Check out diymaternity.com and make-baby-stuff.com! These are great resources for maternity clothing patterns.
Free patterns for shirts, dresses, skirts, nursing items, and more.
Free maternity clothes patterns for wrap skirts, stretchy cotton skirts, maternity shirts and finding cheap maternity clothes.
As a 30 something female, I have had quite a few friends who have had babies during the past decade. As such, I have had a lot of friends who have been in the market for maternity clothing. There are a couple primary complaints that I've heard over and over again.
1) It's tough to find clothes that are reasonably priced.
2) it's tough to find clothes that are stylish.
After a number of these discussions, I got inspired to browse for DIY maternity clothing tutorials. I was blown away by what I found. Hopefully you will be, too. For those of you out there who are pregnant and are skilled at making your own clothing, you can save quite a lot of money by making some or most of your maternity clothing. The best part about the wealth of tutorials out there is that you can pick and choose what you like, resulting in some wonderful, stylish clothing that fits your body. Also, after you have read through a half a dozen or so patterns for the same type of maternity clothing, you will get an idea how these patterns work. This will allow you to start making your own alternations with regular clothing by following some of the basic maternity clothing guidelines.
Shop sales. You may find great, pricier items from Target or Motherhood Maternity that are marked way down.
Shop out of season or at the end of season. Even if you're purchasing t-shirts as you head into fall or winter, you can still layer them with warmer pieces.
Shop secondhand. Goodwill receives Target merchandise that doesn't sell. You may be able to find significantly discounted brand new maternity pieces from brands such as Liz Lange. Additionally, a lot of used maternity clothing is in excellent condition because women don't wear it for a long time.
Shop garage / rummage sales and Craigslist. While you're hunting for used baby items, you may find some maternity clothing, too.
Borrow clothing from similarly sized friends and family members. Again, most used maternity clothing is in good condition.
I Make Stuff.: Big Ugly Shirt Refashioned into Maternity!
Yes, a dress pants tutorial! I know that no one ever has too much maternity formal wear.
Sew Much Ado: Free diaper bag tutorial.
Check out Etsy for more patterns!
maternity pattern on Etsy, a global handmade and vintage marketplace.
check out diymaternity.com for a sewn belly band pattern, too.
Are you looking for even more maternity clothing resources? Check this out!
One of the most fun things about being pregnant, besides being pregnant, and being treated with great regard, is going shopping for all the lovely maternity clothes.
Maternity clothes can be an expensive investment that you will wear for a short time. Therefore, you may want to purchase items which are discounted or on sale to save money. Here are a few options.
Cyndi, nice! Good to get confirmation on Goodwill. Thanks!
Great hub! Enjoyed the read and I know this will help a lot of people.
Thanks, Victoria! I appreciate the link!
Incredible hub! so many resources. Thanks for linking my hub. Going to add yours to mine, too!
You are very welcome! Best of luck.
Good advice, thanks for the tips. I will have to try some of these.
Thank you! It definitely wouldn't hurt! There's no reason not to look good for yourself at home.
I love this hub! I wish I had seen it when I was pregnant. I'll keep in mind for the future!
Thanks! Honestly I don't sew a lot and will be more likely to take your method if I do get pregnant in the future. I think that most people are likely to use a combination of methods for acquiring maternity clothes so it's still important to keep things like that in mind.
Voted up and useful! Great patterns you have listed here. I wish I would've thought about sewing when I was pregnant...I'm pretty decent at it and I might've been able to save more $$$. What I did to save money was go to Ross, TJ Maxx, and Marshall's and find shirts that weren't maternity but were roomier and bought them a couple sizes larger than my own size so that they would fit over my belly. :) Great hub!
Wish I read a hub like this earlier! Pity I have a 7 week old baby and do not think I will be wearing any maternity clothes any time soon!
Thanks Prasetio and Htodd! Have a great weekend, too.
This was so beautiful and I'll show this to my sister. Thanks for share with us. Have a nice weekend!
These are great tips. Not many people know about target donating what doesn't sell to goodwill, but there's a lot of great stuff to be had because of it! Wonderful hub :) Very helpful!
Thanks, I try! Hopefully it'll be me that needs this advice within the next couple years, and I'll be able to get something out of this research as well. Thank you!
You're such a good friend to listen to all your pregnant friends' needs and share your findings in a hub. Well researched info and links. Great job, randomcreative! Voting up!
I agree! A lot of the newer clothes today are much better than they used to be. Thanks!
Maternity clothes are much cuter than they were twenty or thirty years ago! Great links to resouces.


Neuropsychologie Psychischer Storungen is good choice for you that looking for nice reading experience. We hope you glad to visit our website. Please read our description and our privacy and policy page.
Finally I get this ebook, thanks for all these Neuropsychologie Psychischer Storungen can get now!


The trucks have moved. So what?s the problem?
It?s hard to walk around campus lately without getting a petition in your face about it. For students on campus, a number of them first-years who are new and confused, it must seem like a huge travesty has occurred. The trucks? move needs to be kept in perspective.
There seem to be three main complaints: 1) that CFA students will no longer have the time to get food from the trucks in the ten-minute gap between classes; 2) that moving the trucks from Tech Street to Margaret Morrison Street will cause the trucks to lose a significant amount of business; and 3) that parking will be taken away from Margaret Morrison and will not be returned on Tech Street, as the city of Pittsburgh is reserving that area for city vehicles.
But let?s be realistic. We understand that the trucks were outside CFA and a great convenience for students, but they?re only being moved about 500 feet down the road ? a one-minute walk away from their current location. The distance isn?t significant. Walk the extra two minutes and work off some of that pad thai.
The most legitimate concern is the amount of business that vendors expect to lose. The managers of the trucks have said that they expect up to an 80 percent drop in revenue as a result of the move, and students have agreed. In the end, though, it?s hard to imagine that the move will change the way campus will dine.
As far as parking is concerned, the construction of a new level to the parking lot will hopefully free up space for drivers without spots to park in. But we won?t know for sure for some time.
Simply put, if we love the trucks as much as we say we do, we?ll find a way to make it over to them. They?re only moving a block away, so rather than fuss about the move, show your support, walk the extra block, and keep the trucks rollin?.


Every time someone around me or very close to me has a new baby, and there are problems with the labor or the baby, I go into a frenzy. Why? Ten months ago Saturday. That's the reason. His name is Rowen Daniel Rodgers. And that's when he was born...almost ten months ago, this Saturday. It was the hardest thing I've ever had to go through, and the most heart-breaking. Premature, under-developed, not breathing on his own, possible pneumonia...I could go on. Not to mention touching him only once and then not being able to hold him for days on end, only looking at him through the glass incubator, etc...BUT, it all had a happy ending and sometimes I even forget it happened. Many mothers don't walk away as lucky as we did. They walk away empty handed..not just for two weeks. So it's only when a new baby enters my life, do I REEEEEAAAAALLLLLY start reminiscing and worrying and pacing...all for a baby that isn't mine. I wonder if this will last forever???
So to anyone with a new baby, (my sweet friend Court), especially those who may be struggling or having a hard time with the baby's health...please forgive me when I am a spaz. And yes, it will happen...I will be a spaz. At least until I don't cringe still when I look at the pictures of my son hooked up to the machines and tubes (which is why I posted a pic of him AFTER the tubes). At least until that sadness no longer creeps in when I remember every night I had to leave him at the hospital and come home to an empty bassinet. At least until my heart mends completely and fully. And yes, that will happen, too......someday :).


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LBA-HMET PC-06 ECMWF Modeled Precipitation and Surface Flux, Rondonia, Brazil: 1999
N: -10.75
https://doi.org/10.3334/ORNLDAAC/1141
Download Data729.3 KBUser Guide
This data set provides the mean diurnal cycle of precipitation, near-surface thermodynamics, and surface fluxes generated from short-term forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) model. The model outputs were 12- to 36-hour short-range forecasts, run at a triangular truncation of T319 and a vertical resolution of 60 levels, from each daily 1200 (UTC) analysis. The version of the forecast model used to prepare this data product was the operational ECMWF model in fall 2000, which included the tiled land-surface scheme (TESSEL) (Van den Hurk et al., 2000) and recent revisions to the convection, radiation, and cloud schemes described by Gregory et al., (2000). The ECMWF model was run for two Large-Scale Biosphere-Atmosphere Experiment in Amazonia (LBA) campaigns conducted in Rondonia, Brazil, during January and February of 1999: the Wet Season Atmospheric Mesoscale Campaign (WETAMC) and the Tropical Rainfall Measuring Mission (TRMM). See Silva Dias et al.,(2002) for additional information regarding the WETAMAC and TRMM campaigns. There are two comma-delimited data files with this data set: the ECMWF model output data and a file containing the mean hourly precipitation observations used to check the model output for biases.
HEAT FLUX
PRECIPITATION AMOUNT
Betts, A.K., and C. Jakob. 2013. LBA-HMET PC-06 ECMWF Modeled Precipitation and Surface Flux, Rondonia, Brazil: 1999. ORNL DAAC, Oak Ridge, Tennessee, USA. https://doi.org/10.3334/ORNLDAAC/1141
PC06_ECMWF_LBA.pdf

redpajama_set_name: RedPajamaCommonCrawl


Here in North Carolina we are starting to get little tastes of spring, last week we had a few inches of snow and then two days later it was 74 degrees outside! With the warming of the seasons I can't but help thinking about the beach, so I thought this would be a neat small house to show you all. This is actually a rental that you can go stay at, located in the UK, Bembridge, Isle of Wright.
Frank is a carpenter and cabinet maker who travels for work. He built this tiny house so he can take it with him while he is on longer jobs away from his home in NC.
Have you got your tickets yet for the Conference?
So last week I had a crazy tiny house adventure. It involved a potato, a few tiny houses, building codes and a lot of meeting tiny house folks.
I started off staying with Laura and Matt, two tiny housers in Asheville, Laura blogs at 120squarefeet.com (she also has a new book out – click here). I have gotten to know them pretty well and always enjoy hanging out with them. Not only do we talk about tiny houses, but we get to nerd-out too.
From there I met up with my brother and went to my favorite breakfast spot, Sunny Pointe. After an amazing locally sourced organic breakfast we headed out. From there we hit the Blue Ridge Parkway to see the fall colors. I love driving the parkway, its winding roads and amazing views, it's pretty hard to beat. I dropped down from the parkway down into Brevard, saw looking glass falls and grabbed some lunch.
The next day I was off to Dan's workshop where we talked about tiny houses. I gave a talk on building codes and zoning. After lunch Matt and Laura talked about their tiny house and living in it. There were a lot of great questions for both presentations and the workshop allowed for us to chat with a lot of the folks.


text:
For The Rabbits
An Alternative Music Site
What I Listened To When I Listened To Music This Week – Real Estate – Atlas
North American music seems to be going through a crisis, a crisis of mistrust in and fear of suburbia. To be fair, if we defined suburbs the same way they do we'd probably be scared too. Whilst in the UK suburbs are a little belt of residential houses surrounding a built up area, in the states they're more like our commuter towns. So for New Jersey imagine a gigantic version of Milton Keynes, it's pretty damn horrible!
So perhaps it's no surprise then that many a band has chosen to focus on this most unexciting of areas. Most famously perhaps Arcade Fire who's third album The Suburbs was essentially a concept album about life in The Woodlands, Texas, a suburb of Houston. It covered all vagaries of suburban living, a land where "by the time the bombs fall, we were already bored". Win remembered the summers he spent in with a broken arm, living life like a city with no children in it. Most of all they covered the need to escape the suburbs, to stop living in the sprawl. On Sprawl II (Mountains Beyond Mountains) they perhaps summed it up better than anyone ever has
They heard me singing and they told me to stop,
Quit these pretentious things and just punch the clock.
Sometimes I wonder if the world's so small,
Can we ever get away from the sprawl?
Living in the sprawl,
Dead shopping malls rise like mountains beyond mountains,
And there's no end in sight,
I need the darkness someone please cut the lights.
It's surely a familiar feeling to anyone who grew up outside of the city landscapes, the feeling of hopelessness and a lack of like minded individuals is both a great inspiration to do something and a great hinderance to actually getting it done.
Of course it's not a one way street, some bands have gone full circle. Take The National, if Alligator was the sound of a band craving to be "taken to a famous city middle" and Boxer was an apartment story, High Violet saw them all grown up and leaving "the silver city, because all the silver girls gave them black dreams". There's a great power in Berninger's lyrics to communicate a time and place without laying it all out, he doesn't express any love for his new suburban life, he accepts it for what it is, he's not someone pushing to leave his city dreams behind he's someone who wants "to believe in everything you believe".
Music echo's life, and perhaps more and more life echo's music. We all want to get away from the sprawl, and part of the appeal is in the pictures our heroes paint.
REAL ESTATE – ATLAS
Real Estate are of course suburban guys, born and raised in New Jersey. They left that land behind and moved to the bright lights of New York. New York and Bands are something of a match made in Heaven of course. Though one of the major reasons for this is New Yorks ability to pull in people from all across not just the country but the globe. It is a musical sponge, taking talent and drawing it in, in much the same way London does on this side of the pond. However in the same way Wild Beasts reside in London and yet retain a sense of their rural upbringing and are more accepting of the requirement of London life than fond of it, so Real Estate remain routed in the way and sounds of New Jersey, they make a sound far too relaxed to feel like a true New York album. There's none of the claustrophobic, brooding darkness of Interpol's Turn On The Bright Lights, none of the angular art-pop of Yeah Yeah Yeah's Fever To Tell, no Real Estate may be in the city, but they're not part of it. Even the artwork to this their third album, recalls New Jersey as it references a piece of art that adorned a department store in their home city, a giant mural by Polish artist Stefan Knapp, now, along with the store it sat upon, long gone.
2011's Days was the bands second record and one that propelled them to new levels of success and critical acclaim. Pitchfork raved about it, a series of support slots with the likes of Kurt Vile, Girls and Deerhunter followed and the band seemed destined for big things. Three years is a long time in music though and it does feel a long time since Real Estate existed as Real Estate. Not that the band members have been taking it easy, there was a good deal of success for Matt Mondanile's side project Ducktails. Indeed it must have crossed some fans minds that following the release of Ducktails album The Flower Lane. Did Mondanile need Real Estate anymore? Certainly the sound of the two bands are far from dissimilar, the main reason behind that being that it's the beautiful jangling tone of the guitars that propel both bands.
However thank goodness they did get back in the studio again! Three years have passed but from the very first guitar line it's a brilliant reminder of what the were and still are about. It's true there's been no great sonic shift since Days, however there's been an upping in production quality, loosing some of the slightly lo-fi sound of their previous records. Here they've embraced the studio environment, refined their sound and evolved rather than ripping up the rule book. The album was recorded in Wilco's studio in Chicago and whilst Jeff Tweedy and co might well be an influence on the band they've resisted the urge to coat this album in the layers of Americana instrumentation Wilco favour, indeed with the exception of adding keyboardist Matt Kallman to their line up there's very little going on here that wasn't going on previously on Days.
Opening track Had To Hear is an excellent example of the Real Estate blue print. Starting of with a guitar line that would fit nicely anywhere in The Shins back catalogue, it's then joined by a second decending guitar line with a beautifully twangy feel. An understated drum beat enters, before the gorgeous reverb heavy vocal drips over the top. Lyrically Martin Courtney sings about the classics, longing, girls and loneliness. It's hardly new ground but his vocal style and lyrical content fit beautifully into the musical soundbed behind him.
Past Lives is greatly enhanced by the addition of keyboard, the intro is brilliant as a bell like piano is carried along by a brilliant bass line, before the intwined guitar lines return. Part of the great joy at the guitar playing is how heavily routed in melody it is. Whether it's the tone or the mixing, throughout the album it seems to pitch itself as a co-conspirator with the lead vocal, not sat behind it but along side it, vowing for prominence. The playing is incredibly fluid, playfully floating around the fretboard creating not just brilliant riffs but almost extended drawn out solos, but with none of the implied pomp or bravado associated with that, Spinal Tap this ain't, though there is the same sense of competition between talented members each trying to be heard on their own right.
Best of all is single Talking Backwards. A bouncy strummed guitar line plays alongside, a simple but perfectly paced drum beat as again the lead guitar floats around creating gorgeous melodies, it never for a second stands still, always adding something wonderful to the track. Whilst produced entirely differently there's a touch of Johnny Marr's work with The Smiths to the playing, another great weaver of guitar lines. Lyrically it's a tale of not being able to find the words to explain the way you're feeling "and I might as well be talking backwards" is hardly the words of a great poet but you find me a teenage boy who doesn't understand that feeling and I'll show you a false prophet.
April's song is a wonderful instrumental interlude, that sounds a bit like No Age, if No Age were having the best day of their life and were super happy about it. The Bend, starts off all Eric Clapton, and has a vaguely soft-rock feel, before taking a darker u-turn. Sometimes you feel like Real Estate aren't like other bands, whilst most people repeat guitar fragments and let the lyrics change they seem to do the opposite. The Bend is a prime example, and whilst their claim it has "a big bombastic classic rock outro" is so far from the truth it does add a touch of shade to the proceedings. Indeed it's a fairly autumnal sounding album, there's a sense of faded summers and good times gone, but not forgotten. They recall the other great masters of Autumn shades Yo La Tengo in places, which is never a bad thing.
A simple criticism of the record that I have seen some reviewers is that for all it's beautiful jangling tones it lacks the depth of their previous work. This however just isn't true on almost every track there's something wonderful hiding under there. Crime lays out the great fears of a modern day slacker "I don't want to die lonely and up-tight" to the sound of a wonderful guitar line. The acoustic guitar that introduces Primitive, is stunningly good as he lays out the lyrical crux of the matter "I don't know where I want to be, but I'm glad that you're with me, and all I know is it'd be easy to leave" this is a man going through that most everyday of crisis that is debating the point of it all. Pining for the past whilst knowing he doesn't belong there and it wouldn't exist if he ever went back to check on it.
How Might I Live, is the most grandiose number here and with Alex Bleeker taking over vocal duties, sounds like a perfect hybrid of Sparklehore and Grandaddy, it's wonderful. Ok, Horizon is a bit too much in awe of The Shins but it's a rare blip, and just leads the listener into the beautiful hazy perfection of Navigator. It's one of the least likely closing tracks ever, it drifts along like a very mellow Modest Mouse track. A superb bass line playing the counter foil to the albums best of many brilliant guitar lines. Martin Courtney sings "I don't know where that time went" and listening to this album that's a common feeling. It clocks in at 38 minutes, but seems to fly by, it'd be easy to just let it wash over you and move on, but look closely and there's great beauty here, as the last track simply drifts out, with no crescendo, no statement to say this is the end we hope you liked it, nothing, it's just how you'd want it to end.
Atlas the 3rd album by Real Estate is out now on Domino Records
Tagged Arcade Fire, Atlas, Domino Records, New Music, Real Estate, Suburbs, The NationalBy fortherabbitsmusic3 Comments
3 thoughts on "What I Listened To When I Listened To Music This Week – Real Estate – Atlas"
cuttingindieblog says:
Reblogged this on Indie Music.
I really enjoyed what you said about arcade fire. My friend has told me similar things on the album and what he thought it meant. I am definitely showing him this.
fortherabbitsmusic says:
Hey thanks for the re-blog. I've always found The Suburbs the most interesting Arcade Fire album, not necessarily the best but a lot of it is very relevant for someone who grew up away from the city like myself
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No. 31 Broad Street was on the northern corner of New College Lane. Together with No. 32 to the north, it was demolished in 1891 to make room for the second phase (the three right-hand bays) of the Indian Institute. The Institute had to be built in two phases because old leases on this shop and No. 32 did not expire until 1891.
The hosier William Thorp came into possession of this shop through his marriage to Mary Wise, daughter of Mr Wise the mercer, on 23 August 1756 at St Cross Church (now Balliol Historic Collections Centre). When Parson Woodforde was at New College between 1758 and 1763, he visited this shop many times. The 1772 Survey of Oxford clearly shows that Mr Thorp's house was here at the south of the group of four shops that were in Holywell parish, and that it had a frontage of 6 yards 1 ft 6 in.
Thorp and his family lived over the shop here until 1783, when he converted the shop into a front parlour, took his son into partnership, and moved the business to 44 Broad Street.
The 1841 census shows the wine merchant Robert Sheard (35) living here with Charlotte (25), Matilda (5), Edwin (2), and Charlotte (8 months). They have two independent people living with them, and two female servants.
At the time of the 1851 census, No. 31 was occupied by John Minty, a master tailor and robe maker, "in partnership with others: many men". He lived there with his wife and a servant, and had two student lodgers.
From 1861 to 1876 it was a grocer's shop, run by the Paynes. At the time of the 1861 census, Edward is described as a "Grocer & Sheriff's officer", and lives over the shop with his wife Emily, their two daughters, two gentlemen lodgers (one of whom is an Esquire Bedel), and a servant. A firm of accountants took the shop over in 1880, but Mrs Payne continued to live upstairs, and is listed there in the 1881 census: aged 52, she is described as a "householder & share holder", and is living with her daughter and her elderly uncle. They had one servant and two lodgers (one of whom is the ironmonger James Gill).


text:
using System.Web.Mvc;

namespace RouteDebug
{
    public class TestController : Controller
    {
        public ActionResult Index()
        {
            return View();
        }

        public ActionResult SomeJsonService()
        {
            return Json(new { Title = "Some title" }, JsonRequestBehavior.AllowGet);
        }
    }
}

redpajama_set_name: RedPajamaGithub


providing a high quality Montessori education.
providing teachers that are AMS- and/or AMI-trained at the level they teach.
providing classrooms that are beautifully equipped with Montessori materials.
being a small and diverse community that accepts families of various cultural, ethnic, and socio-economic backgrounds. We accept children of various abilities and needs.
valuing every child and the unique promise they carry within.
giving parents the tools they need to incorporate the Montessori principles in their home.
serving the community as a nonprofit organization, which is overseen by a Board of Trustees comprised of volunteer parents, teachers, and community members.
encouraged to share their talents and interests with children, especially in the Elementary levels.
encouraged to support Montessori principles at home.
actively involved by volunteering 15 hours per year. Parents may assist with classroom support, community events, service learning projects, building and grounds maintenance projects, fundraising, and more.
School hours: 8:30 a.m – 11:50 a.m.
~3- to 4-year-olds: 8:30 a.m. to 12 p.m.
~5-year-olds and up: 8:30 a.m. to 3 p.m.


text:
Welcome to PLATFORM 11+
2009 – 2013 PLATFORM 11+ worked as an EU-funded artistic network in which 13 theatres from 12 European countries joined together. The theatres collectively created new work for and with young people aged between 11 and 15 in both the Performing and Visual Arts. Theatres from South America, mainly Argentine, participated in the project as associated partners. At the end of the four-year project, PLATFORM 11+ presented a multi facetted portrait of a young generation, whose presence at the beginning of the 21st century is reflected in numerous works of art. More than 50 new plays were staged as national and international productions in whole Europe and South America and were published in two books (see database). If you are interested in further information, please contact us: dirk(at)platform11plus.eu
At the end of the four year project, PLATFORM 11+ wants to present a multi facetted portrait of a young European generation, whose presence at the beginning of the 21st century will be reflected in numerous works of art.
PLATFORM 11+ in the Web: Please visit us also on our social network site platform11plus.ning.com or/and have a look on our Youtube Chanel.
Random Pic(k)s
Partner Oulun kaupunginteatteri
News Hello from York: SUCCESS! Schoolyard in Town II "Through our eyes"
Researcher Bouke Oldenhof
Production Emil és a detektívek
Platform granted again!
Follow-up EU-project was selected!
We are delighted to announce that the follow-up project PLATFORM shift+ - Digital challenges in the theatre for young audience was selected as one of the Larger Scale Cooperation Projects in the EU-programme Creative Europe. It consists of 11 partners from 9 countries – ten theatres and a university. The leading organisation Pilot Theatre (York (GB) is one of the UK's most renowned companies in delivering performance work for young people and exploring innovative approaches to making and sharing work.
Social Networks – Virtual Meets Reality - 3rd P11+ Youth Encounter in Dresden/Germany
On February 1st there will be the public presentation in the German school Gymnasium Bürgerwiese as highlight of the 3rd Youth Encounter of P11+. What happened the week before, please read the blog of the EEA Street Arts Academy.
Face Me in Budapest
Meanwhile all three parts of the final P11+ production are touring through Europe.
After Norway, Portugal, Slovakia and Italy, Face Me is now shown parallel in UK and Hungary. Watch here pics from the Budapest school!
Hello From
26. January 2013 | Sven
Young people from UK, Italy and Finland are travelling to Dresden, Germany on Saturday 26th January as part of the third ever Platform 11+ International Youth Encounter. They will be participating in collaborative, cross-art form workshops run by Artists from 5 European Theatre companies and will be working towards sharing their ideas with the local community in Germany. Feb1st there will be a public presentation of the workshops. Thanks a million to the German partners Gymnasium Bürgerwiese and tjg-dresden!


* **Long**: Not technically "TupleBundles". This approach simply unions * together a set of results, one per possible world sampled. * **Flat**: Creates a wide result, splitting each non-deterministic column into a set of columns, one per sample. * **Array**: Like flat, but uses native array types to avoid overpopulating the result schema.
At present, only 'Flat' is fully implemented, although a 'Long'-like approach can be achieved by using convertFlatToLong.


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rob delaney
Rob Delaney is a 'lifetime work in progress' after 2-year-old son's death
March 20, 2019 | 11:44am
Delaney's son died last January.
Rob Delaney thinks Carrie Fisher starred in 'Catastrophe' to party in London
March 12, 2019 | 7:48pm
"We don't think she watched the pilot or read the script . . . She literally learned what the show was well after it had already aired."
Rob Delaney celebrates 17 years of sobriety after son's recent death
February 4, 2019 | 10:27am
"Had I not been sober it would have been far worse. As it was, I squeaked by."
Rob Delaney and wife welcome baby months after death of son
December 31, 2018 | 12:21pm
The "Catastrophe" star and his wife Leah lost their third son, Henry, to cancer in January.
Rob Delaney and wife expecting baby months after son's death
July 2, 2018 | 9:16am
Delaney lost his 2-year-old son Henry to cancer in January.
Comedian Rob Delaney's 2-year-old son dies of cancer
February 9, 2018 | 4:50pm
The actor's son died in January.
1 Prince Harry and Meghan Markle abdicate royal titles, public funds	2 Rapper T.I.'s son King filmed fighting during bathroom brawl	3 Taylor Swift attempted to kick Justin Bieber out of her gym


text:
\section*{Introduction}

Quantum logic starts with the idea that quantum theory can be understood as a theory of physics in which standard Boolean logic gets replaced by a different form of logic, where various rules, such as the distributivity of logical and over logical or, are relaxed~\cite{logicqm,handbook}. This builds on the observation that $\{0,1\}$-valued observables behave like logical propositions: such an observable is a projection operator on Hilbert space, and it can be identified with the closed subspace that it projects onto. The conjunction (logical \emph{and}) translates into the intersection of subspaces, while disjunction (logical \emph{or}) is interpreted as forming the closed subspace spanned by two subspaces. In this way, the closed subspaces of a complex Hilbert space $\H$ form the \emph{complex Hilbert lattice} $\mathcal{C}(\H)$, which is interpreted as the lattice of `quantum propositions' and forms a particular kind of orthomodular lattice~\cite{orthomodular,meashilb,ql}.

However, the theory of orthomodular lattices is quite rich and contains many objects other than complex Hilbert lattices. So in order to understand the laws of quantum logic, one has to find additional properties which characterize the latter kind of objects. Much effort has been devoted to this question, resulting in partial characterizations such as Piron's theorem~\cite{piron,pironfix}, Wilbur's theorem~\cite{wilbur} and Sol\`er's theorem~\cite{soler}\footnote{See also the survey~\cite{hilbgeom} for a more recent exposition from a geometrical perspective.}. However, the axioms for complex Hilbert lattices that these results suggest are quite sophisticated: atomicity, completeness or the existence of an infinite orthonormal sequence. These are conditions that cannot be expressed algebraically, i.e.~as \emph{first-order} properties using just a finite number of variables, algebraic operations, and quantifiers. Fortunately, there has also been a substantial amount of work on first-order properties enjoyed by complex Hilbert lattices, and in particular on equational laws that hold in all complex Hilbert lattices $\mathcal{C}(\H)$, such as the algorithmic approach advocated by Megill and Pavi{\v{c}}i\'c~\cite{hleqs,qlexpl}. Such algorithmic approaches are what our present contribution is about: we prove that there cannot exist any algorithm to decide whether an \emph{implication} between equations in complex Hilbert lattices is valid.

To make this statement precise, we keep the lattice operations notationally separate from the external logical connectives and denote the latter in plain English:

\begin{thm}
\label{qlundec}
There is no algorithm to decide whether an implication of the form
\begin{equation}
\label{Eprop}
	\left( E_1 \mathrel{\mathsf{and}} E_2 \mathrel{\mathsf{and}} \ldots \mathrel{\mathsf{and}} E_k \right) \:\mathrel{\mathsf{implies}}\: (0 = 1)
\end{equation}
holds in every complex Hilbert lattice $\mathcal{C}(\H)$, where each $E_i$ has one of the following two forms:
\begin{itemize}
\item an equation of the form $P_1\lor\ldots\lor P_m = 1$, where the $P_j$ are free variables denoting projections and $1$ is the identity projection;
\item an orthogonality relation $P_1\perp P_2$ between two free variables, or equivalently the equation $P_1^\perp \lor P_2^\perp = 1$.
\end{itemize}
\end{thm}

Here, the consequent $0=1$ states that the zero projection is equal to the identity projection, or equivalently that $\H$ is the trivial zero-dimensional Hilbert space. Thus the proposition~\eqref{Eprop} states that the antecedents $E_1,\ldots,E_k$ are jointly contradictory, meaning that the only way to satisfy them jointly is by taking the Hilbert space to be zero-dimensional, $\mathcal{H} = \{0\}$.

\begin{rem}
By replacing each $P_i$ by $P_i^\perp$, it follows that Theorem~\ref{qlundec} remains true if one replaces $\lor$ by $\land$ and $1$ by $0$, so that each $E_i$ is either of the form $P_1\land\ldots\land P_m = 0$ or $P_1^\perp \land P_2^\perp = 0$.
\end{rem}

\begin{rem}
Instead of asking whether~\eqref{Eprop} is valid in all $\H$, one can alternatively negate the question and ask whether there exists a Hilbert space $\H$ with $\dim(\H) > 0$ together with an assignment of projections in $\H$ to the free variables such that the formula
\[
	E_1 \mathrel{\mathsf{and}} E_2 \mathrel{\mathsf{and}} \ldots \mathrel{\mathsf{and}} E_k
\]
holds. This formulation makes it clear that we are dealing with a quantum version of the Boolean satisfiability problem---distinct from the QSAT problem introduced by Bravyi~\cite{QSAT}---which is undecidable as per Theorem~\ref{qlundec}. As we will see in the proof of Lemma~\ref{allH}, if an instance of our quantum satisfiability problem is solvable, then it is also solvable with $\H$ infinite-dimensional separable. Thus it is sufficient to consider e.g.~$\H = \ell^2(\mathbb{N})$ only.

The reason that we prefer the statement of Theorem~\ref{qlundec} over the satisfiability formulation is that we are interested in the laws of quantum logic, i.e.~in those statements that are valid on \emph{all} Hilbert spaces $\H$.
\end{rem}

\begin{ex}
\label{triangle}
The implication
\begin{align*}
(P\lor Q = 1) \mathrel{\mathsf{and}} {} & (Q\lor R = 1) \mathrel{\mathsf{and}} (R\lor P = 1) \\
& \mathrel{\mathsf{and}} (P\perp Q) \mathrel{\mathsf{and}} (Q\perp R) \mathrel{\mathsf{and}} (R\perp P) \:\mathrel{\mathsf{implies}}\: (0=1)
\end{align*}
is valid: in any nonzero Hilbert space, it is impossible to have three projections that are pairwise orthogonal and such that any two of them sum to the identity~\cite{spparable}.
\end{ex}

The key ingredient that leads to Theorem~\ref{qlundec} is an undecidability result of Slofstra~\cite{tp}, who builds on earlier work of Cleve, Liu and Slofstra~\cite{solgroup} and Cleve and Mittal~\cite{bcsg}. Our contribution merely consists of having seen the connection to quantum logic via the hypergraph approach to contextuality~\cite{AFLS}. The mathematical depth necessary for deriving such an undecidability result is to be found in Slofstra's arguments.

The statement that we actually prove first is Corollary~\ref{isc}, which is the \emph{inverse sandwich conjecture} from~\cite{AFLS}. The undecidability of quantum logic in the form of Theorem~\ref{sandwich} is then merely a reformulation---on an even smaller set of sentences than our formulation above. As we will see, the statement remains true if one replaces `holds in every $\mathcal{C}(\H)$' by `holds in $\mathcal{C}(\H)$ for some infinite-dimensional separable Hilbert space $\H$'.

Corollary~\ref{isc} also implies that infinitely many of the hypergraph C*-algebras $C^*(H)$ of~\cite{AFLS} fail to be residually finite-dimensional, as per Corollary~\ref{notrfd}.

\subsection*{Related work}

Lipshitz~\cite{modunsolv} has shown, among other things, that the purely implicational fragment of the theory of all $\mathcal{C}(\mathbb{C}^n)$ is undecidable, already in the signature $(\lor,\land,0,1)$. While this result is similar to ours, it uses techniques specific to a finite-dimensional setting (coordinatization).
A result of Sherif~\cite{orthodec} is that any first-order theory between orthomodular lattices and finite orthomodular lattices is undecidable.
Herrmann~\cite{vna} has proven that the equational theory of the orthomodular lattice of projections of a finite von Neumann algebra factor is decidable; this includes both the $\mathcal{C}(\mathbb{C}^n)$ and the projection ortholattices of factors of type $\mathrm{II}_1$. Other work of Herrmann and Ziegler is also concerned with related decidability and complexity problems~\cite{quantumsat}.

\section*{Solution groups and their group C*-algebras}

Before getting to the proof of our Theorem~\ref{qlundec}, we review the essential ingredient: Slofstra's recent work in combinatorial group theory~\cite{tp}. Subsequently, we will modify his intended interpretation using nonlocal games to one in terms of contextuality. From there, it is only a small step to quantum logic.

Following~\cite{bcsg}, Slofstra considers \emph{linear systems} over $\mathbb{Z}_2$, which are linear equations $Mx = b$ with $M\in\mathbb{Z}_2^{m\times n}$ and $b\in\mathbb{Z}_2^m$. While conventional solutions have $x\in\mathbb{Z}_2^n$, a \emph{quantum solution}~\cite{solgroup} consists of self-adjoint operators $A_1,\ldots,A_n\in\mathcal{B}(\H)$ such that:
\begin{itemize}
\item $A_i^2 = \mathbbm{1}$ for all $i$;
\item If $x_i$ and $x_j$ appear in the same equation, then $A_i$ commutes with $A_j$;
\item For each equation of the form $x_{k_1} + \ldots + x_{k_r} = b_r$, the operators satisfy
\[
	A_{k_1} \cdots A_{k_r} = (-1)^{b_r}\mathbbm{1},
\]
where the order of the factors is irrelevant due to the previous commutativity requirement.
\end{itemize}

The fact that quantum solutions solve the given linear system multiplicatively instead of additively is purely conventional, and allows for simpler notation. The most famous example of a quantum solution of a linear system that is unsolvable over $\mathbb{Z}_2$ is the Mermin-Peres magic square~\cite{peres}. The quantum solution for $\H = \mathbb{C}$ are precisely the conventional solutions over $\mathbb{Z}$, written multiplicatively as $A_i = (-1)^{x_i}$.

The quantum solutions of a linear system are controlled by representations of a certain group associated to the system:

\begin{defn}[Cleve, Liu, Slofstra~\cite{solgroup}]
Let $Mx = b$ be a linear system over $\mathbb{Z}_2$. Its \emph{solution group} is the finitely presented group $\Gamma$ with generators $g_1,\ldots,g_n$ and $J$ subject to the relations:
\begin{itemize}
\item $g_i^2 = 1$ for all $i$;
\item If $x_i$ and $x_j$ appear in the same equation, then $g_i g_j = g_j g_i$;
\item For each equation of the form $x_{k_1} + \ldots + x_{k_r} = b_r$, the generators satisfy
\[
	g_{k_1} \cdots g_{k_r} = J^{b_r}.
\]
\end{itemize}
\label{solgroupdef}
\end{defn}

These relations are precisely such that quantum solutions of $Mx=b$ on a Hilbert space $\H$ are in bijective correspondence with those unitary representations $\pi : \Gamma \to \mathcal{U}(\H)$ for which $\pi(J) = -\mathbbm{1}$.

Slofstra~\cite[Theorem~3.1]{tp} has shown that every finitely presented group embeds into a solution group in a particular way. Concerning undecidability, the following essential result was derived in the proof of~\cite[Corollary~3.3]{tp}.

\begin{thm}[Slofstra]
\label{solgroupundec}
Given a linear system $Mx = b$, it is undecidable to determine whether $J = 1$ in the associated solution group. Equivalently, it is undecidable to determine whether the linear system has a quantum solution.
\end{thm}

We now move on to considering the ramifications of this result, first for the hypergraph approach to contextuality~\cite{AFLS} and then for quantum logic, including the proof of Theorem~\ref{qlundec}.

\section*{Consequences for the hypergraph approach to contextuality}

For us, a \emph{hypergraph} is a pair $H=(V,E)$ consisting of a finite set of vertices $V$ and a subset $E\subseteq 2^V$ with $\cup E = V$. Their relevance lies in the observation that hypergraphs provide a convenient and powerful language to analyze quantum contextuality~\cite{AFLS}:

\begin{defn}
A \emph{quantum representation} of a hypergraph $H=(V,E)$ consists of:
\begin{itemize}
\item A Hilbert space $\H$ with $\dim(\H)>0$,
\item a family of projections $(P_v)_{v\in V}$ in $\H$ assigned to the vertices of $H$ such that for each edge $e\in E$, the associated projections form a partition of unity,
\begin{equation}
\label{pueq}
\sum_{v\in e} P_v = \mathbbm{1}.
\end{equation}
\end{itemize}
\end{defn}

In the case where all projections have rank $1$, this is related to the notion of Kochen-Specker configuration: a finite collection of vectors in a Hilbert space such that certain particular subsets of these vectors form orthonormal bases. The concept of \emph{quantum model}~\cite[Definition~5.1.1]{AFLS} on a hypergraph---considered as a contextuality scenario---is implicitly based on our notion of quantum representation. In general, the idea is that the hyperedges $e\in E$ label measurements with outcomes $v\in V$, and some outcomes may be shared between several measurements, corresponding to vertices being incident to several hyperedges.

\begin{ex}
A quantum representation of the hypergraph
\begin{center}
\begin{tikzpicture}[scale=.85]
\node[draw,shape=circle,fill,scale=.5] (a) at (90:1.4) {} ;
\node[draw,shape=circle,fill,scale=.5] (c) at (210:1.4) {} ;
\node[draw,shape=circle,fill,scale=.5] (e) at (330:1.4) {} ;
\node[below of=a,node distance=3mm] {};
\node[above right of=c,node distance=3mm] {};
\node[above left of=e,node distance=3mm] {};
\draw[thick,blue,rotate=270] (0:.6) ellipse (.4cm and 1.8cm) ;
\draw[thick,blue,rotate=150] (0:.65) ellipse (.4cm and 1.8cm) ;
\draw[thick,blue,rotate=30] (0:.65) ellipse (.4cm and 1.8cm) ;
\end{tikzpicture}
\end{center}
would yield a nontrivial solution to the antecedents of Example~\ref{triangle}. Thus this hypergraph does not have any quantum representation.
\end{ex}

The quantum representations of a hypergraph are equivalently given by the representations of the \emph{hypergraph C*-algebra}, which is the finitely presented C*-algebra
\[
	C^*(H) := \left\langle P_v :\: v\in V\:\bigg|\: P_v = P_v^* = P_v^2,\;\:\sum_{v\in e} P_v = \mathbbm{1} \:\:\forall e\in E\right\rangle,
\]
as already introduced in~\cite[Section~8.3]{AFLS}.
We quickly record a standard observation for future reference:

\begin{fact}
\label{pumo}
Projections that form a partition of unity~\eqref{pueq} are mutually orthogonal, $P_v P_w = \delta_{v,w} P_v$.
\end{fact}

Our central new observation is this:

\begin{lem}
There is an algorithm to compute, for every linear system $Mx = b$, a hypergraph $H$ such that quantum solutions of the linear system are in bijective correspondence with quantum representations of the hypergraph.
\label{algiso}
\end{lem}

This observation should not be surprising, since the original considerations around linear systems and solution groups~\cite{bcsg,solgroup} were inspired by the Mermin-Peres \emph{magic square}, one of the most startling examples of quantum contextuality~\cite{mermin}. The hypergraph construction in the following proof is along the lines of the \emph{measurement protocols} of~\cite[Appendix~D]{AFLS}, combined with forming an \emph{induced subscenario}~\cite[Definition~2.5.1]{AFLS}.

\begin{proof}
Let a linear system $Mx = b$ be given, with $M\in\mathbb{Z}_2^{m\times n}$ and $b\in\mathbb{Z}_2^m$. We write $[n]:= \{1,\ldots,n\}$, and
\[
	N(r) = \left\{\: i \in [n]\;|\: M_{r,i} = 1 \:\right\}
\]
for the set of variables that are contained in the $r$-th equation, with $r\in[m]$. We think of $i\in[n]$ as indexing an observable $A_i$ with values in $\mathbf{2}:=\{-1,+1\}$, and each $N(r)$ as indexing a set of measurements that commute and is therefore jointly implementable. Correspondingly, our hypergraph contains two kinds of outcome-representing vertices,
\[
	V := \{\: v_i^\alpha\: :\: i\in [n],\: \alpha\in\mathbf{2} \:\} \:\cup\: \{\: w_r^\beta \: :\: r\in [m],\: \beta \in \mathbf{2}^{N(r)}_{\pm} \:\},
\]
where the set $\mathbf{2}^{N(r)}_{\pm}$ consists of all those functions $\beta : N(r)\to\mathbf{2}$ which have the correct parity in the sense that $\prod_{i\in N(r)} \beta(i) = (-1)^{b_r}$.

The hyperedges will also be of three kinds: first, $\{v_i^{-1}, v_i^{+1}\}$ for every $i\in[n]$, which is intended to correspond to a measurement of the $\mathbf{2}$-valued observable $A_i$; second, $\{ w_r^\beta\: :\: \beta\in \mathbf{2}^{N(r)}_\pm\}$ for every $r\in[m]$, which corresponds to the possible outcomes of a joint measurement of the $A_i$ with $i\in N(r)$; and third, the sets of the form
\begin{equation}
\label{sedge}
	\{\, v_i^\alpha,\: w_r^\beta \: :\: \beta(i) = -\alpha\, \}
\end{equation}
for every fixed $r\in[m]$, $i\in N(r)$ and $\alpha\in\mathbf{2}$. Intuitively, this is the set of outcomes of the measurement protocol which first measures $A_i$, and if the outcome is $-\alpha$, then also conducts a joint measurement of all other observables $A_j$ with $j\in N(r)$, resulting in a joint outcome $\beta\in \mathbf{2}^{N(r)}_{\pm}$ with $\beta(i) = -\alpha$. This ends the definition of the relevant hypergraph $H$.

We now show how quantum representations of this hypergraph correspond to quantum solutions of the linear system. First, given a quantum representation of the hypergraph, we obtain a quantum solution of the linear system by taking
\begin{equation}
\label{PtoA}
 	A_i := P_{v_i^{+1}} - P_{v_i^{-1}} = 2 P_{v_i^{+1}} - \mathbbm{1}
\end{equation}
for all $i\in[n]$. We need to show that this indeed results in a quantum solution by checking that the $P_{v_i^{+1}} - P_{v_i^{-1}}$ are unitary and satisfy the required relations. Unitarity is clear since $2 P_{v_i^{+1}} - 1$ is a symmetry, which thereby also shows that the relation $A_i^2 = 1$ is respected. For the commutativity $A_i A_j = A_j A_i$ with $i,j\in N(r)$, we use Fact~\ref{pumo} together with the partition of unity relation associated to the second kind of edge~\eqref{sedge}: this relation implies that
\[
	P_{v_i^{+1}} - P_{v_i^{-1}} = \sum_{\beta \: :\: \beta(i) = +1} P_{w_r^\beta} - \sum_{\beta \: :\: \beta(i) = -1} P_{w_r^\beta},
\]
and similarly for $j$, so that we can apply Fact~\ref{pumo}. This expression is also useful for checking that the relation $\prod_{i\in N(r)} \big(P_{v_i^{+1}} - P_{v_i^{-1}}\big) = (-1)^{b_r}\mathbbm{1}$ holds as well, which then follows from $\sum_\beta w_r^\beta = \mathbbm{1}$ upon using that every $\beta$ has even parity.

In the other direction, we put
\[
	P_{v_i^\alpha} := \frac{\mathbbm{1} + \alpha A_i}{2},\qquad P_{w_r^\beta} := \prod_{i\in N(r)} \frac{\mathbbm{1} + \beta(i) A_i}{2},
\]
where we likewise need to check that the relations are preserved, which first requires showing that both right-hand sides are projections. This is clear in the first case and holds by the commutativity assumption $A_i A_j = A_j A_i$ for $i,j\in N(r)$ in the second case. We verify the required partition of unity relations. First, $P_{v_i^{-1}} + P_{v_i^{+1}} = 1$ holds trivially. Second, if we apply the definition of $P_{w_r^\beta}$ also for $\beta$ of the wrong parity, then
\[
	\sum_{\beta\in\mathbf{2}^{N(r)}} P_{w_r^\beta} = \prod_{i\in N(r)} \,\sum_{\beta\in\mathbf{2}} \frac{\mathbbm{1} + \beta A_i}{2} = \mathbbm{1}.
\]
Since $P_{w_r^\beta} = 0$ whenever $\beta$ has the wrong parity, we can ignore these terms and arrive at the desired equation. Third, the relation associated to~\eqref{sedge} takes a bit more work: the expression $P_{v_i^\alpha} + \sum_{\beta\: :\: \beta(i) = -\alpha} P_{w_t^\beta}$ evaluates to
\[
	\frac{\mathbbm{1}+\alpha A_i}{2} + \sum_{\beta\: :\: \beta(i) = -\alpha} \:\prod_{j\in N(r)} \frac{\mathbbm{1} + \beta(j) A_j}{2}  = \frac{\mathbbm{1}+\alpha A_i}{2} + \frac{\mathbbm{1}-\alpha A_i}{2} \sum_{\beta\: :\: \beta(i) = -\alpha} \:\prod_{j\in N(r),\: j\neq i} \frac{\mathbbm{1} +\beta(j) A_j}{2}.
\]
Upon expanding the product, the sum over $\beta$ makes all terms cancel except for the constant one and the $\prod_{j\neq i} x_j$ one, which survives as well due to the parity constraint on $\beta$. Therefore we arrive at the expression
\[
	\frac{\mathbbm{1}+\alpha A_i}{2} + \frac{\mathbbm{1}-\alpha A_i}{2} \cdot \frac{\mathbbm{1} - \alpha (-1)^{b_r} \prod_{j\neq i} A_j}{2} = \frac{\mathbbm{1}+\alpha A_i}{2} + \frac{\mathbbm{1}-\alpha A_i}{2} \cdot \frac{\mathbbm{1} - \alpha A_i}{2} = \mathbbm{1}.
\]
We finally show that these constructions are inverses of each other. Starting with a quantum solution $(A_i)_{i\in[n]}$, it is immediate to show that computing the resulting projections and using~\eqref{PtoA} results in the original $A_i$'s. A similar statement holds for the $P_{v_i^\alpha}$ in the other direction, while a short computation is required to show the same for the $P_{w_r^\beta}$,
\[
	\prod_{i\in N(r)} \frac{1 + \beta(i)\cdot \left(P_{v_i^{+1}} - P_{v_i^{-1}}\right)}{2} = \prod_{i\in N(r)} \left(1 - P_{v_i^{-\beta(i)}}\right) = \prod_{i\in N(r)} \: \sum_{\beta'\: :\: \beta'(i) = \beta(i)} P_{w_t^{\beta'}} = P_{w_t^\beta},
\]
where the last step again uses Fact~\ref{pumo}.
\end{proof}

In~\cite[Section~8]{AFLS}, we had considered the decision problem \texttt{ALLOWS\_QUANTUM}, which asks: given a hypergraph $H=(V,E)$, does it have a quantum representation?\footnote{The formulation of~\cite{AFLS} asks for the existence of a quantum model on $H$, but this is clearly equivalent: the existence of a quantum model requires the existence of a quantum representation to begin with; conversely, one can use a quantum representation and an arbitrary state in its underlying Hilbert space to obtain a quantum model.} Our \emph{inverse sandwich conjecture} hypothesized that this problem is undecidable. Thanks to Slofstra's Theorem~\ref{solgroupundec}, we are now in a position to prove this:

\begin{cor}[Inverse sandwich conjecture]
\label{isc}
There is no algorithm to determine whether a given hypergraph has a quantum representation.
\end{cor}

\begin{proof}
If there was such an algorithm, then Lemma~\ref{algiso} would provide an algorithm to determine whether a given linear system has a quantum solution. This is in contradiction with Theorem~\ref{solgroupundec}.
\end{proof}

This also implies that there are hypergraphs that have quantum representations, but only in infinite Hilbert space dimension~\cite[Section~8]{AFLS}. Translating Slofstra's explicit example~\cite[Corollary~3.2]{tp} into a hypergraph using the prescription of Lemma~\ref{PtoA} will provide an explicit (but large) example.

\begin{rem}
\label{puralg}
In terms of fancier language, one can phrase Lemma~\ref{algiso} as saying that the maximal group C*-algebra~\cite{groupCstar} of the solution group associated to the linear system is, after taking the quotient by the relation $J=-1$, computably isomorphic to a hypergraph C*-algebra.
At the purely algebraic level of \emph{$*$-algebras}, the analogous statement is still true with the same proof, but one needs to throw in the orthogonality relations of Fact~\ref{pumo} separately when defining the finitely presented $*$-algebra associated to a hypergraph.
\end{rem}

\begin{cor}
\label{notrfd}
There are infinitely many hypergraphs $H$ for which $C^*(H)$ is not residually finite-dimensional.
\end{cor}

\begin{proof}
If every $C^*(H)$ was residually finite-dimensional, then we could use the algorithm of~\cite{compnorm} to determine whether $\|1\|=0$ or $\|1\|=1$ in $C^*(H)$, which are the only two possibilities depending on whether $C^*(H) = 0$ (no quantum representation) or $C^*(H)\neq 0$ (there is a quantum representation). This contradicts Corollary~\ref{isc}. If there were only finitely many exceptions to this residual finite-dimensionality, then there would also have to exist an algorithm which simply treats these exceptional cases separately.
\end{proof}

As far as we know, this is the first time that the strategy of~\cite{compnorm} has been successfully employed to show that some finitely presented C*-algebras are not residually finite-dimensional. We do not know \emph{which ones} of these C*-algebras fail to be residually finite-dimensional, and in particular the decidability status of the problem ``For given $H$, is $C^*(H)$ residually finite-dimensional?'' is unclear.

In light of Remark~\ref{puralg}, we also wonder:

\begin{prob}
Is the word problem for the algebras
\[
	\mathbb{Q}[H] := \left\langle P_v :\: v\in V\:\bigg|\: P_v = P_v^2,\;\:\sum_{v\in e} P_v = \mathbbm{1} \:\:\forall e\in E\right\rangle,
\]
i.e.~without imposing the relations of Fact~\ref{pumo}, solvable? Uniformly solvable?
\end{prob}

\section*{Consequences for quantum logic}
\label{mainthm}

The projection operators on a Hilbert space are in bijective correspondence with the closed subspaces. This lets us translate the observations of the previous section into statements about quantum logic.

Although we try to avoid too much jargon, it will be helpful to utilize the basic terminology of model theory~\cite{mtbook}. We work in the signature $(\lor,\perp,1)$, where $\perp$ is a binary relation; any orthomodular lattice can also be considered a structure of this signature due to Remark~\ref{perprem}. We follow~\cite{mtbook} in using the shorthand notation $\bar{P}:= P_1,\ldots, P_n$ for a list of variables, using notation which suggests that we are still thinking in terms of projections.

It is a standard fact that forming a partition of unity~\eqref{pueq} at the level of projections is equivalent to the associated subspaces being pairwise orthogonal and spanning the entire space, which translates into the atomic formula
\begin{equation}
\label{PUeq}
\PU{\bar{P}} = \PU{P_1,\dots,P_n} := \mybigand_{i\neq j} \left( \, P_i \perp P_j \, \right) \, \mathrel{\mathsf{and}} \, \left( P_1 \lor \ldots \lor P_n = 1 \right) ,
\end{equation}
where the notation `$OC$' reminds us of \emph{orthogonality} and \emph{completeness}. All formulas that we use are built out of atomic formulas of this form. If we want to say that already a certain subset $\{P_i \: :\: i\in e\}$ of these projections indexed by $e\subseteq[n]$ forms a partition of unity, then we simply write $\PU{\bar{P}_e}$.

\begin{thm}
The theory of complex Hilbert lattices $\mathcal{C}(\H)$ in the signature $(\lor,\perp,0,1)$ is undecidable: there is no algorithm to decide whether for a given hypergraph $H=(V,E)$, the formula
\begin{equation}
\label{horn}
\Big(\mybigand_{e\in E} \PU{\bar{P}_e} \Big) \:\mathrel{\mathsf{implies}}\: \big(0 = 1)
\end{equation}
holds for all $V$-indexed sets of projections $\{P_v\}_{v\in V}$ or not.
\label{sandwich}
\end{thm}

\begin{proof}
This is now merely a restatement of Corollary~\ref{isc}: the tuples of projections in a Hilbert space $\H$ with $\dim(\H)>0$ such that $\mybigand_{e\in E} \PU{\bar{P}_e}$ holds are precisely the quantum representations of $H$, while $0=1$ is equivalent to $\dim(\H) = 0$.
\end{proof}

Hence the undecidability already holds for the purely implicational fragment: upon unfolding all the $\PU{\bar{P}_e}$'s that appear on the left of~\eqref{horn} via the definition~\eqref{PUeq}, one obtains merely a conjunction of atomic formulas on the left-hand side of the implication.

Finally, we show that the universal theory of complex Hilbert lattices does not really depend on the Hilbert space.

\begin{lem}
Let $\phi(\bar{P})$ be an atomic formula in the signature $(\lor,\perp,0,1)$.
\begin{enumerate}
\item\label{vNaembed} If $f:\mathcal{N}\to\mathcal{M}$ is a normal injective $*$-homomorphism between von Neumann algebras, then $\phi(f(P_1),\ldots,f(P_n))$ if and only if $\phi(P_1,\ldots,P_n)$.
\item Let $\Phi$ be the universal sentence $\forall \bar{P}\; \phi(\bar{P})$.
Then $\mathcal{H}\vDash\Phi$ for all Hilbert spaces $\mathcal{H}$ if and only if $\mathcal{H}\vDash\Phi$ for separable infinite-dimensional $\mathcal{H}$.
\end{enumerate}
\label{allH}
\end{lem}

Since there is only one infinite-dimensional separable Hilbert space up to isomorphism, this states equivalently that the universal theory of Hilbert spaces coincides with the universal theory of \emph{one} particular Hilbert space, e.g.~$\mathcal{H} = \ell^2(\mathbb{N})$. Therefore our undecidability result already holds at the level of a single such Hilbert space.

\begin{proof}
\begin{enumerate}
\item Induction on the complexity of $\phi$. Normality of $f$ is required for showing that $f(P_1\lor P_2) = f(P_1)\lor f(P_2)$.
\item
The nontrivial direction is this: if $\mathcal{H}\vDash\Phi$ for separable infinite-dimensional $\mathcal{H}$, then also $\mathcal{H}'\vDash\Phi$ for any other Hilbert space $\mathcal{H}'$.
\begin{enumerate}
\item [\underline{Case 1:}] $\mathcal{H}'$ is finite-dimensional. In this case, $\mathcal{H}'\otimes\mathcal{H}$ is isomorphic to $\mathcal{H}$, and therefore $\mathcal{H}'\otimes\mathcal{H}\vDash \Phi$. By assumption, we therefore know that $\phi(P_1\otimes\mathbbm{1},\ldots,P_n\otimes\mathbbm{1})$ for any tuple of projections $\bar{P}$ on $\mathcal{H}'$, and hence also $\phi(P_1,\ldots,P_n)$ by~\ref{vNaembed}.
\item [\underline{Case 2:}] $\mathcal{H}'$ is infinite-dimensional. In this case, any tuple of projections $\bar{P}$ generates a separable von Neumann algebra in $\mathcal{B}(\mathcal{H}')$. By separability, we can faithfully represent this von Neumann algebra on a separable Hilbert space, on which we know $\Phi$ to hold due to either the assumption or Case 1. We then conclude $\phi(P_1,\ldots,P_n)$ from two applications of~\ref{vNaembed}. \qedhere
\end{enumerate}
\end{enumerate}
\end{proof}

\begin{rem}
One can also conclude from our results that the theory of complex Hilbert lattices cannot be axiomatized recursively, as hypothesized in~\cite[p.\,69]{rand}, as follows. The lemma implies that the universal theory of Hilbert lattices is complete. Therefore, if one could enumerate the axioms recursively, then one would have a decision procedure for any universal sentence $\Phi$ by simply generating all axioms together with all their consequences until either $\Phi$ or $\lnot\Phi$ has been derived.

Svozil~\cite[p.\,69]{rand} also asks if it is possible to develop an axiomatization of Hilbert lattices in ``purely algebraic'' terms. If one interprets this as asking whether the Hilbert lattices are the class of models of some theory in first-order logic, then the answer is well-known to be negative: the L\"owenheim-Skolem theorem asserts that it is impossible to axiomatize \emph{any} uncountable structure in first-order logic. This holds irrespectively of whether one attempts to axiomatize Hilbert lattices in all Hilbert space dimensions or only in one particular dimension $\geq 2$. The most that one can hope for is categoricity in the relevant cardinality, meaning that every model of the same cardinality as the intended model is isomorphic to the intended models. But there will always be models in other cardinalities as well.
\end{rem}

\subsection*{Acknowledgements} We thank John Harding, Christian Herrmann, Anthony Leverrier, Mladen Pavi{\v{c}}i{\'c}, William Slofstra, Rob Spekkens, Karl Svozil and Moritz Weber for discussions. Special thanks go to Christian Herrmann for copious help with the literature and useful feedback, and to William Slofstra for pointing out that Theorem~\ref{sandwich} actually follows from the arguments used in an earlier version of this paper to prove a weaker result.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


Dimitrios Beach Hotel is just 80 meters away from the beautiful beach and 2 km away from the unique historical center of Rethymno. Is an easy stroll along the boulevard where you will find bars, restaurants and shops.
Rethymno, the most traditional prefecture of the island of Crete!
Rethymno (IPA ['reθimno]), also Rethimno, Rethymnon, Réthymnon, and Rhíthymnos) (Greek: Ρέθυμνο), a city of approximately 40,000 people, is the capital of Rethymno Prefecture in the island of Crete.
It is a place full of contrasts, with a long history going back to the Neolithic times, with nature left intact in many areas, with a vivid living tradition. The old town of Rethymno with the Renaissance style centre, the Fortetza, the museums and the endless beach will certainly charm you. Rethymno is a charming town for all ages. Whether you yearn for a peaceful holiday strolling along the winding streets and admiring the Venetian architecture, or whether you are young and energetic thirsty for adventure, sports and clubbing, then Rethymno is the place to be. Rethymno, a town rich in history, great natural beauty, soaring mountains and endless sandy beaches.
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Members of Seven Brothers S.A.


text:
Speeding up MaaS
Speeding up the mobility transition: Sampo Hietanen, MaaS Global
"We need to offer mixed modes and fulfil the desire of freedom of mobility, just like people have with a car."
With the continuous growth of the population and ongoing urbanization there are numerous mobility challenges. Sustainability, safety and societal impact are amongst our daily concerns. We need to speed up the mobility transition to keep up with the fast changing global dynamics, which requires inventive approaches and better solutions. In this series we share inspiring and innovative cases from all over the world. Sampo Hietanen is the founding father of MaaS or Mobility as a Service. How does he speed up the mobility transition?
Mobility as a Service or MaaS; it has become a big theme. The term has had a global impact on the transport mobility mix where subscription based mobility could replace car ownership. Sampo Hietanen thought of the concept Mobility as a Service and founded MaaS Global in 2015 which now operates the app Whim in several cities around the world. How did you come up with the idea and in what way does it contribute to the mobility transition?
"All of my friends were into mobile business working for Nokia and it bugged me that I was just working in traffic."
'All of my friends were into mobile business working for Nokia and it bugged me that I was just working in traffic. On an airplane in 2006 on my way to a conference to lecture about the disruption of technology in mobility, I decided to compare the disruption of telecom to a comparable situation in the mobility sector. Then I knew this was going to happen, I knew there was something in it. MaaS was born.'
'People want to get around and they pay you to solve problems; not to tell them about problems. The biggest purpose for MaaS is to give people the freedom of mobility without all the hassle that comes with it. You deserve to go to all the places you love in your life, whenever, however. And the only modality that fulfils that promise now is the car. So in order to make the choices in transport more sustainable, we want to offer an alternative for car ownership.'
'However, we have a big dilemma in transport. Us transport engineers think that everything in the world is rational. So there is a big contradiction between what we think people want and what people actually do. People have an irrational feeling of personal freedom. The personal freedom of moving around and the rational way people move do not correspond at all. Transport engineers tell us to use transport and ask why we buy all these cars, while buying cars themselves! This bugs me in all discussions. We need to get these modes mixed to fulfil the aspiration of freedom for people.'
"We have to start admiring the car; it is the only thing people really dream about and fulfils people's desire of freedom."
'We forget about the desirability too often. We have to admire and love the car. It is the only thing people really dream about and it shapes the city, whether we want it or not. It fulfils people's desire of freedom. The individual freedom of mobility a car offers is so big; it is always going to beat everything else.' 'In order to change this, we need to offer a good alternative. To me this means offering all kinds of alternative modes of transport. Don't let that car that you are not using, just be there. We offer you all other modalities instead. If you would get a package that gives you unlimited rides to all kinds of modes, would you give up your own car?'
'20% of household costs is spent on transportation and 76% (Frost & Sullivan) of that money is locked in a car. Unless we cannot liberate the amount of money people spend on cars, we will not be able to change. I once asked a group of Dutch students: What if I gave you every modality available to you in Rotterdam, would you be willing to give up your own car? 20% of the hands raised. And then I asked: What if I would give you the whole world of mobility for the same price of a car? Then every hand went up. You need that spark in the eyes, just like people have with a car. Than we have an alternative, but the car and maybe even the desire to own one, will always exist.'
"20% of household costs is spent on transportation and 76% of that money is locked in a car."
'I myself prefer to go to work by public transport or bike, visit my mum by car and go to the gym by bike. Every destination can offer a different modality. As engineers we think in different modes, but I think this is a huge misunderstanding. You see, for people it is not about the modes. It's about offering a solution.'
'In 2015 I founded MaaS Global to reshape the world's transportation markets. In 2016 we wanted to proof to the world we could be Uber, Google and all sharing companies and public transport together. And that was how the Whim app was born. It serves as an operator between transport services providers, users and third parties. It combines all existing transport services into a single mobile application on the 'single-ticket principle' and offers personalised transport plans tailored to customer needs. The name comes from the feeling of freedom of mobility. I want to go golfing on a Sunday, or visit my mother spontaneously on "a whim". Today we are available in Belgium, Austria, Switzerland and Japan.'
"For the mobility transition to speed up, we should really allow innovation on top of the typical transportation system."
'We like to think that of data and sharing it as the biggest challenge. But I do not agree on this. The backbone of MaaS in Europe is public transport. Cities and governments want these solutions but the cities own entities which are public transport monopoly and slow in the process. For the mobility transition to speed up, we should really allow innovation on top of the typical transportation system. The European transportation services needs to open up, not data, but the actual access to purchasing services so that it becomes the source of innovation. It will happen if there the understanding of the rules of the game improves.'
'What really drives me is when a single mother emails me, explaining she was about to move to downtown Helsinki and she could not afford a car. Thanks to Whim, she could live outside of the inner city. Or a 50 year old man who told me that all modalities have been available for ages, but never before was there a party standing right behind him, that really understood him and talked the same language. What surprised me in one of our researches among our users in Helsinki is that 12% of them had avoided buying a car. And even 12% had sold their cars. It's a big number already and it shows there is a real potential! That means 10 of millions of cars less on the road in Europe!'
"People are lazy by nature; we prefer an easier life so we can use our brains for something different."
'In the future people should no longer care about the mode itself as long as they know it gets you there. The smartest city is the one that allows me to be dumb. People are lazy by nature. We no longer remember phone numbers or addresses. We like to have an easier life so we can worry about other things and use our brains for something different. The choice of transport is being outsourced. They can trust us offering them the best option. The destination matters; not how you get there.'
'COVID showed people that it is easier to make new things happen, and it will ultimately be in favour of MaaS. Transport is the only industry that hasn't improved in CO2 emissions since the nineties. In the EU approximately 25% of the total EU-28 greenhouse gas emissions come from the transport sector. Putting a bit of bike lane here and there does not make the difference. We need to be willing to change to make mobility more sustainable, but without jeopardising the freedom of mobility. We can only be satisfied when people are willing to pay the same amount of money for other modes of transport as they pay for a car.'


Happy Feast Day, dear Saint Anthony! St. Anthony is one of our favorite saints, and his heavenly help was instrumental in bringing us to the archdiocese of San Antonio. We all have our favorite image of him, but what do you think he really looked like? Watch this video to see what a team of Portuguese scientists think.
This entry was posted in Saints & Angels and tagged St Anthony by texasnuns. Bookmark the permalink.


text:
Malavika Binny is an Assistant Professor in the Department of History at the School of Liberal Arts and Basic Sciences, SRM University, India. She was awarded her doctorate in May 2019 from the Centre for Historical Studies at Jawaharlal Nehru University, New Delhi on the topic - Bodies, Power and Identities in Premodern Kerala; An Exploration of Medical and Ritual Traditions.
She was awarded the Erasmus Mundus Visiting Scholarship at The Leiden Institute of History, Leiden University, The Netherlands, under the Erasmus Mundus - IBIES Programme in 2014-2015 and was the recipient of the prestigious Elamkulam Kunjan Pillai Young Historian Prize instituted by the Kerala History Congress in 2017. Her research interests include the histories of science and medicine, gender history and dalit studies.
Website Link : https://srmap.edu.in/faculty/dr-malavika-binny/
Maanvender Singh completed his Ph.D. from the Department of History at the Central University of Sikkim, Gangtok in 2018. He was a Public Policy Scholar at The Hindu Centre, Chennai in 2016.Maanvender Singh's research explores the genesis of an exclusive Other Backward Classes (OBCs) politics at the national level and their transformation from the early 1950s and 1960s from a reductive administrative category to the prime mover in the Indian politics.
His research also probes the democratic potential of alignment of caste groups under the category of OBCs. His research areas also include Constitutional and judicial engagement with the question of backward classes. Social Inclusion and Indian Higher Education. The issue of Equal Access. State and Politics in the Post- Colonial India. Caste, Conflict, and Democratisation.
Website Link : https://srmap.edu.in/faculty/dr-maanvender-singh/


My work is nothing short than a journey into the otherworldly and the exploration of the most authentic kind of magic: human earnest and our detachment from the influence of fairy tales. I do not wish to create a pretty picture as much as I hope to stir feelings in the depths of my viewers' hearts, whether the result is pleasant or otherwise. All of my paintings are the manifestation of my love and soul. I believe that my work should always feel like something truly special, so that's why I take extra care and consideration in charming each piece. In this way I hope to convey each piece of art as worthy of consideration and ultimately its interpretation into a deeper meaning. I think it's important to not take structure too seriously, and that proves to be a considerable factor contributing to my driving force as I construct each piece with love and care.


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text:
Алье́р (, ) — населённый пункт и муниципалитет в Испании, входит в провинцию Астурия. Муниципалитет находится в составе района (комарки) Каудаль. Занимает площадь 375,89 км². Население — 12 582 человека (на 2010 год).

Фотографии

Население

Города-побратимы
 Жамблу, Германия

Примечания

Ссылки
 Официальная страница
 Página del Ayuntamiento
 Federación Asturiana de Concejos
 Aller y sus pueblos

Муниципалитеты Астурии
Населённые пункты Астурии

redpajama_set_name: RedPajamaWikipedia


text:
1206 CROSSTOWN Parkway, Kalamazoo, MI, 49001
Listing Agent: Stephanie Goodman
Courtesy of: Bricks + Mortar Group
Address: 1206 CROSSTOWN Parkway
County: Kalamazoo
City: Kalamazoo
Marijuana facility for sale - Recreational/Adult-Use Retail, Processing, & Cultivation allowed. The building has tons of square footage and heavy power and is already locally permitted, making this the perfect vertically integrated investment. With over 23,000 square feet of office, warehouse, & lab space, there are considerable options with this building.
Listing Agent: Stephanie Goodman Courtesy of: Bricks + Mortar Group IDX provided courtesy of Realcomp II Ltd. via site owner and the originating MLS listed above, ©2022 Realcomp II Ltd. Shareholders. IDX information is provided exclusively for consumers' personal, noncommercial use and may not be used for any purpose other than to identify prospective properties consumers may be interested in purchasing. The accuracy of all information, regardless of source, is not guaranteed or warranted. All information should be independently verified. Updated: 29th January, 2023 12:54 PM (UTC)


text:
Sándor Egervári es un exfutbolista y entrenador de fútbol,que desde el 2009 entrena a Hungría.

Carrera

Como jugador
 1968–1970 Kossuth KFSE
 1971–1972 Budapesti Spartacus SC
 1972–1976 Budapest Honvéd
 1976–1977 Szegedi EOL AK
 1977–1981 MTK
 1971-1972 Primera División de Hungría - Spartacus SE
 1972-1981 Primera División de Hungría - Budapest Honvéd y VM MTK
 1974 Miembro del equipo nacional olímpico

Como entrenador
 1993–1996 BVSC Budapest
 1997 Érdi VSE
 1997 Al-Ittihad
 1998–1999 MTK
 1999–2002 Dunaújváros
 2002–2004 MTK
 2004–2005 Vasas SC
 2006–2007 Al Salmiya Club
 2007–2009 Győri ETO FC
 2009–2013 Hungría
 2016 Diósgyőr VTK

Premios
Egervari ha recogido numerosos premios durante sus años como técnico superior en Hungría y el Oriente Medio. Fue entrenador del año en 1996, 1999, 2000, 2001, 2003 y 2009

Véase también
 Hungría
 selección de fútbol de Hungría

Referencias

Enlaces externos

Centrocampistas de fútbol
Futbolistas del Budapest Honvéd Football Club
Futbolistas del MTK Budapest FC
Entrenadores del Ittihad FC
Entrenadores del Vasas SC
Entrenadores del MTK Budapest FC
Entrenadores del Győri ETO FC
Entrenadores de la selección de fútbol de Hungría
Entrenadores del Al-Salmiya SC
Entrenadores del Diósgyőri VTK


Tim Corder - MOST WANTED.
Tim made the smartest guys in the Central Security Agency look stupid. Now they want payback.
They can watch him through walls. Hear him from miles away. See him from space. And now they want to bring him down.
Can Tim stay one step ahead?


I opened my case to find droopy strings only once! I got perfection pegs, set up a 2 tank humidifier next to my cello and bought a Stretto (inside the case humidifier). No problems since then, thank goodness! It was a scary moment and one I don't want to repeat. LOVE Mimi's DIY humidifiers!


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