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Pedestrian and cycle friendly Belfast could be outcome of coronavirus emergency

Councillor says the emergency could force the city to re-imagine itself




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Stinger used to stop car in dramatic police chase through Co Antrim

The car chase unfolded in the early hours of Saturday morning




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Commander Chuck Adds North Mississippi Radio Group Trio To Traffic Report Affiliate List

ON TIME TRAFFIC NETWORK's COMMANDER CHUCK JOHNSON is now heard on NORTH MISSISSIPPI RADIO GROUP's stations, Classic Hits WOWW-A-W249BN (97.7 GUESS FM), Country WEBL (95.3 THE REBEL), … more




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Clint Marsh Adds SVP Stripes At Futuri Media

CLINT MARSH has been promoted to SVP/Product at CLEVELAND-based FUTURI MEDIA. He joined the company in 2016 as Partner Integration Specialist (NET NEWS 7/25/2016), and was promoted to … more




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John Harrington-WHAT WE USE - Hensel Tria 1500

Here's a video segment on the Hensel Tria 1500 kit, that we use as an add on to our main Hensel lighting kit. A transcription of the video is available after the jump.




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Brooke Scullion among The Voice contestants behind tribute song to NHS

Speaking on the current status of the The Voice’s return Brooke said she’s in constant contact with fellow finalists and production




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Rangers dossier so weak they must have produced it on Dubai trip - Sutton

The Daily Record columnist claims it's a deflection from the club's failures on the pitch this season




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UMe And Spirit Complete Distribution Deal For Ingrid Michaelson Catalog

UNIVERSAL MUSIC GROUP's UMe has inked a deal with SPIRIT MUSIC GROUP for worldwide distribution of the majority of INGRID MICHAELSON's catalog. SPIRIT acquired the majority of … more




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The Very Special Triangles

A recent paper uncovers a unique pair of shapes

-- Read more on ScientificAmerican.com




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Tribune Media

Tribune Media is home to a diverse portfolio of television and digital properties driven by news, entertainment and sports programming.




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Courts and Tribunals Judiciary of England and Wales

Information about the Courts and Tribunals Judiciary of England and Wales. Read the latest judgments, news and speeches.




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Updated treatment guidelines for atrial fibrillation recommend a new class of blood thinners to help prevent stroke

Focused Update Highlights: Newer anticoagulants, known as non-vitamin K oral anticoagulants (NOACs), are recommended over the traditional warfarin to prevent stroke in people with atrial fibrillation (AFib). Weight loss is recommended for overweight or obese people with AFib.




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Treating more than just the heart is critical for geriatric patients

Statement Highlights: Geriatric conditions such as frailty, cognitive impairment, taking multiple medications and having multiple medical conditions complicate care for older people with acute cardiovascular diseases. Most research on how to treat...




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Better lifestyle habits are useful additions to optimize management of atrial fibrillation

Statement Highlights: Improving lifestyle habits – such as attaining and maintaining a healthy body weight and getting regular, moderate physical activity – may be useful additions to physician-guided management of atrial fibrillation (AF), a serious...




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Federal district court strikes down USDA rule that weakens national school nutrition programs

WASHINGTON, D.C., April 14, 2020 — Yesterday, a federal district court struck down a rule by the U.S. Department of Agriculture (USDA) that rolled back nutrition standards in schools.   Last fall, The American Heart Association, the world’s leading...




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Goa Hippy Tribe

Goa Hippy Tribe is an interactive documentary that tells the story of the original Goan hippies, led by the inimitable Eight-Finger Eddie, who first met in the early 70s and re-connected on Facebook to re-unite in 2010. An immersive online trip, the project features interviews shot by director Darius Devas as well as material contributed by Facebook users as part of an initial, groundbreaking social media phase.




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The Many Lands of Manyland – A Trip to a Universe of Creativity

As like must of our readers, we have been stuck home in quarantine for the past weeks. Or is it months? It’s hard to tell. Anyway, we decided to use this spare time to find some games that are both fun and have design value. So, we looked for a game that induced creativity, was...




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Risk of Repeat Concussion Among Patients Diagnosed at a Pediatric Care Network

Concussion is a common childhood injury that may lead to long-term physical, behavioral, and neurocognitive effects, affecting learning and school performance. There is increasing concern about the potential for repeat concussions among professional and high school athletes, with specific attention focused on understanding how sustaining a concussion alters future concussion risk. Addressing repeat concussion risk among youth has substantial implications for clinical practice in terms of managing exposure — particularly regarding youth sports participation — and long-term health and development.




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10 Beautifully Designed, Minimal & Name-Centric Business Cards

Sometimes all you need is a name. It is a powerful thing. It always has a meaning and, even more, it has a subtext and undertone. A name can speak...

The post 10 Beautifully Designed, Minimal & Name-Centric Business Cards appeared first on Speckyboy Design Magazine.




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Task force will make recommendations on how to resume jury trials, given coronavirus concerns

DES MOINES — The Iowa Supreme Court has asked a group of criminal and civil lawyers, judges and court staff from judicial districts across the state to make recommendations on how criminal and...




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What can a 15-year-old stripper in Kentucky tell you about China?

Note: This post is adapted from my original viral Twitter thread. Ffrom November 2003 through July 2005, I worked in the prepaid cell phone and phone card industry. Most of my work was in BFE meth towns and urban ghettoes. I learned things about the poor in America you won’t want to believe… But this […]




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Bohannan: Bring new ideas and energy to House District 85

The upcoming primary election is a pivotal moment for Iowa City. For the past several months, I have talked to people throughout the district who are ready for change. They believe their Democratic representative should show up for people throughout the community, especially those in need. They expect a legislator from Iowa’s bluest district to be a leader in the party, raising money to support Democratic candidates up and down the ticket and making the strongest possible case for progressive legislation. They are ready to start now in building the future of the Democratic Party and state government in Iowa. And I am honored that they are putting their trust in me.

There is a lot at stake in this election. The coronavirus has laid bare and magnified preexisting inequities — inequities brought about by the Legislature’s disinvestment in education, health care, and worker rights and safety. Small businesses are now struggling to survive, when for years the state has been giving large corporations hundreds of millions of dollars in tax credits. Water quality, climate change and gun violence still need our attention, even as we continue to invest in keeping people safe from COVID-19. We have never needed strong leadership more than we do now.

I will be a champion for progressive values because I have lived them. I know how hard it can be for people to get by even when they work hard. I grew up in a trailer in rural Florida. Neither of my parents graduated high school. My dad was a construction worker who suffered for years with emphysema. When his health insurance was canceled, my family had to choose between paying for his medicine and everything else. Fortunately, public education gave me the opportunity for a better life. My teachers taught me well and helped me to apply to college. Public university tuition was affordable then, and I was able to work my way through engineering school and law school.

Today, I am a law professor, an environmental engineer and a mother. I believe I have the skills, energy and passion that Iowa City needs at this critical point in time. I will show up for every member of our community and fight for a better future for all of Iowa.

It’s time for change in Iowa City. Please vote for me in House District 85 and help to build the future that Iowa deserves.

Christina Bohannan is a candidate in the Democratic primary for Iowa House District 85.




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Everly: An electrician, not a politician

I’m Steven the electrician, not the politician. I’m asking for your vote and support in getting there.

• Never held public office in Iowa or Illinois, check my competitors.

• No endorsements so no worries about draining that swamp here.

• Pro-life and Birthright supporter.

• 2nd Amendment and gun rights supporter.

• Legal immigration and revision of laws.

• Supporter of the constitution as written.

• Israel supporter.

• Farm owner and advocate for agriculture and fair trade.

• Check who funded my campaign, I owe no favors or pay backs.

• Still working hard for my family and married 40 years.

• I will budget your money if elected, and no tax increases.

• End of government overreach.

• Proud of our military and their never-ending service.

I’m not the establishment, but your candidate.

Steven Everly is a candidate in the Republican primary for Iowa’s 2nd Congressional District.




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Borchardt: 2nd District needs a true Iowa citizen legislator

I’m running for Iowa’s 2nd district seat in the U.S. House of Representatives. Early last fall, I found that Mariannette Miller-Meeks is running again, after three losses, and that former Illinois Congressman Bobby Schilling is an Illinoisan turned Iowan. The second district seat should be held by a true Iowa citizen legislator.

The House of Representatives was meant to be the people’s house. One where people temporarily left their home and family to serve in Washington, then returned home to resume their life. Being elected to office was never intended to be a lifetime job. If elected I will serve three terms, then return to Iowa and the private sector.

I believe our government should be small, efficient and responsive to its citizens. I would insist that all government programs are reviewed and eliminated if they are not currently serving the public’s interests. I would also push for a budget that does not grow at a higher rate than incoming revenues.

I believe that all law-abiding citizens have the right to own a gun to hunt or to protect themselves from danger. I will not support any additional restrictions placed on law-abiding citizens.

I believe all life is sacred, from conception to natural death, regardless of ability. It is not my intention to tell any woman what to do with her body. I would prefer that each women take full control of her body and the choices she makes before pregnancy occurs.

In the beginning, our country was land rich and people poor. Anyone who could make it to our country was welcome and opportunities abounded. Today, we are crowded and too many struggle to find substantial work. Immigrants are welcome, but I support only legal immigration, to mitigate how many enter the United States, while our county exercises its right to defend its borders by reasonable means, including strengthening barriers to illegal entry.

I grew up in Washington, Iowa and moved to Iowa City in my late 20s. I currently work in retail and my wife works at a food distribution plant. We have two children, ages 11 and 9, who attend public school in Iowa City. On any given day you could see me at the grocery store, the mall, at the children’s school or at their soccer game. I will be a true citizen-legislator and I would like your support.

Tim Borchardt is a candidate in the Republican primary for Iowa’s 2nd Congressional District.




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Bohannan is the best pick in House District 85

The next ten years will prove to be one of the most challenging eras in Iowa history.

Whether we meet those challenges with Iowa-smart, progressive responses will depend largely on the quality of legislators we elect to office.

Christina Bohannan, Democratic candidate for the Iowa House of Representatives, would be a remarkably talented and hardworking legislator, if given the opportunity to serve.

The daughter of blue-collar parents.

Trained as an environmental engineer.

A professor of law at the University of Iowa College of Law.

The former president of the Iowa Faculty Senate.

A mother.

These life experiences inform Christina Bohannan’s pragmatic progressivism.

If elected, she has the skill set to get good things done for Iowa.

Please join me in supporting Democrat Christina Bohannan for the House District 85 seat in the June 2 primary election.

Jim Larew

Iowa City



  • Letters to the Editor

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Task force will make recommendations on how to resume jury trials, given coronavirus concerns

DES MOINES — The Iowa Supreme Court has asked a group of criminal and civil lawyers, judges and court staff from judicial districts across the state to make recommendations on how criminal and civil jury trials will resume with coronavirus health restrictions.

The court is asking the 17-member Jumpstart Jury Trials Task Force to develop temporary policies and procedures for jury trials that will ensure the “fundamental rights of a defendant” to a jury trial, while at the same time “protecting the health and safety” of the jurors, attorneys, judges and the public, said Des Moines lawyer Guy Cook, co-chairman of the task force.

The court, Cook said Thursday, has put together a “good cross-section” of professionals who have experience with civil and criminal trials.

Task force members are:

• Associate Supreme Court Justice Mark McDermott, chairman

• Guy Cook, Des Moines criminal and civil attorney, co-chairman

• 4th Judicial District Judge Michael Hooper

• 5th Judicial District Judge David Porter

• Angela Campbell, Des Moines criminal defense attorney

• Jim Craig, Cedar Rapids civil attorney, president of Iowa Defense Counsel Association

• Janietta Criswell, clerk and jury manager, 8th Judicial District, Ottumwa

• Kathy Gaylord, district court administrator, 7th Judicial District, Davenport

• Patrick Jennings, Woodbury county attorney, Sioux City

• Julie Kneip, clerk of court, 2nd Judicial District, Fort Dodge

• Bill Miller, Des Moines civil attorney, chairman of Iowa State Bar Association litigation

• Todd Nuccio, Iowa state court administrator

• Jerry Schnurr, Fort Dodge civil attorney and president-elect of Iowa State Bar Association

• Jennifer Solberg, Woodbury County chief public defender

• Chad Swanson, Waterloo civil attorney, president of Iowa Association of Justice

• Brian Williams, Black Hawk county attorney

• Mark Headlee, information technology director of Iowa Judicial Branch

The committee will review the current schedule to resume jury trials that the court has established in consultation with public health officials and other health care providers, and recommend whether the schedule should be altered, according to the court’s order.

Jury criminal trials can resume July 13 and civil trials Aug. 3, according to the order.

The task force also will make recommendations for how those trials should proceed, according to the court’s order.

Members should develop policies and procedures aimed at protecting the health and safety of jurors, court staff, attorneys, judges and visitors throughout the trial process, particularly during the identification of potential jurors, summons of potential jurors, jury selection, trials, jury instructions and jury deliberations.

Cook said members will have to consider the challenges for each type of trial. More jurors, for example, are needed in a criminal case, so space and logistics will have to be considered with social distancing requirements.

That will be more difficult in the rural courthouses that have less space.

A pool of 80 to 100 potential jurors are sometimes summoned for felony trials in larger counties, but that, too, may be a challenge with social distancing.

Another possibility would be requiring masks, but how will a mask affect the credibility of a witness if it hides the person’s facial expressions, Cook said.

These are all issues the members may encounter.

Steve Davis, Iowa Judicial Branch spokesman, said the goal is one uniform statewide plan, but it’s possible that each district may have some discretion, as in the previous orders issued during this pandemic, because of the differences in each county.

Davis said the task force members were chosen based on gender, background and geographic area.

The recommendations should be submitted to the court the first week in June.

Davis said he didn’t yet know when the task force would start meeting by phone or video conference or how often.

Comments: (319) 398-8318; trish.mehaffey@thegazette.com




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This trip solidified my conviction to learning photography. A...



This trip solidified my conviction to learning photography. A lot has happened since this shot was taken.
Can you pinpoint the moment you decided to pursue photography? (at Toronto, Ontario)




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Electric Geek Transportation Systems

I've never thought of myself as a "car person". The last new car I bought (and in fact, now that I think about it, the first new car I ever bought) was the quirky 1998 Ford Contour SVT. Since then we bought a VW station wagon in 2011




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The Rise of the Electric Scooter

In an electric car, the (enormous) battery is a major part of the price. If electric car prices are decreasing, battery costs must be decreasing, because it's not like the cost of fabricating rubber, aluminum, glass, and steel into car shapes can decline that much, right?

On an electric scooter




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How to Create a CSS-Tricks Custom Scrollbar

Chris Coyier of CSS-Tricks is an amazing engineer and blogger. He’s not only creative but has always had the drive to put his thoughts to work, no matter how large. He also has a good eye for the little things that can make CSS-Tricks or your site special. One of those little things is his […]

The post How to Create a CSS-Tricks Custom Scrollbar appeared first on David Walsh Blog.




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Unforgettable Road Trips in the UK-A new of enjoying your next travel

Scenic Road Trips in the UK that are Worth Capturing by Camera Some people like hiking. Some people like cycling. But, after chatting with online car dealership Carspring, it seems you can have just as much fun exploring your next trip in the complete, climate-controlled comfort of your car. Here we go through the most unforgettable road trips in England, Scotland and Wales. Drives that offer driving heaven, stunning scenery and plenty of fun along the way. All you need is the right company and you are all set to enjoy! England: Road from Glastonbury to Cheddar Gorge – Check out the route here. This route gives you a proper feel of medieval England. Begin deep in England’s spiritual realm on the outskirts of the hallowed town on Glastonbury (Therefore avoid at a certain summer weekend). Start at the Tor on the edge of town, where hippies will tell you ... Read more

The post Unforgettable Road Trips in the UK-A new of enjoying your next travel appeared first on Digital Photography Tutorials.




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You Might Be Tempted to Use These CSS Tricks But Should You?

The temptation to dive right into new and exciting CSS tricks is strong – you might even do it without knowing it through learning by example or implementing that hot new framework everyone is talking about. It is more important to fully understand new CSS classes and properties, experiment with them and learn their limitations […]


The post You Might Be Tempted to Use These CSS Tricks But Should You? appeared first on Web Designer Wall.





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Trip to Mazirbe

At the very last day of last year (2017) I took an offer to go to Mazirbe – an old fishermen village, located on coast of Baltic sea, West part of Latvia. Trip turned around to be very nice. And I got some nice shots, too.

See rest of photos from trip to Mazirbe.




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‘Utterly Terrifying’: Study Affirms Feedback Loop Fears as Surging Antarctica Ice Loss Tripled in Last Five Years

By Jessica Corbett Common Dreams “The most robust study of the ice mass balance of Antarctica to date,” scientists say, “now puts Antarctica in the frame as one of the largest contributors to sea-level rise.” Scientists are expressing alarm over … Continue reading



  • Climate & Climate Change
  • Climate Change ET
  • Antarctic
  • Antarctic ice sheet
  • Antartic ice loss
  • sea level rise

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Every Day A Post of WordPress Tips and Tricks until Christmas!

The time has come and our loyal reader know already our traditional Advents Calendar. For the people who don’t know, […]




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School District Switches to Local and Organic Meals, Cuts Carbon Footprint—and Saves Money

By Melissa Hellmann Yes! Magazine A new report revealed surprising results when Oakland overhauled its lunch menu at 100-plus schools by serving less meat and more fruits and vegetables. When her eldest son was in elementary school in the Oakland … Continue reading




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Electric Cars and Surging Solar Spell Market Doom for Fossil Fuels

By Jessica Corbett Common Dreams Analyses show how demand for electric vehicles and rapidly falling renewable energy prices could take down oil and gas industry As an increasing number of nations make plans for banning gas and diesel vehicles within … Continue reading



  • Business & Economy

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Warming Weather Could Reduce the Nutritional Value of Rice

UN Environment Press Release Hundreds of millions of people in Asia rely on rice not only as a staple but as their main source of nutrition. But new research suggests the rice they eat will become less nutritious due to … Continue reading




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DJI’s new Matrice 300 RTK drone offers a ridiculous 55-minutes of flight time and 2.7kg payload

DJI has announced their new Matrice 300 RTK “flying platform” (big drone) and the Zenmuse H20 hybrid camera series, to provide “a safer and smarter solution” to their enterprise customers. The M300 RTK, DJI says, is their first to integrate modern aviation features, advanced AI, 6-direction sensing and positioning, a UAV health management system and […]

The post DJI’s new Matrice 300 RTK drone offers a ridiculous 55-minutes of flight time and 2.7kg payload appeared first on DIY Photography.



  • DIY
  • dji
  • DJI M300 RTK
  • DJI Matrice 300 RTK
  • Matrice 300 RTK

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Triangles in graphs without bipartite suspensions. (arXiv:2004.11930v2 [math.CO] UPDATED)

Given graphs $T$ and $H$, the generalized Tur'an number ex$(n,T,H)$ is the maximum number of copies of $T$ in an $n$-vertex graph with no copies of $H$. Alon and Shikhelman, using a result of ErdH os, determined the asymptotics of ex$(n,K_3,H)$ when the chromatic number of $H$ is greater than 3 and proved several results when $H$ is bipartite. We consider this problem when $H$ has chromatic number 3. Even this special case for the following relatively simple 3-chromatic graphs appears to be challenging.

The suspension $widehat H$ of a graph $H$ is the graph obtained from $H$ by adding a new vertex adjacent to all vertices of $H$. We give new upper and lower bounds on ex$(n,K_3,widehat{H})$ when $H$ is a path, even cycle, or complete bipartite graph. One of the main tools we use is the triangle removal lemma, but it is unclear if much stronger statements can be proved without using the removal lemma.




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Set theoretic Yang-Baxter & reflection equations and quantum group symmetries. (arXiv:2003.08317v3 [math-ph] UPDATED)

Connections between set theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and twisted algebras and we derive the associated defining algebra relations for $R$-matrices being Baxterized solutions of the $A$-type Hecke algebra ${cal H}_N(q=1)$. We show in the case of the reflection algebra that there exists a "boundary" finite sub-algebra for some special choice of "boundary" elements of the $B$-type Hecke algebra ${cal B}_N(q=1, Q)$. We also show the key proposition that the associated double row transfer matrix is essentially expressed in terms of the elements of the $B$-type Hecke algebra. This is one of the fundamental results of this investigation together with the proof of the duality between the boundary finite subalgebra and the $B$-type Hecke algebra. These are universal statements that largely generalize previous relevant findings, and also allow the investigation of the symmetries of the double row transfer matrix.




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Linear Convergence of First- and Zeroth-Order Primal-Dual Algorithms for Distributed Nonconvex Optimization. (arXiv:1912.12110v2 [math.OC] UPDATED)

This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first propose a distributed first-order primal-dual algorithm. We show that it converges sublinearly to the stationary point if each local cost function is smooth and linearly to the global optimum under an additional condition that the global cost function satisfies the Polyak-{L}ojasiewicz condition. This condition is weaker than strong convexity, which is a standard condition for proving the linear convergence of distributed optimization algorithms, and the global minimizer is not necessarily unique or finite. Motivated by the situations where the gradients are unavailable, we then propose a distributed zeroth-order algorithm, derived from the proposed distributed first-order algorithm by using a deterministic gradient estimator, and show that it has the same convergence properties as the proposed first-order algorithm under the same conditions. The theoretical results are illustrated by numerical simulations.




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Monochromatic Equilateral Triangles in the Unit Distance Graph. (arXiv:1909.09856v2 [math.CO] UPDATED)

Let $chi_{Delta}(mathbb{R}^{n})$ denote the minimum number of colors needed to color $mathbb{R}^{n}$ so that there will not be a monochromatic equilateral triangle with side length $1$. Using the slice rank method, we reprove a result of Frankl and Rodl, and show that $chi_{Delta}left(mathbb{R}^{n} ight)$ grows exponentially with $n$. This technique substantially improves upon the best known quantitative lower bounds for $chi_{Delta}left(mathbb{R}^{n} ight)$, and we obtain [ chi_{Delta}left(mathbb{R}^{n} ight)>(1.01446+o(1))^{n}. ]




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Grothendieck's inequalities for JB$^*$-triples: Proof of the Barton-Friedman conjecture. (arXiv:1903.08931v3 [math.OA] UPDATED)

We prove that, given a constant $K> 2$ and a bounded linear operator $T$ from a JB$^*$-triple $E$ into a complex Hilbert space $H$, there exists a norm-one functional $psiin E^*$ satisfying $$|T(x)| leq K , |T| , |x|_{psi},$$ for all $xin E$. Applying this result we show that, given $G > 8 (1+2sqrt{3})$ and a bounded bilinear form $V$ on the Cartesian product of two JB$^*$-triples $E$ and $B$, there exist norm-one functionals $varphiin E^{*}$ and $psiin B^{*}$ satisfying $$|V(x,y)| leq G |V| , |x|_{varphi} , |y|_{psi}$$ for all $(x,y)in E imes B$. These results prove a conjecture pursued during almost twenty years.




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High dimensional expanders and coset geometries. (arXiv:1710.05304v3 [math.CO] UPDATED)

High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only known construction of bounded degree high dimensional expanders is based on Ramanujan complexes, whereas one dimensional bounded degree expanders are abundant.

In this work, we construct new families of bounded degree high dimensional expanders obeying the local spectral expansion property. This property has a number of important consequences, including geometric overlapping, fast mixing of high dimensional random walks, agreement testing and agreement expansion. Our construction also yields new families of expander graphs which are close to the Ramanujan bound, i.e., their spectral gap is close to optimal.

The construction is quite elementary and it is presented in a self contained manner; This is in contrary to the highly involved previously known construction of the Ramanujan complexes. The construction is also very symmetric (such symmetry properties are not known for Ramanujan complexes) ; The symmetry of the construction could be used, for example, in order to obtain good symmetric LDPC codes that were previously based on Ramanujan graphs.

The main tool that we use for is the theory of coset geometries. Coset geometries arose as a tool for studying finite simple groups. Here, we show that coset geometries arise in a very natural manner for groups of elementary matrices over any finitely generated algebra over a commutative unital ring. In other words, we show that such groups act simply transitively on the top dimensional face of a pure, partite, clique complex.




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Local mollification of Riemannian metrics using Ricci flow, and Ricci limit spaces. (arXiv:1706.09490v2 [math.DG] UPDATED)

We use Ricci flow to obtain a local bi-Holder correspondence between Ricci limit spaces in three dimensions and smooth manifolds. This is more than a complete resolution of the three-dimensional case of the conjecture of Anderson-Cheeger-Colding-Tian, describing how Ricci limit spaces in three dimensions must be homeomorphic to manifolds, and we obtain this in the most general, locally non-collapsed case. The proofs build on results and ideas from recent papers of Hochard and the current authors.




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Positive Geometries and Differential Forms with Non-Logarithmic Singularities I. (arXiv:2005.03612v1 [hep-th])

Positive geometries encode the physics of scattering amplitudes in flat space-time and the wavefunction of the universe in cosmology for a large class of models. Their unique canonical forms, providing such quantum mechanical observables, are characterised by having only logarithmic singularities along all the boundaries of the positive geometry. However, physical observables have logarithmic singularities just for a subset of theories. Thus, it becomes crucial to understand whether a similar paradigm can underlie their structure in more general cases. In this paper we start a systematic investigation of a geometric-combinatorial characterisation of differential forms with non-logarithmic singularities, focusing on projective polytopes and related meromorphic forms with multiple poles. We introduce the notions of covariant forms and covariant pairings. Covariant forms have poles only along the boundaries of the given polytope; moreover, their leading Laurent coefficients along any of the boundaries are still covariant forms on the specific boundary. Whereas meromorphic forms in covariant pairing with a polytope are associated to a specific (signed) triangulation, in which poles on spurious boundaries do not cancel completely, but their order is lowered. These meromorphic forms can be fully characterised if the polytope they are associated to is viewed as the restriction of a higher dimensional one onto a hyperplane. The canonical form of the latter can be mapped into a covariant form or a form in covariant pairing via a covariant restriction. We show how the geometry of the higher dimensional polytope determines the structure of these differential forms. Finally, we discuss how these notions are related to Jeffrey-Kirwan residues and cosmological polytopes.




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Toric Sasaki-Einstein metrics with conical singularities. (arXiv:2005.03502v1 [math.DG])

We show that any toric K"ahler cone with smooth compact cross-section admits a family of Calabi-Yau cone metrics with conical singularities along its toric divisors. The family is parametrized by the Reeb cone and the angles are given explicitly in terms of the Reeb vector field. The result is optimal, in the sense that any toric Calabi-Yau cone metric with conical singularities along the toric divisor (and smooth elsewhere) belongs to this family. We also provide examples and interpret our results in terms of Sasaki-Einstein metrics.




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The formation of trapped surfaces in the gravitational collapse of spherically symmetric scalar fields with a positive cosmological constant. (arXiv:2005.03434v1 [gr-qc])

Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou's classical criterion by the inclusion of the cosmological term.