text:
Junior learns about world through first-hand experience
"The world is a book, and those who do not travel, read only a page," Saint Augustine wrote.
Not only does junior Cayleigh Reeder travel in books, but she does in person as well.
"My parents think that travel is perfect family time and experiences worth having. I've enjoyed every trip. But I hope to continue to travel with them even after I leave home," Reeder said.
The Reeder family has traveled to many places around the world.
"We went to Thailand three or four years ago. We've gone to the old and new Mexico, almost everywhere in the Northwest U.S., Canada, Seattle, Alaska, which was different and unique, New York, Yellowstone, the Grand Canyon, Alabama, Georgia, and North Carolina," Cayleigh's father, Bruce, Reeder said.
Of the many trips, Reeder's favorite was a cruise to Alaska, which was her first cruise.
"My favorite memory was probably the last night of the cruise [to Alaska]. My brother and I and the two new friends we had made ate dinner together, dinners on the ship were to die for, and then we played hide and go seek and shuffle board out on the deck. Sounds lame…but it was amazing," Reeder said. "Dog sledding was amazing. We went by helicopter from where the ship docked up to the glacier. There was a little camp complete with dog houses, tent kitchen, and sturdy living tents. The ride was a fairly short little circle, but it was an amazing experience all the same."
The Reeder family has also gone to Thailand to visit Bruce Reeder's college friend Jeff Horey and his family Kai, his wife, and Grace, their daughter, who is about the same age as Reeder. The Horey family owns an ostrich farm in Thailand and goes their every summer. Last summer the Horey family was accompanied by the Reeder family.
"When she was in Thailand, she traveled with one of her old friends and she was always afraid that when her old friend, who spoke Thai fluently, spoke to someone in Thai, that they were talking about her," junior Nikki Gregory said.
Gregory traveled to Maryland with Cayleigh during the second week of November to visit her grandparents at their farm.
"We always have fun together. When we went to Maryland we looked at the boards for the flights and like 10 minutes later we found out we were looking at arrivals instead of departures, we felt pretty stupid," Gregory said.
According to Bruce Reeder, his family "makes a point of traveling," almost every summer they travel to "show [the kids] different ways of life."
"I like the opportunity to experience new things together. Every new place we visit is an adventure. I like to see their enjoyment and fears', it's neat to enjoy it and see it through their eyes," he said.
Travel plays a major role in Cayleigh's life.
"I got to travel a lot as a kid; you learn about the world, you get more accepting of the world. It expands your horizon and makes you more open minded. I think everyone should travel as much as they can. It would make the world a better place if people would just travel," Bruce Reeder said.
Bu Genna Owen
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Soccer injury opens door to art
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Seventh-grader strives to bring gymnastics talent to 2016 Olympics
Competitive pizza-tosser gains national attention
Spider-Man is a homerun for Marvel
Winter Break heads into cruise mode
Marvel's 'Hawkeye' debuts to mixed reviews


text:
import * as actionCreators from './store/action-creators';
import {getTotal, getItems} from './store/selectors';
import ReactDOM from 'react-dom';
import React from 'react';
import {Provider} from 'react-redux';
import CartContainer from './components/cartContainer';
import store from './store';

// Get all information about items in the cart
export const cart = () => getItems(store.getState());
export default cart;

// Get total cost of all items in cart
export const total = () => getTotal(store.getState());

// Clear all items from cart
export const clear = () => store.dispatch(actionCreators.clear());

// Add item to cart
export const add = (item) => store.dispatch(actionCreators.add(item));

// Remove item from cart
export const remove = (query) => store.dispatch(actionCreators.remove(query));

export const component = () => {
  return (
    <Provider store={store}>
      <CartContainer />
    </Provider>
  );
};

export const mount = (element) => {
  return ReactDOM.render(component(), element);
};

redpajama_set_name: RedPajamaGithub


text:
March 25, 2010 Culture » Visual Arts
Invisible no more: a survivor of Uganda's war tells his tale
By Whitney Bryen
Invisible Children: Rough Cut and Ugandan guest speaker Tony Bazilo
Monday, March 29, 7 p.m.
Armstrong Theatre, 14 E. Cache la Poudre St.
Free; visit coloradocollege.edu for more.
Silent Auction and Benefit Dinner
Thursday, April 1, 6:30 p.m.
Bemis Hall, 920 N. Cascade Ave.
Tickets: $5; call 389-6607 or visit invisiblechildren.com and outreachuganda.org.
Tony Bazilo was the definition of an "invisible child" when three young American filmmakers met him in 2003. But today he travels the United States speaking about his experiences growing up in war-torn Uganda, and raising awareness about the struggles others are still facing to rebuild his country.
Hosted by the Colorado College chapter of Invisible Children (a global movement to end conflict in Uganda), Bazilo will share his inspiring story Monday, following a showing of Invisible Children: Rough Cut, the documentary that features him at age 14.
Bazilo wasn't even born yet when two main rebel groups, the Lord's Resistance Army (LRA) and the Allied Democratic Forces (ADF), began fighting the Ugandan government for political power. He was forced to move to a domestic refugee camp at age 8, where he lived with his mother and 50,000 others — a small fraction of the more than 2.5 million people who were displaced overall.
Dealing with overcrowding and avoiding rampant HIV — the disease that killed his father — were among the worst challenges he faced there, but another one was simply getting an education. Rebel armies would attack children walking to and from school, kidnapping them and forcing them to become soldiers.
"What they were doing is, if you are a kid and they find you living with parents or your relatives, they'll kill them in your presence and take you to fight with them," Bazilo says. "The rebels knew where the camps are, and waited to abduct us until we left for school."
This was a daily fear for Bazilo and his friends, and the focus of the documentary.
The Rough Cut filmmakers, Jason Russell, Bobby Bailey and Laren Poole, returned to Uganda after shooting and provided funding for Bazilo and others in similar circumstances to pursue higher levels of education similar to high school, a costly privilege 90 percent of Ugandans will miss. Once he's done touring with Invisible Children, Bazilo plans to attend college in southern Uganda to help support and rebuild his country from the destruction of the war, which continues today.
"To me, the filmmakers came as a light in the morning," Bazilo says. "They allow[ed] me to go to school and soon college. I want to help raise money for others to do that too, because you can see from me and my friends who also [work with Invisible Children] that we can be better and have better lives now."
The Invisible Children group at CC will help raise money for the international organization's efforts to support Uganda natives like Bazilo during a benefit dinner and silent auction Thursday, April 1.
"Bring your friends — all of them," Bazilo says, giggling. "Really, you can help and make a better life for us."
— Whitney Bryen
More Visual Arts »
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Review: The Book of Mormon
Give the gift of protein on Valentine's
Uganda's president raps for re-election
Tags: Art News, Invisible children, Tony Bazilo, Uganda, child soldiers, Ugandan refugees
Latest in Visual Arts
Peak Arts Prize 2.0 promises grants for local arts — and you get to decide where it goes
Su Kaiden Cho explores the ambiguity of identity
by Griffin Swartzell
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Maxine Green's artistic legacy shows a love for smooth and weathered forms
More by Whitney Bryen
Social clubs could be the future, if they survive the next few months
Out of the basement
Rushing to beat the polls
Local author and activist Bill Durland puts political and historic twists on A Christmas Carol in a new play.
Into the closet
Before you grow, a few things to know.

redpajama_set_name: RedPajamaCommonCrawl


text:
Mean What You Say
© Copyright – Dave Young Quartet / Modica Music Ltd
Bassist Dave Young,one of Canada's most valuable and beloved musical exports leads a quartet of Canada's leading jazz Musicians
Album Notes
Mean What You Say is an independent release and a thrilling musical collaboration (as well as bass-centric jazz recording masterpiece). In addition to Dave on bass, the quartet recording also features the considerable talents of first-call trumpet genius Kevin Turcotte, as well as gifted pianist Robi Botos and dynamic drummer Frank Botos.
Well-Produced by noted award-winning bassist, composer and producer Roberto Occhipinti, Mean What You Say is comprised of material from some of the most intriguing jazz composers of the modern musical era (e.g. title-track author Thad Jones, Oscar Pettiford, Sam Jones, W.C. Handy, Bud Powell, Cole Porter and Matt Dennis) as well as original pieces by Dave Young himself.
The eclectic, musically sophisticated and deeply swinging material on Mean What You Say includes the title track, written by legendary jazz trumpeter, arranger and bandleader Thad Jones (one third of the Pontiac, Michigan jazz dynasty that includes late drum legend Elvin and still swinging pianist Hank Jones). It's only natural that Thad's tune should be a feature for Kevin Turcotte's agile and sumptuous sound while also including strong rhythmic work from Frank Botos and inspired solos from Robi Botos and Dave. "Will You Still Be Mine" comes from the late, prolific Sinatra inspired vocalist/composer Matt Dennis, and is arranged here as a jaunty, rhythmic swing with an impressive arco solo by Dave as well as more exquisite lead trumpet work from Turcotte and strong solo piano sections from Robi Botos. Innovative bass/cello genius Oscar Pettiford's "Bohemia After Dark" is a bass-centric stand out, and one of the most appealing tracks on the CD. Of particular beauty are penultimate American tunesmith Cole Porter's classic and moving ballads, "Every Time We Say Good-bye" and the sumptuous, more up-tempo "Dream Dancing" – both of which display the communicative sensitivity and superb musicianship of the entire quartet. Other highlights of Mean What You Say include "Celia", by revered seminal bop pianist Bud Powell; Dave Young's original compositions "Sandu" (which features a gorgeous pizzicato bass solo), "Minor 101" and the emotionally evocative "Last Time I Saw Her". Also, avant-garde jazz bassist/composer Sam Jones' progressively smooth bopper, "Seven Minds" and the gospel-tinged bass feature, "Morning Star" from jazz progenitor and rag-time king, W.C. Handy.
Mean What You Say quantity
Category: Modica Music - CDs
This Song is New – CD
La Meglio Giuventù
One Way Up Mantra


A few HTML elements don't play nice with responsive layouts. One of these is the good ol' iframe, which you may need to use when embedding content from external sources such as YouTube. In this article, we'll show you how to make embedded content responsive using CSS, so that content such as video and calendars resize with the browser's viewport.
Note: This technique was originally detailed in Thierry Koblenz's excellent tutorial 'Creating Intrinsic Ratios for Video'. I've used techniques I learned from his tutorial and expanded on them here for additional content types such as calendars.
Services such as YouTube provide code that you can copy and paste into your own website to embed content. I tend to recommend to my clients that they host video with YouTube because it will save them server space and, regardless of the user's browser or device, YouTube will display the video correctly. The two main ways to embed video on a website are the HTML5 video element, which doesn't work in legacy versions of Internet Explorer, and Flash, which doesn't work on iOS devices and isn't standards-compliant.
However, you'll notice that our iframe includes width and height attributes. Remove these and the iframe will disappear because it would have no dimensions. And you can't fix this in your style sheet, unfortunately.
The width attribute means that, on a screen narrower than 560 pixels, the embedded content will protrude outside of its containing element, breaking the layout. In the example below, I've added the code above to a page of my blog. The screenshot is taken from an iPhone in portrait mode (320 pixels wide), and the rest of the page has been shrunk so that the embedded content fits the screen. Far from ideal!
Fortunately, there is a way around this using CSS. First, I'll show you how to do this with embedded video, and then with calendars.
The next step is to add styling to this new wrapper and the iframe within it.
Setting the position to relative lets us use absolute positioning for the iframe itself, which we'll get to shortly.
The padding-bottom value is calculated out of the aspect ratio of the video. In this case, the aspect ratio is 16:9, which means that the height will be 56.25% of the width. For a video with a 4:3 aspect ratio, we set padding-bottom to 75%.
The padding-top value is set to 30 pixels to allow space for the chrome — this is specific to YouTube videos.
The height is set to 0 because padding-bottom gives the element the height it needs. We do not set the width because it will automatically resize with the responsive element that contains this div.
Setting overflow to hidden ensures that any content protruding outside of this element will be hidden from view.
Absolute positioning is used because the containing element has a height of 0. If the iframe were positioned normally, we would have given it a height of 0 as well.
The top and left properties position the iframe correctly in the containing element.
The width and height properties ensure that the video takes up 100% of the space used by the containing element (which is actually set with padding).
Let's move on to other sources of embedded content — specifically, Google calendars.
The CSS to make any form of embedded content responsive is essentially the same, but different content will have different aspect ratios, which means you'll need to set the padding-bottom value accordingly.
Below is a screenshot of a website that I manage for a primary school, a website that embeds a Google calendar. As you can see, the calendar breaks the layout on a small screen. In this case, the website is displayed at the correct width, but the calendar goes beyond the screen's width.
The next step is to style this div.
The CSS for a calendar is almost identical to the CSS for a video, with two exceptions: The aspect ratio will be different, and padding-top isn't needed.
In this case, the iframe is 800 pixels wide and 600 pixels high, which gives us an aspect ratio of 4:3. So, set padding-bottom to be 75%.
This is exactly the same styling that we applied to the video.
As long as you remember to wrap your embedded calendars and videos with the appropriate containing element, then this CSS will work for any new videos and calendars that you add to your website.
The problem, however, is that although you can fit the whole calendar on a page, it's still almost unusable because click targets are so small and no information is visible. If you absolutely have to display Google Calendar, you can, but if you can use more usable responsive calendar solutions like simple CSS (setting display: block on table rows, for example), or w3widgets Responsive calendar or Calendario for your own calendars, your users might appreciate it.
Apart from videos and calendars, another common issue is the embedding of Google maps, responsively. Basically, we again use the same intrinsic ratio technique, and when setting padding-bottom for the wrapper, we just divide the height by width and add the aspect ratio in CSS.
Voilá! Again, we can just use EmbedResponsively to generate the copy-paste-code with one click.
Embedded content has a habit of breaking responsive layouts, because it's contained in an iframe with a fixed width. In this article, we've seen how to add a single containing wrapper, and some CSS, to ensure that all embedded content contained in an iframe resizes with the browser's window.
How do you embed third-party content on your responsive websites? Have you discovered any particular tricks or techniques? What does your workflow for embedding such content look like?
Front page image credits: Juhan Sonin.


Noona's Pizza, opening Wednesday, is taking over the space in the Fitzgerald building that previously housed Two Boots Pizza.
A bar and restaurant from the team behind Dooby's will open to the public this week in Midtown-Belvedere.
Noona's Pizza will open at 5 p.m. Wednesday, owner Phil Han said. The restaurant, located in the space in the Fitzgerald apartment building that previously housed Two Boots Pizza, will offer pizzas, sandwiches, small plates and entrees with Korean and Southern influences.
"We hope to be a really cool, just go-to neighborhood spot," Han said.
Pizza takes the spotlight at Noona's, but other dishes like charred sweet potatoes with honey and ricotta, sandwiches stuffed with crispy monkfish or fried chicken, and braised lamb with farro populate the menu, as well. Prices range from $4 for snacks and sides to $20 entrees.
The kimchi pork belly pizza is a must-try item, Han said.
"I don't think you're going to find that anywhere else," he said.
The Korean-inspired pizza is among the dishes and design elements at Noona's that give a nod to Dooby's, Han's first restaurant in Mount Vernon. The coffee mugs, for instance, are branded with the Dooby's name.
"There are little hints throughout the restaurant that let guests know that we're affiliated with Dooby's," Han said.
When he opened his other bars and restaurants — including Dooby's and Sugarvale — Han said he played it safe with opening menus, taking feedback from customers into account.
But at Noona's opening, the menu and the restaurant's decor will be more expressive, he said.
"We really felt like we had the support and the flexibility to elevate things a little," Han said.
Noona's held a series of "private training nights" to prepare for its full opening Wednesday, and so far the restaurant has been well-received by neighbors, he said.
Noona's kitchen will be open from 11 a.m. to 10 p.m. Sunday through Wednesday, with extended bar hours until midnight. From Thursday through Saturday the restaurant will serve food from 11 a.m. to midnight, and the bar will be open until 1 a.m.


Just the other day, I was flipping through my personal journal. I came across a prayer I had written to the Lord. The entry date was a little over a year ago. I sat amazed because everything I was praying about then, God had answered!!! Not only that, He had answered beyond what I ever could have expected! To be quite honest, I had forgotten about that prayer. But God did not. And that's just like Him. It's what He loves to do with His children. He loves to surprise us with more than we thought possible!
Oh, I know, sometimes the roads we travel down are…well…immensely difficult…but the outcome is so worth the struggle! So often, we run from the pain and the discomfort, when in actuality, we should learn to embrace it. There are lessons to be taught in the place of pain. No amount of time "on the mountaintop" would ever produce the same benefits. Do I think the Lord causes the pain? No. Do I think the Lord uses what "satan meant for evil" to produce some really great stuff in our lives? Yes!
If we understand the Lord as the perfect Father, we understand that it is NEVER His intent to bring us harm. Never. It is His desire to see us whole and healthy…physically, spiritually, mentally, emotionally…all the way around! His word says that He came so that we may have abundant life and I'm telling you, that kind of life can be found even in the midst of pain if you make the Lord, your Father, your dwelling place…your home...your safe haven. And you know what I realized that day as I was reading my journal? I honestly think that maybe for the first time in my life, I really did go a whole year making Him my safe haven…running straight to Him with everything…especially with the hard stuff that I didn't understand. I know that must sound ridiculous, saying this is the first year I had done that, but in the past, truthfully, I would get some crazy thought in my head (a lie from satan) and decide to let it build a wall between the Lord and I (you can travel over here to read an example). This year, I actually relied on faith, believing NOT on what I saw or felt, but rather, on the truth I saw in His word or the truth He impressed upon me. I prayed through the doubt and I took my stuff straight to Him. Would you believe that it works!? Ha! Trust me…you can trust Him!!!
even if you forget that you asked them.
Please watch the following video. You'll be blessed!


OTTAWA — Bob Rae has formally declared his candidacy for the leadership of the federal Liberal party. The former NDP premier of Ontario, who won a Toronto seat in a byelection last March and was re-elected last month, says he has the "judgment, character values and experience" to lead the country. Two others are in the race — Dominic LeBlanc and Rae's longtime friend Michael Ignatieff. Ignatieff is considered the frontrunner going into the leadership convention in Vancouver next May; polls indicate Rae is having trouble shaking the legacy of his deficit-ridden government on the 1990s. Rae says he's proud of his performance as Ontario premier, when he faced large deficits and labour unrest, and he says he's learned from it and won't try to hide it. Rae and Ignatieff were locked in a tight leadership race in 2006 before Stephane Dion came up the middle and won a surprise victory.


text:
Q: ASP Classic >> List all instances of an active session variable Our ASP Classic application assigns a Session("User_ID") for every user that logs in.
I have played around with Session.Contents, but that just returns the sessions associated with my login.
Is there any way to see all of the application's active Session("User_ID") values?
In other words, if the application has assigned Session("User_ID") = "15", Session("User_ID") = "27", Session("User_ID") = "149" and Session("User_ID") = "234", I would like to loop through some collection and get "15, 27, 149, 234".
Is this possible?

A: Usually what you do is to update a database table which has that userID and update a lastActivity datetime column.  Simplest would be to have every page call a common include that updates this.  Another option is if you have a timer that logs them out automatically is to update a flag to say they aren't logged in anymore.

redpajama_set_name: RedPajamaStackExchange


text:
Home TikTok Star Tiktok Adam Dillon Wiki, Bio, Age, Height, Net Worth, Girlfriend
Tiktok Adam Dillon Wiki, Bio, Age, Height, Net Worth, Girlfriend
Shashwat
1 Adam Dillon Wiki
2 Adam Dillon Age
3 Adam Dillon Tiktok Career
4 Adam Dillion Net Worth
Today we are going to provide you with information about one of the successful Instagram stars known as Adam Dillon. But the main thing for which he is famous for is his comedy videos on TikTok. Further, at present, he has its own Merchandise line. She was 19 years old as per 2020, her birthdate is January 8th, 2002. She was originally from the United States. Yes, Adam Dillon has two brothers Zach and Nate Dillon. He loved both of his brothers as three of them grew up with each other. He loves to play travel baseball. He uploads one of his pictures with his baseball team. According to the available information, we like to inform you all that he and his team have also won the State Championship. At this age, he has achieved a lot. Many of us think of it and this guy made it true through his hard work and diligence. Know Adam Dillon wiki, bio, age, height and net worth.
Adam Dillon Wiki
Adam Dillon is well known as a TikTok celeb. Currently, he has more than 1.8 million followers on TikTok. Shockingly, he has more than 82.2 million likes on his videos. His each and individual video get over thousands of likes. He uploads funny sketches on TikTok. A few months before, he was known as the cool guy on TikTok. At that time he used a mashup of the Lil Nas X song Old Town Road on his videos which he titled as White people at the time he recognizes the beat drop is arriving soon. He is rapidly growing in the course of time, therefore tons of people are being crazy for his videos.
Adam Dillon Age
First Name: Adam
Last Name: Dillon
Occupation: Instagram Star
Current Age: 19-year-old as of 2021
Zodiac Sign: Capricorn
Birth Date: January 8, 2002
Height (Feet-Inches): 4 feet 8 inches
Height (in meters): 142 cm (1.42 m)
Weight (kg): 33.5 – 40.8 kg
Weight (pounds): 74 – 90 lbs
Net Worth: $100K USD
Adam Dillon Tiktok Career
As we have already informed you that he has its own merchandise business. Adam Dillion sells goods and items such as printed t-shirt, phone covers, and other related items. He has one website through which he sells his products and the website domain name is teespring.com/stores/cool-store-55'. He also showcases his goods and items while making TikTok videos. There are tons of people, who are searching for him, at present he has more than 1 million followers on Tik Tok account and more than 72K on his IG account.
Adam Dillion Net Worth
According to the information available and sources, we found online, we can say, Adam Dillion's net worth is $100 USD. The main source of his income is Tik Tok social media platform. As per the reports, he earns around $300K by selling his merchandise. He is active on several social media platforms such as Snapchat, Instagram, Tik Tok, etc. He is not only a tik tok star but he is also famous on Instagram as well. He has more than 180K followers on Instagram. On July 22nd, 2018, he uploads his very first post on Instagram. On Snapchat, he is active as 'dareladamd'.
As per the information, tons of people want to know his relationship status, but he is assumed to be single so far at present. He is not dating anyone, it will be updated if we find more updates. That's all for today if you want to know more about him you should follow him on Instagram, and if you still have any questions you can ask us in our comment section, and in last, thanks for reading this article.
adam dillon bio
adam dillon height
adam dillon net worth
adam dillon tiktok
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I too have just done a sudo apt-get dist-upgrade and uname -a says Linux Raspberrypi 4.14.79-v7+. As for you, obconf does not seem to work, nor does lxappearance. That command brings up the error Failed to load module "atk-bridge".
Topic: Help! Start menu icon has disappeared.
Re: Help! Start menu icon has disappeared.
Panic over. The file manager has an icon on the taskbar, and I used its Go menu option to get to the application to reset the default theme.
Help! Start menu icon has disappeared.
Using Raspbian Stretch. The main menu icon is no longer there. I think I must have selected a theme that does not show it. Now I cannot shut down or reset the appearance preferences to the default. Help please!
Topic: Can openbox display filetypes?
Topic: How do I mend the Preferences menu in Pixel?
Re: How do I mend the Preferences menu in Pixel?
Thanks for that. I am reassured.
How do I mend the Preferences menu in Pixel?
The Desktop Preferences option seems to open exactly the same dialog as Appearance Settings. I fear something is wrong, but short of a complete reinstall of Raspbian I do not know how to restore the system. It seems to have gone wrong after I installed Vivaldi.
Topic: Replace file manager by rox-filer. Possible?
Re: Replace file manager by rox-filer. Possible?
Raspbian with PIXEL on Rpi3. If I select Desktop->Preferences from the Main (Start) menu I get the same result as if I had selected Preferences->Appearance Settings. So something is wrong. How do I correct it?
Topic: Is there a log file?
Is there a log file?
Topic: Raspberry Pi hardware compatibility layer?
Re: Raspberry Pi hardware compatibility layer?
I had in mind things like the SWP instruction, valid for the Rpi2's CPU , no longer being valid for the Rpi3's. I had not realized that the default installed gcc took care of that. Sorry for the noise.
Raspberry Pi hardware compatibility layer?
Topic: Readable Code Style, Review Requested.
Re: Readable Code Style, Review Requested.
what is it doing in RISC OS?
Back in Autumn of 2004 I wrote an article Why Lua is not BASIC in Frobnicate#22. Maybe I should bring it up to date with a wimp program for the comparison?
What is it doing in RISC OS? Because it runs under RISC OS. That is why it is called RiscLua. You should try it.
Is this correct? Should the second line be there?


The Biomap Carbonfiber highback is made from Carbon Fiber manufactured with attention to performance. The asymmetrical design is ergonomically engineered to fit the calf and angle of rider's legs to maximize performance and response from the board.
The Biomap is a set of asymmetrical highbacks that provide maximum energy transmission from your body to the board while ensuring proper stance support. That's why our highbacks are designed with Biomechanical technology, to be anatomically compatible with every rider's calf, and simultaneously stabilizing your leg in the right position to transmit power directly to the board without wasting any energy.
The Full Prime highback has fought to revolutionize your riding style with a central spine critical to fortifying the strength necessary to support any pressure put on it. This outstanding highback delivers extra torsional flexibility during turns and rotations.
It's the third year in our collection, the Spade highback is an asymmetrical design to give extra flex to your riding and tweaks featuring a new adjustment system that is both faster to change up and more durable.
The Light Frame family of the highbacks maintains the same benefits of a full frame highback without the added weigt. It's a perfect mix of torsional flexibility and response by giving you more lateral movement while allowing a progressive response in all movement paths. This guarantees greater control over your board with a comfortable and forgiving feel without compromising support.
Perfect for entry-level riders the Eyeback is super light, comfortable, and very versatile.
biological makeup, the Ladfyit is constructed with a shorter, rounded top for extra support and the best possible fit, excellent flex and reactivity with a feminine design touch.


Rattlesnake Master (Snakeroot) - Eryngium yuccafolium - Perennial - Medicinal - This native American prarie plant is a relative of Sea Holly and has long toothed blue-grey leaves and tiny white flowers. It been used to treat snakebite and venereal disease.. A really striking specimen plant. It doesn't like to be disturbed, so choose a spot that will allow it to remain for several years. Full sun; plant height: 4ft.


text:
package org.springframework.samples.mvc.async;

import java.util.concurrent.Callable;

import org.springframework.stereotype.Controller;
import org.springframework.ui.Model;
import org.springframework.web.bind.annotation.ExceptionHandler;
import org.springframework.web.bind.annotation.RequestMapping;
import org.springframework.web.bind.annotation.RequestParam;
import org.springframework.web.bind.annotation.ResponseBody;
import org.springframework.web.context.request.async.WebAsyncTask;

@Controller
@RequestMapping("/async/callable")
public class CallableController {

	@RequestMapping("/response-body")
	public @ResponseBody Callable<String> callable() {

		return new Callable<String>() {
			@Override
			public String call() throws Exception {
				Thread.sleep(2000);
				return "Callable result";
			}
		};
	}

	@RequestMapping("/view")
	public Callable<String> callableWithView(final Model model) {

		return new Callable<String>() {
			@Override
			public String call() throws Exception {
				Thread.sleep(2000);
				model.addAttribute("foo", "bar");
				model.addAttribute("fruit", "apple");
				return "views/html";
			}
		};
	}

	@RequestMapping("/exception")
	public @ResponseBody Callable<String> callableWithException(
			final @RequestParam(required=false, defaultValue="true") boolean handled) {

		return new Callable<String>() {
			@Override
			public String call() throws Exception {
				Thread.sleep(2000);
				if (handled) {
					// see handleException method further below
					throw new IllegalStateException("Callable error");
				}
				else {
					throw new IllegalArgumentException("Callable error");
				}
			}
		};
	}

	@RequestMapping("/custom-timeout-handling")
	public @ResponseBody WebAsyncTask<String> callableWithCustomTimeoutHandling() {

		Callable<String> callable = new Callable<String>() {
			@Override
			public String call() throws Exception {
				Thread.sleep(2000);
				return "Callable result";
			}
		};

		return new WebAsyncTask<String>(1000, callable);
	}

	@ExceptionHandler
	@ResponseBody
	public String handleException(IllegalStateException ex) {
		return "Handled exception: " + ex.getMessage();
	}

}


Turntablism: the evolution of the record player from a device for playing music into an instrument.
The humble turntable has put music in a spin over the last 50 years, giving rise to a whole new genre of sound, artistic skill and culture.
With creating original music using records, turntables and microphones from the early 1970's onward, Hip-Hop pioneers and visionaries developed many of the turntable manipulation techniques that are still central to Turntablism today.
The best-known examples of Turntablism sit within Hip-Hop mostly as Turntablism is one of the 5 elements of Hip-Hop culture.
Abbreviation for disc jockey, A person who mixes recorded music. Considered as an art form (turntablism). Techniques include scratching, flare, chirp, orbit and scribble.
Commonly known as breakdancing, a style of street dance.
Dictionary definition: writing or drawings scribbled, scratched, or sprayed illicitly on a wall or other surface in a public place.
An element made by Afrika Bambaataa and the Universal Zulu Nation. Provides the context that holds the elements of hip hop together. It also explains the differences between hip hip culture and mainstream culture. Many regard KRS-One as the "true teacher" of Hip-Hop culture.
Scratch the documentary cover legends From the South of Bronx in the 1970's to now, explore the world's most recognized and best Scratchers, diggers, Party-rockers, and Producers. A great documentary film to learn more about the "Vinyl" history, culture of the DJ and the evolution of Turntablism.
What are your thoughts on the art of Turntablism?
Let me know in the comment box below, Kudos!


text:
Maternal Fetal, Medicine Specialist
Dr. Deschamps was born and raised in Orem, Utah. He attended Brigham Young University where he earned an undergraduate degree in Management-Information Systems. During this time, he dedicated two years serving a church mission in southern France. Upon graduation he took a position as a Systems Programmer for corporate Wal-Mart. This position moved he and his wife to Bentonville, Arkansas. There his desire to pursue medicine was rekindled, and he returned to school. Dr. Deschamps attended the University of Arkansas for Medical Sciences for medical school in Little Rock. He then moved to Oklahoma where he completed his residency in Obstetrics and Gynecology and his Maternal-Fetal Medicine fellowship at University of Oklahoma.
Dr. Deschamps joined The Perinatal Center in July 2017. He continues to develop software in addition to his clinical activities. He has served on the Informatics Committee for SMFM, and been an informatics consultant for the Perinatal Quality Foundation. He has designed and built mobile apps including the "SMFM Preterm Birth Toolkit" and "Perinatal Calculators" free downloadable apps to be used as tools for obstetrical providers. In his spare time, Dave enjoys biking, playing tennis, and traveling. He also has a passion for Diet Dr. Pepper and gas station nachos. Most importantly, he enjoys spending time with his wife, Jen, and their three children Olive, Elle, and Emerson.
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Select LocationNormanMercy Medical CenterBaptist Medical CenterTulsa
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text:
\section{Introduction}
Artificial neural networks play a key role in current machine learning research and both their performance in practice as well as numerous of their theoretical properties are studied extensively. After the intial success of neural networks in statistical learning problems \cite{krizhevsky2012imagenet} neural networks where used in a variety of fields like generative learning and reinforcement learning but also inverse problems and the numerical analysis of PDEs (cf. \cite{mccann2017convolutional} and \cite{weinan2017deep} respectively). Although partial differential equations are deterministic in nature, some of the deep learning based approaches to their numerical solution are similar to traditional learning problems. In fact, they use the Feynman-Kac formula to approximately evaluate the true solution via Monte-Carlo sampling and then use neural networks for regression of those evaluations (cf. \cite{berner2018analysis}). However, one can also use the variational formulation of PDEs for example for elliptic PDEs and use the associated variational energy as an objective function for the optimisation of the neural networks. In \cite{weinan2018deep} it was demonstrated that this approach yields appealing visual results and a short empirical convergence analysis was carried out. However, it does not provide any guarantees of convergence of this numerical framework for variational problems which is the subject of this work.

\subsection*{Main result}

We will present a version of our main result on the convergence of ReLU networks trained with respect to a regularised Dirichlet energy towards the solution of the Poisson problem and use the following notations. First, we will consider growing sets \(\Theta_n\) of neural networks that we will assume to be universal approximators in \(H^1_0(\Omega)\) and introduce objective functions
\[L_n\colon \Theta_n\to \mathbb R, \quad \theta\mapsto \frac12\int_\Omega \left(\left\lvert\nabla u_\theta \right\rvert^2 - fu_\theta\right)\mathrm dx + n\int_{\partial \Omega} u_\theta^2\mathrm ds, \]
where \(u_\theta\) is the neural network arising from the parameters \(\theta\) and \(f\in L^2(\Omega)\). Now, we assume that \((\theta_n)_{n\in\mathbb N}\) is a sequence of quasi-minimisers of the objective functions, meaning
\[L_n(\theta_n) \le \inf_{\theta\in\Theta_n} L_n + \delta_n, \]
where \(\delta_n\to0\). Then it follows from Theorem \ref{mainresult} that \((u_{\theta_n})_{n\in\mathbb N}\) converges to the true solution of the Poisson problem with right hand side \(f\) weakly in \(H^1(\Omega)\) and thus strongly in \(L^2(\Omega)\). Further, we extend this result to abstract variational problems which for example cover the \(p\)-Laplace operator.

\section{Notation and preliminaries}

\subsection{Preliminaries from neural network theory}

\begin{definition}[Neural network]
Let \(d, m, L\in\mathbb N\). A \emph{standard neural network} of depth \(L\) with \emph{input dimension \(d\)} and \emph{output dimension \(m\)} is a tupel
\[\theta = \left( (A_1, b_1), \dots, (A_L, b_L)\right)\]
of matrix-vector pairs where \(A_l\in\mathbb R^{N_{l}\times N_{l-1}}\) and \(b_l\in\mathbb R^{N_l}\) and \(N_0 = d, N_L = m\). If \(L = 2\) we call the network \emph{shallow} and \emph{deep} otherwise.
\end{definition}

Every matrix vector pair \((A_l, b_l)\) induces an affine linear transformation that we denote with \(T_l\colon \mathbb R^{N_{l-1}} \to\mathbb R^{N_l}\). We refer to the pairs and also to the affine linear transformations as the \emph{layers} of the network and call the layers \(T_1, \dots, T_{L-1}\) the \emph{hidden layers} and say that \(W(\theta)\coloneqq\max_{l=0, \dots, L} N_l\) is the width of the network. Finally, we denote the set of networks of depth \(L\), width \(W\), input dimension \(d\) and output dimension \(m\) by \(\mathcal N\mathcal N_{L, W, d, m}\). We extend this notation and allow \(W=\infty\) and \(L=\infty\) where this means that the width or depth is finite but arbitrary.

\begin{definition}[Realisation of a neural network, \cite{petersen2018optimal}]
Let \(\theta\) be a neural network of depth \(L\) with input dimension \(d\) and output dimension \(m\) and let \(\rho\colon\mathbb R\to\mathbb R\) be a function. The \emph{realisation} of \(\theta\) with respect to the \emph{activation function \(\rho\)} is the function
\[R_\rho(\theta)\colon\mathbb R^d\to\mathbb R^m, \quad x\mapsto T_L(\rho(T_{L-1}(\rho(\cdots \rho(T_1(x)))))). \]
If \(f\) is the realisation of a neural network \(\theta\) we say that the network \(\theta\) \emph{represents} the function \(f\).
\end{definition}

The distinction of a neural network and its realisation has proven to be immensely useful in the theory of neural networks and we will see how this can be used to obtain approximation results. However, we want to stress that the realisation map is also crucial for the optimisation of networks, since the objective function is usually the composition of the realisastion map and some objective function on a suitable function space and we refer to \cite{petersen2018topological} and \cite{berner2019degenerate}.

\begin{definition}[ReLU activation function]
The \emph{rectified linear unit} or \emph{ReLU activation function} is defined via
\[\rho\colon\mathbb R\to\mathbb R, \quad x\mapsto \max\left\{ 0, x\right\}.\]
\end{definition}

From now on we will only consider ReLU networks mainly because the realisations of ReLU networks are precisely the piecewise linear functions. This will be very well suited for the study of the Poisson problem where the classical approach relies on finite element functions which are again piecewise linear.

\begin{definition}[Piecewise linear function]\label{PiecewiseLinear}
We say a function \(f \colon\mathbb R^d \to\mathbb R\) is \emph{piecewise linear} if there exists a finite set of closed polyhedra whose union is \(\mathbb R^d\), and \(f\) is affine linear over each polyhedron. The \emph{number of linear regions of} \(f\) is the number of maximal connected subsets of \(\mathbb R^d\) over which \(f\) is affine linear.
\end{definition}

Note every piecewise linear functions is continuous by definition since the polyhedra are closed and cover the whole space \(\mathbb R^d\), and affine functions are continuous.

\begin{theorem}[Universal representation, \cite{arora2016understanding}]
    Every realisation \(R\colon\mathbb R^d\to\mathbb R^m\) is a piecewise linear function. Conversely, every piecewise linear function \(f\colon\mathbb R^d\to\mathbb R^m\) can be represented by a ReLU network of depth at most \(\lceil \log_2(d+1)\rceil +1\).
\end{theorem}

For the proof of this statement we refer to \cite{arora2016understanding} but shall note that they restrict their studies to \(m=1\). However, the statement above follows easily by building parallelised networks which is straight forward, but for an explicit construction of this parallelisation we refer to \cite{petersen2018optimal}.

One benefit of this result is that it explicitly characterises the range of the realisation map for ReLU networks. A lot of properties of neural networks only depend on their realisations and hence this approach can simplify the study of those. In particular, some approximation capabilities of piecewise linear functions can be transferred directly to ReLU networks. As an example we will present the following universality property of ReLU networks which will be crucial in the proof of the \(\Gamma\)-convergence later on. We will not present the proof since it is the direct consequence of the previous result, the approximation result for piecewise linear functions in the appendix and the density of smooth and compactly supported functions in the Sobolev space \(W^{1, p}_0(\Omega)\). Note, that similar approximation results – for example with non zero boundary values – can be obtained in analogue fashion.

\begin{theorem}[Universal approximation]\label{UniversalApproximation}
Let \(\Omega\subseteq\mathbb R^d\) be a bounded and open set and let \(p\in [1, \infty)\). For all functions \(f\in W^{1, p}_0(\Omega)\) and \(\varepsilon>0\) there is a realisation \(g\in W^{1, p}_0(\Omega)\) of a ReLU network of depth \(\lceil \log_2(d+1)\rceil +1\) such that \[\left\lVert f - g \right\rVert_{W^{1, p}(\Omega)}<\varepsilon.\]
\end{theorem}

\subsection{Reminder on $\Gamma$-convergence}
$\Gamma$-convergence is a notion of convergence for energy functionals that is tightly linked to the convergence of their minimisers and thus extremely well suited to rigorously establish approximation results.
We recall the definition of $\Gamma$-convergence, which we already specialise to the case of reflexive spaces with their associated weak topologies, and show one of its most important features: The convergence of quasi-minimisers of the $\Gamma$-converging sequence to the minimiser of the limit. For further reading we point the reader towards the extensive introduction \cite{dal2012introduction}.
\begin{definition}[\(\Gamma\)-convergence]
    Let \(X\) be a reflexive Banach space, \(F_n, F\colon X\to(-\infty, \infty]\), then \((F_n)_{n\in\mathbb N}\) is \emph{\(\Gamma\)-convergent} to \(F\) if the following properties are satisfied.
    \begin{enumerate}
        \item \emph{Liminf inequality:} For every \(x\in X\) and \((x_n)_{n\in\mathbb N}\) with \(x_n\rightharpoonup x\) we have
            \[F(x) \le \liminf_{n\to\infty} F_n(x_n).\]
        \item \emph{Recovery sequence:} For every \(x\in X\) there is \((x_n)_{n\in\mathbb N}\) with \(x_n\rightharpoonup x\) such that
            \[F(x) = \lim_{n\to\infty} F_n(x_n).\]
    \end{enumerate}
\end{definition}

\begin{proposition}[Limits of quasi-minimisers]\label{limits}
Let \(X\) be a reflexive Banach space and \((F_n)_{n\in\mathbb N}\) be a sequence of functionals that \(\Gamma\)-converges to \(F\). Let \((x_n)_{n\in\mathbb N}\) be a sequence of $\delta_n$-\emph{quasi-minimisers}, i.e.,
\[F_n(x_n) \le \inf F_n + \delta_n \quad \text{for all } n\in\mathbb N,\]
where \(\delta_n\to0\). If \(x_n\rightharpoonup x\), then \(x\) is a minimiser of \(F\).
\end{proposition}
\begin{proof}
By the Liminf inequality we have
\[F(x) \le \liminf_{n\to\infty} F_n(x_n) \le \liminf_{n\to\infty} \big(\inf F_n + \delta_n\big) = \liminf_{n\to\infty} \big(\inf F_n\big) \le \inf F.\]
To see the last inequality, we fix \(y\in X\) and choose a recovery sequence \((y_n)_{n\in\mathbb N}\) and obtain
\[F(y) \ge \limsup_{n\to\infty} F_n(y_n) \ge \limsup_{n\to\infty} \big(\inf F_n\big) \ge \liminf_{n\to\infty} \big(\inf F_n\big).\]
Since \(y\) was arbitrary we can take the infimum of \(y\).
\end{proof}

\begin{definition}[Equi-coercivity]
    Let \(X\) be a reflexive Banach space. The sequence \(F_n\colon X\to(-\infty, \infty]\) is called \emph{equi-coercive} if for all \(r\in\mathbb R\) the set
        \[\bigcup_{n\in\mathbb N}\{F_n\le r\} \]
    is bounded in \(X\) (or equivalently relatively compact wrt the weak topology).
\end{definition}

\begin{corollary}[Convergence of quasi-minimisers]\label{MinimiserCorollary}
    Let \(X\) be a reflexive Banach space and \((F_n)_{n\in\mathbb N}\) be a sequence of equi-coercive functionals that \(\Gamma\)-converges to \(F\) which has a unique minimiser \(x\). Then every sequence \((x_n)_{n\in\mathbb N}\) of quasi-minimisers converges weakly to \(x\).
\end{corollary}
\begin{proof}
Let \((x_n)_{n\in\mathbb N}\) be a sequence of quasi-minimisers. Since we have seen
\(\limsup \big(\inf F_n\big) \le \inf F \)
we obtain
\[(x_n)_{n\in\mathbb N} \subseteq \bigcup_{n\in\mathbb N}\{F_n\le r\}\]
for \(r>\inf F\). Hence, by the equicoercivity \((x_n)_{n\in\mathbb N}\) is relatively weakly compact and since \(X\) is reflexive we are left to show that \(x\) is the only limit point of \((x_n)_{n\in\mathbb N}\). So assume we have \(x_{n_k}\rightharpoonup y\), then \(y\) minimses \(F\) by Proposition \ref{limits} and thus by the uniqueness of the minimser we obtain \(y=x\).
\end{proof}

\section{\(\Gamma\)-convergence for variational energies of deep networks}
In this section we prove our main result, namely the $\Gamma$-convergence for regularised Dirichlet energies on ReLU networks. Furthermore we show that this is in fact very robust and can easily be transferred to more general energies. Finally, as an example of the abstract formulation, we show how it can be applied to the $p$-Dirichlet energy which is associated to a non-linear PDE.

    But before we proceed with the details we will give a quick overview over this approach to solve PDEs. For this, we consider the Poisson problem which is the prototype of an elliptic PDE and given by
    \begin{align*}
        -\Delta u & = f \quad \text{in } \Omega \\
        u & = 0 \quad \text{on } \partial\Omega.
    \end{align*}
    It is well known that for a function \(u\in H^1_0(\Omega)\) and some right hand side \(f\in H^1_0(\Omega)^\prime\) it is equivalent to be a weak solution of the Poisson problem or to be a solution of the variational problem
    \[ u\in \underset{v\in H^1_0(\Omega)}{\arg\min} \; \frac12\int_{\Omega} \left\lvert \nabla v\right\rvert^2 \mathrm dx - f(v). \]
    The minimised functional on the right hand side is called the \emph{Dirichlet energy} and we refer to \cite{struwe1990variational} for further properties like the existence of unique minimisers.
    By the universal approximation property realisations of ReLU networks with zero boundary values are dense in \(H^1_0(\Omega)\). Hence, one could minimise the Dirichlet energy over all such networks. However, contrary to the use of finite element functions it is not straight forward to enforce zero boundary value conditions for realisations of networks. The solution is to relax the problem and consider the realisations of arbitrary networks but to penalise boundary values. This approach was first taken by \cite{weinan2018deep} where an empirical justification for this method is presented. In the following we give a rigorous proof that the networks that are (quasi) optimised with respect to the regularised Dirichlet energy converge towards the true solution of the Poisson problem if the regularisation is increased and if the networks are universal approximators.

\subsection{\(\Gamma\)-convergence for Dirichlet energy}

    We begin by fixing the notation for this section.

    \begin{setting}
    For \(n\in\mathbb N\) we denote by $\Theta_n$ the set of neural networks with input dimension $d\in\mathbb N$, output dimension $1$, depth $\lceil \log_2(d+1) \rceil + 1$ of width at most $n$. Then we look at the realisations of the $\Theta_n$ as a subset in $H^1(\Omega)$ which we call $A_n$ i.e., we set $A_n = R_\rho(\Theta_n)\subset H^1(\Omega)$ where $\Omega\subset\mathbb R^d$ is some open, connected and bounded Lipschitz set and the activation function $\rho$ is ReLU. Note that the functions in $A_n$ are indeed members of $H^1(\Omega)$ as realisations of ReLU networks are of piecewise linear functions.
    \end{setting}

    In the following let $f\in H^1(\Omega)'$, that is $f:H^1(\Omega)\to\mathbb R$ is linear and continuous, and define the sequence of functionals $F_n:H^{1}(\Omega)\to(-\infty,\infty]$
    \begin{align*}
        F_n(u) = \begin{cases}\; \displaystyle \frac12 \int_\Omega |\nabla u|^2\mathrm dx + n\int_{\partial\Omega}u^2\mathrm ds - f(u) &u\in A_n, \\[.4cm] \;\infty   &u\notin A_n. \end{cases}
    \end{align*}
    Further, we define the Dirichlet energy $F:H^1(\Omega)\to(-\infty,\infty]$ with zero boundary values
    \begin{align*}
        F(u) = \begin{cases} \; \displaystyle \frac12 \int_\Omega |\nabla u|^2\mathrm dx - f(u) &u\in H^1_0(\Omega), \\[.4cm] \; \infty   &u\in H^1(\Omega)\setminus H^1_0(\Omega)\end{cases}
    \end{align*}
    and we will show in the remainder of the section that the sequence \((F_n)_{n\in\mathbb N}\) of functionals \(\Gamma\)-converges towards \(F\).
    Note that by the Hahn-Banach theorem every functional in $H^1_0(\Omega)'$ can be extended to some $f\in H^1(\Omega)'$. Having cleared our setting we turn to $\Gamma$-convergence results.
    \begin{theorem}[\(\Gamma\)-convergence]
    The sequence \((F_n)_{n\in\mathbb N}\) of functionals \(\Gamma\)-converges to the Dirichlet energy \(F\) in the weak topology of \(H^1(\Omega)\).
    \end{theorem}
    \begin{proof}
        We start by checking the liminf inequality. We first assume that $u\notin H^{1,2}_0(\Omega)$. By linearity and continuity of the trace operator it follows that $\operatorname{tr}(u_n)\rightharpoonup\operatorname{tr}(u)$ in $L^2(\partial \Omega)$ and by assumption $\operatorname{tr}(u)\neq 0$. Using the weak semicontinuity of $\norm{\,\cdot\,}^2_{L^2(\partial\Omega)}$ it follows that
        \begin{align*}
            \liminf_{n\to\infty}
            \norm{\operatorname{tr}(u_n)}^2_{L^2(\partial\Omega)}
            \geq
            \norm{\operatorname{tr}(u)}^2_{L^2(\partial\Omega)}
            >0.
        \end{align*}
        and therefore clearly
        \[
            \liminf_{n\to\infty}
            \big(
            n\norm{\operatorname{tr}(u_n)}^2_{L^2(\partial\Omega)}
            \big)
            =
            \infty.
        \]
        Using these facts we establish the liminf inequality in this case
        \begin{align*}
            \liminf_{n\to\infty}F_n(u_n)
            \geq
            \liminf_{n\to\infty} n\norm{\operatorname{tr}(u_n)}^2_{L^2(\partial\Omega)}
            -
            \lim_{n\to\infty}f(u_n)
            =
            \infty
            =
            F(u).
        \end{align*}
        Now we treat the case $u\in H^{1}_0(\Omega)$. Then using weak lower semi-continuity we find
        \begin{align*}
            \liminf_{n\to\infty}F_n(u_n)
            &\geq
            \liminf_{n\to\infty}\frac12\int_\Omega|\nabla u_n|^2\,\mathrm dx - f(u)
            \\
            &\geq
            \frac12\int_\Omega |\nabla u|^2\,\mathrm dx
            -
            f(u)
            =
            F(u).
        \end{align*}
        We are left to construct a recovery sequence. Assume that $u$ does not have zero boundary conditions. Then just choose $u_n = u$ for all $n$. Otherwise assume $u$ lies in $H^{1}_0(\Omega)$. By Theorem \ref{UniversalApproximation} there is a sequence $(u_n)_{n\in\mathbb N}$ such that $u_n\in A_n\cap H^1_0(\Omega)$ and $u_n\to u$ strongly in $H^1(\Omega)$ and hence it follows \[ F_n(u_n) = \frac12\int_\Omega|\nabla u_n|^2\,\mathrm dx -f(u_n) \to F(u). \]
    \end{proof}

Now we check the requirements of Corollary \ref{MinimiserCorollary} which will yield the the convergence of quasi-minimisers.

    \begin{lemma}
        The functional $F:H^1(\Omega)\to(-\infty, \infty]$ as defined above has a unique minimiser.
        \begin{proof}
        The existence follows by the direct method of the calculus of variations \cite{struwe1990variational} and the uniqueness by the strict convexity of $F$.
        \end{proof}{}
    \end{lemma}{}

 Before we turn towards the equi-coercity we define the functional \[G_n(u) = \frac12 \int_\Omega |\nabla u|^2\,\mathrm dx + n\int_{\partial\Omega}u^2\,ds - f(u)\] hence $G_n$ agrees with $F_n$ where $F_n\neq \infty$. Note that it trivially holds
    \[
        F_n
        =
        G_n + \chi_{A_n}
    \]
    where $\chi_{A_n}=0$ on $A_n$ and $\chi_{A_n}=\infty$ otherwise. We also remark that
    \[
        F_n \geq G_n \geq G_1.
    \]
    This means to show the equi-coercivity of $(F_n)_{n\in\mathbb N}$ it suffices to prove the coercity of the single functional $G_1$.
The following lemma uses a classical compactness argument to establish a Poincaré type inequality (cf. \cite{alt1992linear}).
\begin{lemma}
    Let $r>0$ be fixed and consider the set $M \coloneqq \{ G_1\leq r \}\subset H^{1}(\Omega)$ i.e., the functions in $H^{1}(\Omega)$  that satisfy
    \begin{align}\label{InequalityM}
        \frac12\int_\Omega |\nabla u|^2\,\mathrm dx
        +
        \int_{\partial\Omega}u^2\,ds
        -
        f(u)
        \leq
        r.
    \end{align}
    Those functions satisfy a Poincar\'e type inequality of the form
    \begin{align}\label{Poincare}
        \norm{u}_{L^2}
        \leq
        C(\norm{\nabla u}_{L^2} + 1),
    \end{align}
    where \(C\) only depends on \(r\) and \(\Omega\).
    \begin{proof}
        The proof consists of two steps. First we will show that the inequality (\ref{InequalityM}) implies that $M$ cannot contain arbitrarily large, constant functions and second we prove that a failure of the Poincar\'e inequality (\ref{Poincare}) means that $M$ contains any large, constant function hence the assertion follows.
        \ \\ \ \\
        \textbf{Step 1.} Let $\xi\in\mathbb{R}$ be a constant function in $M$. We will show that there is some fixed $C>0$ depending only on $r,\norm{f}_{H^1(\Omega)'}$ and $|\partial\Omega|$ such that
        \[
            |\xi|\leq C.
        \]
        Using a scaled version of Young's inequality with $\varepsilon |\Omega|^{1/2} \leq |\partial\Omega|/2$ we compute
        \begin{align*}
            r
            \geq
            \int_{\partial\Omega}\xi^2\,ds
            -
            f(\xi)
            &\geq
            |\xi|^2|\partial\Omega|
            -
            \norm{f}_{H^1(\Omega)'}\norm{\xi}_{H^1(\Omega)}
            \\
            &=
            |\xi|^2|\partial\Omega|
            -
            \norm{f}_{H^1(\Omega)'}|\Omega|^{1/2}|\xi|
            \\
            &\geq
            |\xi|^2|\partial\Omega|
            -
            C(\varepsilon)\norm{f}^2_{H^1(\Omega)'}
            -\varepsilon|\Omega|\cdot|\xi|^2
            \\
            &\geq
            \frac12|\partial\Omega|\,|\xi|^2
            -
            C(\varepsilon)\norm{f}^2_{H^1(\Omega)'}.
        \end{align*}
        Thus we can solve for $|\xi|$ and find a uniform bound in terms of $r,\norm{f}_{H^1(\Omega)'}$ and $|\partial\Omega|$.
        \ \\ \ \\
        \textbf{Step 2.} Now we assume that the inequality fails and will show that this implies that $M$ contains arbitrarily large constant functions. Assume therefore that there is a sequence $(u_k)\subset M$ such that
        \[
            \norm{\nabla u_k}_{L^2} + 1
            \leq
            \frac1k\norm{u_k}_{L^2}.
        \]
        This inequality implies that $\norm{u_k}_{L^2}\to\infty$ and hence for every large but fixed $R>0$ we may assume that $\norm{u_k}_{L^2}^{-1} R\leq 1$ and set $v_k = u_k (R\norm{u_k}_{L^2}^{-1})$. By the star shape of $M$ the $v_k$ are a sequence in $M$ and the above inequality yields upon multiplying
        \begin{align}\label{GradientInequality}
            \norm{\nabla v_k}_{L^2}
            +
            \frac{R}{\norm{u_k}_{L^2}}
            \leq
            \frac{R}{k}
            \to 0.
        \end{align}
        As $\norm{v_k}=R$ and $(\ref{GradientInequality})$ implies a bound on $\norm{\nabla v_k}_{L^2}$ we extract a weakly $H^{1,2}(\Omega)$ convergent subsequence $v_j\rightharpoonup v$ with limit $v$ in $M$ by the weak closedness of $M$. Also from (\ref{GradientInequality}) we deduce that
        \[
            \nabla v_j \rightharpoonup \nabla v = 0
            \quad\text{weakly in }L^2(\Omega)^n
        \]
        and thus there is a constant $\xi\in\mathbb{R}$ such that $v(x)=\xi$ up to a set of measure zero in $\Omega$. To identify $\xi$ we employ the Rellich compactness theorem which yields that $v_j\to v$ strongly in $L^2(\Omega)$ and together with $\norm{v_j}_{L^2}=R$ we conclude
        \[
            R
            =
            \norm{v}_{L^2}
            =
            \norm{\xi}_{L^2}
            =
            |\Omega|^{1/2}|\xi|
        \]
        and as $R>0$ was arbitrary this shows that $M$ contains any large, constant function which manifests the desired contradiction.
    \end{proof}
\end{lemma}
\begin{proposition}
    The sequence $(F_n)$ is equicoercive i.e., for every $r\in\mathbb{R}$ there is a bounded set $K_r\subset H^{1,2}(\Omega)$ such that
    \[
        \bigcup_{n\in\mathbb{N}}\{ F_n \leq r \}
        \subset
        K_r.
    \]
\end{proposition}
    \begin{proof}
    As we discussed before the statement of the theorem it is enough to show that $M=\{ G_1\leq r \}\subset K_r$ for some bounded set $K_r$ in $H^{1}(\Omega)$. The next observation is that upon adding $\norm{\nabla u}_{L^2}$ to the inequality (\ref{Poincare}) we find that
    \begin{align}\label{ModifiedPoincare}
        \norm{u}_{H^{1}} \leq C(\norm{\nabla u}_{L^2} + 1)
    \end{align}
    hence it is enough to provide an $L^2$ bound on the gradients of the functions in $M$. We employ a scaled version of Young's inequality with fitting $\varepsilon>0$ and compute using the inequality (\ref{ModifiedPoincare})
    \begin{align*}
        r &\geq
        \frac12\norm{\nabla u}^2_{L^2}
        -
        \norm{f}_{H^1(\Omega)'}\norm{u}_{H^{1,2}}
        \\
        &\geq
         \frac12\norm{\nabla u}^2_{L^2}
        -
        C\norm{f}_{H^1(\Omega)'}\norm{\nabla u}_{L^2}
        -
        C\norm{f}_{H^1(\Omega)'}
        \\
        &\geq
        \frac12\norm{\nabla u}^2_{L^2}
        -
        \varepsilon \norm{\nabla u}_{L^2}^2
        -
        (C(\varepsilon)+C)\norm{f}_{H^1(\Omega)'}
        \\
        &\geq
        \frac14\norm{\nabla u}^2_{L^2}
        -
        (C(\varepsilon)+C)\norm{f}_{H^1(\Omega)'}.
    \end{align*}
    Rearranging the inequality we see that $\norm{\nabla u}_{L^2}\leq C(r)$ which is sufficient to conclude the proof due to (\ref{ModifiedPoincare}).
    \end{proof}

\begin{corollary}
    Any sequence \((u_n)_{n\in\mathbb N}\) of
    quasi-minimizers
    of \((F_n)_{n\in\mathbb N}\) converges weakly in \(H^{1}(\Omega)\) and hence strongly in \(L^2(\Omega)\) to the solution $u$ of
    \begin{align*}
        -\Delta u & = f \quad \text{in } \Omega \\
        u & = 0 \quad \text{on } \partial\Omega.
    \end{align*}
\end{corollary}

In practice, one will not optimise the functionals \(F_n\) but rather work in the parameter space \(\Theta_n\) and use \(L_n\coloneqq F_n\circ R_\rho\) as an objective function for the optimisation. However, if \((\theta_n)_{n\in\mathbb N}\) is a sequence of quasi-minimisers of \((L_n)_{n\in\mathbb N}\), then \((R_\rho(\theta_n))_{n\in\mathbb N}\) is a sequence of quasi-minimisers of \((F_n)_{n\in\mathbb N}\) since \(\{F_n<\infty\} = R_\rho(\Theta_n)\) by definition. Hence, the previous result yields the convergence of \((R_\rho(\theta_n))_{n\in\mathbb N}\) towards the solution of the Poisson problem and we will fix this in the following.

\begin{theorem}\label{mainresult}
Let \(L_n\coloneqq F_n\circ R_\rho\) and \((\theta_n)_{n\in\mathbb N}\) be a sequence of quasi-minimisers of \((L_n)_{n\in\mathbb N}\). Then \((R_\rho(\theta_n))_{n\in\mathbb N}\) converges to the true solution of the Poisson problem, both weakly in \(H^1(\Omega)\) and strongly in \(L^2(\Omega)\).
\end{theorem}

\subsection{Generalisation to abstract energy functionals}
The above considerations admit a direct extension to a considerably broader class of energies, including energies associated to higer order elliptic equations and also non-linear ones such as the $p$-Dirichlet energy, the Euler-Lagrange equations of which is the $p$-Laplace (cf. \cite{struwe1990variational}). In this section the activation function $\rho:\mathbb{R}\to\mathbb{R}$ is no longer assumed to be ReLU but needs to be chosen according to the energy.
\begin{setting}\label{AbstractSetting}
We begin with the assumptions and the norm structure on the space where the energy will live. Assume $X$  is a reflexive Banach space with norm $\norm{\,\cdot\,}_X$ and that there is an additional norm $|\cdot|$ on $X$, which does not need to render $X$ complete. Furthermore let $Y$ be another Banach space with norm $\norm{\,\cdot\,}_Y$ and let
\( T:(X,\norm{\cdot}_X)\to (Y,\norm{\cdot}_Y) \) be a linear and continuous operator which is linked to the norm $\norm{\,\cdot\,}_X$ in the following way
\[ \norm{x}_X = |x| + \norm{Tx}_Y \quad\text{for all }x\in X. \]
As for the activation function the only thing we require for the moment is that $\bigcup_{n\in\mathbb N}R_\rho(\Theta_n)\subset X$ and we set again $A_n\coloneqq R_\rho(\Theta_n)$. Of course this implies that our Banach space $X$ is some kind of function space.
We turn to the energy and some abstract analogue of boundary values. We assume that there are two maps
\[ E:X\to\mathbb{R} \quad\text{and}\quad \gamma:X\to B \]
where $E$ (the energy) is bounded from below, weakly lower semi-continuous and norm-continuous. Both, the weak topology related to the weak lower semi-continuity and the norm-continuity are meant with respect to the norm $\norm{\cdot}_X$. Furthermore $\gamma$ (trace operator) is a linear and continuous map from $(X,\norm{\cdot})$ into the Banach space $B$ that is the abstract analogue of boundary values. We set $X_0 = \ker(\gamma)$. With this terminology fixed we are able to define our functionals $F_n, F:X\to(-\infty,\infty]$. Let $f\in X'$ and set
    \begin{align*}
        F_n(x)
        =
        \begin{cases}
	    \; E(x) + n\norm{\gamma(x)}^2_B - f(x)
	    &x\in A_n,
	    \\[.2cm]
	    \; \infty   &x\notin A_n.
	    \end{cases}
    \end{align*}
    and for the limit functional
    \begin{align*}
        F(x)
        =
        \begin{cases}
	    \; E(x) - f(x)
	    &x\in X_0,
	    \\[.2cm]
	    \; \infty   &x\notin X_0.
	    \end{cases}
    \end{align*}
\end{setting}
To get an intuition for the setting think of $X=H^1(\Omega)$ where $|\cdot|=\norm{\,\cdot\,}_{L^2}$ and $\norm{\,\cdot\,}_X=\norm{\,\cdot\,}_{H^1}$ such as $T:H^1(\Omega)\to L^2(\Omega)^N$ with $u\mapsto \nabla u$.
The question we ask now is:
\begin{gather*}
    \text{\emph{Under which assumptions do we obtain the $\Gamma$-convergence of \((F_n)_{n\in\mathbb N}\) to \(F\)
    in the weak topology of $X$?}}
\end{gather*}{}
To this end we formulate the hypothesis below.
\begin{enumerate}
    \item[(H1)]\label{AssumptionDensity} The set $\bigcup_{n\in\mathbb N}R_\rho(\Theta_n)\cap X_0$ is dense in $X_0$ with respect to the norm topology on $(X_0,\norm{\,\cdot\,}_X)$.
    \item [(H2)] The space $X$ is reflexive, its norm is given as $\norm{\,\cdot\,}_X = |\cdot| + \norm{T\,\cdot\,}_Y$, for some other norm $|\cdot|$ on $X$ and $T:(X,\norm{\cdot}_X)\to (Y,\norm{\cdot}_Y)$ is linear and continuous into the Banach space $Y$.
    \item[(H3)] The identity $(X,\norm{\,\cdot\,}_X\to(X,|\cdot|)$ maps weakly convergent sequences to strongly convergent ones.
    \item[(H4)] The map $\gamma$ is linear and continuous and for every $r\in\mathbb{R}$ the set $\{ \norm{\gamma(x)}^2_B-f(x) \leq r \}\cap \ker(T)$ is bounded in $X$ by a constant $C=C(r)<\infty$.
    \item[(H5)] The energy $E:X\to\mathbb{R}$ is bounded form below, weakly lower semi-continuous (with respect to the weak topology induced by $\norm{\cdot}_X$) and also $\norm{\cdot}_X$-continuous and satisfies $|E(x)|\geq c_1\norm{Tx}_Y^p-c_2$ for $p>1$ and constants $c_1,c_2$. Furthermore assume that $E$ has a unique minimiser on $X_0$.
\end{enumerate}
We can formulate our main result, its proof is very similar to the case of the Dirichlet energy
\begin{theorem}
    Under the hypotheses \textup{(H1)}-\textup{(H5)} the sequence \((F_n)_{n\in\mathbb N}\) of functionals \(\Gamma\)-converges towards \(F\) and further every sequence of quasi-minimisers of \((F_n)_{n\in\mathbb N}\) converges to the unique minimiser of $F$.
    \begin{proof}
        The proof mainly consists of abstraction of the concepts we already met in the Dirichlet case and therefore we will keep it brief. A look back to the shows that (H1), together with the strong continuity of $E$ from (H5) provides a recovery sequence and the $\liminf$ inequality follows by the lower semi-continuity assumed in (H5).
        The hypothesis (H2)-(H4) take care of the equi-coercivity which deserves some extra comments and we refer the reader to the next lemma.
    \end{proof}
\end{theorem}
\begin{lemma}[Abstract Poincar\'e Inequality]
    Consider the setting described above i.e., let $(X,\norm{\cdot}_X)$ and $(Y,\norm{\cdot}_Y)$ be Banach spaces with a linear and continuous map $T:X\to Y$ and another norm $\lvert\,\cdot\,\rvert$ on $X$ such that $\norm{x}_X=|x|+\norm{Tx}_Y$ and the identity $(X,\norm{\cdot}_X)\to(X,\lvert\,\cdot\,\rvert)$ maps weakly to strongly convergent sequences. Let $M$ be some weakly closed, star-shaped set with center zero. Then $\ker(T)\cap M$ is bounded if and only if there is a constant $C$ such that
    \[ |x|\leq C(\norm{Tx}_Y+1)\quad\textup{for all }x\in M. \]
    \begin{proof}
    This works exactly as in the case $X=H^1(\Omega)$ and $Y=L^2(\Omega)^d$ with $T=\nabla$ which we studied before.
    \end{proof}
\end{lemma}{}
\subsubsection*{The \(p\)-Laplace: An example for a nonlinear PDE}
We illustrate the abstract setting briefly by considering the $p$-Dirichlet energy for $p\in (1,\infty)$ which is given by
\begin{align*}
    E:W^{1,p}(\Omega)\to\mathbb{R}
    \quad\text{with}\quad
    E(u)
    =
    \frac1p\int_\Omega|\nabla u|^p\,dx
\end{align*}
Note that for $p\neq 2$ the associated Euler-Lagrange equation is nonlinear. This PDE is called the $p$-Laplace equation and, in strong formulation, is given by
\begin{align*}
    -\operatorname{div}(\lvert\nabla u\rvert^{p-2}\nabla u) &= f \quad\text{in }\Omega
    \\
    u &= 0 \quad\text{on }\partial\Omega,
\end{align*}
compare also to \cite[First Chapter]{struwe1990variational}. Choosing the ReLU activation function, the abstract setting presented in (\ref{AbstractSetting}) is applicable in this case by the following choices
\[ X = W^{1,p}(\Omega), \quad Y = L^p(\Omega)^d, \quad B = L^p(\partial\Omega), \quad |u| = \norm{u}_{L^p(\Omega)}\]
as well as
\begin{align*}
    \gamma = \operatorname{tr}:W^{1,p}(\Omega) & \to L^p(\partial\Omega)
    \\
    T:W^{1,p}(\Omega) & \to L^p(\Omega)^d\quad\text{with}\quad u\mapsto\nabla u.
\end{align*}
Clearly (H1), (H2) and (H5) are fulfilled and (H3) is due to Rellich's embedding theorem. We look at (H4) and need to guarantee that for every $f\in W^{1,p}(\Omega)'$ and $r>0$ the following set is bounded in $W^{1,p}(\Omega)$
\begin{align*}
    \left\{
    \norm{\operatorname{tr}(u)}^2_{L^p(\partial\Omega)}-f(u) \leq r
    \right\}.
\end{align*}{}
This works similar to the case $p=2$ discussed above and uses again a scaled version of Young's inequality.
\section{Conclusions and further research}

We established a $\Gamma$-convergence result which ensures that ReLU networks can be optimised to approximately solve a large class of stationary PDEs that are Euler-Lagrange equations of variational energies. This can be seen as the first step into the theoretical justification of the deep ritz method introduced in \cite{weinan2018deep}. However, the result is to be enjoyed with a grain of salt and we want to touch on a few limitations.
\begin{enumerate}
    \item It does not take into account the numerical approximation of the Dirichlet energy which is a further potential source of error. Further, the resulting numerical optimisation problem is not studied.
    \item It does not provide any convergence rates and is of purely qualitative nature, hence it can not explain why NNs should be superior to traditional methods.
\end{enumerate}

For future research we propose the following questions:
\begin{enumerate}
    \item Treat the \(p\)-Laplace with this approach.
    \item Work towards higher order problems; in particular one has to abandon the ReLU activation function since ReLU networks are no longer contained in the considered function spaces.
    \item Show \(\Gamma\)-convergence for numerical approximations of the regularised Dirichlet energies; this would show that – up to optimisation of the networks – the deep Ritz method is consistent.
    \item Establish convergence rates.
\end{enumerate}

\bibliographystyle{apalike}

redpajama_set_name: RedPajamaArXiv


General Salsa Making Tip: Habaneros are the hottest chiles in the world! Bright orange and looking like a tiny bell pepper, their flavor is delicious, if used sparingly.
Clean and seed peppers, wear rubber gloves. Chop onions and peppers, mince garlic. Mix all ingredients in a bowl, do not blend.
Refrigerate overnight to allow flavors to marinate.
Get some good chips and beer. This salsa is not for the timid and should be used with caution, it can cause major hiccups.
Salsa Tip: Jalapenos are the most recognizable and widely used of all Mexican chiles. Almost every Mexican table will not be without a small bowl of jalapenos from a can, pickled in escabeche with carrots and onions.


Swizzle sticks assorted that come unwrapped. 72 delicious swizzle sticks that sure taste great. Delicious rock candy swizzle sticks in 6 exciting flavors: blue raspberry, cotton candy, watermelon, cherry, grape, and strawberry. These swizzle sticks will sure bring a delightful sensation to your taste buds.


text:
Royal Family LIVE: Huge row erupts over monarchy – 'Won't be watching Queen's speech!'
Queen Elizabeth has 'no intention' of stepping down says expert
Throughout the last year, the Government has been widely criticised for its handling of the coronavirus pandemic, which has caused more than two million infections and 67,616 deaths across the country.
Over recent weeks, the Government has made U-turns on various rules including announcing travel bans for those in London four days before Christmas.
Last weekend, countries around the world closed their borders to the UK in a bid to stop the spread of a new virulent strain of the coronavirus.
As the borders closed, people flocked to the shops to panic buy fresh produce, stripping the aisles bare.
To add to the panic of the coronavirus pandemic, the Government has also been working on securing a Brexit trade deal with the EU.
But with less than 10 days before the end of the transition period on December 31, a no deal is seeming more likely.
And now, amid ongoing Brexit talks and the coronavirus pandemic, some have taken to social media to attack the monarchy.
One person tweeted: "I am honestly sick to death of hearing that The Queen can do nothing to help this country.
"She is our head of state and it's Her Majesty's Government.
"I won't be watching her speech by the Royal Family this year.
"The words will bee just platitudes and meaningless."
While another person echoed: "The words of our unelected monarch are always just platitudes and meaningless.
"It's all just nonsense aims at keeping the status quo and the money coming in, aided and abetted by a state-sponsored BBC."
Queen Elizabeth II heartbreak as plans for Prince Charles visit RUINED [REVEAL]
Queen and Prince George's homemade mince pies sent as festive gifts [INSIGHT]
Meghan pushes Queen to 'snapping point' with new commercial deals [COMMENT]
Someone else said: "If the Queen asks us all to pull together, I swear I will become a Republican."
While another person said if the Queen can "literally do nothing" then it's hard to see the point of the monarch.
They said: "I mean, if it's true that she can literally do nothing, then it's hard to see what the point of her, or any of her expensive extended family, is."
Others urged for the UK to end the constitutional monarchy and called for the country to "grow up".
One person said: "A head of state that doesn't act to protect her OWN PARLIAMENT from a rogue PM who is actively destroy it and the country, while protecting her son who is wanted by the FBI.
"I was agnostic, but now it's time to end the constitutional monarchy.
"Britain needs to grow up."
Another questioned why the monarch has been so quiet during the pandemic and Brexit negotiations, despite giving a speech to the nation earlier this year.
They said: "Strangely enough, I am wondering why the Queen has been so quiet.
"I understand there is a boundary between the Royal Family and Government.
"But seeing a country going into complete chaos?
"Our King of the Netherlands did show himself and did his best to give us strength."
Another person accused the Queen of being "complicit or completely bloody useless".
Despite being the Head of the State, Queen Elizabeth's role is purely ceremonial meaning the power to pass legislation resides with the elected Parliament.
Many important Governmental actions are done "on behalf" of the Queen or she exercises her powers at the direction of the Prime Minister.
The British Royal Family started losing martial powers due to the signing of the Magna Carter in 1215, which led to the rule of constitutional law in England.
FOLLOW BELOW FOR LIVE UPDATES:
8.15am update: Meghan Markle 'loved' her first royal Christmas: 'Family she never had'
Meghan Markle's first Christmas with the rest of the Royal Family was "amazing" according to Prince Harry, which contrasts with the emerging reports of a feud between the couple and the Firm in recent months.
Meghan and Harry will be spending their first Christmas as a married couple in the US this year, along with their son Archie Harrison.
Reports claim the young family will be celebrating with Meghan's mother, Doria Ragland, and the couple have already been spotted shopping for a tree at a Santa Barbara farm.
The Duke and Duchess of Sussex boycotted royal tradition last year when they decided to spend the festive season in Canada instead, as part of their extended break before they announced they had decided to leave the royal frontline.
8am update: Kate using 'hands on' parenting for Louis as experts claim Prince is Duchess' 'favourite'
Kate, the Duchess of Cambridge's close relationship with her youngest child, Prince Louis, has been analysed by royal commentators who noted her and William's "super hands-on" approach to parenting him.
Prince Louis may be Kate, the Duchess of Cambridge's "favourite" in the family, royal commentators have claimed.
Royally Obsessed podcast hosts Roberta Fiorito and Rachel Bowie discussed the Cambridge family's first official outing this year at the London Palladium pantomime.
Both of them noted the youngest royal's behaviour, and attributed it to Kate and Prince William's parenting style.
Posted in EuropeTagged Aut, ctp_video, headlines, Nation
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Three French police officers shot dead as they respond to domestic violence call


text:
Novel Method Distinguishes the Right Individual Exosomes
by Iswarya on August 26, 2019 at 3:44 PM Research News
Novel method developed can map surface protein complements on large numbers of individual exosomes. The findings of the study are published in the journal Nature Communications.
There is a growing demand for diagnostic markers for early disease detection and prognosis. Exosomes are potential biomarkers for cancer progression and neurodegenerative disease, but it can be difficult to identify what tissue a specific exosome comes from.
Exosomes are released from all cells in the body. They convey protein and nucleic acid cargos between the cells as a form of intercellular communication, and they represent potential circulating biomarkers for tumor progression and metastasis, as well as for early detection of neurodegenerative disease.
'In order to use exosomes as biomarkers of diseases in various tissues, it is important to distinguish them according to their surface protein complements.'
In order to use exosomes as biomarkers of diseases in different tissues, it is vital to distinguish them according to their surface protein complements. Researchers at Uppsala University and Vesicode AB, along with collaborators, have developed a method that can map surface protein complements on large numbers of individual exosomes.
The novel proximity-dependent barcoding assay (PBA) reveals the surface protein composition of individual exosomes using antibody-DNA conjugates and next-generation sequencing. The method identifies proteins on individual exosomes using micrometer-sized, uniquely tagged single-stranded DNA clusters generated by rolling circle amplification.
"This technology will not only benefit researchers studying exosomes but also enable high-throughput biomarker discovery. We will further develop and validate the PBA technology and provide service to researchers starting later this year. We believe single exosome analysis will allow this exciting class of biomarkers to reach its full potential," says Di Wu, researcher, and inventor of the PBA technology and founder of Vesicode AB, commercializing the technique.
"This new technology will allow large-scale screens for biomarkers in disease, complementing a panel of methods for sensitive and specific detection of exosomes that we have previously established," says Masood Kamali-Moghaddam one of the group leaders at the Molecular Tools unit at Uppsala University.
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text:
The A-Z of Geek Cinema: S is for Speed Racer
Let us speak now in praise of Speed Racer.
No, I'm serious. 2008's Speed Racer, written and directed by the Wachowskis. Fresh off the Matrix films, the (then) brothers took ahold of the long languishing production, which had gone through multiple directors and stars, and ran with it straight into the lights. Dayglo technicolor visuals and an anti-corporate plot line combined with the palpable sense of excitement instilled in every frame to make one of the most inventive and, yes, pure FUN movies of that year, or really of the decade. So, of course, it was a critical and commercial failure. People weren't ready for it, I guess, or perhaps it looked too kiddy for the adults and too intense for the kids? I don't know, that's really not for me to say. What there IS for me to say is this: HOLY CRAP, do I love this film.
Let me get this out of the way at the top: Speed Racer is not about racing. Ok, so that's a bit of a stretch. It IS about racing. It is about giant cartoon racing on tracks made of neon and electricity, against vikings and beauty queens and cars that literally shoot bees at you. It is about good and bad and family and corporate sellouts and duty. But it's also about life, in a way that is simple and clear cut. It is about knowing what you're good at, knowing what you were born to do, what you HAVE to do, and doing it the best you can. And all the visual flair and inventive camera work and lightning quick editing are just icing on this heartfelt message.
Like I mentioned above, the Wachowskis made their names with The Matrix, but I think there is more heart and love and humor at the center of this movie than there is in all 3 Matrix films combined. That final race, when Speed is approaching the finish line, with all his family and all the fans and all the announcers cheering for him… THAT is the moment this movie has built to. The idea that someone who knows what he's good at, what he's MADE for (I mean, shit, his name is "Speed Racer", for god's sake), is on the cusp of achieving that goal. And it never fails to get to me, in my gut. It's the same spot that almost all sports movies hit me, like Miracle. People who dismiss this movie as visual candy, as stupid fluff, are ultimately missing the point. And I feel sad for them, because they will never know the joy of this film.
And "joy" is the right word to use. Because every frame of this film is joyous, whether it's in the aforementioned hyperkinetic race scenes, or John Goodman fighting a ninja (!), or Speed & Trixie hanging out. Even the capital-S "Serious" scenes about corruption and dark secrets have a certain spark to them that sanctimonious blockbusters like Transformers could use in spades. Which is the movie's secret weapon: the Wachowskis know that this is all ridiculous. Like I said before, they have VIKINGS driving RACECARS being bribed with ANIMAL PELTS and launching BEEHIVES at people. That's a line that once you cross it, no matter how "serious" you think you're being, you have tread into different territory. And more big budget movies could use that spark, that fun. Movies like Transformers and Battleship and the like treat their inherently goofy subject matter with such po-faced straight lace-ness that it just makes the participants look stupid and immature. Weirdly enough, it's the films that take the more childlike fun approach, like Speed Racer and Avengers, that succeed at what they're aiming for. More people should be aiming for fun. It's a problem I see in the comics industry as well. Unfortunately they, along with the majority of Hollywood, don't seem to want to acknowledge that,
And honestly, they just need to get that weak shit off my track.
Tags: Gran Turismo SportsMarvel Comic Eventnight of the living deadShenmuesoaSpecialsThe Piano GuysTop 7 MCUvillains
The A-Z of Geek Cinema: Z is for Zardoz
Nerds on the Rocks: Oscar Pool 2011
Kaiju Kommentary: Godzilla vs. Hedorah (1971)
Jay V says:
No longer the Wachowski brothers, but just the Wachowskis. In some small way, I long for the alternate universe version where they are still known as the Wachowski brothers. That part of me is also the part that wishes for simpler times, when men were men and moms washed your clothes for you, and unfortunately in this dream world time women are oppressed and people don't talk about sex like it's an everyday occurrence. Ok maybe my world is a bit backwards.
Maybe I'll stick with this universe. LONG LIVE THE WACHOWSKIS. Also, I want to see this film now, if a car shoots bees!
Shazam says:
Love Speed Racer. I want them to direct a Flash movie soooo bad.
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