matrix R is a highly nonlinear function of {f k }. To overcome such nonlinearity, a common scheme is to utilize the fact that the first term A(f )P A H (f ) in (15) is rank-K positive-semidefinite Hermitian Toeplitz and do the re-parameterization:
R = T t + σI, T t ≥ 0, rank (T t) = K,(16)where T t = (t i−j ) N ×N with t = [t 1−N , . . . , t N −1 ]
T and t −j =t j , j = 0, . . . , N − 1. It follows from the Carathéodory-Fejér theorem [45,Theorem 11.5] that the T t above has a one-to-one connection to {f , p} given K < N . Consequently, the original SML problem (15) is transformed into a rankconstrained Toeplitz covariance estimation problem in which R is a linear function of the variables {t, σ}. Once t is solved for, the variables {f , p} can be computed from T t by a subspace method such as root-MUSIC [72].
B. Majorization Minimization
The objective function in (14) is nonconvex with respect to R since the log-det function ln |R| is concave on the positive semidefinite cone. A commonly used locally convergent method is the majorization-minimization (MM) algorithm (see, e.g., [73]) that drives the objective function downhill by minimizing a simple surrogate function. At the jth iteration of MM, the SML objective function is linearized (and thus majorized) at the previous iterate R j−1 = T t j−1 + σ j−1 I, yielding the problem (by omitting constant terms):
min tr R −1 j−1 R + tr R −1 R .(17)
Substituting (16) into (17), we obtain the problem to solve at the jth iteration as:
min t,σ≥0 tr(R −1 j−1 (T t + σI)) + tr (T t + σI) −1 R , subject to T t ∈ S K + ,(18)
where S K + is the set of positive semidefinite matrices of rank no greater than K.
C. Problem Reformulation
Let W = R −1 j−1 and Y be any matrix satisfying that R = Y Y H ,(19)
where Y has at most min(L, N ) columns. The objective function in (18) then becomes:
tr(W (T t + σI)) + tr Y H (T t + σI) −1 Y .(20)
Making use of the following identity [74,Lemma 5]:
tr X H (R 1 + R 2 ) −1 X = min Z tr Z H R −1 1 Z + tr (X − Z) H R −1 2 (X − Z) ,(21)where R 1 , R 2 ≥ 0, the function in (20) becomes a function of t, σ, Z: tr(W (T t+σI))+tr Z H [T t] −1 Z +σ −1 Y −Z 2 F . (22)
Since in (22) the optimizer to σ is given in close-form by:
σ * = 1 tr(W ) Y − Z F ,(23)
the objective in (22) can be concentrated with respect to t, Z, yielding the following problem to solve:
min t,Z tr(W T t) + tr Z H [T t] −1 Z + 2 tr(W ) Y − Z F , subject to T t ∈ S K + ,(24)
or equivalently,
min t,X,Z tr(W T t) + tr(X) + 2 tr(W ) Y − Z F , subject to X Z H Z T t ≥ 0, rank (T t) ≤ K.(25)
We next show that the problem in (25) is equivalent to the following:
min t,X,Z tr(W T t) + tr(X) + 2 tr(W ) Y − Z F , subject to X Z H Z T t ≥ 0, rank X Z H Z T t ≤ K.(26)
In particular, it is easy to see that the constraint rank(T t) ≤ K in (25) is implied by rank (26). To
X Z H Z T t ≤ K in
show the equivalence between (25) and (26), it suffices to show that the latter constraint is feasible for any optimizer to (25). Denote by (t * , X * , Z * ) an optimizer to (25) and suppose
T t * = T T H where T is an L ×K matrix with full column rankK ≤ K. Since X * Z * H Z * T t * ≥ 0, we have Z * = T V
for some V due to the column/row inclusion property and
X * = Z * H (T t * ) † Z * = V H V . Therefore, X * Z * H Z * T t * = V H V V H T H T V T T H = V H T V H T H(27)
whose rank isK ≤ K, completing the proof.
D. Using ADMM
We introduce an auxiliary matrix variable Q and rewrite (26) as
min t,X,Z,Q∈S K + tr(W T t) + tr(X) + 2 tr(W ) Y − Z F , subject to Q = X Z H Z T t ,(28)
which is exactly in the form of (9) by identifying that
x = {t, X, Z}, q = Q, g(x) = tr(W T t) + tr(X) + 2 tr(W ) Y − Z F , h(q) = 0 and D 2 = S K + .
Following the procedures of ADMM, we introduce the Hermitian Lagrangian multiplier Λ and write the augmented Lagrangian function as:
L µ (t, X, Z, Q) = tr(W T t) + tr(X) + 2 tr(W ) Y − Z F + tr((Q − Ax)Λ) + µ 2 Q − Ax 2 F = tr(W T t) + tr(X) + 2 tr(W ) Y − Z F + µ 2 Q − Ax + µ −1 Λ 2 F − 1 2µ Λ 2 F .(29)
The remaining task is to solve the two subproblems in (11) and (12).
To solve (11), by partitioning Q =
Q 1 Q H 2 Q 2 Q 3 and Λ = Λ 1 Λ H 2 Λ 2 Λ 3 as X Z H Z T t ,
we note that the objective function L µ is separable in {t, X, Z} and thus they can be solved for separately. To solve for t, we equate the derivative of L µ with respect to t to zero and obtain the update:
t ← (T * T ) −1 T * Q 3 + µ −1 Λ 3 − µ −1 W ,(30)
where T * is the Hermitian adjoint of T . Similarly, we have that
X ← Q 1 + µ −1 Λ 1 − µ −1 I.(31)
For Z, the optimization problem to solve is given by:
min Z tr(W ) Y − Z F + µ 2 Q 2 + µ −1 Λ 2 − Z 2 F ,(32)
yielding the update:
Z ← Y − 1 − tr(W ) µ L F + L,(33)
where (x) + max(x, 0) and L Y − Q 2 − µ −1 Λ 2 . The detailed derivations of (33) are deferred to Appendix A.
Solving (12) results in the update:
Q ← P S K + X Z H Z T t − µ −1 Λ ,(34)
where P S K + denotes the orthogonal projection onto S K + that can be computed by the truncated eigen-decomposition by keeping only the largest K positive eigenvalues and associated eigenvectors.
Finally, Λ is updated according to (13) as:
Λ ← Λ + µ Q − X Z H Z T t .(35)
The ADMM algorithm runs (30), (31), (33), (34) and (35) iteratively.
The overall MESA algorithm consists of the outer MM loop and the inner ADMM loop. Its computations are dominated by the truncated eigen-decomposition and the matrix inverse to compute W . Consequently, MESA has a computational complexity of O N 3 per inner iteration that is affordable in DOA estimation where the array aperture N is usually small.
IV. MESA IN THE SLA CASE
In this section, we consider the general SLA case and derive the MESA algorithm by repeating the same steps as in the previous section.
A. Re-parameterization
For a general SLA designated by Ω, let Γ ∈ {0, 1} M×N be the row-selection matrix satisfying that
y Ω = Γy(36)
for any N × 1 vector y and its subvector y Ω . Then, we have
R Ω = Ey Ω y H Ω = ΓRΓ T ,(37)
which is an M × M principal submatrix of R, defined in (15), and is re-parameterized as a linear function of (t, σ) following from (16).
B. Majorization Minimization
In this case, the objective function at the jth iteration becomes:
tr R −1 Ω,j−1 R Ω + tr R −1 Ω R Ω = tr Γ T R −1 Ω,j−1 ΓR + tr R −1 Ω Y Ω Y H Ω = tr (W R) + tr Y H Ω R −1 Ω Y Ω ,(38)
where R Ω,j−1 denotes the (j − 1)st iterate of R Ω , W = Γ T R −1 Ω,j−1 Γ, and Y Ω is any matrix satisfying that R Ω = Y Ω Y H Ω and has at most min(L, M ) columns.
C. Problem Reformulation
Making use of [74, Lemma 6], we obtain
tr Y H Ω R −1 Ω Y Ω = min Y Ω tr Y H R −1 Y ,(39)
where the set Ω denotes the complement of Ω. By substituting (39) and (16) into (38), the objective function becomes
tr(W (T t + σI)) + tr Y H (T t + σI) −1 Y(40)
with respect to t, σ, Y Ω , which is exactly in the form of (20). Consequently, the same derivations as in the ULA case can be applied, yielding the following optimization problem:
min t,X, Y Ω ,Z tr(W T t) + tr(X) + 2 tr(W ) Y − Z F , subject to X Z H Z T t ∈ S K + ,(41)
or equivalently,
min t,X,Z tr(W T t) + tr(X) + 2 tr(W ) Y Ω − Z Ω F , subject to X Z H Z T t ∈ S K +(42)
by noting that the solution to Y Ω is exactly Z Ω . In this process, as in (23), we have
σ * = 1 tr(W ) Y Ω − Z Ω F .(43)
D. Using ADMM
The only difference between (42) and (26) is the inclusion of the index set Ω in the term Y − Z F . Consequently, the only difference in the ADMM algorithm occurs in the update of Z. In particular, the objective function to minimize regarding Z changes from that in (32) to the following:
tr(W ) Y Ω − Z Ω F + µ 2 Q 2 + µ −1 Λ 2 − Z 2 F = tr(W ) Y Ω − Z Ω F + µ 2 Q 2 + µ −1 Λ 2 Ω − Z Ω 2 F + µ 2 Q 2 + µ −1 Λ 2 Ω − Z Ω 2 F .(44)
Therefore, it follows from (33) that
Z Ω ← Y Ω − 1 − tr(W ) µ L Ω F + L Ω ,(45)Z Ω ← Q 2 + µ −1 Λ 2 Ω ,(46)
where L is as defined below (33). The ADMM algorithm in this case runs (30)
V. ROBUSTNESS TO SOURCE CORRELATIONS
The assumption of uncorrelated sources is crucial to derive the SML method concerned in the present paper, for which the MESA algorithm is proposed. In this section, we show that the SML method is robust to source correlations, which implies robustness of MESA.
We consider the SLA case that consists of the ULA case when M = N . In order to show the robustness to source correlations, we will not use the statistical assumptions A1-A3 in Subsection II-B. Instead, we make the following (deterministic) assumptions, where f o , S o , σ o denote the true values of the parameters.
Y o Ω = A Ω (f o ) S o ; A5: Y Ω = A Ω (f o ) S o + E, where E is random noise satisfying that E 2 F = N Lσ o > 0 and inf f ,S Y Ω − A Ω (f ) S 2 F is strictly positive; A6:
A Ω (f ) has full column rank in a neighborhood of f o .
Assumption A4 seems necessary if no statistical assumptions are made on the source signals in S o . Note that A4 implies K < M . Given A4, A5 is trivial given random noise E since otherwise, E, translated by a constant vector A (f o ) S o , must be in a K-dimensional subspace. A6 is a technical assumption ensuring that the estimates of source powers are consistent. The following proposition is a result of combining [
K < Spark (Ω) + rank (S o ) − 1 2 ,(47)
where Spark (Ω) is defined as the smallest number of atoms in {a Ω (f )} that are linearly dependent. Our main result is stated in the following theorem. Theorem 1: Under assumptions A4-A6 and letting (f * , p * , σ * ) be the solution to the nominal SML optimization problem given by:
min {f k },{p k ≥0},{σ≥0} ln A Ω P A H Ω + σI + 1 L tr Y H Ω A Ω P A H Ω + σI −1 Y Ω ,(48)
we have that σ * > 0 and
lim σ o →0 σ * = 0,(49)
lim
σ o →0 f * = f o ,(50)lim σ o →0 p * k = 1 L S o k 2 ,(51)
where S o k denotes the kth row of S o .
Proof: See Appendix B. It is shown in Theorem 1 that the SML method produces consistent estimates of the DOAs and source powers as the noise vanishes regardless of (spatial and temporal) source correlations, implying its robustness to (spatially) correlated or coherent sources, at least in the high SNR regime.
Remark 1: Theorem 1 is related to [43,Theorem 2] which is concerned with the problem
min t ln |T t + ǫI| + tr Z H [T t] −1 Z , subject to T t ≥ 0,(52)
where Z = A (f o ) S o is noiseless and ǫ > 0 is a fixed small constant. In contrast to this, Theorem 1 is on the noisy case in which the noise variance σ is a variable to optimize. Another difference is that the source number is explicitly given in Theorem 1, while there is no a corresponding rank constraint on T t in (52). All these differences arise due to the fact that the problem in (52) was introduced in [43] as a surrogate function for the spectral sparsity of Z, rather than a consequence of the SML as in the present paper.
Remark 2: While the focus of this paper is on DOA estimation using SLAs, we note that Theorem 1 is applicable to arbitrary linear arrays for which the sensors are not necessarily located on a regular grid. Moreover, it can easily be extended to general joint sparse recovery problems [60], [75].
VI. NUMERICAL RESULTS
A. Experimental Setup
In this section, we present numerical results to illustrate the performance of the proposed MESA algorithm for DOA estimation using SLAs. In our implementation of MESA, R Ω is initialized with R Ω in general (a small scalar matrix is added if R Ω tends to be singular), while it is initialized as an identity matrix if the ratio of the Kth greatest eigenvalue and the smallest eigenvalue of R Ω is smaller than a threshold (set to 5) for better performance in presence of highly correlated sources. As for the first ADMM loop, Y Ω = R 1 2 Ω and R Ω are used to initialize Z Ω and the corresponding principal submatrix of Q 3 , respectively. Other variables are initialized with zero. The outer MM loop is terminated if the relative change of the negative log-likelihood function at two consecutive iterations is lower than 10 −5 or the number of iterations reaches 20. The ADMM iteration is terminated if the relative and absolute errors are below 10 −5 and 10 −4 , respectively (see [26,Section 3.3.1] for details), or a maximum number 1000 of iterations is reached. To better understand the performance of MESA, we also present its performance with a single MM iteration, termed as MESA-1. Note that the criterion of MESA-1 (when initializing R Ω with R Ω ) has been used in [64], [65] where the source number or the rank constraint is relaxed.
The methods that we use for comparison include SS-MUSIC [46], [47], WLS [52], multiple-snapshot Newtonized orthogonal matching pursuit (MNOMP) [44], [76], reweighted atomicnorm minimization (RAM) [43] and maximum-likelihood estimation of low-rank Toeplitz (MELT) [59]. SS-MUSIC is a popular CBA method and is implemented with forwardbackward SS and root-MUSIC. WLS is the only asymptotically efficient algorithm prior to this work when more uncorrelated sources than sensors are present. It is initialized with SS-ESPRIT following from [52]. MNOMP is a greedy algorithm for the deterministic ML and does not require a complex initialization. RAM tries to minimize the number of sources subject to data fidelity. MNOMP and RAM do not make statistical assumptions on the sources and cannot localize more sources than sensors. RAM requires the noise power rather than the source number. MELT solves the same SML problem as MESA but is usable only for ULAs. We also compare with the CRB that is computed following from [24] for uncorrelated sources, or based on a standard routine in presence of correlated sources.
All sources and noise are generated by using complex Gaussian distributions. All sources have unit powers. The signal-to-noise ratio (SNR) is defined as the ratio of the source power to noise power. The root mean squared error (RMSE) of the frequency estimates is computed as
1 K f − f o
B. Convergence and Optimality
In this subsection, we test the numerical performance of MESA in convergence and optimality by computing the negative log-likelihood function value at each outer MM iteration. To compare with MELT [59], we consider the ULA in (53). As in [59], the frequency domain [− 1 2 , 1 2 ) is approximated by a set of 2N − 1 uniform gridding points and the true frequencies are selected from the gridding points to achieve the best performance for MELT, which though is not required in MESA. We also compare with the function value computed with the true values of parameters and denoted by "ground truth". While the globally optimal function value is hard to obtain, it is expected that good accuracy is achieved if the obtained function value is smaller than the "ground truth". The true noise power σ o is also fed into MELT as in [59].
In Experiment 1, K = 3 sources are generated with DOAs such that the frequencies are taken as the 5th, 7th and 18th gridding points of MELT. We set SNR = 10dB and the number of snapshots L = 100. The curve of the function value with respect to the index of the MM iteration of MESA is plotted in Fig. 1. It is seen that the function value decreases monotonically and converges in 9 iterations. MESA produces a function value smaller than the ground truth and MELT, indicated by the two horizontal dashed lines. MESA takes 534 inner iterations in total.
We tried a total number of 500 Monte Carlo runs and MESA always converges and produces a function value smaller than the ground truth. It performs better than MELT in 498 out of 500 runs.
C. Statistical Efficiency for Uncorrelated Sources
In this subsection, we use the MRA in (54) and test the statistical efficiency of MESA for uncorrelated sources. RAM and MNOMP are considered only in the case of K < M .
In Experiment 2, We consider K = 7 sources with DOAs satisfying that the frequencies are taken in {−0.43, −0.28, −0.21, −0.05, 0.1, 0.26, 0.42}. We fix the number of snapshots L = 200 and vary the SNR from −10 to 20 dB. Our simulation results are presented in Fig. 2. It is seen that WLS and and MESA attain the CRB as SNR ≥ −5dB, while SS-MUSIC always produces an error greater than the CRB. It is interesting to note that the results of MESA-1 and MESA are almost indistinguishable. In this case, the sample covariance is a good estimate of the data covariance and a single outer loop of MESA suffices to produce an accurate estimate. In Experiment 3, we fix SNR = 10dB, L = 100 and vary K from 2 to N − 1 = 13. The K sources are generated with f k = −0.44 + 0.98(k − 1)/K, k = 1, . . . , K. Our simulation results are presented in Fig. 3. Again, WLS and MESA (and MESA-1) attain the CRB or even better whenever the number of sources is smaller or greater than the number of sensors, while SS-MUSIC cannot. NMOMP and RAM can accurately localize only a small number of sources, as expected. In Experiment 4, we consider K = 3 sources with frequencies given by {−0.2, 0.1, 0.1 + δ} and vary δ ∈ {0.001, 0.003, . . . , 0.029}. We fix the number of snapshots L = 100 and SNR = 10dB. It is seen in Fig. 4 that MESA attains the CRB for very closely located sources and thus has a higher resolution than the other methods. MNOMP fails to resolve the closely located sources. A gap is shown between MESA and MESA-1, implying that the MM iterations of MESA are useful to improve the resolution.
D. Robustness to Source Correlations
In Experiment 5, we consider K = 3 sources with frequencies in {−0.2, −0.1, 0.2}, where the first two sources are coherent with the correlation coefficient e iπ/3 (that can be changed to any other value on the unit circle). We use the nested array in (55) for DOA estimation to make sure that the assumptions of Theorem 1 are satisfied, which can be verified according to Proposition 1 since the source matrix S has rank 2 and Spark (Ω) ≥ 6 by noting that the nested array contains a 5-element ULA. We fix L = 100 and vary the SNR from −10 to 20dB. Our numerical results are presented in Fig. 5. It is seen that MESA has stable performance when the SNR is above 0dB, which is consistent with Theorem 1. Remarkably, MESA attains the CRB as in the case of uncorrelated sources. In contrast to this, SS-MUSIC and WLS do not have the same robustness as MESA. Satisfactory performance is also obtained by MNOMP and RAM. In this case, MESA performs better than MESA-1 since the solution to R Ω is significantly different from the sample covariance and an accurate initialization is unavailable. We present in Fig. 6 results of one Monte Carlo run of the previous experiment (at SNR = 20dB). It is seen that MESA can accurately estimate the frequencies/DOAs and the source power, validating Theorem 1. Interestingly, SS-MUSIC and WLS can accurately localize the two coherent sources but mislocate the third source that is uncorrelated with the other two. The reason underlies this behavior needs further investigation. In Experiment 6, we repeat Experiment 5 by changing the nested array to the MRA in (54). In this case, it is difficult to verify the assumptions of Theorem 1. We present our results in Fig. 7. It is seen that all algorithms are affected to a larger extent by the source correlation as compared to the nested array case presented in Fig. 5. Differently from SS-MUSIC and WLS, MESA remains to be robust to source correlations. MNOMP has a poor performance in this case with a small array size. In Experiment 7, we repeat Experiment 2 by fixing SNR = 10dB and letting the first and the fourth sources to be correlated with a correlation coefficient ρe iπ/4 , where the modulus ρ changes from 0 (uncorrelated) to 1 (coherent). MNOMP and RAM are not usable since more sources than sensors are present. It is seen in Fig. 8 that the performance of all methods becomes worse as the correlation increases. In contrast to a steady performance loss of MESA, a sharp loss is shown for SS-MUSIC and WLS in the regime of highly correlated sources. As ρ = 1, in fact, SS-MUSIC and WLS mislocate at least one of the sources in over 10% of the Monte Carlo runs, while MESA always accurately localize the sources. To sum up, we have shown by numerical results that MESA can statistically efficiently localize more uncorrelated sources than sensors and has robust performance in the presence of correlated and coherent sources. This makes it unique among existing coarray-based methods tailored for uncorrelated sources and sparse methods usable for a small number of sources. MESA-1 is a good accelerated approximation of MESA in general, while the latter has improved resolution and robustness. More simulation results can be found in our conference papers [1], [2].
VII. CONCLUSION In this paper, we showed that more sources than sensors can be localized using proper SLAs without sacrificing robustness to source correlations. This is realized by studying the robustness property of the ML method derived under the assumption of uncorrelated sources and proposing the MESA algorithm for the ML method based on elegant problem reformulations. Extensive numerical results are provided that validate our theoretical findings and demonstrate superior performance of MESA in terms of statistical efficiency, resolution and robustness to highly correlated sources as compared to stateof-the-art algorithms.
It is shown in this paper that MESA can localize more sources than sensors even in presence of highly correlated or coherent sources. A theoretical understanding of this behavior is a future work. Moreover, both algorithm-dependent andindependent analyses are of interest to investigate how the number of localizable sources leverages with source correlations. For a particular algorithm, it is shown that using the assumption of uncorrelated sources does not necessarily contradict with its robustness to correlated sources. Therefore, it is of great interest to investigate their robustness for both existing and future algorithms proposed with the uncorrelated setup. It is also shown that the array geometry is another factor affecting the robustness to source correlations. It is interesting to take the robustness into consideration for future array geometry design. APPENDIX A. Proof of (33) To show (33), it suffices to show that
1 − β L F + L = arg miň Z β Ž F + 1 2 Ž − L 2 F(56)
by identifying thatŽ = Y − Z and β = µ −1 . To this end, observe that
g(Ž) β Ž F + 1 2 Ž − L 2 F ≥ β Ž F + 1 2 Ž F − L F 2 = 1 2 Ž F − L F + β 2 + β L F − 1 2 β 2 ,(57)
where the equality is achieved ifŽ has the sign of L. Since the last expression is minimized if Ž F = ( L F − β) + , the overall function g(Ž) is therefore minimized ať
Z = ( L F − β) + sgn (L) = 1 − β L F + L,(58)
completing the proof.
B. Proof of Theorem 1
We first show the following lemma. Lemma 1: Assume A = [a 1 , . . . , a K ] and that P is positive-definite diagonal. Then, it holds for any σ > 0 and k = 1, . . . , K that
a H k AP A H + σI −1 a k < p −1 k .(59)
If, further, A has full column rank, then
lim σ→0 a H k AP A H + σI −1 a k = p −1 k .(60)
Proof: Note that the matrix
p −1 k a H k a k AP A H + σI is posi-
tive definite since so is p −1 k and its Schur complement
AP A H + σI − p k a k a H k ≥ σI.(61)
Consequently, the Schur complement regarding AP A H + σI is positive, yielding (59). Without loss of generality, we next show (60) for k = 1. For any ǫ > 0, diag (−ǫ, p 2 , . . . , p K ) is indefinite and so is Adiag (−ǫ, p 2 , . . . , p K ) A H since by assumption A has full column rank. It follows that for any 0 < σ < −λ min Adiag (−ǫ, p 2 , . . . , p K ) A H , (63) is the Schur complement regarding (p 1 + ǫ) −1 > 0. Since AP A H + σI is positive definite, consequently, its Schur complement must be negative, i.e.,
(p 1 + ǫ) −1 − a H 1 AP A H + σI −1 a 1 < 0,(64)
which combined with (59) yields that
(p 1 + ǫ) −1 < a H 1 AP A H + σI −1 a 1 < p −1 1 ,(65)
of which a direct consequence is (60).
We are ready to prove Theorem 1. For notational simplicity, we omit the subscript Ω in Y Ω , A Ω hereafter and write them as Y , A without ambiguity. It follows from Lemma 5 and Lemma 4 in [74] that
tr Y H AP A H + σI −1 Y = min Z tr Z H AP A H −1 Z + σ −1 Y − Z 2 F = min S tr S H P −1 S + σ −1 Y − AS 2 F ,(66)
which can also be shown directly. Define L (f , p, σ, S) = ln AP A H + σI + 1 L tr S H P −1 S
+ 1 Lσ Y − AS 2 F .(67)
It follows that (f * , p * , σ * , S * ) = arg min f ,p,σ,S L (f , p, σ, S) ,
and we let L * denote the optimal value. We first show σ * > 0. It suffices to show that lim σ→0 L (f , p, σ, S) = +∞ (69) for any (f , p, S). To do so, note by (67) that
L (f , p, σ, S) ≥ ln |σI| + 1 Lσ Y − AS 2 F = M ln σ + 1 Lσ Y − AS 2 F ,(70)
and the only stationary point of the lower bound above regarding σ, which is the global minimizer, is given by
σ = Y −AS 2 F N L
that is bounded from below by a positive number for any (f , S) by Assumption A5. Consequently, the lower bound above always approaches infinity as σ → 0, resulting in (69).
Inserting the ground truth (f o , p o , σ o , S o ) into L and conditioning on σ o ≤ 1, we have that
L * ≤ L (f o , S o , p o , σ o ) = ln A o P o A oH + σ o I + 1 L tr S oH P o−1 S o + 1 Lσ o Y − A o S o 2 F ≤ (M − K) ln σ o + K k=1 ln λ k A o P o A oH + 1 + K + M,(71)
where λ k denotes the kth greatest eigenvalue. Combining (71) and the inequality L * ≥ ln A * P * A * H + σ * I ≥ M ln σ *
yields that
σ * ≤ Cσ o M −K M ,(73)
where C = e 1+K/M K k=1 λ k A o P o A oH + 1 1/M is a constant. A direct consequence of (73) is (49). Inserting the stationary point σ =
Y −AS 2 F N L
into the lower bound in (70) yields that
L (f , p, σ, S) ≥ M ln σ + 1 Lσ Y − AS 2 F ≥ M ln Y − AS 2 F N L + M.(74)
Consequently,
L * = L (f * , p * , σ * , S * ) ≥ M ln Y − A * S * 2 F N L + M.(75)
Combining (75) and (71), we obtain that
Y − A * S * 2 F N L ≤ Ce −1 σ o M −K M .(76)
Therefore, lim
σ o →0 A * S * = A o S o ,(77)
implying consistence of (f * , S * ) (up to perturbations of entries) by Assumption A4. Finally, note by (67) that p * = arg min p ln A * P A * H + σ * I + 1 L tr S * H P −1 S * ,
(78) where all rows of S * are nonzero and A * has full column rank if σ o is small enough due to their consistency as σ o → 0 and Assumption A6. It follows that the derivative of the above objective function with respect to p k vanishes at p k = p * k , yielding that
a H (f * k ) A * P * A * H + σ * I −1 a (f * k ) − S *
is bounded from below by a universal positive number if σ o is small enough. We further apply the second part of Lemma 1 to obtain by (79) and (49) that
0 = lim σ o →0 a H (f * k ) A * P * A * H + σ * I −1 a (f * k ) − S * k 2 Lp * 2 k = lim σ o →0 1 p * k − S o k 2 Lp * 2 k ,(81)
which results in (51) and completes the proof.
II. PRELIMINARIES A. DOA Estimation Using SLAsAn M -element SLA of aperture N −1 composes a subset of an N -element virtual ULA. Let the index set Ω ⊂ {1, . . . , N }, of cardinality M ≤ N , denote the SLA. We first consider the specialized ULA case when Ω = {1, . . . , N } and M = N .
,(31),(45),(46),(34) and(35) iteratively. Again, the overall MESA algorithm consists of the outer MM loop and the inner ADMM loop and it is illustrated in Algorithm 1. It has a computational complexity of O(N 3 ) per inner iteration and degenerates into MESA in the previous section in the specialized ULA case.
SLA Ω, sample covariance R Ω , source number K. Output: Estimates of frequencies f , source powers p and noise power σ. Initialize R Ω , Q, Λ, t, X, Z and calculate W = Γ T R in(16)and W = Γ T R −1 Ω Γ; 9: end while 10: Calculate the estimates of f and p by computing the decomposition T t = A (f ) P A H (f ) using root-MUSIC. A4: f o , S o are uniquely identifiable from their product
averaged over 200 Monte Carlo runs, where f is the vector of estimated frequencies. We consider three different types of SLAs consisting of a 10-element ULA, a 6-element MRA and an 8-element nested array given respectively by Ω ULA = {1, 2, . . . , 10} , (53) Ω MRA = {1, 2, 7, 10, 12, 14} , (54) Ω Nested = {1, 2, 3, 4, 5, 10, 15, 20}.
Fig. 1 .
1Negative log-likelihood function value versus the number of MM iterations of MESA.
Fig. 2 .
2Frequency estimation error for K = 7 uncorrelated sources using the MRA in (54), with L = 200.
Fig. 3 .
3Frequency estimation error for K ∈ {2, . . . , 13} sources using the MRA in(54), with L = 100 and SNR= 10dB.
Fig. 4 .
4Frequency estimation error for K = 3 uncorrelated sources, two of which are separated by δ, with L = 100 and SNR = 10dB.
Fig. 5 .
5Frequency estimation error for K = 3 sources using the nested array in(55), where the first two sources are coherent.
Fig. 6 .
6Results of one Monte Carlo run inFig. 5at SNR = 20dB, where the first two sources are coherent.
Fig. 7 .
7Frequency estimation error for K = 3 sources using the MRA in(54), where the first two sources are coherent.
Fig. 8 .
8Frequency estimation error for K = 7 sources using the 6-element MRA in(54), where the first and the fourth sources are correlated.
41, Theorem 1] and [75, Lemma 1]. Proposition 1: Assumptions A4 and A6 hold true if
the matrix
matrixAP A H + σI − (p 1 + ǫ) a 1 a H 1 = Adiag (−ǫ, p 2 , . . . , p K ) A H + σI(63)is indefinite. Hence, the matrix (p 1 + ǫ) AP A H + σI is indefinite by observing that the matrix in−1
a H
1
a 1
ACKNOWLEDGMENTThe authors would like to thank Prof. Jiang Zhu of Zhejiang University for providing the code of MNOMP.
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| We consider estimating the direction-of-arrival (DOA) in the presence of sensor array error. In the proposed method, a blind signal separation method, the joint approximation and diagonalization of eigenmatrices algorithm, is implemented to separate the signal vector and the mixing matrix consisting of the array manifold matrix and the sensor array error matrix. Based on a new mixing matrix and the reconstruction of the array output vector of each individual signal, we propose a novel DOA estimation and sensor array error calibration procedure. This method is independent of array phase errors and performs well against difference of SNR of signals. Numerical simulations verify the effectiveness of the proposed method. | The traditional direction of arrival (DOA) method generally uses a uniform linear array, and the number of estimable target sources is less than the number of array elements. Classical methods such as multiple signal classification (MUSIC) method [1-3] or estimation of signal parameters via rotational invariance techniques (ESPRIT) method[4,5]use N array elements to estimate at most N-1 target signals, and the degree of freedom of the array is limited. Therefore, in the case of a certain number of array elements, how to optimize the array structure to obtain a larger array aperture to improve the DOA estimation accuracy and multi-target resolution has always been a hot issue for scholars[6][7][8].In recent years, with the continuous in-depth study of the array element structure, domestic and foreign scholars have proposed many non-uniform array structures[9][10][11]. For example, the nested array structure can estimate up to 2N signal sources by using N array elements. The nested array is not only easy to construct, but also easy to obtain the specific position of the array element and higher array freedom. However, because the distance between some elements in the nested array is very small, mutual coupling between the antennas will be caused, thereby affecting the performance of theAbstractAiming at the problem that traditional direction of arrival (DOA) estimation methods cannot handle multiple sources with high accuracy while increasing the degrees of freedom (DOF), a new method for 2-D DOA estimation based on coprime array MIMO radar (SA-MIMO-CA) is proposed. First of all, in order to ensure the accuracy of multisource estimation when the number of elements is finite, a new coprime array model based on MIMO (MIMO-CA) is proposed. This method is based on a new MIMO arraybased co-prime array model (MIMO-CA), which improves the accuracy of multi-source estimation when the number of array elements is limited, and obtains a larger array aperture with a smaller number of array elements, and improves the estimation accuracy of 2-D DOA. Finally, the effectiveness and reliability of the proposed SM-MIMO-CA method in improving the DOF of array and DOA accuracy are verified by experiments. | This letter studies the problem of Direction of Arrival (DoA) estimation from low-resolution few-bit quantized data collected by Sparse Linear Array (SLA). In such cases, contrary to the one-bit quantization case, the well known arcsine law cannot be employed to estimate the covaraince matrix of unquantized array data. Instead, we develop a novel optimizationbased framework for retrieving the covaraince matrix of unquantized array data from low-resolution few-bit measurements. The MUSIC algorithm is then applied to an augmented version of the recovered covariance matrix to find the source DoAs. The simulation results show that increasing the sampling resolution to 2 or 4 bits per samples could significantly increase the DoA estimation performance compared to the one-bit sampling regime while the power consumption and implementation costs is still much lower in comparison to the high-resolution sampling implementations. | DOA Estimation based on Sparse Representation of Covariance Matrix for 4- D Antenna Arrays | Closed-form estimation of DOA and polarization for multisource with a uniform circular array | DOA estimation of quasi-stationary signals based on Khatri-Rao product using joint sparse signal representation | An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, which leads to a multi-dimensional optimization problem with no closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical approach in exploiting the special (Toeplitz) structure of the observations' covariance. However, we offer a substantial improvement over P-K's ordinary Least Squares (LS) estimates by using asymptotic approximations in order to obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS) estimates of the sensors gains and phases offsets with asymptotically optimal weighting, based only on the empirical covariance matrix of the measurements. Moreover, we prove that our resulting estimates are also asymptotically optimal w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates (MLE), which are otherwise obtained by joint ML estimation of all the unknown model parameters. After deriving computationally convenient expressions of the respective Cramér-Rao lower bounds, we also show that our estimates offer improved performance when applied to non-Gaussian signals (and/or noise) as quasi-MLE in a similar setting. The optimal performance of our estimates is demonstrated in simulation experiments, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy in a multiple-sources directions-of-arrivals estimation task. | Efficient 2D DOA estimation of coherent signals in spatially correlated noise using electromagnetic vector sensors |
240 | Stony Brook Business College | Stony Brook University School of Dental Medicine State University of New York at Stony Brook School of Dental Medicine is a school of dentistry located in the United States city of Stony Brook. The school is one of the four dental schools in the state of New York and is one of only two public dental schools in the state of New York along with the State University of New York at Buffalo School of Dental Medicine. State University of New York at Stony Brook School of Dental Medicine is a part of State University of New York. State University | Stony Point Center Stony Point Center is one of three conference centers of the Presbyterian Church (USA). The other two conference and retreat centers are Ghost Ranch and Montreat. Stony Point Center welcomes people of all faiths and nations to discern, discover, learn and lead. Stony Point Center is located on in the Hudson River Valley in the town of Stony Point, New York, north of Manhattan. The facility began about 150 years ago as a ministry of hospitality shaped by four daughters of a Presbyterian minister. In a given year, the center with its 180-bed campus welcomes a wide | Stony Brook Seawolves women's lacrosse The Stony Brook Seawolves women's lacrosse team is a NCAA Division I college lacrosse team representing Stony Brook University as part of the America East Conference. They play their home games at Kenneth P. LaValle Stadium in Stony Brook, New York. Stony Brook is coached by Joe Spallina, who took over in 2012. Spallina was a 1996 graduate of Adelphi University, where he helped the Panthers win Division II national championships in 1993 and 1995. He then earned his Master of Arts in Health Studies from Stony Brook University in 2004. He has coached at | in 1978. Stony Brook Seawolves football The Stony Brook Seawolves football program is the collegiate football team that represents Stony Brook University in the National Collegiate Athletic Association. The program participates in the Division I Football Championship Subdivision and currently competes in the eleven-member Colonial Athletic Association. The program plays it home games at Kenneth P. LaValle Stadium in Stony Brook, New York. Stony Brook first fielded a varsity team in 1983 and rose to Division II in 1994. In 1999, the Seawolves rose to Division I non-scholarship as part of the Northeast Conference until the 2006 season in which | Stony Brook Seawolves The Stony Brook Seawolves are the athletic teams of Stony Brook University in Stony Brook, New York, United States. The school is a member of the National Collegiate Athletic Association Division I and participates in the America East Conference for all sports except football, in which they participate as an associate member of the Colonial Athletic Association, and women's tennis, which competes as an associate member of the Missouri Valley Conference. The official colors of the Seawolves are red, grey, and blue. The Seawolves currently field 18 varsity sports, including football and baseball for men only; softball, | Joe Nathan Field Joe Nathan Field is a baseball field on the campus of Stony Brook University in Stony Brook, New York, United States. It is also referred to as the Stony Brook Baseball Field. The field is home to the team of the NCAA Division I America East Conference. It is located at the northern end of the school's athletics complex. The facility was known as Seawolves Field through the 2002 season, when its name was changed to University Field. In 2011, the stadium was rededicated for then-Minnesota Twins pitcher and Stony Brook alumnus Joe Nathan after Nathan's $500,000 | S.U.N.Y. at Stonybrook: Stonybrook, NY 9/19/71 S.U.N.Y. at Stonybrook: Stonybrook, NY 9/19/71 (titled with slightly different variations in the album packaging) is an archival live album released in 2003 and self-distributed by the Allman Brothers Band. The album includes performances from two shows at the Stony Brook University Gym on September 19, 1971, five weeks prior to the death of Duane Allman. An emergent research university situated roughly fifty-five miles east of Midtown Manhattan, Stony Brook was suffused with a countercultural elan throughout the era. Five Allman Brothers Band concerts at the University in the late 1960s and early 1970s | Stony Brook Seawolves baseball The Stony Brook Seawolves baseball team represents Stony Brook University in NCAA Division I men's college baseball. Stony Brook currently competes in the America East Conference and plays its home games on Joe Nathan Field. Matt Senk has coached the team since the beginning of the 1991 season. The team has won the America East tournament four times in 2004, 2008, 2010, 2012, and 2015. In 2011, the Seawolves claimed the America East regular season championship. Stony Brook has participated in the NCAA tournament on five separate occasions, winning their first game in 2010. In 2012, | 240 | Is business management major competitive at Stony Brook? What are the grade requirements to get into the business college? I applied on the 28th of December but there is no decision yet. | what is the annual undergraduate tuition at stony brook | what sports does stony brook play in college | when did madison business college close for good | New York University of Business & Tech? | Spring 2019 Business School Admissions | How is Columbia College's MBA program? | where does the saunders college of business rank in terms of employment | Marketing planning for colleges and universities |
241 | Magnetic sensors with polysilicon TFTs | Magnetic Sensors and Magnetometers | Using Co-based amorphous wire with nominal composition Co_ 70.4 Fe_ 4.6 Si_ 15 B_ 10 fabricated by in-rotating-water quenching spinning techniques as the sensing materials, a new type of magnetic sensor, with high sensitivity and high linearity, was proposed .The magnetic sensor adopted multivibrator inclduing single amorphous wire core and double-winding as a basic circuit. The relations among output voltage signal of the sensor ,circuit component parameters, the number of turns , the magnetic parameter and size parameter of the sensing core were derived based on building up ideal hysteresis loop model of the amorphous core ,as well as the circuit theory and the electromagnetic theory .The theoretic results were proved to be correct under linear range of the sensor by experiment , and those research results provides scientific foundations to optimize the sensor’s characteristics. At last ,the testing results for the sensor to measure external magnetic field provided by Helmholtz coil were given. | Measuring principle of the thickness and defect of magnetic materials was given. Based on the principle, an experimental set-up with a designed sensor was built. Through the sensor character experiments, some conclusions were obtained: the presence of magnetism-concentrating components, shorter lift-off distance, higher excitation current, more coil turns, less spacing between arrayed sensors and fewer magnetization time are all help to increase the sensor sensitivity. The influence of environment temperature to the measurement errors is less notable. The defect can be qualitatively determined easily, but it is different to give the quantificational parameters. The sensor should be calibrated again when different material objects are tested. | An angle sensor using spin valve materials was designed, fabricated and tested. The spin valve material, composed of a top-pinned synthetic antiferromagnet layer for better standoff fields and a composite free layer for low coercivity and high magnetoresistance, has a structure of Ta-NiFeCo-CoFe-Cu-CoFe-Ru-CoFe-CrMnPt. The spin valve film showed switching of the free layer with low coercivity (5 Oe) and a plateau of the high field region (up to 500 Oe) after annealing at 250/spl deg/C for 1 hour. Two half-Wheatstone-bridges provide cosine and sine functions to uniquely determine angular positions between the angle sensor and a disc-shaped permanent magnet from 0 to 360 degrees at 2-6 mm airgap values. | In-line MZI magnetic sensor based on seven-core fiber and fiber peanut symmetrical structure | Fiber-optic low magnetic field sensor based on fiber-beam-cantilever technique using cobalt-doped nickel-ferrite nanoparticles coated optical fiber is proposed. Sensitivity is increased by incorporating etched single-mode fiber. Magnetic field as low as 2.0mT is successfully detected. | A multiple-point fiber optic sensor for the detection of weak and quasi-steady magnetic fields is described. The optical processing involves a single optical fiber sensing element configured as a two beam interferometer employing magnetostrictive sensing elements. Each sensing element is addressed by a different modulation frequency distinct in the frequency spectrum. The principle of operation is based on narrow band phase sensitive detection technique such that the multiplexing of a number of sensing elements is accomplished in the frequency domain. The fiber sensing elements can be remotely deployed, linked to the processing unit by an arbitrary length of down lead fiber. The investigated optical configuration facilitates the realization of a practical multiplexed magnetic field sensor. | Magnetic field sensing based on tilted fiber Bragg grating coated with nanoparticle magnetic fluid | 241 | Characteristics Research of Hall Magnetic Sensor Based on Nano-Polysilicon Thin Film Transistors | Magnetizing device for magneto-resistive thin-film sensor elements in a bridge circuit | which type of sensor is similar to hall effect-based current sensors | Novel designs of planar Hall effect bridge sensors optimized for magnetic bead detection are presented and characterized. By constructing the sensor geometries appropriately, the sensors can be tailored to be sensitive to an external magnetic field, the magnetic field due to beads being magnetized by the sensor self-field or a combination thereof. The sensors can be made nominally insensitive to small external magnetic fields, while being maximally sensitive to magnetic beads, magnetized by the sensor self-field. Thus, the sensor designs can be tailored towards specific applications with minimal influence of external variables. Three different sensor designs are analyzed theoretically. To experimentally validate the theoretical signals, two sets of measurements are performed. First, the sensor signals are characterized as function of an externally applied magnetic field. Then, measurements of the dynamic magnetic response of suspensions of magnetic beads with a nominal diameter of 80 nm are performed. Fur... | Modeling and implementation of a novel closed-loop Hall current sensor using dual iron-core | Magnetic Measuring Instrumentation With Radiation-Resistant Hall Sensors for Fusion Reactors: Experience of Testing at JET | A closed‐form inversion‐type polysilicon thin‐film transistor dc/ac model considering the kink effect | Magnetoresistance measurements in as-evaporated and annealed amorphous silicon films | New Magnetic Field Sensor Based on Combined Flux-Gate/Hall-Effect Arrangement |
242 | We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise $C^2$, satisfying negative Schwarzian derivative and some summability conditions on the growth of derivatives and recurrence along the turning orbits, then $f$ has finitely many attractors whose union of basins of attraction has total probability, and each attractor supports an absolutely continuous invariant probability measure $\mu$. Over each attractor there exists a renormalization $(f^m,\mu)$ that is exact, and the rates of mixing (decay of correlations) are strongly related to the rates of growth of the derivatives and recurrence along the turning orbits in the attractors. We also give a sufficient condition for $(f^m,\mu)$ to satisfy the Central Limit Theorem. In some sense, we give a fairly complete global picture of the dynamics of such maps. Similarly, we can get similar statistical properties for interval maps with critical points and discontinuities under some more assumptions. |
Introduction
Physical measures were introduced in 1970's by Bowen, Ruelle and Sinai to study the large time behavior of Lebesgue typical points for Axiom A attractors. Such systems do not preserve volume (or any measure that is equivalent to the volume) due to the contracting near the attractor. For this reason, those measures are often supported on a zero volume subset of the manifold, but captures the behavior of points in a large set with positive Lebesgue measure. More precisely, an invariant measure µ is called a physical measure, if the set has positive volume. This set is known as the basin of µ. For Axiom A attractors, many properties of physical measures were studied by many different authors. We refer the readers to the review paper [50] and the book [9] for more details. Later, a program for investigating the physical measures of diffeomorphisms beyond uniform hyperbolicity was initiated by Alves, Bonatti, Viana in a sequence of papers, such as [3,10] to name but a few. They introduced several classes of systems, for which the physical measures exist, and the number of physical measures is finite. Among them are the diffeomorphisms with mostly contracting center, and diffeomorphisms with mostly expanding center. In this paper, we are particularly interested in the latter class.
Diffeomorphisms with mostly expanding center are, roughly speaking, partially hyperbolic diffeomorphisms whose center Lyapunov exponents are positive. This class of systems was introduced by Alves, Bonatti and Viana ([3]) using a different, more technical definition. Later, another definition was given by Dolgopyat [23], and more recently by Andersson and Vásquez [1]. In [1], they also proposed the latter, somewhat stronger, definition as the official definition of having mostly expanding center, which we will follow in this paper.
We call a diffeomorphism f partially hyperbolic, if there exists a decomposition T M = E s ⊕E c ⊕E u of the tangent bundle T M into three continuous invariant subbundles: E s
x and E c x and E u x , such that Df | E s is uniform contraction, Df | E u is uniform expansion and Df | E c lies in between them:
Df (x)v s Df (x)v c ≤ 1 2
and
Df (x)v c Df (x)v u ≤ 1 2
for any unit vectors v s ∈ E s x , v c ∈ E c x , v u ∈ E u x and any x ∈ M . This notation was proposed by Brin, Pesin [12] and Pugh, Shub [40] independently as early as 1970's.
As shown by Bonatti, Díaz and Viana [9] and Dolgopyat [22], physical measures of any C 1+α partially hyperbolic diffeomorphism should be a Gibbs u-state, meaning that the conditional measures of µ with respect to the partition into local strongunstable manifolds are absolutely continuous with respect to Lebesgue measure along the unstable leaves. This definition is comparable to diffeomorphisms with mostly contracting center (see, for example, [24]), and share similar properties with the latter. In particular, C 1 openness of the partially hyperbolic diffeomorphisms with mostly expanding center was recently proved in [47]. Note however, that the inverse of a diffeomorphism with mostly expanding center may not be mostly contracting. This is because the space of Gibbs u-states of f could be very different from that of f −1 .
A list of examples for partially hyperbolic diffeomorphisms with mostly expanding center will be provided in Section 3.
1.1. Index-dim(E cu ) skeleton. In this article, we will introduce a topological structure of f , known as the skeleton, and use it to study the structure of physical measures of f . To this end, for a C 1 partially hyperbolic diffeomorphism f with partially hyperbolic splitting E s ⊕ E c ⊕ E u , we denote by i cu = dim(E cu ) and i s = dim(E s ), where E cu = E c ⊕ E u . Definition 1.2. 1 We say that S is an index i s skeleton of f if S = {p 1 , · · · , p k } consists of finitely many hyperbolic saddles with stable index i s , such that:
(a) i=1,···k F s (Orb(p i )) is dense in M ; (b) S does not have a proper subset that satisfies property (a).
A set S consisting of finitely many hyperbolic saddles with stable index i s and satisfying (a) above is called a pre-skeleton.
Let us observe that in general, a partially hyperbolic diffeomorphism may not have skeleton, since it may not have any hyperbolic periodic orbit at all. Even if it admits a set of periodic points such that the union of their stable manifolds are dense, such set may have infinite cardinality. However, we will see in Section 4 that if f does have a skeleton, then all the skeletons of f (with the same index) must have the same cardinality (Lemma 4.4). Furthermore, every pre-skeleton of f contains a skeleton (Lemma 4.5).
Finally, in Proposition 6.8 we will show that if f is C 1+α with mostly expanding center (or if f is C 1 and close to a C 1+α diffeomorphism with mostly expanding center), then f has an index i s skeleton. Furthermore, in Section 7 we will see that the skeletons are robust under C 1 topology, in the sense that the continuation of a skeleton of f is a pre-skeleton for nearby C 1 maps. Note however, that this property requires f to have mostly expanding center, unlike those skeletons in [24].
The main result of this paper shows that for such diffeomorphisms, skeletons provide rich geometrical information on the physical measures of f . For simplicity, we will frequently suppress the dependence on the Hölder index α and write C 1+ , as the Hölder index α does not play any particular role.
Theorem A. Let f be a C 1+ diffeomorphism with mostly expanding center. Then f admits an index i s skeleton. Moreover, Let S = {p 1 , · · · , p k } be any index i s skeleton of f , then for each p i ∈ S there exists a distinct physical measure µ i such that:
(1) both the closure of W u (Orb(p i )) and the homoclinic class of the orbit Orb(p i ) coincide with supp(µ i ); (2) the closure of F s (Orb(p i )) coincides with the closure of the basin of the measure µ i .
In particular, the number of physical measures of f is precisely k = #S. Moreover, Int(Cl(B(µ i ))) ∩ Int(Cl(B(µ j ))) = ∅ for 1 ≤ i = j ≤ k, where B(µ i ) is the basin of µ i . 1 In [24], a different type of skeleton was defined for diffeomorphisms with mostly contracting center, where the index of saddles in S equals ics = dim(E s ⊕ E c ). Instead of condition (a), there the union of stable manifold of periodic orbits of the skeleton is a u-section. The existence of index ics skeleton is a C 1 open property, but it is not necessarily true any more for index is skeleton. For more discussions, see Section 4.
We would like to mention that the idea of using homoclinic classes to study measures was initiated by [27], see also [24] and [18] for recent similar results.
As a corollary of the previous theorem, we are going to show that any iteration of f still has mostly expanding center; furthermore, the number of physical measures of f k is also determined by the skeleton of f :
Corollary B. Let f be a C 1+ partially diffeomorphism with mostly expanding center, and S = {p 1 , · · · , p k } be any index i s skeleton of f . Then for any n > 0, f n has mostly expanding center, and has finitely many physical measures with number bounded by
(1) P = k i=1 π(p i ), where π(p i ) denotes the period of p i .
Moreover, every physical measure of f P is Bernoulli.
1.2.
Perturbation of physical measures. It was shown in [47] that partially hyperbolic diffeomorphisms with mostly expanding center are C 1 open, i.e., if a C 1+ diffeomorphism f has mostly expanding center, then any C 1+ diffeomorphism g which is sufficiently C 1 close to f also has mostly expanding center. In the following we will analyse how the physical measures vary with respect to the C 1+ diffeomorphisms in C 1 topology, which generalizes a similar result of Andersson and Vásquez ( [2]) under C 1+α topology. The key observation here is that physical measures of f are associated with skeletons, which behaves well under C 1 topology.
Theorem C. Let f : M → M be a C 1+ partially hyperbolic diffeomorphism with mostly expanding center. Then there exists a C 1 neighborhood U of f such that the number of physical measures depends upper semi-continuously in C 1 topology among diffeomorphisms in Diff 1+ (M ) ∩ U. Moreover, the number of physical measures is locally constant and the physical measures vary continuously in the weak* topology on an C 1 open and dense subset U • ⊂ U.
Indeed, the skeletons of f provide even more information on the physical measures for C 1 perturbed C 1+ diffeomorphisms. In particular, the skeletons allow us to describe how the physical measures bifurcate as the diffeomorphism changes. To this end, we write p i (g) the continuation of the hyperbolic saddle p i for g in a C 1 neighborhood of f . Theorem C is a direct consequence of the following, more technical result:
Theorem D. Let f be a C 1+ partially hyperbolic diffeomorphism with mostly expanding center, and S = {p 1 , · · · , p k } be a skeleton of f . There exists a C 1 neighborhood U of f such that, for any C 1 diffeomorphism g ∈ U, there is a subset of S(g) = {p 1 (g), · · · , p k (g)} which is a skeleton. Consequently, for g ∈ Diff 1+ (M )∩U, the number of physical measures of g is no larger than the number of physical measures of f . Moreover, these two numbers coincide if and only if there is no heteroclinic intersection within {p i (g)}. In this case, each physical measure of g is close to some physical measure of f , in the weak-* topology.
In addition, restricted to any subset of V ⊂ U where the number of physical measures is constant, the supports of the physical measures and the closures of their basins vary in a lower semi-continuous fashion, in the sense of the Hausdorff topology.
1.3. Existence of physical measures for C 1 generic diffeomorphisms. Previously, the study of physical measures is mainly focused on maps that are sufficiently smooth, i.e., with C 1+ regularity. Recently, the new technique developed in [28,21] enables us to shows the existence of physical measure for a large family of C 1 diffeomorphisms, such as those with mostly contacting center.
In this paper, we will further show the existence of physical measures for C 1 generic diffeomorphisms close to a partially hyperbolic diffeomorphism f that has mostly expanding center.
Before stating the main theorem of this section, we need the following definition:
Definition 1.4. A set Λ of a homeomorphism f is Lyapunov stable if there is a sequence of open neighborhoods U 1 ⊃ U 2 ⊃ · · · such that: (a) U i = Λ; (b) f n (U i+1 ) ⊂ U i for any n, i ≥ 1.
A set being Lyapunov stable means that points starting near Λ will not travel too far away from this set under forward iterations of f . However, this does not mean that Λ is an attractor.
We have the following C 1 locally generic result, which generalizes Theorem D. We state it as a standalone result since the techniques involved are quite different from Theorem D.
Theorem E. Let f : M → M be a C 1+ partially hyperbolic diffeomorphism with mostly expanding center, and S = {p 1 , · · · , p k } be a skeleton of f . Then there exists a C 1 neighborhood U of f and a C 1 residual subset R ⊂ U, such that every C 1 diffeomorphism g ∈ R admits finitely many physical measures, whose basins have full volume. The number of physical measures of g coincides with the cardinality of its skeleton, which is no more than the number of physical measures of f . Moreover, the physical measures of g are supported on disjoint Lyapunov stable chain recurrent classes, each of which is the homoclinic class of some saddle in its skeleton.
Statistical properties.
Decay of correlations has been proven to be a powerful tool in the study of statistical properties of smooth dynamical systems. It can be seen as the speed at which the system losses dependence. To study such properties for diffeomorphisms with mostly expanding center, we introduce the following definition:
Definition 1.5. Given observables φ, ψ : M → R, we define the correlation function with respect to a measure µ as
C µ (φ, ψ • f n ) =| φ(ψ • f n )dµ − φdµ ψdµ | for n ≥ 1.
To study the speed of decay of correlations for systems beyond uniformly hyperbolic, in [48] Young used a type of Markov partitions with infinitely many symbols to build towers for systems with non-uniform hyperbolic behavior. These structures are nowadays commonly referred to as Gibbs-Markov-Young (GMY) structures (see for instance [4].) And it is well known that such maps have exponential speed of decay of correlations whenever the GMY structure has exponentially small tails. By Alves and Li in [4], the latter case happens if the center bundle has certain expansion and moreover, the tail of hyperbolic times is exponentially small.
We are going to show that Alves and Li's criterion can be applied to partially hyperbolic diffeomorphisms with mostly expanding center, and in particular, we prove exponential decay of correlations and exponential large deviations for the physical measures of f , provided that f has mostly expanding center.
Theorem F. Let f : M → M be a C 1+ partially hyperbolic diffeomorphism with mostly expanding center, S = {p 1 , · · · , p k } be a skeleton of f and P = k i=1 π(p i ). Then for every physical measure µ of f P , there is d > 0 such that
C µ (φ, ψ • f P n ) = O(e −dn )
for Hölder continuous φ : M → R, and ψ ∈ L ∞ (µ).
Corollary G. Under the assumptions of Theorem F, for every physical measure µ of f P and any Hölder continuous function φ, the limit exists:
σ 2 = lim n→∞ 1 n ( n−1 j=0 φ • f jP − n φdµ) 2 dµ.
Moreover, if σ 2 > 0, then there is a rate function c(ε) > 0 such that
lim n→∞ 1 n log µ(| n−1 j=0 φ • f jP − n φdµ |≥ ε) = −c(ε).
1.5. Robustly transitive partially hyperbolic diffeomorphisms. The diffeomorphisms with mostly expanding center also provide a new mechanism to describe the topological transitivity property. To make this article more complete, we collect two results from two other papers without giving their proof. For more details, see the related papers and the references therein.
Theorem H. [47] Let f be a C 1+ volume preserving, partially hyperbolic diffeomorphism with one dimensional center. Suppose f is accessible and the center exponent is not vanishing, then f is C 1 robustly transitive, i.e. every diffeomorphism g is transitive for g in a C 1 neighborhood f which is not necessarily volume preserving.
Theorem I. [45] Let f be a C 1+ partially hyperbolic diffeomorphism with mostly expanding center, such that the stable foliation F s is minimal. Then there is a C 1 neighborhood U of f , such that the stable foliation of any g ∈ U is minimal.
1.6. Structure of the paper. This paper is organized in the following way: In Section 2 we introduce the main tool of this paper: a special space of probability measures, denoted by G(f ), which is defined using the partial entropy along unstable leaves. This space will serve as the candidate space of physical measures. In Section 4, we provide some geometrical properties of skeletons, assuming that such structure exist (which will not be proven until Section 6). In particular, we will show that every skeleton of f must have the same cardinality, and provide a useful criterion for the existence of a skeleton to be used in the later sections.
Section 5 consists of a direct proof on the existence of physical measures for C 1+ diffeomorphisms with mostly expanding center. More importantly, we show that the space G(f ) is a finite dimensional simplex that varies upper semi-continuously with respect to the diffeomorphism in C 1 topology; moreover, every extreme point of G(f ) is an ergodic physical measure of f .
The proof of Theorem A and D occupies the next two sections. We will carefully analyse the non-uniform expanding of f along E c using hyperbolic times, and use the shadowing lemma of Liao to show the existence of skeletons. We then build a one-to-one correspondence between elements of a skeleton and the physical measures of f , and show that physical measures bifurcate as heteroclinic intersections are created between different elements of a skeleton. Then in Section 7, we generalize the result of Theorem D to generic C 1 diffeomorphisms near f . Section 3 contains all the existing examples of diffeomorphisms with mostly expanding center, as far as the author is aware. In particular, we collect some very recent examples from [47]. 1.7. On the regularity assumption. Throughout this article, the regularity assumption on f is changed several times between C 1 and C 1+ . For the convenience of the readers, we summarize those changes below:
(1) having mostly contracting center requires the diffeomorphism to be C 1+ ; as a result, the initial diffeomorphism f is always assumed to be C 1+ ;
(2) the topology is always C 1 . Throughout this article, U is a neighborhood of f under C 1 topology; (3) the geometrical properties of skeletons only require the diffeomorphism to be C 1 ; this involves Section 4, Section 6.2 and certain part of Section 7; (4) the physical measure having absolutely continuous conditional measure on the unstable leaves and the stable holonomy being absolutely continuous requires C 1+ regularity, as shown in the classical theory of physical measures. This affects Section 5, Section 6.3, certain part of Section 7 and Section 9; (5) Section 8 deals with C 1 generic diffeomorphisms in U, thus only requires C 1 smoothness.
Preliminary
In this section, we introduce some necessary notations and results which will be used later. Throughout this section, we assume f to be a partially hyperbolic diffeomorphism on the manifold M , and µ an invariant probability measure of f . In Section 2.1 we will assume f to be C 1+ for the discussion on the Gibbs u-states. In Section 2.2 and 2.3, f is assumed to be C 1 only.
2.1.
Gibbs u-states. Following Pesin and Sinai [39] and Bonatti and Viana [10] (see also [9,Chapter 11]), we call Gibbs u-state any invariant probability measure whose conditional probabilities (Rokhlin [41]) along strong unstable leaves are absolutely continuous with respect to the Lebesgue measure on the leaves. In fact, assuming the derivative Df is Hölder continuous, the Gibbs-u state always exists, and the densities with respect to Lebesgue measures along unstable plaques are continuous. Moreover, the densities vary continuously with respect to the strong unstable leaves. As a consequence, the space of Gibbs u-states of f , denoted by Gibbs u (·), is compact relative to the weak-* topology in the probability space.
The set of Gibbs u-states plays important roles in the study of physical measures for partially hyperbolic diffeomorphisms. The proofs for the following basic properties of Gibbs u-states can be found in the book of Bonatti, Díaz and Viana [9, Subsection 11.2] (see also Dolgopyat [22]):
Proposition 2.1. Suppose f is a C 1+ partially hyperbolic diffeomorphism, then
(1) Gibbs u (f ) is non-empty, weak* compact and convex. Ergodic components of Gibbs u-states are Gibbs u-states. (2) The support of every Gibbs u-state is F u -saturated, that is, it consists of entire strong unstable leaves. Gibbs u-state whose center Lyapunov exponents are negative is a physical measure.
The semi-continuity of Gibbs u-states with respect to C 1+ diffeomorphisms under C 1 topology was recently proved by the author of this article in [47]:
Proposition 2.
2. Suppose f n (n = 1, · · · , ∞) and f are C 1+ partially hyperbolic diffeomorphisms such that f n
C 1 → f . Then lim sup Gibbs u (f n ) ⊂ Gibbs u (f ),
where the convergence is in the Hausdorff topology of the probability space.
The following lemma shows the relation between the Gibbs u-states of a diffeomorphism and its iterations. Lemma 2.3. For any n > 0, Gibbs u (f ) ⊂ Gibbs u (f n ). conversely, let ν be any Gibbs u-state of f n , then 1 n n−1 i=0 f i (ν) is a Gibbs u-state of f . Proof. Let µ be a Gibbs u-state of f , then it is also an invariant probability of f n . Since f and f n share the same unstable foliation, µ must have the same disintegration along the unstable plaques. Then it follows from the definition that µ is also a Gibbs u-state of f n .
On the other hand, it is clear that 1
n n−1 i=0 f i (ν)
is an invariant probability of f . By a similar argument as above, 1 n n−1 i=0 f i (ν) is a Gibbs u-state of f . 2.2. Partial entropy along unstable foliation. In this section, we give the precise definition of the partial metric entropy of µ along the unstable foliation F u of f , which depends on a special class of measurable partitions. The partial entropy has been proven to be a powerful tool in the study of partially hyperbolic diffeomorphisms, thanks to its semi-continuity in the C 1 topology.
Definition 2.4. We say that a measurable partition ξ of M is µ-subordinate to the F -foliation if for µ-a.e. x, we have (1) ξ(x) ⊂ F (x) and ξ(x) has uniformly small diameter inside F (x);
(2) ξ(x) contains an open neighborhood of x inside the leaf F (x);
(3) ξ is an increasing partition, meaning that ξ ≺ f ξ.
Ledrappier, Strelcyn [31] proved that the Pesin unstable lamination admits some µ-subordinate measurable partition. The following result is contained in Lemma 3.1.2 of Ledrappier, Young [32]: Lemma 2.5. For any measurable partitions ξ 1 and ξ 2 that are µ-subordinate to F ,
we have h µ (f, ξ 1 ) = h µ (f, ξ 2 ).
This allows us to define the partial entropy of µ using any µ-subordinate partition:
Definition 2.6. For a C 1 partially hyperbolic diffeomorphism f and an invariant measure µ, the partial µ-entropy along unstable foliation F u , which we denote by h µ (f, F u ), is defined to be h µ (f, ξ) for any µ-subordinate partition ξ.
Proposition 2.7. [47] The partial entropy h µ (f, F u ) varies upper semi-continuously with respect to the measures and maps in C 1 topology.
Although partially entropies are well defined for C 1 diffeomorphisms and behaves well under C 1 topology, one still need higher regularity such as C 2 or at least C 1+ in order to relate it with other quantities such as Lyapunov exponents or Gibbs u-states. The following upper bound for the partial entropy along the unstable foliation F u follows [32,33].
Proposition 2.8. Let f be C 1+ and µ be an invariant probability measure of f , then h µ (f, F u ) ≤ log Jac u (x)dµ(x).
Moreover,
(2) h µ (f, F u ) = log Jac u (x)dµ(x).
if and only if µ is a Gibbs u-state of f .
Proof. The inequality follows by [33, Theorem C ′ ], when f is C 2 . It was pointed out by [13] that the same inequality goes well for C 1+ diffeomorphism. The second part was stated in [30,Theorem 3.4].
The following equality was built in [33, Proposition 5.1], when f is C 2 . As explained above, it also holds under general situation assuming only C 1+ : Proposition 2.9. Let µ be a probability measure of f such that all the center exponents of µ are non-positive, then
h µ (f, F u ) = h µ (f ).
2.3.
Other invariant measure subspaces. Proposition 2.1 (4) states that when f is C 1+ , Gibbs u-states are the natural candidates of the physical measures of f . However, this statement falls apart when f is only C 1 . This is due to the lack of Pesin's formula ((2), Proposition 2.8) for C 1 diffeomorphisms. To solve this issue, we will introduce two candidate spaces of physical measures for such f . See [28], [21] and [20] for their properties.
Definition 2.10. We define:
(A1) G u (f ) = {µ ∈ M inv (f ) : h µ (f, F u ) ≥ log(det(Df | E u (x) ))dµ(x)}; (A2) G cu (f ) = {µ ∈ M inv (f ) : h µ (f ) ≥ log(det(Df | E cu (x) ))dµ(x)} where E cu = E c ⊕ E u .
We denote by
G(f ) = G u (f ) ∩ G cu (f ).
Remark 2.11.
(a) When f is C 1+ , by Ledrappier [30], G u (f ) = Gibbs u (f ). (b) By the Ruelle's inequality for partial entropy (see for instance [51]), one can replace the inequality in the definition of G u by equality:
G u (f ) = {µ ∈ M inv (f ) : h µ (f, F u ) = log(det(Df | E u (x) ))dµ(x)}.
However, the definition of G cu remains unchanged due to the possibility of having negative Lyapunov exponents in E c .
We first observe that the spaces above are non-empty; moreover, the space G(f ) contains all the candidates of physical measures. Proposition 2.12. There is a full volume subset Γ such that for any x ∈ Γ, any limit of the sequence 1 n n−1
i=0 δ f i (x) belongs to G(f ).
Proof. By [20], for x belonging to a full volume subset, any limit of the sequence [21,28], for x belonging to a full volume subset, any limit of the sequence 1 n n−1 i=0 δ f i (x) belongs to G u . We conclude the proof by taking the intersection of the two full volume subsets.
1 n n−1 i=0 δ f i (x) belongs to G cu . Moreover, by
The following property shows that G u (·) shares similar properties with Gibbs u (·) (Proposition 2.1).
Proposition 2.13. [28][Propositions 3.1, 3.5] The space G u (f ) is convex, compact,
and varies in a upper semi-continuous way with respect to the partially hyperbolic diffeomorphisms under C 1 topology. Moreover, for any invariant measure µ ∈ G u (f ), every ergodic component of its ergodic decomposition still belongs to G u (f ).
We need to observe that, in general, the space G(f ) may not have such properties (especially when it comes to the ergodic components). Indeed, in Proposition 5.17, we will show that the above properties holds for G(g), when g is C 1 close to f which is C 1+ with mostly expanding center.
Examples of partially hyperbolic diffeomorphisms with mostly expanding center
For a long time (before [47]), there are only two known examples of diffeomorphisms with mostly expanding center (under the definition that is used in this paper, which is stronger than that in [3]). These examples are due to Mañé [36] (see [3] and [1, Section 6]) and Dolgopyat [23]. We list these examples below, as well as some new examples provided in [47]. Let us recall that the set of partially hyperbolic diffeomorphisms with mostly expanding center is C 1 open among Diff 1+ (M ).
3.1. Derived from Anosov diffeomorphisms. We assume A to be a linear Anosov diffeomorphism over T 3 with 3 positive simple real eigenvalues 0 < k 1 < 1 < k 2 < k 3 .
3.1.1. Local derived from Anosov diffeomorphisms. Let us begin by recalling the construction of Mañé's example, which is a local C 0 perturbation of A. The statement below is a little different from the original construction in the history:
Example 3.1. Let p be a fixed point of A and U a small neighborhood of p. There is a partially hyperbolic diffeomorphism f 0 that coincides with A on T 3 \ U . f 0 is topological Anosov, and (3) | Df 0 | E c (x) |≥ 1
where the equality holds if and only if x = p.
Since Df 0 | E c (·) is expanding everywhere except at the point p, it is clear that f 0 has mostly expanding center. Thus, by [47], f 0 admits a C 1 neighborhood U such that every C 1+ diffeomorphism belonging to U has mostly expanding center.
3.1.2. Generalized Derived from Anosov diffeomorphisms. By the topological classification of partially hyperbolic diffeomorphisms which are isotopic to A ( [11,26,44]), we call such diffeomorphisms derived from Anosov A, and denote by DA(A). The following example by Shi, Viana and the author of this paper [43] revises the fact that C 1+ volume preserving derived from Anosov diffeomorphisms have mostly expanding center whenever the volume has large metric entropy.
Example 3.2. Let f ∈ DA(A) be a C 1+ volume preserving partially hyperbolic diffeomorphism and h vol (f ) > log k 3 , then f has mostly expanding center.
3.2.
Perturbation of volume preserving partially hyperbolic diffeomorphisms. In [23], Dolgopyat showed that: Example 3.3. Let X 1 be the time one map of a hyperbolic geodesic flow on a surface M , then for generic C ∞ perturbation f of X 1 , either f of its inverse f −1 has mostly expanding center.
The following result in [47] allows us to obtain more examples using C 1 perturbation:
Proposition 3.4. Let f be a C 1+ volume preserving partially hyperbolic diffeomorphism with one-dimensional center. Suppose the center exponent of the volume measure is positive and f is accessible. Then f admits an C 1 open neighborhood, such that every C 1+ diffeomorphism in this neighborhood (not necessarily volume preserving) has mostly expanding center.
Proposition 3.4 contains abundance of systems: by Avila [5], C ∞ volume preserving diffeomorphisms are C 1 dense. And by Baraviera and Bonatti [6], the volume preserving partially hyperbolic diffeomorphisms with one-dimensional center and non-vanishing center exponent are C 1 open and dense. Moreover, the subset of accessible systems is C 1 open and C k dense for any k ≥ 1 among all partially hyperbolic diffeomorphisms with one-dimensional center direction, due to the work of Burns, Rodriguez Hertz, Rodriguez Hertz, Talitskaya and Ures [15]; see also Theorem 1.5 in Niţicȃ and Török [37].
Indeed the accessibility assumption in the above proposition can be replaced by another hypothesis:
Example 3.5 (see [45]). Let f be a C 1+ volume preserving partially hyperbolic diffeomorphism with one-dimensional center. Suppose the center exponent of the volume measure is positive and f −1 has mostly contracting center. Then f admits an C 1 open neighborhood, such that every C 1+ diffeomorphism in this neighborhood has mostly expanding center.
Remark 3.6. The hypothesis that f −1 has mostly contracting center is equivalent to the assumption that F s is minimal.
The diffeomorphisms with minimal strong stable and unstable foliations are also quite common; they fill an open and dense subset of volume preserving partially hyperbolic diffeomorphisms with one-dimensional center and has compact center leaves. This follows from a conservative version of the results in [8].
3.3. Product of diffeomorphisms with mostly expanding center. It is shown by Ures, Viana and the author of this article in [45] that: Proposition 3.7. Suppose f 1 and f 2 are C 1+ partially hyperbolic diffeomorphisms over manifolds M 1 and M 2 . Assume that both f 1 and f 2 have mostly expanding center. Then f 1 × f 2 is a partially hyperbolic diffeomorphism over M 1 × M 2 with mostly expanding center. As a result, nearby C 1+ diffeomorphisms (which may not be products any more) also have mostly expanding center.
Properties of skeleton
In this section, we introduce several basic properties for skeletons, although the existence of skeletons will be postponed to Section 6. The main tool in this Section is the Inclination lemma, also known as the λ-lemma.
To state the properties of skeletons under general situations, throughout this section, we assume f to be a C 1 partially hyperbolic diffeomorphism with dominated splitting E s ⊕ E c ⊕ E u , S = {p 1 , · · · , p k } is an index i s skeleton of f . In particular, we will not assume f to have mostly expanding center. It is also worth noting that, unlike in [24], we will not discuss the robustness of skeletons under perturbation of f in this section. Such discussion requires f to have mostly expanding center, and is postponed to Section 7 (see Lemma 7.1).
The first three technical lemmas provide geometrical information on the structure of skeleton. The main result in this section is Lemma 4.4, which states that every skeleton of f must have the same cardinality. The last two lemma provide useful criterion for skeletons, which will be used multiple times in the later sections. (1) For any 1 ≤ i ≤ k, Cl(F s (Orb(p i ))) has non-empty interior;
(2) For 1 ≤ i = j ≤ k, there is no heteroclinic intersection between Orb(p i ) and Orb(p j ), i.e., F s (Orb(p i )) ∩ W u (Orb(p j )) = ∅; (3) Int(Cl(F s (Orb(p i )))) ∩ Int(Cl(F s (Orb(p j )))) = ∅.
Proof. Because S is a skeleton, from (a) of the definition of skeleton,
k i=1 Cl(F s (Orb(p i ))) = M.
Suppose by contradiction that Cl(F s (Orb(p i ))) has empty interior for some 1 ≤ i ≤ k, then j =i Cl(F s (Orb(p j ))) = M . Thus S \{p i } also satisfies (a) of Definition 1.2, which contradicts with (b) of Definition 1.2 and the fact that S is a skeleton. This finishes the proof of (1).
We are ready to prove (2). First by the unstable manifold theorem,
W u (Orb(p j )) is tangent to the bundle E cu . Thus if the intersection F s (Orb(p i )) ∩ W u (Orb(p j ))
is not empty, it must be transversal. By the Inclination lemma, Cl(F s (Orb(p j ))) ⊂ Cl(F s (Orb(p i ))), and thus S \ {p j } is a pre-skeleton, a contradiction.
To prove (3), we assume by contradiction that there are
1 ≤ i = j ≤ k such that U = Int(Cl(F s (Orb(p i )))) ∩ Int(Cl(F s (Orb(p j )))) = ∅. Take x ∈ F s R (Orb(p i )) ∩ U for some R > 0 where F s R (·) is the disk in F s (·) with radius R under leaf met- ric, then there is x n ∈ F s (Orb(p j )) ∩ U such that x n → x. By the continuity of stable foliation, we have F s 2R (x n ) → F s 2R (x)
and thus for n sufficiently large,
F s 2R (x n ) ∩ W u (Orb(p i )) = ∅. Because x n ∈ F s (Orb(p j )), we have F s (Orb(p j )) ∩ W u (Orb(p i )) = ∅,
which is a heteroclinic intersection between p j and p i , a contradiction with item (2).
In the following, instead of using the open set Int(Cl(F s (Orb(p i )))), we are going to consider the set O i = x∈W u (Orb(pi)) F s (x). By the transversality between E cu and E s and continuity of stable foliation, the set O i is open. In the following we will reveal the relation between these two open sets.
For a hyperbolic saddle p, we denote by H(p, f ) the homoclinic class of p with respect to the map f , that is, the closure of homoclinic intersections between W s (Orb(p)) and W u (Orb(p)).
Proposition 4.2. For every p i ∈ S, (i) Cl(W u (Orb(p i ))) = H(p i , f ); (ii) (4) Cl(F s (Orb(p i ))) = Cl(∪ x∈W u (Orb(pi)) F s (x)),
thus O i is open and dense in Int(Cl(F s (Orb(p i )))).
Proof. We first prove (i). From the definition of homoclinic class, we have
Cl(W u (Orb(p i ))) ⊃ H(p i , g).
Now let us prove the other direction of the inclusion. By the definition of skeleton, j=1,··· ,k (F s (Orb(p j ))) is dense in the manifold M . Thus for any x ∈ W u (Orb(p i )), there is p j ∈ S such that x ∈ Cl(F s (Orb(p j )))). According to (2) of Lemma 4.1, there is no heteroclinic intersection between F s (Orb(p j )) and W u (Orb(p i )) when i = j, thus i = j. It then follows that F s (Orb(p i )) and W u (Orb(p i )) have non-trivial intersections arbitrarily close x, meaning that x ∈ H(p i , f ). This completes the proof of (i).
By the discussion above, we have shown that
F s (Orb(p i ))∩W u (Orb(p i )) is dense inside W u (Orb(p i )), thus Cl(F s (Orb(p i ))) ⊃ Cl(∪ x∈W u (Orb(pi)) F s (x)). Meanwhile, because Orb(p i ) ⊂ W u (Orb(p i )), the inclusion Cl(F s (Orb(p i ))) ⊂ Cl(∪ x∈W u (Orb(pi)) F s (x))
is trivially satisfied, and the equality (4) follows immediately.
The next two lemmas show that if one replaces p i ∈ S by another hyperbolic periodic point q ∈ O i with index i s , the new set S ′ = S ∪ {q} \ {p i } is still an index i s skeleton; moreover, any skeleton of f can be obtained in this way. Proof. If q and p i are homoclinic related with each other, take a ∈ F s (q) ⋔ W u (Orb(p i )) and U a neighborhood of a in W u (Orb(p i )). By the continuity of stable foliation, x∈U F s (x) contains a neighborhood of q. Then by Proposition 4.2,
q ∈ x∈W u (Orb(pi)) F s (x) = O i .
On the other hand, suppose q ∈ x∈W u (Orb(pi)) F s (x), then there exists an intersection point a ∈ F s (q) ⋔ W u (Orb(p i )). By Proposition 4.2[(i)], a ∈ H(p i , f ) and thus can be approached by F s (Orb(p i )). By the continuity of stable foliation, F s (Orb(p i )) ∩ W u (q) = ∅. We conclude that q and p i are homoclinic related. Now suppose q and p i are homoclinic related. Then by the Inclination lemma, we have Cl(F s (Orb(q))) = Cl(F s (Orb(p i ))), which means that
p∈S ′ Cl(F s (Orb(p))) = M.
It remains to show that S ′ does not have a proper subset S ′′ that satisfies the above equality.
Assume by contradiction that S ′′ is such a proper subset of S ′ . Because S is a skeleton, S ′′ has to contain q, otherwise S ′′ will be a proper subset of S, which contradicts with the fact that S is a skeleton. By the discussion above,
S = {p i } S ′′ \ {q} is a pre-skeleton. However, this is impossible sinceS is a proper subset of S. Lemma 4.4. Suppose S ′ = {q 1 , · · · ,
q l } is a skeleton of f , then l = k, and after reordering, q i and p i are homoclinic related for i = 1, · · · , k.
Proof. By Definition 1.2 (a), for each q j ∈ S ′ there is some p i ∈ S such that F s (Orb(p i )) approaches p i ; thus W u (q j ) intersects F s (p i ) transversally.
Choose any such p i (we will see in a second that the choice is unique). The same argument applied on p i shows that there exists some q k ∈ S ′ such that W u (p i ) intersects F s (Orb(q k )) transversally. By the Inclination lemma, there is transverse intersection between W u (Orb(q j )) and F s (Orb(q k )). By Lemma 4.1[(2)], this can only happens if j = k. In particular, p i and q j are homoclinically related to one another.
Since being homoclinically related is an equivalent relation, and different elements in a skeleton do not have heteroclinic intersections, it follows that the choice of p i is unique, and the map q j → p i is injective. Reversing the roles of S ′ and S, we also get an injective map p i → q j which, by construction, is the inverse of the previous one. Thus, both maps are bijective and, in particular, #S = #S ′ . Moreover, after reordering, q i and p i are homoclinic related for i = 1, · · · , k.
The following lemma provides a useful criterion on the existence of skeletons, which will be used in Section 6. Proof. Let S ′ = {p 1 , · · · , p l } be a pre-skeleton. We first define a relation between the elements of S ′ : we say p i ≺ p j if W u (Orb(p i )) ⋔ F s (p j ) = ∅. By the Inclination lemma, it is easy to see that ≺ is reflexive and transitive: if p i ≺ p j then (5) Cl(F s (Orb(p j ))) ⊃ Cl(F s (Orb(p i ))).
Moreover, if we have p i ≺ p j and p j ≺ p i , then we say that they belong to the same equivalent class. Two elements belong to the same equivalent class if and only if they are homoclinic related. Now in the set of equivalent classes, ≺ induces a partial order. For every maximal equivalent class under this partial order, we pick up an representative element and then obtain a subset S ⊂ S ′ . By (5), S is clearly a pre-skeleton. Moreover, from the construction, the elements of S have no heteroclinic intersection. Then this lemma is a corollary of the following result: Lemma 4.6. Let S = {p 1 , · · · , p k } be a pre-skeleton of f such that there is no heteroclinic intersection between Orb(p i ) and Orb(p j ) for 1 ≤ i = j ≤ k, then S is a skeleton.
Proof. We prove by contradiction. Suppose S is not a skeleton, then by Definition 1.2 (b), it contains a proper subset S ′′ which forms a pre-skeleton. After reordering, we may assume S ′′ = {p 1 , · · · , p l } where l < k.
Then by the definition of skeleton, 1≤i≤l F s (Orb(p i )) is dense in the manifold M . As a result, there is 1 ≤ i 0 ≤ l such that F s (Orb(p i0 )) approaches p k , and thus F s (Orb(p i0 )) ⋔ W u (p k ) = ∅, which contradicts with the assumption that there is no heteroclinic intersection between elements of S. The proof is complete.
Diffeomorphisms with mostly expanding center revisit
Throughout this section, we assume f to be a C 1+ partially hyperbolic diffeomorphism with mostly expanding center. To make this paper as self-contained as possible, we will provide a direct proof on the existence of physical measures for diffeomorphisms with mostly expanding center. The proof is different from the original argument in [3] and is useful for the discussion in later sections.
One of the main difficulties in the study of diffeomorphisms with mostly expanding center lies in the fact that the space Gibbs u (f ) (or G u (g) for nearby C 1 map g) is 'too large', in the sense that it contains plenty of measures that are not physical. 2 We start solving this issue by introducing the following description for diffeomorphisms with mostly expanding center, which turns out to be equivalent to Definition 1.1. The main advantage is that it gives a uniform estimate on the center Lyapunov exponents for measures in Gibbs u (f ).
Proposition 5.1. [47][Proposition 6.1] Suppose f has mostly expanding center, then there is N 0 ∈ N and b 0 > 0 such that, for anyμ ∈ Gibbs u (f N0 ), (6) log
Df −N0 | E cu (x) dμ(x) < −b 0 .
Remark 5.2. From now on, we assume N 0 = 1.
By the upper semi-continuity of the space G u (f ) with respect to diffeomorphisms in C 1 topology (Proposition 2.13), we can extend this estimate to nearby C 1 maps:
Lemma 5.3.
There is a C 1 open neighborhood U of f , such that for any C 1 diffeomorphism g ∈ U, and any µ ∈ G u (g), we have
(7) log Dg −1 | E cu g (x) dµ(x) < −b 0 .
This is later used in Section 5.1, where we show that for any C 1 diffeomorphism g in a small C 1 neighborhood U of f , and for any µ ∈ G u (g), µ typical points x have infinitely many hyperbolic times for the bundle E cu in its orbit (see Lemma 5.8).
On the other hand, the space G cu (f ) is also 'too large' since it may contain measures with negative center exponents. Such measures need not be a Gibbs ustate, thus not physical due to Proposition 2.1 (4). One way to solve this issue is to take the space of intersection, G(f ), which is a much smaller space to work with. However, this creates another problem: unlike the partial entropy which is upper semi-continuous (which makes the space G u (f ) upper semi-continuous in f ), the metric entropy h µ may not have such property. This is dealt with in Section 5.2, as we introduce fake foliations for partially hyperbolic diffeomorphisms, and show in Lemma 5.12 that the measures in G u (g) for g ∈ U are uniformly entropy expansive. As a consequence, in Section 5.3 it is shown (Corollary 5.16) that metric entropy, when restricted to measures in G u (g), varies in a upper semi-continuous fashion in weak-* topology and with respect the diffeomorphism g ∈ U in C 1 topology.
Finally, Section 5.4 contains the main result of this section: for any C 1+ diffeomorphism g ∈ U, every extreme element of G(g) is an ergodic physical measure of g.
Hyperbolic times.
Definition 5.4. Given b > 0, we say that n is a b-hyperbolic time for a point x if
1 k n j=n−k+1 log Df −1 | E cu (f j (x)) ≤ −b for any 0 < k ≤ n.
Let D be any C 1 disk, we use d D (·, ·) to denotes the distance between two points in the disk. Recall that for the dominated splitting E s ⊕ E cu , one can define the center unstable cone field, which is invariant under forward iteration.
The next lemma states that if n is a hyperbolic time for x, then on the disk f n (D), one picks up an contraction by e −b for each backward iteration. for any point y ∈ D with d f n (D) (f n (x), f n (y)) ≤ r and any 1 ≤ k ≤ n.
Remark 5.6. For fixed b 0 /2 > 0, we can take r = r 1 to be constant for the diffeomorphisms in a C 1 neighborhood of f . By Lemma 5.3 and Proposition 2.12, for any g ∈ U, there is a full volume subset Γ g such that for any x ∈ Γ g , any limit of the sequence 1 n n−1 i=0 δ g i (x) belongs to G(g). Thus for any x ∈ Γ g , lim sup
n→∞ 1 n n−1 i=0 log Dg −1 | E cu g (g i (x)) = lim sup log Dg −1 | E cu g (x) d 1 n n−1 i=0 δ g i (x) < −b 0 < 0.(8)
Define H(b 0 /2, x, g) to be the set of b 0 /2-hyperbolic times for x ∈ Γ g , that is, the set of times m ≥ 1 such that
(9) 1 k m i=m−k+1 log Dg −1 | E cu g (g i (x)) ≤ −b 0 /2 for all 1 ≤ k ≤ m.
By the Pliss Lemma (see [3]), such hyperbolic times have positive density on the orbit segment from 0 to n: there exists n x ≥ 1 and δ 1 > 0 such that (10) #(H(b 0 /2, x, g) ∩ [1, n)) ≥ nδ 1 for all n ≥ n x .
By Lemma 5.5 and Remark 5.6, there is r 1 > 0 which only depends on U and b 0 /2, such that for any x ∈ Γ g , and any disk D tangent to the center-unstable cone field, x ∈ D, n ∈ H(b 0 /2, x, g), we have (11) d D (x, y) ≤ e −nb0/2 d g n (D) (g n (x), f n (y)), for any y ∈ D with d g n (D) (g n (x), g n (y)) ≤ r 1 (We also assume that r 1 satisfies the condition (15) below, which depends only on the neighborhood U.) In particular, for x ∈ U ∩ Γ g and D ⊂ U , g n (D) contains a smaller disk D n with diameter r 1 for n ∈ H(b 0 /2, x, g) sufficiently large. Then ∪ z∈Dn F s (z) contains an open ball with radius r 1 .
Definition 5.7. Denote by H(b 0 /2, g) the set of point x such that for any k ≥ 1,
1 k k−1 i=0 log Dg −1 | E cu g (g −i (x)) ≤ −b 0 /2 for all k ≥ 0.(12)
In other words, for every n > 0, n is a hyperbolic time for the point f −n (x).
The next lemma shows that there are plenty of hyperbolic times on the forward orbit of x, every µ ∈ G u (g) and µ almost every x.
Lemma 5.8. For any g ∈ U and any µ ∈ G u (g), we have
(13) µ(H(b 0 /2, g)) ≥ δ 1
where δ 1 is given in (10).
Proof. By Proposition 2.13, we may assume µ to be ergodic. By Birkhoff theorem, we only need to show that for µ almost every x, lim inf 1 n #{1 ≤ k ≤ n; f k (x) ∈ H(b 0 /2, g)} ≥ δ 1 . It is equivalent to show that for some fixed m x , (14) lim inf 1 n #{1 ≤ k ≤ n; f k+mx (x) ∈ H(b 0 /2, g)} ≥ δ 1 .
By Lemma 5.3, take x be a typical point of µ, such that
lim 1 n n−1 i=0 log Dg −1 | E cu g (g −i (x)) ≤ −b 0 .
We claim that there is m > 0 such that g −m (x) ∈ H(b 0 /2, g). Otherwise for any g −n (x) , there is i n > 0 such that 1 in in−1 0 log Dg −1 | E cu g (g −i−n (x)) ≥ −b 0 /2. Recursively, we obtain a sequence of points: n 1 = i 0 , n 2 = n 1 + i n1 , · · · ; by induction, we have
1 n k n k −1 i=0 log Dg −1 | E cu g (g −i (x)) ≥ −b 0 /2.
This contradicts with the choice of x.
Moreover, it is easy to see that for any k ∈ H(b 0 /2, g −m (x), g), g k−m (x) ∈ H(b 0 /2, g). Then by (10) and take m x = m in (14), we conclude the proof.
Fake foliations.
In order to avoid assuming dynamical coherence of f , we use locally invariant (fake) foliations, a construction that follows Burns, Wilkinson [17] and goes back to Hirsch, Pugh, Shub [29]. We fix U a small C 1 neighborhood of f provided by Lemma 5.3.
Lemma 5.9. There are real numbers ρ > r 0 > 0 only depending on U with the following properties. For any x ∈ M , the neighborhood B(x, ρ) admits foliationŝ F s g,x andF cu g,x such that for every y ∈ B(x, r 0 ) and * = {s, cu}:
(1) the leafF i g,x (y) is C 1 , and its tangent bundle T y (F i g,x (y)) lies in a cone of E i (x); (2) g(F s g,x (y, r 0 )) ⊂F s g,g(x) (g(y)) and g −1 (F cu g,x (y, r 0 )) ⊂F cu g,f −1 (x) (g −1 (y)); (3) we have product structures on the B(x, r 0 ), i.e., for any y, z ∈ B(x, r 0 ), there is a unique intersection betweenF s g,x (y) withF cu g,x (z), which we denote by [y, z].
For g ∈ U and any x ∈ M , we considering the following three types of Bowen balls:
• finite Bowen ball : B n (g, x, ε) = {y ∈ M : d(g i (x), g i (y)) < ε, |i| < n},
• negative Bowen ball : B − ∞ (g, x, ε) = {y ∈ M : d(g i (x), g i (y)) < ε, i < 0}, • (two sided) infinite Bowen ball :
B ∞ (g, x, ε) = {y ∈ M : d(g i (x), g i (y)) < ε, i ∈ Z}.
It was shown in the proof of [35][Theorem 3.1] that: Lemma 5.10. For ε < r 0 /2 and any x ∈ M , B − ∞ (g, x, ε) ⊂F cu g,x (y, 2ε). We may take r 1 in the previous section to satisfy that (15)
r 1 < r 0 /2.
Then as a consequence of Lemma 5.5, we show that for every point in H(b 0 /2, g), the unstable manifold has uniform size:
Lemma 5.11. For any x ∈ H(b 0 /2, g),F cu g,x (x, r 1 ) ⊂ W u loc (x). More precisely, for any y ∈F cu g,x (x, r 1 ), dFcu g,g −n (x) (g −n (x)) (g −n (x), g −n (y)) ≤ e −nb0/2 dF cu g,x (x) (x, y). The goal of this subsection is to show that the measures in G u (g) for g ∈ U are uniformly entropy expansiveness.
Lemma 5.12. For any g ∈ U, and any measure µ ∈ G u (g), for µ almost every point x, B ∞ (g, x, r 1 ) = x.
Proof. By Lemma 5.10 and the choice of r 1 ≤ r 0 /2, we have B ∞ (g, x, r 1 ) ⊂ B − ∞ (g, x, r 1 ) ⊂F cu g,x (x, r 1 ). Let x be a µ typical point, by Lemma 5.8, we may assume that the forward orbit of x enters H(b 0 /2, g) infinitely many times. Suppose there is a distinct point y ∈ B ∞ (g, x, r 1 /2) ⊂F cu g,x (x, r 1 ), we are going to prove by contradiction. Suppose f n (x) ∈ H(b 0 /2, g), then f n (y) ∈ B ∞ (g, g n (x), r 1 /2) ∈F cu g,x (x, r 1 ). By Lemma 5.11, dF cu g,x (x) (x, y) ≤ e −nb0/2 dFcu g,g n (x) (g n (x)) (g n (x), g n (y)) ≤ e −nb0/2 r 1 . Taking n → ∞, we have dF cu g,x (x) (x, y) = 0. Hence x = y, a contradiction with the hypothesis that x and y are distinct. The proof is complete.
Remark 5.13. The classical definition of entropy expansive by Bowen requires that the topological entropy of B ∞ (g, x, r 1 ) to be vanishing for every x ∈ M . However, as observed in [35], this is equivalent to having zero topological entropy for the infinite Bowen ball for every invariant measure µ and µ almost every x. The statement of the previous lemma follows this approach.
Also note that this lemma does not immediate lead to the upper semi-continuity of h µ as in the classical case, since we only have entropy expansive on a subspace of invariant measure. However, we will see in a second that the upper semi-continuity holds for measures in G u .
5.3.
Upper semi-continuity of metric entropy. In this section, we are going to show that the metric entropy for measures in G u (·) is upper semi-continuous, which is a consequence of the uniform entropy expansiveness for measures among G u (·).
Define the ε-tail entropy at x by
h * (g, x, ε) = h top (g, B ∞ (g, x, ε)).
For any probability measure µ of g, let h * (g, µ, ε) = h * (g, x, ε)dµ(x).
As a direct consequence of Lemma 5.12, we get Lemma 5.14. For any g ∈ U and any µ ∈ G u (g), h * (g, µ, r 1 ) = 0.
We also need the following lemma of [19][Theorem 1.2]:
Lemma 5.15. h µ (g) − h µ (g, P) ≤ h * (g, µ, ρ) for any finite measurable partition P with diam(P) ≤ ρ.
By Lemma 5.14 and Lemma 5.15, we conclude that h µ (g) = h µ (g, P) for any finite measurable partition P with diam(P) ≤ ρ. In particular, by a standard argument for upper semi-continuity of metric entropy (see for instance [35][Lemma 2.3]), we have: Corollary 5.16. Let g n (n ≥ 0) be a sequence of C 1 partially hyperbolic diffeomorphisms inside U, and µ n ∈ G u (g n ). Suppose g n → g 0 in C 1 topology and µ n → µ 0 ∈ G u (g 0 ) in weak-* topology, then lim sup n→∞ h µn (g n ) ≤ h µ0 (g 0 ).
Physical measures.
In this section, we will provide a uniform treatment on the existence of physical measures for all C 1+ diffeomorphisms in U. For this purpose, let r 1 > 0 be given by Lemma 5.5 and (15).
Proposition 5.17. Let g be any C 1 diffeomorphism of U. Then G(g) is compact and convex, and every extreme element of G(g) is an ergodic measure. The map: G : g ∈ U → G(g) is upper semi-continuous with respect to diffeomorphisms in U under C 1 topology. Moreover, if g is C 1+ , then G(g) has finitely many extreme points, each of which is a physical measure of g and vice versa. The basin of each physical measure of g contains Lebesgue almost every point of some ball with radius r 1 .
Proof. Recall that
G cu (g) = {µ ∈ M inv (f ) : h µ (g) ≥ log(det(Dg | E cu (x) ))dµ(x)}.
Because the metric entropy function is affine, it follows that G cu (f ) is convex. By Proposition 2.13, G u (g) is convex, so is G(g) = G u (g) G cu (g).
The compactness of G(g) follows from Corollary 5.16. More precisely, suppose there is a sequence of invariant probabilities {µ n } ∞ n=0 of g such that µ n ∈ G(g) and assume lim n→∞ µ n = µ. Because µ n ∈ G cu (g), we have h µn (g) ≥ log(det(Dg | E cu (x) ))dµ n (x).
Note that µ n ∈ G u (g), and by Proposition 2.13, G u (g) is compact, we have µ ∈ G u (g). It then follows from Corollary 5.16 that lim sup n→∞ h µn (g) ≤ h µ (g), which implies:
h µ (g) ≥ log(det(Dg | E cu (x) ))dµ(x).
This means µ ∈ G cu (g), thus µ ∈ G u (g) ∩ G cu (g) = G(g).
Indeed, by Corollary 5.16 and a similar proof as above, for a sequence of C 1 maps g n ∈ U, g n → g ∈ U in C 1 topology and µ n ∈ G(g n ) converging to µ in weak-* topology, we have µ ∈ G(g). Then the map G(·) is upper semi-continuous, as claimed.
Suppose that µ is any extreme element of G(g), then it is contained in G u (g). We claim that:
Lemma 5.18. µ is ergodic.
Proof. Letμ be a typical ergodic component in the ergodic decomposition of µ, we are going to show thatμ ∈ G(g); this implies thatμ is also an extreme element of G(g), thus it coincides with µ.
By Proposition 2.13,μ ∈ G u (g). Thus it suffices to show thatμ ∈ G cu (g). Because g ∈ U, by Lemma 5.3, any measure ν ∈ G u (g) has positive center exponent. By Ruelle's inequality,
hμ(g) ≤ log(det(Dg | E cu (x) ))dμ(x). Because µ ∈ G cu (g), h µ (g) ≥ log(det(Dg | E cu (x) ))dµ(x).
Since entropy function is an affine functional with respect to invariant measures, we must have hμ(g) = log(det(Dg | E cu (x) ))dμ(x) for typical ergodic component µ of µ. Thusμ ∈ G cu (g). The proof is complete.
We continue the proof of Proposition 5.17. Assume that g ∈ U is a C 1+ partially hyperbolic diffeomorphism. First we suppose that µ is an extreme element of G(g). Then by the discussion above, µ is ergodic with positive center exponents. Moreover, by Ruelle's inequality, we get h µ (g) = log(det(Dg | E cu (x) ))dµ(x).
By the entropy formula of Ledrappier-Young [32], the disintegration of µ along the Pesin unstable manifold is equivalent to the Lebesgue measure on the leaves. This means, for µ almost every x, Lebesgue almost every point on the Pesin unstable manifold of x is a typical point of µ. Since the Basin of µ is saturated by stable leaves (we use the fact that E s is uniformly contracting), and the stable foliation is absolutely continuous, the union of the stable leaves of the previous full Lebesgue measure subset of W u (x) is contained in the basin of µ and has full volume inside a ball with center at x. Note however, that such ball may not have uniform radius r 1 .
To obtain a ball with radius r 1 in the basin of µ, we apply Lemma 5.8 to obtain an n > 0, such that g n (x) ∈ H(b 0 /2, g). Then by Lemma 5.11, W u (g n (x), g) contains a disk with radius r 1 , where Lebesgue typical points in this disk are typical points of µ. By the uniform transversality between the bundles E s and E cu , the basin of µ contains Lebesgue almost every point of a ball at g n (x) with radius r 1 , which we denote by B g n (x) (r 1 ). It then follows that (16) µ(B g n (x) (r 1 )) > 0.
To simplify notation, we write any ball obtained in the above way by B µ . Because the basins of different physical measures are disjoint, G(g) has only finitely many extreme elements. We denote them by µ 1 , · · · , µ k . Now we prove that every physical measure µ of g is an extreme element of G(g). Since the basin of µ, B(µ), has positive volume, by Proposition 2.12, Lebesgue almost every point x ∈ B(µ) must satisfy µ = lim 1 n n−1 i=0 δ g i (x) ∈ G(g). Thus it only remains to show that µ is ergodic.
Because G(g) is convex with finitely many extreme elements, µ can be written as a combination: µ = a 1 µ 1 + · · · + a k µ k where 0 ≤ a 1 , · · · , a k ≤ 1 and k i=1 a k = 1. There is 1 ≤ j ≤ k such that a j > 0. Then by (16), µ(B µj ) = a j µ i (B µj ) > 0.
Thus for every point x ∈ B(µ) and n sufficiently large, 1
n n−1 i=0 δ g i (x) (B µj ) > 0. In particular, there is n j > 0 such that g nj (x) ∈ B µj .
Because vol(B(µ)) > 0, take x ∈ B(µ) a Lebesgue density point of B(µ), i.e., it satisfies:
lim r→0 + vol(B x (r) ∩ B(µ)) vol(B x (r)) → 1.
Then the above argument shows that B(µ) B µj = g nj (B(µ)) B µj has positive Lebesgue measure.
Recall that B µj is in the basin of µ j . Therefore the basin of µ and µ j have non-trivial intersection. This implies µ = µ j , and µ is ergodic. The proof of Proposition 5.17 is complete.
Remark 5.19. The C 1+ regularity is used to:
• show that the conditional measures of µ along unstable leaves are absolutely continuous; we need the work of Ledrappier and Young, which requires C 1+ ; • show that the basin of µ contains Lebesgue almost every point in a ball;
there we need the stable foliation to be absolutely continuous.
We will see later in Section 7 that such regularity condition can be bypassed for generic C 1 diffeomorphisms in U.
Proof of Theorem A and Corollary B
In this section, we provide t he proof of Theorem A and Corollary B. Throughout this section, we assume f to be a C 1+ diffeomorphism with mostly expanding center, U a sufficiently small C 1 neighborhood of f . By Proposition 5.1, there is b 0 > 0 such that for any C 1 diffeomorphism g ∈ U and any µ ∈ G u (g), (17) log
Dg −1 | E cu (x) dµ(x) < −b 0 .
The structure of this section is as following: In Section 6.1 we introduce the Liao's shadowing lemma, which will be used in Section 6.2 to construct skeletons. For the discussion in Section 8, we will make the construction for every C 1 diffeomorphism g ∈ U.
Then in Section 6.3, we will show that each element in S(g) is associated to a physical measure, assuming that f is C 1+ . This concludes the proof of Theorem A. Finally, in Section 6.4 we provide the proof of Corollary B.
Liao's shadowing lemma.
Definition 6.1. An orbit segment (x, f (x), · · · , f n (x)) is called λ-quasi hyperbolic if there exists 0 < λ < 1 such that
(18) k−1 i=0 Df −1 | E cu (f n−i (x)) < λ k for any 1 ≤ k ≤ n.
In other words, (x, f (x), · · · , f n (x)) is λ-quasi hyperbolic if n is a (− log λ)hyperbolic time for x. In this subsection we need the following shadowing lemma by Liao, which allows a quasi hyperbolic, periodic pseudo orbit to be shadowed by a periodic orbit with large unstable manifold. Lemma 6.2 ([34,25]). For any λ > 0, there exist ρ > 0 and L > 0, such that for any λ-quasi hyperbolic orbit (x, f (x), · · · , f n (x)) of f with d(x, f n (x)) ≤ ρ, there exists a hyperbolic periodic point p ∈ M such that (a) p is a hyperbolic periodic point with period n and with stable index i s ;
(b) d(f i (x), f i (p)) ≤ Ld(x, f n (x)) for any 0 ≤ i ≤ n − 1;
(c) p has uniform size unstable manifold: there is a constant r > 0 depending on λ, such that the local unstable manifold of p contains a disk with radius r.
Remark 6.3. The parameters in the previous lemma can be made uniform for diffeomorphisms in a C 1 neighborhood U of f . Moreover, one can take δ sufficiently small, then d(f i (x), f i (p)) ≤ Ld(x, f n (x)) is sufficiently small for any 0 ≤ i ≤ n− 1, and then
k−1 i=0 Df −1 | E cu (f n−i (p)) ≤ λ k for any 1 ≤ k ≤ n.
In particular, if one takes λ = e −b0/2 , then the size of unstable manifold of p can be chosen to be r 1 > 0, which is the constant given by Lemma 5.11.
Definition 6.4. A periodic point p of g ∈ U is called a λ-hyperbolic periodic point, if it satisfies (19) k−1 i=0 Df −1 | E cu (f n−i (p)) ≤ λ k
for any 1 ≤ k ≤ π(p).
By the previous discussion and Remark 5.6, we have shown that Lemma 6.5. For any e −b0/2 -quasi hyperbolic periodic point, its unstable manifold contains a r 1 -ball inside the cu-fake leafF cu g,p (p, r 1 ) 6.2. Existence of skeleton. In this section, we will show that any C 1 diffeomorphism g ∈ U admits a skeleton. The main result of this section is Proposition 6.8.
In order to apply Liao's shadowing lemma, we need to establish the existence of orbit segments that are quasi-hyperbolic. This follows from Proposition 2.12 and (17):
Proposition 6.6. Suppose g ∈ U.
There is a full volume subset Γ g such that for Lebesgue almost every point x ∈ Γ g , lim sup
n→∞ 1 n n−1 i=0 log Dg −1 | E cu (g n−i (x)) ≤ −b 0 .
By the Pliss Lemma (see [3]), there exists n x ≥ 1 and δ 1 > 0 such that (20) #
(H(b 0 3/4, x, g) ∩ [1, n)) ≥ nδ 1 for all n ≥ n x ,
where H(b 0 3/4, x, g) is the collection of b 0 3/4-hyperbolic times along the forward orbit of x.
Taking a sequence of integers n x ≤ n 1 < n 2 < · · · such that n i ∈ H(b 0 3/4, x, g)), we may assume that x ni = f ni (x) converges to a point x 0 . For λ = e − 3b 0 4 , ρ and L are obtained by Lemma 6.2. We may further assume that sup i,j {d(x ni , x nj )} ≤ ρ 0 ≤ ρ where ρ 0 satisfies that for any two points y, z ∈ M with d(y, z) ≤ Lρ 0 , we have
(21) | log Dg −1 | E cu (y) − log Dg −1 | E cu (z) |≤ b 0 /4.
Because for any i < j, the pseudo orbit {x ni , x ni+1 , · · · , x nj −1 } is b 0 3/4-quasi hyperbolic, by Lemma 6.2, this pseudo orbit is Ld(x ni , x nj ) ≤ Lρ 0 shadowed by a periodic orbit p x,i,j . Because x ni → x 0 as i → ∞, all the periodic points p x,i,i+1 converge to x 0 .
Moreover, by the choice of ρ 0 in (21), p x,i,j is a e −b0/2 -quasi hyperbolic periodic point. By Lemma 6.5, each periodic point p x,i,j has unstable manifold with size at least r 1 . Their stable manifold already have uniform size due to E s being uniformly contracting (note that all p x,i,j 's have stable index i s ). Thus there is m x such that for any i, j > m x , p x,i,i+1 and p x,j,j+1 are homoclinic related to each other, and
F s loc (x i ) ⋔ W u r1 (p j,j+1 ) = ∅.
Furthermore, F s loc (p i ) will intersect transversally with any disk center at x j , tangent to the cu cone with radius at least r 1 .
To simplify notation, we will write p x,i,i+1 = p x,i .
Lemma 6.7. For any i > m x , x ∈ Cl(F s (Orb(p x,i ))).
Proof. Let U be any small neighborhood of x. Because for any i > m x , all the hyperbolic periodic points p i are homoclinic related to each other, we only need to show that there is i > m x , such that F s (Orb(p i )) ∩ U = ∅, then the lemma will follow from the Inclination lemma. We take ε > 0 small enough such thatF cu g,x (x, ε) ⊂ U . By Lemma 5.5, for i > m x sufficiently large, g i (F cu g,x (x, ε)) ⊃F cu g,xn i (x ni , r 1 ), where the latter is a disk tangent to a cu cone with uniform diameter. This means that when i is sufficiently large, g ni (F u g,x (x, ε)) ⋔ F s loc (p i ) = ∅. By the invariance of the stable manifold under the iteration of g, we have U ∩ F s (Orb(p i )) = ∅.
The proof is complete. Now we are ready to construct the skeleton for g ∈ U. By Proposition 6.6, for each x ∈ Γ g , we fix any one of p x,i for i > m x and denote it by p x . Then by the previous lemma, the union x∈Γ F s (Orb(p x )) is dense in the manifold M .
Moreover, since each periodic point p x has stable and unstable manifold with size at least r 1 , there are only finitely many of them that are not homoclinically related to each other, with number uniformly bounded from above. Take {p 1 , · · · , p k } a subset of {p x } x∈Γ which are not homoclinic related and has maximal cardinality.
We claim that i=1,··· ,k F s (Orb(p i )) is dense in the manifold M . Assume that this is not the case, then we can take p x for x ∈ M \ i=1,··· ,k Cl(F s (Orb(p i ))). By the choice of {p 1 , · · · , p k }, p x must be homoclinically related to some p i . However, this means that Cl(F s (Orb(p i ))) = Cl(F s (Orb(p x ))) by the Inclination lemma. Lemma 6.7 then shows that x ∈ Cl(F s (Orb(p i ))), which is a contradiction.
Thus {p 1 , · · · , p k } forms a pre-skeleton. By Lemma 4.5, we have shown that:
Proposition 6.8. Every C 1 diffeomorphism g ∈ U admits a skeleton S(g) = {p 1 , · · · , p k }, such that for any 1 ≤ i ≤ k, W u (p i ) contains a ball in the fake cu leaf with center at p i and radius r 1 .
From now on, we fix S(g) = {p 1 , · · · , p k } a skeleton obtained as above.
6.3. Skeleton and measures. In this section we assume g ∈ U to be C 1+ , then by Lemma 5.3, g has mostly expanding center. We will establish a one-to-one correspondence between elements of S(g) and the physical measures of g. By Proposition 5.17, g has only finitely many physical measures {µ 1 , · · · , µ l }. Moreover, from Lemma 5.8 and Proposition 5.17, there is r 1 > 0 only depending on U and b 0 such that, for any physical measure µ j of g, there is a µ j regular point x j , such that:
(a) x j ∈ H(b 0 /2, g), thus has Pesin unstable manifold with size larger than r 1 ; (b) µ regular points consists of Lebesgue almost every point on the Pesin unstable manifold of x j .
The main result of this section is the following:
Proposition 6.9. The number of physical measures and the number of elements of skeleton of g are the same, i.e., k = l. Indeed, there is a bijective map: j → i(j) such that for any physical measure µ j of g, there is p i(j) ∈ S(g) such that supp(µ j ) = Cl(W u (Orb(p i ), g)), and Lebesgue almost every point on W u (Orb(p i ), g) belongs to the basin of µ j . Moreover, the closure of F s (Orb(p i )) coincides with the closure of B(µ j ).
Proof. Fix any physical measure µ j of g. By (a) above, there is
p i ∈ S(g) such that F s (Orb(p i )) ⋔ W u r1 (x j , g) = ∅. By the Inclination lemma, g n (W u r1 (x j , g)) converges to W u (Orb(p i ), g). Because W u r1 (x, g) ⊂ supp(µ j ) by (b) above, we have Cl(W u (Orb(p i ), g)) ⊂ supp(µ j ).
To show the reversed inclusion, note that for n large enough, by the Inclination lemma, g n (W u r1 (x, g)) approaches W u loc (p) in the following sense: there is stable holonomy map from W u loc (p) to g n (W u r1 (x, g)) induced by the stable foliation. Because the set of µ j typical points is invariant under iteration, Lebesgue almost every point of g n (W u r1 (x, g)) is also typical for µ j . Since stable foliation is absolutely continuous, and the basin of µ j is s-saturated, it follows that Lebesgue almost every point of W u (Orb(p i ), g) belongs to the basin of µ j .
Take any point y ∈ W u (p i )∩B(µ j ). Because g n (y) ∈ W u (Orb(p i )) for any n ≥ 0, thus µ j = lim 1 n δ g i (y) is supported on Cl(W u (Orb(p i ), g)). As a conclusion, (22) supp(µ j ) = Cl(W u (Orb(p i ), g)).
Because Lebesgue almost every point on W u (Orb(p i ), g) belongs to the basin of µ j , the map j → i(j) is injective; in particular, we have k ≥ l. After reordering the periodic points of S(g), we may assume that i(j) = j for j = 1, · · · , l.
In order to prove k = l, we only need to show that {p 1 , · · · , p l } is a pre-skeleton, i.e., l i=1 F s (Orb(p i )) is dense in the manifold M . By Proposition 5.17, the union of basins of physical measures has full volume, thus it suffices to prove that for each 1 ≤ i ≤ l, the closure of F s (Orb(p i )) coincides with the closure of B(µ i ).
By (22) we have p i ∈ supp(µ i ). Take r > 0 sufficiently small such that µ i (B r (p i )) > 0 and B r (p i ) ⊂ O i = y∈W u (Orb(pi),g) F s (y). For any x ∈ B(µ i ), since we have
1 n n−1 i=0 δ f i (x) → µ i , there is n sufficiently large such that 1 n n−1 i=0 δ f i (x) (B r (p i )) > 0. This shows that there is m > 0 such that f m (x) ∈ B r (p i ) ⊂ O i . By (ii) of Proposition 4.2, f m (x)
is accumulated by F s (Orb(p i )), so is x. Thus we have shown that the basin of µ i is contained in the closure of F s (Orb(p i )), while the reversed inclusion follows immediately from the u-saturation of supp(µ i ). We now conclude that k = l.
The proof is complete.
Proof of Theorem A. By Proposition 6.8, f admits an index i s skeleton. Let S = {p 1 , · · · , p k } be any index i s skeleton of f . By Proposition 6.9, the number of physical measures is precisely k = #S, and for each p i ∈ S there exists a distinct physical measure µ i such that
(1) the closure of W u (Orb(p i )) coincides with supp(µ i ) and by (ii) of Proposition 4.2, they also coincide with the homoclinic class of the orbit Orb(p i ). Because {p 1 , · · · , p k } is an index i s skeleton of f , i q∈Orb(pi) F s (q) is dense in the manifold M , which means that S = {q ∈ Orb(p i ), i = 1, . . . , k} is a pre-skeleton of f n for every n ≥ 0. By Lemma 4.5, it has a subset which is a skeleton of f n . It follows from Theorem A that f n has finitely many physical measures with number bounded by P = k i=1 π(p i ) = #S. Moreover, because elements of S are all distinct fixed points of f nP for any n > 0, it is a skeleton for f nP , n > 0. Then by Theorem A, f nP have the same number of physical measures for every n > 0. Let µ be a physical measure of f P . By Proposition 5.17, µ is ergodic, and its conditional measures along the Pesin unstable manifolds are equivalent to the Lebesgue measure on the leaves. Below we will show that µ is ergodic for f nP for all n > 0.
To this end, letμ be any ergodic component of µ with respect to f nP , then the conditional measures ofμ along the Pesin unstable manifolds are still equivalent to the Lebesgue measure on the leaves. It then follows from the argument of Proposition 5.17 thatμ is a physical measure of f nP . Since the number of physical measures of f nP are constant,μ must be the only ergodic component of µ with respect to f nP . It then follows that µ =μ which is ergodic for f nP .
Then, by the classical work of Ornstein and Weiss [38], every physical measure of f P is a Bernoulli measure.
Proof of Theorem D
In this section, we study the robustness of the skeleton and physical measures under C 1 topology among C 1+ diffeomorphisms and prove Theorem D For this purpose, we assume that f : M → M is a C 1+ partially hyperbolic diffeomorphism with mostly expanding center, and U a C 1 neighborhood of f satisfying Lemma 5.3 and Proposition 5.17. Let b 0 be given in Lemma 5.3 and r 1 be given by Proposition 5.17. We take S(f ) = {p 1 , · · · , p k } a skeleton of f . Since k i=1 F s (Orb(p i (f )), f ) is dense in the manifold M , by the continuity of stable foliation with respect to diffeomorphisms in C 1 topology, we may assume that U is sufficiently small such that for any C 1 diffeomorphism g ∈ U, the continuation of S(f ) given by the continuation of hyperbolic saddles: S(g) = {p i (g), · · · , p k (g)} satisfies that k i=1 F s (Orb(p i (g)), g) is r 1 dense, i.e., for any x ∈ H(b 0 /2, g),
k i=1 F s (Orb(p i (g)), g) ⋔ W u r1 (x, g) = ∅,
where W u r1 (x, g) is given by Lemma 5.11. Note that S(g) may not be a skeleton. In the following, we will show the relation between skeletons of diffeomorphisms in U. For the discussion in the next section, we will state the following lemma for C 1 diffeomorphisms in U.
Lemma 7.1. For C 1 diffeomorphisms in U, the number of elements of skeleton varies upper semi-continuously. More precisely, for g ∈ U:
(1) S(g) = {p 1 (g), · · · , p k (g)} is a pre-skeleton of g, thus it contains a subset which is a skeleton of g; (2) suppose that {q 1 (g), · · · , q l (g)} is a skeleton of g, then there is a C 1 neighborhood V of g such that for any h ∈ V, {q 1 (h), · · · , q l (h)} is a pre-skeleton of h.
Proof. By Proposition 6.8, g admits a skeleton {q 1 (g), · · · , q l (g)} and each q j (g) (j = 1, · · · , l) has unstable manifold with size r 1 . Then by the previous assumption on U, for every 1 ≤ j ≤ l, there is an 1 ≤ i ≤ k such that F s (Orb(p i (g)), g) ⋔ W u r1 (q j (g), g) = ∅. Thus, by the Inclination lemma, F s (Orb(q j (g)), g) is accumulated by F s (Orb(p i (g)), g), which implies that ∪ k i=1 F s (Orb(p i (g))) is dense in the manifold M . This finishes the proof of (1).
The proof of (2) is quite similar. Take V sufficiently small such that for any
C 1 diffeomorphism h ∈ V, the continuation {q 1 (h), · · · , q l (h)} satisfies the condi- tion that ∪ k i=1 F s (Orb(q i (h))
, h) is r 1 dense. By Proposition 6.8, every h ∈ V ⊂ U admits a skeleton {q ′ 1 (h), · · · , q ′ t (h)}. has unstable manifold with size r 1 . Then for every 1 ≤ j ≤ t, there is an 1 ≤ i ≤ l such that F s (Orb(q i (h)), h) ⋔ W u r1 (q ′ j (h), h) = ∅. Thus, by the Inclination lemma, F s (Orb(q ′ j (h)), h) is accumulated by F s (Orb(q i (h)), h), which implies that ∪ k i=1 F s (Orb(q i (h)), h) is dense in M . This finishes the proof of (2).
Thus, by Lemma 4.4, the number of elements of the skeleton of g is bounded from above by k = #S(f ). It follows that, restricted to an C 1 open and dense subset U • ⊂ U, the number of elements of a skeleton for diffeomorphisms of U • is locally constant. More precisely, for any 1 ≤ i ≤ k, denote by U i = {g ∈ U; skeleton of g has less than i number of elements.} Then U i is an open set, and U • = U 1 2≤i≤k (U i \Cl(U i−1 )) satisfies our requirement.
By Theorem A, the number of physical measures for C 1+ diffeomorphisms in U • is locally constant.
Suppose f n ∈ U • be a sequence of C 1+ diffeomorphisms such that f n → f 0 ∈ U • . We assume that all f n have m ≤ k physical measures. By the previous argument, all the diffeomorphisms f n and f 0 have the same number of elements in their skeletons. In particular, by Lemma 7.1, we may take a skeleton S(f 0 ) = {p 1 (f 0 ), · · · , p m (f 0 )} of f 0 such that its continuation S(f n ) = {p 1 (f n ), · · · , p m (f n )} is a skeleton of f n . For f n (n ≥ 0), denote by µ n,1 , · · · , µ n,m the physical measures of f n associated with the periodic point p j (f n ) as explained in Theorem A. In the following we are going to show that:
Lemma 7.2. µ n,i weak * −→ µ 0,i .
Proof. For simplicity, we will only prove it for i = 1. We prove by contradiction, and assume (after taking subsequence if necessary) that µ n,1 weak * −→ µ = µ 0,1 . By Proposition 5.17, the space G(·) is compact and convex; extreme elements of G(·) are precisely those physical measures, and it varies in a upper semi-continuous fashion with respect to diffeomorphisms in U under C 1 topology. Thus µ n,1 ∈ G(f n ) and µ ∈ G(f 0 ). Moreover, µ can be written as a combination of the physical measures of f 0 : µ = a 1 µ 0,1 + · · · a m µ 0,m . By our assumption, a 1 = 1, thus there is 1 < i ≤ m such that a i > 0. We will show that this implies heteroclinic intersection between p 1 (f n ) and p i (f n ), which is a contradiction.
Take r > 0 sufficiently small, such that B r (p i (f 0 )) ⊂ ∪ x∈W u (pi(f0),f0) F s (x, f 0 ). Then by the continuity of unstable manifolds of p i (·) and the continuity of stable foliation with respect to diffeomorphisms, there is n 0 such that for any n > n 0 , any point x ∈ B r (p i (f n )),
(23) F s loc (x, f n ) ⋔ W u (p i (f n ), f n ) = ∅.
By Theorem A, p i (f 0 ) ∈ supp(µ 0,i ) and µ 0,i (B r (p i (f 0 ))) > 0. Since µ n,1 → µ which also assigns positive measure to B r (p i (f 0 )), there is n > n 0 such that µ n,1 (B r (p i (f 0 ))) > 0. In particular, we have supp(µ n,1 ) ∩ B r (p i (f 0 )) = ∅. Again by Theorem A, supp(µ n,1 ) = H(p 1 (f n ), f n ), thus F s (Orb(p 1 (f n )), f n )∩B r (p i (f 0 )) = ∅. By (23),
F s (Orb(p 1 (f n ))) ⋔ W u (p i (f n ), f n ) = ∅,
which contradicts the fact that {p 1 (f n ), · · · , p k (f n )} is a skeleton of f n and thus by Lemma 4.1[(1)] there is no heteroclinic intersection between p i (f n ) and p j (f n ) for
1 ≤ i = j ≤ k.
To prove Theorem D, it remains to show that for diffeomorphisms in Diff 1+ (M )∩ U • , the supports of corresponding physical measures and the closures of their basins vary in a lower semi-continuous fashion, both in the sense of the Hausdorff topology.
Indeed, by the unstable manifold theorem of fixed saddle, for each R > 0, the local invariant manifolds W u R (Orb(p i (g), g)) vary continuously with g ∈ U; moreover, the stable foliation also varies continuously with respect to g. Thus the closures of W u (Orb(p i (g), g)) and x∈W u (Orb(pi(g)),g) F s (x, g) both vary in a lower semicontinuous fashion with g, relative to the Hausdorff topology. By Theorem A, this means that the supports and the closures of the basins of the physical measures vary lower semi-continuously with the dynamics. The proof of Theorem D is now complete.
Proof of Theorem E
In this section we will generalize the result of Theorem D to C 1 generic diffeomorphisms in U. The proof is similar to [28,Theorem B]. The key observations are:
• C 1+ diffeomorphisms are dense in C 1 topology;
• skeletons are upper semi-continuous in U;
• the support of physical measures for C 1+ g ∈ U are homoclinic classes, which are (generically) Lyapunov stable and lower semi-continuous with the dynamics; • the candidate space of physical measures, G(·), is upper semi-continuously. These properties will allow us to find a residual subset of U, consisting of continuous points of H(p i (·), ·) and G(·). We will prove Theorem E on this residual subset of U.
Throughout this section, let f : M → M be a C 1+ partially hyperbolic diffeomorphism with mostly expanding center, S(f ) = {p 1 , · · · , p k } be a skeleton of f , and U be the C 1 neighborhood of f provided by Theorem D. Recall that by Lemma 7.1, the cardinality of skeleton varies in an upper semi-continuous way, we may choose a C 1 open and dense subset U • ⊂ U, such that the cardinality of skeleton is C 1 locally constant for diffeomorphisms in U • .
Take any C 1+ diffeomorphism g ∈ U • , then g has l ≤ k physical measures due to Theorem D. Furthermore, there is a subset of the continuation S(g) = {p 1 (g), · · · , p k (g)} which forms a skeleton of g. After reordering, we may assume {p 1 (g), · · · , p l (g)} to be a skeleton of g. Then by Lemma 7.1[(2)], there is a C 1 neighborhood V ⊂ U • of g, such that for any C 1 diffeomorphism h ∈ V, {p 1 (h), · · · , p l (h)} forms a skeleton of h.
Then by Lemma 4.1[(2)], for any C 1 diffeomorphism h ∈ V and any 1 ≤ i = j ≤ l, W u (Orb(p i (h)), h) ∩ F s (Orb(p j (h)), h) = ∅. Using Bonatti and Crovisier's connecting lemma ( [7]), we see that for any diffeomorphism h ′ ∈ V and any 1 ≤ i = j ≤ l,
Cl(W u (Orb(p i (h ′ )), h ′ )) ∩ Cl(W s (Orb(p j (h ′ )), h ′ )) = ∅,
since otherwise one can create a non-trivial intersection between W u (Orb(p i (·)), ·) and F s (Orb(p j (·)), ·).
By Proposition 4.2,
Cl(W u (Orb(p i (h ′ )), h ′ )) = H(p i (h ′ ), h ′ ) ⊂ Cl(W s (Orb(p j (h ′ )), h ′ )).
Thus, we have
(24) H(p i (h ′ ), h ′ ) ∩ H(p j (h ′ ), h ′ ) = ∅, and(25)Cl(W u (Orb(p i (h ′ ), h ′ ))) ∩ Cl(W u (Orb(p j (h ′ )), h ′ )) = ∅.
We need the following generic property proved by Morales and Pacifico [17]:
Proposition 8.1.
For every h that belongs to a C 1 residual subset of diffeomorphisms R 0 and every periodic point p of h, the set Cl(W u (Orb(p), h)) is Lyapunov stable.
Recall that the map G which maps a diffeomorphism h ∈ V to G(h) is upper semi-continuous by Proposition 5.17. Let R 1 ⊂ V be the residual subset of diffeomorphisms which are continuous points of the map G. For each 1 ≤ i ≤ l, also consider the map I i from V to compact subsets of M :
I i (h) = H(p i (h), h).
Because homoclinic classes vary lower semi-continuously with respect to diffeomorphisms (since they contain hyperbolic horseshoes), there is a residual subset of diffeomorphisms R 2 ⊂ V consists of the continuous points of I i for every 1 ≤ i ≤ l. Now let us take R = R 0 ∩ R 1 ∩ R 2 ⊂ V. We are going to show that the residual set R satisfies the conditions we need. Proposition 8.2. Every C 1 diffeomorphism h ∈ R has exactly l physical measures, each of which is supported on Cl(W u (Orb(p i (h)), h)) for some i = 1, · · · , k. Furthermore, the basin of each physical measure covers a full volume subset within a neighborhood of its support.
Proof. For any C 1+ diffeomorphism h ′ ∈ V, denote by µ h ′ ,1 , · · · , µ h ′ ,l the ergodic physical measures of h ′ . Then by Proposition 5.17, G(h ′ ) is the simplex generated by {µ h ′ ,1 , · · · , µ h ′ ,l }. For any h ∈ R, by the continuity of the map G at h, we see that G(h) = G(h) is a simplex of dimension m h ≤ l. In particular, the number of extreme elements of G(h) is at most l. Below we will show that it is in fact l.
Denote the extreme points of G(h) by µ h,1 , · · · , µ h,m h . Let h n be a sequence of C 1+ diffeomorphisms converging to h in C 1 topology. By continuity of G(·) and relabelling if necessary, we may assume that lim µ hn,i = µ h,i for i = 1, · · · , m h . Note that µ h,i is supported on W u (Orb(p i (h)), h). This is because by Theorem A, µ hn,i is supported on W u (Orb(p i (h n )), h n ) = H(p i (h n ), h n ), and h is a continuous point of the map Γ i (·), so we must have lim n H(p i (h n ), h n ) = H(p i (h), h).
Next, we claim that m h = l. Assume that this is not the case. Then we take m h < j ≤ l and take a weak- * limit µ h = lim n µ hn,j . Note that µ h ∈ G(h) is supported on W u (Orb(p j (h)), h) by the discussion above. Take any ergodic componentμ h or µ h , thenμ h ∈ G(h) by Lemma 5.18 and is still supported on Cl(W u (Orb(p j (h))), h). Thus by (24),μ h = µ h,i for every i = 1, · · · , m h . We have thus created a new extreme point of G(h), which is a contradiction.
To finish the proof, we have to show that each µ h,i is a physical measure. Since Cl(W u (Orb(p i (h)), h)) is Lyapunov stable, we can take U i ⊃ V i open neighborhoods for each Cl(W u (Orb(p i (h)), h)), such that {U i } i=1,··· ,l are disjoint and for each i and any n > 0, h n (V i ) ⊂ U i . By Proposition 2.12, there is a full volume subset Γ i ⊂ V i such that for any x ∈ Γ i , any limit µ of the sequence 1 n n−1 i=0 δ h i (x) belongs to G(h). Note that since x ∈ V i , we have h n (x) ∈ U i for all n ≥ 1. As a result, µ is supported on U i . On the other hand, µ h,i is the only ergodic measure in G(h) that is supported on U i . It follows that µ = µ h,i . This implies that Lebesgue almost every point of x ∈ V i belongs to the basin of µ h,i . The proof is complete.
We conclude the proof of Theorem E with the following lemma: Lemma 8.3. The basins of µ h,i for i = 1, · · · , l covers a full volume set.
Proof. Let Γ be the full volume subset given by Proposition 2.12. We are going to show that vol(Γ \ l i=1 B(µ h,i )) = 0. We prove by contradiction. Write Λ = Γ\ l i=1 B(µ h,i ) and suppose that vol(Λ) > 0. Let x ∈ Λ be a Lebesgue density point of Λ, which means that for any r > 0, we have vol(B r (x) ∩ Λ) > 0. Let µ be any limit point of the sequence 1 n n−1 i=0 δ h i (x) . Since µ ∈ G(h), µ can be written as a combination of µ h,i : µ = a 1 µ h,1 + · · · + a l µ h,l , where a 1 + · · · + a k = 1.
Suppose without loss of generality that a 1 > 0, then µ(V 1 ) > 0 where V 1 is the neighborhood of Cl(W u (Orb(p i (h)), h)) in the proof of the previous proposition. Thus there is n > 0 such that 1 n n−1 i=0 δ h i (x) (V 1 ) > 0. In particular, there is 0 ≤ m ≤ n − 1 such that h m (x) ∈ V 1 . Take ε > 0 sufficiently small, we have h m (B ε (x)) ⊂ V 1 . By Proposition 8.2, f m (B ε (x) ∩ Λ) intersects with the basin of µ h,1 on a positive volume set. Because the basin of a measure is invariant under iteration of h and h −1 , we have vol(Λ ∩ B(µ h,1 )) > 0, which contradicts with the choice of Λ.
Gibbs-Markov-Young structure
To study statistical properties of some non-uniformly hyperbolic systems, in [48] Young constructed Markov towers, which are Markov partitions with infinitely many symbols and certain recurrence property. In particular she uses tower to study statistical properties of these non-uniformly hyperbolic systems, including the existence of physical measures, exponential decay of correlations and the validity of the Central Limit Theorem for the physical measure. These structures have some properties which address to Gibbs states and they are nowadays commonly called as Gibbs-Markov-Young (GMY) structures.
Alves and Li in [4] obtained GMY structures for partially hyperbolic attractors and they managed to prove the exponential decay of correlations: if the lack of expansion of the system at time n in the center-unstable direction is exponential small, then the system has some GMY structure for physical measures with exponential decay of recurrence times. In this section we will show that their criterion is satisfied for any physical measures of any C 1+ diffeomorphisms with mostly expanding center.
As before, we assume f to be a C 1+ partially hyperbolic diffeomorphism with mostly expanding center, {p 1 , · · · , p k } be a skeleton of f and µ 1 , · · · , µ k are the corresponding physical measures of f in the sense of Theorem A. Recall that P = k i=1 π(p i ). By Corollary B, {f nP } n>0 also have mostly expanding center, and they share the same physical measures and skeletons. Therefore, to simply notation, we may assume that {p i } k i=1 are all fixed points and P = 1. Moreover, by Proposition 5.1, we may assume that there is b 0 > 0 such that for any µ ∈ G u (f ): (26) log
Df −1 | E cu (x) dµ(x) < −b 0 .
The notations below are used by Alves and Li [4] and clearly resembles our definition of hyperbolic times: We need the following two propositions from [4] which play the key role in the proof of decay of correlations and center limit theorem. Then some power f l has an physical measure µ and there is d > 0 such that
C µ (φ, ψ • f ln ) = O(e −dn τ )
for Holder continuous φ : M → R and ψ ∈ L ∞ (µ). Then some power f l has an physical measure µ; moreover, given any Hölder continuous function φ, the limit exists: where Λ ⊂ D is some subset with positive volume.
With these notations, we are ready to prove Theorem F and Corollary G. It suffices for us prove only for physical measures µ 1 : Take D = W u r (p 1 ). We will show in the end of this section that D satisfies the following property: Then we conclude the proof Theorem F and Corollary G.
It remains to show the proof of Lemma 9.5.
Proof. We need the following result: where S n (A) = n i=1 A(f i (x)). Fix B to be any foliation box for the unstable foliation F u such that D ⊂ B. By (26), for A = log Df −1 | E cu (x) , I A ⊂ (∞, −b 0 ). Applying the previous proposition with ε = b 0 /2, we obtain C > 0, δ > 0 such that for any plaque L of F u | B, (29) vol L ({x :
1 n n i=1 log Df −1 | E cu (f i (x)) ≥ −b 0 /2}) ≤ Ce −δn .
Note that
{x : E b0 > n} ⊂ m≥n {x : 1 n n i=1 log Df −1 | E cu (f i (x)) ≥ −b 0 /2}.
Thus by (29), there are C ′ and δ ′ such that for any unstable plaque L ⊂ B, vol L (E b0 > n) ≤ C ′ e −δ ′ n .
Because D is the local unstable manifold at p 1 , F u also induces a sub-foliation of D (note that dim D = dim E cu ). It is well known that F u is absolutely continuous, so is the sub-foliation of D. Then the previous inequality implies that there is C 0 > 0 such that (30) vol D (E b0 > n) ≤ C 0 e −δ ′ n .
Then Lemma 9.5 follows with τ = 1.
April 25, 2019. J.Y. is partially supported by NNSF 11871487, CNPq, FAPERJ, and PRONEX..
Definition 1.1. A partially hyperbolic diffeomorphism f : M → M is mostly expanding along the central direction if f has positive central Lyapunov exponents almost everywhere with respect to every Gibbs u-state for f .
Remark 1. 3 .
3From the proof of Theorem A, we have more detailed description on the basins of µ i : for every p i ∈ S, denote byO i = x∈W u (Orb(pi)) F s (x),then O i contains an open neighborhood of Orb(p i ). We are going to show that O i is open and dense in Cl(F s (Orb(p i ))) = Cl(B(µ i ))). Moreover, B(µ i ) is a full volume subset of O i , and O i ∩ O j = ∅ for 1 ≤ i = j ≤ k. This shows that the basin of different physical measures are topologically separated.
( 3 )
3For Lebesgue almost every point x in any disk inside some strong unstable leaf, every accumulation point of f j (x) is a Gibbs u-state. (4) Every physical measure of f is a Gibbs u-state; conversely, every ergodic
Lemma 4 . 3 .
43Let q be an index i s hyperbolic periodic point, then q ∈ O i if and only if q and p i are homoclinic related with each other. Moreover, S ′ = {q} S \ {p i } remains an index i s skeleton.
Lemma 4. 5 .
5Any pre-skeleton contains a subset which forms a skeleton.
Lemma 5. 5 ([ 3 ]
53Lemma 2.7). For any b > 0, there is r > 0 such that, given any C 1 disk D tangent to the center-unstable cone field, x ∈ D and n ≥ 1 a b/2-hyperbolic time for x, we have d f n−k (D) (f n−k (y), f n−k (x)) ≤ e −kb/2 d f n (D) (f n (x), f n (y)),
( 2 )
2the closure of F s (Orb(p i )) coincides with the closure of the basin of the measure µ i .Moreover, by (ii) of Proposition 4.2,Int(Cl(B(µ i ))) ∩ Int(Cl(B(µ j ))) = ∅ for 1 ≤ i = j ≤ k. The proof is finished. 6.4. Proof of Corollary B.We finish this section with the proof of Corollary B.Proof of Corollary B. Let f be C 1+ . For any n > 0, and ν an ergodic Gibbs u-state of f n , by Lemma 2.3, µ n i * (ν) is an invariant Gibbs u-state of f . It is easy to see that for ν typical point x, its center exponents with respect to f n are n times of the corresponding exponents respect to f . In particular, the center exponents of every Gibbs u-state of f n are positive. Thus f n has mostly expanding center as well.
Definition 9 . 1 .loglog
91Given b > 0, we say that f is b non-uniformly expanding (b-NUE) at a point x in the central-Df −1 | E cu (f j (x)) < −b.If f satisfies (b-NUE) at some point x, then the expansion time function at x(28) E b (x) = min{N ≥ 1 Df −1 | E cu (f i (x)) < −b/2 for any n ≥ N }is defined and finite. We call {x : E b (x) > n} the tail of b/2-hyperbolic times (at time n).
Proposition 9.2. [4] Assume for b > 0 that there is a local unstable disk D of f and constants 0 < τ ≤ 1, c > 0 such that vol D (E b > n) = O(e −cn τ ).
Proposition 9. 3 . [ 4 ]
34Assume for b > 0 that there is a local unstable disk D of f and constants 0 < τ ≤ 1, c > 0 such that vol D (E b > n) = O(e −cn τ ).
φ
• f jl − n φdµ) 2 dµ. Furthermore, if σ 2 > 0, then there is a rate function c(ε) > 0 such that lim n→∞ 1 n log µ(| n−1 j=0 φ • f jl − n φdµ |≥ ε) = −c(ε).
Lemma 9 . 5 .
95There are constants 0 < τ ≤ 1 and c > 0 such thatvol D (E b0 > n) = O(e −cn τ ).Then we may applying Proposition 9.2 and Proposition 9.3 on some physical measure µ for some power f l of f . Moreover, by Proposition 6.9, Lebesgue almost every point belongs to the basin of µ 1 , and thus by Remark 9.4, for any subset Λ ⊂ D with positive volume, f i (Λ) = µ 1 .
Proposition 9. 6 .
6[22][Proposition 3.1] Let B be any foliation box for the unstable foliation F u of f , A be any Hölder function and I A = { Adµ} µ∈Gibbs u (g) . Then ∀ε > 0, ∃δ > 0, C > 0 such that for any plaque L of F u | B,vol L ({x : d( 1 n S n (A)(x), I A ) ≥ ε}) ≤ Ce −δn ,
In comparison, if f has mostly contracting center, then every measure in Gibbs u (f ) is a physical measure, and finiteness follows easily. See[24] and[28] for the discussion there.
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| Let f be a holomorphic endomorphism of \(\mathbb {P}^k\) of degree d. For each quasi-attractor of f we construct a finite set of currents with attractive behaviors. To every such attracting current is associated an equilibrium measure which allows for a systematic ergodic theoretical approach in the study of quasi-attractors of \(\mathbb {P}^k\). As a consequence, we deduce that there exist at most countably many quasi-attractors, each one with topological entropy equal to a multiple of \(\log d\). We also show that the study of these analytic objects can initiate a bifurcation theory for attracting sets. | We consider piecewise twice differentiable maps T on [0,1] with indifferent fixed points giving rise to infinite invariant measures. Without assuming the existence of a Markov partition and only requiring that the first image of the fundamental partition is finite, we prove that the interval decomposes into a finite number of ergodic cycles with exact powers plus a dissipative part. T is shown to be exact on components containing indifferent fixed points. We also determine the order of the singularities of the invariant densities. | Transformations of aggregation operators preserving the class of copulas and quasi-copulas, respectively, are shown to be concave automorphisms of the unit interval. Attractors of copulas are discussed, special attention being paid to power transformations and the relationship between the corresponding attractors and the so-called maximum attractor (quasi-)copulas. The class of quasi-copulas stable under power transformations is characterized, and it is conjectured that it coincides with the class of all maximum attractor quasi-copulas. Also, examples of copulas not belonging to the maximum domain of attraction of any copula are provided. | Abstract Let τ be a mapping from an interval I into itself. For a large class of such maps there exist ergodic measures invariant under τ which are absolutely continuous (with respect to Lebesgue measure) and others which are continuous, but not absolutely continuous. The aim of this paper is to deal with the question: which of these ergodic measures best describes the ‘real’ dynamics of τ. To do this we shall model the dynamics of τ by a Markov chain, which reflects the perturbations inherent in experimental work or the truncation error in computations. When τ is expanding, it is the absolutely continuous invariant measure that acts as a global attractor. This explains the observed effect that the absolutely continuous invariant measure is the one that appears in experimental and numerical work. | We consider the dynamics of strongly dissipative H\'enon-like maps in the plane, around the first bifurcation parameter $a^*$ at which the uniform hyperbolicity is destroyed by the formation of homoclinic or heteroclinic tangencies inside the limit set. In [Takahasi H.: Commun. Math. Phys. {\bf 312} 37-85 (2012)], it was proved that $a^*$ is a full Lebesgue density point of the set of parameters for which Lebesgue almost every initial point diverges to infinity under forward iteration. For these parameters, we show that all Lyapunov exponents of all invariant ergodic Borel probability measures are uniformly bounded away from zero, uniformly over all the parameters. | We consider the invariant measure of a homogeneous continuous- time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geo- metric distribution. Second, we show that a countable linear combina- tion of geometric terms can be an invariant measure only if it consists of pairwise-coupled terms. As a consequence, we obtain a complete characterization of all countable linear combinations of geometric dis- tributions that may yield an invariant measure for a homogeneous continuous-time Markov process in the quarter-plane. | Central limit theorems and invariance principles for Lorenz attractors | 242 | For piecewise C 1 interval maps possibly containing critical points and discontinuities with negative Schwarzian derivative, under two summability conditions on the growth of the derivative and recur- rence along critical orbits, we prove (1) the nonexistence of wandering intervals, (2) the existence of absolutely continuous invariant measures, and (3) the bounded backward contraction property. The proofs are based on the method of proving the existence of abso- lutely continuous invariant measures of unimodal map, developed by Nowicki and van Strien. 1. Introduction and main results The concept of wandering intervals plays an important role in studying dynamical behavior of non-uniformly hyperbolic dynamical system. In the area of interval dynamics, most important results are related to the absence of wandering intervals. Our main aim in this paper is to obtain a condition on the orbits of the critical values to ensure the absence of wandering inter- vals for piecewise C 1 interval maps with critical points and discontinuities, and to give a sufficient condition to the nonexistence of wandering intervals for multimodal maps whose orders of critical points are different to the left and to the right. The motivation to show nonexistence of wandering intervals are well known. Firstly, it is relevant to the isomorphism problem of dynamical system. In the 1880s, Poincare proved that each orientation preserving homeomorphism of the circle without periodic points is semi-conjugate to an irrational rotation. Denjoy showed that for the C 2 diffeomorphism of the circle without periodic points such wandering interval cannot exist, and this semiconjugacy is indeed a conjugacy. Analogue of Denjoy's theory also holds for a C 3 unimodal map f with a non-flat critical point (whose orders are equal to the left and to the right) and negative Schwarzian derivative, | Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points | On semi-unimodal maps of the plane and the structure of their sets of non-wandering points | Sharkovskii proved that, for continuous maps on intervals, the existence of 3-cycle implies the existence of all others. Li and Yorke proved that 3-cycle implies chaos. To establish a domain of uncountable cycles in the logistic map and to understand chaos in it, the fixed points of 3-cycle are obtained analytically by solving a sextic equation. At one parametric value, a fixed-point spectrum, resulted from the Sharkovskii limit, helps to realize chaos in the sense of Li and Yorke. | A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface. PACS numbers: 02.70.Bf, 05.45.Ac, 05.45.DfThe quest for simple deterministic models that exhibit complex and unpredictable temporal evolution 1-4 has been the subject of intense interest. Most remarkable examples are provided by systems of nonlinear ordinary differential equations leading to chaotic behavior, as the Lorenz 5 or the Rössler 6 systems, and by time-discrete difference equations, as the logistic map 1,7 or the Bernoulli shift 3 . All these systems involve dynamical variables taking on numerical values that can be expanded in terms of a (generally infinite) convergent series of rational numbers in a radix (base) p ∈ N (p > 1). The latter are each formed by an integer power of the radix p multiplied by an integer in the interval [0, p − 1] called a digit. In this work, by directly addressing and manipulating digits (by means of a digit function that we have recently introduced 8-11 ) we uncover a digit replacement operator that allows a generic map for nonlinear dynamical systems to be formulated. Our model is exactly solvable in wide regions of parameter space and encompasses a wide variety of complex nonlinear dynamical behavior from a new perspective. | Over-rotation intervals of bimodal interval maps | We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition. | Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete dynamical systems generated by the iterations of that type of maps. When there is a Markov matrix, the spectral radius of this matrix is the inverse of the least root of the kneading determinant. | In many dynamical systems, countably infinitely many invariant tori co-exist. The occurrence of quasiperiodicity on any one of these tori is sometimes sufficient to establish strong global properties, like dense trajectories and periodic points. In this paper, we establish sufficient conditions for a countably infinite collection of parameterized circle diffeomorphisms to have quasiperiodic behavior on at least one of the circles, for a full Lebesgue measure set of the parameter values. As an application, we study parameterized families of skew-product maps on the torus and prove sufficient conditions for the existence of at least on quasiperiodic circle for Lebesgue-almost every parameter value. |
243 | Food52 Mighty Salads by the Editors of Food52 et. ... | Made an awesome salad.
Pic -
ingredients
- fried chicken (with olive oil)
- fried mushroom (with olive oil)
- lettuce
- crumbled bleu cheese
- shredded parmesan cheese
- 1/2 avacado
- slice of pickle
- caesar salad dressing | I sent them this email shortly after the visit.
Hey Guys! So, I went to your shop "simply salad" today it tasted great! but something bothered me. There are a lot of CHOICES! To me, there is nothing simple about it. To me, choices are complicated, so I did a little math to find out How many salads you guys actually offer.
If you feel so inclined, you can do the math yourself using these basic rules:
(I had to place limits on a few things that you had on your menu, for practicality sake)
* There are 6 types of lettuce that can be mixed and matched, but not repeated. and order does not matter.
* I have 32 topping choices in a salad and I can choose up to 5 (excluding extras) toppings out of those 32. They Can be repeated. Order does not matter.
* Then we have 12 premium toppings you can choose to add, which can be repeated. and order does not matter. Conditionally you could choose up to 2 if you want.
* There are 9 meats you can only choose 2
* There are 4 seafood items and you can choose 2
* If you choose a seafood and a meat, (Conditionally) you can only choose 1 each.
* There are 26 Dressings to choose from and you can mix and match 2 at a time but they can't be repeated and obviously the order doesn't matter.
How many Salads can I make?
(you can understand my inkling there is nothing simple about "simply salad").
Here is the answer:
**69,991,381,684,224 possible salads.**
That's **70 Trillion** possibilities.
If You had a person try all the salads...1 per minute without sleeping it would take them
**133.2 million years.**
In a sense, you are correct. You guys simply make "salads"
but with this many possibilities...It seems somewhat...complicated.
Anyway. I hope you enjoy this thought.
It really means nothing. But It was a fun math problem. :)
Thanks for the great salad! | Have been slowly changing my really horrible eating habits and making sure its sustainable. Ive never been the biggest fan of veggies :( But I've been having salads more frequently now but Ive always enjoys Caeser salads the most - love leafy veggies and the 'heavier' kind of dressing.
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I realise its not sustainable to stick to one type of salad if i want to keep doing this in the long run. What other types of salads would you recommend? Am open to anything, just trying to be healthy | What food group does salad come under? | I tried to make a salad today, with salad dressing and all. It turned out pretty meh. This not the first time I screw up a salad either. I made a roughly chopped cucumber Chinese side dish and Japanese Sunomono before, both very average. And I make the occasional sort-of-good coleslaw from time time. My salads are bad and I should feel bad, my friends.
I'm not sure what the problem is. Take today's salad for example, it had all the goods: chopped tomato, cucumber, finely chopped red onion, grated carrot and some small green apple cubes. And for the dressing: moderate amounts of vegetable oil, vinegar, lemon, mustard, and small pieces of pickled olive. All mixed in a small jar that has less than a teaspoon of mayo left. I added the dressing carefully without overdoing it. See? It *should* be good but it just ain't.
I love salads and I want to do them justice. They seem simple enough but when I make them, the end result is never as satisfying as I imagine it to be. I mean I got apple pie right from the first try for god's sake, you'd think I should be able to put some raw vegetables together and make them taste good. | Yes, my life is now a sad state of salads and power walks! 😿 I’m looking for a good hearty salad that doesn’t taste deep fried ( sorry Doc Greens! ). Bonus points if it’s Organic or Farm to Table! Thanks Reddit Fam!! | I mean salad as we know it today. When is the first time that various grown/harvested veggies with nuts, fruits, etc, was piled together and coated with a dressing?
Alternate question: What's the earlier place and time you could time-travel to with a salad from a salad bar and have people know immediately what it is? | 4.5 stars
Salads are so wonderful when someone else makes them. It should be such an easy food to make with everything available in the grocery stores and farmers markets. I belong to a CSA from late May through October, and every fresh vegetable and fruit is mine to explore.
Amy Pennington's new book gave me so many good suggestions to liven my salads. The photographs alone made my mouth water. I am such a fan of tomatoes, and the photograph of mouth watering tomatoes, red, orange and varying hues was the best. Amy gives us her ideas and philosophy of salads, they are not just side dishes anymore. Salads can now be the main meal. In fact there are salads for breakfasts in her book. The one salad that interested me the most was pomegranate seeds and sliced onions. That is one salad for me!
In this book there are 75 salads. The photographs help make each salad look so delicious. There are grain bowl salads, fast and fresh salads, winter salads, noodle salads, fruit salads, cooling salads, and salads for a crowds. Salad dressings are also featured, and there is nothing better than home made salad dressing.
Recommended. prisrob 04-09-17 | 243 | Food52 Mighty Salads by the Editors of Food52 et. al. is a free NetGalley ebook that I read in early April.
From the website/book/blog/podcast/merchantile conglomerate that is Food52 comes a contributor-compiled salad cookbook that categorizes them by leafy, non-leafy, grain/legume, pasta, fish & seafood, and meat-based salads. With the mixture of flavors, origins, non-cooked & cooked textures, and choices of homemade dressing, there's changes in the styles of photographs (a recipe in progress at home or ready for placement on a bistro table). | what kind of meat is in a chef salad | Delicious Salads For Everyone | What food group does the salad goes in? | how many saladworks locations are there in the us | Looking for new and exciting salad recipes, give me your favorites! | Word salad is a `` confused or unintelligible mixture of seemingly random words and phrases '' , most often used to describe a symptom of a neurological or mental disorder . | 50 salad dressing recipes to enhance your awesome...or salad. | [Request] Salad Recipe for Doc Green's Tomahawk Salad |
244 | I need a dress for a Wedding size 11 anyone want to swap or be nice enough to let me borrow a dress? | Does anyone know of anywhere to donate a wedding dress or anyone that specifically needs a wedding dress? I would love to donate to a great organization or an individual in need. TIA | Where can you get a nice plus size cocktail dress? | I'm looking for a female dress form to borrow for this week (I will pay you to borrow it)for a project..the ones on craigslist are all sold.Preferably a size 10, but anything will do. You never know what people at RIT may have laying around, so I figured I'd ask! | I want to keep things less than $150 for my bridesmaids. Any sites you guys have liked that create a good quality dress that’s still budget friendly ? I figure they will still have to get it fitted. I likely will go with an online shop bc I bridesmaids live in a different state than me.
Bonus if you know of a place with lilac colors!!
Thanks y’all! | How much do wedding dresses cost? | I am hoping to (FINALLY!!) buy my dress next Thursday when the store it's from is having a 20% off sale (woop woop!!), but I've read reviews that their alteration services are not the best.
I was hoping someone could recommend a reliable place to get my dress altered (if need be) in Philly or the surrounding area (I can easily get over the Tacony, Walt Whit, Betsy Ross, or Ben Franklin into Jersey, I live near Bucks County).
Also, the size 6 currently fits like a glove. I would love to lose like 15lbs before the wedding - is this too much weight, or reasonable for alterations?
Thanks in advance for the help!! | I need two matching flower girl dresses ASAP that don't cost a lot (under $50 each), I've shopped at places like Marshalls, JC Penney, etc., but if I find something, there is usually only one dress in the size I need, not two. | The average a bride spends between $75 and $250 on alterations. If you know the wedding dress alterations you will need, feel free to call around and get some telephone bids. You do not necessarily have to use the alterations service from your bridal shop, but do not cut corners that you might regret. | 244 | Hey Girls I need a dress for a wedding, I hate buying dresses because I only wear them once and then they just sit in my closet. I am willing to trade or someone could be nice enough to let me borrow a dress I am an honest and trustworthy.
Thanks,
P.S. I do reddit gift so you can see I don't flake. | I want to get married with a red wedding dress, know any place where I could find it??? | I need help finding a wesite where i can browse AND PURCHASE bridesmaid dresses. Anybody know of any? | Searching for a wedding dress | SoCal AA Brides! Borrow my dress? Short/Plus Sized | Hey I just met you and this is crazy, but I don't have any girlfriends in Raleigh yet and need help picking a wedding dress, so do you any of you girls wanna come with me, maybe? | Help me find a party dress for my wedding? | Buying a Wedding Dress Online | My dress didn’t exist at my store until I asked! Some advice from a picky bride to you! |
245 | Moroccan Dreams: Oriental Myth, Colonial Legacy | The history of Moroccan migration to Europe is one of unexpected developments and unplanned effects. This is true of colonial migration, labor migration, and most lately, undocumented migration. Adopting a postcolonial historical approach, this chapter reviews the various features of Moroccan migration to Europe and tentatively draws a few parallels from these experiences by covering, in particular, the cases of migration to France, Spain, Italy, the Netherlands, Belgium, Germany, and the United Kingdom. | Navigating Modernity: Lessons in Government and Statecraft in Precolonial Morocco | As a person who lives under a rock, I have absolutely no idea on what is going on around the world, let alone Morocco.
I've been hearing rumours from random people about a group of Islamic terrorists threatening to bomb Morocco Mall and Twin Center. I also heard another threat about attacking the north, meaning Tangier and suburbs.
Can anyone tell me what the fuck is going on? | Amazingly detailed view inside the minds of different personalities within very opposite religeous and cultural people... an exciting adventure of these turbulent times in the middle east. You feel you are in the middle of it all. | Set in southwestern Libya, in what appears to be sometime in the 1960s, this quasi-mythical tale concerns Asouf, a bedouin hermit goatherd. Through leaps of time and flashbacks, we learn of his upbringing by a father who believed men to be corrupt and evil, and thus took his family to the edges of civilization to live. Unfortunately, Asouf's isolation leaves him ill-equipped when the wicked hunter Cain and his sidekick (both fellow Libyans) show up and demand to be guided to the lair of the moufflon (a wild sheep said to be extinct). The novel depicts a kind of backwoods type of Islam, in which God resides everywhere, spirits are to be placated, and charms are bartered from African magicians to protect oneself. It's an interesting view of a part of the Arab world not commonly seen, however the dive into magical realism gets far too magical for my own tastes. There is a great deal of symbolism and Biblical allusion that goes right over my head (not having read the Bible), but the central metaphor of Cain destroying his own land (with the assistance of an American military man) is clear enough, as is the Christ imagery at the end, with its apparent message of redemption. Ultimately, neither the style nor story ever really grabbed me, but perhaps those with a firmer sense of the spiritual may derive great sustenance from this tale. | Hey there!
I'm in need for help. For a tabletop game, I'm creating a surrealistic setting in the 1950's in southern Arabia, which largely plays in the Muscat Sultanate. For this story, I'm looking for some folklore, as the story heavily ties into people finding out that many of the things they thought were just mythology, are actually true.
Do you perhaps have good local myths and stuff which I should dive into? I would love to base it on actual real life lore. If you have sources for me to read in to, that would also be greatly appreciated!
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Thanks in advance :) | Hi !
I've some korean friends who really want to know more about modern morocco, but unlike french documentary, it's really hard to find any long one about Morocco in english.
Do you have anything? A television documentary about a road trip in morocco, traveling through Marrakech, Fez, the desert, amazighs villages, modern streets of Casablanca and so on ? Also showing the rich side of morocco and not only the poor one if possible.
Thank you! | What is a traditional story for culture and beliefs? | 245 | Morocco has long been a mythic land, firmly rooted in the European colonial imagination. For more than a century it has been appropriated by travellers, explorers, writers and artists. It is just these images and imaginings that are now being reconstructed for nostalgic consumption. In Moroccan Dreams, Claudio Minca examines this aestheticised re-enactment of the colonial, exploring the ways in which Moroccans themselves have become complicit in the re-writing of their homes and lives. Richly illustrated, the book provides a fascinating journey that will engage and delight all those enamoured of Morocco and its extraordinary geographies. | This article focuses on furnishing practices in the domestic space of the homes of white Flemish and Dutch Muslim female converts to Islam who made hijra (Islamic migration) to Morocco. Fed up with European Islamophobia and longing for a place that supports and strengthens their faith, they decided to emigrate to a Muslim country. However, remarkably, once settled in Morocco, many experience discontent with regard to a perceived "lack of true Islam" in the country. To gain insight into the positions and experiences of these women, I look at how they create a sense of belonging through furnishing practices in the domestic space of their new homes. I am interested in how various senses of belonging are expressed and come together in relation to their construction of religious belonging and place, and are renegotiated through domestic decoration practices. Building on literature on home, transnational migration, conversion, and material religion, I demonstrate that mechanisms of distinction and notions of religious (im)perfection intersect in the organization of the domestic space. Based on ethnographic accounts, I argue that my interlocutors bring a "culturalized" West-European Islam to Morocco, with tastes and sensibilities that jostle uneasily against local Moroccan religious practices but also allows them to repair some of the privileges they lost upon their conversion in their homeland. Lastly, this article shows that it is through the engagement with mundane material forms, but also with absence and empty spaces, that Islam becomes present in their domestic spaces, enhancing the cultivation of their ethical selves. | MUST HAVE book for anyone who love Morocco, design, pattern, color, magic or all of the above! | The sersera of the guembri: anthropological approach to the device in the context of Gnawa diasporas in Brussels and Morocco | Interesting plot and really liked the 'feel' of the Morocco - for women as ... | the essence of Moroccan cooking | Fiction Book Set in Morocco | Rock art conservation in Morocco | Languages, Identities and Cultures between Spain and Morocco: Questions in Modern Hispanoarabistics |
246 | Our dog didn't like it at first | My dogs didn't really care for the taste of it. | I came back and bought another as one of my dogs likes it so much she was sad when one of the other dogs had it. | Why did your dog eat his own tail? | Why does your dog put her butt in other dogs faces? | My dog was so excited to get a new toy but he chewed thru it the first night we had it. | Why did dog throw up? | Actually, its my dogs that don't like this.
I thought it was a good deal......
I have two German Shepherd dogs. The blue blooded male sniffed it and did not even put this in its mouth. The garbage disposal female actually picked it up and chewed on it; and for the every first time in all the years since we adopted her, she dropped it and gave us that "WTF is this ? Don't you love us anymore ?" look.
That hurts.
Your doggie may like it. | Dog goes nuts over this!! Sometimes I cant tell if he hates it or loves it when he plays with it | 246 | Wow, this takes a ton of hair off my dog, which thankfully won't end up in my carpets! We weren't expecting our dog to shed so much, so this cuts down on vacuuming a lot. Our dog didn't like it at first, but is getting used to it after a week or so. It's very sturdy and well made. Should last a long time. | I have 2 large dogs that shed and these units act like vacuums. After 3 months they were so caked ... | ... have cats and dogs and this electric vacuum is fantastic for picking up the hair and also the cat ... | This vacuum is absolutely amazing when it comes to pet hair | I definitely would not recommend it if you are vacuuming pet hair as it ... | Looking for dog groomer that allows you to stay with the dog | I have a german shepherd so there's dog hair EVERYWHERE and this handles it like a champ | It takes pet hair off furniture easily. | It sheds a little but its super cute and super fluffy |
247 | Occlusion of the left main coronary artery and collateral circulation via the conus branch. | There are few reports of electrocardiogram (ECG) changes of conus branch occlusion. A conus branch artery supply to the outflow tract of right ventricle. A conus branch artery is considered as the substrate of Brugada syndrome. We report a case of conus branch occlusion during angioplasty with ST segment elevation in V 1-3 like Brugada syndrome ECG. We need to bear in mind that this ECG change may cause lethal arrhythmia. | A case of open-ended-pattern coronary circulation that protected the left ventricle when one large vessel was occluded is presented. | To investigate the bidirectional functional adequacy of collateral perfusion, we performed percutaneous transluminal coronary angioplasty (PTCA) on highly stenosed or occluded coronary arteries visualized by the collateral circulation,which were fed by the contralateral coronary artery with severe stenosis. After successful PTCA in all three patients, the contralateral artery was reversely filled by good collateral circulation originating from the dilated coronary artery. These findings indicated that dilation of the receiving coronary artery reversed the pressure gradient across the collateral network, establishing collateral flow in the opposite direction. It was concluded that human collateral channels serve as a bidirectionally functional conduit. | An anteriographic study has been made of the coronary collateral circulation of 100 consecutive patients who had complete occlusion of at least one coronary artery on coronary arteriography but who had contracting myocardium in the area once supplied by the occluded artery. Twenty-four additional patients were included who had coronary occlusion with a ventricular aneurysm. | Circumflex branch of left coronary artery The "LCX", or left circumflex artery (or circumflex artery, or circumflex branch of the left coronary artery) is an artery of the heart. It follows the left part of the coronary sulcus, running first to the left and then to the right, reaching nearly as far as the posterior longitudinal sulcus. There have been multiple anomalies described, for example the left circumflex having an aberrant course from the right coronary artery. The circumflex artery curves to the left around the heart within the coronary sulcus, giving rise to one or more left marginal arteries | Vertebral artery loops in surgical perspective | Vertebral artery loops in surgical perspective | Contrast Agent Bolus Dispersion in a Realistic Coronary Artery Geometry: Influence of Outlet Boundary Conditions | 247 | We report the case of a 71-year-old-man, a smoker, admitted for unstable angina. Subsequent investigation revealed complete proximal occlusion of the left main coronary with an unusual collateral circulation. The left coronary artery was filled by a large conus branch originating from the right sinus of Valsalva. This case shows the importance of looking for atypical collateral circulation in patients with chronic occlusion of the left main coronary artery and normal left ventricular function. | An angiographic and clinical study of coronary collateral circulation | Contralateral External Carotid Artery as Collateral to Internal Carotid Artery in a Patient with Common Carotid Artery Occlusion | Anomalous origin of the left anterior descending and circumflex coronary arteries by two separate ostia from the right sinus of Valsalva. | Anomalous origin of the left main coronary artery from the main pulmonary artery in an elderly patient. | A case of stent thrombosis presenting as acute myocardial infarction related to right coronary artery originating from the left coronary system | [The collateral circulation for occlusion of the three unpaired abdominal arteries (author's transl)]. | Left Internal Mammary-to-Left Circumflex Coronary Artery Collateral Pathway in a Patient With Occluded Left Circumflex Artery | Coronary-to-pulmonary artery collaterals in pulmonary atresia |
248 | which country has won the most global management challenges | Looking at the UN's My World survey it made me curious about what challenges other countries are facing right now and I want to learn more about it! | G-Zero world that want their leader's focus to be domestic community, not the international one. Some of these developed countries include: the United States, Britain, Germany, France, and Japan. As developed countries start to focus on their domestic issues, the lack of global leadership increases which in turn increases the transnational problems. As global leadership decreases, clashes between countries are also increasing such as America and China having different views on “statedriven and free-market varieties of capitalism”. There are also issues arising in East Asia between nations such as China and Japan in the East China Sea. The U.S. has to also | What are the effects of globalisation on human resourse management? | Global competition is rapidly becoming the norm in which nearly all business organizations must compete in one fashion or another. The complexity and value of strategic global human resource management (SGHRM) will continue to compound in significance as globalization becomes the predominant form of business. Both practitioners and researchers grapple with understanding the global phenomena and the resulting impact on the entire human resource management system. The economic centre of gravity is shifting from the developed markets to the developing markets. This is a huge opportunity for the Asian economies and India in particular. But underlying the growth in economic capital has to be an equally strong foundation of building the intellectual and human capital of the nation. This means investing in our people. We need to impart ski ll s, training and education at all levels to match the needs of a changing India. | in India with six offices in India, besides having a few representatives working overseas in the US. Founded by Ranjini Manian, Indian, and Joanne Huskey, American, in 1995. Global Adjustments Global Adjustments Services Private Limited is an expatriate services company that provides support for relocation and cross-cultural services, helping families move from and to India. Global Adjustments was started by Ranjini Manian in 1995. The idea was a suggestion of her friend, a diplomat's wife, Joanne Grady Huskey. Initially, the company set about helping expatriates move to India. The company started off with a few individual clients, and subsequently signed | The US-European financial meltdown and resultant global recession of 2008–2009 have many implications for global trade as worldwide production and flows of goods have slumped in both developed and developing countries. When confronted by such conditions, it is relatively easy to forget that trade promotion has been essential to the successful advancement of many developing economies in recent decades. As protectionist pressures mount and people begin losing faith in globalization (Stevenson 2009), policymakers should remember those benchmarking cases and sound theories that have supported the opening of global trade thus far. | Critical success factors when going global : the basic challenge | Management has always been a challenge. But managing in the modern world has become ever more difficult and time-consuming. Not only are people harder to manage, we seem to have created organizations in which many of our managers are now even less well equipped for the task. | 248 | Global Management Challenge Italy, Kazakhstan, Latvia, Macau SAR (China), Mexico, Morocco, People's Republic of China, Poland, Portugal, Romania, Russia, Singapore, Slovakia, Spain, Turkey, Ukraine, United Kingdom and Venezuela. For the 2010-2011 session, two new African countries are entering the contest: Ivory Coast, Benin, in partnership with Educarriere.net, a leading website in Ivory Coast which have been famous because it used to publish the result of many exams. Each country organizes its own National competition, the model producing all material in the language of that country. The winners of the National competition meet to contest the International Semi-Finals and, if successful, go on to | when does the country showdown national take place | which country is the host of the 'ttokyo international conference on africa development | in which sections of the african development trophy is the competition played | what does the millennium challenge corporation aim to promote in recipient countries | Abstract The African Leadership Conference on Space Science and Technology (known as “the ALC”) is a regional conference to promote intra-African cooperation in the uses of space science and technology to support Africa’s development. The first such conference was held in 2005 in Abuja, Nigeria, followed by South Africa (2007), Algeria (2009) and Kenya (2011). The ALC has come to be regarded as a representative African forum in the global space community. This paper provides an overview of the structure and activities of the ALC and presents the highlights and outcomes of the first four conferences and their contribution to shaping the development of the African space arena. The paper concludes with an analysis of the challenges facing the ALC and some proposed measures to enhance its effectiveness. | how many students have participated in the global challenge | Which African Countries Are In The World Cup Finals 2010? | The ECOWAS Platform and the Persisting Challenges of Integrating the West African Region: A Discourse |
249 | I hope these hold up better than the last pair | Bought these about a year ago and are still holding strong. Very good quality and price was worth it. My son loves them and wears them all the time. | This is my 5th pair in the last 15 years, and they are not as well-made as any previous pair. I like them a lot (obviously), but I can tell that they will not last as long as the others. | Holds up well. My husband wears these as his every day shoes. He has had 3 pairs in the last 6 years. | Have had these for awhile now and they're holding up great. Very durable and do their job. Love the various sizes too | So far so good. Hopefully these will hold up like the traditional pairs i used to purchase at jcpenney. My husband is very happy with them so far as they are comfortable and long, | I have been trying for about a year to get a decent pair, and these are very good if not excellent. | Almost every day use for the past year and a half and they're still going strong will be buying another pair here soon | Had a previous pair that finally wore out. This one is as good as the previous. | 249 | I had a pair that I bought from a store years ago. They lasted about 4 or 5 years. I finally decided that it was too me to buy some new ones (exact same style and brand) and they fell apart in 3 months. I just bought yet another pair... I hope these hold up better than the last pair. The glue comes apart. | I've had several other pairs of these that I loved and still have a pair that is several years ... | First pair I had lasted a year. | the last pair bought in 2007 are still in fairly good shape just wore down on the bottoms without to ... | These are awesome! The last pair lasted 12 years (until I ... | I purchased my first pair over five years ago and ... | Very disappointed since my last pair lasted about 3 years | My last pair lasted me 14 years. The comfort ... | I bought a pair and one went bad within 6 weeks |
250 | Purification and cloning of aggrecanase-1 | The agglutinating effects of Concanavalin A (Con A) on protoplasts isolated from cell suspensions of Daucus carota were studied. Con A was shown to agglutinate the plant protoplasts in a manner similar to the way some animal cells are agglutinated. The agglutination process is dependent on the Concanavalin A concentration, protoplast density, treatment time, the temperature, and the membrane condition, α-D-Methylgluco-pyranosid completely inhibited Con A induced agglutination. The results are discussed in relation to membrane structure and morphology. | β-1,3-glucanase ( BG2 )gene was introduced into Populus, G1, mediated by Agrobacterium tumefaciens. The young plants of Populus were used as the material and the subculture system has been established. The traditional transformation method by Agrobacterium tumefaciens was improved and many transgenic plants harbored with BG2 gene have been obtained. PCR and PCR-Southern analysis showed that BG2 gene was integrated into the genome of populus. | Comparison of expression of the endo-β-1,3-1,4-glucanase gene from Bacillus subtilis in Saccharomyces cerevisiae from the CYC1 and ADH1 promoters | Abstract Aspergillus niger (ATCC 6275, A-98) was mutated by gamma rays and N -methyl- N ′-nitro- N -nitrosoguanidine. Selected mutants were tested in fermentation on apple distillery waste substrates to get improved hydrolytic activities and technological properties, e.g. improved filtration, reduced values for chemical oxygen demand and higher raw protein content in the dry filter cake. A scheme of the combined mutagenic treatment is given. A mutant selected after the fourth series of mutagenic treatment was compared with the parent strain and found to have four times higher endo-1,4-β- d -glucanase (1,4(1,3;1,4)-β- d -glucan 4-glucanohydrolase, EC 3.2.1.4) and exo-1,4-β- d -glucanase (1,4-β- d -glucan cellobiohydrolase, EC 3.2.1.91) activities, ten times higher aryl-β- d -glucosidase activity and essentially higher pectolytic and amylolytic activities than the parent strain. | The gene egl3 of the filamentous fungus Penicillium canescens endo-1,4-β-glucanase, belonging to family 12 glycosyl hydrolases, was cloned and sequenced. The gene was expressed in P. canescens under the control of the strong promoter of gene bgaS, coding for β-galactosidase of this fungus, and efficient endoglucanase producer strains were obtained. The recombinant protein was isolated from the culture liquid of the producer strain EGL3-13 and purified to homogeneity; its specific activity was 31.7 IU; molecular weight, 26 kDa; and pH and temperature optimums, 3.2 and 54°C, respectively. The K m and V m values for CMC hydrolysis were determined; they amounted to 17.1 g/l and 0.31 μM/(mg s), respectively. | Cloning and expression of a thermostable β-1,3-1,4-glucanase from Bacillus amyloliquefaciens ATCC 23350 | Isozyme polymorphism of endo-β-1,4-glucanase inAspergillus nidulans | Agrobacterium tumefaciens is capable of gene transfer to both plant and non-plant organisms. Indeed, upon infection of eukaryotic cells, Agrobacterium tumefaciens transfers a piece of its tumor inducing (Ti)-plasmid, called T-DNA, to the host cell nucleus, which subsequently integrates into the host genome. The VirD2 virulence protein which has relaxase endonuclease activities covalently binds to the 5'end of T-DNA and facilitates its transfer, nuclear localization and integration into the host genome in collaboration with the interacting proteins of the host cell. The VirD2 is essential for Agrobacterium–mediated transformation of both plants and non-plant cells. Here, using yeast Green Flourescent Protein (yGFP) technology, we studied the subcellular localization of VirD2, expressed in the model eukaryote Saccharomyces cerevisiae. Fluorescence microscopy showed that an N-terminal yGFP fusion of VirD2 (i.e. 5' GFP-VirD2 3'), was located in the nucleus of yeast. With C-terminal fusions of VirD2 to yGFP (i.e. 5' VirD2-GFP 3'), no particular subcellular concentration of fluorescence was seen. This further confirms nuclear localization of VirD2 in eukaryotic cells and more importantly highlights the role of Nuclear Localization Signal sequences (NLS) of the C-terminal of VirD2 in this phenomenon. | 250 | Purification and cloning of aggrecanase-1: a member of the ADAMTS family of proteins. | Age-related changes in aggrecan glycosylation affect cleavage by aggrecanase. | Construction of a yeast vector directing the synthesis and release of barley (1→3, 1→4)-β-glucanase | Cloning of the Penicillium canescens endo-1,4-β-glucanase gene egl3 and the characterization of the recombinant enzyme | where does 2 ag come from in the digestive system | Bacterial 1,3-1,4-β-glucanases: structure, function and protein engineering | Ethylene regulation of β-1,3-glucanase in tobacco | what is the name for the glycoproteins that cause rbcs to agg | Developmentally related changes in the production and expression of endo-beta-1,4-glucanases in Aspergillus nidulans. |
251 | Pike Service - LSC Needle O-Ring | Recently I had a Seymour Duncan P-Rail and Triple Shot mounting ring for coil switching installed in my guitar, but the thing is that I forgot to ask my tech which way he installed the mounting ring, so I have no idea what the controls do for each coil- I can discern some of it by ear, but I'm a bit unsure. Is there a surefire way to find out what coil is currently engaged on a humbucker? | Items came they were what they said my only problem was in somebody the gauge kits the tappers weren't both the same size and neither were the o rings | Arrived on time but unfortunately does not work for carbine 68. At all wrong type and number of O-rings | The directions that came with it explained everything except the two o rings that came in a plastic baggie. Did not specify at all where they went I'm very disappointed with the directions. Can anyone tell me where these belong? | An optimization design method for O ring expansion joint was introduced. The optimum design of single wave O ring expansion joint performed by the method was capable of reducing the consumption of material as well as manufacturing costs while its mechanical strength and fatigue life were guaranteed to be satisficd. | Last week I purchased a Voigtländer Bessa R and a Helios 44-2 58mm F2 in M39/LTM (haven’t measured the thread pitch) and tried it out. But even tho it mounts without problems onto the camera, the focusing doesn’t work. Turns out the Helios last element is too small of a diameter to engage the focusing knob inside the camera. Now my question is can i just print or turn a cylinder which goes around the last element, to up the diameter and engage the knob? is the amount the element moves back and forth the same compared with proper lenses made for the Bessa R? Or do i need to get a new lens? | After an initial issue, I contacted the seller and received excellent service. Seller corrected and the o-rings are perfect for my 2013 SeaDoo GTI SE 130's. | Some people like to carry one swap out weapon, others have three of every equipment. Where do you fall?
View Poll | 251 | Was servicing my Pike and the last step was bleeding the damper. While doing so I removed the o-ring on the lsc needle, went to install new o-ring from kit and no luck as the o-ring is larger in diameter and is loose in the groove in the needle.
Everything points to me having the correct kit. Just that maybe this o-ring isnt in the kit or wasnt included. Anybody know for certain on this?
Picture for reference:
| The O-rings had bad flashing and had to be replaced | I contacted the seller and received excellent service. Seller corrected and the o-rings are perfect ... | Was missing a few important parts like the distributor cap o-ring and the gromet for the ... | I replaced the o-rings with slightly oversized ones from a harbor freight o-ring kit and it works fine. | Zero Customer Service! - Can't get replacement o-rings | Fit new o-ring in SVD. Now Tanks won't fit. | O-Rings not Hose Washers | Replacement o-ring for Atlantis drip tip? |
252 | what are thermionic valves in the heath robinson | What is the difference between usual valves and reed valves | What is the torque for f150 valve cover bolts? | How do the valves on brass instruments work? | Beware!!!! You must be careful to not bend you valves. The tool is very cool but if you are not careful you can bend valves. I bent an intake and did not catch it till I had the head back on the engine. The tools is great for taking valves off in that you need only to provide a small force. Putting the valves on requires a great deal of force. I had rages placed to keep the vales in place while I struck the valve with a hammer. I can only guess that the rags moved and the valve struck the table I was using causing it to bent. | sharp. For example, a BB tuba becomes (in effect) an A tuba when the first valve is depressed. The third valve is long enough to lower the pitch of a BB tuba by three semitones, but it is not long enough to lower the pitch of an A tuba by three semitones. Thus, the first and third valves used in combination lower the pitch by something "just short" of five semitones, and the first three valves used in combination are nearly a quarter tone sharp. The fourth valve is used in place of combinations of the first and third valves, | water from diesel fuel water separators on some trucks. The large MAN six-cylinder diesel engines used on German U-boats had petcocks that enabled the engineers to verify combustion in each cylinder. Opening one with the engine running would result in a long blue-white flame if the cylinder was firing correctly. The procedure is described in the novel Das Boot and shown in the film version. Petcock A petcock is a small shut-off valve used to control the flow of liquid or gas. Historically, petcocks were threaded valves controlled by a butterfly handle; modern petcocks are typically ball valves. Compared to | The utility model discloses an it is two towards sodium chamber valve, including valve head and valve stem, the valve stem is inside to be equipped with cylindrical pole portion towards sodium chamber along its axial, be equipped with in the valve head and directly be greater than towards the sodium intracavity towards sodium chamber and head towards the head of the coaxial intercommunication in sodium chamber with pole portion pole portion towards the sodium intracavity directly, pole portion packs towards the sodium intracavity with the head towards the sodium chamber has sodium, this two -chamber towards the sodium valve can be better walk the valve neck with the heat conduction that valve head end face centre located to gather to it is even to make the valve heat dissipation. | What event cacuses the semilunar valves to open? | 252 | Heath Robinson (codebreaking machine) by a battery of ten photocells, an eleventh for the sprocket holes and two additional ones for the "stop" and "start" signals that were hand-punched between the third and fourth and fourth and fifth channels. This was designed by Tommy Flowers of the Post Office Research Station at Dollis Hill in North London. It used thermionic valves (vacuum tubes) to implement the logic. This involved the Boolean "exclusive or" (XOR) function in combining the various bit-streams. In the following "truth table", 1 represents "true" and 0 represents "false". (At Bletchley Park these were known as x and • respectively.) Other | what are the channels in theath robinson codebreaking machine | [High School Computing] How was binary code invented? | Returns the BinaryNodeTranslation of the Union.
@param input1 The first input of the union, as a common API operator.
@param input2 The second input of the union, as a common API operator.
@return The common API union operator. | Magnetic logic gate for binary computing | Write a code to implement hamming code? | Binary BCH Code BM Decoding Algorithm and Software Realization | how many binary representations are there in bitwise operation | what is the operation that shifts all of the bits of a binary number |
253 | Taxonomic comments on some protobranch bivalves from the northeastern Atlantic | ABSTRACT Bivalves play a vital role in estuarine ecosystems, but are vulnerable to rapid or prolonged changes in the physico-chemical environment. The St Lucia estuarine lake exhibits sub-decadal changes from wet to dry periods, resulting in fluctuating physico-chemical conditions. This paper represents a census of the diversity of bivalve molluscs in this estuary, emphasising changes associated with climate-induced hydrological states. Twenty-four bivalve species were recorded within St Lucia between 1925 and 2011. Twelve that had not been reported previously from St Lucia in the literature were encountered during the present study. These are Anadara natalensis, Anomia achaeus, Arcuatula capensis, Chambardia wahlbergi, Corbicula fluminalis, Dendostrea sandvichensis, Fulvia fragilis, Mactra cuneata, Martesia striata, Meretrix meretrix, Saccostrea forskahlii and Tellina s.l. bertini. Single shells of another two previously unrecorded species, Anodontia edentula and Timoclea lavrani, were also found, althou... | Bivalves in a bottleneck: taxonomy, phylogeography and conservation of freshwater mussels (Bivalvia: Unionoida) in Australasia | The white marlin Tetrapturus albidus (Istiophoridae) is considered to be among the most overexploited species under international management jurisdiction in the Atlantic Ocean, resulting in diverse stakeholder concerns. Efforts have been made to add it to the US Endangered Species List. Its population status has become uncertain with the realization that: (1) longstanding misidentifica- tions of white marlin have occurred with the recently recognized, morphologically similar and sym- patric roundscale spearfish T. georgii; and (2) the 2 species have unknowingly been assessed and managed as a species group. We show that roundscale spearfish currently constitute a substantial proportion (~27%) of the overall 'white marlin' catch in the western North Atlantic, with high spatial variation within this region. Consequently, the accuracy of current biological knowledge on white marlin, some of which has formed the input for past population status modeling, is compromised by 'contamination' due to misidentification. Population assessment simulations in the western North Atlantic incorporating the proportion of roundscale spearfish (27%) were run; these indicated that historical changes in the ratio of the 2 species, as well as differences in the population growth rates between T. albidus and T. georgii, affect simulation results. Our findings suggest misidentifications between the species may have affected the accuracy of past T. albidus population assessments in the western North Atlantic, which therefore need re-visiting to permit improved management and recov- ery of this species. New collection of life history data for T. albidus and T. georgii is also recom- mended to corroborate the results of historical studies. | Reproduction of the Sandbar Shark in the Western North Atlantic Ocean and Gulf of Mexico | The flyingfish, Hirundichthys rondeleti, two priacanthids, Cookeolus boops and Priacanthus arenatus, and the carangid, Seriola dumerili are reported for Canadian Atlantic waters. Single specimens of each species were captured during August–November 1970–72, in the vicinity of Prospect Bay or St. Margaret’s Bay, Nova Scotia. This is the first record of each species north of Cape Cod, Mass. | Recent and Consecutive Records of the Atlantic Blue Crab (Callinectes sapidus Rathbun, 1896): Rapid Westward Expansion and Confirmed Establishment along the Southern Coast of Portugal | Diversity changes in Cretaceous inoceramid bivalves of Japan |
Introduction
In a review of morphological [1] and genetic data [2,3], minke whales were recently divided into two species [4]; the Antarctic minke whale (Balaenoptera bonaerensis) which is confined to the southern hemisphere, and the common minke whale (B. acutorostrata) which is cosmopolitan. The common minke whale is further divided into three sub-species; the North Atlantic common minke whale (B.a. acutorostrata), the North Pacific common minke whale (B.a. scammoni), and the dwarf common minke whale (B.a. unnamed sub-species), which is thought to be confined to the southern hemisphere.
A combination of mark-recapture [5], ecological markers [6,7], and sighting surveys [8] indicate that B. bonaerensis undertake seasonal migrations between feeding grounds in the Antarctic waters in the summer (south of 60uS), and breeding grounds in the tropical or temperate regions in the winter. Sighting data from the period 1976-1987 [8] showed that B. bonaerensis moved southward from the breeding areas by October-November, and that most of them had migrated into Antarctic waters by January.
B.a. acutorostrata occur in the entire North Atlantic during the northern hemisphere summer months, limited in the northern range by the ice [9]. Although their winter distribution is not fully elucidated, they probably migrate to southern latitudes, inhabiting temperate and tropical waters. Sightings have been made as far south as 16uN on the western side [10], 14uN on the eastern side [11] and 10u409N in the offshore Northeast Atlantic [12]. B.a. acutorostrata has been exploited in small-type whaling operations since the 1920s [13]. Since 1996, Norway has maintained an individual based DNA register for B.a. acutorostrata. In 1996 (whale 1) and 2007 (whale 2), individual whales deviating from the genetic profile for B.a. acutorostrata were captured in the Northeast Atlantic.
Size, girth and blubber thickness were similar to B.a. acutorostrata [14], but whale 1 lacked the characteristic white patch on the flippers (Table 1). No deviating morphological characteristics where reported for whale 2, although it is not possible to exclude the possibility that this was overlooked at sea. Size of both whales suggests a minimum age of 15 years [15]. Here, we report the identification of these two whales using a combination of genetic data from both mtDNA sequencing and microsatellite DNA fragment analysis.
Methods
Samples
The Norwegian DNA register for B.a. acutorostrata consists of 7066 genetic profiles from 7139 individuals captured in the Northeast Atlantic in the period 1996-2008. Individual genetic profiles are produced through a combination of 10 microsatellite loci, sequencing part of the mtDNA control region, and a mysticetes sex marker (Supporting Text S1). In 1996, and 2007, two whales deviating from the typical genetic profile for B.a. acutorostrata were captured in the Northeast Atlantic (Fig. 1). In order to identify these two individuals, a mixture of mtDNA (to look at maternal contribution) and microsatellite DNA analyses (to look at both paternal and maternal contribution) were conducted.
Previous studies based on mtDNA [16,17] have shown fixed differences between B. bonaerensis and B. acutorostrata, as well as among the sub-species of B. acutorostrata. To identify maternal contribution to whales 1 and 2, mtDNA control region sequences from these individuals were compared to published sequences from minke whales worldwide of known species and geographic origin [16,17]. In contrast to mtDNA, there is no previous study of minke whales worldwide based on microsatellites. Consequently,
Laboratory analyses
MtDNA sequencing of whales 1 and 2 was conducted at the Institute of Marine Research by amplifying DNA and thereafter sequencing the PCR product in both the forward and reverse direction. The PCR conditions for the two directions were identical except for the primers: (MT4(M13F) and MT3(M13Rev) (modified from [18]) for the forward PCR product, and BP15851(M13F) (modified from [19]) and MN312(M13R) (Modified from [20]) for the reverse PCR product. All PCR reactions were performed with GoTaqFlexi DNA polymerase (Promega). The amplicon was sequenced by a standard Big Dye Terminator 3.1 protocol (Applied Biosystems) and M13F for forward PCR product and M13R for the reverse PCR product. Sequencing primers and full amplification conditions are presented in Supplementary Text S1.
A total of 13 microsatellites and a sex marker were amplified for all species/sub-species samples including whales 1 and 2. Ten of the microsatellites and the sex marker are routinely used in the Norwegian DNA register for B.a. acutorostrata (PCR 1-3), while the remaining three microsatellites (PCR 4) were chosen specifically for this study based upon the fact that they display high or very high F ST values (and therefore provide diagnostic identifications) between minke whale species. The exact amplifications conditions for PCR amplification are presented in Supplementary Text S1. Markers were arranged in four polymerase chain reaction (PCR) multiplexes: [23]. PCR fragments were separated and sized in a capillary based ABI 3730XL genetic analyser. Genotypes were first automatically called, then, manually checked by two persons before exporting data. All samples were genotyped twice, and poorly amplified individuals removed from the data set. Whale 1 and 2 were genotyped up to 10 times for each marker on two separate DNA isolations (no inconsistencies were observed between multiple genotyping). Following genotyping, the microsatellites GT310 and GATA098 were excluded from the study due to unreliable binning of alleles and poor PCR amplification respectively.
PCR 1 = GT509 [21], GATA098 [22], EV001Pm [23], EV037Mn [23], GT310 [21]; PCR 2 = GT211 [21], GT575 [21], sex marker [24]; PCR 3 = GATA417 [22], GATA028 [22], GT023 [21]; PCR 4 = DIrFCB14 [25], EV104Mn [23], EV94Mn
Statistical analyses
MtDNA sequences from whales 1 and 2 were aligned to sequences of B. bonaerensis and sub-species of B. acutorostrata [17]. The genealogy of the mtDNA haplotypes was estimated using the Neighbor-Joining method [26] as implemented in the program PHYLIP. Genetic distances among haplotypes were estimated using the program DNADIST of PHYLIP, based on Kimura-2parameter model. A transition-transversion ratio of 5:1 was used. The genealogy was rooted using the homologous sequence from nine baleen whale species [18]. To estimate support for each node, a total of 1,000 bootstrap simulations were conducted and the majority-rule consensus genealogy estimated.
In order to characterize the minke whale species/sub-species using the microsatellite data generated here, population genetic summary statistics, F ST values, and potential deviations from Hardy Weinberg equilibrium (HWE) were computed in the programs MSA [27] and Genepop [28]. Following initial characterization of the species/sub-species, data from all 11 microsatellite loci, and a reduced set consisting of 8 loci (see results) was used to perform genetic identification of whales 1 and 2. Identifications based upon microsatellite data were conducted in two programs that use different and complimentary analytical approaches.
The first identification of whales 1 and 2 was performed by Bayesian cluster analysis as implemented in the program Structure [29,30]. This program was run by using an admixture model, no population prior for all individuals, and the burn-in set to 100 000 MCMC steps, followed by a further 250 000 steps. This was conducted for numbers of populations (K) set to 3 (i.e., the number of baseline species/sub-species samples) and 4 (to investigate whether any cryptic structure existed within any of the species/ sub-species samples which may assist in the identification of whales 1 and 2), each with three iterations (to check for consistency). In addition to identification of whales 1 and 2 by Bayesian cluster analysis, genetic assignment was conducted in the program GeneClass2 [31]. Prior to identification of these two whales however, simulations with the baseline data (i.e., the three species/sub-species samples in addition to 90 F1 hybrids generated in HYBRIDLAB1.0 [32] between B.a. acutorostrata and B. bonaerensis, and B.a. scammoni and B. bonaerensis) using the self-assignment and leave one out approach was implemented in the GeneClass2. The self-assignment tests give an estimation of the level of accuracy expected from the assignment tests. Following self-assignment simulations, identification of whales 1 and 2 were conducted by using the direct assignment approach. Direct assignment places the individual(s) to be identified in the genetically most similar baseline sample, irrespective of absolute level of similarity. In addition, the probability of excluding each of the two whales from each of the baseline samples in turn was calculated. Exclusion was conducted by Monte-Carlo re-sampling of the baseline with 1000 individuals [33]. All GeneClass2 analyses were in re-computed for whale 2 after having changed the genotype at two loci due to potential genotyping irregularities at these loci (Supplementary Table S1).
Results and Discussion
MtDNA analyses
The final data set (whales 1 and 2 and minke whales worldwide examined in [17]) included the first 287 nucleotides of the mtDNA control region. In this data set the sequences of whales 1 and 2 represented singletons. MtDNA sequences for whales 1 (HQ162497) and 2 (HQ162498) have been deposited in the Genbank.
The Kimura -two-parameter distance between whale 1 and the sequences of B. bonaerensis in [17] averaged 0.0104. The distance ranged from 0.0730 and 0.0808 when whale 1 was compared with sequences of the sub-species of B. acutorostrata in [17]. The distance
Microsatellite DNA analyses
Summary statistics for the 11 microsatellite loci are presented ( Table 2). Deviations from HWE were observed in all three species/sub-species, however, at the more stringent significance level (a0.001), only the deviations observed in the sample of B. bonaerensis remained significant. Some statistical genetic tests assume that the data used adhere to a given set of conditions, for example, that markers are in HWE. Although it has been demonstrated that minor and even serious violations of the assumptions for genetic assignment tests do not necessarily bias the result [34,35,36,37], subsequent analyses were conducted with all 11 loci, in addition to a sub-set of 8 loci (excluding GT509, GT575 and EV037Mn).
Data from the microsatellite markers revealed highly significant genetic differentiation among the three species/sub-species (Table 2). When pooling data from all 11 loci, B. bonaerensis was the most genetically distinct. Although these comparisons need to be treated with caution, due to the fact that some of the markers were deliberately chosen to provide the greatest possible diagnostic power for identification of whales 1 and 2, these data concord with the pattern of relatedness among these species/sub-species from previous studies of minke whales using mtDNA [2,3,16,17]. The genetic distinctiveness of the three species/sub-species samples was confirmed through Bayesian clustering analysis (Fig. 2). In Figure 2. Bayesian cluster analysis identifying two atypical minke whales captured in the Northeast Atlantic. Each vertical line represents a single individual (which can be admixed), and each colour a genetic cluster. Note that colour scheme is not universal between the four runs presented. doi:10.1371/journal.pone.0015197.g002 addition, the sample of B. bonaerensis displayed considerable genetic sub-structure when the number of clusters was set to 4.
The level of genetic differentiation displayed by many of the microsatellites in the present study was very large (seven displayed a pair-wise F ST value over 0.1, four displayed a value over 0.2, and two displayed a value over 0.6). The ability to accurately perform genetic assignment depends upon several factors including the level of genetic differentiation among the baseline (potential source) samples, the number of loci included in the analyses, in addition to sample sizes [34,35,38,39]. The sample sizes, number or loci and level of genetic differentiation in the present data set indicates very good opportunity for genetic identification according to simulations of optimal combinations [38]. Furthermore, this was demonstrated by the self-assignment simulations conducted here. All three species/sub-species samples revealed 100% selfassignment accuracy (i.e., all of the individuals were correctly classified back to their source species/sub-species) when using both 11 and 8 loci. When simulated hybrids were incorporated into the computations (thus increasing baseline sources to 5), accuracy of self-assignment remained very high (11 loci = 98%; 8 loci = 96%), demonstrating the suitability of the suite of microsatellite markers to perform identifications of whale 1 and 2, to both species/subspecies and F1 hybrid combinations.
Using data from both 11 and the reduced set of 8 microsatellite loci, whale 1 was diagnostically identified as a pure B. bonaerensis (Table 3; Fig. 2; Supplementary Table S1), confirming this individual's migration from the Antarctic to the Arctic. This represents the first documentation of this species north of the tropics. A combination of Bayesian cluster analysis (Fig. 2), genetic assignment (Table 3) and genotype break-down (Supplementary Table S1) rejected whale 2 as pure B. bonaerensis. When combined with the fact that the mtDNA haplotype for this whale was B. bonaerensis, these data represent the first documentation of a hybrid between a minke whale species. The source, and proportion of B. acutorostrata sub-species contribution to this individual was not conclusively resolved however. Examination of available data (Naohisa Kanda unpublished) for nine dwarf minke whales (B. acutorostrata unnamed sub-species) genotyped for six markers overlapping with the panel implemented in the present study did not shed further light on this identification. Consequently, while it is not possible to conclusively identify the paternal contribution to whale 2, nor exclude it from being a F1-Fx hybrid between B. bonaerensis and any of the B. acutorostrata sub-species, results from Bayesian cluster analysis (Fig. 2) and direct genetic assignment (Table 3) indicate the most likely paternal contribution from B.a. acutorostrata.
General discussion
Whilst inter-species hybridization has been previously observed between blue (B. musculus) and fin (B. physalus) whales [40], our study presents the first example of hybridisation between minke whale species. Furthermore, accepting paternal contribution from B. a. acutorostrata as most likely, based upon the present analyses, and the fact that whale 1, a pure breeding migrant, was observed in the Northeast Atlantic approximately a decade before the hybrid was reported in the same region, whale 2 represents the first example of a hybrid between two whale species from separate hemispheres. The two alternative paternal contributions to this hybrid, i.e., fathered by B.a. scammoni and migrated from the North Pacific to the North Atlantic, or fathered by the B.a.subs. (dwarf minke whale) found in the southern hemisphere migrating to the Northeast Atlantic, represent equally unique and dramatic results from an ecological perspective.
Although whales display considerable potential to undertake long migrations, inter-oceanic migrations outside the species boundaries are extremely rare, and previously reported only for the humpback whale within the same hemisphere (Megaptera novaeangliae) [41]. It is very possible that the migrations documented here were random events, which may or may not represent a scouting behavior having occurred over many years. Indeed, the Norwegian minke whale DNA register, which provides the unique opportunity to document this infrequent behavior, only goes back as far as 1996. Coincidently, this is the same year that the pure B. bonaerensis individual (whale 1) was captured in the Northeast Atlantic. Assuming a total population abundance of 107000 B.a. acutorostrata in the Northeast Atlantic [42] a pro-rata estimate of the number of individuals with B. bonaerensis mtDNA haplotypes present in this region is 30 (95% CI: 4-107). Consequently, the Northeast Atlantic does not appear to be a major destination of B. bonaerensis migration outside its previously documented distribution.
Supporting Information
Text S1 Extended materials and methods for genotyping conditions. (DOC)
Table S1 Presence of alleles for two atypical whales in the genetic baseline. (DOC) Table 3. Identification of two atypical minke whales captured in the Northeast Atlantic based upon exclusion (i.e., probability) and direct assignment (i.e., closest match).
in order to identify both paternal and maternal contribution to whales 1 and 2, microsatellite analyses were conducted on samples of B. bonaerensis and sub-species of B. acutorostrata from different ocean basins. These included 91 B. bonaerensis (Antarctic 2004), 91 B.a. acutorostrata (Northeast Atlantic 2007), and 95 B.a. scammoni (Northwest Pacific 2006). All whale samples, including those from the Norwegian minke whale DNA register and the Japanese whale research programs under special permit in both the western North Pacific and Antarctic, existed prior to this study.
Figure 1 .
1Global distribution of minke whales during northern hemisphere summer feeding season. A: Balaenoptera a. acutorostrata, B: B. a. scammoni, C: B. bonaerensis, D: B. a. unnamed subspecies (dwarf minke).1996 and 2007 refers to locations of capture for two atypical whales. doi:10.1371/journal.pone.0015197.g001
Locus 1 =
1DIrFCB14, 2 = EV104 Mn, 3 = EV94 Mn, 4 = EV001 Pm, 5 = EV037 Mn, 6 = GT509, 7 = GT211, 8 = GT575, 9 = GATA028, 10 = GATA417, 11 = GT023. * = significant from HWE at 0.05, ** = significant deviation from HWE at 0.001. Atl = B.a. acutorostrata, Pac = B.a. scammoni, Ant = B. bonaerensis. A T = total number of alleles, He = expected heterozygosity for each locus. doi:10.1371/journal.pone.0015197.t002between whale 2 and the sequences of B. bonaerensis averaged 0.0286. The distance ranged from 0.0806 and 0.0865 when whale 2 was compared with sequences of the sub-species of B. acutorostrata. In the neighbour-joining based genealogy, sequences of whales 1 and 2 clustered within the B. bonaerensis clade with high bootstrap values. In a comparison with a larger data set of B. bonaerensis mtDNA sequences (n = 1165, data not published) whale 1 matched the haplotype of 4 individuals while whale 2 was represented by a singleton.
Table 1 .
1Biological records for two atypical minke whales captured in the Northeast Atlantic.Individual
Position
Biological stats
Comments
Whale 1
30 June 1996
70u579N, 8u519W
Male, length 820 cm, girth 386 cm,
blubber 50, 140, 30 mm*
No white patch on flippers. One of six whales captured
in the close vicinity within 3 days (29 June-1 st July)
Whale 2
20 June 2007
78u029N, 11u439E
Female**, length 825 cm, girth 400 cm,
blubber 35, 140, 35 mm*
No abnormalities reported. One of eight whales taken in the
close vicinity on the same day.
*Blubber measured dorsal behind blowhole, behind dorsal fin, lateral above flipper, respectively,
**Reproductive status not determined.
doi:10.1371/journal.pone.0015197.t001
Table 2 .
2Genetic variation within (allelic variation) and among (F ST values) three species/sub-species of minke whales based upon the analysis of 11 microsatellite loci.Species N
Locus
Loci
pooled
1
2
3
4
5
6
7
8
9
1 0
1 1
A T
Allelic variation
Atl
91
2
2*
3
12
7
12
9
9
11
12
8
87
Pac
95
5
3
5
19
11*
15
13
9
12
8
13*
113
Ant
91
4
16
17
11
20**
37**
16
18**
39
47
16
241
Total
277 9
16
19
28
22
39
18
18
44
51
16
280
He
0.36
0.57
0.48
0.83
0.75
0.88
0.85
0.84
0.87
0.86
0.84
F ST values
Atl x Pac
0.038
0.029
0.404
0.099
0.325
0.091
0.045
0.057
0.009
0.086
0.105
0.128
Atl x Ant
0.640
0.248
0.600
0.171
0.152
0.073
0.027
0.068
0.087
0.073
0.130
0.211
Pac x Ant
0.608
0.176
0.430
0.151
0.137
0.050
0.023
0.046
0.062
0.129
0.019
0.171
Global F ST
0.537
0.175
0.481
0.141
0.216
0.072
0.032
0.057
0.054
0.097
0.085
0.172
Global (P value) ,0.0001 ,0.0001
,0.0001
,0.0001
,0.0001 ,0.0001 ,0.0001 ,0.0001 ,0.0001
,0.0001
,0.0001 ,0.0001
Atl = B.a. acutorostrata, Pac = B.a. scammoni, Ant = B. bonaerensis, Atl x Ant and Pac x Ant = simulated F1 hybrids. Whale 2* = individuals genotype changed for two loci according to potential genotyping irregularities (SupplementaryTable 1). Loci refers to number of microsatellite DNA loci included in the statistical analyses. doi:10.1371/journal.pone.0015197.t003Individual
Loci
Probability of false exclusion from baseline sample
Direct assignment
Atl
Pac
Ant
Atl x Ant
Pac X Ant
Whale 1
11
,0.001
,0.001
0.209
0.003
0.001
Ant
8
,0.001
,0.001
0.553
0.073
0.112
Ant
Whale 2
11
,0.001
,0.001
,0.001
,0.001
,0.001
Atl X Ant
8
,0.001
,0.001
,0.001
,0.001
,0.001
Atl X Ant
Whale 2*
11
,0.001
,0.001
,0.001
0.016
0.015
Atl X Ant
8
,0.001
,0.001
,0.001
0.038
0.039
Atl X Ant
December 2010 | Volume 5 | Issue 12 | e15197
PLoS ONE | www.plosone.org
AcknowledgmentsWe would like to acknowledge Michael M. Hansen, Lars Walløe, and two anonymous referees for comments on earlier drafts of this manuscript. The roles of both Norwegian and Japanese crew members involved in sampling minke whales collected prior to this study are acknowledged.Author Contributions
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| 253 | Abstract Most of the small northeastern Atlantic protobranchs classically referred to Leda, Portlandia, Yoldiella, Yoldia etc., are discussed and figured to facilitate identification. Yoldiella solidula sp.n. was previously included in Y. fraterna Verrjll & Bush, but is here considered a distinct, arctic species. The following new synonymies are made (the valid name mentioned first): Yoldiella lucida (Loven, 1846) = Y. subangulata Verrill & Bush, 1898 = Y. iris Verrill & Bush, 1898. - Yoldiella nana (M. Sars, 1865) = Yoldiella fraterna Verrill & Bush, 1898 = Yoldiella inconspicua Verrill & Bush, 1898. - Yoldiella propinqua (Leche, 1878) = Yoldia pygmaea var. symmetrica Friele, 1878 = Portlandia persei Messjatsev, 1931. - Yoldiella messanensis (Seguenza, MS, Jeffreys, 1879) = Leda acuminata Jeffreys, 1873. - Yoldiella philippiana (Nyst, 1845) (neotype designated) = Yoldiella frigida mediterranea Nordsieck, 1974. - Megayoldia Verrill & Bush, 1987 = Microyoldia Verrill & Bush, 1987. - Megayoldia thraciaeform... | ABSTRACT Deep-water samples off the Oregon coast yielded two new genera, four new species, and resulted in a further description of a previously described species of the Suborder Mysida. The following mysids are described: (1) The new genus Bacescomysis, which includes B. pacifica, new species, and five species of Hansenomysis: H. birsteini Băcescu, H. peruvianus Bacescu, H. tattersallae Băcescu, H. abyssalis Lagardere, and H. atlantica Lagardere. In this genus, closely related to Hansenomysis, the unjointed plate on the exopod of the uropod is the distinguishing feature. Bacescomysis pacifica is distinguished by its eyeplate, second thoracic endopod, second male pleopod, and telson. (2) The new species Boreomysis pearcyi is unique in its antennal scale, third thoracic endopod, telson, and body length. (3) Dactylerythrops latisquamosa, new species, is distinguished by its telson, eye, antennal scale, and endopod of first limb. (4) Paramblyops sp. is recognized as a new species by its rostrum and eyeplate, but is too damaged for a complete description. (5) The new genus Gibbamblyops resembles Dactylamblyops and Pseudamblyops, but is distinguished by the anterior margin of the carapace, eye, antennal peduncle, fourth male pleopod, and telson. These characters also define the uniqueness of its species, G. longisquamosa. (6) Thalassomysis tattersalli Nouvel, 1942, had been partially described from a single specimen. Four additional specimens of this species are recorded here. Slight differences are discussed, plus a complete description of the antennal peduncle and telson, which were lacking in the original description, are provided here. (7) Seven specimens of Holmesiella anomala Ortmann provided information on regional variation and allowed an opportunity for detailed drawings. | The abundance and composition of zooplankton down to 3000 m depth was studied in the subtropical and tropical latitudes across the Atlantic, Pacific and Indian Oceans (35 • N-40 • S). Samples were collected from December 2010 to June 2011 during the Malaspina Circumnavigation Expedition. Usually, low abundances were observed with the highest values found in the North Pacific Ocean, Benguela, and off Mauritania, and the lowest in the South Pacific Ocean. No significant differences in abundance and zooplankton composition were found among oceans, with depth being consistently the most important factor affecting their distribution. Each depth strata were inhabited by distinct copepod assemblages, which significantly differed among the strata. The contribution of copepods to the zooplankton community increased with the depth although, as expected, their abundance strongly decreased. Among the copepods, 265 species were identified but 85% were rare and contributed less than 1% in abundance. Clausocalanus furcatus and Nannocalanus minor dominated the epipelagic strata. Pleuromamma abdominalis and Lucicutia clausi were of importance in the mesopelagic layer, and Pareucalanus, Triconia, Conaea and Metridia brevicauda in the bathypelagic layer. Our results provide a global-scale assessment of copepod biodiversity and distribution, providing a contemporary benchmark to follow future ocean changes at low latitudes. Diversity 2019, 11, 203 2 of 22research vessels, sampling efforts of the deep-sea zooplankton are often too expensive. In addition, the zooplankton community in the subtropical-tropical regions is poorly studied, particularly in the southern hemisphere, which contains almost 80% of the ocean surface. These areas are widely unexplored in comparison to coastal areas, and most studies so far are carried out in northern neritic waters[3].Overall, the deep-sea zooplankton community is characterized by strong latitudinal and bathymetric gradients and its diversity mainly regulated by complex interactions among environment and the species-specific performances. However, the major driving mechanisms generating the structure of the pelagic deep sea still poorly understood[4,5]. In this vast environment, zooplankton supports life and represents a key component in the functioning of the ocean food web. Therefore, understanding the response of this community to hydrographical and meteorological forcing is crucial in the present context of anthropogenic global change[3,6]. The current interest on whole ocean ecosystem models makes it necessary to ascertain whether it is possible to identify different zooplankton assemblages and if so, how they are distributed at the relevant spatial and depth scales. Although the first goal of the expedition was to explore the open ocean areas, we sailed through different domains and biogeographical provinces [7] of different biological productivities such as the warm ocean and upwelling systems [8], promoting contrasting ocean scenarios. Moreover, environmental factors affect the spatial and vertical distribution of the zooplankton including mainly temperature, oxygen minimum zones[9], and food availability[8,[10][11][12].The sparse data on the distribution of the main zooplankton groups in particular copepods, in subtropical and tropical result, from a series of expeditions mostly in the Atlantic Ocean [13-17] and fewer data in the Indian[18][19][20][21]and in the Pacific oceans[22][23][24]. Nevertheless, these studies were regional in scope and used different methodologies, which hinders comparisons of the results obtained. According to them, the tropical and subtropical zooplankton community is mainly characterized by high species diversity, complex trophic networks and small changes of biomass throughout the year. Due to the absence of physical barriers allowing co-occurrence and wide latitudinal ranges of many oceanic species the horizontal distribution in these low latitudes is almost unrestricted. In contrast, a vertical structure could appear due to the physiological performances of the different species[17,25,26].However, available data show that zooplankton abundance in the deep-sea decreases with depth [27], the rate of this decrease varies in different geographical areas[5,[28][29][30], and changes in diversity and community structure still are poorly resolved. The feeding mode of zooplankton also varies with depth, with herbivorous and omnivorous species occurring in the epipelagic, and carnivores and detritivores copepods increasing toward the bathypelagic zone[31]. In the latter zone, species tend to be geographically widespread. However, community structure data tends to be relatively coarse as it requires quantitative taxonomic assessments across multiple taxa, where taxonomic expertise is increasingly harder to find and largely dependent on time consuming microscopical observations. The remarkable paucity well into the 21st Century of data on deep-sea zooplankton in the subtropical and tropical oceans is a major gap in our understanding of the ocean, provided the key role of zooplankton in the functioning of the marine food webs and associated biogeochemical cycles[4]. Copepods, are the dominant zooplankton group throughout the water column[10,27], major prey of the meso-and bathypelagic fauna[32,33]and a relevant component of the biological pump transporting organic matter to the deep ocean throughout their diel or seasonal vertical migration[27,34,35].Hence, there is a impending need to sample the subtropical-tropical ocean using consistent methods down to the ocean interior to produce a global reference baseline of zooplankton community structure[6,36,37]. Accordingly, the main goal of this work was to describe and study the structure of the marine zooplankton community from the epipelagic to bathypelagic layers across the subtropical and tropical ocean, with a particular focus on copepods collected during the Malaspina Circumnavigation Expedition, which sailed the three main oceans (Atlantic, Indian and Pacific Oceans) between December 2010 and June 2011 to explore the ecology of the deep sea[38]. The cruise track was planned to Diversity 2019, 11, 203 3 of 22sample open-ocean regions, including poorly studied domains of the subtropical and tropical ocean, using consistent and standardized procedures. The data acquired provides a global contemporary benchmark to resolve responses of zooplankton communities to future ocean changes. | Dalpadado, P., Borkner, N., Bogstad, B., and Mehl, S. 2001. Distribution of Themisto (Amphipoda) spp. in the Barents Sea and predator-prey interactions. – ICES Journal of Marine Science, 58: 876–895. Themisto abyssorum and Themisto libellula were the dominant amphipod species observed in the central and the northern Barents Sea during 1984–1996. T. abyssorum was predominant in the subarctic waters, T. libellula in the Arctic waters. A third species, Themisto compressa, was rare and was restricted to the Atlantic waters. Our study showed peak abundances of T. abyssorum and T. libellula in summer and in early autumn. High abundances were usually associated with Polar Front waters. T. libellula has a more near surface distribution than T. abyssorum. Followed by a decrease in the capelin stock from 1985–1987 there was an increase in the abundance of Themisto abyssorum and T. libellula, probably due to the reduced grazing pressure from capelin (Mallotus villosus). In the mid-1980s and 1990s when the capelin stock was at extremely low levels, cod (Gadus morhua) switched from capelin to alternative prey such as amphipods and krill. Detailed analysis of amphipods in the cod stomachs from 1984–1999, showed that cod fed mainly on Themisto spp., especially on T. libellula. Themisto species were consumed by most age groups of cod. With an increase in the capelin stock from 1987–1991, a corresponding decrease in the abundance of Themisto abyssorum and T. libellula was observed. During 1993– 1996 when the capelin stock again was at low levels, the abundance of these two amphipod species increased. The increase in abundance was less pronounced in the mid-1990s for T. libellula probably owing to higher grazing pressure from cod and other predators such as harp seal (Phoca groenlandica) and arctic sea birds. The stock size of cod in the mid-1990s was about twice the amount as in the mid-1980s. These results illustrate strong predator-prey interactions between macrozooplankton species as amphipods and capelin and cod in the Barents Sea. The amphipod populations in the Barents Sea appear to be to a large extent controlled by predation. | Plicodendrocrinus n. gen. is erected for dendrocrinids with solid pentalobate columns, strong stellate ridges on the aboral cup plates, and highly plicate anal sac plates. Five species are assigned: Middle Ordovician; P. proboscidiatus (E. Billings, not W. R. Billings) n. comb., from the Trenton of Canada and the Dunleith of Iowa and Minnesota. Upper Ordovician; P. casei (Meek) n. comb., from the Richmond and Gamachian of the midcontinent; P. rugocyathus (Ramsbottom) n. comb., from the Ashgill of England; P. collapsus (Donovan) n. comb.; and P. granditubus (Ramsbottom) n. comb., from the Ashgill of Scotland. The Middle Ordovician dendrocrinids from the Dunleith Formation (Trentonian) of northern Iowa and southern Minnesota are P. proboscidiatus (E. Billings), Dendrocrinus acutidactylus E. Billings, and Quienquecaudex springeri (Kolata). All species are also known from the Middle Ordovician of Ontario and Quebec. In addition, O. springeri (Kolata) is recorded from the Platteville Group of Illinois. Biogeographically, the Dunleith dendrocrinids are most similar to those of the northern Appalachians. Plicodendrocrinus casei (Meek) ranges widely in the midcontinent and has been obtained from the Maysvillian and Richmondian Maquoketa Formation of Iowa and Minnesota, several Richmondian units in the Cincinnati area, and the Gamachian Girardeau Limestone of Illinois and Missouri. A quantitative cladistic analysis of Ordovician cladid and flexible crinoids produces five groups: primitive forms including Aethocrinus, Compagicrinus, Ottawacrinus , and Grenprisia ; cyathocrinids with Carabocrinus, Palaeocrinus, Illemocrinus , and Porocrinus ; merocrinids with Archaetaxocrinus, Merocrinus, Praecupulocrinus, Polycrinus , and Aithriocrinus ; dendrocrinids with Esthonocrinus, Eoparisocrinus, Dendrocrinus, Quienquecaudex, Plicodendrocrinus and perhaps Eopinnacrinus ; and Cupulocrinus and the flexibles, Protaxocrinus, Clidochirus , and Proanisocrinus. These groups are not consistent with the present taxonomy and several suggestions for restructuring are presented, notably grouping flexibles with cladids and adjusting the taxonomic level of cyathocrinids. The cladograms for early cladids and flexibles are poorly correlated with stratigraphic position because of numerous unfilled range zones for the taxa or their ancestors. Thus, the cladograms generate predictions that can be tested by later finds in the Lower and the lower part of the Middle Ordovician. The overall evolutionary trends are highly mosaic with numerous parallelisms and reversals. | Abstract The data presented were collected from one trawl and three longline exploratory surveys to the Mid-Atlantic Ridge and covered the depths between 400 and 2000 m, but mainly between 500 and 1200 m. Information on 56 species from 27 families is presented with regard to temperature, geographical distribution and depth. For some species, new information on geographical distribution is presented. In the northern part of the Ridge (north of 52°N) sub-Arctic species such as Sebastes spp., tusk ( Brosme brosme ) and Greenland halibut ( Reinhardtius hippoglossoides ) are dominant. In the southern part (south of 48°N), sub-tropical species such as golden eye perch ( Beryx splendens ) and cardinal fish ( Epigonus telescopus ) are the dominant species. The area between 48 and 52°N is a region of faunal change where some species seem to be at either the northern or southern limit of their distribution. | The European earwig, Forficula auricularia L. 1758 (Dermaptera: Forficulidae), is a household pest and an invasive species with cosmopolitan distribution. It is native to Europe, Western Asia and probably North Africa, although it has spread to all continents except Antarctica (Crumb et al. 1941; Clausen 1978; Shakai 1987). Earwigs are carried from one place to another on clothing or commercial products such as lumber, ornamental shrubs, newspaper bundles and groceries. Euro pean earwigs are nocturnal omnivorous scaven gers and predators, most commonly found in tem perate climates. They prefer moist and warm hab itats, having an optimum mean growth tempera ture of 24 °C, and are most active when the daily temperature has minimal fluctuation (Crumb et al. 1941; Capinera 2001; Jacob 2009). The species has been known to cause significant damage to crops, flowers, and fruit orchards when they occur at high population densities (Vickery & Kevan 1986; Walker 1997; Capinera 2001; Weems & Skelly 2009). Forficula auricularia was recorded a number of times in North America along the 19th century before becoming established on the continent (Vickery & Kevan 1983; Guillet et al. 2000). The first known colony of the species on the Atlantic coast appeared in Newport, Rhode Island in 1911 (Glaser 1914; Guillet et al. 2000), whereas on the Pacific coast, the earwig was present in Seattle al ready in 1907 (Coyne 1928) and in Oregon in 1909 (Guillet et al. 2000). Since then, the species has spread on both coasts of the US (Wirth et al. 1998), as well as to several Canadian provinces. Expansions were initiated by population bursts in harbors, a phenomenon never observed in Eu rope, and the species rapidly became a nuisance, thus causing concern on the part of agricultural authorities, who used different measures to erad icate this pest, including poisoning campaigns. The geographic range of F. auricularia has clearly expanded since, as it has continuously been re ported in different localities farther inland (Crumb et al. 1941; Wirth et al. 1998). Despite this ability to colonize new environments, there were no precise records of F. auricularia in Mex ico and Central America prior to this work (Scud der 1868; De Bormans 1893; Hebard 1917; Clausen 1978; Young 1986; Maes & Haas 2006; Weems & Skelly 2009). During a recent field trip carried out at the La gunas de Zempoala National Park, in the state of Mexico (municipality of Ocuilan; 2824 m absl; 21 VIII-2010), we found a reproductive aggregation of about 20 specimens of F. auricularia, which was grouped under loose bark on a vertical fence pole. This fence separates the surrounding pas tures from one of the tourist stands at Lagunas de Zempoala. Most of the specimens dropped from the pole after being exposed, but 6 were captured and photographed (Fig. 1). No other specimens were found immediately nearby. Furthermore, we observed an explosive irrup tion of F. auricularia on the Mexican island of | Ten species of Haploniscidae Hansen, 1916 were sampled in Icelandic waters during expeditions in the framework of the BIOICE project. Nine of these were known from the North Atlantic Ocean, i.e. Haploniscus aduncus Lincoln, 1985, H. ampliatus Lincoln, 1985, Haploniscus angustus Lincoln, 1985, H. bicuspis (Sars, 1877), H. foresti Chardy, 1974, H. hamatus Lincoln, 1985, H. spinifer Hansen, 1916, Antennuloniscus simplex Lincoln, 1985 and Chauliodoniscus armadilloides (Hansen, 1916). All but H. bicuspis and H. angustus were restricted to the Atlantic Ocean south of the Greenland-Iceland-Faeroe Ridge (GIF Ridge), while H. bicuspis occurred at considerable depth ranges both north and south of the GIF Ridge. A new species, Haploniscus astraphes n. sp., is described based on material from the Denmark Strait, North Atlantic and the Guinea Basin, South Atlantic. H. astraphes n. sp. belongs to a group of Haploniscus species closely related to the genus Antennuloniscus and shares several characters with species from that genus, especially the spine row on pleopod 1, the stout sensory seta on the carpus of pereopod 7 and characters of the antennae. H. astraphes n. sp. is characterized by a rectangular body shape, the straight frontal margin of the head and the strongly convex posterior margin of the pleotelson. | Abstract The family Cladorhizidae (Porifera) comprises a particularly interesting group of sponges that has developed a carnivorous feeding strategy unique within the phylum. Cladorhizids are typically considered deep-sea sponges, are frequently found at oceanic ridges and seamount systems, and new species are continuously discovered as new areas are explored. In this study we describe nine new cladorhizid sponges collected on three seamounts of the Southwest Indian Ocean Ridge (SWIOR) during the RRS “James Cook” cruise JC066: Abyssocladia boletiphora , Ab. corniculiphora , Ab. hemiradiata , Asbestopluma (Asbestopluma) unguiferata , As. (A.) jamescooki , As. (A.) laminachela , As. (A.) pseudoisochela , As. (A.) ramuscula and Chondrocladia (Meliiderma) rogersi ; and re-describe four species, viz. Ab. symmetrica , Ch. (M.) stipitata , Cladorhiza moruliformis and Cl. tridentata collected during the “Challenger” expedition in the Southwest Indian Ocean. Barcodes and a phylogenetic analysis showing the systematic position of the new species are included as additional information. Our results show that the cladorhizid fauna of the Southwestern Indian Ocean is diverse and seems to be bathymetrically structured with no observed overlap between the newly reported upper bathyal species (~1000 m) and previously described lower bathyal and abyssal species from the area. While the upper bathyal SWIOR species are unique and represent a regionally endemic cladorhizid fauna, similarities in morphology and spicule characters as well as molecular evidence suggests biogeographical affinities to species from the SW Pacific and SW Atlantic, but no similarities to previously reported Antarctic fauna were found. A table of cladorhizid species from the Southwest Indian Ocean and neighboring areas is provided. |
254 | Optimization of epoxy passivation process to fabricate silicon radiation detectors | Trench sidewall passivation is a key step in the SCREAM (single crystal reactive etching and metallization) process for releasing suspended MEMS structures. In this paper, the parylene thin film is reported to serve as the passivation layer owing to its excellent conformality, chemical inertness, mechanical performance, and especially, low growth temperature. The deposited parylene films are characterized and the test structures are released through SCREAM process utilizing the parylene films as a passivation layer. The results show that as a passivation layer the parylene has more merits than the PECVD SiO2 film. | The effects of different passivation methods applied to the same planar high-purity germanium gamma radiation detector have been studied. By means of the scanning with a low-energy collimated gamma source, it has been found that the surface passivation gives rise to a dead layer below the intrinsic Ge surface, whose thickness and distribution are strongly dependent on the passivation type. Measured bulk detector properties like the peak-to-Compton ratio and efficiency have shown a dependence on the passivation and an influence of the passivation type on the depletion voltage, whilst the optimal energy resolution has been the same for all the passivations. | Abstract DLTS measurements are used to detect two new defect states in irradiated p-type silicon. The amplitude and the rate of annealing of the E(0.39) state depende on the minority carrier injection level. It is supposed that the E(0.39) trap is a silicon interstitial related defect because the annealing of this state enhanced the concentration of interstitial carbon. The other new defect H(0.35) is identified as a metastable precursor to the C i O i H(0.38) center. An energy barrier of 1 eV separates the MH(0.35) state from the stable C i O i configuration. | Low energy ion beam etching of InP using methane chemistry | Thirty years ago planar technology was first successfully applied to the manufacture of silicon detectors and this technique led to detectors with better performance than traditional surface barrier and diffused junction types. Today, these detectors are widely used in nuclear and high-energy physics research and are widely deployed in the industrial market as well. These silicon detectors are used in health physics, X-ray fluorescence and diffraction, medical imaging, space applications, and photon (light) detection. As an industrial company, Canberra was challenged to provide detectors with high reliability along with low leakage current, thin entrance windows, a wide range of thicknesses, low noise, and position sensitivity in both single devices and arrays. A new challenge is the readout of pixilated devices. Electronics integrated into or onto the detector chip is a topic of current interest. | We have determined that mechanisms of irreproducibility in measurement of lifetime arise from two sources: (i) improper wafer cleaning, and (ii) instability of I-E solution when in contact with a Si wafer. This paper describes a sequential optical oxidation and chemical cleaning procedure that can reproducibly yield the correct values of bulk lifetime. We have observed that surface passivation is optically activated, which often causes an initial increase in the measured lifetime. This initial activation time can be greatly reduced by exposing the wafer in the bag to higher intensity light such as a solar simulator for 5–10 minutes. This procedure yields reproducible, very low recombination surfaces, suitable for measuring tb as high as 2 ms. We will discuss why this cleaning procedure is necessary and propose mechanism of instability in the passivation of I-E/Si. | An IR sensitive, charge-coupled linear imaging array using palladium-silicide Schottky-barrier detectors has been designed, fabricated, and tested. Thermal scenes as low in temperature as 110/spl deg/C were imaged. It was shown theoretically that in the vidicon mode of operation, nonuniformities in the transfer process and in detector capacitance do not degrade the video signal. Good uniformity was indeed obtained in this mode. A scheme for removing the background signal from the detectors before loading into the charge-coupled device (CCD) was incorporated into the design of the chip, and operation in this mode was also demonstrated. This imager, though made with a single level of metallization with gaps, had reasonably good transfer efficiency and is free of smearing and blooming. | Accelerated deactivation of the boron–oxygen-related recombination centre in crystalline silicon | 254 | Passivation of surface using twocomponent epoxy at room temperature is followed to fabricate silicon surface-barrier type of detectors. Proper curing of the epoxy resin using the right amount of amine-based hardener is crucial to minimize moisture intake and hence obtain stable detector performance. A simple experiment was conducted to test hardening and water intake of the cured epoxy by varying the resin to hardener ratio. The data obtained helped us to fix the proper resin to hardener ratio and fabricate charged-particle detectors with lower leakages and better stability. | A chemiluminescence study of the properties and degradation of epoxy resins as coatings | Application progress of waterborne epoxy resins coatings. | In the present study the effect of weight percentage of nanoclay with epoxy resin coating on mechanical properties ( impact strength , hardness, and wear rate ), Adhesion test and thermal properties (thermogravimetric analysis (TGA), thermal expansion coefficient (CTE),the weight percentage of nano clay at ( 0,1,3,5,7) wt% ,has been investigated.Results indicated,that when increase the weight ratio of nano clay the value of impact strength increased, hardness and decreasing wear rate up 5wt% , and at 7 wt% that the impact strength , hardness would be decreased and wear rate increase due to agglomeration of nano clay . The strength adhesion pull off of the epoxy coating was 1.76 Mpa ,when adding nano clay,improve the adhesion properties of the epoxy coating at the ratio of 5%. The improved the thermal stability of the nanoclay filled with epoxy coating. Thermal stability is very important for coating materials. | STUDY ON THE EFFECT OF SEPIOLITE ON EPOXY RESIN REACTION | Epoxy resin safety question | Epoxy resin for potting electronics for deep water | Development of a new curing agent for epoxy resin | IntroductionThe epoxy resins were introduced as industrial products more than 70 years ago. They immediately aroused a great interest due to the valuable properties that distinguish them from other plastics. They found the application in various fields of a technology, especially in electronics and an electrical engineering. Due to their extremely favourable properties and relatively simple processing methods, the epoxy resins are increasingly used in the industry [1]. Their polar nature causes good adhesion of the resins to many different materials, such as a glass, the metals, the polymers, the ceramics and a concrete. During the curing of the resin, slight shrinkage occurs and the castings accurately follow the shape of the mould, making it possible to obtain them without exertingAbstractThe aim of the article was to determine the compressive strength and compressive strain of an unmodified and a modified epoxy compounds containing a montmorillonite filler, as well as to determine the effect of temperature and an aging time on the mechanical parameters of the considered epoxy compounds. The subject of the research was both the unmodified and the modified adhesive compounds. The unmodified epoxy compounds were made in four variants, which included the epoxy resins based on a bisphenol A as well as the curing agents: a triethylenetetramine and a polyamide curing agent. The modified compounds containing the montmorillonite filler, were also made in four variants. The samples were subjected in a thermal chamber at 80 °C for 1 and 2 months and in a thermal shock chamber in the temperature range from − 40 °C to 80 °C for 1 and 2 months. The reference samples were seasoned at room temperature 20-25 °C. The epoxy compounds samples were subjected to the compression strength tests in accordance with ISO 604 standard. The compressive strength is influenced by the environment and temperature, the aging time and the presence of the modifying agent. The epoxy compounds subjected at elevated or variable temperatures have higher compressive strength than the reference epoxy compounds. The operation of the climatic chamber or the thermal shock chamber makes the samples more deformable than the reference samples.Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
255 | Rhabdomyolysis after bariatric surgery: a potentially fatal complication | Prevention of Rhabdomyolysis in Bariatric Surgery | Acute pediatric rhabdomyolysis: causes and rates of renal failure. | The case report by Steidl et al.[1][1] described a morbidly obese man, who developed rhabdomyolysis “related to overuse of phentermine hydrochloride.” Significantly, the patient had engaged in strenuous activity, lifting and moving heavy furniture, after which he developed back pain, inguinal | “Kris Knife” Brachioplasty After Bariatric Surgery and Massive Weight Loss | Acute Kidney Injury Due to Rhabdomyolysis in Narcotic Drug Users | Poster: "ECR 2011 / C-0710 / Bariatric surgery: Spectrum of complications at imaging." by: "M. D. C. Garcia Vazquez, E. GARCIA CASADO, J. A. Alvarado Rosas, A. Vicente Bartulos, I. Villar Blanco, O. Sanz de Leon, L. Cubillo De Olazabal, M. C. Gonzalez Gordaliza, R. PEROMINGO FRESNEDA; MADRID/ES" | Hypokalemia and rhabdomyolysis. | Treatment Strategies for Perianal Rhabdomyosarcoma: Report of Two Cases | 255 | Rhabdomyolysis in Bariatric Surgery: a Systematic Review | Pressure-induced rhabdomyolysis after bariatric surgery. | Comparing Outcomes of Two Types of Bariatric Surgery in an Adolescent Obese Population: Roux-en-Y Gastric Bypass vs. Sleeve Gastrectomy | Gastric adenocarcinoma with rhabdoid morphology | Vaginoscopic resection for rhabdomyosarcoma of the vagina: a case report and review of the literature. | The effects of bariatric/metabolic surgery on glycemic control in obese type 1 diabetic patients are controversial. We herein report a case of a morbidly obese 35-year-old woman who completely recovered from slowly progressive type 1 diabetes (SPIDDM) following laparoscopic sleeve gastrectomy. Preoperatively, her body mass index (BMI) was 49.8 kg/m 2 and hemoglobin A1c was 5.7% with intensive insulin therapy. Six months after bariatric/metabolic surgery, her BMI decreased to 33.2 kg/m 2 and her glycemic control was normal despite the discontinuation of all diabetic medicine. This case demonstrates the usefulness of bariatric/ metabolic surgery for achieving glycemic control in morbidly obese patients with SPIDDM in Japan. | Revisional bariatric surgery can improve refractory metabolic disease | Bariatric surgical patients increasingly seek cosmetic procedures | Bariatric surgery: Spectrum of complications at imaging. |
256 | countries that require citizens to renounce their citizenship | implicitly recognizes the right to renounce citizenship. Renunciation of citizenship is particularly relevant in cases of multiple citizenship, given that additional citizenships may be acquired automatically and may be undesirable. Many countries have pragmatic policies that recognize the often arbitrary nature of citizenship claims of other countries and negative consequences, such as loss of security clearance, can mostly be expected only for actively exercising foreign citizenship, for instance by obtaining a foreign passport. People from some countries renounce their citizenship to avoid compulsory military service. However, some people may wish to be free even of the purely theoretical obligations and | In a purely hypothetical situation for me (American with a liberal arts/humanities degree), what countries would it be easiest to gain citizenship in?
Excluding ancestry, marriage, and buying citizenship. | Aoa,
Has anyone renounced PK citizenship on this sub? What country did you apply from and how long did it take to get the renunciation certificate?
Thanks! | i am trying to look for countries that allow dual citizenship, but are not too hard to get. i get the same thoughts going on with Australia, Canada, Norway and Switzerland for example, but it seems it gets harder and harder to get citizenship due to tougher regulations, especially if you're middle-eastern.
what are some places, in Europe for example, which are easier with their citizenship and allow dual nationality?
i''m researching German right now, and would love some feedback and other opinions out there! | Visa policies of British Overseas Territories Grenada, Guatemala, Honduras, Hong Kong, Iceland, India, Japan, Kenya, Kiribati, Lesotho, Liechtenstein, Macau, Malawi, Malaysia, Maldives, Marshall Islands, Mauritius, Mexico, Micronesia, Monaco, Namibia, Nauru, New Zealand, Nicaragua, Norway, Palau, Panama, Papua New Guinea, Paraguay, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Samoa, San Marino, Seychelles, Sierra Leone, Singapore, Solomon Islands, South Africa, South Korea, Sri Lanka, Swaziland, Switzerland, Taiwan, Tanzania, Tonga, Trinidad and Tobago, Tunisia, Turkey, Tuvalu, Uganda, United States, Uruguay, Vanuatu, Vatican City, Venezuela, Zambia and Zimbabwe. Permanent residents of the United States, Canada or the United Kingdom do not require a visa. They must | Hey, I'm curious about a hypothetical issue in Asylum and Refugee Law.
For context, I'm an IR/Conflict Studies person, and the International Law of War is more my cup of tea... but when it comes to other facets of International Law, I'm lost in a cornfield.
Basically, I'm curious about the processes for a country either acquiring or losing "Safe Country of Origin" and "Safe Third Country Status" I understand that UNHCR and EU have separate structures and processes for this and that at least conceptually, this is based in the Geneva Conventions.
I'm specifically curious as to what processes exist for countries to determine the granting or rescinding of such status to another country in their own asylum policies.
Thanks for your help in advance. | Which country you can go with out passport? | With the unification of Germany, as well as the independence of Poland and Czechoslovakia, the question of national identity for many citizens has been raised in the newly unified Germany. With roughly 14 million Germans forcibly removed from Eastern Europe, many have lived in Germany longing for the return to their ancestral homes.
Unfortunately, much of these people have lost their land in Poland and in Czechoslovakia, though their desire to return to the respective nations has not been lost. Though they are still ethnically German, many have begun petitioning the German government to allow for the migration of these displaced people to the former German territories of Poland and Czechoslovakia. While the German government has no issue with this, as our efforts on the international stage are to push towards a greater, unified Europe, we understand there maybe hesitations from Poland and Czechoslovakia. We hope that in an effort to promote peace and prosperity among European states, the repatriation of ethnic Germans back into Poland and Czechoslovakia will be welcomed.
We look forward to further cooperation between our countries, as we look to improve the relationships in post-Cold War Europe. | 256 | about to relinquish their citizenship do not become a stateless person and many countries require evidence of another citizenship or an official promise to grant citizenship before they release that person from citizenship. Some countries may not allow or do not recognize renunciation of citizenship or establish administrative procedures that are essentially impossible to complete. Mexico requires renunciation of all other citizenships as a condition of naturalization. Israel allows dual citizenship upon naturalization through the Law of Return, but Knesset (Israeli parliament) members are required to renounce all foreign citizenships. Renunciation of citizenship is most straightforward in those countries which | who does not have israeli citizenship under the law of return | where does renunciation of citizenship occur in the immigration and nationality act | nigerian citizens can renounce their citizenship if they are signatories to which international | who decides if swiss citizens have multiple citizenship | Can you renounce your citizenship while not belonging to another country? | Citizenship Renunciation Timeline | the concept of flexible citizenship is also known as | Renouncing US Citizenship? |
257 | Robert Permane | What movies were Robert Pattenson in? | John Perin (born 10 June 1948) is an Australian former football (soccer) player and coach. Perin played five times for Australia.
Perin is a member of the Australian Football Hall of Fame.
References
1948 births
Living people
Australian soccer players
Australia international soccer players
Association football midfielders | Henry Pering Pellew Crease let the Indians alone." In 1870 he was appointed a judge of the Supreme Court of British Columbia and retired from his government post. Crease was suspicious of both Confederation and responsible government, largely because they threatened greater government control over judges and central Canadian domination of patronage. Like many British Columbians, he was disappointed that London seemed to have given up on BC as an independent colony, abandoning either it to annexation to the United States or confederation with Canada. "I believe that England is sick of her Colonies," he wrote, "and to be a Colonist, whatever your POSITION | What is Dave Pelzer? | What is ryan sheckler's adresses? | Who are the agents for john robert powers? | Where can i find more pictures of dave pelzer when he was young? | John Henry Holland ( February 2 , 1929 -- August 9 , 2015 ) was an American scientist . He was Professor of Psychology and Professor of Electrical Engineering and Computer Science at the University of Michigan , Ann Arbor . | 257 | Robert Constantin "Bobby" Permane (January 21, 1924 – October 24, 2017) was a Thoroughbred horse racing jockey whose successful career included riding future Hall of Fame inductee Stymie to thirteen wins. Fittingly, in 1951 Permane won the Stymie Purse at Bowie Race Track in Maryland.
Entertainment career
Robert Permane was born in Camden, New Jersey to parents who were vaudeville performers. At age eight he was competing in equestrian events for ponies. Prior to embarking on his career as a jockey in Thoroughbred racing he had success as a singer, performing on radio and touring the United States and Australia.
Jockey career
In August 1943 Permane made his professional riding debut at Garden State Park Racetrack in Cherry Hill, New Jersey where on August 31 he earned his first win. The following year he was the leading jockey at Tropical Park Race Track in Miami, Florida. In April, during the track's 1944 spring meet, Permane rode a record five winners three days in a row. Permane was also second in total wins in New York State in 1944 and third in 1948. He was severely injured in March 1949 in a racing accident at Gulfstream Park which would require eight operations that put him out of racing for fifteen months, not returning until June 3, 1950.
Among his other major successes, Robert Permane won the 1944 Jockey Club Gold Cup aboard Bolingbroke, and the 1946 Santa Anita Derby for Maine Chance Farm aboard Knockdown. Then, in the U.S. Triple Crown races, he rode Knockdown to a fifth place finish in the 1946 Kentucky Derby and to fourth in the Preakness Stakes. In 1947 Permane won the Hollywood Gold Cup and Sunset Handicap aboard Cover Up and in 1950 rode the filly Busanda to victory in the Alabama Stakes.
When his racing career was over, Robert Permane and his wife made their home in Florida where they built Carlyn Estates Trailer Park in Palmetto. He died on October 24, 2017 at age 93.
References
1924 births
2017 deaths
American male singers
Vaudeville performers
American businesspeople
American jockeys
People from Camden, New Jersey | in what year was jockey irad ortiz born | when did rené r douglas become a jockey | where was junior alvarado jockey born | when did armstrong's barn win a michelin star | Bobby Cunliffe (footballer, born 1945) | in which year did british jump jockey bob champion form the bob champion cancer | how old was pert kelton when she died | where is the jockey cash asmussen born |
258 | A FULLY AUTOMATED TEST BENCH FOR THE MEASUREMENT OF THE FIELD DISTRIBUTION IN RFQ AND OTHER RESONANT CAVITY | The response of electric field probes to realistic RF environments | This paper reports a novel technique to estimate the total averaged power emitted by a device under test placed inside the working volume of a reverberation chamber in a radiated emission test. The electromagnetic field inside the chamber is stirred by the application of the multiple monopole source stirring in receiving mode, that is a particular way to implement the source stirring technique; in this scenario an array of monopole antenna is placed onto the chamber walls and sequentially connected to the measurement system to get the stirring action. The procedure for the radiated emission estimation requires that chamber has to be calibrated by a set of measurements. In the paper the calibration results are compared to the prediction of the analytical model, developed to predict the chamber's performances. | Simple analytic methods have been developed for high‐accuracy measurement of the quality factor Q of reflection and transmission microwave cavities. These methods are based on the consideration of cavity equivalent electronic circuit models and use measured cavity parameters over a narrow frequency range spanning the cavity resonance frequency to determine the Q factor. Since only straightforward frequency and power measurements are necessary, these methods are well suited to computer‐aided data acquisition and analysis. Specific results are presented for a standard X‐band reflection cavity with a Q of 2699.1±0.5 and a high‐Q X‐band cylindrical cavity with a Q of 23112±4. | In this paper, we discuss the calibration method of non-resonant probe. The complex antenna factor measurement with three-antenna method is used. In the experiment, a nonresonant probe and two reference dipole antennas are used for the measurement in anechoic chamber. The validity of the proposed method is verified through simulation and measurement. | Equivalent circuit model is used to calculate field distribution of a coupled cavity chain. An RF cavity can be represented as a resonant LC circuit and the coupler as an idealized transformer. By solving the equations of the circuit model and simulating each cavity shape, the field distribution of the entire cavity chain is calculated. This method is very useful in particle dynamics simulation and accelerator geometry design. Calculation result and experimental measurement of a 16MeV BTW(backward traveling wave) linac is presented. | A superconducting accelerator module is developed for the CAEP THz-FEL facility, which contains two 1.3GHz 4-cell TESLA-type cavities. This paper presents the microwave properties study of the 4-cell cavity. The microwave parameters of the cavity were simulated, such as frequencies, R/Q values, and HOM passbands etc. The most harmful mode types have been identified according to simulation results. And the frequency and field flatness of the fundamental mode were adjusted to satisfy the operation requirement. The Qe of the pickup port and the HOM coupler ports were measured by microwave measurement at room temperature. The measurement techniques and results are revealed in this paper. | Abstract A field distribution with azimuthal symmetry and longitudinal uniformity, which is required for a four vane type RFQ cavity, could be generated in the 300 MHz model cavity driven by a single loop coupler. The field is tuned by using end capacitive tuners. An effective area of a coupling loop required for the impedance matching is estimated well by an equivalent circuit analysis. The vane tips approximated by a circular arc generate the electric field distributions expected in the acceleration bore sufficiently. This paper also describes the experiments for examining the following subjects: (1) effect of changing the end spaces of the cavity on the field distribution, (2) effect of interstitial vanes on the mode separation between the TE210 and TE110 modes, and (3) field tuning in the cavity when a positioning error of one vane is consciously enlarged. | Three cavity resonators for the investigation of the electrical surface characteristics of conductors at millimeter−wave frequencies are described. They are an H−guide resonator and two rectangular cavity resonators optimized to give high accuracy and good repeatability of measurements. The investigation in which these cavities are used involves Q−value measurements at 35 Ghz with polished and rough surfaces. | 258 | As part of the RF studies of the resonant cavities of the “IPHI” accelerator project (“Injector of Proton High Intensity”), a fully computer controlled bench for the field distribution measurement has been developed. Based on the perturbation method, the acquisition of the s21 transmission coefficient phase shift is synchronized with the displacement of a bead. A systematic study of the noise and uncertainties has led to a clearly enhanced signal over noise. The measured raw data are then converted to a quantity proportional to the electromagnetic field magnitude. Specifically for the RFQ tuning study, different transverse section positions where to guide the bead have been tested on our RFQ cold model. | Integration of LHCD system with SST1 machine and its high power rf performance in vacuum | A new Schottky-pickup for the Cooler Synchrotron COSY [1] at the Forschungszentrum Julich was developed, tested and installed. The new pickup with four diagonally arranged plates replaces the two 1 m long Schottky–pickups used until now in COSY. The previous ones were removed mainly to gain space for new installations (e.g. rf-cavity, experimental devices), but also to increase the horizontal aperture. The available space for the new pickup is only 0.8 m. The pickup plates can be combined by means of relays to measure either in the horizontal or in the vertical plane. The pickup can also be used either as a sensitive broadband beam position monitor or as a tuneable narrowband pickup for Schottky-noise analysis with ultahigh sensitivity. A new method for resonant tuning of the Schottky-pickups for transversal measurements was developed. The differentially excited resonant circuitry enhances the sensitivity by about a factor of 30. The pickups are also used for dynamical tune measurements (tune meter) in the acceleration ramp [2]. | We present energy spread and bunch length measurements at the Accelerator Test Facility (ATF) at KEK, as functions of current, for different ring rf voltages, and with the beam both on and off the coupling resonance. We fit the on-coupling bunch shapes to those of an impedance model consisting of a resistor and an inductor connected in series. We find that the fits are reasonably good, but that the resulting impedance is unexpectedly large. | Electromagnetic analysis and modeling of the coax-to-triplate transition for the pulse-compression section the ZR accelerator | Emittance and proton fraction measurement in High current electron cyclotron resonance proton ion source | A POSSIBLE RF SYSTEM FOR CERN RCS | As part of the LHC Injector Upgrade project, the CERN PS Booster will be required to operate at nearly doubled intensity with little allowable increase in emittance growth or beam loss. A campaign of nonlinear optics measurements from turn-by-turn trajectory measurements, with the goal of characterizing and then compensating for higher-order resonances, is planned for after Long Shutdown 1. The trajectory measurement system is expected initially to require high intensity beam in order to have good position measurement resolution, so understanding space charge effects will be important for optics analysis. We present the results of simulations of driven beam oscillations with space charge effects, and comparison with trial beam trajectory measurements. | Development of a fast scintillator based beam phase measurement system for compact superconducting cyclotrons. |
259 | Is discipline really superior to motivation ? | I'd like to get everyone's idea as to what motivation is. Answer what it is, how it affects people, how to be motivated, and why it's important.
I think motivation is a state of mind revolving around a goal. And a goal is a really loosely used term here. Motivation is the desire and discipline to achieve it.
Motivation causes action in people. Without motivation, action would be almost nonexistent. For example, you are hungry. Your goal is to eat and get rid of that feeling, so you get your fat ass off the couch, and grab some mac n cheese.
How to get motivated? Educate yourself about what it takes to achieve your goal, and take action towards achieving it. Often easier said than done.
Finally, motivation is important because without it, our world would not be great. People in general are hard wired to maximize reward, and minimize risk. Less work, more money. Lot's of dopamine, for very little effort.
One more thing- Motivation isn't something people are born with. I believe its something people develop based on their goals, experiences, and upbringing. I think that much like physical power, will power is something you must work on every single day. | Many people make fun of Tony Robbins’s show because of his advice that sometimes seems trivial, such as “to achieve something one should start doing it”. But his shows always fill stadiums, thousands of people buy enormously expensive tickets to get to the show that looks more like a pop star concert than a business event. Why do they do so? Because they need motivation.
There are tons of books about motivation. A lot of people feel a lack of motivation and look for a way to increase it. It is considered that the most successful people in the world are the most motivated ones. It seems that they always have enough energy to work hard and to remained creative. But this is a dangerous illusion.
Everyone who tried to do something big, something time-consuming (such as constructing a building or launching a new business), knows that discipline is much more critical than motivation. It is a hard everyday work, and to plan it carefully is more important than to keep motivated. And if you have a good plan, you just do it – step by step, whether you feel much desire to do it at any particular moment or not.
But an idea of hard work is not easy to sell. People don’t want to buy and read books about hard, tedious work. They’d rather read something promising, a book helping them get quick results – and to do it easy. So the books of that kind are bestsellers.
Motivation is essential for everything – for business, for work, for education. But motivation is not enough. Motivation comes and goes, and it is quite reasonable. Sometimes we just feel too tired, exhausted. Sometimes we hate our job. Such things happen, and discipline is the thing that helps overcome it.
But people don’t like discipline; they search for motivation because it is more emotional. Work brings more fun when you overwhelmed by positive emotions. So when people do not feel much desire to “go the extra mile”, they buy a new motivating book.
The problem is that when they finish the book, they believe that the mission is accomplished, the job is done. They think that it’s enough. The success formula looks as “motivation + discipline,” and the lack of the later can’t be compensated by the excess of the former. One needs both to be successful.
Sometimes motivation is just an illusion of doing, as posting many posts on Facebook is an illusion of political or social activity. This is especially true for younger generations. My conception of Life Strategy, described in a book that was published in Russian two weeks ago (and soon, I hope, will be translated to some more languages) is much more about discipline than motivation.
Would you like to be successful? Be disciplined. | While existing research has demonstrated that intrinsic motivation can increase task performance, jobs are composed of multiple tasks, and it remains to be seen how intrinsic motivation in one task... | Motivation is the energising force that initiates and sustains behaviour and ultimately produces results. Many motivation theories focus on the amount of motivation, with a larger quantity said to result in improved outcomes. However, as educators we should not focus on generating more motivation from our learners but instead focus on creating conditions that facilitate the internalisation of motivation from within our learners. | So, if you identify your values rationally, put them in a hierarchy and plan the ways to pursue them, you don't need to boost motivation. Having motivation in this case is self-evident. Correct? | Self-discipline is indeed a vital factor in achieving success that one desires. This book is an effective tool to build that self-discipline. It has great tips and advice. I learned that some traits/skills that I thought are positive and could help me achieve my desired success are, otherwise, disadvantages and that they would make me more unproductive. This book is enlightening for me and teaches me to do away with these traits, change my perspective and build self-discipline. This is a great book indeed. | Abstract Nygard, R. 1976. Persistence at a Difficult Task with Alternative Task of Intermediate Difficulty: Some Comments on Feather's Study. Scand. J. educ. Res. 20, 41‐48. According to Atkinson the motivation to avoid failure among subjects (Ss) in whom the motive to avoid failure is stronger than the motive to achieve success (Mf > Ms) reaches its maximum when the subjective probability of success (P3) is .50. On this basis Feather suggests that when Mf> Ms Ss are confronted with a very difficult task (Ps Ms Ss. An alternative, probabilistic use of the achievement motivation theory is suggested, according to which the likelihood of a shift to the alternative task should be higher among Mf > Ms Ss with a relatively high Ps ... | Motivation the initiation of behavior and the end state is close. With an overly restricting time restraint, the subject could potentially feel overwhelmed, which could deter the subject from achieving the goal because the amount of time provided is not sufficient or rational. This explains why some children are more motivated to learn how to ride a bike than to master algebra. A goal should be moderate, not too hard or too easy to complete. Most people are not optimally motivated, as many want a challenge (which assumes some kind of insecurity of success). At the same time people want to | 259 | I wanna start by saying that I perfectly understand why discipline is an important quality to have. Discipline is the thing that makes you go to the gym even if you feel lethargic and depressed so that you go there, lift heavy things and end up doing a fantastic training.
Discipline is the thing that allows you to wake up in the morning to do the job that will pay for your bills
But what about the severely depressed people ? The ones who have neither motivation nor discipline?
The low T, depressed betas. Can they really strive with discipline alone, when their discipline is so weak ? I think not
I think people like that need to believe at 200% that they can change. They need to believe that they can be happy, they need to become incredibly optimist, so that they can now understand why discipline has a purpose and how things will get better if they stick to it and never give up.
So how does one get motivated ? Swallowing the red pill can be very bleak for blue pilled addicts who got their views totally shattered.
Have we underestimated the roles of motivation, testosterone and realistic optimism in this road of se elf-improvement? | I read a post about how what you need isn't motivation, but discipline. How do you cultivate discipline? | Struggling to stay motivated when not progressing | [NeedAdvice] Has anyone here beat depression, or know how to become disciplined while depressed? | Daily discipline? My poor butt | Great guidelines for how to start setting up a positive discipline system in the house | Need help staying motivated and focused | Tips on how to achieve Self-Discipline? | New Ideas on how to build self discipline |
260 | Keynote Speaker 2 Intelligent Pattern Recognition and Applications - An Interactive E-Learning System, Modelling and Simulation | "Eigenlips" for robust speech recognition | In this paper, TMS320C541 was used to realize auto speaker recognition system. The system utilizes a new eigenvector aggregate of phonetic signal and takes advantage of fuzzy technique to realize speaker recognition based on text related. The experiment result reveals to be with high recognition rate, real-time, and with little memory consumption, so this system is an effective hardware realization. | This paper addresses the problem of speaker diarization in the specific context of meeting room recordings. Some new enhancements to the E-HMM-based speaker diarization system are reported. These involve a different approach to speaker modelling utilising EM/ML-based training rather than MAP adaptation as in our previous work. Using the new system we investigate the effects of speech activity detection through speaker diarization experiments conducted on 23 meetings extracted from the NIST/RT evaluation campaign datasets. We propose a new approach, which assigns confidence values according to the type of information carried by the signal and incorporates these values directly into the speaker diarization system. Experimental results show that, perhaps surprisingly, the non-speech segments do not systematically affect the robustness of the speaker diarization system, and more precisely the speaker model training process. | Speaker-Corrupted Embeddings for Online Speaker Diarization | Speaker-Corrupted Embeddings for Online Speaker Diarization | What is the state of real-time speaker diarization in 2021? It is real hard to find any working examples online. | Abstract A typical spoken content retrieval solution integrates multiple technologies that belong to the areas of automatic speech recognition and information retrieval. Due to the rich set of challenges – many of them language specific – as well as widespread impact, numerous research sites in the world are actively engaged in this research area. This special issue highlights some of the recent advances in spoken content retrieval. | Performing speaker diarization of a collection of recordings, where speakers are uniquely identified across the database, is a challenging task. In this context, inter-session variability compensation and reasonable computation times are essential to be addressed. In this paper we propose a two-stage system composed of speaker diarization and speaker linking modules that are able to perform data set wide speaker diarization and that handle both large volumes of data and inter-session variability compensation. The speaker linking system agglomeratively clusters speaker factor posterior distributions, obtained within the Joint Factor Analysis framework, that model the speaker clusters output by a standard speaker diarization system. Therefore, the technique inherently compensates the channel variability effects from recording to recording within the database. A threshold is used to obtain meaningful speaker clusters by cutting the dendrogram obtained by the agglomerative clustering. We show how the Hotteling t-square statistic is an interesting distance measure for this task and input data, obtaining the best results and stability. The system is evaluated using three subsets of the AMI corpus involving different speaker and channel variabilities. We use the within-recording and across-recording diarization error rates (DER), cluster purity and cluster coverage to measure the performance of the proposed system. Across-recording DER as low as within-recording DER are obtained for some system setups. | 260 | This talk deals with fundamental aspects of Intelligent Pattern Recognition (IPR) and applications. It basically includes the following: Overview of 3D Biometric Technology and Applications, Importance of Security: A Scenario of Terrorists Attack, What are Biometric Technologies? Biometrics: Analysis vs Synthesis, Analysis: Interactive Pattern Recognition Concept, Importance of Measurement, How it works: Fingerprint Extraction and Matching, Iris, and Facial Analysis, Authentication Applications, Thermal Imaging: Emotion Recognition. Synthesis in Biometrics, Modelling and Simulation, and more Examples and Applications of 3D Biomedical Imaging and Vision in Interactive Web/Video Networking Fuzzy e-Learning Environment. Finally, some future research directions are discussed. | DATA TRANSMISSION IN BIOMETRICS OVER THE INTERNET | Investigation of multidimensional data using the interactive pattern analysis system ispahan | An application of biometrics in the web regarding health insurance | This paper briefly reviewed the research background of iris recognition and its development.Gave a survey of existing automatic iris recognition methods,mainly aiming at the latest progress.Concluded and distilled key factors of research difficulties as suggestion to future research. | Today, the use of mobile phone among individuals with an advanced technology, acquisition and computation resources is crucial in securing personal data and services as well as in identifying a person. Furthermore, there has been growing interest of researchers using mobile as an acquisition device to capture an eye image in a non-cooperative environment (static motion and at different distances) for iris recognition. However, the use of mobile as an acquisition device still facing some noise factors because the quality of image captured in this environmental condition is low compared to a camera device. Besides, low awareness of user in handling the mobile devices and lack technical experiences in capturing iris images with this environmental condition is generally uncontrolled contribute to producing unpredictable low quality of eye images. Due to these issues, it led to incorrect segmentation of iris boundaries and subsequently lowered the ability to match the iris features. Hence, this condition contributes to performance degradation of iris recognition system. Therefore, to improve the ability to match the iris features in mobile iris recognition system, a combination with neural network is proposed. The iris database used to test against these methods is CASIA-Iris-M1-S2. The proposed method, a combination of Hamming distance and neural network has achieved a better result where it increases the existing method in term of accuracy for mobile iris recognition under non-cooperative environment. | Biometric authentication is an effective method for automatically recognizing a person’s identity. In our previous paper, we have considered palm print for human authentication. Recently, it has been found that the Finger Knuckle Print (FKP), which refers to the inherent skin patterns of the outer surface around the phalangeal joint of one’s finger, has high capability to discriminate different individuals, making it an emerging biometric identifier. In this paper, the local convex direction map of the FKP image is extracted. Then, the local features of the enhanced FKP are extracted using the Scale Invariant Feature Transform (SIFT), the Speeded Up Robust Features (SURF) and frequency feature. SIFT are formed by means of local patterns around key-points from scale space decomposed image. Feature vectors through SURF are formed by means of local patterns around key-points which are detected using scaled up filter. The frequency range of pixel levels in each image is employed by using Empirical Mode Decomposition (EMD). For the authentication of FKP image, we used shortest distance between the query image and the database, to evaluate their similarity. Here, we use PolyU FKP database images to examine the performance of the proposed system. The proposed biometric system is implemented in MATLAB and compared with the previous palm print human authentication system. For the same person, the matching score of the two methods are fused for the multimodal biometric recognition. The experimental results demonstrated the efficiency and effectiveness of this new biometric characteristic. | Violent crime scenes often register incomplete/broken bloodstained footprint impressions. It is often difficult to make predictions from broken footprints obtained from a crime scene. Though it is easy to differentiate a complete footprint from complete shoeprint, such differenti ation does not stand easy when attempt is made to distinguish an incomplete footprint from an incomplete shoeprint owing to large variation in foot size, shoe size and shoe make. Hence, this study is an attempt to develop a computer based methodology that an incomplete bloody shoe and footprint. When tested on a dataset of 237 prints, a footprint/shoeprint classification accuracy of 81 % was achieved (Sensitivity | Lecture attendance data at universities is a reference in showing the credibility of each student used by lecturers as data for student grades as well as an evaluation material for the success of teaching and learning activities in lectures, but there are several examples of cases related to student attendance data currently prevalent in the world of education or lectures is the phenomenon of "Leave Absence" or better known as TA. In addition, other problems also arise from lecturers and administrative staff, namely difficulties in monitoring student attendance and efforts to validate attendance data because of the large amount of student data. Therefore in this study a system was proposed to reduce the level of fraud in filling the attendance list and effectiveness of student data processing using a system of applying the concept of the Internet of Things (IoT) with the fingerprint presence method. Existing system modeling results are expected to be able to support the service of processing academic data automatically and produce accurate and accurate statistical data and be able to reduce data manipulation factors from irresponsible parties. |
261 | White tree ? ( Garden of Tranquillity ) | Anyone know the name of the tree that is flowering right now with tons of bright-white flowers?
They aren't common, but they're doing their thing right now and it always makes me happy since they're usually in a sea of bright green spring leaves and the blooms just blast through with white...
There aren't many in town - one in Pier park maybe. | Any help on where to rid your tree would be great! NE, SE, SW, NW? | Hey all,
I've been trying to build a tree park to get my second last room done, but I haven't come across a leafy tree anywhere in the game.
I'm also stuck with the last room on the list as it seems none of the lists on Google go that far.
Sorry if these are stupid questions but im so stuck right now. | Two trees that dont have flowers? | Splendid pear trees of the Citadel Park in Poznań | Total and Merchantable Volume of White Spruce in Alaska | The top of the tree is called its? | Were can you find a lime tree? | 261 | Did they keep the white tree with the remake of the white wolf mountain ?
I need it for the Garden of Tranquillity quest and can't seem to find it. | who owns the ski resorts at white wolf mountain | Where can you find white berries in runescape? | Kingsisle needs to update the Celestial Wolf Mount | who owns the rights to a whiter shade of pale | who owns the rights to whiter shade of pale | when was whiter shade of pale released | Is there a complete list of White Wolf books available? | what kind of tree is in mountain lake wilderness |
262 | It is unfortunate that the the inspiration tree, designed for "creative rule bending," has kind of just turned into the "free gold with some perks" tree. | This Xmas tree stand is out of this world, never easier to putting a tree up. Self centers as you push on level. | This is an awful tree, i demand to know why the devs created shared trees only to make them suck. Have any of you mercenaries had luck with the pyrotech tree? | I hate how boomkin looks but I have to change into this form...why not keep the tree? Used to be pretty neat. | What does a tree symbolizes? | I love seeing everyday designs while on acid. Trees are a favorite of course. I always see thousands of polygons between the tree branches. Anyone have anything they've seen that blew your mind? | LOVED THIS. It even has a smoked wood smell that was amazing as I took it out of the box. I really loved the font and size of the ornament. Perfect weight so once on our tree it will not pull down the branches. Great find and can't wait to put it on our tree. | a perimeter access road, so the size of the grove is static and is unlikely to continue spreading. The grove can be seen in the Disney true life adventure/fantasy film "Perri" (1957). Crooked Trees The Crooked Trees, Crooked Bush, Twisted Trees or the Crooked Trees of Alticane are a grove of deformed trembling aspen trees of type Populus tremuloides Michx. found in Saskatchewan, Canada. They are found approximately twenty kilometers north-north-west of the town of Hafford, Saskatchewan and just over five kilometers south-west of Alticane. The trees, prominent in Saskatchewan folklore, are dramatically different from the un-twisted aspens just across | Who wroteThe Giving Tree? | 262 | The most meta choices from this tree include:
Klepto- most of the power comes from free gold, though i wont pretend the items arent nice.
Slightly magical boots- free 300 gold boots, 50 gold discount to upgrade. Movespeed is nice.
Stopwatch- i would say the power is actually mostly in the active but quite a bit is the free 300 gold (or a bit less if you sell it)
The above three are the most meta choices from inspiration. I guarantee whatever source you use, if you look at champs that are running inspiration primary, klepto is nearly always their keystone with the two other runes (with a few exceptions) i mention, probably with the 5% cdr as well.
Champs that go inspiration secondary usually take free boots and free stopwatch.
I know that some supports will take hexflash for the mid pressure. I fully admit this.
The other exception is that lots of supports like futures market, which kind of also boils down to FREE GOLD!
I just feel like this tree had a ton of promise, but just turned into the free gold tree and thats kind of sad. | What is your non-meta rta pick that you still use more often? | Best build for MF or Lucian | What is your favorite off-meta champion role/build/rune setup? | Strongest sorcery build in the game hands down. | [HC] Best non-RF build to play with Mana Guardian? | Best Sonya Build for my Team Comp? | What's your favorite non-meta perk to use? | Who are the current best split-pushers for Gold/Plat Elo? |
263 | what is the life of the nissan fuga hybrid | Nissan Fuga the Fuga is a replacement for the long running Nissan Cedric and Nissan Gloria series of cars and later succeeded the Nissan Cima along with the Nissan President. The name of the vehicle is the Italian word for the fugue, a composition musical form. The name Fuga was chosen to suggest that the long, storied histories of the Cedric, Gloria, Cima, and President are being combined into a new vehicle. When the Prince (Nissan) Gloria was first introduced in 1959, it was based on a stretched version of the original Prince (Nissan) Skyline, which was first introduced in 1957. Nissan | How is the hybrid car good for he invirment? | The scope of the research project “Hybrid Concept with Minimal Diesel Engine” (FVV 937) was to analyse and evaluate designs of hybrid vehicles with simplified diesel engines using computer simulation. The project was conducted in cooperation between the Institute for Internal Combustion Engines (TU Munchen) and the FZG Gear Research Centre (TU Munchen). It is the goal to find advantages for hybrid vehicles compared to conventional reference vehicles in the trade-off between fuel economy, emissions, vehicle dynamics and cost. | Abstract In the last few years, the different teams have dramatically improved the directly injected, electrically assisted turbocharged, internal combustion engine of FIA F1 hybrid electric cars. With limited fuel flow rate, but unlimited boost, the engine is now delivering peak power at fuel conversion efficiencies about 45% running lean stratified with the help of some sort of jet ignition. The paper analyses the energy flow of a FIA F1 hybrid electric car covering one lap of the Monte Carlo race track of length 3.370 km. The amount of energy recovered is minimal, at the most 2 of the 9.77 MJ of braking energy, or 20.6%. The fuel consumption per lap, 1.16 kg of fuel, or 50.34 MJ of fuel energy, needed to deliver the 16.28-18.28 MJ of propulsive energy, at an outstanding average efficiency of 32 to 36%, may still be dramatically reduced. New rules are thus proposed to promote the development of technical features that could be beneficial to passenger car applications, from advanced turbo-compounding, to enhanced thermal and mechanical energy recovery, and better hybridization. | Practical, simple, sturdy, reliable, understated…. All the things you’re supposed to look for and like in a soulmate, right? Not all of us listen to the adults in our lives, even though their words of wisdom are often worth heeding. If your anciaños are telling you (wisely) to get a smart, practical car so you can have more party money, listen to them, because they just may direct you to the 2017 Nissan Sentra.
Believe it or not, at one point in time, this car used to be snazzy and whiz-bang and reeked of German engineering, with a bit of BDSM thrown in to boot. Today, it’s matured a bit, and now the Sentra is a ‘smart’ car offering plenty of interior room and even a turbo for right around $22K. And if you don’t want or need a turbo, get the base level S trim and save five-grand, since the base model starts at $17K, which nowadays is a steal.
Driving this sentry around town, it was easy to forget about it, because it doesn’t wow or dazzle you. It’s sorta like the rescue pet that chose you and now it will always be there, waiting patiently outside, to rescue you and deliver you from sin or whatever antics you may find. It’s one thing to go crazy, it’s another thing to get home in one piece. The 2017 Nissan Sentra will always get you home safely.
New this year is the offering of a 1.6-liter turbocharged engine on the SR trim. (The alphabet soup of trims goes from base to top with S, SV, SR, SL, SR Turbo and NISMO.) I tested the turbo, and it was truly a lot of fun in a safe, practical way. The SR Turbo trim won’t win you any drag races, but it does give a pep to the car that can make you feel like you aren’t completely without power. I can’t say you really need a turbo on the Sentra, so I would start with the base S trim and see if you can live with 29 city / 37 highway miles per gallon. (The turbo does slightly less, coming in at a combined 28 mpg.)
One of the most impressive features about this small sedan is that there really is plenty of room inside and in the rear. Piling a bunch of bears in the Sentra is not too difficult because it does offer a fair amount of head and hip room, something that can be tough to find in any car with practicality. Spilled nachos or shamrock shakes in the car are a breeze to clean, although you first have to remove the bears before you bring in Mr. Clean. (Check on this incredibly GAY commercial for Mr. Clean from the 1950s.) With all seats up, you get about 15 cubic feet of space in the rear, and that ain’t bad for the class. I enjoyed the Sentra, my passengers didn’t really notice it, and nothing adverse happened, other than the hot fast food that hit the ground when I was a little stiff with the clutch.
(Speaking of which, the 2017 Nissan Sentra has one of the easiest clutches I have driven in a while. I admit, I’m lousy with a clutch, Prada or otherwise, but I had no trouble shifting this one while also handling a Cher CD, nachos from Kum n Go and a shamrock shake from McDonald’s.)
Be sure to check out the other cars in this small sedan category, to include the Nissan Versa, a car I really like because it’s smaller but not tighter, has four doors and a generous amount of interior room. If street parking is a concern, the Versa is easier to handle than the Sentra, but both maneuver well through any rough or smooth situation.
When it comes to the loves of your lives, like sands through the hourglass, so go our loves, but hopefully they leave you with good memories. No car lasts forever, so why not get a car that you can afford and will be always ready to rescue you and take you home every night of the week? The Sentra can do that for you.
And that smart choice will give you more money for the burly blond who only orders call drinks when you’re buying….
Like this: Like Loading... | Given the chance, would you buy one again? Or would you go with a standard TT or fifth wheel? I love the layout and extra space the fold-out beds provides, but I haven't found info from anyone who has gone full time with a hybrid.
We would get the heated beds and stay in more temperate climates, so I wouldn't think winters would be too big of a deal. (And I'm used to fall camping in the northern Midwest). | Kia Optima economy ratings. A Hybrid version has not yet been announced, however, it is likely that Kia will release a hybrid Optima by 2017. Like its Hyundai Sonata Hybrid platform mate, the existing Optima Hybrid will most likely continue to be sold as a 2016 model, with the new model debuting by mid-2016. An all-new, upscale interior will offer an optional UVO infotainment system, with support for both Apple's CarPlay and Google's Android Auto technologies. Top-of-the-line Optimas will include a hand-stitched dashboard, quilted luxury leather seating surfaces, high-quality aluminum interior trim panels, Advanced Smart Cruise Control, a Surround-View Monitor, and Bi-Xenon | The performance characteristics of current and future electric vehicles are examined and compared to projected heat engine vehicle parameters. The shortcomings of electric vehicles in the near-term time frame are discussed. It is predicted that the all-electric vehicle will not gain wide acceptance in the near future because of degraded performance characteristics. Because the near-term low-acceptance level of electric vehicles is caused by their overall lower performance level, a hybrid concept is examined which the authors believe can give an enhanced performance level in the short-range future. This type of vehicle is proposed as a much needed transition system to provide an evolutionary change from the heat-engine system vehicle of today to electric vehicles with acceptable performance in the future. (ERA citation 03:007066) | 263 | Nissan Fuga and the transmission, produces from 1.3kWh lithium-ion batteries that are expected to have a service life of 10 years. The batteries are installed upright behind the rear seats. The Fuga Hybrid introduced Nissan's first in-house developed electric hybrid technology, and Nissan claims it will double the fuel economy of its gasoline-powered version. A driving mode selector knob has been installed as standard equipment on all models, situated below the transmission gear lever and between the heated and ventilated front seat controls, providing four selections labeled "Standard", "Sport", "Eco", and "Snow", allowing the 7-speed transmission, engine and various systems to optimize | is nissan kicks a hybrid? | the nissan fuga is a replacement for which car | what type of alloy is used in the nissan fuga | when did nissan change the engine in space arrow | where was the nissan maxima made in australia | who did nissan end its relationship with in 1991 | what is the power of a car in the china f1 | what is the nissan rd diesel engine called |
264 | to refill over and over would get expensive after awhile and may as well just buy a better bag with better filling | Just what I needed to refill my son's Big joe chair! There is plenty of filling to accomplish refilling your chair and then some, in case your wondering as I was before purchasing.... | This is a great product, it works excellently, and is easy to hide under clothing. This system comes with one fill of hand sanitizer (which smells great, by the way). But what I didn't realize was that you can't refill the pouch... you have to buy new ones from the manufacturer's website for $4.50 each!! And considering the amount in these, that is definitely NOT a good deal....needless to say, I'm going to try to figure out some way to refill this. Otherwise, I don't see myself purchasing over-priced refills for the rest of this product's life. | These bags were not reuseable. Some did not work well often losing air and puffing back up again. Frustrating. Oh well....live and learn. | Very happy with the bean bag refill. Just what we needed. | Hi everyone! I hope this is allowed here.
I've started making choux puffs and craquelins. Have filled them with custards and diplomat creams. Unfortunately they need refrigeration and right the next day the puffs becomes yucky and soggy. Are there any fillings that don't require the fridge?
If not, am i storing/filling them wrong?
Thanks!!! | It never over heats but no way to make bags up. they want you to buy the pre sealed bags. | Not as expected. I bought cheaper ones that had more resilient filling than this one. Just seems cheap to me. | As promised. Easy to fill and empty. Would reorder or recommend. | 264 | for the price it was decent, but the filling went flat quick. to refill over and over would get expensive after awhile and may as well just buy a better bag with better filling. | I think its over priced and the process of filling ... | Excellent quality Bean Bag Filling | easy to refill and it is solidly attached | Looks like the refill was already empty | Happy with Bean Bag Refill | Works great, but hard to fill | Chinese toilet with no refill tube not filling | For Sale is a great filler game |
265 | This textbook was interesting and easy to read | Great read and easy to understand in spite of the fact that it is a textbook I purchased for a class. Got an A! | This book is a decent text however it's not an easy read. I had to reread some parts to totally get the concept. It's not the worst textbook I have ever been assigned thought. | This is a textbook for school. It was in good shape as advertised. | I learned fairly quickly with this book due to how wonderfully simplified everything was. Examples that the author provided helped a lot in understanding the material. I would recommend buying this book!!! | Unfortunately, this is the book my professor thought we should use for a textbook for a class I'm taking. The author does an extremely poor job of explaining things in this book. No tutorials, which is what helps me the most. Maybe it's good for someone else, but for a textbook, it's awful. | I ordered the actually textbook and they sent me a workbook... Not useful, since I don't have the textbook that I actually ordered | This book is full of useful information. It has came in handy many times. Thank you for including this in your library! | Not interesting, but thoroughly explains the history of the American Constitution. More of a textbook than a book for reading pleasure. | 265 | I used this book for my Intro to Cinema class. This textbook was interesting and easy to read. | I found this book very easy and specific for beginners | A great book if you already understand photography basics, otherwise might be confusing | This is a great book for first time videographers | This book is easy to use and very informative | If you are a visual learner I highly recommend getting this book | I found this book very useful and in depth | This book had lots of helpful information and was an easy read and easy to follow | Got this book for class and its a great tool for learning |
266 | Price of scooty pep plus? | What is the sale price of vicodin on the street? | How much does a 12 pack coke cost? | What is the price of a ps 3 in pakistan? | Specifics: 2004 Rav4; 48k miles; few body dings; excellent interior; no known mechanical issues; winch for a scooter.
I think I have two options
1) sell the car, scooter and winch as a whole unit
2) sell them as individual units
If I find someone that's in need of this exact set up I'd sell it cheap. But I have no idea how to price it. Does the scooter and winch increase the value? Will I make more removing the winch?
Edit: spelling | Trav’s Outfitter has the Roadie 20 for just $119 with free shipping. Here’s the link.
| How much does a case of pabst blue ribbon cost? | The Kawaii T has jumped up in price by almost double, has this been discontinued or is it manipulation? | What is a wooden coca cola crate worth? | 266 | Price of tvs scooty pep? | price of scooters for charge | How much thes ecplies the DVD cost? | How much yo gotti worth? | Cripps prices. I'm not getting it. | What is everyone’s current sky tv package price? | How much is gta vice city for the psp? | Nice television for the price | What are the prices of mr2s? |
267 | Virtual reality as a support tool in the shoe life cycle | ShoeSoleSense is a proof of concept, novel body worn interface - an insole that enables location independent hands-free interaction through the feet. Forgoing hand or finger interaction is especially beneficial when the user is engaged in real world tasks. In virtual environments as moving through safety training applications is often conducted via finger input, which is not very suitable. To enable a more intuitive interaction, alternative control concepts utilize gesture control, which is usually tracked by statically installed cameras in CAVE-like-installations. Since tracking coverage is limited, problems may also occur. The introduced prototype provides a novel control concept for virtual reality as well as real life applications. Demonstrated functions include movement control in a virtual reality installation such as moving straight, turning and jumping. Furthermore the prototype provides additional feedback by heating up the feet and vibrating in dedicated areas on the surface of the insole. |
Introduction
Traditionally, use of technology in footwear manufacturing has been mainly focused on applying CAD/CAM processes to improve shoe appearance and ergonomics [1]. Technology enables the shoe industry to reduce defects, achieve high-quality standards [2], and perform personalized pieces [3]. Besides, virtual reality (VR) technologies are being Guillermo successfully applied to create new footwear models, providing interactive experiences for the visualization of fashion shoes [4].
Throughout the last decades, many efforts have been made by the shoe industry to fully or partially automate some parts of the manufacturing process [5]. However, shoe making involves many tasks, and many of them still employ human operators. Some of these tasks are done by a worker using manual shoe making tools, while others involve human interaction with a specific machine, i.e., material cutting of each shoe pattern, sewing machines for stitching, cementing and pressing machines for assembling parts together, etc. For this reason, the future of automation in footwear industry will require promoting the use of robots [6]. In state of the art, there are innovative solutions combining image processing [1,7] or 3D visual perception with robots [8], e.g., to generate trajectories to cut leather [9] or for robot shoe-groove tracking from feature extraction on the surface of a scanned shoe upper [10]. Furthermore, we can find shoe glue application systems based on visual techniques using shape reconstruction and guided by robotic end-effectors [11,12], and kinematic control of robots to perform buffing and roughing operations on shoe uppers [13,14]. Moreover, robots have also been introduced in other finishing operations such as polishing cream and spraying [15] or collaborating with humans in shoe-packaging process [16]. However, there are tasks where robots have not been introduced yet or they have not been correctly adapted to the variability of the manufacturing process.
In this work, we propose a robotic workcell with a novel visual perception method to compute grasping points in two different scenarios that occur in the manufacturing process. The first scenario consists of soles travelling on a conveyor belt, while the second has soles resting on a custom location. Fashion trends induce high variability in shoe shape and make the grasping task challenging. Recently, reinforcement learning techniques driven by computer vision were used to perform isolated operations of shoe grasping [17]. Even with these techniques, it is still difficult to accomplish a re-configurable robotic workcell at a competitive working speed. Our work is inspired by [18], but, unlike this one, our cell works without the support of other specific machines (e.g., for roughing and cementing). In that work, authors tested the proposal with only one type of shoe, while our system has been tested with 20 different models. Footwear grasping is also present in [19], where authors defined a system to perform pickand-place operations on the last taking 3D model templates as references. We propose to increase system flexibility without using templates or prior knowledge of the shoe model, and without relying on reinforcement learning. Our goal is to move towards a flexible and automated footwear industry 4.0 according to the fundamental underlying design principle presented in [20].
RGBD cameras and robots were successfully used for glue application on shoe soles as shown in [8]. Our proposal allows a robotic arm endowed with a gripper and a RGBD camera to grasp any type of sole regardless of size and model. Usually, size depends on foot length and model defines the kind of material (rubber, plastic, leather, etc.), texture (rough, smooth, etc.), and color. Our method grasps the sole from its contour, avoiding parts with adhesive/glue, so that the gripper is not damaged and the pressing process can be done successfully later. We tested our workcell with 20 real soles of various sizes and characteristics, performing 10 tests per sole in a real environment at INESCOP facilities.
This paper is organized as follows. Section 2 presents the footwear manufacturing process and the current level of automation. Section 3 presents our robotic cell for sole manipulation in assembling operations of footwear manufacturing. Section 4 details the algorithm used in the cell to select the best grasp on soles. Section 5 shows the obtained results using real soles with different features. Finally, Section 6 summarizes our findings and contributions, shows the main limitations of this work, and draws some future research lines.
Traditional issues of footwear manufacturing
Shoe making has always been considered a traditional handicraft process. Shoe manufacturing process consists of many operations which depend on the variety of materials (i.e., fabric, plastic, leather, rubber, foams, etc.) the shoe is made of, as well as on its design. Design is very different according to the kind of shoe (dress, sport, boot, sandal, etc.), its application (i.e., business shoes, derby, sneakers, etc.), and fashion trends. Some of the main operations are cutting, stitching, assembling, cementing, and finishing ( Fig. 1). Each of them requires several tasks.
Cutting deals with the upper of the shoe and it is composed of tasks such as leather selection, marking the pattern within the selected leather piece, and cutting the shape of the upper. The upper patterns must be cut distributing them along the leather sheet, in order to make the best use of space, but, at the same time, avoiding any flaws in the raw material.
Stitching encompasses all the tasks performed to assemble the pieces that make up the shoe. This operation requires a minimum of two workers, one for part assembling and other for sewing. Furthermore, in this phase, some pieces are split so that the overlap among them does not increase its thickness. Besides, some degree of edge thickness is removed to enable bending motion. Prior to stitching, other tasks, such as stamping of some pieces or punching to add the eyelets where the shoelaces would be, can be required.
During the assembling process, the finished upper is molded into a foot shape using a piece called the last (Fig. 2). To do this, the insole is fixed to the last. Both the upper and insole are fixed to each other with adhesive or nails. Then, a stiffener and a side lining piece are included to give support to the sides of the upper when the last is removed. Finally, exterior and interior pieces are assembled and closed together.
The next phase is cementing. First, the molded upper is bevelled, staples or nails removed from the insole, and the surface smoothed. Afterwards, adhesive is applied on previously defined areas of the outsole to fix it with the assembled insole and upper. Sometimes, adhesive activation with heat is required before proceeding with the binding together of the insole and outsole. Last, the outsole is placed on the insole and pressed to consolidate their anchoring. Finally, the finishing process comprises adding finishing touches such as attaching heel, extracting the shoe from the last, ironing, and polishing.
In the last years, footwear manufacturing has become a hybrid process combining three kinds of operations: handmade, machine-aided, and completely automatic with appropriate specific machines. Table 1
(a) (b) (c) (d) (e) (f)
characteristics of the stages shown in Fig. 1. Nowadays, cutting operations have been fully automated with shoe pattern design software and laser cutting robots, while stitching is mostly made by humans with little or almost no machine assistance. On the other side, assembling and cementing are often performed by humans using nonautomatic machines. This work focuses on presenting an automation solution based on strategies of robotic manipulation and 3D computer vision techniques to automate some tasks of the cementing operation. Our aim is to replace operators and machines working at this operation with a combination of robotic arms and fully autonomous machines. The most challenging task of the cementing phase is outsole manipulation. Outsoles are very thin objects, which makes them difficult to grasp.
Fabrication cell architecture
Virtual scenario
We assembled a virtual scenario of the fabrication cell ( Fig. 3) to assess its performance. The virtual scenario emulates the real setup of the cell and it will be imported into Robot Operating System (ROS) [21] to allow simulated runs of the process and diagnose potential issues before performing real experiments. Our fabrication cell is made up of several stations with well-differentiated tasks: scanning and grasping station, rotation station, and assembling station. Each of them uses different visual perception systems to accomplish the interaction with the environment and in each one the number of robots involved is different. First station performs three main tasks on the outsole: scanning, applying glue, and picking up. We use two robots and a laser digitizer for this task. Once the sole is picked up, it is transferred to the rotation station. This station consists of a specially crafted place easily accessible from above and below. This allows the sole to be picked up a second time from below to be correctly orientated to carry out the assembly. In the assembly station, the sole is left on a last to be pressed in a future extension of the cell. For these last tasks, we used a single robot with eye-to-hand configuration and a RGBD camera instead of the laser digitizer.
Real implementation
First, when a sole is placed on the starting position, the conveyor belt turns on and the process begins. For outsole scanning, we use a Gocator 2350D 3D Laser Line Profile Scanner containing a megapixel image sensor that provides up to 1280 points per profile with a resolution of 0.150 mm along the line and 0.019 mm in depth. The scanner is mounted on a structure and attached to a certain position on the conveyor belt. Once the outsole comes out from the scanning box, the belt stops and a Comau Smart Six-6-1.4 robot with a nozzle on its end-effector applies hot glue to it. Finally, the outsole reaches the pickup zone and an UR10 CB3 robot with a Robotiq 2F-140 gripper picks it up. In this first station, we will focus on the grasping of the outsole from the conveyor by the UR10 robot. Our input is the digitized outsole obtained from the scanner and the conveyor position obtained from the encoder of its electric motor. We can make a Gantt chart of the activities performed in this fabrication cell to show their dependencies and what we will focus on (Fig. 4). Once the outsole is scanned, the digitized data is available and the grasping point process calculation starts. Grasping points must be calculated during the time required for the application of hot glue and before the outsole reaches the pickup zone, in order to avoid idle times and perform the process as fast as possible. This requirement makes the grasping point calculation our critical task. It is one of the main contributions of this work. We must find a way to calculate these grasping points in a fast and effective manner from the point cloud acquired from the digitizer.
Once the sole is grasped and picked up, it is directly transferred to the rotation station. The sole is now resting on two metal rods that allow it to be easily accessed from below. In order to be assembled on the last, the sole must be picked up from below. The UR10 CB3 robot has a Intel RealSense D415 depth camera attached to its end-effector and it is positioned below the sole to take a picture of the inferior part of it. Grasping points are now calculated again to pick the sole from this new position and transfer it to the assembly station. The process ends with the sole laying on the last to be pressed in a future stage.
ROS implementation
We will reproduce the grasping task of this scenario in ROS, with the aim of simulating, and eventually controlling, the real robot during the process (Fig. 5).
For this task, we use Ubuntu 16.04 and ROS Kinetic. We use RViz, the primary visualizer in ROS, with the MoveIt! Motion Planning Framework [22] plugin to build a virtual environment that will be ultimately configured to connect to the physical robot and perform the real motion. We import all the CAD models of the physical bodies interacting in the scenario to the simulation. While the UR10 robotic arm, the 2F140 gripper and the RealSense D415 camera have ROS models available from their manufacturers, we must also import several custom bodies into ROS: conveyor belt, scanner box, UR10 structure, rotation station, and assembly station.
Calibration
For the real setup to work correctly, the relative positions of all the elements must be correctly defined (Fig. 6). In order to make the assembly easily reproducible in case of an eventual relocation, all of the elements are fixed to a custom structure that lays underneath, which makes calibration easier avoiding undesired relative movements of the elements.
First of all, we define the global reference frame, F o , at the base of the UR robotic arm. The transformation e o T defines the position and orientation of the reference frame end-effector of the robotic arm, F e , and it is calculated using the Denavit-Hartenberg algorithm [23]. The model is finetuned using the calibration parameters retrieved from the robot's controller. We have calibrated the position of the laser scanner reference frame, F s , using the CAD model of the virtual scenario and verified it using the robot's endeffector, therefore obtaining the transformation matrix s o T . Glue application, which is not in the scope of this work, requires the transformation s r T from the COMAU reference frame, F r , to the scanner reference frame, as well as the position of the COMAU end-effector frame F n , which are calculated the same way as before.
The final step, and probably the most important one, is camera calibration. We are obtaining depth pictures from the camera with a height of 720 pixels and a width of Using this information, depth images are transformed to point clouds by our software. We have used a custom software to obtain the camera's extrinsic parameters. We need to obtain the transformation c e T from the camera reference frame, F c , to the UR end-effector frame. This problem is usually referred as camera hand-eye calibration with a robot-mounted sensor (eye-in-hand). In order to do this, a calibration checkerboard grid is located on a known position on the conveyor belt structure and the robot end-effector is moved to several positions where this board is visible, where we take pictures at each of those positions and detect the center of the board in every picture. Using this information, we can fit a transformation between the end-effector position and the camera origin, obtaining the extrinsic parameters of the current camera configuration. A point expressed in the camera's reference frame, p c , is converted to global coordinates, p o , using:
p o = e o T c e T p c .
Robotic grasping algorithm
Grasping points
In the scanning and grasping station, we use a custom version of the GeoGrasp software modified for the specific task in hand. GeoGrasp [24] is an algorithm designed for the computation of grasping points for unknown objects using a point cloud acquired from a single partial view of a scene. Even though originally designed for usage with RGBD cameras, it has been adapted to process point clouds obtained from a laser scanner. It is an important contribution of this work. This algorithm extracts geometric features, i.e., centroid and first eigenvector, from the object point cloud using principal component analysis (PCA). We use standard methods from Point Cloud Library (PCL) [25] to perform PCA on the point cloud. Using these features, the algorithm obtains two candidate regions Q 1 and Q 2 . These regions are determined by the intersection of the outermost part of the cloud with a plane defined by the centroid c and the first eigenvector v, considering gripper grasping tip width. The algorithm ranks combinations of points from these regions based on local curvature using a custom ranking function. The best-ranked pair guarantees the most stable grasp configuration G = {g 1 , g 2 }, given the view conditions (Fig. 7). A more detailed explanation can be found at [24]. Unlike point clouds obtained from RGBD cameras containing a few thousand points, those obtained from laser line profile scanners have a much bigger resolution, usually containing several hundred thousand points for similar dimension objects. We have tested these extremely dense point clouds with this algorithm and it is unable to process them. We could only achieve grasping point generation with aggressive voxelization, reducing significantly point cloud size and obtaining grasping points inside the contour of the outsole, making them unsuitable for this application.
Assuming the object to grasp has a uniform density and no significant differences in height, which is normally the case for an outsole, we can keep only the outermost points of the object. This contour is exactly the place where the outsole should be grasped. Under these assumptions, the center of gravity of the contour is an acceptable approximation of the center of gravity of the original object. We will obtain the contour of the point cloud taken as a 2D hull on the dominant plane, reducing point cloud complexity and significantly decreasing processing time. The algorithm performs PCA feature extraction, i.e., centroid and first eigenvector, from the contour to calculate grasping points. However, if the sole has very distinct characteristics, deviations introduced by hull generation are corrected with those extracted from the original cloud (Algorithm 1), using these features to calculate the grasping points on the outsole contour. Figure 8 shows that this method is useful to correct deviations produced by gaps in hull generation (Fig. 8d), non-uniform hull sampling (Fig. 8b), or by non-standard sole typologies (Fig. 8c).
In order to extract the object's contour, we must obtain a hull of it. To achieve this task, we will use alpha shapes, a well-known concept in computational geometry introduced in [26], and for which there is a straightforward implementation in PCL. First, we will define α as the curvature of a disk of radius r = 1/α. This is the main parameter of the alpha shape. Taking as input a finite set of points, two members of it make up an edge of the alpha shape if a disk of radius r with those two points lying on its boundary, and containing none of the other points of the set, exists. Alpha value determines two types of hulls: convex and concave hulls.
The least computationally expensive process is convex hull generation. This corresponds with a value of α = 0, causing the disk to become a half-space. Intuitively, we can think of a convex hull as the smallest polygon enclosing a given distribution of points. This hull is greater than (or equal to) the real contour; some points that belong to the real contour are left inside, but none outside of its borders. When the contour has a certain concavity, a convex hull is not a valid approximation to the real contour. We will perform this using the ConvexHull function implemented in PCL, which uses the QuickHull method [27]. This algorithm reduces point cloud size in a short amount of time.
Concave hull algorithms are significantly more complex and require much more computational power. In this case, PCL also provides a function to calculate concave hulls, ConcaveHull, from the same authors [27]. This case corresponds with an alpha value of α > 0, and we must provide this value to the function. An optimum value for sole hull generation of α = 0.005 was obtained in a previous experimentation found in [28].
Once this concave hull is obtained, it is used as input for the GeoGrasp method as shown in Algorithm 1. In our For the rotation station, we use GeoGrasp on the point cloud C n×4 c obtained from the RGBD camera mounted on the robotic arm's end-effector. In this case, the obtained point cloud has such a size that it can be processed directly by the algorithm. We must trim the raw point cloud to remove the background and select only the region of interest where the object appears for the algorithm to calculate the grasp in that region. For this purpose, we use geometric segmentation to select the range in threedimensional coordinates where the grasping calculation should focus on. Thus, we compute D k×4 which represents the region of interest. In this case, it is the place between the metal rods shown in Fig. 3, which is where the gripper will access the lower part of the sole to perform the grasp. Workflow is shown in Algorithm 2.
Kinematic analysis and planning
Shoe soles have a wide variety of sizes and shapes, we must select a gripper capable of performing grasps with different widths and depths. Our dataset is composed of sole samples with a height ranging from 0.5 to 3.5 cm and a width between 5 and 8.5 cm at their central section.
We have selected the 2F-140 gripper from Robotiq which has an maximum opening range of 14 cm and an available CAD model from the manufacturer. We can easily determine the kinematics of the gripper to obtain analytical expressions for the opening of the gripper (Eq. 1) and the distance from the base to the tips of the fingers (Eq. 2).
Opening = 2 L 2x + L 2 cos(Θ 2 + Θ o ) − L p (1) H eight = L 2y + L 2 sin(Θ 2 + Θ o ) + L h(2)
The gripper is symmetric left to right (Fig. 9). For this analysis, we reduce the gripper mechanism to a 2D planar four-bar linkage on the right symmetric part. It is a quadrilateral mechanism with a parallelogram configuration. The lengths of its sides are equal in pairs; this causes the mechanism to have purely rotational motion around the anchor points while the orientation of its end-effector is fixed. The outermost bar has a passive degree of freedom that allows the gripper to adapt to the surface of the object it is grasping. We must also consider that the angle expected by the gripper is relative to the maximum opening angle.
This gripper has six parameters and one degree of freedom. The first two parameters, L 2x and L 2y , are the coordinates of the pivoting point of the mechanism in the local coordinate reference frame. L 2 parameter defines the finger length, while L p and L h are the fingertip pad width and length respectively. The maximum opening is 14 cm, and corresponding with Θ 2 = 0. Θ o is the angular offset of the finger with respect to the local x-axis at the starting position. From the desired grasp width, we calculate the required distance of the robot end-effector to the sole to perform a successful grasp.
Execution of grasps on the real implementation has shown to be dependent on the gripper characteristics, beyond the correctness of the calculation of the grasping points. The 2F-140 gripper has rigid thumbs that are unable to adapt to the shape and materials of the soles, producing slippage when performing the grasp and pickup of soles from the conveyor. We developed a specially crafted thimble printed using a flexible plastic material to increase the friction and obtain a better fit to the sole shapes. All the grasps in the conveyor and the latter rotation station were performed with a thimble-equipped gripper, calibrating gripper fingertip parameters L p and L h to account for it. To assure repeatability in an industrial environment, nothing can be left to chance or sheer luck. The MoveIt! Motion Planner uses the Open Motion Planning Library (OMPL) based on randomized motion planners. It takes starting and target points (or starting and target robot poses) as input and outputs a suitable trajectory: a series of intermediate positions (or robot poses) the robot has to reach in order to perform the motion. In most cases, when planning the motion of the robot from one location in Cartesian space to another, it will find a smooth trajectory following the shortest or optimal path (resembling a straight line if there are no collision obstacles). However, due to the random nature of the planner, it can find a path that performs some strange or sharp motions outside of the predictable trajectory. Despite that the working range can be limited by safety plane boundaries, these uncontrolled motions can be dangerous in an industrial environment and when working in a location frequented by human operators.
We have implemented a planned motion checker to avoid this kind of undesirable behavior (Algorithm 3). When the motion planner calculates a trajectory for the robot, the role of the planned motion checker is to validate it. The distance from the starting and target position of the endeffector is compared to the total distance travelled along the points that the planner has calculated for the trajectory. If the deviation is greater than a specified value, the planner is commanded to calculate a new trajectory; otherwise, the trajectory is taken as valid. Recalculation of the trajectory is performed a given number of times, if all of them result in defective trajectories the execution is interrupted awaiting user confirmation. This is a fail-safe mechanism that allows our cell to be suitable for application in an industrial environment. We will set a maximum admissible deviation parameter m d that is dependent on the motion to be executed; in most cases, setting a maximum deviation 20% is enough to obtain safe trajectories, but there are some cases (i.e., when the end-effector has to perform a considerable orientation change) when this value has to be manually set to a much higher value. Figure 10 shows a comparison of two trajectories generated by the MoveIt! Motion Planner for the sole pickup task at the conveyor station. Both trajectories were generated using the same starting and target points, and both of them are seemingly valid. However, one of them follows almost a straight line, while the other performs a high deviation trajectory that makes the robot go outside the reasonable working space. Figure 10b shows the endeffector position for both of the calculated trajectories. The number of points in the planned trajectory, k, can vary greatly from one planned motion to another. At first, the number of trajectory points could seem like a way to distinguish between suitable and unsuitable trajectories, but checking the travelled distance has been proven to be much more robust and reliable. The distance between the starting point (red) and the target point (green) is 0.518 m. A suitable trajectory will try to follow the shortest path possible; in this case, it results in a path with a covered distance of 0.534 m, resulting in a 3% distance deviation. A high deviation trajectory finds another possible trajectory where the end-effector pose achieved is the same, but a much longer distance is travelled, 2.63 m corresponding to a 407% deviation. When a high deviation trajectory that exceeds the maximum permitted value is found, as in this second case, the checker flags it as unsuitable and planner is commanded to recalculate the trajectory.
Experiments
Grasping points calculation from the conveyor belt
The input to our algorithm (Algorithm 1) is a dense point cloud obtained from a digitizer. GeoGrasp can successfully calculate grasping points on the concave hull of an outsole in tens of milliseconds, while it could not calculate them in the original cloud due to the great amount of points it contained. To check how good a representation of the real outsole this concave hull is, we perform a comparison between grasping points generated in three scenarios. In scenario 1, we calculate the grasping points for the concave hull of a outsole with α = 0.005. For scenario 2, this concave hull is extended with its k-Nearest Neighbors (k = 10) using the PCL implementation based on FLANN [29]. The third scenario calculates grasping points on the concave hull correcting its center of mass and principal component to those of the original cloud computed using PCA. To do this, we have created a dataset with 20 sole models from commercial footwear. These soles are of various sizes and have different characteristics. We have chosen all of them from the right foot to be able to make a fairer comparison between them, but the method would work the same way if they were left foot soles. First, we perform PCA on complete clouds, obtaining the centroid and first eigenvector of them. We can compare these values to those obtained from PCA on the concave hull and its extension containing the hull's 10-NNs. Figure 11 shows the mean and standard deviation of the centroid and first eigenvector with respect to the PCA of the original cloud, along with individual values for each of the outsoles, normalized to expected value (Eq. 3).
P CA(C n×3 s ) − P CA(P s (C n×3 s )) P CA(C n×3 s )(3)
We can see a decrease in deviation of the hull cloud centroid with respect to the original one if we enhance the cloud with its nearest neighbors (NN), while the first eigenvector deviation remains practically the same. The improvement is not significant enough to compensate for the processing time required to look for 10-NNs of all of the points of the hull (Fig. 12), but we can try a different approach. Because we want to perform grasps along the contour of the sole, we can try enhancing grasping point calculation by correcting PCA values of the hull with those of the original cloud when calculating the grasping points. This is the motivation of scenario three.
We can proceed to calculate the grasping points on soles for these three scenarios using our proposal of new GeoGrasp described in the previous section, and obtain the total elapsed time to obtain a result for the three scenarios: concave hull, enhanced concave hull with 10-NNs, and concave hull with PCA correction (i.e., using centroid and first eigenvector of original cloud when calculating grasping points on the hull). Total elapsed time includes all of the computations performed on the original cloud applicable for each scenario: hull generation, PCA, NNs, grasping point calculation, etc. Figure 12 shows mean values and standard deviations for the complete process of grasping point generation for all outsole samples, elapsed time is measured on a laptop with a 2014 Intel®Core™i7-4600U Processor.
Overall, the most time-consuming process is nearest neighbor calculation on very dense point clouds, while concave hull generation is performed much faster. Adding PCA correction increases generation time, but includes characteristics from the original cloud to perform better grasps on the hull.
Grasping from rotation station
Grasping from the rotation station has a series of peculiarities that makes it a challenging task. Unlike the grasping station where we grasped the sole from the flat surface of the conveyor belt, the rotation station requires the gripper to perform an aerial grasp. The sole is lying on two metal rods that allow an inferior approach, which means that there is not a solid surface supporting the sole during the grasp.
The sole arrives to the rotation station directly from the grasping station and it is left lying on the rods. The positioning on the rods is precisely height controlled using the kinematics of the gripper and the height of the grasp obtained from the scanned point cloud. The robotic arm performs a 180°rotation to reach the rotation station from below and takes a picture using the RGBD camera on its end-effector. Due to space limitations in the physical implementation, unlike the scanner point cloud (Fig. 13a), the point cloud obtained from the camera is not a complete view of the sole and lacks the shoe tip (Fig. 13b). This cloud is then segmented to keep only the section of the shoe between the metal rods, which is the place where the grasp can be performed. The grasping points are calculated using only this section of the sole (Algorithm 2).
If we consider the grasping points computed from a complete point cloud, G, as ground-truth (Algorithm 1), we can perform a comparison between the grasping points obtained from the complete view of the sole and those calculated with the partial view as RGBD, G (Algorithm 2). We must perform some kind of matching between both point clouds. This is not a straightforward task for two main reasons. First, they have been obtained from different sensors with different resolutions; in the grasping station a laser scanner is used, while in the rotation station we use a RGBD camera. Second, the point clouds are of two different views of the sole; the laser scanner obtains a top view of the sole, while the RGBD camera records a bottom We opted for an automated matching procedure based on two affine transformations. First, we perform a translation to bring together the end points of the sole's heel and a rotation to align the position of the sole (Fig. 14a). This initial matching is then adjusted obtaining the optimal affine transformation between five corresponding points of the sole present in both point clouds (Fig. 14b); this method uses singular value decomposition (SVD) to minimize the least-square error between the point sets [30].
Once the matching is done, we can compare the grasping points obtained at the conveyor grasping station G = {g 1 , g 2 } with those of the rotation station G = g 1 , g 2 . This can give us an idea of how close they are to each other, and see the difference it makes to use the whole sole or only the central part of it to calculate the grasping points. This will be more noticeable when the sole has a non-standard shape or a relatively prominent heel. Although our dataset is composed of 20 soles, Fig. 15 only shows the error obtained in 13 of the 20 soles shown in Fig. 11, made with material of low and medium flexibility. This error is calculated as the root mean square error (RMSE) between the grasping points in both scenarios (Eq. 4).
1 2 2 i=1 g i − g i 2(4)
The error analysis shows that the matching error is greater in soles with heel and there is no significant difference between low and medium flexibility. In this experiment, we have preferred to show only low and medium flexibility errors because high-flexibility soles sometimes cause dynamic problems in the grasping task from the rotation station, which will be discussed in the next section. Nevertheless, it is possible to note that our algorithm to compute grasping point on soles works well with any type of sole (Fig. 16), including not only low and medium flexibility but also full flexibility.
From model to production
Here, we tested our setup for the entire dataset of soles with varying sizes, colors, and shapes, repeating the process 10 times for each one. Therefore, 200 tests were carried out. All shoe soles are made of materials with some level of flexibility, to allow the natural actions of movement of the human foot. In our experimentation, we have classified our sole samples into three categories: low, medium, and full flexibility. This measure of flexibility accounts for the degree of deformation suffered by the object when grasped under the action of gravity. Low flexibility refers to minimum deformation, almost unnoticeable, while medium flexibility accounts for a slight bend of the sole. In the full flexibility group, all the soles experience a considerable deformation that changes its original shape. From the results shown in Table 3, we can see that low and medium flexibility soles work well with our cell. Soles that are very flexible and change their shape when grasped are highly likely to slip when grasped in the rotation station. The rotation station requires an aerial grasp, which is very difficult to perform if the sole changes its shape and there is no deformation control in the system.
We can go further in our analysis and see how the presence of a heel affects the process in case of low and medium flexibility soles, classifying them further into soles with Table 2 show that the absence of heel produces a very high success rate, while heels have a great impact on the grasping performed in the second station. Heels change the geometric characteristics of the sole and are difficult to represent by the point cloud when only an upper or lower view of the sole is present. Point clouds obtained by laser sensors and RGBD cameras record only points on the surface; they are not able to give a representation of the volume of the object without further post-processing. From the data in Fig. 15, we can confirm that heel presence has a considerable impact on the location of the centroid of the object.
We have obtained the measurement accuracy for grasping points as the positioning error in the conveyor and rotation stations. We have calculated this value for all of the trials performed using outsoles without heels (10 soles with 10 trials per sole), representing it as the RMSE between the position of grasping points computed on the point cloud and those points in which the end-effector grasps the objects. The value for the conveyor station is 1.5 mm, while the value for the rotation station is 3.9 mm. As shown in Table 3, these values obtain 100% and 95% success rates, showing that sole typology (flexibility and heel presence) is a bigger determinant in grasping success than positioning error. We can conclude that our method and the designed cell prototype can be recommended to be used with low and medium flexibility soles without heels. Future work will include end-effector force control to improve grasping success for the different sole typologies. Once the whole process for one sole was tested correctly, we implemented queues to make the process more efficient. Several soles can be present on the conveyor and their scanned models are stored in a queue. These soles are processed as they arrive to the pickup zone. While the robot arm is performing the tasks for rotation and assembly station, more soles are being processed at the scanner until one reaches the pickup zone. When the robot arm has finished the process, it returns to the pickup zone to grasp the next sole and the process starts again. The usage of queues endows for an asynchronous processing of soles and reduces idle times. Figure 17 shows some frames of the grasping tasks in our real and virtual sole assembling robotic workcells for footwear manufacturing: the first frame illustrates sole grasping from conveyor pickup zone, the second frame presents sole drop on the rotation station, and the third frame shows sole grasping from below the rotation station.
We are using a Local Area Network (LAN) with four different physical nodes: an Ubuntu computer with the main process, a Windows box with the laser scanner digitizer software, the UR10 robot, and a Raspberry Pi with the RGBD camera. The main node is an Ubuntu 16.04 box with a 2019 Intel®Core™i7-9700F and 16 GB of RAM. At idle state, the process requires 1040 MB of RAM. The network usage is 60 KB/s because the robot position is being broadcast continuously to the main node. Each digitized cloud from the conveyor takes up 6 MB in the queue. Considering the distance between the beam of light of the digitizer and the pickup zone, there could be a maximum of 4 soles simultaneously in the queue before the first one is processed. In the rotation station, the complete scene obtained from the RGBD camera is 28 MB, but only one scene is processed at a time. When the process is running, network usage can increase to several MB/s considering point cloud transmission between nodes.
Processing time of the complete process is not very dependent on the type of sole to be processed. Larger soles result in bigger point clouds that need more time to be processed in the conveyor station (i.e., concave hull generation and PCA feature extraction). As shown in Fig. 12, processing time for grasping point calculation is in the order of seconds for the conveyor station, but because there are intermediate processes (glue application and conveyor motion) between the scanning and the picking up, it does not really influence the overall processing time (Fig. 4). For the rotation station, no hull must be generated making the process much faster, the time needed for GeoGrasp to process the sole and obtain grasping points is in the order of milliseconds. Complete sole processing by the robot takes around 50 s: this includes from sole pickup in conveyor station to assembly station dropping and returning to starting position. With the introduction of queues, while the robot is performing the required motion with the sole, the conveyor is turned on and the laser scanner continues processing soles until one reaches the pickup position.
A flowchart of the final prototype implemented is shown in Fig. 18, where the three independent tasks running in parallel are shown. The first task processes soles on the conveyor as they arrive to the scanner, adding their digitized versions into a queue. The second task is waiting for a sole to reach the pickup zone on the conveyor and once this happens it stops the conveyor motion, populating the position queue with the sole current location. The first and second tasks are set on hold when the conveyor stops, waiting for the sole at the pickup zone to be picked up by the robotic arm. The third task controls robot arm operation and it is continuously processing soles that arrive to the pickup zone. Once the sole is picked up, the conveyor is set on motion and tasks 1 and 2 resume. The robot arm task will process the sole through all the stations and return to the starting position to pick up the next sole that should be ready at the pickup zone.
Conclusions
In this work, we have proposed important improvements in GeoGrasp, introducing an algorithm based on concave hull generation. In this way, we can quickly obtain the outsole's contour and compute grasps overcoming the limitations of GeoGrasp working with dense clouds. We have tested three scenarios of grasping points generation on concave hulls: without modifications, enhancing the hull with its 10-NNs, and using PCA correction. We can improve grasping points computation performing a PCA on the original point cloud and correct the hull's characteristics, i.e., centroid and first eigenvector, with those of the original cloud. Concave hull enhancing with PCA correction provides information about the typology of the outsole, providing data about its density and interior features that has been lost when generating the hull; therefore, it can be used to obtain grasping points that are better aligned with the original point cloud characteristics.
In the real-world application, we have studied two grasping procedures with their own peculiarities. First, once the sole is scanned, we pick it up from the conveyor belt. In this case, a concave hull is obtained to reduce the grasping point generation time, correcting it with the PCA values of the original cloud. This sole is taken to a second station where an aerial grasp from below must be performed. We use an RGBD camera on the end-effector to obtain a partial point cloud of the sole and calculate grasping points. To produce safe robot motion, we have implemented a planned motion checker to restrict the deviation in the trajectory of the end-effector when calculating point-to-point motion.
There are some limitations to this method. One of the main disadvantages of 2D hull generation is information loss about the interior characteristics of the object. This is not an issue if the sole has a uniform thickness all around, but it can be an issue if the sole has different heights (e.g., a high heel) or non-symmetric internal features. This inconvenience has been partially mitigated using PCA correction. The sole's characteristics have a significant impact on the performance of the method. Picking up soles from the conveyor has a very high success ratio overall, while soles with a very high flexibility have a low success when performing the aerial grasp necessary for the rotation station. The presence of heel also affects the performance of the aerial grasp, due to the fact that a partial lower view is used to calculate the grasping points in the rotation station.
Heel presence modifies the location of the centroid of the sole and it is impossible to notice without further postprocessing in the cloud obtained from the RGBD camera.
In conclusion, the current implementation of our method and the designed cell prototype can be recommended to be used with low and medium flexibility soles without heels. We plan to mount force sensors on the gripper to perform force control on outsole grasping and expect to improve grasp success on all sole typologies. Future research lines include tackling outsole manipulation, using a dual-robot setup to grasp the sole from both ends in the rotation station and actively control its deformation while pressing it together with the finished upper. if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creativecommonshorg/licenses/by/4.0/.
Fig. 2
2Diagram of a shoe and its last
Fig. 3
3Virtual scenario
Fig. 4
4Gantt chart of the fabrication cell. Color code: green, activities developed in this work; striped green, critical task maximum duration; grey, inputs for developed activities; black,
Fig. 5
5Layout of the ROS implementation
Fig. 6 ⎠
6Real scenario calibration scene 1280 pixels. The camera intrinsic parameter matrix, , is obtained from the camera's firmware, along with depth-scale parameter (d = 0.001).
Fig. 7
7GeoGrasp algorithm on a shoe sole
Fig. 8
8Example of generated grasping points G obtained using Algorithm 1 on concave hulls with PCA correction. a BallerinasEVA outsole. b Unisa outsole. c 9100 outsole. d Trip outsole input to correct those of the concave hull P s and grasping points G are calculated (Algorithm 1).
Fig. 9
9Kinematic characteristics of the gripper
Fig. 10
10Planned motion checking using Algorithm 3. a Motion to be planned. b 3D representation of trajectories. c Trajectory joint values. Solid lines: suit-able trajectory, dashed lines: high deviation trajectory
Fig. 11 Relative differences of hulls with respect to PCA of original cloud computed from 20 sole models
Fig. 12
12Total elapsed time for grasp generation view. The upper and bottom sides soles have very different characteristics making feature extraction unsuitable for matching.
Fig. 13 Different point grasping computed from upper view from scanner and bottom view from RGBD camera
Fig. 14
14Matching of scanner top view and camera bottom view. a First step. b Second step and without heel. The results in
Fig. 15
15Distance of grasping points from conveyor to rotation station
Fig. 16
16Several examples of our shoe sole dataset
Fig. 17
17Grasping tasks in our proposal of conveyor and rotation station: real workcell versus virtual scenario
Fig. 18 Flowchart of the overall operation of the implemented proposal. Three independent tasks run at the same time: sole scanning, sole pickup positioning, and robotic arm controlling. Algorithms 1 and 2 are used in grasping controller blocks for grasping points calculation and Algorithm 3 is used in the motion controller to check planned motions
Supplementary informationThe online version contains supplementary material available at (https://doi.org/10.1007/s00170-021-06697-0).
Automatics, Robotics and Artificial Vision Lab (AUROVA), Computer Science Research Institute, University of Alicante, San Vicente del Raspeig, SpainOliver
[email protected]
Pablo Gil
[email protected]
Jose F. Gomez
[email protected]
Fernando Torres
[email protected]
1
2
Footwear Technological Institute (INESCOP), Elda,
Alicante, Spain
summarizes the main Fig. 1 Several shoe manufacturing stages. a Cutting. b Stitching. c Shaping. d Adhesive application. e Sole assembling. f Pressing
Table 1
1Characterization of shoe manufacturing stages according to the required skills and the automation level more frequently usedStage
Skill
Precision
Force
Machine-aided
Cutting
Low
Medium
Low
Laser cutting machine/robot
Stitching
High
High
Low
Sewing machine
Assembling upper and insole
High
Medium
Medium
Stapler/pre-forming/pulling over machine
Applying adhesive (cementing)
Medium
Medium
Low
Manual with hand tools
Sole assembling (cementing)
High
High
Low
Manual without hand tools
Pressing (cementing)
Low
Medium
Low
Pressing machine
Finishing
High
Medium
Low
Iron/cutter/spray gun/brush machine
Table 2
2Grasping success ratio for soles according to flexibility levelLow
Medium
Full
No. of soles
9
4
7
Conveyor
98.9%
100%
75.7%
Rotation
84.3%
85%
34%
Table 3
3Grasping success ratio for low and medium flexibility soles
classified according to the presence of heel
No heel
Heel
No. of soles
10
3
Conveyor
100%
96.7%
Rotation
95%
48.3%
Author contribution P. Gil and F. Torres conceptualized the proposal. J.F. Gómez was responsible for describing traditional issues of footwear manufacturing and designing the fabrication cell. Then, G. Oliver implemented the virtual fabrication cell in ROS and, more later, all the authors implemented the physical fabrication cell. The robotic grasping algorithm was designed and implemented by G. Oliver and P. Gil. The experimental methodologies, formal analysis, and results validation were carried out by P. Gil, F. Torres, and G. Oliver. Finally, G. Oliver and P. Gil were responsible for writing the draft and F. Torres and F.J. Gómez supervised the work. All the authors reviewed and edited the final document.Availability of data and materialsThe authors confirm that the data supporting the findings of this study are available within the article and/or its Supplementary Materials. The raw data that support the findings of this study are available from the corresponding author, P. Gil, upon a reasonable request.Code availability Custom code developed is considered industrial intellectual property and is not to be released to the public domain. Individual software applications can be requested to the corresponding author, P. Gil, upon a reasonable request.DeclarationsConflict of interestThe authors declare that they have no conflict of interest nor competing interests.Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate
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3D is here: point cloud library (PCL). R B Rusu, S Cousins, 10.1109/ICRA.2011.59805672011 IEEE int. conf. on robotics and automation, shanghai. Rusu RB, Cousins S (2011) 3D is here: point cloud library (PCL). In: 2011 IEEE int. conf. on robotics and automation, shanghai, pp 1-4. https://doi.org/10.1109/ICRA.2011.5980567
On the shape of a set of points in the plane. H Edelsbrunner, D G Kirkpatrick, R Seidel, 10.1109/TIT.1983.1056714IEEE Trans Inf Theory. 294Edelsbrunner H, Kirkpatrick DG, Seidel R (1983) On the shape of a set of points in the plane. IEEE Trans Inf Theory 29(4):551-559. https://doi.org/10.1109/TIT.1983.1056714
The Quickhull algorithm for convex hulls. C B Barber, D P Dobkin, H Huhdanpaa, 10.1145/235815.235821ACM Trans Math Softw. 224Barber CB, Dobkin DP, Huhdanpaa H (1996) The Quickhull algorithm for convex hulls. ACM Trans Math Softw 22(4):469- 483. https://doi.org/10.1145/235815.235821
Robotic workcell for sole grasping in footwear manufacturing. G Oliver, P Gil, F Torres, 2020 25th IEEE International conference on emerging technologies and factory automation (ETFA). Vienna, AustriaOliver G, Gil P, Torres F (2020) Robotic workcell for sole grasping in footwear manufacturing. In: 2020 25th IEEE International conference on emerging technologies and factory automation (ETFA), Vienna, Austria 2020
Fast approximate nearest neighbors with automatic algorithm configuration. M Muja, D G Lowe, 331-340. 10.1.1.160.1721Int. conf. on computer vision theory and applications (VISAPP). LisboaMuja M, Lowe DG (2009) Fast approximate nearest neighbors with automatic algorithm configuration. In: Int. conf. on computer vision theory and applications (VISAPP), Lisboa, pp 331-340. 10.1.1.160.1721
Least-Squares Fitting of two 3-D point sets. K S Arun, T S Huang, S D Blostein, 10.1109/TPAMI.1987.4767965IEEE Trans Pattern Anal Mach Intell. 95Arun KS, Huang TS, Blostein SD (1987) Least-Squares Fitting of two 3-D point sets. IEEE Trans Pattern Anal Mach Intell 9(5):698-700. https://doi.org/10.1109/TPAMI.1987.4767965
| PURPOSE: A functional health shoe is provided, which doubles interest of walking by vibration and magnetic force and can improve blood circulation. CONSTITUTION: A functional health shoe comprises a casing(300) in which a working chamber is formed inside the uppers of leather part or the outsole part; a vibrator(200) equipped in the working chamber; an uppers of leather part; an outsole part(120) equipped in the bottom of the uppers of leather part; and a vacuum space part formed in the outsole part. The vibrator includes more than one vibration plate; a first magnet attached to the other end tip of the vibration plate; and a repulsion magnet. | I have purchased many dance sneakers over the years and none have the support that this shoe model has. I love this shoe for dance. | By analyzing the trends and development of virtual reality technology,Proposed the Method of combined with data gloves to in teract the items in the virtual scene by virtual reality software EON.In order to achieve gesture recognition,virtual crawl and other func tions,using VC + +6.0 and other development tools,with EON software for data exchange and combined these functions to look into the future of virtual reality technology application. | After years of too much support, my feet, knees and hips feel much better when I let my feet move naturally. Great shoe. | I was very pleased with this idea of having the shoes off the floor. Liked the first one so much I purchased a second one. One for winter, one for summer shoes. After only 2 months the bottom 2 shelves have snapped off breaking the plastic where the holes are to screw it. This makes it unrepairable. These shelves need more support or they pull away from each other. I need to mention that The winter shoes have not had much use since April. The one that broke has my summer sandals and beach shoes (lightweight) on it. | our research focuses on developing Virtual Supporting System (VSS). In this paper, we implement tangible baseball supporting system on virtual world. In virtual world, Second Life, Croquet, Wonderland, etc. we can enjoy shopping, watching movie, dancing and so on. In this paper, we discuss about collaborative supporting method among virtual world users and sensory effect using wearable hap tic devices and smart-phone. Also, we developed avatar control, motion based cheering and chatting using smart phone and wiimote. The main idea of this paper is to extend virtual world's mean by adding collaborative group cheerleading and hap tic devices. | 267 | The life cycle of an industrial product goes through several stages, from the initial idea to the finished product, and on to the purchase and recycling. Virtual reality environments (VRE) allow the user to interact with a digital representation of a product, and so can be used to perform aesthetical, ergonomic, functional tests as well to support customer decisions in the selling process; mainly for customized products. In this contribution, ITIA-CNR presents two important applications in the shoes context: VRShoe and MagicMirror. VRShoe is a VRE for designing shoe aesthetics. MagicMirror, currently under development, is an augmented reality (AR) system for supporting the decision-making processes of customer customized shoes. | Shopkeeper Simulator VR - Own a shop - Now on itch.io | A unique and timely book for the Virtual & Augmented Reality industries | Macy's will use VR to let shoppers 'see' furniture in their homes | i was looking for stores that sell vr | Leap_Magic: Showcase of VR game I did | This paper proposed a new interaction paradigm in the virtual reality (VR) environments, which consists of a virtual mirror or window projected onto a virtual surface, representing the correct perspective geometry of a mirror or window reflecting the real world. This technique can be applied to various videos, live streaming apps, augmented and virtual reality settings to provide an interactive and immersive user experience. To support such a perspectiveaccurate representation, we implemented computer vision algorithms for feature detection and correspondence matching. To constrain the solutions, we incorporated an automatically tuning scaling factor upon the homography transform matrix such that each image frame follows a smooth transition with the user in sight. The system is a real-time rendering framework where users can engage their real-life presence with the virtual space. 1 | Scaling VR in VRML: integrating different VR methodologies in a VRML browsing system | Augmented Reality (AR) based on Head-Mounted Displays (HMDs) has gained significant traction over the recent years. Nevertheless, it remains unclear what AR HMD-based applications have been developed over the years and what their system performance is when they are run on HMDs. In this paper, we aim to shed light into this direction. Our study focuses on the applications available on the Microsoft Hololens application store given the wide use of the Hololens headset. Our study has two major parts: (i) we collect metadata about the applications available on the Microsoft Hololens application store to understand their characteristics (e.g., categories, pricing, permissions requested, hardware and software compatibility); and (ii) we interact with these applications while running on a Hololens 2 headset and collect data about systems-related metrics (e.g., memory and storage usage, time spent on CPU and GPU related operations) to investigate the systems performance of applications. Our study has resulted in several interesting findings, which we share with the research community. |
268 | Purchased as a gift for a friend whom had one ... | This was purchased as a gift, and the recipient really liked it. | Purchased as a gift. Recipient very pleased with it! | This was a gift for a friend, who greatly enjoyed it. | Purchased as a gift, but I also have one and like it a lot. | It was a gift. The person who received it was very pleased. When the item was broken, she wanted it replaced with the exact one given to her for Christmas. | Bought as a Christmas gift for my son. He was pleased with it. | Purchased as a gift for my husband, who was delighted with it. | This was purchased as a gift. The recipient loved it | 268 | Purchased as a gift for a friend whom had one and it tore so I found her another one. She really likes using it wanted one where her belongings were covered and couldn't fall out. | It fell apart after one use, | I bought a pice of junk on this one! It was used, torn in three places!!! It was a huge, huge disappointment. Never again wil | Had one that got knocked over and broke while in ... | Fell apart after 2 years carrying it around in my ... | The very worst - actually falls to pieces. Do not buy. | mine came torn. just a small rip, but ... | Ordered because of good reviews but once I got it and tore it ... | Bought two, one broke before it was used. ... |
269 | Traffic design method of expressway ramp with adjacent intersection | Three connection modes of ramp of interchange and main line of expressway planned to be widened in future are introduced.Characteristics of each mode are analyzed and the three kinds of modes are analyzed through contrast,providing references for readers. | In order to relieve traffic congestion and accidents caused by vehicles merging into main road from ramp, the important influence factors of merging behavior were analyzed firstly. Then, traffic conditions under different traffic volume of ramp and main road and different length of acceleration lane were simulated by Vissim. According to security and efficiency evaluation measured by conflict intensity and average delay, reasonable acceleration lane length was selected under certain traffic condition. Finally, the simulation model was compared with several other common models. Researches indicated that the model conformed to the actual situation. | The interchange nodes are main parts of Beijing urban expressway system.Exploring evaluation methods and estimating the LOS of interchange nodes have great significance to identify the traffic jam formulation and propose relevant countermeasures.The paper analyzes main type and category of Beijing urban expressway interchanges and presents concept about urban interchange LOS.Then,using the index of travel speed,traffic volume of off-ramp and on-ramp,and speed of weaving and non-weaving sections,the LOS are evaluated for the main line,ramp and weaving sections.The LOS criterion is provided.At the final section,the Madian interchange,a very important intersection of Beijing urban expressway,is selected as an example to estimate its LOS and test the effeteness of the proposed method. | Geometric design of freeway off ramp-street junction is a very important partin freeway off ramp geometric design.The latest research on it was analyzed from the following aspects:terminal access spacing,sight-distance design,left-turn and right-turn design,channelization design and the traffic control selection.According to the insufficiency of the exited regulation in China and the relative successful practice abroad,we thought that proper geometric design methods of it could provide technology and theoretical support for the junction’s safety and capacity improvement. | Urban interchanges are a means of facilitating traffic movements between arterial streets and freeway ramps. The single point diamond interchange (SPDI) and the conventional diamond interchange are two specific interchange designs. Essentially, both designs can be treated as signalized intersections. Deviation from the standard signalized intersection operation can be attributed to factors such as longer clearance interval, larger turning radii, different phasing schemes, and different signal offsets between adjacent intersections. Available computer software was reviewed to determine its ability to simulate the operation of the urban diamond interchanges. Data collected at two sites in the Phoenix metropolitan area were used. Five programs were chosen: PASSER II-87, PASSER III-88, TRANSYT-7F, TRAF-NETSIM, and TEXAS. An assessment of each program was conducted to determine its ability to simulate both the SPDI and the conventional diamond interchange. It was concluded that the PASSER III-88 and the TEXAS models simulated the SPDI fairly well. All models except the TEXAS model were able to simulate the conventional diamond design. | Through considering the level of economic development,the characteristics of industrial layout,future economic development strategies,development of the road network and many other factors,and combining traffic location method with node important degree method,the distribution of expressway network in Shanxi Province is discussed.The general direction of expressway in Shanxi is obtained by traffic location method,the largest tree for line important degree is calculated by node important degree method.On this basis,line optimization is conducted,and the final distribution result of expressway network is given,that is,"herringbone skeleton,central 9 cross 9",total length of 4056 km.This result has been adopted and implemented by " 11th five-year plan"of Shanxi national economy and 1752 km of expressway has been built up. | This paper expatiates the meaning of the optimization of traffic operation in signal intersection and introduces crossing clear methods in the optimization of traffic operation in signal intersection,intersection channelization design and intersection signal design,etc.based on the summary of optimization design flow of traffic operation,and provide corresponding design flow chart. | Seagull intersection out of the side road. Different methods are used to control traffic where two right-turning movements and the through movement meet. Most intersections use traffic lights, while others use give way (yield) and stop signs, and sometimes roundabouts. This design type has been proven to provide sustainable benefits when compared the traditional T-intersection design. By reducing delay through the intersection, automobiles use less fuel on average passing through the intersection, and thus emissions are reduced across the intersection. The savings per vehicle may not seem very significant, but when scaled to account for all automobiles passing through the intersection, the | 269 | Problems of vehicle interleaving between a ramp and a ground,the loss of green time,and the shortage of the capacity of adjacent intersections were introduced.Spatial-temporal design methods were applied to avoid interleaving and conflict,a lane functionality replacement was used for the import lanes of intersection in the space,and for the time according to the principle of saturation equilibrium in traffic flow.A design idea about signal combination phase was put forward,which can decrease the loss of effective green time.One example was introduced to prove the methods in the pretext.The results indicate that grade separation capacity was improved,the average vehicle delay was greatly reduced.Moreover,the vehicle interleaving between a ramp and a ground was almost eliminated.The benefits were improved obviously. | ABSTRACTThe type of control at intersections has a major effect on the operation of any urban corridor. Different pre-defined procedures are available to calculate some of the main operational characteristics, such as capacity, delay, and level of service in order to select the best type of control. However, there are other important factors that affect major arterials operational characteristics, which are not fully addressed, such as the impact of emissions. In this study, a microscopic simulation approach using VISSIM and MOVES was developed to assess the environmental effect of converting four three-lane roundabouts to signalized intersections along a heavily congested urban corridor in Qatar. A decision was made to switch all roundabouts to traffic signals for better operations. Preliminary results indicated that the signal control outperformed the roundabout in the range of 37% to 43% reduction in emissions. A more detailed analysis revealed that roundabout corridor operations effect on emission rat... | what is the method by which time is stopped in road traffic is reduced | Abstract Traffic signal countdown timers (TSCTs) are innovative, practical, and cost effective technologies with the potential to improve safety at signalized intersections. The purpose of these devices is to assist motorists in decision-making at signalized intersections by providing them with real-time signal duration information. This study examines US driver responses in the presence of a green signal countdown timer (GSCT) and the implications those responses have on intersection safety. A driving simulator study was conducted to record driver responses to virtual GSCTs. Fifty-five participants (32 male and 23 female) responded to 1100 simulated traffic signals, half of which had GSCTs. A predictive model was developed and validated to estimate the change in driver’s probability to stop at different distances from the stop line in the presence of a GSCT. The presence of a GSCT increased average driver stopping probability in the dilemma zone by 13.10%, while decreasing average driver deceleration rates by 1.50 ft/s 2 . These results suggest that GSCTs may contribute to improved intersection safety in the US. | Signal Timing Optimization of Urban Truck Road by Synchro | The use of information technology in traffic management can increase the capacity of traffic intersections and reduce vehicle delays. In cities, adaptive traffic control at traffic lights intersections has been well established. Adaptive regulation is applied mainly on isolated traffic lights, where the traffic flow has a predominantly exponential distribution of intervals. It was established experimentally that the effectiveness of the method decreases with a supersaturated traffic flow, which makes it difficult to find a "cutoff point", a convenient moment for switching the traffic light signal. The article shows that at isolated multi-band intersections, the search for a convenient signal switching time is difficult at low loading levels. At uninsulated intersections, the incoming flow will have clear periods of time without vehicles, which makes the operation of adaptive traffic control in these conditions at a multi-lane crossing more efficient. This suggests the need for further study of the patterns of distribution of intervals between cars in urban environments at the approaches to non-isolated intersections and at the approach to intersections operating without coordination with other traffic lights. | the methods by which time is stopped in road traffic is reduced is called | Headway or inter-arrival time of vehicles is an important parameter in traffic flow, especially in urban roads, since this is one of the main parameters to determine the minimum (safe) gap between vehicles and the capacity. The studies done on headway analysis have mostly concentrated on homogeneous traffic where the flow follows lane discipline. This ideal situation does not exist on Indian urban roads, where the traffic is very heterogeneous, and do not follow lane discipline. A study of headway at different but similar locations of urban four lane divided (two lanes for each direction of flow) roads of a metropolitan city in India (Chennai) was made. The peak hour flow at these locations were observed to be high (varying from 3189 to 9987 vehicles). The study of headway, after removing the 5 % of long headways, at these location indicate that Log normal 2, Inverse Gauss and the Exponential distributions are the most appropriate ones for these conditions of flow. An attempt was made to study the individual inter arrival time of each category of vehicles in the traffic stream. Extensive data extraction was done and the analysis of headway of categorized traffic was made. Appropriate distribution for each category is recommended. The study will be a good input for modeling vehicle generation in simulation studies. | This paper designs distributed dynamic traffic signal control policies for urban traffic networks. Vehicles at the end of an approach to an intersection queue up in separate lanes corresponding to different possible turn maneuvers at the upcoming intersection, according to fixed turn ratios. The departure rate of vehicles from the queue is governed by traffic signal control at the intersections. We consider traffic signal control architectures under which, at every intersection, only a subset of non-conflicting approaches get green light simultaneously. We propose a class of cooperative green light policies, under which traffic signal control at an intersection requires information only about the occupancy levels on the lanes incoming at that intersection. In particular, such a policy does not require information about turn ratios, external arrival rates or departure rates. We show that such minimalist policies are maximally stabilizing for acyclic network topologies under some scenarios, and, when the network is stabilizable, the network admits a globally asymptotically stable equilibrium under these policies. Simulations to illustrate the applicability of our results to cyclic network topologies are also presented. |
270 | 33 [M4F] Tampa area - Looking for sugar baby on the side... | 33F - Bethlehem PA 4.6.21
Hello! I’m a married 33F mother who will be in the Bethlehem area Tuesday 4.6.21. 170lbs 5’7” I’d love to be abducted and impregnated/abused. I’m not on birth control. I drive a green ford escape, have long brown hair, and if you ask me where I’m going I will answer ‘to be examined.’ Please take advantage of my fertile womb. My uterus craves you.... | 47 year old white male in Tampa Bay area. This is my first time posting I think I may have done it wrong. | 28 \[T4M\] MADISON HEIGHTS- hosting gloryhole for horny guys who need to get drained. snap/kik DestinyBeauty26. will also rim/bottom. private location so just let me know when you can stop by, let yourself in and pop on a porno if you want to watch something while your snake gets slurped. HMU today. | (F)34 (M)33 looking for a (F) to start joining us end of September. Were looking for someone we can get to know and join us for some fun now and again. Those interested DM no single guys | ##
If you are in the Goldenrod/Curry Ford area of ORLANDO FL., or can travel to me, and want some Deepthroat and Swallow head, Let me know! STR8/BI/Curious Guys HMU. Older, Blue-Collar, Regular Joes, Rednecks, Papis, all are Hot! Would like to find someone to service on a regular basis. Totally Private and Discreet! | I take regular visits to Tampa, Clearwater or St. Petersburg and I was looking for a woman who wants to chat/meet/. We can have a drink and see what happens. No strings attached. I am d & d free and game for anything. PM me for further details. I have pics and would be happy to exchange photos to gauge your interest. | Hey there Tampa! My boyfriend and I are seeing Brendon Walsh tomorrow night, Friday 1/24. The show is at 10:30 but you have to be there by 9:45 to get seating. I already reserved 4 seats but all of our friends are busy so I figured I'd reach out to find another comedy loving couple! We're early twenties and looking for a couple around the same age if possible. PM me if you are interested! | 31 white male located near central CT looking for a good time tonight, or maybe later this week.
Looking to give a female (pref 18-40, race, body type don't matter) oral. Reciprocation appreciated, but not necessary. Possibly more if that's what you want.
Pics available to share. Send me a message with a little bit about yourself and lets talk. | 270 | Hello, I'm a 33 white male business owner in the tampa area. I work late nights at my office. I do have a GF but shes always back at home and I would like some extra fun on the side. Message me and we can work out the details. Also my kik is the same as my username here if you have kik. Message me anytime, i'm up all night. | (23 Casual kik )FB4A/FU/M Limitless bimboi Cow hella horny in need of a serious fucking looking for some fun and really dirty role-playing half decent role player with 3 to 4 lines minimum not picky would love to have fun please hit me up If you're looking for it | [M4F] Looking for a lonely housewife for a virtual affair | I(26M) need some fun help with great "getting to know you" questions I can ask a (21F) potential GF. | 30 [M4F] #Tampa - my gf of 3 years just broke up with me, looking for a rebound with my tongue | Anyone interested in helping my become a sissy? Message me if so! | [Request] non amateur Cuckolding / cheating girlfriend? Also any military cuckolding? | 33 [MM4FF] coworker and I on a business trip in Santa Monica next Monday and Tuesday looking for a fun double date | 21 year old male looking for some fun |
271 | Sex pheromone in the shore crab Carcinus maenas, and the site of its release from females | How do male crabs romance? | Toward the identification of female gonad-stimulating factors in crustaceans | for attracting a mate. Another conspicuous difference is the form of the pleon (abdomen); in most male crabs, this is narrow and triangular in form, while females have a broader, rounded abdomen. This is because female crabs brood fertilised eggs on their pleopods. Crabs attract a mate through chemical (pheromones), visual, acoustic, or vibratory means. Pheromones are used by most fully aquatic crabs, while terrestrial and semiterrestrial crabs often use visual signals, such as fiddler crab males waving their large claws to attract females. The vast number of brachyuran crabs have internal fertilisation and mate belly-to-belly. For many aquatic species, | forces the crab's body to release hormones, causing it to act like a female crab, even to the point of performing female mating dances. Although all energy otherwise expended on reproduction is directed to the "Sacculina", the crab develops a nurturing behavior typical of a normal female crab. The natural hatching process of a crab consists of the female finding a high rock and grooming its brood pouch on its abdomen and releasing the fertilized eggs in the water through a bobbing motion. The female crab stirs the water with her claw to aid the flow of the water. When | Do crab lay eggs? | My baby crabs love it, they are a couple and they like to spend the whole day sleeping at the hotel. | Abstract The reproductive cycle and recruitment period of a ghost crab population from Ubatuba, Sao Paulo, Brazil were investigated by means of examining the developmental stages of gonads of breeding crabs and the ingress of young recruits to the studied population. Monthly collections over a one-year period were carried out during nocturnal low-tide periods at “Vermelha” beach. The morphology of the abdomen and pleopods was used for sex determination. All captured crabs were measured for carapace width and dissected for the determination of the development stage of the gonads. A total of 582 specimens was captured: 271 males, 241 females, and 70 juveniles. Size ranged from 8.5 to 37.5 mm for males, from 9.5 to 39.2 mm for females, and from 5.8 to 12 mm for early juveniles. Median size of males and females did not differ statistically. The frequency of ovigerous females was markedly low. The onset of sexual maturity in females is achieved at around 23 mm of carapace width. Mature females with advanced go... | Sexual maturity of the edible crab (Cancer pagurus) in the Skagerrak and the Kattegat, based on reproductive and morphometric characters | 271 | Primer and Short-Range Releaser Pheromone Properties of Premolt Female Urine from the Shore Crab Carcinus maenas | Variation in relative quantities of airborne sex pheromone components from individual femaleEphestia cautella (Lepidoptera: Pyralidae) | what does the sacculina crab release to make it a female crab | Effects of sex and color phase on ion regulation in the invasive European green crab, Carcinus maenas | ON SPERMATOGENESIS AND SPERM ULTRASTRUCTURE OF BLUE CRAB PORTUNUS TRITUBERCULATUS (CRUSTACEA, DECAPODA) | IMMUNOLOGICAL STUDIES OF THE SPERM AND SEMINAL FLUID IN THE HORSESHOE CRAB LIMULUS POLYPHEMUS L. (MEROSTOMATA) | Causes of a male-biased operational sex ratio in the fiddler crab Uca crenulata | Effects of polychaetes (Perinereis nuntia) on sperm performance of the domesticated black tiger shrimp (Penaeus monodon) | In insects, male-derived substances transferred during copulation often alter female physiology. Thus these substances may affect female behaviour, including mating receptivity and release of sex pheromone. In the sorghum plant bug Stenotus rubrovittatus (Matsumura) (Hemiptera: Miridae), males transfer a spermatophore into the bursa copulatrix of females during copulation. Mated females of S. rubrovittatus do not mate again for at least 3 days and release lower amounts of sex pheromone than virgin females. A previous study indicates that females that receive a spermatophore are less likely to be sexually receptive to males. Therefore, we tested whether an extract of the male reproductive organ affected female mating receptivity and whether this extract and spermatophores per se affected the release of sex pheromone by females. The mating receptivity of virgin females injected with an extract of male reproductive organs was significantly lower than that of control females injected with distilled water, but not significantly different from that of females injected with an extract of male thorax (the negative control). The amount of sex pheromone released by females, however, did not differ among the different treatments. When the interval between two subsequent copulations of males is less than 1 h, males do not transfer a spermatophore during the second copulation. It is thus possible to produce artificially mated females with and without a spermatophore. However, the amount of sex pheromone released by mated females with and without a spermatophore did not differ. These results indicate that male-derived substances do not suppress release of sex pheromone by female S. rubrovittatus but, they may reduce their mating receptivity. |
272 | Great for support of paper plates | What are the materials used in paper plates? | Papier collé Papier collé Papier collé (French: "pasted paper" or "paper cut outs") is a type of collage and collaging technique in which paper is adhered to a flat mount. The difference between collage and papier collé is that the latter refers exclusively to the use of paper, while the former may incorporate other two-dimension (non-paper) components. As the term papier collé is not commonly used, this type of work is often simply called collage. Cubist painter Georges Braque, inspired by Pablo Picasso's collage method, invented the technique and first used it in his 1912 work, "Fruit Dish and Glass". Braque continued | This is a terrific filament. We use a lot of it on our Prusa for printing robotics parts. Many objects that require support in PLA can be printed without support in this PETG. Layer adhesion is great, and the deep blue color is beautiful. | The descriptions doesn't say PAPER! I thought they were real plates.
IT'S NOT WORTH MORE THAN 50 cents, they would be 2 for $1 at the Dollar Store, maybe 4 for a buck.
They are s***! I will prob never use because why spend 75 cents to use a tiny paper plate? | Maybe have them in thicker paper, like laminated almost. I didn't care for how thin of paper they came in. | It's a decent product, but the blocks are all made of paper with the designs glued on. After a few uses some of the edges are already lifting. I'm trying to figure out a way to secure the papers to all the sides so it can withstand some use. | I use it for paper-craft. Gives a good protective sheen without damaging the paper. | I use these chipboards for shipping paper items that I don't want to get bent. Great quality. Very thick. | 272 | Outstanding. Great for support of paper plates. Do not advise use in microwave, but will last a while. | M̶̼̟̦͇̰͍͆̄̒́̌Į̸̬̯̞̤̯̞̰̩͈̪͓͉̗͍͝ͅͅC̷̹̙͉͙̹͈͕͉̙̯̈́̓̅͂̊́̊̄̇̀͆͋̅̐͘͝R̴̫͓̩̮̩͒̾́̒̑̊̽̊͘͠Ó̴̡̮̟͚̘̟͖͖̳̱̞͈̯̜̞͓̖̂̌̎͘W̵͈̤͚̹̼̤̘̓̍̑Ẫ̵̦͂̓̓̐̂̚V̴̡̧̡̨̞̳̫̹̠͕̘̪͓͓̟̫̦͇̎̊̓̀E̵̯͂͊̋̎̔̇̒̍̍͊͑͠͠͝ ̷̣͖̒̉̂̆́͋̈́̏̐̾̐̽̽̎̄͠͝͠ | Great plates you cannot use in the microwave. | Can paper plates go in the microwave? | The plates are sturdy and can survive the microwave without leaking | Exactly what I need to replace my broken microwave plate ... | MICROWAVE WEAPONRY'S USE ON PEOPLE EXPLAINED | Non-destructive testing of materials by microwave systems | Plates work, tray useless |
273 | Tailoring of nickel silicide contacts on silicon carbide | To explore the potential of nickel-silicide:carbon (NiSi:C) as contact technology for MOSFETs with silicon-carbon (Si:C) source/drain (S/D) regions, we examined the effects of incorporating 1.0 at.% of carbon in Si prior to nickel silicidation. The addition of carbon was found to improve the morphological and phase stability of NiSi:C contacts. This is possibly due to the presence of carbon at the NiSi:C grain boundaries and NiSi:C/Si interface, which will modify the grain-boundary and interfacial energies. This will influence the kinetics of NiSi:C silicidation. In this letter, we have also demonstrated the first integration of NiSi:C contacts in MOSFETs with Si:C S/D regions. We further show that NiSi:C silicidation suppresses the formation of active deep-level defects, leading to superior n+/p junction characteristics. | Low resistance contracts to highly doped silicon carbide (SiC) are investigated. Using a novel test structure that is easy to fabricate and easy to use, this paper demonstrates how it is used to reliably determine relatively low specific contact resistivities which vary with heat treatment. The test structure requires no error correction and is not affected by parasitic resistances. Using the test structure, small changes in specific contact resistivity are determined for small temperature changes. Results will be presented and discussed on the application of this novel test structure for nickel to highly doped SiC. | This present work is investigating the HIP diffusion bonding of NITRASIL Si3N4 and REFEL SiC ceramics to the nickel-based superalloys INCOLOY 909 and INCONEL 718. | The authors have recently developed Ni/Ti/Pt ohmic contacts to p-GaAs. They exhibit the extremely low ohmic contact resistivity of 2/spl times/10/sup -7/ cm/sup 2/ to a p/sup +/-GaAs layer with a doping level of 2/spl times/10/sup 19/ cm/sup 3/ at the annealing temperature of 400/spl deg/C, which is higher than the optimised annealing temperature of the Pt ohmic contacts, and is almost equal to that of AuGe/Ni ohmic contacts to n-GaAs. The Ni/Ti/Pt ohmic contact system is very advantageous in fabricating high speed GaAs based HBTs. | Abstract In this study, we report on the structural characterization of Ni layer and Ni/Ti bilayer contacts on n-type 4H–SiC. The resulting Ni-silicides and the redistribution of carbon, after annealing at 950 °C, in the Ni/SiC and the Ni/Ti/SiC contacts are particularly studied by Rutherford Backscattering Spectrometry (RBS) at E α = 3.2 MeV, nuclear reaction analysis (NRA) at E d = 1 MeV, scanning electron microscopy (SEM) and Energy Dispersive X-ray Spectrometry (EDS) techniques. | Optical Properties and Applications of Silicon Carbide in Astrophysics | Optical Properties and Applications of Silicon Carbide in Astrophysics | Abstract: This chapter discusses the silicide and germanide technology for interconnects in ULSI applications. After a brief introduction about silicide and contacts for ULSI, the formation of silicides and germanides on Si and SiGe is reviewed. Then, the chapter discusses crystalline properties of silicides and the effect of incorporation of third materials, such as Ge, Pt, and Pd, into silicide. The electrical properties of metal/Si, SiGe and Ge contacts are also reviewed. | 273 | Co-deposition technique by means of simultaneous ion beam sputtering of nickel and silicon onto SiC was performed for tailoring of Nisilicide/SiC contacts. The prepared samples were analysed by means of XRD and XPS in order to obtain information about the surface and interface chemistry. Depth profiling was used in order to analyse in-depth information and chemical distribution of the specimens. XRD results showed that the main phase formed is Ni2Si. The XPS analysis confirmed the formation of the silicide on the surface and showed details about the chemical composition of the layer and layer/substrate interface. Moreover, the XPS depth profiles with detailed analysis of XPS peaks suggested that tailoring of C distribution could be monitored by the co-deposition technique employed. (C) 2007 Elsevier B.V. All rights reserved. | Research of Ni-P-SiC Complex Chemical Plating | Application Of Sic-X-Ray Masks For Fabricating Sub-Micron Devices | Impact of a Treatment Combining Nitrogen Plasma Exposure and Forming Gas Annealing on Defect Passivation of SiO2/SiC Interfaces | This paper presents results of using silicon carbide (SiC) and silicon-rich silicon nitride (SiNx) as membrane for X-ray masks in technology of X-ray lithography. Microcrystalline silicon carbide film was deposited on silicon substrate by electron synchrotron resonance plasma-enhanced chemical vapor deposition at 300 degrees C utilizing a SiH4/CH4/H2/Ar gas mixture. Low tensile stress film which is suitable as X-ray membrane can be achieved by annealing after silicon carbide film deposition. The microwave power over 800 watts and the gas ratio (Methane:Silane) larger than 1.5 are needed for the stoichiometry of SiC film. On the other hand, we deposited silicon-rich silicon nitride film on silicon substrate by low pressure chemical vapor deposition at 850 degrees C to 900 degrees C. In order to get low tensile stress film, different gas flow ratios (Dichlorosilane:Ammonia) were tested. The increased gas flow ratio (Dichlorosilane:Ammonia) and the increased deposition temperature are related to the decrease of tensile stress of film. Roughness, uniformity, optical transmittance and soft X-ray transmission of both films are reported. The absorption bands of both films were measured by FTIR spectroscopy. The surface morphology was monitored by AFM. The photon transmission of both films was measured in the range of 400 to 800 nm for visible light and 800 to 1600 ev photon energy for SR soft X-ray transmission was conducted at the Synchrotron Radiation Research Center, Hsinchu, Taiwan. The deposition rate of both films are 13 nm/min and 40 nm/min for silicon nitride and silicon carbide, respectively.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only. | Electrical Properties of Atomic-Layer-Deposited La2O3/Thermal-Nitrided SiO2 Stacking Dielectric on 4H-SiC(0001) | Fabrication of Ni–Co–SiC composite coatings by pulse electrodeposition — Effects of duty cycle and pulse frequency | Effect of Deposition Parameters on the Property of SiC Layer in TRISO-Coated Particles | Elucidation of the Structural Texture of Electrodeposited Ni/SiC Nanocomposite Coatings |
274 | where does years of living dangerously air | The Year of Living Dangerously (novel) a journalist soars. Billy keeps photographs and notes about the people he knows, recording his observations of their character and their lives and making up stories about their possible motivations. Hamilton is alarmed to discover that Billy is keeping a file on him, too, but decides to trust Billy anyway. Hamilton and others frequently confide in the narrator, Cookie, who intersperses the story with details from Billy's files, such as that Billy is supporting a local woman, known only as Ibu, and her children living in Jakarta's slums with food and money. Billy introduces Hamilton to Jill Bryant, a beautiful | The Year of Living Dangerously (novel) young diplomat at the British embassy. Billy and Jill are close friends, even to the extent that Billy poses as her boyfriend so she can avoid unwanted attention, and Billy subtly manipulates events so that Hamilton and Jill continue to encounter one another. Hamilton quickly falls in love with Jill, and their relationship starts soon after a trip to the port of Priok. Hamilton also learns that Billy is a strong supporter of the Sukarno regime but is very concerned with the extreme poverty afflicting Indonesia. Jill's diplomatic work is a cover for her real job as an intelligence officer | Dangerously They Live claims to have amnesia; she cannot remember who she is. The driver reports this to his superiors. Mike is excited, as this is his area of study, and persuades Dr. Murdoch (Roland Drew) to let him take the case. John Goodwin (Moroni Olsen) shows up and claims Jane is his daughter. However, after he leaves, Jane tells Mike that he is lying, and that she is actually working for British Intelligence. Mike does not quite believe her, especially when Goodwin returns with a famous specialist, Dr. Ingersoll (Raymond Massey), from whom Mike took a class. When Jane adamantly refuses to | Dangerously They Live claims to have amnesia; she cannot remember who she is. The driver reports this to his superiors. Mike is excited, as this is his area of study, and persuades Dr. Murdoch (Roland Drew) to let him take the case. John Goodwin (Moroni Olsen) shows up and claims Jane is his daughter. However, after he leaves, Jane tells Mike that he is lying, and that she is actually working for British Intelligence. Mike does not quite believe her, especially when Goodwin returns with a famous specialist, Dr. Ingersoll (Raymond Massey), from whom Mike took a class. When Jane adamantly refuses to | How to Live Safely in a Science Fictional Universe are headed back to the hanger so Yu's past self can shoot him. Yu realizes as he flies in that he loves TAMMY and she loves him. He steps out of his time machine and gets shot, but lives as it was just a shot to his stomach. In the appendix, Yu talks about visiting the place and time displayed by the diorama. He finds his father, trapped because his time machine broke down. Yu makes amends with his father and then travels to the present. He reunites his dad with his mom, then sets off to find "The Woman | that time was in more need of help and support. Danny decides it is better to not tell Connie the truth, and asks Miss Templeton to keep the secret, while he goes off to serve his life sentence in prison. Dangerous Years Dangerous Years is a 1947 American drama film produced by Sol M. Wurtzel, directed by Arthur Pierson, starring Billy Halop and Ann E. Todd. Marilyn Monroe makes her first on screen appearance as Evie the waitress in the restaurant scene. The God-fearing residents of Middleton are worried that the Gopher Hole, a new road house restaurant outside of | that time was in more need of help and support. Danny decides it is better to not tell Connie the truth, and asks Miss Templeton to keep the secret, while he goes off to serve his life sentence in prison. Dangerous Years Dangerous Years is a 1947 American drama film produced by Sol M. Wurtzel, directed by Arthur Pierson, starring Billy Halop and Ann E. Todd. Marilyn Monroe makes her first on screen appearance as Evie the waitress in the restaurant scene. The God-fearing residents of Middleton are worried that the Gopher Hole, a new road house restaurant outside of | Escape set An escape set (in German "Tauchretter" = "diver rescuer") is a breathing set, which lets its wearer survive for a time in an environment without (sufficiently) breathable air, in particular underwater, primarily or originally intending mainly to survive long enough to reach safety where the air is breathable. Early escape sets were rebreathers and were used to escape from a submarine which was submerged so long that its onboard air supply ran out, and for technical or military reasons the submarine could not surface: one example is the Davis Submerged Escape Apparatus. Escape sets were also used ashore, | 274 | Environmental Content. Years of Living Dangerously Years of Living Dangerously is an American documentary television series focusing on global warming. The first season was broadcast in the US in 2014 on "Showtime". It won an Emmy Award as Outstanding Documentary or Nonfiction Series. The second season aired on the National Geographic Channel in 2016. Executive producers included James Cameron, Arnold Schwarzenegger, and series creators Joel Bach and David Gelber (formerly of "60 Minutes"). Joseph Romm and Heidi Cullen were the chief science advisors. The weekly episodes featured celebrity hosts with a history of environmental activism and well-known journalists with a | who is the executive producer of years of living dangerously | when does years of living dangerously air on national geographic channel | the 1982 film ‘the year of living dangerously’ is set in which as | how many reviews did rotten tomatoes give the year of living dangerously | who directed the documentary lives worth living | when was the living years music video released | when was the book commentaries on living published | who plays jo in this life tv series |
275 | Kim will always be Kris's true favorite. | Kim Kardashian by Kardashian and Ray J in 2003 was leaked. Kardashian filed a lawsuit against Vivid Entertainment, who distributed the film as "Kim K Superstar". She later dropped the suit and settled for a reported 5 million. In October 2007 Kardashian, in addition to her mother Kris Jenner, her step-parent Caitlyn Jenner (Bruce), her siblings Kourtney, Khloé, and Rob Kardashian, and half-sisters Kendall and Kylie Jenner, began to appear in the reality television series "Keeping Up with the Kardashians". The series proved successful for E!, and has led to the creations of spin-offs including "Kourtney and Kim Take New York" and | i think that KIM is really doing all the sacrifice so that the relationship can hold, but at the same time i think no one understood Jimmy like KIM, kot even his own brother. I mean she really knows how jimmy needs to be treated and supports him and helps him (with the slippin jimmy style, making him incorporate tricks in with her clients and all). May be i’m overthinking! | Ho is Kim's sidekick in Kim Possible? | Upon Apple's release of the Apple Watch, several critics drew similarities between the real-life device and the Kimmunicator, especially when Kim's device was downsized to a wristwatch during the final season. Kim Possible (character) Kimberly Ann Possible is a fictional character who appears in the animated television series "Kim Possible", voiced by actress Christy Carlson Romano. Created by Bob Schooley and Mark McCorkle, the character debuted in the pilot "Crush", which premiered on June 7, 2002. After starring in each of the show's 84 episodes, Kim made her final appearance in the finale "Graduation, Part 2", which originally aired on | Kim Possible (character) (Nancy Cartwright) and computer genius Wade (Tahj Mowry). The character lives in fictional Middleton, USA with her parents James (Gary Cole) and Ann (Jean Smart), a rocket scientist and neurosurgeon respectively, and her younger brothers, identical twins Jim and Tim. Kim goes on extraordinary missions to save the world from danger at the hands of various supervillains and evil geniuses. Her most consistent adversaries are mad scientist Dr. Drakken and his sidekick Shego, the latter of whom is a former superheroine and skilled martial artist who has the ability to generate powerful energy blasts from her hands, and thus poses | I just got done watching Joe Rogan & kanye & I have a new gut feeling...Kim won't ever leave kanye, but he will leave her. It seems before, she was his obsession & now, he has a new one, North & religion. like the way he barely even acknowledges Kim or even how he won't say her name, he'll be the one to divorce her | > A source told the site that Kim is returning to "RHOBH" as a friend. The women will be targeting her, questioning whether she's really sober. This is a recycled storyline from seasons past. According to the insider, season 7 will be no different. Some of the women will be going after Kim, unconvinced that she's sober.
Really? You have all those fancy, high fashion loving, platinum visa card carrying, sometimes working, gossiping, at times backstabbing women on this show and that's the best storyline you can come up with?
I'd rather have a show without that storyline. And it's not even because it's a repeat from every other season. I'm beginning to feel sorry for that woman! She's trying to stay sober, and instead of finding friends that genuinely support her, she has to put up with women who really shouldn't be throwing stones. Sure, she's done a lot of messed up things, but come on! We all know it! We've all seen it! No need to go through it *again*.
Also, Kyle got annoyed when Lisa brought up her husband's alleged affair on camera, because of her children. Eileen didn't want to speak about her affair because it was in the past and because it affected others not on the show. Brandi freaked out when her parenting skills were questioned, LVP worried that a camera crew at her daughter's wedding was imposing, yet all women are okay with discussing Kim's alcoholism - a genuine disease!? Anyone ever wonder what Kim's kids might go through? | Jevil:runs at Kris
Kris:what are you doing?
Jevil:I CAN DO ANYTHING!! (Becomes Jevil’sknife, cuts Kris in half | 275 | I know it's an open joke in the family that Kris's favorite is whichever kid is most famous at the moment -- aka Kim for many years, Khloe for a bit when Lamar was doing good in the Lakers, Kendall when her modeling career was looking really promising, and now Kylie because of how well she's doing financially.
But honestly throughout it all, I really believe no matter what that Kim will always be her favorite. Kim is exactly what Kris wanted - a gorgeous daughter who is as business minded as she is but also deferential to Kris.
Kim always wants to please Kris (Khloe & Kourtney aren't this way). Kim is incredibly ambitious and a go-getter (Kendall isn't this way). Kim spent enough time around her mom to develop a really close relationship (Kylie didn't get this).
Kim is the daughter that Kris can discuss business with, make plans with, but also have a mother-daughter like bond because Kim loves her so much too. | are kylie and kendall on kuwtk? | Love Kris or Hate Kris...She is Smart, Beautiful, Open, and Rich! Living Her Best Life!!!! | Alright alright, Kelly is a snob | what reality tv show did kim kardashian star in | OMG Kath and Kim where have you been all my life?! | Thoughts on Kimura's career | KC and Jenna’s relationship | Kim Kardashian and her fiancé Kris Humphries could be set to get their own reality spin-off show. |
276 | how many pounds of respiratory toxicant emissions did dominion have in 2002 | In the 1990s, metered dose inhalers (MDIs) containing chlorofluorocarbons were replaced with dry-powder inhalers (DPIs) and MDIs containing hydrofluorocarbons (HFCs). While HFCs are not ozone depleting, they are potent greenhouse gases. Annual carbon footprint (CO2e), per patient were 17 kg for Relvar-Ellipta/Ventolin-Accuhaler; and 439 kg for Seretide-Evohaler/Ventolin-Evohaler. In 2017, 70% of all inhalers sold in England were MDI, versus 13% in Sweden. Applying the Swedish DPI and MDI distribution to England would result in an annual reduction of 550 kt CO2e. The lower carbon footprint of DPIs should be considered alongside other factors when choosing inhalation devices. | More than 15,000 Americans get sick from carbon monoxide every year and the odorless, toxic gas kills 480 people, the Centers for Disease Control and Prevention said on Thursday. |
Introduction
Worldwide, there are 2.1 million HIV-infected children under 15 years of age, 70% of whom reside in Sub-Saharan Africa (SSA) [1]. In this region, air pollution is a major public health concern [2]. Air pollution is a mixture of natural and man-made substances, including particulate matter (PM), carbon monoxide (CO), polycyclic aromatic hydrocarbons (PAHs), and sulfur dioxide [3]. Exposure to air pollution is associated with multiple morbidities, including pneumonia and cardiovascular events [4,5]. In SSA where 77% of households use solid fuel for cooking or heating, household air pollution (HAP) poses a significant health risk, and is a major contributor to ambient air pollution [2, 6,7]. In 2012, HAP was attributed to 581,300 deaths in SSA [8]. The known implications of solid fuel use on HAP has resulted in efforts to promote use of cleaner fuels, such as kerosene [9]. However, there are few data to describe HAP and its impact on health outcomes in highly populous peri-urban communities in low and middle-income countries where biomass is less commonly used [9,10].
A growing evidence base implicates chronic early life air pollution in neurocognitive insult [11][12][13][14]. Significant brain developmental processes continue from prenatal life into early childhood and adolescence, making this entire period a critical window for central nervous system (CNS) development [15,16]. Environmental toxins in air pollution may cross the blood brain barrier, where they drive activation of microglia and astrocytes and trigger release of neurotoxic molecules [13,17]. Cellular damage may result in white matter changes that further impair brain development and function [13,18]. Recent studies have linked prenatal exposure to particulate matter (PM 2.5 ), CO, and nitrogen oxide (NO 2 ) in air pollution with impaired global cognition [19], visual spatial reasoning, short and long term memory [20], and fine motor skills in early childhood [20]. Prenatal PAH exposure is associated with deficits in nonverbal reasoning ability [21], developmental delay [22], reduced IQ [23,24], and verbal IQ [24,25]. Likewise, chronic early childhood exposure to higher levels of black carbon, NO 2 , and PAH in air pollution are associated with deficits in attention [26], verbal IQ [25], and learning ability [27,28].
Perinatal HIV infection can also cause a broad spectrum of cognitive impairment and neurologic disease, including progressive HIV-encephalopathy (PHE), neurocognitive delay and impaired cognition [29][30][31][32]. While the advent of antiretroviral therapy (ART) has substantially reduced the incidence of PHE [30], HIV-infected children on ART often have lower neurocognitive functioning compared to their uninfected peers and population norms [29,[33][34][35]. HIV-infected children may manifest deficits in numerous domains including processing speed, memory, visual-spatial skills, global cognition, executive function, and reasoning [29,31,32]. Similar to environmental neurotoxicants, HIV neuropathogenesis involves both microglia and astrocytes and a neuroinflammatory molecular cascade that damages neurons [36]. White matter microstructural damage is common in HIV-infected children [37,38].
We hypothesize that HIV and chronic exposure to air pollution may impact neurocognition either through shared pathways, or through additive insult on existing damage. To date, no studies have investigated the impacts of air pollution on neurocognition in HIV-infected children. In this study, we tested whether HIV modifies the relationship between air pollution and cognition. We measured the magnitude of CO and PAH exposure among HIV-infected and uninfected children, and examined the relationship between these exposures and neurocognition in these two groups.
Materials and Methods
Participants and Recruitment
This study includes early-treated HIV-infected children and HIV unexposed uninfected (HUU) children and their caregivers. Participants in ongoing studies involving annual comprehensive cognitive and motor assessments were recruited for the Nairobi, Kenya-based Health Impacts of Household Air Pollution on Women's Health and Child Survival (HAPK) Study. HIV-infected children had previously participated in the Optimizing HIV-1 Therapy Study (OPH03; NCT00428116), a trial designed to measure growth and development in infants randomized to continued or interrupted ART [39]. All enrolled children initiated ART during infancy (at <12 months of age) and had monthly study visits for up to 42 months. At the end of follow-up, children and their caregivers were invited to participate in a cohort study with extended follow-up and annual cognitive and motor assessments. From 2011-2013, HUU children were recruited from the Mathare North Maternal Child Health Clinic in Nairobi. Key eligibility criteria included: Age 5-12 years, and both biological mother and child confirmed HIV negative. Ethical approval for this study was obtained from the University of Washington (UW) Institutional Review Board (45269, 27 August 2013) and the University of Nairobi/Kenyatta National Hospital (KNH) Ethics and Research Committee (P23/6/2013, 27 November 2013).
Data Collection
At HAPK Study enrollment, study staff collected demographic information and information about typical cooking behaviors and fuel use using standardized questionnaires. To assess household air pollution (HAP), two home visits were conducted by study staff, 24-h apart, between December 2014 and December 2016. During the first study visit, staff conducted household surveys of cook-stove location and provided and installed air monitors. Twenty-four hours later, staff returned to collect air monitors, and administer questionnaires regarding caregiver adherence to wearing air monitors, and behavior related to air pollution exposure over the 24-h monitoring period. Additionally, study staff collected spot urine samples from caregivers and children for measurement of PAH metabolites.
Caregiver personal CO exposure was measured during the 24-h monitoring period using Lascar electronic continuous CO monitors (EL-USB-CO). Caregivers were instructed to wear the monitors during waking hours and were asked to perform typical daily household activities. During the same 24-h monitoring period, household-level CO exposure was measured using a Lascar electronic continuous CO monitor (EL-USB-CO) hung in home cooking areas.
PAH exposure was estimated by determination of a key PAH metabolite, 1-hydroxypyrene (1-OHP), in child urine samples. While PAH exposure is a mixture of compounds, pyrene is typically found in the mixture. Thus, its metabolite, 1-OHP, is often used as a proxy of PAH exposure from multiple sources [40]. Urinary metabolites are considered a useful biomarker for airborne PAH exposure [41]. Spot urine samples were stored at −70 • C on the same day as sample collection and were shipped to the University of Washington for metabolite analysis by high performance liquid chromatography with fluorescence detection. The analytical method was based on that reported by Chetiyanukornkul et al. [42], with modifications. The HPLC system was an Agilent 1100 series and the column was an Agilent Poroshell 120 SB-C18 (100 × 2.1 mm, 2.7 µm). Mobile phases were 10 mM sodium acetate (pH 5) and methanol. The lower limit of quantification was set at the concentration of the lowest calibration standard and all urine samples had 1-OHP greater than this. One-hydroxypyrene was measured in ng/mL, and values were creatinine-adjusted for dilution and expressed in µmol/mol of creatinine using the following formula:
1 − OHP in ng/mL creatinine clearance measured in µmol/L × 10 6 218.3 g/mol(1)
A battery of neurocognitive assessments was performed by trained study staff, all with undergraduate degrees in psychology or graduate coursework in clinical psychology. Scripts for each assessment were translated from English to Kiswahili and back-translated to ensure accuracy. Tests were administered in the preferred language of the child, either Kiswahili or English. The Kaufman Assessment Battery for Children, Second Edition (KABC-II) was used assess the global cognition, short term and delayed memory, visual-spatial skills, learning, and non-verbal test performance [37]. The KABC has been used in Senegal [38] and Zaire [39], and in HIV-infected Ugandan children [40], and had good construct validity when administered to Ugandan children aged 7-16 years. The Test of Variables of Attention (TOVA) is a computer-based test that measures sustained attention based on visual stimuli. The TOVA has been used to characterize attention deficits in HIV-infected children [41] and children with a history of cerebral malaria [42] in Uganda [40]. The Behavior Rating Inventory of Executive Function (BRIEF) was used to measure executive function and consists of a caregiver-administered questionnaire. Previously, the BRIEF has been used in Ugandan children with HIV [43]. The Bruininks-Oseretsky Test of Motor Proficiency Brief Form (BOTMP-Brief Form), was used to assess overall motor proficiency. It has been previously used in HIV-infected populations ( [34,38], pp. 309-332). Raw scores for each domain or scale were scaled and standardized using US norms. For ease of interpretation, scores are presented as z-scores.
Statistical Analysis
Analyses were stratified by child HIV-infected status because of our a priori hypothesis that the impacts of HAP may differ by infection status. Descriptive statistics for study population characteristics and neurocognitive outcomes (z-score) were calculated. Carbon monoxide (ppm) and 1-OHP (µmol/mol creatinine) variables were examined as both continuous and dichotomous variables. We dichotomized CO exposure (high/low) based on the 24-h WHO recommended limit of 6.11 ppm and PAH exposure (high/low) based on the cohort median for 1-OHP (0.68 µmol/mol creatinine). We calculated the arithmetic mean, standard deviation, median, interquartile range, minimum, and maximum 1-OHP and CO values. We compared 24-h mean CO and 1-OHP values by child HIV-infection status using 2-sample t-tests and compared medians with a non-parametric equality of medians test. We used chi-square tests to test whether high/low CO and 1-OHP exposure differed by child HIV infection status.
Continuous 1-OHP and CO were log 10 transformed because the distributions of both variables were skewed. We evaluated cofactors for continuous CO and 1-OHP concentrations using univariate regression models (continuous cofactors), two-sample t-tests (dichotomous cofactors), and one-way ANOVA (cofactors with 3+ levels). We estimated the association between CO or 1-OHP concentrations and neurocognitive function using multivariate linear regression models. Confounders were selected a priori and included child age at time of neurocognitive testing and household monthly rent. All adjusted models were run with an exposure*HIV-infection interaction term and a likelihood ratio test was used to assess the statistical significance of the interaction term. Pearson correlation coefficients were used to evaluate the correlation between caregiver CO, household CO, child urine 1-OHP, and caregiver urine 1-OHP. All analyses were performed using Stata 14.0 (StataCorp, College Station, TX, USA) [43].
Results
Population Characteristics
Our sample included 49 HUU children and 45 HIV-infected children who had available data for either caregiver CO or urinary 1-OHP concentration. Caregiver CO data were available for 33 and 38 HIV-infected children and 38 HUU children, respectively, and child urinary 1-OHP data were available for 32 HIV-infected children and 43 HUU children. Mean age at time of neurocognitive testing was 6.6 years for HIV-infected children and 6.7 for HUU (Table 1). In both groups, the majority of caregivers were the child's biological mother. Compared to HUU children, caregivers of HIV-infected children were less likely to be employed, less likely to be married, and reported a higher household monthly rent (mean 4105 vs. 2247 Kenyan Shillings), but had similar levels of education (9.5 vs. 9.0 years). Paraffin (kerosene) was the most common primary type of cooking fuel for both HUU children (76.5%) and HIV-infected children (45.5%). A significant proportion of the households for the latter group used propane as a primary fuel (34.1%).
Magnitude of HAP
Mean 24-h caregiver CO was higher in HIV-infected children than in HUU children (11.59 ppm vs. 5.16 ppm, p = 0.04). The proportion of children with a caregiver 24-h mean CO exceeding the WHO recommended 6.11 ppm threshold, household mean 24-h CO values, and the proportion with household 24-h CO levels exceeding the WHO threshold did not differ significantly by HIV status (Table 2). Child 1-OHP concentration was similar in HIV-infected (0.9 µmol/mol creatinine) vs. HUU children (0.7 µmol/mol creatinine) (p = 0.6). The proportion of children with urine 1-OHP values exceeding the median was similar by HIV status (p = 0.7).
Socioeconomic Indicators
Caregiver employment status
Cofactors for HAP
In HIV-infected children, having an unemployed caregiver was significantly associated with higher urinary PAH (p = 0.01) and using a non-electric lamp for lighting was significantly associated with higher caregiver CO (p = 0.01). (Table 3). No other cofactors were significantly associated with HAP exposure.
HAP and Neurocognition
In HIV-infected children, after adjustment for child age and household monthly rent, having a urine 1-OHP value exceeding the median (high 1-OHP) was associated with a global cognitive ability score that was −0.5 z-scores lower compared to children with a urine 1-OHP value less than the median (low 1-OHP) (β = −0.5, p = 0.04). High 1-OHP values were also associated with lower scores in the delayed memory (β = −0.7, p = 0.01), and attention (β = −1.1, p = 0.03) domains (Table 4a). In addition, HIV-infected children had an inverse linear relationship between increasing log 10 1-OHP concentration and attention scores (β = −0.8, p = 0.03) (Table 4b). After adjustment for child age and household monthly rent, caregiver 24-h CO concentration was not significantly associated with score in any domain among HIV-infected children. In HUU children, after adjustment for child age and household monthly rent, neither caregiver 24-h CO nor child urine 1-OHP concentration were associated with neurocognitive scores. We observed a statistically significant interaction between high child urine 1-OHP concentration and HIV-infection in the delayed memory (β = −0.80, p = 0.03) and attention (β = −1.1, p = 0.02) domains, and a significant interaction between high caregiver CO concentration and HIV-infection in the attention domain (β = 0.21, p = 0.02).
Correlations between Measurements of HAP
Correlations between measurements of HAP ranged from weak to strongly correlated (Table 5). Correlation was highest between household and caregiver CO (r = 0.70, p < 0.0001) and lowest for caregiver CO and child 1-OHP (r = 0.13, p = 0.4). Table 5. Spearman correlation coefficient between log 10 transformed measurements of household air pollution.
HAP Measurement
Household
Discussion
We examined the potential adverse neurocognitive health consequences of chronic exposure to common air pollutants (CO, PAH) among HIV-infected and HUU children in peri-urban Kenya. We hypothesized that impacts would be greater among HIV-infected children. Consistent with our hypotheses, we observed that HIV-infected children with higher 1-OHP in urine, a proxy for PAH exposure, had lower scores for global cognition, delayed memory and attention. Furthermore, there was a statistically significant interaction between high 1-OHP concentration and HIV-infection in the delayed memory and attention domains. In contrast, HUU children did not have differences in neurocognitive scores in relation to either their PAH or CO exposures.
Our results are consistent with those of previous epidemiological studies. Edwards et al. [21] observed an association between prenatal PAH levels and non-verbal intelligence at school age and Jedrychowski et al. [25] observed an association with lower verbal IQ in the same cohort. Similarly, in an urban New York cohort, Perera et al., found that higher prenatal PAH exposure was associated with lower IQ at age 5 [23]. We did not find any association between CO exposure and neurocognition, unlike Dix-Cooper et al. [20], who found associations between prenatal CO exposure and lower function in the visual-spatial integration, motor, short term memory, and long term memory domains. Our study differed in that it examined chronic childhood exposures, rather than prenatal exposure.
It is possible that the exposures we measured were similar to earlier prenatal exposures in the same household and that observed effects reflect prenatal exposure. However, it also is plausible that both prenatal and postnatal exposures are associated with neurocognitive outcomes, given ongoing neuroplasticity during childhood [15,16].
To our knowledge, these data are the first to assess associations between postnatal exposure to HAP and neurocognitive outcomes in HIV-infected children. Our findings of associations between 1-OHP and multiple neurocognitive outcomes in HIV-infected but not HUU children suggests that the combination of HIV and environmental pollutants may have a detrimental impact on child neurocognitive outcomes. We and others have shown lower neurodevelopmental and neurocognitive functioning between HIV-infected compared with HUU children, despite antiretroviral therapy (ART) [29,30,32,33,35]. Similar to environmental toxins, HIV enters the CNS and triggers an inflammatory process in which small molecules, cytokines and chemokines disrupt neuronal function and cause neuronal cell death [14,36]. HIV-infected children may have pre-existing neurocognitive compromise that is worsened by exposure to environmental pollutants. Alternatively, or in addition, perinatal exposure to environmental toxins may also increase risk in HIV-infected children. In HUU, exposure to elevated levels of environmental pollutants did not have discernable impact, perhaps due to smaller magnitude of effects in this group. Mechanisms by which PAHs adversely affect the developing brain are not fully understood, but may involve endocrine disruption, binding of PAHs to placental growth factors, and oxidative stress [44][45][46]. Our data suggest that it would be useful to define mechanisms for synergies between HIV and PAH neurotoxicity and to decrease PAH exposures in HIV-infected children.
In this Nairobi cohort, kerosene and propane, rather than biomass, were the most commonly reported cooking fuels, consistent with demographic surveys [47]. Kerosene is typically perceived by users as a cleaner alternative to biomass fuels [9], and propane is considered a low polluting fuel. However, multiple studies have linked kerosene use with high levels of emissions such as PM 2.5 [9,28] and the associated health impacts [9]. An alarming 39% of children in our sample had levels of CO higher than WHO recommended limits for indoor levels. The mean maternal 48-h CO exposure in a Guatemalan cohort known for substantial wood smoke exposure is 3.8 ppm, while the mean 24-h caregiver CO in Nairobi families was 8.2 ppm. Similarly, mean 1-OHP levels were also high in our cohort, exceeding levels observed in other studies of young children. Mean 1-OHP levels in Ukrainian pediatric cohorts were 0.69 µmol/mol creatinine, and 0.34 µmol/mol creatinine, with the former corresponding to a cohort of children living near a steel mill [48]. The mean level in our cohort was 0.81 µmol/mol creatinine. The high levels of air pollution observed in our study underscore the need to further understand the key contributors to air pollution exposure in peri-urban cohorts, and the health impacts of these exposures, and whether interventions to decrease exposure to combustion byproducts can provide benefit.
Strengths of this study include use of detailed neurocognitive assessment data, measurement of personal and household air pollution exposure (CO), and measurement of biomarkers for PAH exposures (1-OHP in urine). The neurocognitive assessments used in our study have been used previously in African and HIV-infected cohorts ( [49][50][51][52][53][54][55][56], pp. 309-332).
Our study has several limitations. First, this analysis was limited by a small sample size. Due to this study's exploratory nature, we did not adjust for multiple comparisons. We were unable to control for some potentially important confounders, including nutritional factors, maternal IQ, psychosocial stimulation during early childhood, and exposure to other environmental toxicants. Our analysis only measured exposure to CO and PAH and we were unable to account for ambient air pollution exposure or other components of air pollution such as non-PAH PM 2.5 constituents, nitrogen dioxide, metals, and ozone which also impact neurocognition [13].
The timing of collection of air pollution exposure data, which was performed when children were school-aged, may not reflect critical windows of neurodevelopment in the perinatal period. However, there are ongoing neurodevelopmental processes that continue into school age, which may be influenced by concurrent childhood exposures [11,16]. Additionally, we relied on a proxy measurement of child CO exposure; there are likely differences in the child's versus the caregiver's inhalation exposures due to differing minute ventilation, and the fact that school-age children are mobile. We employed an exposure assessment approach based on practical and cultural acceptability considerations. We can assume children spend a large proportion of their time (including sleeping time) in and around the home environment compared with other environments. Furthermore, we found strong correlation between caregiver and household CO measurements, suggesting compliance with wearing the monitors, and supporting the idea that caregiver CO is a reasonable proxy for household CO exposure. We would expect non-differential misclassification of CO exposure, which would bias our estimates toward the null. Another limitation of our exposure measurement is that use of the urinary 1-OHP biomarker does not allow us to differentiate the sources of PAH exposure, as it reflects exposure not just to HAP, but also to tobacco smoke, ambient air pollution, and dietary sources.
HIV-infected children in our study were originally recruited for an RCT, and the unknown consequences of the trial intervention may be confounding our results. However, we did not find any differences in neurocognitive scores by randomization arm. Nonetheless, the impacts of this intervention on neurocognition should be carefully evaluated, though it is beyond the scope of this analysis. Another limitation of our study is the differing sample sizes between analyses. Children were included in our sample if they had either available caregiver CO data or urinary 1-OHP data. Thus, even though there was substantial overlap, the models assessing each exposure included slightly different samples (20 HIV-infected children and 32 HUU children who had both CO and 1-OHP data). While we did not find any meaningful differences in neurocognitive test scores or demographic characteristics between those with data for both exposures and those with data for either exposure, this could, in part, explain the differences between the 1-OHP and CO results.
Conclusions
Despite limitations in timing of exposure assessment, use of a caregiver proxy CO measurement, and a modest sample size, our results provide further support of evidence that early life exposure to air pollutants such as PAH may compromise healthy neurocognition. The susceptibility among HIV-infected children, but not HUU children, is a novel and important observation. Given the large global population of children co-exposed to higher levels of air pollution and HIV in SSA, continued emphasis on characterizing and reducing risk factors for poorer neurocognitive health in the HIV-infected population is merited. Last, taking a multi-faceted interventional approach-combining biomedical interventions like ART with interventions to improve indoor air pollution-may be necessary to optimize neurocognitive outcomes for children with HIV in regions with high air pollution exposures. collected the data; Michael J. Boivin, Paul Bangirana provided study oversight and trained neurocognitive testers; Michael Paulsen, Christopher D. Simpson, Niloufar Ghodsian processed urine samples; Megan K. Suter, Laurén A. Gómez analyzed the data; Megan K. Suter wrote the manuscript. All co-authors contributed to the editing of the manuscript.
Conflicts of Interest:
The authors declare no conflict of interest.
in the table are of those who had non-missing values for that variable. Missingness for all sociodemographic characteristics was <10%.
cofactors, p-values were calculated by comparing means of the log 10 transformed HAP values with a t-test or one-way ANOVA. For continuous cofactors, coefficients and p-values were calculated by regressing the log 10 transformed HAP values on the cofactor. * Indicates statistically significant difference between HIV = infected and HUU groups at α = 0.05.
Table 1 .
1Summary of study population sociodemographic characteristics and neurocognitive outcomes (z-score).HIV-Infected n = 45
HIV Uninfected n = 49
n (%) or Mean (SD)
n (%) or Mean (SD)
Sociodemographic Characteristics
Male sex
29 (64.4)
22 (44.9)
Child age at neurocognitive assessment (years)
6.6 (0.8)
6.7 (1.4)
Caregiver is biological mother
42 (93.3)
48 (98.0)
Caregiver is married
26 (57.8)
33 (70.2)
Caregiver is employed
11 (24.4)
16 (34.0)
Smoker in household
7 (15.6)
6 (12.8)
Cooks in living area
28 (62.2)
45 (93.8)
Garbage is burned nearby
12 (26.7)
16 (33.3)
Primary type of cooking fuel
Wood
2 (4.6)
0 (0.0)
Propane
15 (34.1)
8 (17.0)
Charcoal
7 (15.9)
3 (6.4)
Paraffin (Kerosene)
20 (45.5)
36 (76.6)
Caregiver age (years)
33.2 (6.1)
31.1 (5.7)
Caregiver education (years)
9.5 (2.7)
9.0 (2.7)
Household people/room
3.4 (2.1)
4.4 (1.6)
Household monthly rent (Kenyan Shillings)
4105 (4801)
2247 (1311)
Time between neurocognitive assessment and air monitoring (months)
2.4 (3.6)
6.4 (3.
Table 2 .
2Caregiver 24-h CO levels (ppm), household 24-h CO levels (ppm), and child urine 1-OHP
(µmol/mol creatinine).
Caregiver 24-h CO, ppm
Caregiver 24-h CO Mean >6.11 ppm
n
Mean (SD)
Median (IQR)
Range
n (%)
HIV-infected
33
* 11.6 (18.0)
6.1 (0.8, 13.2)
0.03, 83.0
16 (49)
HUU
38
* 5.2 (6.5)
3.7 (0.4, 7.1)
0.00, 31.6
12 (32)
Household 24-h CO, ppm
Household 24-h CO Mean >6.11
ppm
n
Mean (SD)
Median (IQR)
Range
n (%)
HIV-infected
35
13.9 (19.4)
4.3 (1.2,27.0)
0.00, 95.2
16 (46)
HUU
40
9.2 (13.3)
3.8 (1.0,10.2)
0.00, 54.1
15 (38)
Child Urine 1-OHP (µmol/mol Creatinine)
High Child Urine 1-OHP
n
Mean (SD)
Median (IQR)
Range
n (%)
HIV-infected
32
0.9 (0.7)
0.6 (0.4, 1.3)
0.05, 2.7
14 (44)
HUU
43
0.7 (0.5)
0.7 (0.4, 1.0)
0.07, 2.4
23 (53)
* Indicates statistically significant difference by HIV-infection status (p < 0.05). Means were compared with a t-test,
medians were compared with a non-parametric test of equal medians.
Table 3 .
3Cofactors for HAP exposure.Cofactor
HIV-Infected
HIV Uninfected
Caregiver CO (ppm)
Urinary 1-OHP
(µmol/mol Creatinine)
Caregiver CO (ppm)
Urinary 1-OHP
(µmol/mol Creatinine)
Household Characteristics
Geometric Mean
(SD) or β (95%CI)
p
Geometric Mean
(SD) or β (95%CI)
p
Geometric Mean
(SD) or β (95%CI)
p
Geometric Mean
(SD) or β (95%CI)
p
Type of cooking fuel
Wood
0.8 (-)
0.1
2.6 (-)
0.3
-
0.8
-
0.2
Propane
3.4 (12.8)
0.5 (3.1)
3.4 (5.4)
0.4 (2.7)
Charcoal
3.7 (2.9)
0.6 (1.8)
2.0 (3.4)
0.7 (1.2)
Paraffin
2.7 (7.5)
0.6 (2.8)
1.9 (6.6)
0.6 (2.2)
Smoker in household
Yes
3.1 (7.8)
0.9
0.6 (1.8)
0.9
7.0 (1.4)
0.1
1.0 (1.6)
0.08
No
3.8 (7.2)
0.6 (2.9)
1.5 (6.3)
0.5 (2.3)
Cooks inside living area
Yes
3.3 (5.9)
0.9
0.5 (2.4)
0.2
2.0 (5.9)
0.8
0.6 (2.2)
0.6
No
3.1 (9.8)
0.9 (3.4)
2.4 (18.4)
0.4 (2.7)
Non-electric lamp for lighting
Yes
* 8.3 (4.0)
0.01
0.4 (2.9)
0.08
1.3 (7.3)
0.3
0.62 (2.5)
0.6
No
* 1.5 (8.4)
0.8 (2.4)
2.8 (5.4)
0.53 (1.9)
Garbage burned nearby with smoke entering kitchen
Yes
1.9 (3.5)
0.4
0.7 (2.6)
0.4
1.9 (7.6)
0.8
0.6 (2.2)
0.8
No
3.7 (8.7)
0.5 (2.8)
2.1 (5.9)
0.6 (2.2)
Table 4 .
4(a) Adjusted difference in neurocognitive test score (z-score) between children with high 1-OHP (>0.68 µmol/mol creatinine) and low 1-OHP (≤0.68 µmol/mol creatinine); (b) Linear regression results of log10 transformed child urinary 1-OHP levels and neurocognitive test scores; (c) Linear regression results of caregiver 24-h CO exposure and neurocognitive test scores.(a)
HIV Infected
HIV Uninfected
Difference in z-Score by High vs.
Low Child 1-OHP
Difference in z-Score by High
vs. Low Child 1-OHP
Neurocognitive Test Scores
n
β
95%CI
n
β
95%CI
Global cognition
31
* −0.5
−0.9, −0.03
39
−0.05
−0.6, 0.5
Short-term memory
31
−0.4
−1.0, 0.2
39
0.2
−0.4, 0.8
Visual-spatial skills
31
−0.4
−1.0, 0.1
39
−0.3
−1.0, 0.3
Learning
31
−0.6
−1.3, 0.003
39
0.2
−0.4, 0.8
Nonverbal test performance
30
−0.3
−0.8, 0.2
39
−0.5
−1.1, 0.2
Delayed memory
27
* −0.7
−1.2, −0.2
33
0.2
−0.4, 0.7
Executive function
31
0.05
−0.7, 0.8
40
0.0008
−0.6, 0.6
Attention
27
* −1.1
−1.7, −0.4
35
0.2
−0.5, 0.9
Motor
30
−0.3
−1.0, 0.4
40
0.2
−0.3, 0.7
* Indicates statistical significance at α = 0.05. All models adjusted for child age at time of neurological testing and
household monthly rent.
(b)
HIV Infected
HIV Uninfected
Child 1-OHP
Child 1-OHP
Neurocognitive Test Scores
n
β
95%CI
n
β
95%CI
Global cognition
31
−0.3
−0.8, 0.3
39
0.2
−0.5, 1.0
Short-term memory
31
−0.04
−0.7, 0.6
39
0.4
−0.4, 1.2
Visual-spatial skills
31
−0.4
−1.1, 0.2
39
0.008
−0.9, 0.9
Learning
31
−0.2
−1.0, 0.6
39
0.3
−0.5, 1.2
Nonverbal test performance
30
−0.3
−0.9, 0.3
39
−0.3
−1.2, 0.6
Delayed memory
27
−0.3
−0.9, 0.4
33
0.1
−0.8, 1.0
Executive function
31
0.06
−0.8, 0.9
40
0.02
−0.8, 0.8
Attention
27
* −0.8
−1.6, −0.07
35
0.04
−0.9, 1.0
Motor
30
−0.3
−1.1, 0.5
40
0.3
−0.4, 1.0
* Indicates statistical significance at α = 0.05. 1-OHP was log 10 transformed. All models adjusted for child age at
time of neurological testing and household monthly rent.
Table 4 .
4Cont.(c)
HIV Infected
HIV Uninfected
Caregiver 24-h CO
Caregiver 24-h CO
Neurocognitive Test Scores
n
β
95%CI
n
β
95%CI
Global cognition
30
0.08
−0.2, 0.3
35
0.05
−0.3, 0.4
Short-term memory
30
0.04
−0.3, 0.4
35
0.1
−0.2, 0.4
Visual-spatial skills
30
0.05
−0.2, 0.3
35
−0.04
−0.4, 0.3
Learning
30
0.05
−0.4, 0.5
35
0.3
−0.05, 0.6
Nonverbal test performance
29
−0.3
−0.6, 0.04
35
−0.1
−0.5, 0.3
Delayed memory
26
0.1
−0.2, 0.5
28
0.1
−0.2, 0.5
Executive function
30
−0.4
−0.8, 0.07
35
−0.08
−0.5, 0.3
Attention
26
−0.05
−0.4, 0.3
30
−0.2
−0.7, 0.2
Motor
30
0.09
−0.3, 0.5
35
0.2
−0.1, 0.5
All models adjusted for child age at time of neurological testing and household monthly rent. CO was
log 10 transformed.
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Acknowledgments: This work was supported by the Eunice Kennedy Shriver National Institute of Child Health
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Prenatal Airborne Polycyclic Aromatic Hydrocarbon Exposure and Child IQ at Age 5 Years. F P Perera, Z Li, R Whyatt, L Hoepner, S Wang, D Camann, V Rauh, 10.1542/peds.2008-3506Pediatrics. 124PubMedPerera, F.P.; Li, Z.; Whyatt, R.; Hoepner, L.; Wang, S.; Camann, D.; Rauh, V. Prenatal Airborne Polycyclic Aromatic Hydrocarbon Exposure and Child IQ at Age 5 Years. Pediatrics 2009, 124, e195-e202. [CrossRef] [PubMed]
Neighborhood Social Context and Individual Polycyclic Aromatic Hydrocarbon Exposures Associated with Child Cognitive Test Scores. G S Lovasi, N Eldred-Skemp, J W Quinn, H Chang, V A Rauh, A Rundle, M A Orjuela, F P Perera, 10.1007/s10826-013-9731-4J. Child Fam. Stud. 23PubMedLovasi, G.S.; Eldred-Skemp, N.; Quinn, J.W.; Chang, H.; Rauh, V.A.; Rundle, A.; Orjuela, M.A.; Perera, F.P. Neighborhood Social Context and Individual Polycyclic Aromatic Hydrocarbon Exposures Associated with Child Cognitive Test Scores. J. Child Fam. Stud. 2014, 23, 785-799. [CrossRef] [PubMed]
Prenatal exposure to polycyclic aromatic hydrocarbons and cognitive dysfunction in children. W A Jedrychowski, F P Perera, D Camann, J Spengler, M Butscher, E Mroz, R Majewska, E Flak, R Jacek, A Sowa, 10.1007/s11356-014-3627-8Environ. Sci. Pollut. Res. 22PubMedJedrychowski, W.A.; Perera, F.P.; Camann, D.; Spengler, J.; Butscher, M.; Mroz, E.; Majewska, R.; Flak, E.; Jacek, R.; Sowa, A. Prenatal exposure to polycyclic aromatic hydrocarbons and cognitive dysfunction in children. Environ. Sci. Pollut. Res. 2015, 22, 3631-3639. [CrossRef] [PubMed]
Associations between traffic-related black carbon exposure and attention in a prospective birth cohort of urban children. Y H M Chiu, D C Bellinger, B A Coull, S Anderson, R Barber, R O Wright, R J Wright, 10.1289/ehp.1205940Environ. Health Perspect. 121PubMedChiu, Y.H.M.; Bellinger, D.C.; Coull, B.A.; Anderson, S.; Barber, R.; Wright, R.O.; Wright, R.J. Associations between traffic-related black carbon exposure and attention in a prospective birth cohort of urban children. Environ. Health Perspect. 2013, 121, 859-864. [CrossRef] [PubMed]
Association of traffic-related air pollution with cognitive development in children. C Freire, R Ramos, R Puertas, M.-J Lopez-Espinosa, J Julvez, I Aguilera, F Cruz, M.-F Fernandez, J Sunyer, N Olea, 10.1136/jech.2008.084574J. Epidemiol. Community Heal. 64PubMedFreire, C.; Ramos, R.; Puertas, R.; Lopez-Espinosa, M.-J.; Julvez, J.; Aguilera, I.; Cruz, F.; Fernandez, M.-F.; Sunyer, J.; Olea, N. Association of traffic-related air pollution with cognitive development in children. J. Epidemiol. Community Heal. 2010, 64, 223-228. [CrossRef] [PubMed]
Association of black carbon with cognition among children in a prospective birth cohort study. S F Suglia, A Gryparis, R O Wright, J Schwartz, R J Wright, 10.1093/aje/kwm308Am. J. Epidemiol. 167PubMedSuglia, S.F.; Gryparis, A.; Wright, R.O.; Schwartz, J.; Wright, R.J. Association of black carbon with cognition among children in a prospective birth cohort study. Am. J. Epidemiol. 2008, 167, 280-286. [CrossRef] [PubMed]
HIV-Associated Cognitive Impairment in Perinatally Infected Children: A Meta-analysis. N Phillips, T Amos, C Kuo, J Hoare, 10.1542/peds.2016-0893Pediatrics. 138PubMedPhillips, N.; Amos, T.; Kuo, C.; Hoare, J. HIV-Associated Cognitive Impairment in Perinatally Infected Children: A Meta-analysis. Pediatrics 2016, 138, e20160893. [CrossRef] [PubMed]
Neurologic disease in HIV-infected children and the impact of combination antiretroviral therapy. C S Crowell, K M Malee, R Yogev, 10.1002/rmv.1793Rev. Med. Virol. 24PubMedCrowell, C.S.; Malee, K.M.; Yogev, R. Neurologic disease in HIV-infected children and the impact of combination antiretroviral therapy. Rev. Med. Virol. 2014, 24, 316-331. [CrossRef] [PubMed]
Neurologic complications of pediatric human immunodeficiency virus: Implications for clinical practice and management challenges in the African setting. K A Donald, J Hoare, B Eley, J M Wilmshurst, 10.1016/j.spen.2014.01.004Semin. Pediatr. Neurol. 21PubMedDonald, K.A.; Hoare, J.; Eley, B.; Wilmshurst, J.M. Neurologic complications of pediatric human immunodeficiency virus: Implications for clinical practice and management challenges in the African setting. Semin. Pediatr. Neurol. 2014, 21, 3-11. [CrossRef] [PubMed]
Review article Neurodevelopment in perinatally HIV-infected children: A concern for adolescence. B Laughton, M Cornell, M Boivin, A Van Rie, 10.7448/IAS.16.1.18603J. Int. AIDS Soc. 16PubMedLaughton, B.; Cornell, M.; Boivin, M.; Van Rie, A. Review article Neurodevelopment in perinatally HIV-infected children: A concern for adolescence. J. Int. AIDS Soc. 2013, 16, 18603. [CrossRef] [PubMed]
Comparison of developmental milestone attainment in early treated HIV-infected infants versus HIV-unexposed infants: A prospective cohort study. S Benki-Nugent, D Wamalwa, A Langat, K Tapia, J Adhiambo, D Chebet, H M Okinyi, G John-Stewart, 10.1186/s12887-017-0776-1BMC Pediatr. 17PubMedBenki-Nugent, S.; Wamalwa, D.; Langat, A.; Tapia, K.; Adhiambo, J.; Chebet, D.; Okinyi, H.M.; John-Stewart, G. Comparison of developmental milestone attainment in early treated HIV-infected infants versus HIV-unexposed infants: A prospective cohort study. BMC Pediatr. 2017, 17, 24. [CrossRef] [PubMed]
Early viral supression improves neurcognitive outcomes in HIV-infected children. C S Crowell, Y Huo, K Tassiopoulos, K M Malee, R Yogev, R Hazra, R M Rutstein, S L Nichols, R A Smith, P L Williams, 10.1097/QAD.0000000000000528AIDS. 29PubMedCrowell, C.S.; Huo, Y.; Tassiopoulos, K.; Malee, K.M.; Yogev, R.; Hazra, R.; Rutstein, R.M.; Nichols, S.L.; Smith, R.A.; Williams, P.L.; et al. Early viral supression improves neurcognitive outcomes in HIV-infected children. AIDS 2015, 29, 295-304. [CrossRef] [PubMed]
Impact of HIV and Atiretroviral Therapy on Neurocognitive Outcomes Among School-Aged Children. H Brahmbhatt, M Boivin, V Ssempijja, J Kagaayi, G Kigozi, D Serwadda, A Violari, R H Gray, 10.1097/QAI.0000000000001305J. Acquir. Immune Defic. Syndr. 75PubMedBrahmbhatt, H.; Boivin, M.; Ssempijja, V.; Kagaayi, J.; Kigozi, G.; Serwadda, D.; Violari, A.; Gray, R.H. Impact of HIV and Atiretroviral Therapy on Neurocognitive Outcomes Among School-Aged Children. J. Acquir. Immune Defic. Syndr. 2017, 75, 1-8. [CrossRef] [PubMed]
HIV-1-Related Central Nervous System Disease: Current Issues in Pathogenesis, Diagnosis, and Treatment. Cold Spring Perspect. S Spudich, F Gonzalez-Scarano, 10.1101/cshperspect.a0071202PubMedSpudich, S.; Gonzalez-Scarano, F. HIV-1-Related Central Nervous System Disease: Current Issues in Pathogenesis, Diagnosis, and Treatment. Cold Spring Perspect. Med. 2012, 2, 1-18. [CrossRef] [PubMed]
White matter micro-structural changes in ART-naive and ART-treated children and adolescents infected with HIV in South Africa. J Hoare, J.-P Fouche, N Phillips, J A Joska, R Paul, K A Donald, K G F Thomas, D J Stein, 10.1097/QAD.0000000000000766AIDS. 29PubMedHoare, J.; Fouche, J.-P.; Phillips, N.; Joska, J.A.; Paul, R.; Donald, K.A.; Thomas, K.G.F.; Stein, D.J. White matter micro-structural changes in ART-naive and ART-treated children and adolescents infected with HIV in South Africa. AIDS 2015, 29, 1793-1801. [CrossRef] [PubMed]
Relationship between apolipoprotein E4 genotype and white matter integrity in HIV-positive young adults in South Africa. J Hoare, J Westgarth-Taylor, J P Fouche, M Combrinck, B Spottiswoode, D J Stein, J A Joska, 10.1007/s00406-012-0341-8Eur. Arch. Psychiatry Clin. Neurosci. 263PubMedHoare, J.; Westgarth-Taylor, J.; Fouche, J.P.; Combrinck, M.; Spottiswoode, B.; Stein, D.J.; Joska, J.A. Relationship between apolipoprotein E4 genotype and white matter integrity in HIV-positive young adults in South Africa. Eur. Arch. Psychiatry Clin. Neurosci. 2012, 263, 189-195. [CrossRef] [PubMed]
Treatment initiated during acute/early HIV in infancy: A randomized trial. D Wamalwa, S Benki-Nugent, A Langat, K Tapia, E Ngugi, H Moraa, E Maleche-Obimbo, V Otieno, I Inwani, A Barbra, 10.1097/QAD.0000000000001158AIDS. 30PubMedWamalwa, D.; Benki-nugent, S.; Langat, A.; Tapia, K.; Ngugi, E.; Moraa, H.; Maleche-obimbo, E.; Otieno, V.; Inwani, I.; Barbra, A. Treatment initiated during acute/early HIV in infancy: A randomized trial. AIDS 2016, 30, 2303-2313. [CrossRef] [PubMed]
Guidelines for indoor air quality. WHO Guidel. D Penney, V Benignus, S Kephalopoulos, D Kotzias, M Kleinman, A Verrier, 10.1186/2041-1480-2-S2-I19454Penney, D.; Benignus, V.; Kephalopoulos, S.; Kotzias, D.; Kleinman, M.; Verrier, A. Guidelines for indoor air quality. WHO Guidel. 2010, 9, 454. [CrossRef]
Benchmark guideline for urinary 1-hydroxypyrene as biomarker of occupational exposure to polycyclic aromatic hydrocarbons. F J Jongeneelen, 10.1016/S0003-4878(00)00009-0Ann. Occup. Hyg. 45Jongeneelen, F.J. Benchmark guideline for urinary 1-hydroxypyrene as biomarker of occupational exposure to polycyclic aromatic hydrocarbons. Ann. Occup. Hyg. 2001, 45, 3-13. [CrossRef]
Simultaneous determination of urinary hydroxylated metabolites of naphthalene, fluorene, phenanthrene, fluoranthene and pyrene as multiple biomarkers of exposure to polycyclic aromatic hydrocarbons. T Chetiyanukornkul, A Toriba, T Kameda, N Tang, K Hayakawa, 10.1007/s00216-006-0628-6Anal. Bioanal. Chem. 386PubMedChetiyanukornkul, T.; Toriba, A.; Kameda, T.; Tang, N.; Hayakawa, K. Simultaneous determination of urinary hydroxylated metabolites of naphthalene, fluorene, phenanthrene, fluoranthene and pyrene as multiple biomarkers of exposure to polycyclic aromatic hydrocarbons. Anal. Bioanal. Chem. 2006, 386, 712-718. [CrossRef] [PubMed]
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Cytochrome c: Functions beyond respiration. Y.-L P Ow, D R Green, Z Hao, T W Mak, 10.1038/nrm2434Nat. Rev. Mol. Cell Biol. 9PubMedOw, Y.-L.P.; Green, D.R.; Hao, Z.; Mak, T.W. Cytochrome c: Functions beyond respiration. Nat. Rev. Mol. Cell Biol. 2008, 9, 532-542. [CrossRef] [PubMed]
The impact of polycyclic aromatic hydrocarbons and fine particles on pregnancy outcome. J Dejmek, I Solanský, I Benes, J Lenícek, R J Srám, 10.1289/ehp.001081159Environ. Health Perspect. 108PubMedDejmek, J.; Solanský, I.; Benes, I.; Lenícek, J.; Srám, R.J. The impact of polycyclic aromatic hydrocarbons and fine particles on pregnancy outcome. Environ. Health Perspect. 2000, 108, 1159-1164. [CrossRef] [PubMed]
A teratologic suppressor role for p53 in benzo[a]pyrene-treated transgenic p53-deficient mice. C J Nicol, M Harrison, R R Laposa, I L Gimelshtein, P G Wells, 10.1038/ng0695-181Nat. Genet. 10PubMedNicol, C.J.; Harrison, M.; Laposa, R.R.; Gimelshtein, I.L.; Wells, P.G. A teratologic suppressor role for p53 in benzo[a]pyrene-treated transgenic p53-deficient mice. Nat. Genet. 1995, 10, 181-187. [CrossRef] [PubMed]
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Research|Children's Health Urinary 1-Hydroxypyrene as a Biomarker of PAH Exposure in 3-Year-Old Ukrainian Children. A P Mucha, D Hryhorczuk, A Serdyuk, J Nakonechny, A Zvinchuk, S Erdal, M Caudill, P Scheff, E Lukyanova, Z Shkiryak-Nyzhnyk, 10.1289/ehp.7898Environ. Health Perspect. 114PubMedMucha, A.P.; Hryhorczuk, D.; Serdyuk, A.; Nakonechny, J.; Zvinchuk, A.; Erdal, S.; Caudill, M.; Scheff, P.; Lukyanova, E.; Shkiryak-nyzhnyk, Z.; et al. Research|Children's Health Urinary 1-Hydroxypyrene as a Biomarker of PAH Exposure in 3-Year-Old Ukrainian Children. Environ. Health Perspect. 2006, 114, 603-609. [CrossRef] [PubMed]
A preliminary examination of the construct validity of the KABC-II in Ugandan children with a history of cerebral malaria. P Bangirana, P Seggane-Musisi, P Allebeck, B Giordani, C J Chandy, O R Opoka, J Byarugaba, A Ehnvall, M J Boivin, Afr. Health Sci. 9PubMedBangirana, P.; Seggane-Musisi, P.; Allebeck, P.; Giordani, B.; Chandy, C.J.; Opoka, O.R.; Byarugaba, J.; Ehnvall, A.; Boivin, M.J. A preliminary examination of the construct validity of the KABC-II in Ugandan children with a history of cerebral malaria. Afr. Health Sci. 2009, 9, 186-192. [PubMed]
Effects of early cerebral malaria on cognitive ability in Senegalese children. M J Boivin, 10.1097/00004703-200210000-00010Dev. Behav. Pediatr. 23Boivin, M.J. Effects of early cerebral malaria on cognitive ability in Senegalese children. Dev. Behav. Pediatr. 2002, 23, 353-364. [CrossRef]
Neurocognitive and motor deficits in HIV-infected Ugandan children with high CD4 cell counts. T D Ruel, M J Boivin, H E Boal, P Bangirana, E Charlebois, D V Havlir, P J Rosenthal, G Dorsey, J Achan, C Akello, 10.1093/cid/cir1037Clin. Infect. Dis. 54PubMedRuel, T.D.; Boivin, M.J.; Boal, H.E.; Bangirana, P.; Charlebois, E.; Havlir, D.V.; Rosenthal, P.J.; Dorsey, G.; Achan, J.; Akello, C.; et al. Neurocognitive and motor deficits in HIV-infected Ugandan children with high CD4 cell counts. Clin. Infect. Dis. 2012, 54, 1001-1009. [CrossRef] [PubMed]
HIV-subtype A is associated with poorer neuropsychological performance compared with subtype D in antiretroviral therapy-naive Ugandan children. M J Boivin, T D Ruel, H E Boal, P Bangirana, H Cao, L A Eller, E Charlebois, D V Havlir, M R Kamya, J Achan, 10.1097/QAD.0b013e3283389dccAIDS. 24PubMedBoivin, M.J.; Ruel, T.D.; Boal, H.E.; Bangirana, P.; Cao, H.; Eller, L.A.; Charlebois, E.; Havlir, D.V.; Kamya, M.R.; Achan, J.; et al. HIV-subtype A is associated with poorer neuropsychological performance compared with subtype D in antiretroviral therapy-naive Ugandan children. AIDS 2010, 24, 1163-1170. [CrossRef] [PubMed]
A preliminary evaluation of the cognitive and motor effects of pediatric HIV infection in Zairian children. M J Boivin, S D Green, A G Davies, B Giordani, J K Mokili, W A Cutting, 10.1037/0278-6133.14.1.13Health Psychol. 14PubMedBoivin, M.J.; Green, S.D.; Davies, A.G.; Giordani, B.; Mokili, J.K.; Cutting, W.A. A preliminary evaluation of the cognitive and motor effects of pediatric HIV infection in Zairian children. Health Psychol. 1995, 14, 13-21. [CrossRef] [PubMed]
Cerebral Malaria in Children Is Associated With Long-term Cognitive Impairment. C C John, P Bangirana, J Byarugaba, R O Opoka, R Idro, A M Jurek, B Wu, M J Boivin, 10.1542/peds.2007-3709Pediatrics. 122PubMedJohn, C.C.; Bangirana, P.; Byarugaba, J.; Opoka, R.O.; Idro, R.; Jurek, A.M.; Wu, B.; Boivin, M.J. Cerebral Malaria in Children Is Associated With Long-term Cognitive Impairment. Pediatrics 2008, 122, e92-e99. [CrossRef] [PubMed]
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| Flue gas samples were collected from 17 waste incinerators with a big combustion capacity in large urban cities and the suburbs in Japan, in order to evaluate a real situation for PCDDs, PCDFs and non-ortho chlorine substituted coplanar PCBs (CoPCBs) emitted into the air through the flue gas. The average concentrations (ngTEQ/Nm3 of 2,3,7,8-PCDDs, 2,3,7,8-PCDFs and Co-PCBs were 17.4, 20.9 and 3.11, respectively. This indicates PCDFs give higher environmental impact than do PCDDs or CoPCBs. On the basis of above data, total amounts of PCDDs, PCDFs and CoPCBs annually emitted via flue gas from 397 continuous combustion type and big scale incinerators in Japan were estimated to be 2.0, 5.1 and 0.36 TEQKg, respectively. The total was 7.5 TEQkg. | Effect of air pollution on chronic respiratory disease in the New York city metropolitan area, 1972. | Monitoring Space Shuttle air quality using the Jet Propulsion Laboratory electronic nose | Launceston, Tasmania air pollution in Launceston and surrounding areas during the winter period is caused by wood smoke, while about 8% is from motor vehicle pollution. During the early 1990s about 60% of households used wood heaters, but since the mid 2000s only 25–30% of households use wood heating. According to the 2011 Tasmanian Air Monitoring report, particulate matter met the Air NEPM goals starting in 2006, and did not exceed the PM10 standard in the years 2009–2011. Launceston is situated at the confluence of the South Esk River and the North Esk River, forming the Tamar River estuary. It is used | Chamber-based insights into the factors controlling epoxydiol (IEPOX) secondary organic aerosol (SOA) yield, composition, and volatility | 276 | Hope Bay. In 2002, Dominion was responsible for 1,110,703 pounds of gastrointestinal or liver toxicant emissions, 1,440,000 pounds of musculoskeletal toxicant emissions, and 1,489,763 pounds of suspected respiratory toxicant emissions, and 1,478,383 pounds of suspected skin or sense organ toxicant emissions among other emissions that are suspected to be hazardous. Dominion Energy Dominion Energy, Inc., commonly referred to as Dominion, is an American power and energy company headquartered in Richmond, Virginia that supplies electricity in parts of Virginia and North Carolina and supplies natural gas to parts of West Virginia, Ohio, Pennsylvania, and eastern North Carolina. Dominion also has generation | what is the name of dominion energy's charitable foundation | how much money did the dominion fund contribute to highways | how much money did the dominion fund contribute to roads | gexa energy is based in which city | which company owns british energy, a nuclear power company | how many states does oneroof energy have offices in | Life Cycle Emissions and Cost of Producing Electricity from Coal, Natural Gas, and Wood Pellets in Ontario, Canada | Energy Regulatory Office |
277 | how many female servants are there in hogarth's servants | Women in the House of Lords was the first woman leader of the House of Lords in 1981. Baroness Hale of Richmond became the first female Law Lord in 2004. Since the passage of the House of Lords Act 1999, hereditary peeresses remain eligible for election to the Upper House; there is one (Countess of Mar) among the 90 hereditary peers who continue to sit. Following a change to the law in 2014 to allow women to be ordained bishops, the Lords Spiritual (Women) Act 2015 was passed, which provides that whenever a vacancy arises among the Lords Spiritual during the ten years following the Act | What is The role of a Maid of Honour? | How do spell wives? | The reason this question came to mind is because of the recent rise in vegetarianism in the west. Animal rights are becoming more and more an issue that people want to defend and I thought it was interesting that there are religions, like Jainism, that got this issue right thousands of years ago. Unfortunately Jainism, like most religions, completely fail on the issue of women's rights. I shouldn't have to go over most modern religions. Judaism segregates men and women, women aren't allowed to be Pope or even Bishops in the Catholic Church, menstruating Muslim women aren't allowed to do a whole bunch of stuff, the list is too long.
So does anyone know a religion that, like Jainism on animal rights, didn't fail in this respect?
PS. Of course you can argue to what extend the modern world has established women's rights but I think we can all agree that the right answer is that women at least should be equal and whether they currently are is not the topic of this question. | Women in ancient and imperial China among the Han Chinese proved impossible. As in previous periods, women were expected to obey the Three Obediences and obey their fathers in childhood, their husbands when married, and their sons in widowhood. Women's personal names are typically unknown; they were referred to as, "the wife of [X]," or, "mother of [X]." A woman's achievements during her life were closely connected to her ability to bear children; those who could not were looked down upon by their husbands, in-laws, and neighbours. If a woman did not given birth within a few years, the husband would typically take a concubine. Letters | Please help my research. Thank you in advance
**EDIT**
*So*, after counting here is some hero with distinct lore and can be generalized to female/woman.
1. Legion Commander
1. Drow Ranger
1. Mirana
1. Vengeful Spirit
1. Templar Assassin
1. Luna
1. Naga Siren
1. Phantom Assassin
1. Broodmother
1. Spectre
1. Medusa
1. Crystal Maiden
1. Windranger
1. Lina
1. Enchantress
1. Queen of Pain
1. Death Prophet
1. Winter Wyvern
1. *Dark Willow*
Sorry about dark willow, totally forgot about her
Thank you | Mende people Mende are a well-documented example of a non-western, pre-industrial society in which, at least historically, women took more political leadership positions relative to men. In the pre-colonial era, the Mende had female chiefs and war leaders. One such female chief, Madam Yoko (1849–1906), was the leader of the vast Kpa Mende Confederacy. She was formally recognized by the British as a Paramount Chief in 1894, ruling an area that was eventually divided into fourteen chiefdoms. Although it is impossible to know the extent to which other Mende women rose to leadership positions comparable to Madam Yoko's, historians believe that perhaps | the long gallery piers. These figures are dressed in Roman armour. In the late fourteenth century, Lady Worthies began to accompany the Nine Worthies, though usually not individualized and shown as anonymous Amazon-styled warriors. In later years, nine of the "Most Illustrious Ladies of All Ages and Nations" were chosen from scripture, history and legend to be placed alongside their male counterparts, though the choices for the Lady Worthies were not usually standardized and often varied by region, author and artist. Eustache Deschamps to the "neuf preux" adds "neuf preuses" (women), including Penthesilea, Tomyris, and Semiramis. Together with their male | 277 | Hogarth's Servants the work. The three female figures have similarly youthful appearances, not children but also not old. The male figures progress in age from a boy at the top centre, through a mature man at the bottom centre, to a more elderly man at the top right. The older man is possibly Ben Ives; the other servants may be "Samuel"; Mary Lewis, Hogarth's wife's cousin, who later inherited the painting; and Mrs Chappel, who was known to have worked for the Hogarths in Chiswick. Ronald Paulson believes the servants featured could be a coachman, valet, page, housekeeper and two housemaids. The | who are the four judges on the bench in hogarth | when was hogarth's servants sold to the tate gallery | where is the story of william hogarth found in the bible | what is the name of boss hogg's wife | who does madame masque end up with in heroic age | where does the hogfather live in the movie | when did the hogfather come out in order | in what year did congressman hogg invite reverend gunn to the white house for |
278 | High temperature superconducting components for microwave systems | High temperature superconductors (HTS) for aerospace applications | Brief introduction to the high temperature superconducting oxides which have been discovered is presented. And also possible mechanisms for the superconductivity are surveyed. | In the second decade following the discovery of high-temperature superconductivity (HTS), wireless communications has emerged as the earliest large commercial market. The enormous growth of the wireless industry coupled with its increasing technology demands has created a significant opportunity for HTS technology in wireless base stations. These systems combine high-performance HTS RF filters with cryocooled semiconductor preamplifiers to offer enhanced sensitivity to improve signal reception and exceptional selectivity to reject interfering signals. There are now thousands of installed HTS systems and the prospects are good for widespread future deployment. This paper discusses the underlying technologies that support HTS wireless applications, based upon the characteristic microwave properties of HTS thin films and substrates. HTS filter design technology has been under development for a decade and has gained a fair measure of maturity in terms of design tools, simulation techniques, and available topologies. The need for extremely narrow-band filters, highly selective filters, frequency-agile filters, and very compact filter designs has led to many technology advances. On the system level, comparable advances in cryocooler technology and cryopackaging have enabled the development of a broadly deployable technology. We discuss industry trends and the methodologies and results of simulations and real-world measurements of HTS filter systems. | Superconductors require expensive, difficult cooling on earth. But why don't space probes, spacecraft, satellites, the space station, etc., utilize the coldness of space to take advantage of superconductors—for example, for magnetic leviation systems for positioning and maneuveing elements, for high-efficiency motors (to better utilize limited solar power), or (more dramatically) for complex devices such as superconducting CPUs (utilizing Josephson junctions) or single-photon detectors? | Design of a High Temperature Superconducting Generator for Wind Power Applications | High temperature superconducting (HTS) Josephson junction arrays (JJAs) fabricated on bicrystal substrate were embedded in a Fabry–Perot (F–P) resonator. We detected the radiation from the JJAs at about 74.08 GHz. By investigating the Current–Voltage (I–V) characteristics of the JJAs, the influence of the substrate on height of the Shapiro steps was studied. The result showed that the JJAs located at different positions of the substrate had different coupling strength. Also, the influence of the substrate was explored by presenting the comparison of radiation at different frequencies. Electromagnetic simulation was used to explain the experiment results. | A Study on High Temperature Superconducting Coil of Different Coil Arrangements | The authors fabricated several versions of Zimmerman-type RF SQUIDs (superconducting quantum interference devices) from bulk ceramic YBa/sub 2/Cu/sub 3/O/sub x/ samples and studied their characteristics. The SQUIDs operated reliably at liquid nitrogen temperature and proved to be stable over time. Some of their properties were similar to those of RF SQUIDs based on conventional superconductors, but there were also some major distinctions. The latter may be due to the fact that because of the macroscopic size of the weak link, the magnetic flux vortex enters reversibly (without respect to the RF current) the body of the weak link without crossing it. One of the SQUIDs operated as a conventional nonhysteretic SQUID, but the small value of the critical current of the weak link led to a lower operating temperature (T > | 278 | Abstract Starting with an overview of the various requirements placed on substrates for superconducting microwave applications, the current state of the art of high temperature superconducting thin films on different substrate types is discussed. Recent results for several superconducting microwave components that could form important building blocks for advanced microwave systems are presented, including performance data on experimental devices such as narrow band-pass and band-stop filters, superconducting circulators and miniature, low-frequency spiral resonators. Some examples of system types that can most likely benefit from high temperature superconductivity are identified. | High temperature superconductor films and devices for the microwave communication industry | Microstrip filters for wireless communications using high-temperature superconducting thin films | FORTY-FIFTH ANNUAL SYMPOSIUM ON FREQUENCY CONTROL HIGH-TEMPERATURE SUPERCONDUCTING RESONATORS | Method and system for producing high-quality superconducting tape | Contributions of the surface resistance of high-temperature superconducting films to the insertion loss of the microwave filters | Primary trends in superconductive microwave radioelectronics | High-temperature superconducting strip conductor with high allowable current load | We have developed a low-profile high-sensitivity sub-array module for an active phased array antenna. By using this sub-array module, a low noise receiving antenna can be easily available for wireless applications such as radar systems, communication systems, and so on. In this paper, we describe the new 16 elements S-band multichannel receiving sub-array module using high-temperature superconducting (HTS) filters as a key component for an active phased array antenna. Each receiving channel correspond to an antenna element consists of a HTS filter, a low noise amplifier (LNA), and interface circuits. In the sub-array module, 16 channel circuits are contained within a 200 mm×240 mm×30 mm vacuum chamber and cooled by a small cooler to 77 K. By using HTS filters and the cooler, feed-line loss and internal noise can be substantially reduced. Therefore, high sensitivity for an active phased array antenna can be realized. Additionally, radio wave interferences can be suppressed effectively by sharp frequency selectivity of the HTS filter with high-Q factor. |
279 | When was rome sacked by goths? | Who did th goths move into the roman empire? | What two Germanic groups invaded Rome? | Hw were christians punished in acient rome? | When did rome defeat and destory Carthage? | What did Rome conquer during the ones in the Punic Wars? | Did the Romans defeated the Greeks in Latium? | Early Middle Ages hidden wealth. As newly converted Christians, the Goths respected church property, but those who found sanctuary in the Vatican and in other churches were the fortunate few. The Roman Empire was not "conquered" by Germanic tribes, but overrun and even completely displaced by the flood of Germanic migrants. The Goths and Vandals were only the first of many waves of invaders that flooded Western Europe. Some lived only for war and pillage and disdained Roman ways. Other peoples had been in prolonged contact with the Roman civilization, and were, to a certain degree, romanized. "A poor Roman plays the Goth, | Why did Rome and Carthage become bitter rivals? | 279 | What year was rome is sacked by the vandals? | in which battle of 456 ad was the roman fleet defeated by the vandals | who sacked rome in 390 bc? | When did the Roman Civilization end? | What war destroyed the roman empire? | Why do you think the sack of Rome was so sevastating? | What do you call a roman soldier? | Rome 2 - Why do my units just stop attacking randomly | How did the romans get defeated? |
280 | Subsea oil loading system for tankers | Abstract SUBSIS is a subsea separation and injection system from ABB, developed to increase recovery and improve the economics of offshore oil and gas fields while also having a positive impact on the environment. The key task of SUBSIS is to separate the bulk water from the wellstream and to treat it for either discharge into the sea or re-injection into the reservoir. Modularized and self-contained, it will set new standards for the economic and environmentally friendly production of oil and gas. | The now decommissioned Maureen oil field in the UK sector of the North Sea was home to the world's largest steel gravity platform. The giant 110 000 t steel structure delivered over 200 million barrels in two decades but was finally removed and towed ashore last summer. This paper describes the technical challenges of hydraulically jacking the massive triple-tank platform out of the seabed and controlling its rise to the surface, 95 m above. | Optimal Operation of Subsea and Onshore Oil Transmission Pipeline | Identifying Challenges in the Maintenance of Subsea Petroleum Production Systems |
Introduction
The development of offshore oil and gas fields on the continental shelf is one of the priority tasks for the development of the resources of the world's oceans. This topic is becoming more and more relevant in connection with the growing needs of mankind for raw materials and energy, limited reserves and a significant depletion of continental resources. Thus, the Russian oil and gas industry has ambitious plans to develop offshore hydrocarbon fields located in the frontier Arctic regions and other areas with similar conditions. The total of 78 licenses have been registered for development of the Russian shelf sector. Most of them are located in the Arctic region. Development of these licenses will require advanced scientific knowledge and high-tech technology for production of unconventional resources.
The complexity of the development of Arctic hydrocarbon deposits
The Russian Arctic has the most challenging environment and extreme weather conditions including presence of ice, hummocks, icebergs, low temperatures, permafrost, strong winds, waves, currents, and a short navigation season. Another important consideration is that the Arctic is a remote area with no infrastructure.
This requires extended use of unmanned facilities, application of special equipment and work procedures in full compliance with the relevant standards and regulations. Additionally, all materials used in the Arctic region shall be designed for low temperature applications [1]. The subsea production technology can be an efficient solution for offshore field development applications in the Arctic region.
SPS. Promising technology and solutions, but a challenge
Subsea production systems are widely used in offshore development projects worldwide. Since 1961, quite a few offshore fields have been developed and brought on stream using subsea production systems or their components (West Cameron field in the Gulf of Mexico). Currently, over 130 offshore fields [2] use technological processes designed for subsea hydrocarbon production.
Russia has a very limited experience in the use of subsea production systems. There is only one SPS system installed and operated in Kirinskoye gas condensate field (Russian Federation), however the demand for subsea system components in Russia over the period until 2035 is estimated at 400 components.
The subsea production technology can be used to address multiple problems encountered during field development activities in the Arctic region. Nevertheless, the cost and complexity of manufacturing and installation of subsea production systems is quite high, and the average facility would cost hundreds of millions of USD. For example, in 2012 the total worldwide CAPEX and OPEX for subsea production was over $250 billion [3]. Application of more efficient design methods is a potential option for cost reduction during implementation of subsea production systems.
An optimization approach is needed to reduce costs and solve design problems
Analysis shows that there is a number of models used for optimization of line facilities primarily for onshore field development applications and construction of different infrastructure facilities.
Thus, attempts were made to optimize the routes of highways based on the algorithm of a probabilistic roadmap taking into account the relief of the Earth's surface and obstacles [11]. That is, we consider the search for the optimal road route with the minimum value of the objective function of the construction cost from the starting point to the final point on a given surface, bypassing obstacles.
The National University of Oil and Gas "Gubkin University" conducted a global study to select the best trunk pipeline route [4][5][6][7][8][9]. The study used export/trunk pipeline route optimization methods based on Bellman's optimality principle (dynamic programming principle) and Lee's algorithm. 2D network models were used for simulations. Figure 1 shows network geometries used for calculations: rectangular with diagonals, and arbitrary. Another study conducted by Kornienko O.A. reviews different methods to select the most efficient installation sites and types of subsea production systems, facility capacity estimation methods for offshore infrastructure facilities, and selection of optimized layouts for offshore field development applications. Nevertheless, all proposed models are deemed to be project-specific and localized solutions for subsea production optimization [10].
Further analysis showed that SPS optimization using the methods developed for main pipelines will be limited and it was decided to consider the path of the well fluid as a whole -from the bottom of the well and beyond. However, the existing optimization models based on 2D networks turned out to be inapplicable and the possibility of implementing the optimization approach on 3D networks with diagonals was considered.
Optimization approach for Arctic field development design
The current study is the first ever attempt to use an optimization method based on selection of the shortest optimal path using 3D models with diagonals.
Note that the proposed approach is universal and can be used for selection of the best layout at any location and in any environment, but its application will be most efficient in the Arctic region. Optimization for this case is a very challenging task (SPS systems include seafloor facilities) since SPS system layout greatly depends on field development pattern (bottomhole locations) and produced fluid intake facility location (platform / FPSO / onshore).
SPS systems with horizontal line facilities (pipelines for various purposes, umbilicals, etc.) and vertical facilities (wells) are considered jointly in this article. Therefore, this method suggests projecting SPS systems and wells to a spatial (3D) network model (see Figure 2). It is suggested to select the most efficient SPS system layout using a 3D model built on a regular grid with parallelepiped diagonals and specific number of nodes on different axis:
M -nodes along the x-axis N -nodes along the y-axis L -nodes along the z-axis
The starting point H corresponds to the center of the deposit and has coordinates х Н , y Н , z Н . Location of this point is fixed and defined by geologists. The start point overlaps with the nearest host. The top plane of the 3D model is deemed to correspond to the bottom surface, including the coastline (if necessary), and the end point shall be located on this plane and correspond to one of the nodes.
K is the end point with coordinates х К , y К , z К . The segments between adjacent nodes define the value of the selected optimality criteria (hereinafter called C costs since it is the most frequently used criteria).
The Allocated costs (e.g. cost per 1 km of well / pipeline / umbilical) Focused costs (e.g. subsea well completions, manifold, subsea storage, etc.) For the purposes of SPS optimization for Arctic projects or similar areas, cost estimates shall incorporate all driving factors which might impact the cost. Thus, the main task is to select the shortest cost path between the start (s) and end points in the proposed 3D model. That means that we need to select Wоpt points from the set of points in the W 3D model which meet the following criteria:
С Wopt = min from a variety С W , Where,( 1 )
i -Number of nodes sitting on the optimal path
The workflow requires generation of multiple paths in the network for consequent analysis using the Bellman -Ford algorithm where each path has specific features such as node coordinates for different components, cost of reaching a final node along the selected path, and other parameters.
The basic principles of this approach are shown below using an example case study for SPS optimization. In this example, the search is carried out from the start point corresponding to the bottomhole location to the end point, which can be a horizontal projection of the platform/FPSO or landfall point. The start and end points are aligned with the nodes of the 3D network. Selection of the best field development option using SPS systems is performed on the basis of the selected criteria and potential limitations.
Note that the optimality criteria are not a linear (additive) parameter, and therefore, conventional optimization methods are not applicable in this case. For example, a surface well has a dramatic increase of optimality criteria due to a subsea well completion. With this increase, characteristics of the test path also change. It extends along a two-dimensional network with other values of the criteria. A fragment of the block-diagram for the case "One start point -one end point" are shown in Figure 3, and Figure 4 shows a detailed fragment of a part of the block diagram.
Basic assumptions include: For the purposes of this calculation, the cost of network sections is proportional to the measured length of the sections. The cost criteria for segments not belonging to the bottom surface С p is equal to 1 million of conventional units. It actually corresponds to construction of 1 well length. For the segments belonging to the bottom С b , the unit of length is 0.5 million conventional units. Physically, it would mean the cost of laying the umbilical and pipeline. A cost increase is observed when the bottom is reached. It corresponds to С с . It occurs due to the cost of the equipment at that point (template, X-mas tree, protective cover, etc.).
С p = f (С e , С s , С con , С a )( 2 )С b = f (С e , С s , С con , С a )( 3 )С с = f (С e , С s , С con , С a )( 4 )
Where С e -cost of facilities, С s -cost of delivery, С con -cost of installation and С a -other costs Meanwhile, the cost of each parameter depends on the location, hydrometeorological conditions, water depth and other characteristics, which will be discussed in more detail at a later stage. The search is carried out using two lists: "List 1" and "List 2". Theoretically, we need to build the paths in all directions allowed by the network, however, for the sake of time saving, calculations will be performed for the paths with physical meaning only. Then the path with the minimum cost will be selected (in case of multiple paths only one is selected). The process will continue using the same workflow: every selection from the remaining paths in List 2 shall end up with selection of a path with minimum cost. At some point the selected trial path will reach the bottom. When it happens, the constant value С с is added to the cost of the original trial path, and adjacent points located on the bottom plane will be integrated. During the next phase, the paths which run only through the bottom will be generated. Their cost will be equal to F (С b ). The remaining paths continue to be generated using the same procedure.
The process will continue until an end point is added to List 1. After that, the selected path will be restored. To achieve this end, the Step Number column from the table in List 1 and 2 will be used. List 2 is used to define an adjacent point in the same line of List 1. This process will continue until the start point is reached.
This particular case example (one start point -one end point case) describes the particular problem that shall be solved. In addition, this case shows a typical workflow to solve the general case with several wells located on a template with consequent production and transfer of the product via subsea processing facilities to a fixed/floating facility or directly to an onshore installation, and it also can be used for the case with product transfer from reservoirs to treatment facilities.
Conclusions
From this study, the following conclusions are drawn: The analysis of the possibility of optimizing subsea production systems showed that it is incorrect to consider them only as linearly extended objects. Optimization in this case will be incomplete. It is necessary to consider the subsea production system and wells together, however, it is impossible to use the existing optimization methods developed for 2D networks. In this regard, an optimization approach based on the use of a 3D model was proposed. The developed algorithm and block diagram for the simplest, but real case -one start point-one end point -make it possible to make a statement about the possibility of optimization when taking into account SPS and wells together, using the Bellman -Ford optimality principle and the Lee algorithm. The analysis also showed that the proposed method will be most effective for Arctic conditions.
Figure 1 .
1Networks used for selection of the best pipeline route using 2D models (with diagonals, arbitrary).
Figure 2 .
2Example of the 3D model with diagonals for selection of the most efficient SPS design for future field development (diagonals are shown in one cell only for illustrative purposes).
Figure 3 .
3-Block diagram of the selection process during optimization of the field development pattern using a subsea production system, particular case.
IOP Publishing doi:10.1088/1757-899X/1201/1/0120712
IOP Publishing doi:10.1088/1757-899X/1201/1/0120713
Therefore, value of the criteria shall be determined for each segment. This includes a value for capital investments:most important optimization criteria may include:
Expenses over the project life
Time index
Risks including safety
Other criteria
IOP Publishing
doi:10.1088/1757-899X/1201/1/012071
4
IOP Publishing doi:10.1088/1757-899X/1201/1/012071 А1.GENERATE COORDINATES FOR THE NEXT ADJACENT NODE IN 3D MODEL А2.IS THE NODE LOCATED WITHIN OPTIMIZATION AREA ALONG X AXIS? А3. .IS THE NODE LOCATED WITHIN OPTIMIZATION AREA ALONG Y AXIS? А4. .IS THE NODE LOCATED WITHIN OPTIMIZATION AREA ALONG Z AXIS? А5.IS THE NODE LOCATED UNDER THE SURFACE? А6. GENERATE COST FOR REACHING THE ADJACENT NODE (WELL) А7.CHECK FOR PATH LIMITATIONS? А8. IS THE FINAL NODE REACHED? А9. ARE ALL ADJACENT NODES INCLUDED? No Figure 4 -Block diagram: field development pattern optimization using SPS systems, particular case (continuation). doi:10.1088/1757-899X/1201/1/0120716
a
b
Yes
No
No
Yes
Yes
Yes
Yes
No
А10.COST OF PATH
REACHES HIGH VALUE
AND THE PATH IS
DISCARDED
No
No
d
А11. ADD FIXED
COST OF SUBSEA
WELLHEAD
EQUIPMENT
INCLUDING
TEMPLATE AND
PROTECTION
COVER
А12.PATH
INDICATOR
CHANGES
c
d
Yes
No
А13. TRANSIT TO
PATH RECOVERY
Yes
e
a
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[11] Shcherbakov V S and Korytov M S 2012 Optimization of a highway route on a relief with obstacles using the probabilistic roadmap method, Vestnik SibADI, p 5.
Engineering aspects related to Arctic offshore developments. O Gudmestad, Gubkin University' Publishing Center57Gudmestad O T 2007 Engineering aspects related to Arctic offshore developments, Gubkin University' Publishing Center, 57 р.
Evolutions in subsea oil and gas production, Gazovaya promyshlennost. D V Lyugai, M N Mansurov, 6Lyugai D V and Mansurov M N 2018 Evolutions in subsea oil and gas production, Gazovaya promyshlennost', № 6 2018.
. Yong B Qiang, B , Subsea Structural Engineering Handbook. Elsevieerр 919Yong B and Qiang B 2010 Subsea Structural Engineering Handbook, Oxford: Elsevieer, р 919.
Selection of optimal routes for long-distance export pipelines, VNIIOENG. P P Borodavkin, E M Soshchenko, B I Kim, O V Bragilevsky, 57Borodavkin P P, Soshchenko E M, Kim B I and Bragilevsky O V 1977 Selection of optimal routes for long-distance export pipelines, VNIIOENG, 57 p.
Selection of the optimal routes of main oil product pipelines taking into account the arrangement of pumping stations, Candidate Dissertation. B Kim, Technical Sciences at Gubkin University. 163special code: 05.15.07. in RussianKim B I 1974 Selection of the optimal routes of main oil product pipelines taking into account the arrangement of pumping stations, Candidate Dissertation, Technical Sciences at Gubkin University (special code: 05.15.07), 163 p, in Russian.
Investigation of sectioning of the linear part of the main oil and product pipelines, Candidate Dissertation. B Samoilov, Technical Sciences at Gubkin Universityspecial code: 05.00.00), 154 p, in RussianSamoilov B V 1971 Investigation of sectioning of the linear part of the main oil and product pipelines, Candidate Dissertation, Technical Sciences at Gubkin University (special code: 05.00.00), 154 p, in Russian.
Optimization of the transport scheme for the construction of the main pipeline: Candidate Dissertation. V Mulenko, Technical Sciences at Gubkin University (special code: 05.15.07). 207pin RussianMulenko V N 1981 Optimization of the transport scheme for the construction of the main pipeline: Candidate Dissertation, Technical Sciences at Gubkin University (special code: 05.15.07), 207 p, in Russian.
Automation of choice of decisions in the design of pipelines, Candidate Dissertation. I Kuvychko, Yu, Technical Sciences at Gubkin University (special code: 05.15.13). 182pin RussianKuvychko I Yu 1991 Automation of choice of decisions in the design of pipelines, Candidate Dissertation, Technical Sciences at Gubkin University (special code: 05.15.13), 182 p, in Russian.
Development of methods for optimizing the routes of main gas pipelines and their branches for networks of arbitrary configuration, Candidate Dissertation. V Bezkorovainy, Technical Sciences at Gubkin University. 197special code: 05.15.07Bezkorovainy V P 1978 Development of methods for optimizing the routes of main gas pipelines and their branches for networks of arbitrary configuration, Candidate Dissertation, Technical Sciences at Gubkin University (special code: 05.15.07), 197
. In Russian, p, in Russian.
Development of rational methods for the arrangement of hydrocarbons of the Arctic shelf fields, Abstract of Candidate Dissertation. O Kornienko, Technical Sciences at Gazprom VNIIGAZ LLC. 22pspecial code: 25.00.18. in RussianKornienko O A 2007 Development of rational methods for the arrangement of hydrocarbons of the Arctic shelf fields, Abstract of Candidate Dissertation, Technical Sciences at Gazprom VNIIGAZ LLC (special code: 25.00.18), 22 p, in Russian.
| Semi-submersible platform high stability allows them to lift extremely high loads safely. Semi-submersibles are particularly suited to a number of offshore support vessel roles because of their good stability, large deck areas, and variable deck load (VDL). Some of the most prominent vessels are; When oil fields were first developed in offshore locations, drilling semi-submersibles were converted for use as combined drilling and production platforms. These vessels offered very stable and cost effective platforms. The first semi-submersible floating production platform was the "Argyll FPF" converted from the "Transworld 58" drilling semi-submersible in 1975 for the Hamilton Brothers North Sea Argyll oil field. | Hydraulic tanker An hydraulic tanker is an oil tanker designed to use water as an incompressible fluid for loading and unloading petroleum cargo. Each cargo tank is kept full at all times so oil floating on water will be pressed against the top of the tank. A cargo tank initially filled with water is loaded with the desired quantity of oil by pumping oil into the top of the tank displacing water which overflows through an opening at the bottom of the tank. The cargo tank is unloaded by removing oil from the top of the tank as water is | Tyra West – F3 pipeline is a long natural gas submarine pipeline connecting Danish and Dutch continental shelf pipeline systems. It facilitates the export of Danish gas into North West Europe. The pipeline, which cost over US$200 million, runs from the Maersk-operated Tyra West platform on the Danish continental shelf to the F3 – FB platform on the Dutch continental shelf. From F3 – FB platform, gas is fed through the NOGAT pipeline system to the Netherlands natural gas hub in Den Helder.
The pipeline is operated by Maersk Oil & Gas and owned by Royal Dutch Shell (23%), Maersk Oil (19.5%), Chevron Corporation (7.5%) and Energinet (50%). The pipeline has a capacity of of natural gas per year. It is operated by Maersk Oil. The pipeline gives each owner divided rights to transport gas from Denmark for subsequent sale at Den Helder.
References
Energy infrastructure completed in 2004
North Sea energy
Natural gas pipelines in Denmark
Natural gas pipelines in the Netherlands
Shell plc
Chevron Corporation
Maersk Oil
Denmark–Netherlands relations | 280 | The offshore oil loading systems known up to the present have many disadvantages with respect to safety and costs. Feasibility studies have therefore been carried out to examine the concept of a subsea oil loading system. This work was followed up by design of the individual components. The investigations are being carried out by DEMINEX, TNSW and AEG. This has resulted in new solutions which enable economical and reliable operations with a high utilization factor even in marginal fields and in water depths down to 200 meters. The fact that the fixed components of the loading system are located on the seabed means that application of the system is also feasible in ice hazard areas. | A subsea power source for offshore oil production | who developed the plan to put undersea oil pipelines under the ocean | A system of containment to prevent oil spills from sunken tankers. | Submarine oil production activities require the operation of underwater hydraulic or electric equipment. The conventional solutions to the problem of power and signal transmission involve the use of complex umbilical cables connected to the surface. However, the complexity and inherent cost of acquisition and installation of these umbilical cables is very high, mainly in deep level oil wells. The authors describe how a thermoelectric generator, to be installed in production oil subsea wellheads, was therefore designed. A 1 W and a 10 W prototype were constructed and successfully tested. > | An intelligent approach to optimize multiphase subsea oil fields lifted by electrical submersible pumps | Design of mooring system of oil storage barges in shallow water | who developed the first subsea oil well in the gulf of mexico | what is the name of the floating oil platform used in deep waters |
281 | Very useful and handy tool plus the quality of Leatherman is amazing | Husband loves this tool. Any leatherman is a good leatherman to own. So versatile. | I do a lot of leather work and hand sewing and this tool works great. | This product is very good and I am a huge fan of leatherman's but my only issue is that when I was prying something, the tip of the screwdriver broke off. I mean a majority of the tools still work and I still carry it, just the metal may not be the best. Overall it is a great tool and I do recommend it highly. | Very handy tool, good price, and received in two days | Very useful tool to have around. Easy to use & at this price, a good addition to my craft room. | Comes in handy on the road and I have had to use it often. My only complaint is that when you use one of the tools and have it pointing out for use, the tool feels loose and does not stay in position or even better, lock into position. If anyone has a Leatherman you will know what I mean. Sometimes this is not a problem, but with something like the phillips screw tool, I want that to stay firm as I'm turning a screw when loosening or tightening. Hard to describe here but you will know when you use it and find the rest of the tool is moving as you are turning. A minor complaint but I wish there was a way to tighten the individuals tools. | works great. really easy to sharpen up my kitchen knives. I don't use it for my Leatherman but really does a good job in the kitchen. | Nothing not to like here. Good price for a useful tool. | 281 | This is my first multi tool from Leatherman. It's great for everyday fixes and handy enough to handle serious jobs. The quality is excellent and the feel of the metal is what you expect from Leatherman. | Must have for Leatherman Multitools | Fantastic Multi-Tool quality! Great value and quality product! | Very cool multi-tool. It is heavy but I carry it ... | Leatherworking Tools Edgers, French Skivers and more | Stiff tool access, also comparison with Leatherman PS4 | Leatherman Squirt ES4 - Great Tool! | Great feel for a multi-tool | Just a quick question about acquiring a better multi-tool |
282 | how many parts are there in octavio paz's labyrinth of solitude | The invention discloses a labyrinth device with a gemel four-bar mechanism. The labyrinth device comprises a base (1), a map plate (2), a crank (3), a connecting bar surface plate (4), a connecting bar adjustment mechanism (5), a rocking bar adjustment mechanism (6) and a rocking bar (7), wherein the map plate (2) is arranged at the bottom side of the base (1) of which the upper surface is transparent; the crank (3) is arranged at the top side of the base (1); the connecting bar surface plate (4) is connected with the crank (3); the rocking bar (7) is connected with the connecting bar surface plate (4); the connecting bar surface plate (4) is provided with the connecting bar adjustment mechanism (5); and the rocking bar (7) is provided with the rocking bar adjustment mechanism (6). The labyrinth device with the four-bar mechanism is convenient in use, flexible and variable in playing method, simple in structure and convenient to manufacture. | this book gives a clear understanding of what and how labyrinth work, why have one and how to build one | #Moon's Labyrinth
##Author: Hungry Panda
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**Chapter 172**
#Chapter 172
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**Synopsis**
His friend and his wife betrayed him. The only thing left to him was his massive debt and his precious daughter. He was without hope as he lived at the bottom. However, a last chance had come to Sungyoon. He was a ‘man without a heartbeat’, and he will explore the Moon’s Labyrinth. He’ll explore the parts of the dungeon yet to be seen!
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Translated by NaughtyOtter | Browning directed the production with Herbert Grossman serving as conductor, Noel Taylor as costume designer, and Warren Clymer as set designer. Labyrinth (opera) Labyrinth is an opera in one act by composer Gian Carlo Menotti. The work was commissioned for television by the NBC Opera Theatre and uses an English language libretto by the composer. Unlike Menotti's previous television operas, such as "Amahl and the Night Visitors", this opera was written with no intention of being moved to live stage performance later. Menotti intended for this work to utilize the special effects unique to television which could not be recreated | Along with the figure of Narcissus, Durrell's image of the labyrinth commands center stage in his work—art made live through imitation so that life might imitate, might be, art. Thus humankind might live more fully and completely. Durrell's work mentions the labyrinth most prominently in The Dark Labyrinth; Tunc and Numquam in The Revolt of Aphrodite; Justine, Balthazar, and Clea in The Alexandria Quartet; and Monsieur, Constance, and Quinx in The Avignon Quintet. Clearly the image has been both ubiquitous and constant in Durrell's thought, the vulnerable omphalos of mankind's body and experience, the center of creation and destruction, itself beyond both time and causation. | Most people are familiar with the BRIO labyrinth game and the challenge of guiding the ball through the maze. The goal of this project was to use this game to create a platform for evaluation of co ... | This beautiful book about labyrinths embodies the heart / love energy of the universe. It will always guide the way for our little ones to remember the sacred space that is forever held inside each one of us. Gina B. | Welcome readers, to our frequent discussions of different books! This discussion is based on the book *Uncharted: The Fourth Labyrinth* by Christopher Golden. Please use this thread to discuss the book and other books that you feel fans of *Uncharted: The Fourth Labyrinth* would also enjoy. | 282 | the subject that you are studying so that the argument remains critical yet rational and objective. As the intellectual gets more involved with the political environment, his arguments can often become influenced by other factors such as political motivation and pressure to conform. The Labyrinth of Solitude The Labyrinth of Solitude () is a book-length essay by Octavio Paz, first published in 1950. One of his most famous works, it consists of nine parts: "The Pachuco and other extremes", "Mexican Masks", "The Day of the Dead", "The Sons of La Malinche", "The Conquest and Colonialism", "From Independence to the Revolution", | Labyrinth is a Labyrinth of Characters and Story | Solitude and Its Ambiguities in Modernist Fiction | 8 Labyrinthine Narratives and Peripheral Intellectuals | """labyrinth of fortune"" is the subtitle of which poem by juan de men | what does the general in his labyrinth not pay much attention | who wrote the novel ‘a maze of death’ | This beautiful book about labyrinths embodies the heart / love energy ... | when does the general in his labyrinth take place |
283 | still fits though but I naturally have a very slim waste, I just have a little jiggly tummy from ... | This fit as expected. I was able to breath in it. I have an issue with by belly sticking out on the sides and in front of my jeans. I wear this and its smooth.my jeans even fit looser on the wast. It is a great help until I am able to burn of the belly by work out and diet | Everything fits good except for the waste! Just wish it was a little thinner. Other than that love the color and the fit in the arms and shoulders! | can I say the fit is great. I have a question are all of your pants with the a justable waste v com | The shaper is not tight fitting especially in the areas where I need it. It does not hold in my post pardom belly and I even ordered a size xs. I wish I could return it. | IT FITS LIKE IT SHOULD, I ORDERED MY REGULAR SIZE, ITS VERY FORM FITTING AND DEFINATELY RESTRAINS THE TUMMY AREA. | this is the first time i am loving a tummy control product :) it fits everywhere, no bulges. gives a slight control that doesn't suffocate or create discomfort. | It's actually looser on your waste even if the size is right at the shoulders. I gave 3 starts because the fit is not as fit as shown. The material is cheap and feels like a body bag rather than a shirt. But for the price.. you get what you get. | This product is great!!!!!! Fits as espected. My belly is fat and when i put it on all that fat is tuck in!!!!! I love it. I would recommend it. It is the best cincher i have ever had. I bought the 25 steel bond cincher. | 283 | Really tight! I bought a large and it is VERY tight...I am 5'7 and 160...still fits though but I naturally have a very slim waste, I just have a little jiggly tummy from have two babies so thats really what I wanted flattened but it doesn't do a great job at that...also the straps are really awkward, like practically in my armpits....its still wearable with certain dresses, but not amazing....I'd buy a different shaper if I could reorder :/ | it is not too loose or too tight and the length in the body and arms is perfect. | The chest is tight but the arms and around the hips are fine. These are inconsistent with sizing | Fit quite tight. My wife is petite and when ... | I'm a thick girl and it fits great and its pretty good about hiding all my tummy ... | A little tight in the chest but otherwise a good fit. Nice | The fit is fine as long as your skinny in the stomach area | I'm 5'11 170lb like my close a lil loose got a "large small" ... | The swimsuit fit me perfect the high waist covers most of my stomach |
284 | Is anyone else getting Dark Cloud 2 vibes? | Anyone else getting major CXG vibes from the new Taylor Swift music video or is it just ME!? I made a Twitter thread. | Has anything changed in this regard since the initial Substratum/Andromeda release? At first I was so happy to finally have dark themes on my Pixel XL but now it's getting annoying keeping up with all the app updates and re-applying the themes. Phone breaks, Camera breaks, Play Store breaks, and other Google apps. How do you deal with it? | Is it just me who feels that the scenes involving Frank and Claire have a dull and grey background and dim lighting? Sometime, even the light seems to fluctuate between the scenes (unless there is something wrong with my TV or my eyes). Even the wedding anniversary is shot in white clothes.
I have seen first 7 episodes, and I am hardly to see any colourful scenes or scenes shot in sunny days. Could there be a reason to have a continuously pessimistic theme in season 3?
I believe that Apple product placement issue has been discussed before, but it feels very prominent in S3 | First time watching this show(yea its pretty good, prob gonna get something from it added to my sleeve), only on season 4 right now. But my sister came in the room and said this show is dumb.
Few days later im in the bathroom and i hear a very distinct jake voice. Im like oh so now your watching it, “....its good....” HaHa | Out of the Shadows features thoughtful lyrics with creative music. I haven't heard popular artists produce engaging music that makes you really want to listen and know what the author/singer is trying to get you to think about. This CD encourages thought as well as enjoyment. The tunes are catchy and I found myself singing along after just a few listens. A definite CD to own. Looking forward to the next one! | Is there any update on this being fixed? The worlds are so beautiful with HDR on, but dark colors are TOO dark and washed out.
Plus it’s a major annoyance toggling HDR on and off when i go between Destiny and Assassins Creed lololol | Yesterday i watched the documentary about Travis Scott on netflix and was amazed by his shows.
So i went ahead and watched a liveshow on youtube and damn, that atmosphere is some next levels shit..
Especially when he plays butterfly effect. Only few shows have this much people jumping.
Here is the video that gave me goosebumps many times if you care:
| Got a notification from SoundCloud that said "Listen to Hikari-Ultra's latest releases". I haven't clicked on a notification faster. Then I got the disappointing sight of gang green as the latest release and realized that I got bamboozled hard. | 284 | Been playing Xenoblade since last night, and between the music and some aspects.. I can't help but keep attaching my mind to Dark Cloud 2 xD.
Curious if anyone else has felt the same! | Beat xenojiiva, feels great. | How many of you Nintendo-only people are playing Dragon's Dogma: Dark Arisen for the first time? | Now that it's been out for awhile, Conqueror feels good. I think it was a big success by Riot. | Just hit my first real Db2 in chest! Feels good! | Borderlands 2 very unstable (please for the love of god dont skip my post lol( | Still relatively new to this game (and I love it!) but desync in single player truly bothers me when you potentially trade experience for it. | Nearly done with my 2nd faction run. I can't believe I'm still playing this game as much as I am. So much content. It's amazing and a bit overwhelming. | Anyone else TTC for what feels like forever? |
285 | AP Chemistry | I was never strong in chemistry and thought AP chemistry was especially difficult, so I just want to go in knowing what to expect, especially for first semester. Thanks for your help! | Anyone have any Ap chemistry practice problems categorized by unit? Preferably with answer keys? | and physical sciences, as well as any of the biological sciences. The course aims to prepare students to take the AP Chemistry exam toward the end of the academic year. AP Chemistry topics include atomic theory, chemical bonding, phases of matter, solutions, types of reactions, chemical equilibrium, reaction kinetics, electrochemistry, and thermodynamics. The College Board recommends successful completion of High School Chemistry and Algebra II; however, requirement of this may differ from school to school. AP Chemistry usually requires knowledge of Algebra II; however, some schools allow students to take Algebra II concurrently with this class. The requirement of regular | and physical sciences, as well as any of the biological sciences. The course aims to prepare students to take the AP Chemistry exam toward the end of the academic year. AP Chemistry topics include atomic theory, chemical bonding, phases of matter, solutions, types of reactions, chemical equilibrium, reaction kinetics, electrochemistry, and thermodynamics. The College Board recommends successful completion of High School Chemistry and Algebra II; however, requirement of this may differ from school to school. AP Chemistry usually requires knowledge of Algebra II; however, some schools allow students to take Algebra II concurrently with this class. The requirement of regular | Preface: I don’t have an interest in us history
I’m wondering if I should take apush, I wanna have a job in my junior year (currently a sophomore) so I wanted to lighten the load a little. Granted I am taking ap chem lol but I like chemistry.
So what do you think? Also I wanna take ap psych and am wondering about ap computer sci principles
Help, thank you! (: | Hi,
So I'm a freshman in a reasonably OK school, and I was considering taking Honors Chemistry over the summer, and then taking AP Chem my sophomore year. I know that AP Chem is one of the hardest AP classes, but I was wondering if it would still be possible to do well in the class even having taking the foundation in a more compressed format. | What are the chemical engineering colleges in ap? | Project for class 12th chemistry? | 285 | Advanced Placement Chemistry (also known as AP Chemistry or AP Chem) is a course and examination offered by the College Board as a part of the Advanced Placement Program to give American and Canadian high school students the opportunity to demonstrate their abilities and earn college-level credit. AP Chemistry has the lowest test participation rate, with around half of AP Chemistry students taking the exam.
Course
AP Chemistry is a course geared toward students with interests in chemical biologies, as well as any of the biological sciences. The course aims to prepare students to take the AP Chemistry exam toward the end of the academic year.
AP Chemistry covers most introductory general chemistry topics (excluding organic chemistry), including:
Reactions
Chemical equilibrium
Chemical kinetics
Stoichiometry
Thermodynamics
Electrochemistry
Reaction types
States of matter
Gases, Ideal gases and Kinetic theory
Liquids
Solids
Solutions
Structure of matter
Atomic theory, including evidence for atomic theory
Chemical bonding, including intermolecular forces (IMF)
Nuclear chemistry (removed for May 2014 test)
Molecular geometry
Molecular models
Mass spectrometry
Laboratory and chemical calculations
Thermochemistry
Chemical kinetics
Chemical equilibrium
Gas laws calculations
Exam
The annual AP Chemistry examination, which is typically administered in May, is divided into two major sections (multiple-choice questions and free response essays).
Old test (2013 and earlier)
The old test was composed of two sections: a multiple-choice section consisting of 75 questions with five answer choices each, and a free-response section consisting of six essay prompts that required the authoring of chemical equations, solution of problems, and development of thoughtful essays in response to hypothetical scenarios.
Section I, the multiple-choice portion, did not allow the use of a calculator, nor did it provide any additional reference material, other than a periodic table. Each question contained five answer choices. 90 minutes were allotted for the completion of Section I. Section I covered the breadth of the curriculum.
Section II, the free response section, was divided into two sections: Part A, requiring the completion of three problems, and Part B, also containing three problems. Part A, lasting 55 minutes, allowed the use of calculators, while Part B, lasting 40 minutes, did not. The first problem in Part A concerned equilibrium related to solubility, acids and bases, or pressure/concentration. The first question of Part B was a chemical equation question in which 3 scenarios were presented and the student was required to work all 3 scenarios, authoring a balanced net ionic chemical equation for each scenario and answering questions about the equations and scenarios. If time permitted, students may have edited their responses from Part A during the time allotted for responding to Part B, though without the use of a calculator. The student needed to have completed all six questions.
While the use of calculators was prohibited during Section I and Section II Part B, a periodic table, a list of selected standard reduction potentials, and two pages of equations and conventions are available for use during the entirety of Section II.
New test (2014 and later)
The 2014 AP Chemistry exam was the first administration of a redesigned test as a result of a redesigning of the AP Chemistry course. The exam format is now different from the previous years, with 60 multiple choice questions (now with only four answer choices per question), 3 long free response questions, and 4 short free response questions. The new exam has a focus on longer, more in depth, lab-based questions. The penalty for incorrect answers on the multiple choice section was also removed. More detailed information can be found at the related link.
Topics
Structure and Matter, 20%
States of Matter, 20%
Reactions, 35–40%
Descriptive Chemistry, 10–15%
Laboratory, 5–10%
Grade distribution
The score distributions since 2007 were:
Prerequisites
The College Board recommends successful completion of High School Chemistry and precalculus; however, requirement of this may differ from school to school. AP Chemistry usually requires knowledge of precalculus; however, some schools allow students to take Pre-CalcI concurrently with this class. The requirement of regular or honors level High School Chemistry may also be waived, but usually requires completion of a special assignment or exam.
See also
Chemistry
Glossary of chemistry terms
References
External links
Test format change in 2007
AP Chemistry Exam Overview
Chemistry education
Advanced Placement | who teaches the ap chemistry course in high school | I agreed to teach my AP Chem class | what is the equivalent of ap chemistry in high school | Self Study AP Chem? In honors chemistry right now | Incoming undergradatuate- did poorly in chem and ap bio in high school | Compilation and Practice about the Experiment Textbook on College Chemistry | how many sections does ap chemistry have in it | The purpose of this study was to investigate the problem-solving skills (PSS) and chemistry learning experiences (LE) of teacher candidates. 191 pre-service chemistry teacher (130 women, 61 men) were taken as the research sample using the purposive random sampling technique. The research design used a cross-sectional survey with focus group interviews. The quantitative data obtained were analyzed using the MANOVA test and while the interview data using the Patton analysis technique. The research findings show that: 1) the level of the chemistry learning experience of pre-service chemistry teacher (LE) is higher than the ability of problem-solving skills (PSS); 2) the level of ability of female chemistry teacher candidates for PSS and LE was found to be higher than that of males; (3) there are differences in PSS and LE based on grades levels, but there is no difference based on gender; 4) there is a difference in PSS and LE between freshman, sophomore, and junior grades. The findings of the interview are relevant to the results of the survey which proved that male and female students both have positive attitudes towards chemistry, however, it was found that there were differences in PSS and LE between grade level (1 st grade, 2 st grade, 3 st grade). Thus, it is suggested that the learning process in universities prioritizes the development of LE and PSS in chemistry learning so as to improve the soft skills and academic achievement of prospective chemistry teachers. |
286 | Where is the best place to level up in ff7? | Hi guys. I was wondering where some good locations to level up in the early game. I'm currently level 2-3 and I have metal armour, a hunting rifle, a 10mm handgun and sub-machine gun, a 44. magnum, and a shotgun. I want to level up some more so I can progress confidently in the game knowing I have a good set of skills to do so. Thank you for looking at my post. | whats the best leveling method right now? (pc version) | \[F76\] Whats the best way to level without using glitches or anything that abuses a systems. Im level 53 just to give you a mark of where I am. | Hey,
i want to level fast with the Double XP + 100 exp. What would be the best? Doing quests or grinding somewhere, if yes, where ?
Thanks | Best way to level up on farmville? | Just want to know if I should be doing dailies now or just grind the level for now? Because I don’t have waypoints yet and not familiar with all the map locations and waypoints. | So I just got a few new subs but I don't know where to level them. I've looked at various leveling spots but none of them mention ones that are for subs. So are there any sub specific leveling spots? Or should I just grind them like my other ships? What equipment should I be using while grinding levels? | I'm BL 86 and I'm pretty sure I'm good to go but I was curious where others were at when they did the DLC and how it was. I've got 50 SKL and 25 STR with a +10 Beasthunter Saif. Side note - this weapon is amazing and I can't believe I slept on it. So versatile.
Sub-question: What's a recommended level for starting out NG+ on? | 286 | Final Fantasy 7 where is the best place to level up for a level 65? | Sooooo... How do one level up after level 65? | Best way to level up from 50 to 65? | Is it possible to at least get level 65 | what is the leveling system in final fantasy xv called | Highest Level in League of Legends | what is the highest level you can be in realm of the mad god | What's the best bonus level of any game? | What is the highest level i can reach? |
287 | Curious about Monster Hunter Words past events | Words to decraibe movement of a monster? | What does the word Greek mythology mean? | Monster with nine heads greek myths? | Nisse (folklore) in many works of Scandinavian literature. With the romanticisation and collection of folklore during the 19th century, the nisse would gain popularity. In the English editions of the fairy tales of H. C. Andersen the word has been inaccurately translated as "goblin" (a more accurate translation is "brownie" or "hob"). The nisse/tomte is an echo of ancient ancestral cult. He was sometimes seen as the farmer who cleared the forest to build the farm and who in pre-Christian times would have been buried on the farm in a mound. He was sometimes referred to as the or , from the | Why did the greeks tell mythololgical stories? | What are some words that are past tense? | Past tense of the word shake? | I've been reading through portions of Edith Hamilton's *Mythology* and saw that she tried to steer away from using Ovid, citing his lack of belief in the stories he was telling:
>I prate of ancient poets' monstrous lies, / ne'er seen or now or then by human eyes.
Was this perception of these older tales commonplace among the writers and poets of Roman society in Ovid's time, or is the truth more nuanced? It seems odd to think that a civilization that roots their origin in stories connected with Greece would speak of so many of their stories as mere nonsense. | 287 | So im thinking about picking this up very soon on PC, and was wondering if any of the past events are still in the game. The big one im really curious about is the Monster Hunter Worlds x Final Fantasy 14 crossover stuff. Because the fight looks amazing, I love anything with Dragoons on it, the moogle is cute, and i just love FFXIV in general, So was curious to know if I buy the game and level up and such, if im still able to get those things. Thank you for any information anyone is able to give on this! Hope to join you all soon! Happy Hunting! | Final Fantasy Weekly Discussions: Week 40 - Square has decided to remake your favorite Final Fantasy and put you in charge! | Any news on fan made battlegrounds? | New game similar to Battleheart Legacy? | PSA: the Outer Worlds is on sale | Was Warner Bros. and Legendary's Monsterverse doomed to begin with? | A Final Fantasy game is coming out this week that I feel needs to be honored in FFBE. | how many episodes are in final fantasy xv remake | A VERY different Final Fantasy than earlier games, but still provides a fun time with its fresh and rapid battle system! |
288 | Does anyone have the LoR sound assets? | The music for Regular Level, Boss Level, Gold Helm, Level 100M, and whatever else you can find. I don't know how you guys got the assets, but I (and I'm sure many others) would like to download these assets. | [Muisc]
Basically looking for new vintage sounding R'n'B.
I do know of /r/SoundsVintage, just wondering if I'm missing out on any good artists..
I'll post some links below:
Nehzuil -
Mura Masa -
J-Louis -
The Weeknd - | Yope, I'm looking for a couple simple pieces for use on my Soundcloud; an avatar and a banner or cover picture or whatever Soundcloud calls it. The avatar would be a simple black and white piece and the banner would be a white background with some colorful graffiti (my artist name). I can pay through PayPal or whatever you may prefer.
Thank you. | Does anyone know where to find yy audios where there are more than one charecter or even poly relationships? Cause those are my favorites and I've just found a couple of them. | anyone got soundtoys complete for mac?? (working with catalina) | Hi, I recently found out Loona 1/3's physical copies of the limited album have remixes, Love & Live Remix and You and Me Together Remix. I was wondering if anyone had a download link for them? I really want them in my music library.. Or if anyone here has the albums and wants to be a saint and upload them for download, that would be really cool! | (sorry if I make mistakes, I'm french, baguette fromage omelette)
Hey guys o/
I started a Fellow Feeling x Technicolor mashup recently, and some people asked for the samples from Fellow Feeling, so here it is c:
#!H1QGDbKJ!e9vANFmL99MuQ5Jq0mLB2wTumIbeyiX5pkUGCHLeSp0
My Soundcloud : | Exquisite and highly sensitive performances of these piece by William Boughton and the ESO. Typically spacious and atmospheric sound from Nimbus. | 288 | So, I really want some sfx to use as notification sounds and stuff, so I wonder if anyone have access to said files (most specifically, the die roll sound effect and the Angela snap sound effect)
I don't really want to use an asset extractor myself to avoid finding something I shouldn't, so if anyone happen to have those sfx, leave a link or something in the comments | Is there any way to view the game's sound files? | anyone know where i can find the undertale audio files? | Download Link for MW2/3/4 Bitchin' Betty sound effects | How do I find my own style/sound? | Where do you guys get your sound effects? | Could someone make a thread containing all/most music assets used in the game? | Can anybody please share a .flac file of Danny L Harle's remix of Superlove please? | Thalamuslab XSL Free Sound Collection & Open Collaboration |
289 | Nice shoes and a good fit | nice shoes but its a small cut so you have to order 2 sizes bigger for a good fit | Very nice shoes and great fit. Amazon's sizing guide worked just right. | Great shoes for the price. Had a pair previously, and these also fit well, and wear well. A good bargain. | Nice shoes. I enjoy them a lot. Very comfortable. | Great shoe. Fits great... comfort and support in a good looking sneaker. Great for trail runs , walking , gym work outs!!! | Great shoe! Get tons of compliments and i can wear them for a long period of time. Fit was true to size. | Fit good and got one of the few compliments ever on shoes in my life. A good buy, fit well, look good. | Very comfortable shoe and a good fit for me. | 289 | Nice shoes and a good fit. I didn't check "provides good arch support", but really I've never found a pair of shoes that does. They simply don't design them to since they wouldn't seem comfortable to the average consumer. Everything else was fantastic. | Reasonable arch support but not great. Good looking shoe and nice for warm weather | ... review ask me to answer 'Do these shoes provide good arch support | but heel and arch support are great. Would recommend these shoes to anyone looking for ... | I don't know if they have good arch support or not because I couldn't even get ... | Good shoes, wish there are more arch support | Well made shoe just wish it had some arch support ... | Best arch support for any shoes I've owned | the arch support is not perfect in these shoes |
290 | ras al-khaimah is a city in which country | Al Makha District () is a district of the Taiz Governorate, Yemen. As of 2003, the district had a population of 18,155 inhabitants. The capital lies at Mocha.
Location
It is located in north-west of Taiz governorate. It is bordered by Maqbanah and Al Khawkhah to the north, Al-Mandab to the south, Mawza and Maqbanah to the east, the red sea to the west.
References
Districts of Taiz Governorate | Al-Makhzan al-Qai (المخزن القاعی) is a village in south-western Yemen. It is located in the Abyan Governorate.
External links
Towns and villages in the Abyan Governorate
Populated places in Abyan Governorate
Villages in Yemen | Ar Rass Rass (also spelled Ar Rass, or Al-Ras; ) is a Saudi Arabian town, located in the Al Qassim Province. It lies southwest of Buraydah, the capital of the province and also north of Riyadh, the national capital. It is the third largest city in Al Qassim Province by population, with an estimated population of 133,000 (2010 census). It has an area of about 60 km². Rass means "an old well" in Arabic, and it was mentioned in a poem of Hassan Bin Thabit, the poet who was a companion (Sahaba) of the Islamic prophet, Muhammad. The city is | ammonium phosphate. In July 2011, King Abdullah changed the name of Ras Az-Zour to Ras Al-Khair (with "Khair" meaning light or bright to have a more positive naming), according to a statement by President of the Royal Commission for Jubail and Yanbu Prince Saud bin Abdullah bin Thunayan to the Saudi Press Agency on 6 July 2011. Ras Al-Khair Ras Al-Khair (Also called Ras Az-Zour, Ras Azzour) is a town and port currently under development on the eastern coast of Saudi Arabia 60 km north of Jubail. It is also known under its project name of "Minerals Industrial City". The | of her audience. They were also known as "awālim" (singular "alma", transliterated almeh in French as "almée"). Both terms are 19th-century euphemisms for "erotic dancer"; "almeh" literally means "learned woman" and came to be used as a replacement for "ghaziya" after the "ghawazi" were legally banned in 1834. The term "ghawazi" is inherited from the Northern Indian term "Gowaar" meaning singer. The term "Gaon" is equal to the verb "sing" and the term "Gana" means song. This explains the inheritance of Nawari or Dom people from the group of performing artists known as "Bazigar" in Punjab. An almeh in origin | Ras Muhamad spend time with his youngest brother. Subsequently, Muhamad continued his studies in art at the Borough of Manhattan Community College Faculty Liberal Arts and graduated in 2005. His debut studio album "Declaration of Truth" was released while he was living in Brooklyn. The album was launched in New York City. His debut album brought him some popularity in his birth country. Two years later, returning to Indonesia, Muhamad released debut studio album "Reggae Ambassador" on January by Equinox DMD, a company distributing music in iTunes. Indonesian Rolling Stones awarding him as Best Reggae Act in 2008 and earning nominations for | Al Mahrah Governorate Al Mahrah or Mahra ( "") is a governorate ("muhafazah") of Yemen in the southern Arabian Peninsula. Situated in the area of the former Mahra Sultanate, its capital is Al Ghaydah and it has international borders with Saudi Arabia and Oman. A sizeable part of the Al Mahrah population does not speak Arabic as their primary language. Non-Arabic-speakers primarily speak Mehri or Mahri, a Modern South Arabian language similar to the adjacent Dhofar Governorate of Oman. The people that speak Mahri call themselves Mahris and are presumed to be descendants of the ancient people of 'Ad. The | its various subdivisions. As of January 2015, the Ministry is led by Abdulkadir Sheikh Dini. The constitution recognizes Mogadishu as the capital of Somalia. The Parliament of Somalia meets in the city, which is also the seat of the nation's Supreme Court. In addition, Mogadishu is the location of the presidential palace, Villa Somalia, where the President resides. The Prime Minister also lives in the city. The Federal Government of Somalia is internationally recognized as Somalia's official central government. It occupies the country's seat in the United Nations, the African Union, and the Organisation of Islamic Cooperation (OIC). The Somali | 290 | al-Qasimi, joined the United Arab Emirates. Its rulers were: In 1975, the total population of Ras Al Khaimah was 43,845 of which 29,613 were nationals and 14,232 were foreigners. This figure increased to 73,918 (39,148 locals; 34,770 foreigners) in 1980, 96,578 in 1985, 143,334 in 1995, and 210,063 in 2005. The total population, as of 2015, was estimated to be about 345,000 people, both Emiratis and expatriates. Important towns, settlements and areas include: Notable landmarks in Ras Al Khaimah include: Ras Al Khaimah's desert climate (Köppen climate classification "BWh") is hot and arid with very hot summers and mild winters. | what was the population of ras al khattah in 1985 | what is the name of the people living in the area of avadh | what percentage of the population of phulwari sharif is male | what is the population of indians in qatar | what type of land is the umm al samim | how long did it take to increase the population of the himalayan tahr | when did the population of rendham change | what percentage of the population of mahudha is male |
291 | Used the recommended method of installing the wire into the holes | I don't have the right screwdriver for it, but i need to get this done soon. Am I able to use solder in the screw terminal, to secure the wire? | Unclear instructions. Not good quality connecting wire, would bend easily. Sent back. | I thought i was living the life before using one of these connectors. Now i have it too easy! Never again will i stuff those teeny 8 wires in. | No directions for install, looks like only a bunch of wires. | If I didn't already know I needed to add holes to the seams of these cones, I would have been lost. There's no instructions. BUT they work great. You need to take a push pin and place a couple of holes about 2 inches apart on the seam of each one before use. This allows for air circulation and proper water flow. | This fixed my bad socket. Wires were plenty long to allow easy soldering while on the car. | The metal connectors don't fit tightly no matter how hard I try. The only way to securely fasten the fittings to the wire is with a lot of solder and electrical tape. | I much prefer the x2 screw on Banana Plug . Much better secure . You strip the wire tightly twist it , put it through the brass hole nice fit the with the 2 screws on each side , screw them nice and tight a secure fit pull it and it will stay in screw the brass cover over it and your done . Nice looking and very secure ! Rather than strip the wire stick it in and bend it back .No Good. | 291 | Used the recommended method of installing the wire into the holes. I had to really crank down on the screws for a secure grip. REALLY crank on the screws hard to the point I thought they would strip. If I didn't, the wire would slide out.
Granted it was 12-2 wire, but it should have held the wires better imo. May change rating if the usb does not fail within a week as other have stated. | Kenwood dmx125dab cant connect usb | First Time Installing AIO (Kraken M22) - Help Needed With Plugging Wires | why isn’t the exposed usb wire technique not working for my cart | I removed the wire connectors except for three and soldered ... | Not really sure what to do with this wire. ... | Can't remove wiring harness on a mondeo | Trouble when doing wiring for Friendship Travel Package | I had to rewire the plug. The tip of ... |
292 | Wildey (surname) | What is christopher wildes name? | On 3 January 1882, Oscar Wilde, a twenty-seven-year-old "genius"-by his own reckoning-arrived in New York. The Dublin-born Oxford man had made a spectacle of himself in London with his fashion sense, acerbic wit, and passion for art and design, and was hired to go to America to lecture on interior decorating. But Wilde had his own business plan: he would promote himself. And he did, creating a template for fame creation that still works today. Wilde presented himself as a "star", taking the stage in satin breeches and a velvet coat with lace trim as he sang the praises of sconces, embroidered pillows and himself. What he so presciently understood is that fame could launch a career as well as cap one. An enchanting tale of travel and transformation, comedy and capitalism, Wilde in America teaches us about our present as well as our past. | Olivia Wilde Wilde was born in New York City and grew up in the Georgetown neighborhood of Washington, D.C., while spending summers at Ardmore in County Waterford, Ireland. Her parents were prominent in the Washington, D.C. social scene, hosting dinner parties. Her mother once recounted a story of a four-year-old Wilde eavesdropping one night on a conversation between diplomat Richard Holbrooke and rock singer of the Rolling Stones Mick Jagger, until Jagger noticed her and shooed her to bed. She attended private school at Georgetown Day School, in Washington, D.C. and boarding school at Phillips Academy, in Andover, Massachusetts, graduating in 2002. | It has come to my attention that the most queer and dandiest of all gentleman, Sir Oscar Wilde has recently passed away. I know that many of you here shared many a conversation with this most illustrious gentleman as he was amongst our most esteemed members. Others, not so fortunate, engaged in battle of wits with him -- armed with but a spoon to his rapier.
In memoriam of his passing, doth anyone here care to share a story, or a fond memory of Sir Oscar Wilde?
IN MEMORIAM | The names of betsy ross' sibblings? | Olivia Wilde Wilde, who holds Irish as well as American citizenship, derived her stage name from Irish author Oscar Wilde. She changed her surname while in high school, to honor the writers in her family, many of whom used pen names. Wilde was accepted to Bard College, but deferred her enrollment three times in order to pursue acting. She then studied at the Gaiety School of Acting in Dublin. Her mother, Leslie Cockburn, is an American-born "60 Minutes" producer and journalist. Her father, Andrew Cockburn, also a journalist, was born in London to a British family and raised in Ireland. For a | Libby is a feminine given name, usually a diminutive form of Elizabeth. It is also a modern Hebrew name (ליבי), meaning "my heart". It is also a surname. | Why isnt curleys wife name mentioned? | 292 | Wildey is a surname. Notable people with the surname include:
Doug Wildey (1922–1994), American cartoonist and comic book artist
Edna Wildey (1882–1970), American tennis player
Thomas Wildey (1782–1861), British-born American civic leader | what is the meaning of hardy and lippy's name | Andy Bernard family nicknames | where did hart merriam schultz grow up | Mondale (surname) | where does the last name muriel originate from | where does the last name melville originate from | How do people end up getting "known as" a certain arrangement of their first,middle,last name/initials? Why do we know him as Louis C.K for example, or her as Sarah Huckabee Sanders? | What is the real name of the first name to play lassie? |
293 | [2012 Only][DEAL] Official ASUS docking station for cheap | I've been looking night and day for this thing and I cant seem to find it anywhere? Maybe it didn't get released with the other ASUS boards? If anyone has any info that would be awesome. ASUS support didn't have any info either :(. | I can't seem to find one cheap ,only the really expensive Acer / Asus monitors .. | ~~I made the jump to the Fossil Hybrid HR a few months ago and I'm really enjoying it so I've retired my Pebbles. They've just been sitting in a drawer but are fully functional and come with their original chargers. The P2 SE is on the left and has a black and blue Pebble strap and the P2 HR is on the right and has a Milanese loop off of Amazon. Both buttons are in good condition as far as I can tell and the P2 HR also has a screen protector installed.~~
~~I'd be asking $45 for the P2 HR and $35 P2 SE with shipping to the continental US included. DM me and/or leave a comment if you're interested, I will edit this post with updates as they sell.~~
~~Pics: ~~
Edit: Both sold! | Looking for an iPhone 11 and 12 pro (ATT or Unlocked). Must be in excellent condition.
Please comment before DMing.
edit: also interested in 11 pro max | This is probably spelled out in a spec document somewhere but I can't seem to find it.
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It looks like I can directly drive two 4K displays with this machine:
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Would the display on the notebook itself work at the same time (for a total of three 4K screens)? I'd be grabbing the OLED version of the notebook when they finally have stock of it in Canada.
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Any general advice on external displays would be great as well because I'd be buying those around the same time. It looks like you can get a display with thunderbolt 3 connections right on it. Would this be preferable to a displayport connection? I want to minimize my chances of incompatibilities.
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It looks like 24" OLED monitors aren't a thing yet which is a shame :<
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Also, does anyone have advice on a good dock that I could use that would support charging the machine? I plugged my brother's Gen8 Core i5 spectre into my anker charger and it wouldn't charge. I guess I can understand that they don't want to allow the machine to charge off just anything but it would have been nice to get that trickle charge on the airplanes that offer a usb port these days.
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What do I need to look for in a hub that will actually charge these machines? Do I just need Power Delivery or something more?
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The HP docks Ive seen are pretty "meh" and I've seen older spectres where people bought the recommended dock and it wouldn't charge it.
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Thanks for any advice | TS:
- Samsung Galaxy IconX: The pod has seen better days, its got a little crack on it, but the earbuds and pod still function want $50 shipped
- ~~PlayStation VR: Barely used, like new want $175 shipped~~ | Hey guys! This isn’t an ad or anything, I just thought I’d share in case anybody else was in the market for a dock right now.
I’ve been in need of a dock for longer than I’d care to admit and I’d always debated between the CalDigit and the OWC 14 port dock. They both have roughly the same specs from what I’d seen, were priced about the same and I just couldn’t ever decide which one to go with.
For some reason, I went to Caldigit’s site last week to look it over for the thousandth time and saw that it was part of a “back to school” sale and priced at $210.
Given how much we all spend on our gear I thought that was enough of a deal to go with it. I’ve used it on one job already and it’s been great so far! So just in case any of you were looking for a good deal on a dock, now might be the time to pull the trigger.
| Timestamps
Item | Description | Price
---|---|----
~~Akitio Thunder2 External GPU Setup~~ | ~~Includes Dell DA-2 power supply and custom made adapter to connect to 6pin GPU. Everything you need to connect to an GPU with 6 pin power.~~ | ~~$160 shipped, $150 local~~ **Sold on eBay**
Henge Dock Vertical Docking Station for 15" Retina MacBook Pro | Great condition | $75 shipped, $65 local | 293 | Not sure if it has been like this for a while or not, but the docking station is now pretty cheap. Also not sure if it works on the 2013 but I imagine it won't. Just thought I'd share the possible news. | Docking station annoyance | This dock works great with my Surface Pro 3 | SP3 docking station for my SP4 | ASUS RT-68R loses internet connection when laptop is disconnected from docking station | Docking Points broken or just missing something about building an outpost at them? | this is NOT the 2013 version. Beware | Not as Advertised - Obviously a Returned or Defective Docking Station. | Quick question about using surface pro 7 docked. |
294 | where did satyapal chandra go for his graduation from | Satish K. Gupta Government of India for scientific research, awarded him the Shanti Swarup Bhatnagar Prize for Science and Technology, one of the highest Indian science awards for his contributions to Medical Sciences in 1997. Born on 20 April 1953 at Chhachhrauli in the Indian state of Haryana to Gur Prasad Gupta and Satya Rani, S. K. Gupta did his early college studies at the University of Delhi from where he earned his graduate degree (BSc). Moving to the All India Institute of Medical Sciences, Delhi, he completed his master's degree and started his career as a research officer at National Institute of | of the Government of India for scientific research, awarded him the Shanti Swarup Bhatnagar Prize for Science and Technology, one of the highest Indian science awards, in 1989, for his contributions to biological sciences. Subhash Chandra Lakhotia, born on 4 October 1945 in Churu, a city near Thar desert in the Indian state of Rajasthan, to Dwarka Prasad-Suryakala couple, did his early schooling in Churu and then in Kolkata and graduated from Vidyasagar College, Calcutta University in Zoology Honours in 1964 before obtaining his master's degree in Zoology and Comparative Anatomy in 1966, both from Calcutta University. Continuing his doctoral | of the Government of India for scientific research, awarded him the Shanti Swarup Bhatnagar Prize for Science and Technology, one of the highest Indian science awards, in 1989, for his contributions to biological sciences. Subhash Chandra Lakhotia, born on 4 October 1945 in Churu, a city near Thar desert in the Indian state of Rajasthan, to Dwarka Prasad-Suryakala couple, did his early schooling in Churu and then in Kolkata and graduated from Vidyasagar College, Calcutta University in Zoology Honours in 1964 before obtaining his master's degree in Zoology and Comparative Anatomy in 1966, both from Calcutta University. Continuing his doctoral | includes 354 recognised Sanskrita pathashalas throughout the state. Karnataka Samskrit University Karnataka Samskrit University is a university in Bangalore, Karnataka. Its aim is the development and research in Sanskrit language. The university was established in 2010 by the Karnataka Government. Karnataka Sanskrit University has been formed exclusively for the development of Sanskrit language. Sanskrit has a hoary, scientific, literary, cultural tradition and heritage. Its contribution in the area of Prose, Poetry, Drama, Dance, Sculpture, Paintings, Fine arts, Medicines, Philosophy and other allied areas is far more extensive and lasting than has been realised by the Indian scholars till today. The | present to study as a part-time student. SCD Govt College - SCD Govt College earlier known as SD college was renamed in 1976 after the name of great scientist and physicist Satish Chandra Dhawan. Mr Dhawan was the mentor of India's most favourite president Dr. APJ Abdul Kalam. SCD is situated at the College Road near Nehru Rose garden. SCD college is considered as the top most college of Panjab University and one of the top colleges of north India. It offered academic courses on graduate and post graduate level. Ludhiana is well connected by road and rail as Ludhiana | Sri Sathya Sai Super Speciality Hospital heart bypass operation, or a kidney transplant, or a lung operation or brain surgery, everything will be done free. This has been decided upon from the very starting of the project." Sri Sathya Sai Baba Sai Baba added that the hospital would be inaugurated on 22 November 1991. The first cardiothoracic operations were carried out successfully exactly one year later. The Sri Sathya Sai Institute of Higher Medical Sciences was inaugurated by Sri Sathya Sai Baba and the then prime minister of India, Shri P. V. Narasimha Rao, on 22 November 1991. "The second phase was inaugurated a year later | Satyapal Dang 1920 at Rasoolpur (then in Gujranwala district) of the British India and did his early schooling in Lahore. Getting involved in the Indian freedom movement during his student days, he worked with the leftist wing of the Indian National Congress in the beginning but moved the Communist Party of India and became an active worker in the "Bombay Commune" of the party in the 1940s. Later, he became the general secretary of the All India Students Federation at the age of 25, and participated in the 1st Party Congress hed in Mumbai in 1943. It was during this time, he | Kalam SAT Kalam SAT is a Femto Satellite and widely claimed to be the world's lightest satellite. It is named after former Indian president Dr. A. P. J. Abdul Kalam and was built by an Indian High school student team, led by Rifath Sharook, an 18-year-old from the Tamil Nadu town of Pallapatti. The high school team participated in Cubes in Space, a STEM-based education program by Idoodle Learning.Inc and NASA. As selected student competitors, the team won an opportunity to design experiments to be launched into space on a NASA rocket. Kalam SAT was launched by NASA along with | 294 | Satyapal Chandra to learn English. Various phases of his professional life nurtured his true artistic passion. Later on he enrolled himself in School of Open Learning, University of Delhi to obtain a graduation degree. His academic accomplishments included various accolades and awards. He deeply believes in the ideology of Liberal Humanism. He is deeply influenced by Hinduism, Islam and Buddhism. He loved the poetry of different Hindi, Sanskrit and Urdu's writers. Islam has played a very crucial role in the initial phase of his life. He has also adopted an Islamic name for himself, Nemtullah Khan, and still widely recognises by this | when did satyapal chandra release his tenth book | when did chandrasekhar become a fellow | what does the name chandra mean in sanskrit | what is the real name of chandrakanta | when was heramba chandra college shifted to calcutta | when did chandra win the order of friendship of peoples | how old was nur muhammad taraki when he came to india | how old was satyapal anand when he wrote his first novel |
295 | Proffessional/skilled (no charge for erotic/Domination) 49m tist Looking for Subject/slaves | Hello, my Mistress is look for more slaves to serve her online, If you are in search of a an experienced Domme, who's specialities include JOI, CEI, Cuckolding, SPH, Sissy Play, RP, CP, Slave Training and much more. Please contact me for more info and testimonial... slaveofElla | I am looking for a master who is looking for a possible long-term slave to brainwash, train and use for their pleasure. Not very many limits. | I am looking for a slave to serve me and own seriously. | Hey everyone,
I'm a 20 y.o. domme from Melbourne, Australia. I'm looking for slaves who are very submissive and enthusiastic about working for their mistress' pleasure.
I'm looking for people roughly my age or younger, and ideally I like a slim/skinny/toned body type. If you're unsure just PM.
I'm into a lot of things, starting with voyeurism. I love to watch so my ideal sub would be an exhibitionist or otherwise comfortable on cam. I love control play and everything about teasing and denial, orgasm control, ruined orgasm, JOI, the usual stuff. I'm also into uniforms (of all kinds: school, work, sports, etc). And I love tight-fitting underwear and clothing. That's among other things too, so again just PM.
I'm looking for a sub/slave who is very obedient, submissive and loves to be used for pleasure and controlled. As I mentioned, I love control play and would be happy to take all the control you're willing to surrender.
That should be enough to get my vibe, so send me a PM with a little about who you are and what you're looking for. Im much more inclined to respond if you attach a pic, and leave a kik username :) I'm happy to verify of course
If you're in Melbourne, I am happy to talk about meet ups but thats only after we have something successful online going for some time. | Hello, 23M here! Looking for a 20+ female Sub/Slave as a part of a Dom/Sub - Master/Slave but also include blackmail as a part of this dynamic. Be it I remote control your machine and watch you whenever I want to at any part of the time, have a bunch of your photos and information that I can hold over you, etc.
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Kinks: dom/sub, bondage, freeuse, humiliation, edging
Limits: blood/gore/bodily fluids etc., dd/lg
Here's a full list | Hello there my Cuties,
I’m a fulltime librarian who's just gotten so bored of dusting off old books far too easily... I’m looking for a 24/7 slave who can handle my intruding on their day to day affairs as well as what goes on behind closed doors. I am desperately bored due to the pandemic and would love to micromanage a little pet to eat my day up
My biggest kink is electro play expect to endure that as well as general humiliation if you don’t behave.
PM me if you dare | I'm a 31 year male slave looking for an online Mistress to control me. I do freelance work so I have a lot of free time and spend most of my time at home. I'm passionate about computers, music, and BDSM. I've been looking for a Mistress for a long time but with no luck. Please help me fill this void in my life. I've very obedient and loyal. I also have plenty of toys to play with. I'm into cbt, tease and denial, chastity, and I'm willing to explore almost anything as long as it doesn't involve piss, shit, or blood.
Please PM me so we can discuss limits and how I can best serve you. I'm looking forward to hearing from you. | Mistress Amanda here to command you.
I love edging **good**, masculine boys. My specialty is edging and JOI. I can command you on skype but I do not C2C with first time slaves *unless* you are VERY obedient. I like working slaves out, making them beg, and deny my pets.
Rules: Must have quality cam. mic must be earned I will NOT c2c unless you are VERY obedient so do not bother adding me if you are not prepared. I require face but will make exceptions on a case by case basis.
Preferences:
* muscular or athletic (not skinny)
* mic
* married
* fleshlight
* condoms
* forced bi
* underarmour/tight underwear
* business suits
* compression pants
* mature men
* CEI
These are only preferences, NOT requirements. *I do not charge money*
I do require a photo for reference and attractive guys move to the front.
Please message me, don't just leave a comment. If you have questions, check my FAQ on my profile :\*
***\*IF NOT A SLAVE DO NOT BOTHER ME\**** | 295 | I'm in the process of changing the way I find subjects to have long term erotic/Domination/mind control relationships with and I need a few willing volunteers, I'l give you want you're seeking if you test out my mp3s and videos prior to me posting them on youtube and warpmymind. All my subjects leave happy, it's just getting them i the door. | [Hobby] Team looking for someone/people to handle music & audio for Ludum Dare game jam | The Gold Rush It's Over - Don't waste your time with Erotica self-publishing! | Request for the hosts to help with my concentration as a homosexual | Are there any sex positive organizations I can volunteer at? | Softcorn / Erotica for prudish 39yo wife | Good help for sex scenes for mainstream lit, not erotica | Please help! Looking for an experienced submissive woman to help a younger, vulnerable woman | Research Survey Invite for any of the following: Men over age 50, military or veteran, LGBTQ |
296 | My smok stick prince is being scuffed | It starts sticking after a while. Had this for more than an year. Ended up scrubbing the inside using a hard sponge. It cleans it up and keeps sticking after a few fries. | Keef Trouble is a sleeved-on metal tube for greater volume and a crisper percussive sound. The Zob Stick is rhythmically bounced on the floor and the metal sleeve hit with a wooden stick. The stick itself, (usually an adapted hockey stick because of its durability,) is serrated to achieve a scraping sound effect when necessary. Although the resultant construction is heavy, requiring strength for continual use, this weight gives it a volume and 'clout' that the traditional monkey stick might not match, especially in a live and loud band situation. A Keith Trussell / Malvern Hostick composition, 'Hello Mum', had been recorded | Like many of you guys my analogue stick rubbers started to go uncomfortably soft and sticky. Thanks to posts on this sub mentioning that contacting 8bitdo support yielded free replacements, about three months after asking by email my replacements arrived and now my analogue sticks are comfortable to use again! I'm pretty sure the controller is well past its warranty so it's awesome to know that both the manufacturer and this community stands behind their products. | I must own dozens of pairs of sticks. But I just purchased an electronic drum kit which has black rubber pads instead of normal skins used on a normal acoustic drum. I had noticed while searching for an electronic kit that the black rubber showed a great deal of the effect of the striking of them. It always seemed that these were being caused by your standard wooden sticks. Enter rubber-tipped! I started using them yesterday and they have definitely impressed me with the lack of scuff marks left on the pads. And as an added bonus, the rubber tip seems to add a slight bit of rebound to it's contact. It might be my imagination, but one thing's for sure, I am very pleased with them. | I'm using an etokki omni (kr version) and all of a sudden I can hear my stick squeaking and feel rubber on runner only when I input d/b. Earlier I used a slightly wet wipe to clean my stick, though I doubt water would get in. Any advice on what to do about the squeaking would be great. Thanks | I brought these sticks they broke the first day I starting with them crazy thing I was even playing hard before that happened | Stupid fire stick didn't even last a whole month before it completely gave up on me. Never wasting my money on this again! | The top layer ended up peeling away after a week of use and now there are gel bits all over my desk. | 296 | My smoke stick prince is leaking into the air intake, also it tastes slightly burnt nothing to bad but still annoying considering I replaced the coil 3 days ago primed it, havent let the ammount of vape juice drop below minimum and have been doing my best not to chain vape!
The vape also gurgles but doesn't spit.
How do i stop leaking into air intake?
How do I make sure I dont get dry hits?
How do I prevent my coils from burning so quickly?
How do I stop my gurgling and any other advice for a relatively new vape owner
I use a 0.17 ohm v12 prince max mesh coil, the tank that came with my stick prince, am not sure about the vg and pg but use 6mg nic juice | Need some help with Lost Vape coils | Vape feels like its burning? Help | Why does my new vape juice taste like burnt garbage? | New to vaping and having tank problems, any help much appreciated | HELP: All juice tastes bad. Not vapors tongue. | Vape exhale causing me to cough? | Please help! Smoke coming from my vape..no idea why | Vape reading .09ohms, but my coils rated at .2ohms need some advice |
297 | the black ones were bad already. The sole on the left shoe was ... | I kept waiting for the other shoe to drop, but it didn't. I really thought they would get all the bad guys. That was different. | The shoes are fine except the color is different then pictured. They are more of a silver ran in the picture they were more black. | Very disappointed in this shoe. Maybe I got a bad pair, but I have had to crazy glue several areas of the waffle on the sole that have come off. | Great shoe, but within 2 weeks part of the sole on the left shoe was torn and had to be glued back in place | Unfortunately even though at first it felt like a good shoe after a fairly short amount of time the sole separated from the main shoes. I mean on both of them. The rest of the shoes look like they had fairly light to medium wear which they do but they must have used defective glue or whatever methods they did use were to no avail. For a shoe that is pretty costly I have to say that they are junk. They have the durability of a cheap 30 dollar set of sneakers. I would never buy anything in the 928 series again and am totally rethinking buying any shoes at all from them. Mine are the MW928. i did contact customer service and they were less than helpful. The one star I posted here is a gift. :( | Excellent choice I purchased the same shoe in black, gray and my son purchased for me the chochlate color Gamut he lives in another state I was visiting and those appeared to have been worn they were supposed to new they were dulled | It seems like there isn't enough depth over the toes...other wise I think they would have been very good shoes. | The box was delivered broken, the bottom of the shoes were dirty as if someone wore them, and inorder optical white and there were pink marks on the fabric and tounge of the shoes. | 297 | I bought two pairs of these. One in black and the other in the sand color. When I received them, the black ones were bad already. The sole on the left shoe was splitting. The seller, fashion for play, was very helpful and sent out a replacement page that I recieved in less than a week. The sand color ones started splitting after one use. I don't think these shoes will last me too long. But they were very comfortable, especially after a few hours of wear so they start to stretch and mold to your feet. I wouldn't buy these again, but they fit very well, are pretty comfortable, and are pretty cheap. | Soles are coming apart already. Just received them for ... | I purchased 3 pairs of these shoes in different colors ... | Disappointing quality, soles splitting | 2 shoes for same foot | Soles wear out fast. Get half soles sewn on right away | they only lasted 1 year and they are falling apart - the soles are all broken up at the edges and obviously they are not a good | These shoes are falling apart after only a few weeks ... | Very cheep material after only one week the black sole ... |
298 | So happy with this product | Great product, just as expected. Excellent, very happy! | So far loving the product. Better then I expected. Awesome!! | Finally received my purchase after a long while. Am happy with product. | I am happy with that product is super good. I like is quality. Thank you so much Amazon and the seller. I recommended that product. | Excellent product! Seller was very responsive, and we love this stuff! | Product works well. I'm very satisfied with it. | thank you, so very much for this great product/it works better then GREAT....100%+ | Product was exactly as described. Happy with my purchase. | 298 | So happy with this product! Was searching everywhere for one and glad to pay the price I did for them! | This item is fantastic. I have been looking for one for the ... | I am so happy that I found a reasonably priced one on Amazon | Glad to have found it and at a great price ... | WOW these guys have an awesome product! They have great customer services | I was pleased to find this item at such a great price | Great product - I can't believe I found one of ... | Truly thrilled with this product. We looked at many ... | This is great!! I ordered same brand |
299 | Planetary Science Postdoc & Career Salary Prospects? | supplements and out of hours payments, depending on experience, education, and position. Job growth for the profession has been forecasted as follows: According to the US Bureau of Labor Statistics (BLS), the 2010-2011 occupational outlook report suggests that biomedical scientist employment is expected "to increase 40 percent over the 2008-18 decade, much faster than the average for all occupations." According to the 2010 BLS report, the median salaries for biomedical scientists in the United States in particular employment areas are: These figures include the salaries of post-doctoral fellows, which are paid significantly less than employees in more permanent positions. Biomedical | I'm applying to a postdoc which doesn't list their salary stating that it's whatever the NSF guidelines permit. The only thing I'm able to find is data from 2012 (45k) didn't know if anyone had more recent numbers. | I have ~3 years of experience with Rails with some sprinklings of React, Angular and Vue.
Just wondering what a reasonable salary would be for remote, London based companies?
I've had 5 interview requests in the last week from companies based in London via a jobs site after setting my salary requirement to £62,000 which I thought was about right but I'm wondering if I should have put it a tad higher given the requests I'm getting.
At the same time, I don't want to ask for a salary that I feel I might not be able to earn. Many of the requests come with "Senior" titles but I don't quite feel at that level yet.
Thoughts? | Hello! Hope everyone is doing well.
I am an MSc Physics and B. Engg. Electrical and Electronics Engineering (double major) undergrad from India and wanted to ask about the Ph.D. stipend rates (paid by the university). (Preferably Natural Sciences and Engineering)
What is the net salary paid?
Is this salary enough to save and survive in Norway? (Considering that I would prefer to live in a private 1 bedroom apartment, am a nonsmoker, and don't drink alcohol)
What are the taxation rates like?
**\*** **I am not sure if this is the right place to ask this question, however, the university subreddits I found were mostly inactive. In case posts like these are not allowed on this subreddit, kindly excuse my mistake and remove it \***
TIA! | As per title, I’m looking for resources that show the employment and salary trends by profession in Australia. I’m doing a presentation on postgraduate student retention in in the STEM areas and this data would come in handy to see what industry is offering.
Thanks! | I was hired straight out of college 5 years ago for an embedded software engineering position about 10 miles north of Boston. My starting salary as a level 1 software engineer was $64K. I am now a level 3 engineer with a salary of $96K at the same company. Compared to what I see online, this feels pretty low. I told my leadership I was starting to look elsewhere, and they seem very motivated on getting me to stay. With that said, what would be a reasonable salary to ask for? We're not FAANG, so I'm not expecting anything crazy, but those are the kinds of companies I was looking at. A co-worker in the same exact situation (same salary & YOE) recently took an offer elsewhere for \~$120K. Various salary estimating tools I've used online put me between $110K and $145K. Does anyone have any insight? | Does anybody know what kind of salaries the presenters for these news companies get paid? Also, what is the work schedule like for them? I heard Eamonn Holmes was on a very good salary, something like £1 million a year. Also, Kay Burley who works for sky is on around 300k a year. Do you know the average salaries for the other (less famous) presenters who work on Sky, ITV etc.
I am a bit nosey haha, but also fascinated by news presenters work, and am genuinely interested what the salaries are like at these big news companies. I know they wake up early (like 3am if on early morning shift) and it can be hard work, but interested how much they earn. My personal favourite early morning presenters are Sky presenters Stephen Dixon and Sarah Jane. | All BCaBAs working in the Bay Area, what is your salary like? Are you finding competitive wages across different companies?
I’m leaning towards getting the certificate and I’m just curious what the going rate is for the certificate. I currently make over 45,000...under 55,000 as an RBT with 10+ years experience. | 299 | Hi folks! I've been searching for salary information for planetary scientists, but I haven't found much information. Any ideas on where I could find salaries after grad school, the potential for growth, etc? Thanks so much! | Regarding the Ph.D. salaries paid by universities. | Questions regarding a planetary science career. | Who's interested in a /r/geologycareers salary survey? | where is the under secretary for science located | How much does Nasa makes? | What is the pay cap for an astronomer? | What is a "good" salary to live with in Munich as a frontend React dev? | How much money does an astronomer earn per year? |
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