Involving Edmonton citizens in the proposed Downtown Arena and Entertainment District is a priority.
Creating a community advisory committee, representing areas near the arena district, to identify and address issues.
A senior member of the Oiler's operations will meet with the committee at least once a year.
Development and facilitation of training for low-income/high need Edmontonians.
The City has held two extensive public consultations processes on the proposed arena and entertainment district.
Spring, 2012, to gather feedback on the schematic designs.
Read the full results of the Spring 2012 consultation.
Read the full results of the Winter 2010 consultation.
Get the latest information on the Downtown Arena and Entertainment District by signing up for our e-newsletter.


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Tag Archives: Samuel L. Jackson
Casting calls information for 'The Avengers: Age of Ultron' actors and extras
Hawkeye and Black Widow will be a big part of "The Avengers: Age of Ultron".
Marvel Studios and The Walt Disney Studios are now in pre-production on the upcoming sci-fi themed superhero feature film "The Avengers: Age of Ultron", and casting directors are auditioning actors for starring, co-starring, and supporting roles. The film's photo doubles and stand-ins for the starring actors, as well as general extras and featured background actors will be cast closer to the start of filming. The locations where outdoor principal photography will take place are in and around London, England. Indoor sound stage filming will take place at Shepperton Studios. Shooting begins in February, 2014.
"The Avengers: Age of Ultron" Disney Casting Calls
Standard | Posted in Acting Auditions, Auditions, Disney Actor Casting, Disney Casting, Entertainment, Extras Casting, London Casting Call, Los Angeles Casting Calls	| Tagged 2013 London Actors Resource Guide eBook, Aaron Taylor-Johnson, Ant-Man, Anthony Mackie, Captain America: The Winter Soldier, Chris Evans, Chris Hemsworth, disney auditions, Disney Casting Calls, Disney Casting Director, Disney Talent Search, Guardians of the Galaxy, Jeremy Renner, Mark Ruffalo, Robert Downey Jr, Samuel L. Jackson, Scarlett Johansson, The Amazing Spider-Man 3, The Avengers: Age of Ultron, Thor: The Dark World	| 0 comments
'Captain America: The Winter Soldier' L.A. and Cleveland casting calls
Chris Evans reprises his role as Steve Rogers in "Captain America: The Winter Soldier".
Marvel Studios is set to begin shooting the superhero feature film sequel "Captain America: The Winter Soldier" on March 1, 2013. The locations where filming will take place are Los Angeles and Cleveland, Ohio. Some additional filming will take place in Washington D.C. according to Leslie Green, Senior Communications manager with the DC Film Office. Principal actor casting will take place in Los Angeles and Cleveland, with extras also being cast in both cities. Walt Disney Studios Motion Pictures has announced that they will release the film in theaters on April 4, 2014. The working title for "Captain America: The First Avenger" was Frostbite, and the working title for "Captain America: The Winter Soldier" will be Freezerburn.
"Captain America: The Winter Soldier" Casting Calls
Standard | Posted in Acting Auditions, Auditions, Cleveland Casting Calls, Disney Actor Casting, Entertainment, Extras Casting, Film Casting, Los Angeles Casting Calls, Open Casting Calls, Talent Search, Teen Acting Auditions, Walt Disney Films, Washington DC Casting Call, Washington DC Casting Calls	| Tagged 2012 Los Angeles Actors Resource Guide eBook, alan baltes, Anthony Mackie, Anthony Russo, auditions, Captain America, Captain America: The First Avenger, Captain America: The Winter Soldier, casting calls, Chris Evans, Cleveland, Cobie Smulders, disney auditions, disney casting, Frank Grillo, Freezerburn, Joe Russo, Lillian Pyles Casting, los angeles, Marvel Studios, Pain & Gain, Samuel L. Jackson, Sarah Finn, Scarlett Johansson, Sebastian Stan, talent search, Thor: The Dark World, Walt Disney Studios, Walt Disney Studios Motion Pictures, Washington D.C	| 2 Comments
Acting auditions and extras casting for major feature film 'RoboCop'
Swedish actor Joel Kinnaman has been cast in the lead role of RoboCop.
Metro-Goldwyn-Mayer Studios in association with Columbia Pictures and Strike Entertainment are in pre-production on the reboot of the 1987 Orion Pictures science fiction action film "RoboCop". Casting for the film's lead roles has been taking place in Los Angeles, and additional casting for supporting and day player roles are being cast in Toronto, Canada where filming is set to begin on September 5, 2012. All of the extras will be hired in Ontario throughout production which is scheduled to continue through January 11, 2013.
Feature Film "RoboCop" Acting Auditions and Extras Casting
Standard | Posted in Acting Auditions, Auditions, Entertainment, Extras Casting, Film Casting, Los Angeles Casting Calls, Talent Search, Toronto Casting Calls	| Tagged Abbie Cornish, amanda seyfried, Clive Owen, detroit casting, Diane Kerbel, Eric Newman, film auditions, Francine Maisler, Gary Oldman, Hugh Laurie, Jackie Earle Haley, James Vanderbilt, Jay Baruchel, Jennifer Ehle, Joel Kinnaman, Jose Padilha, Joshua Zeturner, Julianne Moore, justin timberlake, leonardo dicaprio, los angeles, Marc Abraham, Marianne Jean-Baptiste, Metro-Goldwyn-Mayer, Michael Kenneth Williams, Nick Schenk, RoboCop, RoboCop Casting Call, Samuel L. Jackson, Seann William Scott, Strike Entertainment, talent search, The Infiltrator, The Rock, toronto, toronto extras, Zamaret Kleiman	| 0 comments

redpajama_set_name: RedPajamaCommonCrawl


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Buffett is about to release his annual letter to Berkshire Hathaway Inc shareholders, here's what he may discuss
On Saturday lots of investors are likely to shift their attention to the U.S. heartland, when the billionaire will release the letter to his shareholders
Berkshire Hathaway CEO Warren Buffett performs with the Fruit of the Loom guys at a previous shareholders' meeting.
11:34 AM EST
Few things have mattered more to markets this year than the daily headlines (and tweets) streaming out of Washington. On Saturday, though, lots of investors are likely to shift their attention to the U.S. heartland, when billionaire Warren Buffett releases his annual letter to Berkshire Hathaway Inc. shareholders.
Here are some of the topics the 86-year-old Sage of Omaha may discuss:
– Airlines, Apple: Investors will be eager to learn more about some big and surprising additions to Berkshire's stock portfolio last year. As of Dec. 31, the company held US$6.6 billion of shares in Apple Inc. and US$9.3 billion in the four largest U.S. airlines: American Airlines Group Inc., Delta Air Lines Inc., Southwest Airlines Co. and United Continental Holdings Inc.
The bets seem to go against some of Buffett's long-held ideas. He's generally avoided investing in technology companies, because he finds it harder to predict whether they'll be around for the long haul. He's also spent years criticizing airlines as terrible businesses.
Berkshire investment manager Ted Weschler could have helped spur the shift in thinking. He explained to a German magazine last year how cloud computing and apps had made customers more loyal to the iPhone maker. People familiar with the matter have said that Weschler studied up on the airline industry last year after seeing a presentation from American Chief Executive Officer Doug Parker.
Wall Street analysts have speculated that Berkshire could eventually buy one of the airlines. Buffett previously acquired railroad BNSF after taking a minority stake in the company and two of its competitors.
– Trump? Buffett was an outspoken supporter of Hillary Clinton in last year's election, so Donald Trump's victory in November will be a delicate subject. Since then, the Berkshire chairman has called for unity and said he "overwhelmingly" supported the president's choices as he picked a cabinet. Buffett also reiterated that the U.S. economy will do fine over the long run, regardless of who's in the Oval Office.
That tone is almost certain to carry over to Saturday's letter. While Buffett may not mention Trump by name, it's possible he could comment on some of the business before the new administration and the Republican-led Congress, like an overhaul of the corporate tax code. The letter could also strike a different note than Trump on immigration.
– Earnings power: Beyond stock bets and politics, Buffett always uses his letter to update shareholders on the sprawling, US$418 billion conglomerate he's run for more than five decades. While Berkshire's share price surged 23 per cent last year, earnings through the first nine months showed more muted gains.
The addition of two manufacturing businesses, Precision Castparts and Duracell, helped lift operating profit at Berkshire by 4 per cent to US$13.2 billion through Sept. 30, even as income dropped at its railroad, BNSF.
The long-term earnings power of Berkshire's 80-odd subsidiaries are of deep importance to Berkshire shareholders. As Buffett has shifted his focus from picking stocks to buying companies outright, more of the company's value is tied to he fortunes of these businesses. Expect Buffett to devote a lot of attention to how they fared last year and what they're doing to advance their competitive positions.
Mike Faille
– The deal hunt: Cash has been piling up at Berkshire, so investors are going to want an update on Buffett's hunt for acquisitions. One possible target — Unilever — just came and went. That proposed transaction would have been done with 3G Capital, a buyout firm that Buffett has teamed up with on profitable takeovers in the food industry.
The billionaire also knows how to go it alone. He's purchased insurers, retailers, the railroad, manufacturers, newspapers, electric utilities and a network of auto dealerships. That range of interests will keep spectators guessing on what he might do next. With almost US$85 billion on hand at the end of September, there are many options.
No 'sweet spot': Buffett takes his own advice in walking away from Unilever bid
Buffett 's Berkshire does some buying raising stakes in U.S. airlines and Apple Inc
– Value-destroying fees: Buffett usually includes a passage on a general investing topic in his letter. This year, he's suggested it'll be about the fees that investment managers and consultants charge. (Hint: He thinks they're excessive.) It's part of why he's become a booster of low-cost funds that passively track stock market indexes like the S&P 500.
For some of his disciplined followers, the message has been jarring. After all, Buffett became one of the wealthiest people on the planet by refusing to settle for average returns. His example inspired legions of people to try to beat the market. Those investment pros will be eager to read his latest thoughts on the matter.
WatchS&P 500 hits 3,000 for the first time as Powell's comment lifts rate cut hopes
Stocks plunge on growth concerns, trade tensions
Dow plunges almost 800 points over flattening yield curve, lost confidence on U.S.-China trade deal
U.S. stocks fall, S&P 500 flirts with correction on fresh trade angst
Crude's bull run made this oilsands producer Canada's top stock
Legal marijuana, oil send Canadian stocks to record high
WatchCannabis shares surge at open on Senate marijuana bill passage, but gains short-lived for some
TSX hits all-time high in broad-based rally
FANG insiders are on track to sell more than $5 billion of stock
Nasdaq-listed Amazon, Alphabet halted for the day after malfunction at NYSE
U.S. markets dove today as industrial and FAANG stocks got hammered
Spotify shares surge 26 per cent in market debut via direct listing


Extend your Philips Hue system with additional white ambience spots and enjoy warm to cool white light. The Hue bridge is a smart control that comes with the starter kit. Connect the spot to the bridge and control it however you like.


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Home/chile/Joker, from Person 5, will be the first hero as DLC
Joker, from Person 5, will be the first hero as DLC
chile December 7, 2018 chile
We're on December 7th, which means Super Smash Bros. Ultimate will be available today in all stores, something Nintendo wanted to celebrate the 2018 Games awards, with an explanation that surprised us to reveal what will be the first character will come in the form of DLC to Nintendo's best video game this year.
Breaking all pools that are distributed on the net will be nothing more than nothing joker of Persona 5, which leaves the door open for the next additions to be the heroes of other third parties, although this makes us wonder in the past, will the fantastic RPG to the Nintendo's hybrid console?
We do not know when this first set of characters will be available, although we remember that you can do with season passed by Super Smash Bros. Ultimate to get the five that will arrive in the coming months and this will give you access to another set of items.
share Joker, from Person 5, is the first character to hit Super Smash Bros. Ultimate in the form of DLC [TGA 2018]


Fraser joined Andusia in January and brings a wealth of knowledge about the waste industry following 32 years in the hazardous waste sector. Spending the last 10 years managing the waste from a large regional hospital for the NHS. He has dealt with every type of waste and has a wide range of experience in sourcing disposal outlets for waste types.
Andusia recently also announced they are sole waste supplier to a new clinical waste treatment plant in Worcestershire. The new plant, which is being developed in an existing, retired plant in Malvern, is the first of its kind to be built in the UK in the last decade and is one of four planned in the next few years. From January 2020, Andusia will be supplying 40,000 tonnes of hazardous and clinical waste for high temperature treatment under a 5 year deal.
If you would like to speak to Fraser about your hazardous ro clinical waste requirements, please don't hesitate to contact him on +44 (0)7824 567603 or email fraser@andusia.co.uk.
Please contact NPAG directly for more information about the event and to book a space. Note the event is targeted at waste managers and specialitsts from across the NHS only. Tel: 01245 544600.


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Working in Germany For Members
Working in Germany: A weekly roundup of the latest jobs news and talking points
The Local - [email protected] • 11 Aug, 2021 Updated Wed 11 Aug 2021 12:08 CEST
People work on laptops at the WeWork co-working space in Berlin Potsdamer Platz. Photo: picture alliance / WeWork/dpa-tmn | WeWork
Every week The Local brings you a roundup of the latest jobs news and topics around working in Germany. Here we look at the impact of Covid on industry, the survival of the humble office, and the extension of the Kurzarbeit scheme.
Office not dying out - despite pandemic 'home office'
Regardless of the trend towards working from home in the pandemic, the office will not disappear from everyday working life for the time being, new research shows.
Although companies in Germany are still holding back when it comes to renting new office space, there has not yet been a move away from the office on a grand scale. Economists, brokers and real estate experts expect Covid to revolutionise the world of work with more people to work from home, but they believe it is premature to sound the death knell for the office.
In July, only a quarter of people were still working at home at least some of the time, according to estimates from the Munich-based Ifo Institute. Economists attribute this not only to the end of the government's 'home office obligation' for companies, which business associations opposed, but also to people wanting to socialise with their colleagues.
About a year and a half ago, millions of workers switched to the home office virtually overnight because of the pandemic; in the meantime, lots of employees are already back at their workplace.
End of home office: Are employees in Germany ready to return to the workplace?
OPINION: Why not all Germans will embrace working from home post-pandemic
"People are again looking more often for personal contact in the office," said Ifo researcherJean-Victor Alipour.
Fourth lockdown would cost 'extra €10 billion'
The Institute of the German Economy (IW) has warned against a fourth Covid lockdown in view of the threat of billions in damage to the economy.
Although large parts of the German economy are currently recovering after the lifting of many Covid restrictions, the loss of value added in the second half of 2021 would amount to €30 billion euros, the IW said this week, reported Spiegel.
A new lockdown would increase this loss by another €10 billion in the fourth quarter, the IW said.
READ ALSO: German unemployment rate drops after Covid restrictions relaxed
All in all, the IW put the damage caused by the pandemic, including the second quarter of 2021, at a massive €300 billion. A fourth lockdown would further exacerbate this balance, the pro-employer institute warned.
In view of the spreading Delta variant, the IW called for more speed in the vaccination campaign. "Both from a health and an economic point of view, the vaccination drive remains the only way out in the long term," said IW Director Michael Hüther.
Extension of the Kurzarbeit scheme - and more financial aid for businesses
At the meeting between Angela Merkel and the 16 state leaders on Tuesday, ministers agreed to continue offering financial support for businesses until the end of 2021. In addition, legislation to make it easier for employers to access funding for Kurzarbeit (shorter working hours for employees) will also be continued, according to DPA.
Munich's Ifo Institute estimates that around a million workers in Germany are currently relying on the scheme as they continue to work reduced hours.
In recent weeks, Economics Minister Peter Altmaier (CDU) and Finance Minister Olaf Scholz (SPD) had already raised the idea of continuing the bridging assistance for companies, while Labour Minister Hubertus Heil (SPD) had spoken out in favour of extending the Kurzarbeit allowance for employees working fewer hours.
Both are central government instruments worth billions to cushion the impact of the pandemic on jobs and companies.
READ ALSO: Kurzarbeit: German minister plans to extend reduced working hours scheme
A few weeks ago, the federal government decided that the 'Bridging Aid III' subsidies, which were previously limited until the end of June, would be continued as 'Bridging Aid III Plus' until September.
Now ministers will also include what they are terming a 'Restart Bonus', which will allow companies to receive higher subsidies for personnel costs if they take on new staff or bring furloughed staff back into the firm.
No decision on mandatory home office
In the days leading up to Tuesday's roundtable, several German media outlets speculated that the country would soon see a return to mandatory home office.
Proposals put forward by the Ministry for Labour and Social Affairs (BMAS) ahead of the talks envisioned a requirement for employees to work from home if the 7-day incidence of Covid infections per 100,000 people rose above 50 in a certain area.
If infection rates continue to rise, BMAS is likely to push for mandatory home office once again. Photo: picture alliance/dpa | Thomas Frey
But amid key decisions on paid-for Covid tests and Germany's health pass system, working regulations appear to have fallen by the wayside.
READ ALSO: EXPLAINED: How Germany aims to increase vaccinations and control the Covid fourth wave
"No decision was made [on mandatory home office]," a spokesperson for BMAS told The Local.
"In principle, flexible working made an important contribution to protecting the health of employees during the pandemic. Working from home is a crucial measure for minimising the risk of infection while still doing necessary work from home."
This doesn't, however, mean that the proposals are off the table. Should higher infection rates occur in autumn, mandatory home office could once again be revisited as a means of stemming the spread of the virus.
"BMAS is continuing to monitor infections very closely," the spokesperson said.
"In the event of a sharp increase in the nationwide incidence of Covid-19, BMAS advocates reinstating tried and tested measures so that home office once again becomes a mandatory requirement. More remains to be seen."
#Working in Germany


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Those who have built their family in a non-traditional way often have one common question: How can I bond with my baby if I'm not the one who carried him or her?
Here at American Surrogacy, we understand your concern. Society tells us that there is no connection like that between a pregnant woman and her child — but that doesn't mean you can't foster the same kind of connection if someone else was the one to give birth to your baby. While it may take a little extra effort, you can feel just as connected as anyone else who built their family in a "traditional" way.
For suggestions on how to forge that connection while your baby is in utero, check out this article. Here, we'll focus on the steps you can take after you bring your bundle of joy home. All babies need contact, communication and love from their parents after birth. Use these tips to create a meaningful, healthy bond with your baby from the moment they are born.
1. Pay Attention to and Respond to Your Baby's Needs.
This is the first tip for bonding with a baby for a reason — it's the cornerstone of being a successful parent. You may be overwhelmed with your new bundle of joy, especially if this is your first experience being a parent, but you will learn quickly. You may not correctly anticipate your baby's every need at first, but the more you pay close attention to them, the better you will get to know them and understand what they want. This mutual understanding will facilitate your bonding. After all, a baby will bond to the person who responds to their cries, which is why some experts advise that only the baby's parents tend to their needs during the first couple of months, to help them recognize your role in their life.
2. Take Advantage of Feeding Time.
Along the same note, feeding time is one of the most important times you can address your baby's needs. Take steps during mealtime to make eye contact, limit distractions and more to help your baby focus solely on you.
Did you know that even intended parents can breastfeed their baby? You can further facilitate this bonding by breastfeeding your child or giving plenty of skin-on-skin contact as you bottle-feed your baby. Talk with your doctor about the possibility of breastfeeding as an intended mother.
3. Don't Skimp on Affection.
Naturally, you'll be holding your baby a lot when you bring them home — whether to soothe them, feed them, or simply to marvel at this little wonder. All of this contact will comfort your baby, who will feel closer to you just from hearing your heartbeat.
Don't be afraid to lay on other kinds of affection at this time, either. You may be worried about spoiling your baby, but that's not a concern at this age. You cannot give a newborn too much affection, as it encourages the bonding process and helps them confirm you as a parental role.
Skin-on-skin contact is important for any parent bonding with their child but especially important for intended parents in surrogacy. While a baby will need to have skin-on-skin contact with the surrogate directly after birth to confirm his or her senses, the transfer to the intended parents for skin-on-skin contact is crucial to helping the baby recognize his or her parents.
Skin-on-skin contact is also helpful for improving physiologic stability for mother and baby, increasing maternal attachment behaviors, protecting against the negative effects of maternal-infant separation, and more. So, the research is clear: Don't be afraid to share this important contact with your baby directly after birth and after you bring them home.
5. Always Talk to Your Baby.
New parents are bound to do this anyway, but the importance of talking to your new baby can't be overstated. When your baby hears your voice, they are comforted that you are near, and it helps them better recognize your role as their parent.
In addition, talking to your baby helps them develop their own language skills. Children learn a lot from listening so, if you want your baby to start talking back early, don't be afraid to chat them up to help them absorb information and language.
Bringing home a new baby can be overwhelming for everyone, but especially for parents through surrogacy who are getting their first experience with their little one. Remember, your surrogacy specialist will always be here to help you prepare for this step and offer advice as you adjust to your new life as parents.
To learn more about our agency services, please contact us at 1-800-875-BABY(2229).


Follow three people who struggle with being content and come to resolution through the realization of their inherent worth and God-given blessings.
Hear a youth perspective on the meaning of the 4th commandment.
Meet Manny, a young man who's taking a few hits to his dignity from people who aren't weighing the impact of their words.
Children play on a playground and we see a glimpse of how boundaries make us free.
Four friends enjoy some time together over a board game and learn something in the process.


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Capitals Vs. Penguins: Rival Washington Heads To Pittsburgh For Early-Season Clash
The Pittsburgh Penguins will likely be without Evgeni Malkin and Sidney Crosby as they face the Washington Capitals tonight.
By Jordan Ruby Oct 13, 2011, 9:44am EDT
Share All sharing options for: Capitals Vs. Penguins: Rival Washington Heads To Pittsburgh For Early-Season Clash
It feels a little early in the season for this kind of game, but the Penguins and the Capitals are getting together Thursday night for a renewal of their budding rivalry. The game starts at 7:00 and can be seen on NHL Network and Root Sports.
The rivalry loses a little bit of it's luster because the individual matchup of Sidney Crosby and Alex Ovechkin, which the rivalry was largely built on, won't be able to happen tonight as Sidney Crosby is still recovering from the concussion. But if somebody else can still upstage Ovechkin, I'm sure Penguins fans won't be too disappointed that it isn't Crosby doing it.
The Capitals have only played two games so far this season, but they have won both of them. Ovechkin has yet to score his first goal of the year, but he still has to be treated like the threat he is.
We'll have more on this game all day, in this StoryStream. For more on the Penguins head over to PensBurgh. For more on the Caps, check out Japers' Rink and SB Nation DC.
Capitals Vs. Penguins: Pens Lose In Overtime
Arron Asham Fight: League Will Not Penalize Penguins Forward


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Q: Writing to a text file with a Servlet How to set up three textfields on a HTML page and store the data input in a text file on the server by using an Servlet?

A:     <input type="text" name="firstname" id="firstname" />
 <input type="text" name="middlename" id="middlename" />
 <input type="text" name="lastname" id="lastname" />

    in servlet

    String firstname=request.getParameter("firstname");
String middlename=request.getParameter("middlename");
String lastname=request.getParameter("lastname");

A: *

*Create a form in the HTML page and have the action set to the name of the Servlet.

*Within that Servlet, call the parameters with request.getParameter("...");

*Append the combined String to the file using something like:
PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("FileName", true)));
out.println(createFullNameString(firstName, middleName, lastName));
out.close();

redpajama_set_name: RedPajamaStackExchange


The Brentwood Library, known as the 'crown jewel' of the city, was established as a city library in 1983. At that time, there were a few shelves of paperbacks in a dry cleaner's shop. It has grown significantly.
In fact, the library, owned and operated by the City of Brentwood, has proved to be so popular that an expansion and renovation project was completed in June 2009. This expansion created a state-of-the-art 55,000-square-foot facility holding more than 150,000 collection items, 120 computers, and many welcoming spaces for readers and learners. The project included a new children's wing that provides space for children's theater productions and story time events. It also added a larger audiovisual area and several small meeting rooms equipped with computers and big screens for mini-conferences.
Every Brentwood resident or property owner has free borrowing privileges at the library, which in addition to books, also offers audiobooks, DVDs, music CDs and reference databases. A large collection of newspapers and magazines is also available.
The library is one of the busiest in Tennessee with more than 1,000 visitors daily. It has been recognized as one of the premier public libraries in the state and was named one of the nation's Top 10 Libraries for Children by Livability.com.
Visit the Brentwood Library website.


Enchanted 2007 full movie download. Featuring CARRIE UNDERWOOD' S brand new single " Ever Ever After" Disney Legend ALAN MENKEN , songs , score by Grammy Award Winning Broadway' s " Wicked" Composer STEPHEN SCWARTZ. Get the must own MUSICAL from what' s sure to be the Holiday Movie of the Year! Someone get Amy Adams on.
Fulfillment by Amazon ( FBA) is a service we offer sellers that lets them store their products in Amazon' s fulfillment centers, and we directly pack, ship, and provide customer service for these products. Hairspray is a musical romantic comedy film based on the Broadway musical of the same name, which in turn was based on John Waters' s 1988 comedy film of the same name.
The film was a British- American venture produced by Ingenious Media and Zadan/ Meron Productions. Adapted from both Waters' s 1988 script and Thomas Meehan and Mark O' Donnell' s book for the stage musical by.


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Arts & Culture » The B-List
Blue colors
This is how it always happens. In that wicked space between free radical dream association (typically involving the Queer Eyes, Michael Jackson and everyone else I hate) and my first mind-numbing beverage, I'm faced with the prospect of utter humiliation by way of the telephone interview. The phone is ringing its rhythmic hate across the room, and I'm bundled up like a junkie in severe regret. I'm shaking. I'm shaking. Omigod, Cyndi Lauper's calling and I haven't got a thing to ask her!
In fairness, I've spent many a phoner with Cyndi over the past five years, and have already asked her everything that's important to me about hair tips, wrestling and being gay (which she isn't, we should note). She is the perfection against which I measure myself and is quite possibly the mother I never had. And she's an awful interview. Or I'm an awful interviewer.
Whatever. The sky is falling. Wolf!
"Hello?" I shiver into my destiny, er, phone.
"How ah ya?" it blows back.
How am I? Practically dead, thank you. "Cyndi, I have to tell you that every time I interview you I gush and tend to ruin everything. So, um, I'm gonna try not to gush this time," I incisively Donahue.
"Um, OK. How ah ya?" she reiterates, neither taking my bait nor lessening her grip. I'm a goner.
You with your sad heart, don't be discouraged, though I realize it's hard to take courage ... is what I'm waiting for, drowning in my true colors. Instead, it's this dead air -- dead air, dead air, dead air -- and I want my mommy. In lieu of retreading the refried follicles of Cyndi's '80s heyday, I opt instead to focus on the now. After all, she has been re-signed to Epic and has just released, to remarkable acclaim, a covers album of pseudo-standards called At Last. It's awful weepy, though. And so am I.
"How was your New Year?" she softens me up, shakes me back to a relative time/space and reminds me that I have an interview to do.
"Good!" I fart. "And yours? It was very public." Cyndi did the Times Square honors, you see, soaring to the sky while the bomb -- er, ball -- dropped on Dick Clark in the middle of everybody who's anybody. I know this because I'm an idiot.
"I went out there in the middle of everybody when I was 18," she Times Squares. "So it was great to come back there and be the one up there when he was dropping the ball. It's amazing. It's been an amazing journey."
One surely highlighted by this worthless phone call, but I digress. Because I do. "You've been really, really busy over this past year," I really, really. "I don't know how you keep up, or keep yourself centered."
"Well ... ," more dead air, possibly responding to the thought that maybe she thinks I think she's too old for all of this -- which I don't. "Unfortunately, I am still very self-centered, ha ha. Every time I go out on the road, I'm more apt to be doing yoga, you know, more than I do."
Precisely why I never go out on the road. So, on to the record, then. An odd choice for reintroduction, if you don't count the fact that Cyndi's never stopped making music. (There are about four albums you haven't heard, and they're really, really good.)
"Everybody's view of things is very odd. But I always view things opposite of what they see it to be, sometimes."
I always sometimes do too.
"People view it as kitsch. I try to paint it in a color that makes it more fact. And as I tried to put it all together, I was like, 'Eh, deez ah a lot of syad tings! Let's do a little upbeat! Happy-go-lucky in some kinda way.'"
"It's a real showcase for your voice," I deflate.
"Well, it was supposed to be that."
Oh. And here's where I really flub. "It seems you've really sidestepped the nostalgia market by taking other people's nostalgia songs and making them your own," I make no sense. "You've made other people's nostalgia somehow irrelevant, mathematically."
Meanwhile, Duran Duran's playing on VH1 Classic and I just want to paint my toenails and throw up.
"There's a twist on it. As I went along, I realized that I was treating the pop songs like standards and the standards like pop songs," she is obviously related to me, mathematically. "But then again, if you're gonna reinterpret something you gotta bring what you know to the table, which is what I did."
Speaking of tables, what if I ask her about the extreme botox boredom of the Democratic primaries? Now I'm reaching. Tellingly, Cyndi was all for Carol Moseley Braun, which is sorta cool, I guess.
"I think we need an African-American woman and a white woman to run this country," she says, inserting the word "shitty" somewhere when describing Bush and asking me not to print it. "Their Clean Air Act, or whatever that is. They chop the trees down. It gives them permission to chop the trees down."
The conversation veers, safely, into "Taboo" territory, where Cyndi will go on to chastise the press for killing Rosie's Boy George fetish. Cyndi knows Boy George (or George O'Dowd, as we call him), which means I totally do too.
Realizing that all of this is going nowhere, I opt for the one comedic thing I have written on the back of my hand ... besides my own phone number. There was this one time, at band camp, when I programmed Cyndi's cell phone number into my cell phone for shits and/or giggles, and it produced both. Except when somebody sat on my phone and it speed dialed her, um, at 3 a.m. prompting her to call back all pissed off.
"Oh, yeah," she scratches her extensions. "I remember. You apologized and said that you had interviewed me and ..." blah, blah, blah.
"Well, I'm still really, really sorry," I cower.
"Oh, it's OK." She is the most perfectest person ever.
"I love you!" I crumble to the floor.
"Oh. Ha, ha."
And I'm sorry.
The B-List The B List


text:
\section{Introduction}

Line surveys of molecular gas are a treasure trove for the study of the properties and dynamics of the interstellar medium (ISM~\citealt{2001RvMP...73.1031F}). While the dominant fraction of molecular gas is molecular hydrogen (\Htwo{}), its line emission is inefficient in the cold and dense phase, due to the large spacing of its energy levels.
The energy levels of carbon monoxide (CO), on the other hand, are much more closely spaced, rendering it radiatively more efficient in the same environments. To a first approximation, the density of \Htwo{} and CO are linearly related, making CO the preferred proxy for \Htwo{}. In particular the $J=1 \to 0$ emission of $\mathstrut^{12} \text{CO}$ at $115 \, \text{MHz}$ has become the observable of choice in the study of the molecular ISM in the Galaxy. While $\mathstrut^{12}\mathrm{CO}$ is almost always in the optically thick regime, the emission from its isotopologue $\mathstrut^{13}\mathrm{CO}$ is in the optically thin regime, thus complementary (e.g.~\citealt{2014MNRAS.445.4055S}), but still bright enough to allow mapping over large regions of the Galaxy (e.g.~\citealt{2021MNRAS.500.3064S}).

Ever since its observational discovery~\citep{1970ApJ...161L..43W}, the coverage, sensitivity and angular resolution of CO surveys have continuously improved. Such surveys have enabled the study of the molecular ISM on scales as small as individual star-forming clumps of a few solar masses up to the total Galactic \Htwo{} mass of the order of $10^9 M_{\odot}$. The applications of CO surveys are thus wide-ranging. Studies of galactic structure on the largest scales, in particular of features such as spiral arms or nuclear bars are interesting in their own right~\citep{2014A&A...569A.125H}, but also offer invaluable clues for the theory of galaxy evolution~\citep{2019ARA&A..57..511K}. The processes at play in the formation and dissolution of molecular clouds can be investigated through the study of individual clouds, but also the statistical analysis of cloud catalogues (e.g.~\citealt{2017ApJ...834...57M}). As stellar nurseries, regions of dense molecular gas are central in the study of star formation~\citep{2012ARA&A..50..531K}. Due to its superior angular resolution compared to broad band emission in other wavelengths, the correlation between different emission processes relies on precise information on the molecular phases. One concrete example is diffuse emission produced by non-thermal cosmic rays~\citep{2012ApJ...750....3A}. Here, the molecular gas (together with atomic gas) provides the target for high-energy cosmic rays, resulting in the production of non-thermal gamma-ray emission, either through bremsstrahlung or the production and subsequent decay of pions into high-energy gamma-rays and neutrinos. While the study of all such processes in the Galaxy is interesting in its own right it is also important to study and calibrate the correlations with other processes in order to use the observations of CO lines for extragalactic astrophysics (e.g.~\citealt{2018ApJ...860..172S}).

Due to our vantage point in the Galaxy the galactic distribution of CO and \Htwo{} is not readily available from the gas line surveys. However, due to Galactic rotation, different emission points along a line of sight in general posses different relative velocities with respect to the observer. Thus, the emission integrated along a line of sight consists of a spectrum that encodes the distribution of emission with distance. The data products of gas line surveys thus consist of spectra for individual lines of sight, oftentimes provided on a three-dimensional grid in longitude $\ell$, latitude $b$ and velocity with respect to the local standard of rest (LSR), $\varv_{\text{LSR}}$. For a given Galactic rotation curve or more generally given a gas flow model, such spectra can be deprojected \emph{in principle} to find the three-dimensional distribution of CO and \Htwo{}.

Unfortunately, a couple of complications hamper the deprojection of the $\ell{}b\varv$-cubes of gas line surveys into a three-dimensional $xyz$-cube of gas densities:
\begin{itemize}
\item Along a given line of sight and for a given velocity, most gas flow models exhibit two distance solutions inside the solar circle. For the velocity range affected by this effect, it is a priori unclear what fractions of the emission are residing at the near and far distances. This effect is commonly referred to as the near-far-ambiguity.
\item For circular rotation, sight lines close to the Galactic centre (longitude $\ell \simeq 0^{\circ}$) and anti-centre (longitude $\ell \simeq \pm 180^{\circ}$) directions exhibit little to no radial velocity, thus lacking kinematical resolution: All emission piles up around $\varv_{\text{LSR}} = 0 \, \text{km} \, \text{s}^{-1}$ and cannot be deprojected along the line of sight.
\item Finally, peculiar velocities, that is random motions of gas on top of the large-scale gas flow, for instance due to stellar winds, supernova explosions or spiral structures, perturb the smooth mapping of distance to radial velocity. Such perturbations become visible as artefacts in the deprojected gas maps. Oftentimes, the distribution of gas gets smeared out along the line of sight, leading to the famous ``finger-of-god'' effect.
\end{itemize}

\begin{figure}[t]
\includegraphics[scale=1]{figures/vLSR_diagram_w_circles}
\caption{Contour plot of the line of sight velocity $\varv_{\text{LSR}}$ for positions $(x,y)$ in the Galactic plane, assuming purely circular motions with speed $V(R) = 220 \, \text{km} \, \text{s}^{-1}$. We also indicate lines of fixed longitude (dotted) and both, the solar circle and the tangent point circles.}
\label{fig:circular}
\end{figure}

We illustrate the first two of these issues for the simple (and unrealistic) example of purely circular rotation. In this case, the radial velocity $\varv_{\text{LSR}}$ along $(\ell, b)$ for emission from the galacto-centric radius $R$ is given by
\begin{equation}
\varv_{\text{LSR}}(R, \ell, b) = \cos b \sin{\ell} \left( \frac{R_{\odot}}{R} V(R) - V_{\odot} \right) \, .
\label{eqn:circular-vLSR}
\end{equation}
Further assuming a flat rotation curve, $V(R) = 220 \, \text{km} \, \text{s}^{-1}$, we show $\varv_{\text{LSR}}$ as a function of position in the Galactic plane ($b = 0^{\circ}$) in Fig.~\ref{fig:circular}. We have assumed the observer to be located at Cartesian coordinates $(x, y) = (R_{\odot}, 0)$ with $R_{\odot} = 8.15 \, \text{kpc}$ and the relation from longitude $\ell$, latitude $b$ and distance along the line of sight $s$ to Cartesian coordinates $x$, $y$ and $z$ is
\begin{align}
    x &= s \cos \ell \cos b - R_{\odot} \, , \label{eqn:x} \\
    y &= s \sin \ell \cos b \, , \label{eqn:y} \\
    z &= s \sin b \, . \label{eqn:z}
\end{align}

The lack of kinematic resolution around the Galactic centre and anti-centre direction is readily visible: Each point along $\ell \simeq 0, \pm 180^{\circ}$ is observed without any Doppler shift, since there is no velocity component along the line of sight. It is also evident that the near-far-ambiguity only affects positions within the solar circle, the circle centred on the Galactic centre with radius $R_{\odot}$. Here, a given velocity $\varv_{\text{LSR}} < 0$ ($\varv_{\text{LSR}} > 0$) corresponds to two solutions for $-90^{\circ} < \ell < 0^{\circ}$ ($0^{\circ} < \ell < 90^{\circ}$). The two solutions are separated by the tangent point circle: a circle of radius $R_{\odot}/2$, centred at $(x, y) = (R_{\odot}/2, 0)$, the locus of points on the line of sight that are tangent to lines of constant $\varv_{\text{LSR}}$. Note that for a given line of sight the tangent point is an extremum of $\varv_{\text{LSR}}$.

There have been a number of previous attempts of deprojecting the results of gas line surveys into three-dimensional gas distributions and each study had to adopt a way for dealing with the issues discussed above. As for the lack of kinematic resolution towards the Galactic centre and anti-centre, \citet{2006PASJ...58..847N} adopted a circular gas flow model, thus ruling out the possibility of directly reconstructing gas near $\ell = 0^{\circ}$ and $\ell = 180^{\circ}$. Instead, they resorted to interpolations between sidelines with small, but finite, radial velocities, at least for this side of the Galactic centre. The region beyond the Galactic centre with little to no kinematical resolution were excluded. \citet{2008ApJ...677..283P} instead adopted the result of a numerical simulation~\citep{2003MNRAS.340..949B} of the gas flow which includes non-circular motions. Towards the Galactic centre and anti-centre this provides several finite kinematic solutions, thus somehow aggravating the distance ambiguity, but also providing some kinematic resolution. Gas could thus be constructed also close to $\ell = 0^{\circ}$ and $\ell = \pm 180^{\circ}$ without interpolation.

As for the near-far-ambiguity, assuming an exponential or Gaussian distribution of gas in the direction perpendicular to the plane of the disk, the projection along the line of sight with a double-valued distance solution leads to a latitude profile that is composed of two Gaussians. Performing fits to the latitude distribution in individual velocity bins, thus allows to determine the relative distribution of gas between the two distance solutions. This method is know as the double Gaussian method and a number of studies have adopted this technique (e.g.~\citealt{1988ApJ...327..139C}). Both \citet{2006PASJ...58..847N} and \citet{2008ApJ...677..283P} have also used the double Gaussian method to break the near-far degeneracy in their deprojection. Specifically, \citet{2008ApJ...677..283P} iteratively deprojected limited velocity ranges, assuming a certain thermal width, until the residual velocity spectra were in agreement with observational noise. Yet, some artefacts are clearly present in their gas maps. \citet{2006PASJ...58..847N}, on the other hand, managed to suppress some potential artefacts, but at the cost of adopting a rather coarse resolution, given the level of detail and small-scale structure available in the CfA CO survey compilation.

An alternative to the deprojection that manages to evade the above mentioned problems to a certain degree is forward modelling. For this, a parametric model for the gas distribution needs to be produced. Recently, \citet{2018ApJ...856...45J} provided such models for atomic and molecular hydrogen and determined the free parameters by fits  to existing survey data. Note that here both the near-far-ambiguity and the lack of kinematic resolution are fixed by assuming a coherent distribution of gas across the offending regions. The authors managed to constrain a large number of parameters by their fit and the properties of the spiral arms bear some resemblence due to other, complementary data sets. However, as the authors admit themselves, not all the gas implied from the survey data can be succesfully deprojected such that the gas maps are to be considered as a lower limit of the real gas maps.

An important additional physical constraint that the gas densities have to fulfil but which is not leveraged by any of the previous studies is the existence of correlations. Such correlations must exist on a range of scales, and are due to a variety of processes. On the largest scales, these are due to the large-scale structure of the disk and the spiral arms, thus ultimately consequences of the formation history and density waves~\citep{2016ARA&A..54..667S}. On smaller scales, the correlations are determined by the turbulent nature of the interstellar medium~\citep{1941DoSSR..30..301K}, affecting both the fluctuation of gas density and velocity as well as magnetic fields. Modelling the three-dimensional gas density as a (Gaussian) random field, these correlation can be parametrised by the power spectrum of gas densities. In fact, there is some support for the hypothesis of a log-normal random field~\cite{1999intu.conf..218N,2001ApJ...546..980O}, thus we will consider the log of gas densities to behave like a Gaussian random field. Such a reconstruction problem for the gas density under the priors of a given correlation structure is most conveniently formulated in a Bayesian framework. We note that with a general enough inference method, the parameters for the power spectrum do not need to be assumed, but can be determined by the inference method together with the gas density. In addition, the Bayesian inference method provides not only an estimate of the gas density, but also quantifies its uncertainty. To our knowledge, none of the previous studies provided such an uncertainty estimate.

\begin{figure*}
\includegraphics[width=\textwidth]{figures/Dame_all_lb_sm} \\
\includegraphics[width=\textwidth]{figures/Dame_all_lv_sm}
\caption{\textbf{Top:} Velocity-integrated skymap of Galactic CO emission from the \citet{2001ApJ...547..792D} compilation of surveys, after correcting for the updated local parameters. \textbf{Bottom:} $\ell$-$v$-diagram of Galactic CO emission, integrated over latitudes from $-30^{\circ}$ to $30^{\circ}$, after correcting for the updated local parameters.}
\label{fig:data}
\end{figure*}

One would hope that taking into account the existence of correlations, one would be able to predict gas densities for regions for which data is less constraining, e.g. along $\ell = 0^{\circ}$ and $\ell = \pm 180^{\circ}$. The quality of the deprojected data for these regions will of course be reflected in an increased uncertainty for these regions. Additionally, it can help break the near-far-ambiguity: Due to the coherence on large scales, the two solutions with gas at different distances will not exhibit the same likelihood and the inference algorithm will thus be able to distinguish between those solutions. Finally, taking the presence of observational noise into account in our inference mehtod naturally allows denoising the observations.

The remainder of this paper is organised as follows: In Sec.~\ref{sec:method}, we briefly review the survey data used, introduce the two gas flow models we adopt and present the Bayesian method adopted for the deprojection as well as our data model. Our results are shown in Sec.~\ref{sec:results} in a variety of representations. We compare both our gas maps and supplemental results with those of previous studies. We conclude in Sec.~\ref{sec:Summary} and provide some thoughts on future directions. Details and supplemental information on one of the gas flow models are provided in appendix~\ref{app:gas_flow_model}.

\section{Method}
\label{sec:method}

\subsection{Survey data}

We are using the $\mathstrut^{12} \text{CO}$ ($1 \to 0$) line spectra as compiled by \citet{2001ApJ...547..792D}. This comprises 37 individual surveys that were performed with two 1.2 meter millimeter wave telescopes operated at Columbia University in New York City, NY, at the Centre for Astrophysics in Harvard, MA, and at Cerro Tololo in Chile. Together, these surveys cover the entire Galactic plane in longitude, extending to $\pm 30^{\circ}$ in latitude, thus covering virtually all areas for which significant emission has been reported. The velocity range is from $-319.8$ to $319.8 \, \text{km/s}$ in velocity. Between individual surveys, the angular resolution varies from $1/16$ to $1/2$, as does the rms noise level which we conservatively fix to $0.3 \, \text{K}$ per channel. The survey data were downloaded from the SAO Radio Telescope Data Centre\footnote{\url{https://www.cfa.harvard.edu/rtdc/}}.

Note that before publication the raw survey data had been corrected for the motion of the Earth and the Sun with respect to the LSR. Since the time of the publication of \citet{2001ApJ...547..792D}, better estimates of these relative velocities have become available, however. Therefore we have corrected the survey data by taking into account the updated parameter values as described in Sec.~4.1 of \citet{2018ApJ...856...52W}, adopting the parameter values of a recent, parallax-based determination of the distances to $\sim 200$ masers~\citep{2019ApJ...885..131R}. Specifically, we have coverted the standard cartesian velocity component $(U, V, W) = (10, 15, 7) \, \text{km/s}$ of the original surveys with the values $(U', V', W') = (10.6, 10.7, 7.6) \, \text{km/s}$ of model A5 of \citet{2019ApJ...885..131R}. In Fig.~\ref{fig:data}, we show two projections of the corrected $\ell b \varv$-cube, that is integrated over velocity, the so-called zero-moment map (top panel) and integrated over latitude, the $\ell-\varv$ diagram (bottom panel). In particular the $\ell$-$\varv$ diagram nicely illustrates the coherent structures that will help cure some of the deficiencies of the usual deprojection techniques.

After the deprojection, we will convert from the inferred CO emissivity to \Htwo{} gas density, adopting a linear relation between them. This relation is commonly assumed to exist between the \Htwo{} column density $N_{\mathrm{H}_2}$ and the velocity-integrated CO brightness temperature $W_{\text{CO}} \equiv \int \dd \varv \, T_{\text{b}}$, $N_{\mathrm{H}_2} = X_{\text{CO}} W_{\text{CO}}$, thus establishing the conversion factor $X_{\text{CO}}$. While the relative abundances of \Htwo{} and $\mathrm{CO}$ depend on a number of local factors (e.g.\ density, temperature, metallicity) it is customary to adopt an average value of the order of $10^{20} \, \text{molecules} \, \text{cm}^{-2} \, (\text{K} \, \text{km} \, \text{s}^{-1})^{-1}$. The value $X_{\text{CO}} = 2 \times 10^{20} \, \text{molecules} \, \text{cm}^{-2} \, (\text{K} \, \text{km} \, \text{s}^{-1})^{-1}$ with an uncertainty of $\pm 30 \, \%$ has been recommended~\citep{2013ARA&A..51..207B}. For a recent review of molecular gas surveys, see~\citet{2015ARA&A..53..583H}.

\subsection{Gas flow models}

\begin{figure}
\includegraphics[scale=1]{figures/vLSR_BEG03}
\includegraphics[scale=1]{figures/vLSR_SBM15}
\includegraphics[scale=1]{figures/vLSR_difference}
\caption{Comparison of the two gas flow models that we adopted. \textbf{Top:} $\varv_{\text{LSR}}$ for the BEG03 model. \textbf{Middle:} $\varv_{\text{LSR}}$ for the \citetalias{2015MNRAS.449.2421S} model. \textbf{Bottom:} Difference between $\varv_{\text{LSR}}$ in the BEG03 and the \citetalias{2015MNRAS.449.2421S} model. Note that the color scale is different in the bottom panel.}
\label{fig:vLSR}
\end{figure}

The distribution of CO brightness temperature in $\ell$, $b$ and $\varv$ depends, apart from the three-dimensional gas density field that we wish to reconstruct, on the three-dimensional velocity field which is also unknown. While it might seem that the assumption of purely circular rotation is the most model-independent assumption possible, it is problematic in two ways: practically, as it does not provide any kinematic resolution towards the Galactic centre and anti-centre directions and factually, as the gas flow is known \emph{not} to be purely circular in the inner Galaxy due to the well-established presence of the Galactic bar~\citep{1991ApJ...379..631B} that induces radial motions in the inner few kiloparsec. While the existence of non-circular motions is qualitatively not challenged, the details are everything but certain. In order to estimate the systematic uncertainty due to this, we have adopted two gas flow models.

The first is the result of a smoothed particle hydrodynamics simulation~\citep[][hereafter BEG03]{2003MNRAS.340..949B}. Apart from the gravitational potential of bulge and bar, some assumptions were made about the presence of spiral arms, in particular a four-armed spiral structure was assumed. The resulting $\ell$-$\varv$-diagrams exhibit some resemblance with the CO data, but clearly miss some of the finer structure of the \citet{2001ApJ...547..792D} composite survey. We show their distribution of radial velocities in the top panel of Fig.~\ref{fig:vLSR}. Here, we have extended the gas flow model with a flat rotation curve beyond $8 \, \text{kpc}$, in a similar fashion as \citet{2008ApJ...677..283P}. The assumed presence of the spiral arms is clearly visible in gradients in the velocity field. While newer simulations are available (e.g.~\citealt{2010PASJ...62.1413B,2014MNRAS.444..919P}) we have focussed here on~\citetalias{2003MNRAS.340..949B} to allow for our results to be contrasted with the ones by \citet{2008ApJ...677..283P} who used the same gas flow model.

In addition we have constructed a gas flow model based on a semi-analytical model for gas-carrying orbits in the potential dominated by the Galactic bar~\citep{2015MNRAS.449.2421S}. We provide details of our model in appendix~\ref{app:gas_flow_model}. In the middle panel of Fig.~\ref{fig:vLSR}, we show the resulting radial velocity map as seen by an observer at a distance of $8.15 \, \text{kpc}$ from the Galactic centre~\citep{2019ApJ...885..131R} at an angle of $20^{\circ}$ with respect to the major axis of the bar and moving with the velocity of the LSR. We also show the difference between the velocity fields of~\citetalias{2003MNRAS.340..949B} and the \citetalias{2015MNRAS.449.2421S} model in the bottom panel of Fig.~\ref{fig:vLSR}. Three major differences are evident: First, while the overall agreement inside the solar circle is good, the agreement in the inner $2 \, \text{kpc}$ is less so. Second, the perturbations due to the spiral structure present in the model of \citetalias{2003MNRAS.340..949B} are clearly absent in our \citetalias{2015MNRAS.449.2421S} model. The difference is mostly of the order of $\pm 10 \, \text{km/s}$, but can be as large as $\pm 30 \, \text{km/s}$ in limited regions. Finally, outside the solar circle the difference in the adopted rotation curves is marked and can lead to differences as large as $\pm 30 \, \text{km/s}$. Note however that there is little molecular gas at the relevant distances.

\subsection{Bayesian inference}

In deprojecting gas line surveys, we follow two connected goals: First, we want to reconstruct the three-dimensional gas density under the constraint that the density possesses a certain spatial correlation structure. While we can be sure that such correlations exist, the details are not well-constrained and ideally we would hope for the data to constrain the correlation structure itself. Second, we would also like to obtain an estimate of the uncertainties. Both these goals are most directly achieved by adopting a Bayesian framework.

We consider the deprojection of the three-dimensional gas density from line survey data as a high-dimensional Bayesian inference problem, that is we are seeking the posterior distribution of the gas density for the given the survey data. According to Bayes' theorem~\citep{1763RSPT...53..370B} the posterior is proportional to the likelihood, that is the probability for the observed brightness temperature given the gas density, times the prior, that is the probability of the gas density. We could constrain ourselves to finding the maximum of the posterior, however, the maximum can be uninteresting if the posterior is multi-modal or has degenerate directions. In addition, we would need to estimate the uncertainty separately, e.g.\ adopting the Laplace approximation~\citep{Laplace:1774zz} that equates the covariance at the maximum posterior position with the inverse Hessian. Instead, it is advantageous to keep track of the uncertainty while exploring the posterior.

Monte Carlo Markov Chain (MCMC) methods~\citep{Hastings:1970aa} do exactly that and they can approximate arbitrary posteriors given large enough sample sizes. However, with growing dimensionality, they become computationally expensive and for the large dimensionality of the current problem, prohibitively so. Variational inference~\citep{2016arXiv160100670B} instead approximates the posterior with a parametric distribution, for instance a multivariate Gaussian. The parameters of the parametric distribution can be determined if the ``distance'' between the approximate distribution and the true posterior can be estimated, for instance through the Kullback-Leibler divergence~\citep{1968its..book.....K}. For a multi-variate Gaussian, this would in principle involve the inversion of the large covariance matrix which is again computationally prohibitive. Instead, it has been suggested~\citep{2019arXiv190111033K} to approximate the covariance with the inverse Fisher information metric, a method known as Metric Gaussian Variational Inference. This method has recently been applied to problems ranging from reconstruction of the three-dimensional dust density in the Galaxy from reddening data~\citep{2019A&A...631A..32L} to radio interferometry~\citep{2019A&A...627A.134A}.

In practice, this is implemented as an iterative scheme, alternating between estimating the covariance at the current mean and updating the mean for the current estimate of the covariance. Specifically, adopting standardisation of the parameters, the computation of the (inverse) Fisher information metric requires the Jacobian of the standardisation map. This can be obtained either analytically or numerically by automatic differentiation. The mean is estimated by minimising the Kullback-Leibler divergence with respect to the mean. Note  that this does not require explicitly computing the covariance matrix, which would entail the inversion of the Fisher information metric. Instead, the Kullback-Leibler divergence can be estimated stochastically, that is by drawing samples from a Gaussian with said covariance, which can be implemented with implicit operators. The application of the covariance in drawing the samples constitutes a linear system that can be solved by using a conjugate gradient algorithm.

\subsubsection{Data model}

The relation between the CO emissivity $\varepsilon(x, y, z)$ that we want to reconstruct and the brightness temperature $T(\ell,b,v)$ from the \citet{2001ApJ...547..792D} survey is given by a linear map $R$ from signal space $(x,y,z)$ to data space $(\ell, b, \varv)$,
\begin{equation}
R [ \varepsilon ](\ell, b, \varv) = \int_0^{\infty} \dd s \, \varepsilon (\vec{r}) \, \delta(\varv - \varv_{\text{LSR}}(\vec{r})) \Big|_{\vec{r} = \vec{r}(\ell, b, s)} \, ,
\label{eqn:response_map}
\end{equation}
with $\vec{r}(\ell, b, s)$ specified in eqs.~\eqref{eqn:x} to~\eqref{eqn:z} above. Setting $T = R [ \varepsilon ]$ would result in a deterministic likelihood $p(T | \varepsilon)$,
\begin{equation}
p(T_{\ell b \varv} | \varepsilon_{xyz} ) = \delta \left( T_{\ell b \varv} - R [ \varepsilon_{xyz} ] \right) \, ,
\end{equation}
but we have to take into account the presence of additive noise $n$, thus altering out data model to
\begin{equation}
T_{\ell b \varv} = R [ \varepsilon_{xyz} ] + n_{\ell b \varv} \, .
\label{eqn:data_model}
\end{equation}
We assume this noise to be Gaussian distributed, $n \sim p(n) = \mathcal{G}(n, N)$, with covariance $N$ that is diagonal in harmonic space, $\tilde{N} = 2 \pi \sigma_n^2 \delta(\vec{k} - \vec{k}')$, that is white noise. Given the properties of the individual surveys combined in \citet{2001ApJ...547..792D} we fix $\sigma_n = 0.3 \, \text{K}$. We marginalise over the noise, thus obtaining a Gaussian likelihood,
\begin{align}
\tilde{p}(T_{\ell b \varv} | \varepsilon_{xyz}) &= \int \dd{n} \, p(T_{\ell b \varv} | \varepsilon_{xyz}, n_{\ell b \varv} ) p(n_{\ell b \varv}) \\
&=  \int \dd{n} \, \delta \left( T_{\ell b \varv} - R [ \varepsilon_{xyz} ] - n_{\ell b \varv} \right) \mathcal{G}(n, N) \, .
\end{align}
Finally, we have to take into account the fact that the measured $\varv$ can differ from the actual radial velocity $\hat{\varv}$ of the emitting gas, e.g.\ due to thermal line width or turbulence. We take the difference $(\varv - \hat{\varv})$ to be normal distributed with variance $\sigma_{\varv}^2$ and fix $\sigma = 5 \, \text{km} \, \text{s}^{-1}$. In principle, this requires another marginalisation, but we approximate this through a smearing of the linear map $R$ instead,
\begin{align}
& p(T_{\ell b \varv} | \varepsilon_{xyz}) \\ &\equiv \int \dd \hat{\varv} \int \dd{n} \, \delta \left( T_{\ell b \hat{\varv}} - R [ \varepsilon_{xyz} ] - n_{\ell b \varv} \right) \mathcal{G}(n, N) \mathcal{G}(\varv - \hat{\varv}, \sigma_{\varv}^2) \\
&\simeq \int \dd{n} \, \delta \left( T_{\ell b \varv} - R' [ \varepsilon_{xyz} ] - n_{\ell b \varv} \right) \mathcal{G}(n, N) \\
&= \mathcal{G} \left( T_{\ell b \varv} - R' [ \varepsilon_{xyz} ], N \right) \, ,
\end{align}
where
\begin{align}
R' [ \varepsilon_{xyz} ] &\equiv \int \dd \hat{\varv} \, \mathcal{G}(\varv - \hat{\varv}, \sigma_{\varv}^2) R [ \varepsilon_{xyz} ] \\
&= \int_0^{\infty} \dd s \, \varepsilon(\vec{r}) \, \mathcal{G}(\varv - \varv_{\text{LSR}}(\vec{r}), \sigma_{\varv}^2) \Big|_{\vec{r} = \vec{r}(\ell, b, s)} \, .
\end{align}

To be able to define the posterior distribution, we still need to specify the signal prior. We model the CO emissivity $\varepsilon(\vec{r})$ as a log-normal distributed random field, that is $s(\vec{r}) \equiv \ln (\varepsilon(\vec{r}) / \varepsilon_0)$ is normal distributed. Under the assumption that $s$ is statistically homogeneous, i.e.\ the two-point correlation in configuration space, $\langle s(\vec{r}) s(\vec{r}') \rangle$, is a function of the distance |$\vec{r} - \vec{r}'|$ only, the two-point correlation in the harmonic domain becomes ``diagonal'', that is $\langle \tilde{s}(\vec{k}) \tilde{s}(\vec{k}') \rangle = 2 \pi P(k) \delta(\vec{k} - \vec{k}')$ where $P(\vec{k})$ is the power spectrum. We further assume that the power spectrum $P(\vec{k})$ is isotropic, $P(\vec{k})$ = $P(k)$.

Instead of assuming a form for the power spectrum $P(k)$, we would like to determine it during the reconstruction as well. Following \citet{2019A&A...631A..32L}, we therefore adopt a statistical model for the power spectrum, with a Gaussian distributed normalisation $y$, a Gaussian distributed power law index $m$ and add a Gaussian random field in $\log(k)$,
\begin{align}
\sqrt{P(k)} = \exp & \left[ (\mu_y + \sigma_y \phi_y) + (\mu_m + \sigma_m \phi_m) \log(k) \right. \\
& \left. + \mathcal{F}^{-1} \!\! \left\{ \frac{a}{1 + t^2/t_0^2} \tau(t) \right\} \right] \! .
\end{align}
Here, $\phi_y$ and $\phi_m$ are random variables and $\tau(t)$ a random field (in $\log(k)$) that are encoding the power spectrum and are reconstructed at the same time as the signal itself. $\mathcal{F}^{-1}$ represents the inverse Fourier transform from the variable $t$ that is the conjugate of $\log(k)$. The parameters, $\mu_y$, $\sigma_y$, $\mu_m$, $\sigma_m$, $a$ and $t_0$ are meta-parameters and we have fixed them to the following values: $\mu_y = -13$, $\sigma_y = 0.1$, $\mu_m = -4$, $\sigma_m = 0.1$, $a = 1$ and $t_0 = 0.1$. We stress that the above representation of $P(k)$ is flexible enough to closely approximate the true underlying power spectrum for $k$ where the data is constraining enough; where it is not, the shape is interpolated or extrapolated.

Finally, assuming $s$ to be a homogeneous random field must fail when the deviations from this assumption for the real gas density become too strong. This is certainly the case when considering the confinement of molecular gas to the Galactic plane. In order to not be biased in the reconstruction, we have scaled the log-normal signal field $\varepsilon_{xyz}$ with an exponential profile in $z$, $\exp[ - |z|/z_h ]$. We have adjusted $z_h$ to values such that the signal field $\varepsilon_{xyz}$ averaged over different portions of the Galactic disk does not show strong gradients in the $z$-direction and found $z_h = 40 \, \text{pc}$ to give satisfactory results. We have also tested a Gaussian profile $\exp[ - z^2/(2 \sigma_z^2) ]$, but found the results to be virtually unchanged.

\subsubsection{Details on the implementation}

As we are performing our computations on a computer, the signal field is not a continuous field of gas densities, but rather a discretised version thereof. We adopt a Cartesian grid with the $x$, $y$ and $z$-coordinates indexed with $\alpha,\beta,\gamma$, that is $\varepsilon_{\alpha \beta \gamma} = \varepsilon(x_\alpha, y_\beta, z_\gamma)$. Specifically, we have considered a $512 \times 512 \times 16$ Cartesian grid stretching from $-16 \, \text{kpc}$ to $16 \, \text{kpc}$ in the $x$- and $y$-directions and from $-0.5 \, \text{kpc}$ to $0.5 \, \text{kpc}$ in the $z$-direction, thus achieving a spatial resolution of $1/16 \, \text{kpc} = 62.5 \, \text{pc}$.

Given that the data are the spectra from a binned survey, they are already discretised, that is $T_{i j k} = T(\ell_i, b_j, \varv_k)$. We have degraded the data from their native resolution on a $2880 \times 481 \times 493$ grid to a $1440 \times 241 \times 247$ grid. The discrete version of the linear map of eq.~\eqref{eqn:response_map} is
\begin{equation}
R_{ijk}^{\alpha \beta \gamma} \!\! = \!\! \int \! \dd \ell \, \dd b \, \dd \varv \, \dd s \, \frac{\varepsilon_{\alpha\beta\gamma}}{\Delta\ell \Delta b \Delta \varv}  \theta(\text{if $\vec{r}$ in ${\alpha\beta\gamma}$} ) \delta(\varv \! - \! \varv_{\text{LSR}}(\vec{r})) \Big|_{\vec{r} = \vec{r}_{ijk}} \! .
\end{equation}
Our data model, eq.~\eqref{eqn:data_model}, can thus be represented by a multiplication with the sparse matrix $R_{ijk}^{\alpha \beta \gamma}$.

For a specific implementation of the Gaussian variational inference, we have made use of the \texttt{nifty5} package\footnote{\url{https://gitlab.mpcdf.mpg.de/ift/nifty}}.

\section{Results and Discussion}
\label{sec:results}

\begin{figure*}[!th]
\includegraphics[width=\textwidth]{figures/surfmassdens_mean_uncert_BEG03} \\
\includegraphics[width=\textwidth]{figures/surfmassdens_mean_uncert_SBM15}
\caption{Two-dimensional projection of reconstructed three-dimensional maps of molecular hydrogen. \textbf{Top left:} Mean gas surface density $\Sigma$ for the \citetalias{2003MNRAS.340..949B} gas flow model. \textbf{Top right:} Standard deviation of the gas surface density $\Sigma$  for the \citetalias{2003MNRAS.340..949B} gas flow model. \textbf{Bottom left:} Mean gas surface density $\Sigma$ for the \citetalias{2015MNRAS.449.2421S} model. \textbf{Bottom right:} Standard deviation of the gas surface density $\Sigma$ for the \citetalias{2015MNRAS.449.2421S} model.}
\label{fig:mean_uncert}
\end{figure*}

The main result of our analysis are the 3D gas maps obtained from the two gas flow models and the corresponding uncertainties. Our gas maps provide the highest resolution three-dimensional deprojections of CO gas line surveys to date with a number of robust and well-localised emission regions and should prove useful in the study of Galactic structure and diffuse emission. We make our maps available to the community\footnotemark.

\footnotetext{\url{http://dx.doi.org/10.5281/zenodo.4405437}}

In Fig.~\ref{fig:mean_uncert} we show the projection of the \Htwo{} density onto the Galactic plane and its standard deviation, both for the BEG2003 gas flow model (top panels) and the \citetalias{2015MNRAS.449.2421S} gas flow model (bottom panels). For either gas flow model, the survey data have been successfully deprojected into localised clusters of emission. The total gass mass reconstructed is $1.1 \times 10^9 M_{\odot}$ for the \citetalias{2003MNRAS.340..949B} model and $1.6 \times 10^9 M_{\odot}$ for the \citetalias{2015MNRAS.449.2421S} model.

Some elongated structures, spurs or spiral arm segments are immediately visible. Some of the structures are more easily visible for the \citetalias{2003MNRAS.340..949B} model than for the \citetalias{2015MNRAS.449.2421S} model. For instance, the two vertical spurs stretching from $(x, y) = (4, -1) \, \text{kpc}$ to $(x, y) = (4, 3) \, \text{kpc}$ and from $(x, y) = (6, -1) \, \text{kpc}$ to $(x, y) = (6, 3) \, \text{kpc}$, respectively, are easily identified for the \citetalias{2003MNRAS.340..949B} model (top left panel of Fig.~\ref{fig:mean_uncert}), but blend into a more extended emission for the \citetalias{2015MNRAS.449.2421S} model. Revisiting Fig.~\ref{fig:vLSR} and in particular its bottom panel, it is clear that such structures are oftentimes linked to local extrema in the radial velocity field. For instance the two spurs discussed above coincide with maxima of the velocity field of the \citetalias{2003MNRAS.340..949B} model, but are absent in the \citetalias{2015MNRAS.449.2421S} model. These are due to the spiral arms which have been put in by hand in the case of the \citetalias{2003MNRAS.340..949B} model, but not in the \citetalias{2015MNRAS.449.2421S} model. We can also identify a spur that coincides with the tangent point circle, stretching from $(x, y) = (2, -3) \, \text{kpc}$ to $(x, y) = (6, -4) \, \text{kpc}$. This is likely an artefact pointing to too narrow a velocity range in the \citetalias{2015MNRAS.449.2421S} model.

\begin{figure*}[p]
\centering
\includegraphics[scale=1]{figures/surfmassdens_BEG03} \\
\includegraphics[scale=1]{figures/surfmassdens_SBM15}
\caption{Projected mean gas density $\Sigma$ on a logarithmic colour scale, overlaying both contours in $\varv_{\text{LSR}}$ and a grid in longitude. \textbf{Top:} For the \citetalias{2003MNRAS.340..949B} gas flow model. \textbf{Bottom:} For the \citetalias{2015MNRAS.449.2421S} model.}
\label{fig:details1}
\end{figure*}

We note that the gas density comprises a rather large dynamical range as expected for a log-normal density. Some of the fainter features are therefore difficult to identify on a linear scale. In order to highlight them, we show the mean of the posterior, again projected onto the Galactic plane on a logarithmic colour scale in Fig.~\ref{fig:details1}. We have also overlaid a longitude grid and the contours of the respective radial velocities. This should allow to more easily identify certain features with the corresponding features in the $\ell-\varv$-diagram of Fig.~\ref{fig:data}.

\begin{figure*}[p]
\centering
\includegraphics[scale=1]{figures/surfmassdens_snr_BEG03_spiral} \\
\includegraphics[scale=1]{figures/surfmassdens_snr_SBM15_spiral}
\caption{Signal-to-noise ratio S/N of the mean gas density, with the spiral arms of \citet{2019ApJ...885..131R} overlaid. \textbf{Top:} For the \citetalias{2003MNRAS.340..949B} gas flow model. \textbf{Bottom:} For the \citetalias{2015MNRAS.449.2421S} model.}
\label{fig:details2}
\end{figure*}

\begin{figure*}[t]
\includegraphics[scale=1]{figures/BEG03} \includegraphics[scale=1]{figures/SBM15} \\
\includegraphics[scale=1]{figures/nakanishi_sofue} \includegraphics[scale=1]{figures/pohl_et_al} \\
\caption{Comparison of both our gas surface density construtions (top left and top right) with those of \citet{2006PASJ...58..847N} (bottom left) and \citet{2008ApJ...677..283P} (bottom right).}
\label{fig:comparison}
\end{figure*}

However, looking at the mean of the posterior alone can be misleading as some of the localised features also have a rather large uncertainty. Unlike the previous deprojections, however, we now have a means of judging the validity of certain features by comparing the mean $\mu$ of the posterior with its uncertainty $\sigma$. To this end, we define a signal-to-noise ratio (S/N) as $\mu / \sigma$. We show S/N in Fig.~\ref{fig:details2}, again for the \citetalias{2003MNRAS.340..949B} model in the top panel and in the bottom panel for the \citetalias{2015MNRAS.449.2421S} model. One can clearly identify localised emission with a S/N ratio of 3 or higher. In Fig.~\ref{fig:details2}, we have also overlaid the spiral arms, as determined from fits to a set of $\sim 200$ masers~\cite{2019ApJ...885..131R}. (See their Tbl.~2 for the fitted spiral parameters.) Many of the local emission features obtained for either gas flow model can be easily associated with a spiral arm: for the \citetalias{2003MNRAS.340..949B} model for all spiral arms, but most impressively for the Norma, Sagittarius-Carina, Local and Perseus arms. We comment on a couple of noteworthy differences and similarities between the significant features obtained for the \citetalias{2003MNRAS.340..949B} and the \citetalias{2015MNRAS.449.2421S} models:
\begin{itemize}
\item The gas density in the \citetalias{2015MNRAS.449.2421S} model is generally more scattered and does not cluster in regions as large as the emission in the \citetalias{2003MNRAS.340..949B} model. This is again due to the presence of local extrema in the radial velocity field in the \citetalias{2003MNRAS.340..949B} model which boost the clustering. Such local extrema are all but absent in the \citetalias{2015MNRAS.449.2421S} model and hence the gas density is less clustered.
\item Yet, some of the spiral arms are obvious also for the \citetalias{2015MNRAS.449.2421S} model, e.g. the segments along the Scutum-Centaurus and the Sagittarius-Carina arms for galacto-centric azimuths $\varphi$ between $\sim 200^{\circ}$ and $\sim 280^{\circ}$. Other examples are the segments along the Norma arm ($90^{\circ} \lesssim \varphi \lesssim 150^{\circ}$), the local arm ($330^{\circ} \lesssim \varphi \lesssim 0^{\circ}$).
\item Some emission, in particular beyond the solar circle, is placed at different distances in the \citetalias{2003MNRAS.340..949B} and \citetalias{2015MNRAS.449.2421S} models due to the different rotation curves adopted here. Given the rather small velocity gradient, this easily translates into differences of the order of a kiloparsec and thus affects the association with spiral arms. One example is emission around $\ell \sim 110^{\circ}$ and with $\varv_{\text{LSR}}$ between $-60$ and $-50 \, \text{km}/\text{s}$, see Fig.~\ref{fig:data}, bottom panel. With the \citetalias{2003MNRAS.340..949B} model, this emission is located around $(x, y) = (10, -6) \, \text{kpc}$. With the \citetalias{2015MNRAS.449.2421S} gas flow, this instead ends up at $(x, y) = (9.5, -5) \, \text{kpc}$. In the former case, an association with the Norma arm suggests itself, in the latter case, the association with the Perseus arm is more likely.
\end{itemize}

In Fig.~\ref{fig:comparison}, we revisit the mass surface densities obtained with either gas flow model (top panels) and compare them with the deprojections of \citet{2006PASJ...58..847N} (bottom left) and \citet{2008ApJ...677..283P} (bottom right). Note that all gas densities are shown with the same dynamical range, however, the mass surface density of \citet{2006PASJ...58..847N} is significantly smoother. Some similarities are apparent between the map of \citet{2008ApJ...677..283P} and our maps. This is even more so the case for our map that is based on the \citetalias{2003MNRAS.340..949B} model, the same gas flow model adopted by \citet{2008ApJ...677..283P}. However, there are also some differences:
\begin{itemize}
\item Spiral arms are more homogeneous in \citet{2008ApJ...677..283P}. While in our reconstruction, the width is oftentimes varying along the segments, in the gas density of \citet{2008ApJ...677..283P}, some ring segments appear to have constant width. This might be an artefact of the particular algorithmic reconstruction chosen there.
\item An artefact, that is affecting both the \citet{2008ApJ...677..283P} map and our \citetalias{2015MNRAS.449.2421S} map is the emission concentrated along an arc of the tangent point circle (see discussion above).
\item The peak in the gas density reconstructed for both our gas flow models near $(x, y) = (-9, 2) \, \text{kpc}$ is absent in the \citet{2008ApJ...677..283P} map, possibly due to the chosen suppression at large galacto-centric radii.
\item Another class of artefact, that is apparent in the \citet{2008ApJ...677..283P} maps are the features elongated along the lines of sight, the so called ``fingers of god'', especially in regions of low gas densities. These are almost completely absent in our reconstructions.
\item Finally, \citet{2008ApJ...677..283P} show some gas density in regions where we have found (almost) none, in particular beyond the solar circle. Unlike the structures solidly identified with spiral arms of the \citetalias{2003MNRAS.340..949B} model, some of these might actually be statistically not significant. This is to be compared with emission seen for our reconstruction in Fig.~\ref{fig:details1} near $(x, y) = (-14, -1) \, \text{kpc}$ and $(x, y) = (-14, -4) \, \text{kpc}$ which is not statistically significant, see Fig.~\ref{fig:details2}.
\end{itemize}

\begin{figure}[htb]
\includegraphics[scale=1]{figures/profiles}
\caption{Radial profiles of the surface mass density $\Sigma_{\mathrm{H}_2}$ (top panel), FWHM of the $z$-profile (middle panel) and midplane offset (bottom panel). We compare the results for both our gas flow models (\citetalias{2003MNRAS.340..949B} and \citetalias{2015MNRAS.449.2421S}) with the results of earlier studies: \citet{1987ApJ...315..122G}, \citet{1988ApJ...324..248B} and \citet{2006PASJ...58..847N}.}
\label{fig:profiles}
\end{figure}

We conclude our discussion by looking at some properties of the derived distributions in galacto-centric radius. In Fig.~\ref{fig:profiles}, we have plotted the surface mass density averaged in galacto-centric rings $R_i \leq R < R_{i+1}$ where $R_i = i \Delta R$ with $\Delta R = 0.5 \, \text{kpc}$. Close to the Galactic centre, the average gas density is a few tens of $M_{\odot} \, \text{pc}^{-2}$ and subsequently decreases towards $r \simeq 3 \, \text{kpc}$. Beyond, there is a local maximum at $r \simeq 5 \, \text{kpc}$, the well-established molecular ring (or possibly a convergence of spiral arms~\cite{2012MNRAS.421.2940D}). Here, we find the average gas density to be $\sim 1 \, M_{\odot} \, \text{pc}^{-2}$. Beyond, the gas density decreases further. While it appears to reach a plateau of $2 \times 10^{-2} M_{\odot}$ around $12 \, \text{kpc}$, we recall that we have not detected much significant emission beyond $r \simeq 10 \, \text{kpc}$.

We have fitted Gaussian profiles $g_i(z) \propto \exp[-(z-z_{0,i})^2/2 \sigma_i^2]$ with means $z_{0,i}$ and standard deviations $\sigma_i$ to the gas density distribution in the same galacto-centric rings $i$ as before by minimising the $\chi^2$ over all rings,
\begin{equation}
\chi^2 \equiv \sum_i \sum_{\gamma} \frac{ \langle n_{\Htwo{},\alpha\beta\gamma} \rangle_{\alpha\beta,i} - g_i(z_\gamma) }{\tilde{\sigma}_i^2} \, .
\end{equation}
Here, $\langle \mathellipsis \rangle_{\alpha\beta,i}$ denotes the averaging over all grid points $\alpha\beta$ in the $i$-th ring. We have fixed the uncertainty $\tilde{\sigma}_i$ to $0.15$ of the maximum of $\langle n_{\Htwo{},\alpha\beta\gamma} \rangle_{\alpha\beta,i}$ for that particular ring $i$. For most rings, the Gaussian profile is a fair approximation, $\chi^2 < 1$. (Of course, different $z$ will be correlated, hence $\chi^2$ is usually $< 1$.) For other rings, however, the average profile in $z$ is only poorly described by a single Gaussian (see also~\citealt{1985ApJ...297..751D}). We have thus removed these bins. We stress that the ensemble of samples from the posterior consists of full 3D distributions. Also uncertainties and correlations contained, so allow for any statistical analysis beyond the axisymmetric quantities and simple error estimates.

We show the FWHM, that is $2 \sqrt{2 \log 2} \sigma$, a measure of the vertical extent of the gas distribution, as a function of galacto-centric radius in the middle panel of Fig.~\ref{fig:profiles} and compare to a number of previous estimates. We note that our reconstructed gas densities seems to be more extended vertically, at least in the inner few kiloparsecs. Note that \citet{2008ApJ...677..283P} does not determine this parameter but instead uses it as an input for the analysis.

In the bottom panel of Fig.~\ref{fig:profiles}, we show the dependence of the midplane offset $z_0$ on the galacto-centric radius and again compare to a number of previous estimates. While the general trend with galacto-centric radius is the same as that seen in previous studies, our error bars are consistently smaller. We stress that the ensemble of samples from the posterior consists of full 3D distributions. Also uncertainties and correlations contained, thus allowing for any statistical analysis beyond the axisymmetric quantities and simple error estimates.

\section{Summary}
\label{sec:Summary}

We have presented a new deprojection of the CO line survey of~\citet{2001ApJ...547..792D} with unprecedented spatial resolution of $62.5 \, \text{pc}$. This is based on a Gaussian variational Bayesian inference which allows exploring the posterior distribution of this high-dimensional inference problem. While we have assumed correlations in configuration space to exist, we have not assumed any particular power spectrum, but determined the power spectrum during the reconstruction. We have considered two gas flow models, that both take into account the presence of the Galactic bar, one based on a simulation of the gas flow in a predetermined potential~\citep[]{2003MNRAS.340..949B}[BEG03], the other based on a a model for gas carrying orbits in the bar potential~\citep[]{2015MNRAS.449.2421S}[SBM15].

Our results are the three-dimensional distribution of molecular gas, assuming a fixed $X_{\text{CO}}$ factor of $2 \times 10^{20} \, \text{molecules} \, \text{cm}^{-2} \, (\text{K} \, \text{km} \, \text{s}^{-1})^{-1}$. We have made our mean gas maps and their uncertainty available to the community\footnotemark[\value{footnote}]. We have shown the mean and the standard deviation of the gas density projected onto the Galactic plane and compared with previous studies. Unlike those earlier studies, we have the capacity to distinguish between statistically significant structures and noise artefacts. We have found that some of the most prominent structures are influenced by the assumed spiral structure in the \citetalias{2003MNRAS.340..949B} gas flow model, but that significant coherent structures, some of which align with spiral arms (as for instance defined by parallax measurements of masers) are present in the \citetalias{2015MNRAS.449.2421S} model as well. We have projected some radial profiles out of the 3D gas distribution and found the results of previous studies largely confirmed.

In the future, a couple of extensions of the current analysis are noteworthy. Having successfully applied our methodology to molecular line surveys to determine the \Htwo{} density it would be interesting to apply it to surveys of atomic hydrogen, like the recently completed HI4PI survey~\citep{2016A&A...594A.116H}. While the HI distribution is known to show less clustering than molecular hydrogen, we are optimistic that the advantages of our approach carry over. In addition, a couple of shortcomings of the present study are due to our ignorance of the gas flow. If the velocity field could be determined at the same time as the gas density, such deficiencies could be remedied. We can envisage two ways to help regularise this underdetermined problem: Data from the above mentioned parallax measurements~\citep{2019ApJ...885..131R} could be included, thus providing at least a couple of loci to which the velocity field could be anchored. In addition, physical correlation between gas densities and flow velocities could link the reconstruction of both fields, of course, this would require additional model inputs.

\bibliographystyle{aa}

redpajama_set_name: RedPajamaArXiv


I wrote this lj entry.
So, I did walk home from Federal Street, Boston to Somerville. It took 1 hour and 5 minutes to walk along the snowy route (bus 92, specifically). The route is approximately (as far as I can tell from MapQuest) about 3.36 miles. Not too bad for snow-covered streets and one annoying traffic problem.
I then checked my email, which told me that ye olde GM creature was home sick and that we could have our mini session early, and so I went and got a bus pass (much sighs for my stupidity aside) and met up for mini gaming.
Chloe talked to her coach (she went home to France). He will not change what he did to her, admits to it, and apparently gave her the pendant. He is not aware that she knows a lot more than she is letting on. So, life is sort of good.
However, her coach is still working with her boyfriend and it looks like he is doing something to Xavier that is less than healthy. So, Chloe left France feeling disconnected from her boyfriend by both the distance to the States, the distance of time (4 months or so apart), and the distance of events (well, Chloe has been beaten by a ravenger and mauled by a werewolf among other things). So, Chloe gets to start off the next session mildly depressed.
And then I went back to Davis to catch bus 90, which just left as I was getting to the stop, so I continued to Powderhouse and caught the 89. And then I came home and had a single piece of chocolate and some potato things and checked email and did stuff and now I am going to stretch a bit and then probably go to bed.
Listening to: clementines, darn you solipsisnation!


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En > Aviation events > > Crash > Spectacular slowed fall of a Cirrus SR22
Video - Spectacular slowed fall of a Cirrus SR22
Published on 11/03/2016 11:00 | Updated on 22/12/2016 10:36 - By aeronewstv.com
Spectacular slowed fall of a Cirrus SR22
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Two people escaped almost totally unscathed after their plane, a four-seater single-engine Cirrus SR22, fell out of the sky. A surveillance camera recorded the scene.
The incident, which occurred on 5 March, right next to an office building on Long Island, USA, was due to engine failure according to US media. The occupants of the aircraft, a father and daughter, received only minor injuries.
It was the deployment of the Cirrus' Airframe Parachute System, at about 1,000 ft (500 metres), that prevented a tragedy.
More than a hundred lives have been saved thanks to the existence of this type of parachute on their 'planes, estimated US manufacturer, Cirrus Aircraft, whose headquarters are located in Duluth, Minnesota.
This type of parachute for light aircraft was developed by BRS Aerospace. It is fitted as standard on all Cirrus SR20's since it was certified in 1998, and can also be mounted on Cessna's.
In January 2015, off the Hawaiian Islands, having run out of fuel, but again thanks to its onboard parachute system, a Cirrus SR22 had an even softer landing in the Pacific Ocean. The pilot who was safe and sound was rescued by boat.
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Solar Flares May Bring Major Aurora, Minor Disruptions
By By Alex Sosnowski, expert senior meteorologist.
March 11, 2012, 11:16:43 PM EDT
A series of solar flares this week may yield additional episodes of the aurora borealis (Northern Lights).
Areal coverage of the displays produced by each coronal mass ejection are difficult to gauge ahead of time. The Northern Lights were visible over part of the Great Lakes region Wednesday night.
The best chance for viewing the show tonight, if the Earth's magnetosphere cooperates, will be in the northern Plains, part of the Midwest and much of the West.
There will be a nearly full moon tonight, which could detract from viewing the show somewhat. However, the display was still impressive last night, despite the full moon.
Experts at Space Weather.com state that not only do the magnetic storms unleashed by the flares cause the aurora borealis, but they can be somewhat disruptive.
The expanse of the Northern Lights and disruptions depend on whether or not the flare directly strikes the Earth versus a glancing blow, as well as the strength of the coronal mass ejection itself.
In the extreme case, there can be brief disruptions to radio and gps signals.
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Q: Finding the Transformation of a Matrix I am working on learning how to solve matrix problems similar to this one and would appreciate an example if someone were willing to walk me through it.

Let T: $R^2$ -> $R^3$ Have the standard matrix
  $$ \begin{bmatrix} 1\space\space\space\space\ \ 2 \\ 2\space\ -1 \\ 1 \space\space\space\space\space\ \ 0  \end{bmatrix} $$
   B is the basis $B$ = $ \{\ \begin{bmatrix}  1 \\ 1 \end{bmatrix} \ \ ,\ \begin{bmatrix}  1 \\ -1  \end{bmatrix} \ \}\ of \space R^2 $$
\quad \text {C is the Basis} \ C = $$ \{ \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix} , \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} , \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}\} \space of \space R^3$ Find the matrix for $T$ relative to the Bases $B$ and $C$

Any suggestions will be appreciated

A: You know that $T(1,1)=T(1,0)+T(0,1)=(1,2,1)+(2,-1,0)=(3,1,1)$.
Now you need to find the vector $(3,1,1)$ w.r.t. the basis $C$. Thus you need to solve the following system of equations:
$$\begin{pmatrix}
1&0&1&\mid&3\\
0&1&1&\mid&1\\
1&1&0&\mid&1
\end{pmatrix}=\begin{pmatrix}
1&0&1&\mid&3\\
0&1&1&\mid&1\\
0&1&-1&\mid&-2
\end{pmatrix}=\begin{pmatrix}
1&0&0&\mid&\frac{3}{2}\\
0&1&0&\mid&-\frac{1}{2}\\
0&0&1&\mid&\frac{3}{2}
\end{pmatrix}$$
Hence $(3,1,1)=\frac{3}{2}(1,0,1)-\frac{1}{2}(0,1,1)+\frac{3}{2}(1,1,0)$. It follows that the matrix of $T$ w.r.t. the bases $B$ and $C$ is given by $$\begin{pmatrix}
\frac{3}{2}&*\\
-\frac{1}{2}&*\\
\frac{3}{2}&*
\end{pmatrix}$$.
Find the second column yourself. The key is to remember that the matrix of a transformation $P$ w.r.t. the bases $A$ and $B$ is given by the following procedure:
Find $P(a_i)$ ($P$ applied to the $i$-th basisvector of $A$). Write $P(a_i)=\sum_{j}\lambda_{ji}b_j$. That is, write $P(a_i)$ w.r.t. the basis $B$. The coefficients $\lambda_{ji}$ make up the $i$-th column of the matrix that we are looking for.