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People may well wonder if there is certainly solution to this particular evergreen issue. Progress of the united states is always ceased at this point, which should be prioritized industrialization or even environmental defense? The answer to that is, both there would be zero purpose pertaining to existence of a single without the different. A state that is nicely industrialized having polluted setting is connected with no worth and or viceversa. Effective company ordination and co-operation between the two pillars is quite necessary for the nation to face on the top ranks.
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text:
Kliznica je gravitacijsko prenosilo izrađeno od drva, umjetnog materijala, čeličnih limova ili limova od lakih metala. Klizne plohe kliznica često se oblažu specijalnim materijalima da bi se smanjilo trošenje (habanje) i trenje. Nagib kliznice ovisi o svojstvima materijala koji se prenosi. Nagib mora osigurati takvo klizanje materijala niz kosinu da bi brzina v na kraju kliznice ne postane prevelika. Gornja granica brzine iznosi od 1,5 do 2 m/s. Da bi se roba pokrenula, kut nagiba kliznice mora biti od 5° do 10° veći od kuta trenja mirovanja. Ako je djelić materijala težine G, što kliže niz kliznicu s kutom nagiba β, imao na početku brzinu v0, porast kinetičke energije tog djelića na kraju kliznice iznosi:

gdje je: g - ubrzanje sile teže (oko 9,81 m/s²). Djelić se ubrzava niz kliznicu zbog djelovanja sile G∙sinβ. Tom se gibanju suprotstavlja sila trenja između djelića i kliznice μ∙G∙cosβ, gdje je: μ - koeficijent trenja. Rad tih dviju sila na kliznici duljine l jednak je porastu kinetičke energije tog djelića materijala, pa je:

Sa

dobiva se nagib kliznice:

i brzina v na kraju kliznice:

Srednje vrijednosti kutova nagiba kliznica navedene su u sljedećoj tablici:

Klizne plohe ravnih kliznica oblikuju se kao žljebovi pravokutnog ili polukružnog oblika. Za prašinasti materijal upotrebljavaju se zatvoreni žljebovi ili cijevi.

Ako nema dovoljno mjesta da se postave ravne kliznice, grade se zavojne kliznice sa žlijebom što se ovija kao zavojnica oko okomite osi. Unutrašnji rub žlijeba pričvršćen je na središnji stup, ili je vanjski rub žlijeba pričvršćen na unutrašnju stijenu cijevi velikog promjera. Zavojne kliznice vanjskog promjera od 1 do 1,5 m imaju maseni protok od 200 do 500 t/h sipkog materijala (na primjer ugljena, pijeska, šljunka). U usporedbi s ravnim kliznicama zavojne kliznice imaju prednost u tome što je ubrzanje materijala manje zbog povećanja trenja djelovanjem centrifugalne sile).

Pneumatska kliznica
Pneumatske kliznice veoma su prikladne za prijenos prašinastih i sitnozrnatih materijala, kao na primjer cementa, gipsa, šećera, brašna i ugljene prašine. Takve kliznice prenose materijal kao da je u stanju sličnom tekućem stanju. Zrak pod tlakom od 102 do 105 kPa struji iz zračnog kanala kroz porozni pod u materijal koji treba prenositi. Kad tlak zraka premaši tlak kojim materijal djeluje na pod, mirujući materijal prelazi u takozvani vrtložni sloj. Između djelića materijala, nošenih strujom zraka, smanjuje se trenje na veoma malu vrijednost, pa se materijal ponaša slično tekućini. Kaže se da je materijal fluidiziran. Kliznica ima mali nagib, obično od 1 do 6° (do 15°), pa fluidiziran sipki materijal teče niz kosinu zbog djelovanja sile teže. Žlijeb kliznice može biti otvoren ili zatvoren, već prema vrsti materijala koji se prijenosi. Pneumatske kliznice sa žlijebom širine od 125 do 630 mm imaju volumni protok od 7 do 720 m3/h. Snaga motora kompresora iznosi oko 0,8 kW po metru duljine prijenosnog (transportnog) puta. Prednosti su pneumatskih kliznica prema mehaničkim prenosilima stalne dobave: jednostavna i jeftina konstrukcija, velika pogonska pouzdanost i mala potrošnja energije. Nedostatak im je što za prijenos materijala trebaju određenu visinu.

Gravitacijska prenosila
Na gravitacijskim prenosilima materijal se giba niz kosinu djelovanjem sile teže. Ona se veoma jednostavno grade i zahtijevaju veoma male troškove održavanja jer nemaju vlastitog pogonskog uređaja, pa se zbog toga često upotrebljavaju. Gravitacijska prenosila često se uvrštavaju između dvaju prenosila stalne dobave s pogonom, kao vezni članak u prijenosu. Nadalje, služe kao slagači robe na strojeve, te za strmo i okomito ubacivanje sipkog materijala i komadne robe.

Padalica

Padalica je okomita ili kosa cijev kroz koju pada neosjetljivi sipki materijal na skladišta, u brodove i slično. Često su padalice izvedene teleskopski da bi se mogle prilagoditi visini padanja. Za velike visine u cijev se umeću limovi za skretanje, koji smanjuju brzinu padanja, oštećenje materijala i trošenje (habanje) cijevi. Tako nastaju stepenaste padalice koje se upotrebljavaju u rudnicima i za visine padanja veće od 600 metara.

Izvori

Strojevi
Građevinarstvo
Metaloprerađivačka industrija

redpajama_set_name: RedPajamaWikipedia


text:
Did DB Cooper's aircraft land safely with the aft stairs open?
I've never seen a 727's aft stairs open, but presumably, based on an Wikipedia image and common sense, they do reach the ground when the aircraft is on the ground. Furthermore, (as I understand it), airliners land with a positive pitch, which means that assuming a level runway, the rear of the aircraft will touch down first. However, this suggests that if the aft stairs of the 727 were open during landing, they would impact the ground during landing and, given the pitch, do more than scrape the ground and cause damage to the aircraft.
However, DB Cooper's jump left the aft stairs open, and (as far as I can tell) it seems that the landing was uneventful besides the stress of having a hijacker potentially on board (although it's quite understandable if no one made any record of it, given there were slightly more important things to deal with).
If DB Cooper's flight did land without damage, why is that—did the 727's aft stairs not fully touch the ground? If the stairs did impact the ground, was there sufficient damage to require repairs?
(I meant this question to be more about the 727 than DB Cooper, but since his was the only landing with stairs open, there wasn't much room for speaking in general terms).
safety landing boeing-727
Pondlife
waiwai933waiwai933
$\begingroup$ wikipedia say they were deployed $\endgroup$
$\begingroup$ Its possible that they were not fully deployed, i.e., not completely down and locked. $\endgroup$
– fooot ♦
The aft airstair was partially deployed for the duration of the approach and landing.
The transcripts of ATC communications between NW305 and various ground stations are freely available (and a fascinating read). The relevant communications (with Reno) begin on PDF page 87 (numbered 213). Below are the mentions of the airstairs from that point on, with times given in PST, 1971-11-24. I added the text in brackets for clarity.
22:35, NW305: OKAY AH WE'RE TRYING TO MAKE CONTACT WITH [Cooper in] THE BACK [of the airplane] NOW AND AH WE'RE GOING TO GET THESE STEPS UP BEFORE WE CAN MAKE OUR LANDING...
22:43, RENO: NORTHWEST THREE ZERO FIVE WHAT'S THE STATUS ON THE STAIRS NOW SIR
22:43, NW305: AH WE HAVEN'T BEEN ABLE TO GET AHOLD OF ANYBODY [in the back of the plane] YET UH TRYING TO CONTACT HIM AND THEY'RE STILL DOWN SO I WE HAVEN'T DECIDED YET AH WE MIGHT COME IN AND LAND WITH THEM DOWN THERE'D BE SOME SPARKS SO
22:48, NW305: APPROACH AH THREE ZERO FIVE WE CAN'T SEEM TO RAISE HIM BACK THERE WE KIND OF HATE TO WE'D JUST AS SOON LAND WITH THE THING HANGING DOWN IT ISN'T ALL THE WAY DOWN AND THEN PROBABLY WON'T HAVE ANY PRESSURE ON IT SO WE HOPE IT'LL (unintelligible) FREE...
22:57, NW305: ...WE'RE NOW MARKER INBOUND AND UH AH WE'RE GOING TO BE LANDING WITH THE AIR STAIR IN THE DOWN POSITION AH WE DON'T SEEM TO GET ANY RESPONSE FROM OUR FRIEND IN THE BACK
[The aircraft touches down and is taxiing.]
23:03, NW305: SEE ANY SPARKS COMING OFF THE TAIL AT ANY TIME ON AH TOUCHDOWN
23:03, RENO: NEGATIVE NONE AT ALL THE ONLY THING THAT'S VISIBLE ON THE TAIL IS LIGHT AH APPARENTLY ON YOUR RAMP
23:03, NW305: ROGER UNDERSTAND STAIR LAMPS AH STAIR LIGHTS
23:03, RENO: I DO SEE SOME AH SPARKS NOW JUST A FEW AH TRAILING YOU AH AS YOU'RE TAXIING IN
23:03, NW305: OUR AH PASSENGER TRIED TO DISEMBARK
23:03, RENO: I STILL DON'T AH GETTING A FEW SPARKS NOT VERY MANY AT ALL
23:03, NW305: OKAY WE'LL TRY TO SLOW OUR TAXIING HERE AS MUCH AH IT PROBABLY IS DRAGGIN AH
Why did the crew not retract the airstair before landing?
The airstair can only be operated from two positions: one in the main cabin and one on the exterior of the aircraft. It cannot be operated from the flight deck. The testimony of Tina Mucklow, the flight attendant whom Cooper interacted with almost exclusively, reveals that
Approximately four minutes after takeoff, [Cooper] stood up, told [Mucklow] to go to the cockpit and close the first-class curtains, and for no one to come out from behind the curtains.
It should be noted that the airstair was still closed and locked at this point. In fact, it was Cooper himself who performed the deployment:
...he asked her to demonstrate to him the procedure for opening the rear door and extending the stairway. She did this and was under the impression that he understood how to do it. She commented that it occured to her at this time that this was the only function of the aircraft which she had discussed with the hijacker during the time she had been with him which he did not seem to be fully aware of.
Even though before Mucklow left Cooper in the cabin "...she pleaded with him to take the bomb with him and he said he would take it with him or disarm it...", nobody could be sure, so complying with his demand for no one to enter the cabin was the obvious choice. Even after the crew suspected he had jumped, there was still some chance that he was present. That—on top of the clearly dangerous situation of being unrestrained in an airborne jet transport with a door open—compelled the crew to sit tight in the cockpit and land with whatever configuration they could control from there. Indeed, third officer and right-seater on the flight Bill Rataczak stated that
...no member of the crew departed from the cockpit to check on the presence of the hijacker following the arrival in the compartment of hostess Mucklow, who had locked the door behind her.
How did the airstair remain partially deployed on its own?
The airstair is in contact with the tarmac when deployed on the ground. In fact, it's designed to essentially wedge itself against the ground and act as a tail stanchion to keep the airplane from tipping backward during loading and unloading. Early 727s such as N467US had mechanical locks for the airstair in both the extended and retracted positions to accomplish this function.
However, the crew had evidence that the airstair was not locked, as Mucklow "observed the red indicator light go on the [flight engineer's] panel indicating that the stairs had been lowered." On the 727-100, that light would be de-energized only if the airstair was locked either up or down. (On the -200, a green light was added to indicate a fully extended and locked position.) The ATC transcript indicates the captain's later belief that the airstair wasn't "all the way down", so it's reasonable to assume the warning light remained illuminated.
That the airstair didn't lock down when deployed indicates that it never fully extended. It is likely that the air loads simply prevented full extension. The airstair hydraulic actuators were not designed with the strength necessary to overcome a 170-knot airstream, especially on early 727s. The extension was limited by the airspeed and subject to fluctuations with changes in the airstream and the weight of Cooper upon the stair.
The inability to fully extend the airstair in flight was even known on the ground beforehand, as the transcript of communications between NW305 and the airline's base at MSP reveal (I cleaned these up):
18:38, MSP: DON'T KNOW OF ANY WAY TO LOCK STAIRS IN AN INTERMEDIATE POSITION.
18:40, NW305: ...STAIRS WILL OPEN ABOUT 20 DEGREES AT 120 KNOTS. IS THAT ENOUGH FOR AN INDIVIDUAL TO ESCAPE THE AIRCRAFT?
18:40, MSP: WITH HIM ON STAIRS WILL OPEN POSSIBLY ENOUGH FOR HIM TO GET OUT. REMAIN UNPRESSURIZED. BE IN LANDING CONFIGURATION WITH FLAPS. SLOW TO [APPROACH] SPEED BEFORE TRYING TO EXTEND STAIRS.
As it turns out, the stair could not be opened much if at all at 170 knots during a climb, and the captain had to "have 'er about down to a hundred and sixty knots" and level off at 7,000 feet to get the resistance low enough. It makes sense that a higher angle of attack would cause a greater air load on the door due to the increased frontal area. It also makes sense that the airflow alone would be insufficient at any speed to completely re-close the door due to the geometry of the empennage, the weight of the stair, and some hydraulic damping. Once the door was open, the crew were able to climb again to 10,000 feet and keep the airspeed "in the vicinity of one seventy, one eighty [knots]".
Although the hydraulic actuators would have provided damping, the swirling wakes from the landing gear and flaps—not to mention the aircraft turbulence inherent when flying low and slow over mountains in a storm—undoubtedly wrenched the stairs up and down considerably. Cooper's exit has been romanticized as a high-dive into the unknown, but it was more like trying to exit a springboard during an earthquake, with his own weight just exacerbating the problem. We know as much from Richard McCoy, Jr., a copycat hijacker who survived his jump (at the same airspeed) and was later captured and interviewed:
...[McCoy] stood geared up in the open doorway for a very long time before descending the aft stairs. It was almost midnight, the sky was black, and the wind was freezing, yet his hands were sweating. Finally, he was able to collect his wits, take a deep breath and step outside onto the stairs.
As he stepped out, the entire stairway dropped two feet under his weight. Knocked off balance with his 70-pound duffle bag between his legs, he grabbed the right handrail and wrapped both arms around it, desperately holding on. The stairs shook and vibrated. The noise from the jet engines on either side of him was horrendous.
In fact, it was cabin-pressure fluctuations caused by Cooper descending and exiting the airstair that allowed for the determination of exactly when he jumped (8:11pm PST):
Crew reported oscillation of cabin rate-of-climb indicator. This probably due to [Cooper's] weight now on stairs, stairs extended further, resultant effect on cabin pressure.
The FBI's analysis was that "When [Cooper] jumped, the air stairs were forced closed (by outside air pressure) causing an increase in air pressure similar to shutting a car door with the windows up". Although we've established that the door was not forced completely closed and locked, it's clear that the airstair was able to hang somewhat freely in the airstream, its deflection affected by air loads, the weight of Cooper, its own weight, and any dampening provided by the actuators.
What was the risk of landing with the airstair deployed?
The crew knew from the cockpit indication that the airstair was neither down and locked nor up and locked. But they had prepared somewhat for the idea of landing with a deployed airstair before they even departed Seattle:
19:27, MSP: IT WOULD PREVENT ANY SUBSEQUENT TAKEOFF IF YOU LAND WITH [THE AIRSTAIR] DOWN.
Mucklow advised Cooper more than once of this fact, given that Cooper had stated intentions to get to Mexico and that Reno was just a necessary refueling stop along the way due to Cooper's wanting to be flown low and slow.
Landing with a deployed airstair could have a range of consequences that had never been investigated or analyzed, so most likely the airline was playing it safe. At the very least, a detailed inspection would need to be carried out before the airplane flew again. If the stair were downlocked, the results of a landing would depend on what failed first. If only the latch failed, you might get away with just dragging the stair, which would cause some exterior damage but overall that'd be a relatively minor fix. If nothing on the airstair failed, I suppose you could bend the entire fuselage. I'd also worry about bits and pieces of failed components being rocketed around the empennage or into the cabin.
Fortunately, at this point the crew was safe from the worst outcomes because the stair was not downlocked. In fact, as we've seen, the crew knew that even at 120 knots the airstair would not be deployed far enough to strike the ground upon touchdown. That speed is in the ballpark for an empty 727 on landing, but even at a lower speed it's entirely plausible that the airstair did not strike the ground on touchdown, and was only able to fully extend once the aircraft was at taxi speed.
What damage did the aircraft sustain?
Given everything we've covered so far, the damage was probably not extensive. Dragging the stairs along at taxi speed would mean not much more than some sheet-metal repair. Looks like some of the railing paneling sheared away, probably in the air: There's also the placard found in the forest a few years later that got ripped away at some point during the flight.
In any case, the crew was able to easily deplane via the deployed aft stairs:
23:14, NW305: ...WE'LL GO DOWN THE BACK STEPS AND AH AH WE'LL BE TAKING LEAVE OF THE AICRAFT AND SHUTTING IT DOWN AT THIS TIME...
Peter SchillingPeter Schilling
$\begingroup$ "The transcript does not prove that the stair was down." Um, it kind of does. $\endgroup$
– Organic Marble
$\begingroup$ AH? Is that some kind of marker or code, because it appears quite often? $\endgroup$
$\begingroup$ @Peter Just a transcription of pilot talk. $\endgroup$
– Peter Schilling
$\begingroup$ Trying to locate the PDF containing the ATC transcript - the link to the Seattle PI blog post is now broken. Anyone? Thanks. $\endgroup$
– Thomas Hanser
$\begingroup$ @ThomasHanser I've updated the link. $\endgroup$
I do not think they landed with the airstairs down: The airstairs are powered to get them back up since they are heavy, and this feature can be operated from inside the aircraft as well.
The following answer is of Yahoo answers and while I can't confirm is accuracy, it sounds very plausible:
There are 2 control handles for the airstairs on a B727, one under a panel on the lower fuselage right beside the stair forward hinge point, and one at the top of the stairs behind a panel on the left side which can only be accessed when the rear cabin door is open. Because the cabin door can only be opened when the aircraft is unpressurized, this usually would prevent its actuation in flight. However, after the D B Cooper hijacking a device was added referred to as an anti-hijack vane that would swing over when the aircraft was in flight and prevent the door opening. To close the door either an electric hydraulic pump has to be turned on in the cockpit, or a hand pump beside the lower control operated while either handle is held to the close position. The door will free fall open without hydraulic pressure, but the support arms may have to be pushed to an overcenter position.
Assuming that the air stairs were deployed, it may be that the force of the airflow passing by would have been sufficient to spare the stairs from a tailstrike. The stairs have a large surface area and moving at perhaps around 100 knots when the nosewheel touches down would still generate a considerable force to push them into the fuselage.
The term deployed may also suggest that the airstairs may have been damaged and uable to retract the whole way, leaving it halfway stuck but still out of tailstrike range.
The aircraft was empty at the time which would have helped in either situation.
voretaq7
I am a B727 pilot to this day (5,000 hours on type) and I am pretty sure that if one tried to land a 727 with the airstair locked down, there would be a considerable amount of damage and the possibility of a serious accident. The two hydraulically operated struts that operate the airstair are downlocked "over center", They are operated by B system hydraulics which would have been working throughout the flight. Trying to retract the stairs while standing at the rear door with the airstair deployed in flight would be very daunting. You have to hold the handle towards you until the stairs are fully up, at which time the handle moves to an over center position and the stairs remain locked up. If the handle doesn't move to the over center position, the stairs will deploy again to the down position. The only way they won't lock down is if you remove B system hydraulics. In flight it is also possible that the force of the airflow on the airstair at 120 knots could be strong enough to prevent the airstair from reaching the down and locked position. Therefore I suggest that if they did not retract the airstair before landing (which apparently they didn't), and the B system was working normally, the only other possibility is that the force of the airflow on the door kept it floating halfway up.
As a matter of interest, the airstair was removed for the test crash of a 727 in the Mexican desert as this is probably the case.
You can see the over-center downlock in this video. I will make a video of the operation of the handle at the rear door in a few days if there is enough interest.
RafflesRaffles
$\begingroup$ It would be desirable if the source of these two images (the aft stairs system and the flight engineer's lower panel) were identified. $\endgroup$
– DFS346
$\begingroup$ They come out of the Boeing 727 Flight Manual. $\endgroup$
– Raffles
The fact is simple geometry would prevent landing a 727 with the aft airstairs in the extended position. These stairs are have almost no clearance from the ground when they are extended. Check the relation ship of the tail strike bumper to the profile of the Aft airstair. You simply couldn't complete an approach at a flat enough angle for a successful landing. So maybe the aft airstair were damaged during the landing? Not possible. The 727 being a T-Tail with 3 rear engines is extremely tail heavy. So much so that the rear airstair doubles as tail support structure for the aircraft when parked or loading. Just the weight of the demountable engines are roughly 4700 lbs each, so we're talking 14,000 lbs independent of the T-Tail structure. When powering back a 727 from the gate the most important rule is to never use the aircraft brakes to slow the rearward roll. The aircraft will sit on its tail everytime. All of this is to illustrate how strong the aft airstair structure is on the 727 as well as how critical weight and balance limitations are on this particular aircraft. The conclusion drawn from this information is reports of landing a 727 with the airstair extended cannot be true.
CosmobeauregardCosmobeauregard
$\begingroup$ A bit of formatting would go a long way toward making this more readable. Maybe that's why I'm not seeing how your reasoning supports your conclusion that one cannot(?) land a 727 with the rear stairs open. Also, just because one shouldn't doesn't mean that they didn't in this one very special case, and you don't seem to address the case of the specific, hijacked aircraft that was asked about. $\endgroup$
$\begingroup$ Also, please note Peter Schilling's answer (posted after yours) that includes ATC transcripts indicating that they in fact did land with the rear air stairs open. The stairs did hit the tarmac, but, it seems only once the aircraft slowed to taxi speed. It seems that your conclusion is flat wrong. $\endgroup$
$\begingroup$ Basically his answer is correct. unless they landed flaps up with a very flat attitude or disabled the B System hydraulics so that the the stairs were floating. $\endgroup$
$\begingroup$ @Raffles as you admit in your answer, it's possible that the stairs didn't lock down. This is corroborated by the ATC transcript provided in Peter Schilling's answer. While I agree with both of you that landing with the air stairs locked down would cause significant damage, the facts of this incident show that they never did lock down, therefore the final conclusion in this answer that it "cannot be true" is categorically wrong since history proves that it is actually true. Also, causing damage and not being possible are 2 different things. $\endgroup$
$\begingroup$ @FreeMan you are right about the last sentence. The author should revise it. $\endgroup$
Not the answer you're looking for? Browse other questions tagged safety landing boeing-727 or ask your own question.
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redpajama_set_name: RedPajamaCommonCrawl


text:
New Era Dawns At Sunfinity
Solar Company launches Utility Scale Division
Sunfinity Renewable Energy, LLC
DALLAS, Aug. 1, 2018 /PRNewswire/ -- Sunfinity Renewable Energy, LLC (www.sunfinityre.com) has announced a name change (the company was formerly Sunfinity Solar, LLC), to accompany significant growth initiatives for the company, including the launch of a utility scale solar division with current plans in the works for three major solar projects.
Sunfinity began business in 2016. John Billingsley, Chairman and CEO, said "The new name, Sunfinity Renewable Energy, reflects a more aggressive and comprehensive vision for the solar company as one of America's leading developers of clean, renewable energy."
UTILITY SCALE SOLAR DIVISION
The utility scale solar division kicks off with several projects in early-stage development, including the Flatland Solar Farm in Scurry County, Texas. The project is located on a 950-acre secured site and has capacity ranging from 140-180 megawatts (MW), with expansion possible during later phases.
"If our Flatland solar project was online today, it would be among the five largest operating solar farms in Texas," said Billingsley. "On the conservative end, Flatland will produce enough power for over 31,000 homes, depending on customer demand during the hotter months."
The Flatland Solar Farm is expected to break ground in 2019 and require approximately 12-14 months to complete. Almost 690,000 solar panels will be installed as part of the construction process. A second West Texas project is in negotiations with a solar capacity of 120 MW. A third utility-scale solar project, located in Colorado, is currently under negotiations and will be announced at a future date.
Sunfinity's utility scale division's management team will be headed by W. Richard Grosdidier, formerly Director of Development and Head of U.S. Solar Power for European-based Innogy Renewables, where he was responsible for starting and building the company's U.S. utility scale solar business. Prior to this post, he ran the utility scale renewable business at NRG Renew (formerly NRG Solar). As a founding member of NRG Solar, Grosdidier helped build the company from launch into a utility scale solar portfolio of 1.8 gigawatts (GW) through acquisition and green-field development in a four-year period. Grosdidier also spent five years at NextEra Energy in senior finance positions. Solar industry veteran Dallas Tharpe also has joined the utility scale solar team as Senior Vice President of Development Engineering; he was a founding member of the NRG Solar start-up team, leading their development engineering and joins Sunfinity from the leading solar independent engineer, Denver-based Luminate.
"The U.S. economy is in a state of rapid transition. Much of this change is being driven by growing availability and market demand for cleaner and lower-cost renewable energy," Billingsley said. "Our utility scale solar division is well positioned to capitalize on this increasing demand."
SOURCE Sunfinity Renewable Energy, LLC
https://www.sunfinityre.com


text:
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redpajama_set_name: RedPajamaGithub


text:
T-20 World Cup: Footylight created additional Fan Engagement through Video Widget for Prothom Alo
Footylight partnered with Prothom Alo during T-20 world Cup. Prothom Alo is the largest circulated newspaper in Bangladesh. It has more than 6.6 million daily readerships online. They launched Footylight Widget on their cricket page. The target was to create additional fan engagement through the...
IPSEM Squared launches a recruitment website aimed at Asian Sports market
Our members IPSEM Squared have launched a recruitment website aimed at the Asian Sports market, in particular Southeast Asia plus Hong Kong and Macau. This is one of the few sports specific job sites in Asia. This jobsite can be found at www.ipsemrecruit.asia. People are currently...
Team Vitality launched One of the most innovative loyalty programs in the world powered by Tezos
More than just an app, V.Hive is the first support-to-earn app in esports based on blockchain. It allows Team Vitality fans to be rewarded for their loyalty! How does it work? Once I downloaded the app for free and connected it to my social media accounts,...
LEVERADE kicks the board by being the first one to deliver digital trophies at a World Cup
This historic event for the sports industry took place in Mexico during the first Baseball World Cup5, thanks to an agreement between LEVERADE and the World Baseball and Softball Confederation (WBSC) to deliver digital trophies to the winning team, MVPs, best coach, and more. The WBSC...
One to One MCCP Express Support "Towards the Badges"
We help Microsoft partners achieve their Solution Areas in skilling by designing a combined proposal to achieve their goals of services offered and intermediate and advanced certifications they need in order to achieve the badges. Our main goals are: Offer the partner awareness of all the resources...
The power of fandata in the sponsorship model of Team Jumbo-Visma
The cycling team of Jumbo-Visma is the number one team in the world, winning on 48 occasions in 2022. The most remarkable being of course the Tour de France victory by Jonas Vingegaard from Denmark. It's important for Team Jumbo-Visma (TJV) to not only rely...
With Escoita sports can and should be for everyone
According to WHO data, blindness affects an estimated 39 million people worldwide and 246 million suffer from moderate or severe vision loss. But not all sports are followed with real-time reporting. Considering this gap in the sports industry, ARMIS Digital Sport created the Escoita App,...
Dundee United becomes the first club in Scottish premiership to adopt Iterpro football intelligence
Dundee United FC, which plays in the Scottish Premiership, collaborates with Iterpro, the most advanced football intelligence solution in the industry. Through Iterpro's platform, Dundee United will be able to create a digital framework that allows all its staff members to streamline communications, operate effectively...
Ukrainian founders are fighting on the startup front
The war changed the lives of tens of millions of Ukrainians. Everyone is fighting on their own front. The Ukrainian founders of the startup AiSport choose leadership in the world of sports innovations. Two Ukrainian women from Kryvyi Rih, Anna Stepura and Dariia Hordiiuk, created a...
tiivii reaches 1,500 annual events produced by AI and will reach 5,000 by 2023
cinfo, a Spanish automatic production company, has already reached 1,500 annual events produced in November 2022 with more than 3,000 hours of broadcasts governed by artificial intelligence. tiivii clients are Sports Clubs, Federations, City Councils, Provincial Councils, Theaters and Music Halls, Televisions and Internet Video Platforms...


Five Little Monkeys Collection #1 contains five delightful tales of five little monkeys who don't always get things right, but they have a great time! This great app contains: Five Little Monkeys Jumping on the Bed, Five Little Monkeys Bake a Birthday Cake, Five Little Monkeys Wash the Car, Five Little Monkeys Sitting in a Tree, and Five Little Monkeys With Nothing to Do! Numerous life messages for our kids in all of these stories in a format sure to entice them! Each book features its' reading readiness assistance. This is so important for our kids to be able to see and hear words used in context! You can also zoom in and pan out on the pages! This app is presented to us by Oceanhouse Media.
Five Little Monkeys Bake a Birthday Cake!
Five Little Monkeys Wash the Car!
Five Little Monkeys Sitting in a Tree!
Five Little Monkeys With Nothing to Do!
**Parents note: A link to OM's site is in the app. If you want to change the iPad settings go to our Parents pages and view the video for that.


The sun was shinning when we flew out of Portland. It has just set when we landed in Seattle. But it rained hard on the plane when we landed in Ketchikan. I felt sorry from the poor folks that had to direct the plane up to the terminal. I felt like I had been away from Aki and home for months, not weeks. The little dog greeted us at the Juneau Airport, making her other human and I feel like we were missed. I can't wait to take her for a proper walk.
This entry was posted in Uncategorized on January 27, 2019 by Dan Branch.


#WomenNotObjects was created by agency founder Madonna Badger in reaction to the rampant objectification of women in advertising that has been the norm for years.
IBM, that old school, not-so-cool, computing juggernaut that once ruled the technology landscape, is upping its digital game of late.
Now, under the auspices of its parent company, McCann Worldwide, the Mithun name will be retired in favor of McCann Minneapolis.
Well this is awesome. And something Cindy Gallop will love!
Multicultural agency Dieste Inc. has named Ciro Sarmiento its new chief creative officer.


The rebalance maintained a zero percent increase in the 2019 budget, Executive Director Ray Otten emphasized.
Otten says a new facility is overdue and a shift in call location makes now a good time to begin the process of planning for such a project.
The Corps would like to build new, Otten said, and has considered working with the same architects who are involved in the county emergency services building project. Locating a new building in the Milton area would improve call response times, Otten said. The Corps is looking to move the station north to the area around the Saratoga County Airport, across from the town center.
"The town of Milton is trying to get more businesses in there and trying to reinvigorate," Otten said. Ideally, the Corps would like to locate next to the Rock City Falls firehouse. "We would have an emergency services complex," Otten said.
The current location has had three renovations and still the Corps is struggling to house its life-saving equipment, supplies and office space.
"We currently have four ambulances," Otten said. Four days a week, the Corps can often staff three ambulances. "You have to be there when the public need is there," Otten said. Calls often happen in waves, Otten said, meaning one crew may be out when the next call comes in and multiple crews and vehicles are needed to respond.
In addition to the ambulances, the Corps also has three first response vehicles, some of these are used by the chief and assistant chief responding from their homes, and the other is kept in the Corps building.
"We need to have room for seven vehicles at any given time," Otten said.
It's not so simple as parking a vehicle outside or in any building, he explained further. "The building has to be temperature controlled," he said. Certain medications can't be above body temperature, or be too cold.
And it's not just the vehicles that are proving difficult to store, Otten said. Supplies in general are spilling over. "Training supplies, uniforms, public outreach products, general equipment," Otten said. Even backboards. If a hospital needs to keep a patient on one, the Corps needs backups in their building and must store them.
The Corps is in the early stages of looking at financing needs, as well as talking to local representatives about grants to help fund the building. "If you're already a tax district, it's tough to fundraise," Otten said.
The Community Emergency Corps has 40 medics and EMTs and five volunteers. For more information, visit the Corps website.
To comment on this story, login and post below. Don't forget to visit the Ballston Journal on Facebook to keep up to date on local news.


text:
KSAT 12 5 O'Clock News
The KSAT 12 News Team offers a report on the latest news of the day, as well as updates on sports, San Antonio area weather and rush-hour traffic issues.
2 child abduction emergencies in effect for 33 counties in the area
Texas Tribune
Shannon Najmabadi
Updated: December 23, 2020, 6:38 AM
Tags: Politics, Donald Trump
Suspect shoots, kills 2 men on Northeast Side before calling police on himself, affidavit says
Trump commutes remaining prison term of former Texas GOP congressman Steve Stockman, who was convicted of misusing charitable funds
Published: December 22, 2020, 7:00 PM Updated: December 23, 2020, 6:38 AM
Former U.S. Rep. Steve Stockman, R-Friendswood, right, leaves the United States District Courthouse in Houston in 2018. Outgoing President Donald Trump commuted the remainder of Stockman's 10-year prison sentence for misuse of charitable funds. (Credit: Michael Stravato for The Texas Tribune)
Sign up for The Brief, our daily newsletter that keeps readers up to speed on the most essential Texas news.
President Donald J. Trump on Tuesday commuted the remaining prison sentence of former Republican Texas congressman Steve Stockman, who was sentenced to 10 years in 2018 after he was convicted of nearly two-dozen felonies, including fraud.
Prosecutors said the conservative firebrand from Friendswood misused $1.25 million in funds from political donors to pay for expenses like hot air balloon rides, kennel bills and a new dishwasher — rather than for charity like the donors were told. He was also accused of planting an undercover intern in the state House office of a political rival.
Former U.S. Reps. Bob McEwen and Bob Barr, Republicans from Ohio and Georgia respectively, were among the public figures who called for Stockman's release, according to a statement from the White House Press Secretary, announcing the outgoing president had pardoned 15 people and commuted the sentences of five.
Stockman, 64, has underlying health conditions that place him at heightened risk during the pandemic. He has already been infected with the coronavirus while in prison, the release said.
He has served more than two years of his decade-long sentence, and will "remain subject to a period" of supervised release and a requirement that he pay $1 million in restitution, the release said.
Trump also pardoned former Border Patrol agents Ignacio Ramos and Jose Compean, who were convicted in 2006 of shooting an unarmed drug smuggler and covering it up. Each was sentenced to more than a decade in prison, but President George W. Bush commuted their sentences in 2009.
2020 Texas Tribune


text:
\section{Introduction}

An important perspective of quantum information is to transfer and process classical information by taking advantage of quantum physics. Taking dense/super-dense coding protocol \cite{BW92DenseCode, LLTL02densecode, LAH02densecode, BDL04densecode, HHL04densecode, WDLLL05densecode, PPA05densecode} as an example, the idea is to use previously shared entangled state between a sender and the receiver(s) to send more classical information than is possible without the resource of entanglement.  Another example is the machine learning by tensor network (TN) \cite{SS16TNML, LRWP+17MLTN, HWFWZ17MPSML, GJLP18MPOML, GPC18gTNML, S18MERAML, HPWS18TNQML, CWXZ19generateTTNML}. The aim is to employ TN (see some reviews of TN in Refs. \cite{VMC08MPSPEPSRev, CV09TNSRev, S11DMRGRev, O14TNSRev, HV17TMTNrev, RTPC+17TNrev}) as a novel machine-learning model to learn, classify, and/or generate classical information in the quantum many-body Hilbert space. Similarly, classical techniques can assist quantum approaches. One example is to use compressed sensing \cite{D06CS} (see also the book in Ref. \cite{EK12CSbook}) to improve quantum state tomography \cite{GLFBE10STCS, FGLE12QSCS, SRAS+13QSCS, KKD15QSCS}.

We here combine the ideas of compressed sensing \cite{D06CS}, quantum communication \cite{NC02Qcmp}, and unsupervised TN machine learning \cite{HWFWZ17MPSML}, aiming at developing novel quantum communication schemes. Compressed sensing is a powerful scheme for classical data compression by sampling, which is particularly useful when the samplings of the data are difficult or expensive. For instance in the magnetic resonance imaging, compressed sensing can largely compress the required samplings, thus significantly improve the efficiency \cite{lustig2008compressed}. In quantum communication, measurements are also expensive, since quantum states are difficult to prepare and each measurement will collapse or disturb the state. Consequently, the quantum communications of realistic data (e.g., images of $O(10^2)$ bits or more), even including the corresponding simulations of the quantum processes on classical computers, are extremely challenging. Recently, booming progresses have been made in TN machine learning, with which the realistic data (e.g., hand-written digits and photos of articles) can be processed and analyzed by quantum approaches (see \cite{SS16TNML} for instance). High efficiencies haven been demonstrated at least for the classical simulations of these quantum processes. These achievements allow and motivate to develop novel quantum schemes that could not be efficiently simulated even classically, which will provide valuable results for the future investigations on the genuine quantum hardwares \cite{HPWS18TNQML}.

In this work, we propose tensor-network compressed sensing (TNCS), which permits efficient quantum communications of realistic data. The main idea is to encode and communicate the information by the measurements on the quantum state $|\Psi \rangle$ (also called Born machine \cite{cheng2018information}) trained by the unsupervised TN machine learning. To explain TNCS, let us consider the following scenario. Alice wants to send a piece of classical information $\{x\}$, e.g., an image of hand-written digit ``3'', to Bob in a secured way. She intends to send only a small number of pixels (or features in the terminology of machine learning) denoted by $\{x^{\text{sent}}\}$ to Bob by classical communication which might be unsafe or even public. The rest information $\{x^{\text{rest}}\}$ (with $\{x\} = \{x^{\text{sent}}\} \cup \{x^{\text{rest}}\}$) will be encoded in the Born machine $|\Psi \rangle$. To recover $\{x^{\text{rest}}\}$, Bob measures $|\Psi \rangle$ that is previously provided by Alice in the way determined by $\{x^{\text{sent}}\}$. After the measurements, $|\Psi \rangle$ will be projected to another entangled state denoted as $|\Phi\rangle$, and by design, $\{x^{\text{rest}}\}$ will be encoded in the separable state that has the minimal distance to $|\Phi\rangle$. Therefore, Bob can reliably recover $\{x^{\text{rest}}\}$ by measuring on $|\Phi\rangle$. A flowchart of TNCS is given in Fig. \ref{fig-TNCS}

There remain two key questions: how to construct $|\Psi \rangle$ and how to design the measurements on it, so that $\{x^{\text{rest}}\}$ can be encoded in $|\Phi\rangle$ in the above way. Our proposal is the following. First, Alice trains $|\Psi \rangle$ by the unsupervised TN machine learning algorithm \cite{HWFWZ17MPSML}, so that $|\Psi \rangle$ represents the probability distribution of a huge amount of information that Alice considers to send. $|\Psi \rangle$ is called a Born machine since the probability of each piece of information is the square of the corresponding coefficient in $|\Psi \rangle$ \cite{cheng2018information}. Then to send a specific piece of information, she chooses to send Bob the pixels, with which the uncertainty of the rest of the pixels in the probability distribution will be minimized. The full information $\{x\}$ is efficiently compressed to (or in other words, can be accurately reconstructed from) a small part of the image $\{x^{\text{rest}}\}$ and the Born machine $|\Psi \rangle$, similar to the (classical) compressed sensing schemes assisted by machine learning models, e.g., the auto-encoders \cite{Bora2017CSML, grover2018uncertainty}.

\begin{figure}[tbp]
	\centering
	\includegraphics[angle=0,width=1\linewidth]{TNCS.png}
	\caption{(Color online) Illustration of the main steps of TNCS: (1) train the Born machine $|\Psi \rangle$ representing the probability distribution of the data that Alice considers to send; (2) encode the specific piece of information to be sent by measuring $|\Psi \rangle$; (3) decode the information as a generative process by the measured Born machine.}
	\label{fig-TNCS}
\end{figure}

We testify our TNCS with the datasets of hand-written digits and fashion images (namely MNIST \cite{MNIST} and fashion-MNIST \cite{fMNIST}). Any image in the training or testing sets can be reconstructed reliably and efficiently. The efficiency is indicated by the compression ratio $r = \#\{x^{[\text{sent}]}\} / \#\{x\} \simeq 10 \%$, where $\#\{x\}$ denotes the number of pixels in $\{x\}$. In other words, the information Bob accesses is about 10 times of the information that Alice needs to send through the classical channels. Most part of the information is encoded in the Born machine (quantum state), with the security guaranteed by the basic quantum principles. Similar to the compressed sensing, randomly choosing $\{x^{[\text{sent}]}\}$ already leads to small compression ratios. Better performance is reached by choosing $\{x^{[\text{sent}]}\}$ with a sampling protocol based on the entanglement of $|\Psi\rangle$, and by implementing post-selections to access $\{x^{[\text{rest}]}\}$. Finally, q-sparsity to characterize the sparsity of quantum state is proposed. For TNCS, q-sparsity characterizes how fast the Shannon entropy of the prbability distribution will decrease by measuring the Born machine $|\Psi\rangle$, and how efficient the compressed sampling can be via $|\Psi\rangle$. An empirical equation to estimate the required number of pixels for reliable reconstructions is given.

\section{Tensor-network compressed sensing}

Suppose Alice wants to send Bob an image of a hand-written digit ``3'' by TNCS (Fig. \ref{fig-TNCS}). She firstly trains the quantum state $|\Psi \rangle$ as the generative model for the training set of many ``3'' images in MNIST. This can be done with the unsupervised TN machine learning algorithm \cite{HWFWZ17MPSML}. The idea is to firstly map the images to quantum states. For example, the $n$-th each pixel ($0 \leq x_n \leq 1$) is mapped to a state of a qubit as
\begin{equation}\label{eq-featuremap}
x_n \to |s(x_n)\rangle = \cos (x_n\pi/2) |0\rangle + \sin (x_n\pi/2) |1\rangle,
\end{equation}
with $|0 \rangle$ and $|1 \rangle$ the two eigenstates of the Pauli matrix $\hat{\sigma}^z$. In this way, one image with pixels $\{x\} = (x_1, x_2, \cdots)$ is mapped to a separable state $|\psi \rangle = \prod_n |s(x_n)\rangle$. Then the Born machine $|\Psi \rangle$ is optimized to capture the probability distribution of the training set, by minimizing the distance (negative-log likelihood) to the probability distribution of the images in the training set. See more details in Appendix \ref{append-GTN}. Here, we take $|\Psi \rangle$ in the form of matrix product state (MPS) \cite{PVWC07MPSRev}. Note that TNCS is a general scheme, where one may also choose other TN forms to represent $|\Psi \rangle$, such as tree TN or MERA \cite{LRWP+17MLTN, HPWS18TNQML, CWXZ19generateTTNML}, or simply a quantum state without a specific entanglement structure.

In the sense of machine learning, though we only use the ``3'' images in the training set to optimize $|\Psi \rangle$, it is expected that $|\Psi \rangle$ approximately gives the probability distribution of any ``3'' images. In other words, $|\Psi \rangle$ learns the probability distribution of the ``3'' images from a finite (training) set, but can generalize to generate and/or recognize arbitrary ``3'' images that $|\Psi \rangle$ has never learned. The ability of a machine-learning model to process the information beyond the training set is known as the generalization power (see, e.g., \cite{PhysRevLett.59.2229}). As shown in the previous works \cite{SS16TNML, LRWP+17MLTN, HWFWZ17MPSML, GJLP18MPOML, GPC18gTNML, S18MERAML, HPWS18TNQML, CWXZ19generateTTNML}, TN models (including MPS) possess remarkable generalization power that is competitive to neural networks. Notably, TN models surpass neural networks as they allow to implement quantum process.

As $|\Psi \rangle$ gives the probability redistribution of the ``3'' images in the training set and beyond (due to its generalization power), it is then possible to use $|\Psi \rangle$ to communicate any ``3'' image. As a direct advantage, Alice can train $|\Psi \rangle$ without knowing the specific ``3'' image that will be sent to Bob. In other words, different ``3'' images can be communicated with the same state $|\Psi \rangle$, as long as $|\Psi \rangle$ can ``recognize'' (in the sense of machine learning) it as an image of ``3'' (see Appendix \ref{append-corr} for more discussions).

In the communication, Alice sends Bob only a small part of this image $\{x^{\text{sent}}\}$ and $|\Psi \rangle$; then Bob measures $|\Psi \rangle$ according to $\{x^{\text{sent}}\}$ as
\begin{equation}\label{eq-measure}
|\Phi\rangle = \prod_{x_{n} \in \{x^{[\text{sent}]}\}}  \langle s(x_{n}) |\Psi \rangle / C,
\end{equation}
with $C$ a constant to normalize $|\Phi\rangle$. $\{x^{\text{sent}}\}$ should be selected so that Bob can accurately reconstruct the rest of the pixels $\{x^{\text{rest}}\}$ from $|\Phi\rangle$. The selection of $\{x^{\text{sent}}\}$ is analog to the sampling process of compressed sensing. One may randomly choose $\{x^{\text{sent}}\}$ from $\{x\}$ (remind $\{x\} = \{x^{\text{sent}}\} \cup \{x^{\text{rest}}\}$). Each measurement by $|s(x_{n}) \rangle$ in Eq. (\ref{eq-measure}) is in fact a projection towards the separable state $|\psi \rangle = \prod_n |s(x_n)\rangle$. With sufficient $\{x^{\text{sent}}\}$, $|\Phi\rangle$ will Eventually be projected to such a state, where $\prod_n |s(x_n)\rangle$ ($x_n \in \{x^{\text{rest}}\}$) is the separable state that has the minimal distance to $|\Phi\rangle$ among all separable states. Therefore, Bob can access $\{x^{\text{rest}}\}$ by simply measuring on $|\Phi\rangle$.

Let us consider that Bob only has one copy of $|\Psi\rangle$ (therefore only one copy of $|\Phi\rangle$), dubbed as one-shot measurement. To generate $\{x^{\text{rest}}\}$ from $|\Phi\rangle$, he measures the qubits in the basis of the Pauli matrix $\hat{\sigma}^z$. The probability $P(x_n)$ of the $n$-th pixel $x_n = 0$ or 1 is determined by $\hat{\rho}_n$ as $P(x_n) = \langle x|\hat{\rho}_n|x \rangle$ with $x = 0, 1$.
$\hat{\rho}_n$ is the reduced density matrix with respect to the $n$-th qubit
\begin{equation}\label{eq-rhon}
\hat{\rho}_n = \text{Tr}_{/n} |\Psi \rangle \langle \Psi|,
\end{equation}
with $\text{Tr}_{/n}$ the trace over all degrees of freedom except for the $n$-th qubit. Note $\sum_x P(x) = \text{Tr} \hat{\rho}_n = 1$ due to the normalization of $|\Psi \rangle$. From the perspective of machine learning, such a way of obtaining $\{x^{\text{rest}}\}$ is in fact to generate $\{x^{\text{rest}}\}$ by the Born machine $|\Phi \rangle$ \cite{HWFWZ17MPSML}, and it is feasible in experiments. One drawback is that only black-or-white pixels ($x=0$ or 1) will be generated, not gray-scale ones.

We testify the TNCS with random selection and one-shot measurement on MNIST and fashion-MNIST datasets, which consists of realistic images of hand-written digits and Zalando's articles, respectively. Each dataset contains 10 classes of images, and in total has 60,000 training images and 10,000 testing images. Each image contains $28 \times 28 = 784$ gray-scale pixels. In Fig. \ref{fig-PSNR_Nf} (a) and (b), we show the accuracy of TNCS with different compression ratios $r=N_f/N$ (green solid and the purple dash lines). The accuracy is characterized by the average peak signal-to-noise ratio (PSNR), which (say between $\{x\}$ the reconstructed images $\{y\}$ ) is defined as
\begin{equation}\label{eq-PSNR}
\text{PSNR}(\{x\}, \{y\}) = 10 \log_{10} \frac{784}{\sum_n (x_n - y_n)^2}.
\end{equation}
We average the PSNR by the results of reconstructing all the images in the testing set, which the Born machine did not learn in the training process. We take the bond dimensions of the MPS $\chi=16$ and $40$. Generally, the PSNR increases with $r$ and $\chi$ as expected, and TNCS works well by simply sampling a small number of $\{x^{\text{sent}}\}$ randomly from $\{x\}$ and implementing one-shot measurement on $|\Psi\rangle$.

\begin{figure}[tbp]
	\centering
	\includegraphics[angle=0,width=1\linewidth]{PSNR_Nf1.png}
	\includegraphics[angle=0,width=1\linewidth]{PSNR_Nf2.png}
	\caption{(Color online) Average peak signal-to-noise ratio (PSNR) of the constructed images in the testing dataset of the handwriting digits ``3'' in MNIST and the dresses in fashion-MNIST. The images are generated from $|\Phi \rangle$ in the one-shot way [(a) and (b)] or with the post-selection [(c) and (d)]. The dimension of the MPS is taken as $\chi=16$ or $40$. The number of known pixels for reconstruction ranges from about $N_f/N=0\%$ to $10\%$.}
	\label{fig-PSNR_Nf}
\end{figure}

\section{Improving efficiency with entanglement-ordered sampling protocol and post-selections}

In the following, we propose to improve the performance (i.e., of higher PSNR and higher efficiency with smaller compression ratio) by incorporating with a sampling protocol based on entanglement and the post-selections of measurements.

Regarding the sampling, the results will change if Alice selects differently the $\{x^{\text{sent}}\}$. A natural selection way dubbed as variance ordering (VO) is to select the pixels according to the variance. The variance of the $n$-th pixel is calculated from the training set as
\begin{equation}\label{eq-variance}
V_n = \sum_i [x_{i, n} - (\sum_j x_{j, n} / K)]^2 / K.
\end{equation}
where $x_{i, n}$ is the $n$-th pixel in the $i$-th image of the training set and $K$ is the number of the training images. By choosing $\{x^{\text{sent}}\}$ as the pixels with the highest variance, the PSRN is obviously improved [see the black diamonds and orange pentagons in Fig. \ref{fig-PSNR_Nf} (a) and (b)].

A more reasoned way is to select based on the entanglement of $|\Psi\rangle$, so that $\{x^{\text{sent}}\}$ will minimize the uncertainty of $\{x^{\text{rest}}\}$ from the probability distribution given by the Born machine. Knowing $\{x^{[\text{sent}]}\}$, the (conditional) probability distribution of  $\{x^{[\text{rest}]}\}$ satisfies
\begin{equation}\label{eq-Px}
P(\{x^{[\text{rest}]}\} | \{x^{[\text{sent}]}\}) = |\prod_{x_{n} \in \{x^{[\text{rest}]}\}} \langle s(x_{n})| \Phi \rangle|^2,
\end{equation}
where $|s(x_{n})\rangle$ stands for the state associated with the $n$-th pixel $x_{n}$ [see Eq. (\ref{eq-featuremap})], and $|\Phi\rangle$ satisfies Eq. (\ref{eq-measure}). The task is to find the $N_f$ pixels $\{x^{[\text{sent}]}\}$ that minimize the Shannon entropy
\begin{eqnarray}\label{eq-Shannon}
S^{\text{Shan}} =&& -\sum_{\{x^{[\text{rest}]}\}} P(\{x^{[\text{rest}]}\} | \{x^{[\text{sent}]}\}) \nonumber \\&& \ln P(\{x^{[\text{rest}]}\} | \{x^{[\text{sent}]}\}).
\end{eqnarray}

Aiming at this task, let us begin with a simpler question: which pixel should be sent if Alice sends only one pixel? This can be determined by the single-site entanglement entropy (SEE) that (say for the $n$-th qubit) is defined as
\begin{equation}\label{eq-SEE}
S^{\text{ent}}_n = - \text{Tr} \hat{\rho}_n \ln \hat{\rho}_n.
\end{equation}
$S^{\text{ent}}_n$ quantifies the information of the rest of the system that will be gained if one has the information of the $n$-th qubit. Such a quantity has been utilized to safely reduce the number of pixels for efficient supervised TN machine learning \cite{LZLR18entTNML}. With $S^{\text{ent}}_n$, Alice can choose the $\tilde{n}$-th pixel with $\tilde{n} = \arg \max_{n} S^{\text{ent}}_n$, so that Bob will gain as much information as possible from one sent pixel.

Based on the above scheme, we propose the following Markov sampling strategy to select $\{x^{[\text{sent}]}\}$, dubbed as entanglement-ordered sampling protocol (EOSP).
\begin{enumerate}
	\item With an $N$-qubit state $|\Psi(N) \rangle$ (initialized as $|\Psi \rangle$), calculate the SEE $S^{\text{ent}}_n$ of all qubits, and find the qubit that has the maximal $S^{\text{ent}}_n$, i.e., $\tilde{n} = \arg \max_n S^{\text{ent}}_n$.

	\item From the reduced density matrix of the $\tilde{n}$-th qubit, $\hat{\rho}_{\tilde{n}}$, calculate its dominant eigenstate $|s_{\tilde{n}}\rangle$.

	\item Measuring the $\tilde{n}$-th qubit of $|\Psi(N) \rangle$, a $(N-1)$-qubit state is obtained as $|\Psi(N-1)\rangle = \langle s_{\tilde{n}}|\Psi(N) \rangle /C$, with $C$ a constant to normalize $|\Psi(N-1)\rangle$.

	\item If $N_f$ qubits have been measured, record the positions of these qubits, and transfer the pixels at these positions of the image to Bob. Note we have $|\Psi(N-N_f) \rangle = |\Phi \rangle$ [Eq. (\ref{eq-measure})]. Otherwise, go back to Step 1 and start again with $|\Psi(N-1) \rangle$.
\end{enumerate}

In short, EOSP selects the pixels in the order of entanglement (EO). A simple example that helps to understand the EOSP is provided in Appendix \ref{append-EOSP}. Similar strategies have been used in the classical compressed sensing. \cite{Bora2017CSML, grover2018uncertainty}, where the authors proposed to utilize the auto-encoders to significantly reduce the compression ratio. Note that these schemes are classical methods, where the security is not guaranteed by quantum physics. As shown in Fig. \ref{fig-PSNR_Nf} (a) and (b), EO achieves the highest PSNR among the three selection ways. Some discussions about the possible quantum advantages in the TNCS are given in Appendix \ref{append-quantum}.

Regarding the generation of $\{x^{[\text{rest}]}\}$ by the Born machine, we propose to use post-selections \cite{PhysRevLett.60.1351} to generate gray-scale images for higher accuracy (as the images in the datasets are gray-scale). We generate the pixels $\{x^{[\text{rest}]}\}$ by locating the separable state with maximal probability, i.e.,
\begin{equation}\label{eq-generatex}
\{x^{[\text{rest}]}\} = \arg\max_{\{x\}} |\prod_n \langle s(x_{n}) | \Phi \rangle|^2,
\end{equation}
where the product $\prod_n$ goes through $\{x^{[\text{rest}]}\}$. It means that each measurement basis $| s(x_{n}) \rangle$ is the dominant eigenstate of the corresponding single-site reduced density matrix of $|\Phi\rangle$ [Eq. (\ref{eq-rhon})]. Post-selections are required to realize such measurements. Fig. \ref{fig-PSNR_Nf} (c) and (d) show the results with post-selections. One can see that the PSNR's for all three selection ways (EO, VO, and RO) are significantly improved. With EO and post-selections, the image can be accurately and efficiently communicated to Bob (with PSNR$\simeq 20$) for $r\simeq 10 \%$. Same as the existing quantum communication schemes, the security of the communications with TNCS are guaranteed by the fundamental principles of quantum physics (more discussions are given in Appendix \ref{append-QCM}).

\section{Q-sparsity}

\begin{figure}[tbp]
	\centering
	\includegraphics[angle=0,width=0.9\linewidth]{see_av.png}
	\caption{(Color online) SEE [Eq. (\ref{eq-SEE})] per site of $|\Phi \rangle$ in EOSP versus the number of the unmeasured qubits $N-N_f$. The more steeply the SEE per site decays, the faster the information of a quantum state can be gained by measurements.}
	\label{fig-see_av}
\end{figure}

A prerequisite for the conventional compressed sensing to work is the sparsity of the signals. For processing images, it is known that the signals are usually not sparse in the real space. Therefore, transformation (such as discrete cosine/wavelet transformation) is implemented to transform to another space in which the signals are sparse.

In TNCS, sparsity is gained in a completely different way, which is by mapping the data to the higher-dimensional quantum Hilbert space. This is analog to the support vector machines \cite{CV95SVM} by mapping to a higher-dimensional space where the data can be better classified. In the unsupervised TN machine learning algorithm, each pixel $x$ is mapped to the state of a qubit [Eq. (\ref{eq-featuremap})], then one image is mapped to the direct product state of $N$ qubits with $N$ the number of pixels. Such a vector is defined in a $(2^N)$-dimensional space $\mathcal{H}$. The MPS $|\Psi \rangle$ describes the joint probability distribution of the ``vectorized'' images in $\mathcal{H}$. Essential, one still deals with the data in the real space. However, the probability distribution becomes sparse in this higher-dimensional real space, since it can be well captured by an MPS. An MPS is sparse because such a representation can only reach a small corner of $\mathcal{H}$ that satisfies the so-call 1D area law of entanglement entropy \cite{ECP10AreaLawRev, F13arealawTRG}.

However, it is not easy to characterize the sparsity of an MPS, as its dimension is exponentially large. We here propose to use EOSP to do so. In each step of EOSP, the qubit with the maximal SEE is measured. The entanglement of the state $|\Phi \rangle$ formed by the unmeasured qubits decreases after each measurement. Fig. \ref{fig-see_av} shows the SEE per site $\bar{S}(\tilde{n}) = \sum_n S^{\text{ent}}_n(\tilde{n}) / \tilde{n}$ of $|\Phi(\tilde{n}) \rangle$ [see Eq. (\ref{eq-SEE})] with different number of unmeasured qubits $\tilde{n}$. One can see that $\bar{S}(\tilde{n})$ decays rapidly with $N-\tilde{n}$, meaning the unmeasured qubits are almost in a separable state for small $\tilde{n}$. For $\bar{S}(\tilde{n})=0$, no information will be gained by knowing the unmeasured pixels. It means all information is contained in the measured pixels, and there is no uncertainty for the rest pixels, when $\bar{S}(\tilde{n})$ becomes zero.

From the implication of $\bar{S}(\tilde{n})$ discussed above, we define q-sparsity to qualitatively describe the sparsity of a quantum state (including MPS) as
\begin{equation}\label{eq-sparsity}
\mathcal{S}^q = \prod_{\tilde{n}=1}^{N} d^{\frac{\bar{S}(\tilde{n})}{\ln d} - 1},
\end{equation}
with $d$ the dimension of one vectorized pixel. For qubits, we have $d=2$. The Q-sparsity characterizes how fast the information of a quantum state can be gained (or how fast the uncertainty of the rest can be reduced) by measurements. Take the $N$-qubit GHZ state as an example. We have $\bar{S}(N) = \ln 2$ originally, and $\bar{S}(\tilde{n} \neq N) = 0$ after one measurement. Therefore, we have $\mathcal{S}^q = 2^{-N+1}$. For the conventional $k$-sparsity, we have $\mathcal{S}^k = 2/2^N = 2^{-N+1}=\mathcal{S}^q$ since it only has two non-zero coefficients in the $2^N$-component vector. Take the maximally-entangled state \cite{GB98maxent} as another example. We have $\mathcal{S}^q=1$ since $\bar{S}(\tilde{n}) = \ln 2$ for any $\tilde{n}$. For the generative MPS's, we numerically have $\mathcal{S}^q = 2^{-768.6}$ and $2^{-765.6}$ with $\chi=16$ for MNIST and fashion-MNIST, respectively, and $\mathcal{S}^q = 2^{-770.0}$ and $2^{-767.5}$ with $\chi=40$.

For TNCS, $\mathcal{S}^q$ characterizes the efficiency, i.e., the compression ratio. The smaller $\mathcal{S}^q$ is, the faster $\bar{S}(\tilde{n})$ decays in general with the measurements, and the less $\{x^{[\text{sent}]}\}$ Bob will require to accurately reconstruct the full information by TNCS. Therefore, analog to the conventional compressed sensing, TNCS requires the probability distribution to be sparse in the higher-dimensional Hilbert space, i.e., $N + \log_2 \mathcal{S}^q \ll N$. Based on our results, the required number of $\{x^{[\text{sent}]}\}$ to reach $\text{PSNR} \simeq 20$ can be estimated as
\begin{equation}\label{eq-nf}
N_f \simeq c (N+\log_2 \mathcal{S}^q),
\end{equation}
with $c\simeq 6$ for both MNIST and fashion-MNIST.

\section{Summary}
In this work, we propose a quantum compressed sensing approach by combining the ideas of compressed sensing, quantum communication, and unsupervised TN machine learning. The key step is to train the quantum state $|\Psi \rangle$ (a Born machine) by the unsupervised TN machine learning algorithm, so that the targeted piece of information can encoded in the separable state with the minimal distance to $|\Phi \rangle$ that is obtained by measuring on $|\Psi \rangle$ in a designed way. The q-sparsity is proposed as a fundamental property of quantum states, and is used to estimate the efficiency of TNCS. We apply TNCS to the realistic datasets (hand-written digits and fashion images). Unique advantages of TNCS are demonstrated, where images can be compressed and transferred in a comparable efficiency and accuracy than the classical methods, and at the same time the security of the communications is guaranteed by the fundamental quantum principles.

\section*{Acknowledgments}
SJR is grateful to Ding Liu for helpful discussions. This work was supported by Beijing Natural Science Foundation (No. 1192005 and No. Z180013), National Natural Science Foundation of China (No. 11675113) and Beijing Municipal Commission of Education (KZ201810028042). ML acknowledges the Spanish Ministry MINECO (National Plan 15 Grant: FISICATEAMO No. FIS2016-79508-P, SEVERO OCHOA No. SEV-2015-0522, FPI), European Social Fund, Fundació Cellex, Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341 and CERCA/Program), ERC AdG OSYRIS and NOQIA, EU FETPRO QUIC, and the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314. ZZS and GS are supported in part by the NSFC (Grant No. 11834014), the National Key R\&D Program of China (Grant No. 2018FYA0305800), the Strategic Priority Research Program of CAS (Grant No. XDB28000000), and Beijing Municipal Science and Technology Commission (Grant No. Z118100004218001).

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Crude Oil Production in Croatia decreased to 11 BBL/D/1K in September from 12 BBL/D/1K in August of 2020. This website uses to provide services, personalize ads, and analyzing visitor cookies. With 3 million listed companies, mainly manufacturers, wholesalers, distributors and service providers, every month EUROPAGES attracts more than 2 million decision-makers searching for business partners, suppliers or service providers in Europe and worldwide. Thanks to rich knowledge and experience, INA's exploration and production of oil and gas accounts for over 50 percent of Croatian primary energy production. INA, Crodux Derivati Dva, Vermilion Zagreb Exploration and Aspect Croatia are expected to invest some 78 million euro in exploratory activities, Croatian Hydrocarbon Agency (CHA) quoted Energy and Environment Protection Minister Tomislav Coric as saying. Croatia's largest company INA is a mid size European oil and gas firm that is coming under increasing pressure to divest itself of its concessions in Syria The raw material required for vehicle operation,... For use inside and outside, for manufacturing or retrofitting windows with bars. In early August 2019, the oil company Vermilion Zagreb Exploration d.o.o. This has also been confirmed by Croatian Energy Minister Tomislav Coric. Four oil companies will invest EUR 80 million in exploring oil and gas in Croatia over the next five years, Tportal reports. PPD has its headquarters in Croatia and companies in Switzerland, Hungary and Bosnia and Herzegovina and Slovenia, through which it operates its business throughout Europe. A. Adria LNG; I. INA d.d. LUKOIL in the Republic of Croatia LUKOIL has been present in the Republic of Croatia since late 2007, when it registered a local subsidiary — LUKOIL Croatia d.d.o. Gain access to the best database of targeted leads from Electricity, Oil & Gas companies in Croatia. J. Jadranski naftovod; P. Plinacro This page was last edited on 1 July 2020, at 01:21 (UTC). Refining and Marketing INA's refineries produce EURO V gasoline and diesel fuels and lubricants in line with the highest European standards. INA Group has leading role in Croatian oil business and a strong position in the region in the oil and gas exploration …
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