ni

10 Design Principles to Reduce Cognitive Load

If you’re not familiar with cognitive load and how it impacts interface design, it’s worth reviewing our previous blog post. If you’re already convinced cognitive load is important, the next step is addressing it. Reducing cognitive load is accomplished by reducing or offloading mental effort (which are similar but different concepts.) Reducing mental effort is […]

The post 10 Design Principles to Reduce Cognitive Load appeared first on Psychology of Web Design | 3.7 Blog.




ni

5 Critical Lessons Learned Organizing WordCamp Ann Arbor for the Third Time

In early 2014 I had just gotten married and recently moved into a new home. With two major life events out of the way, I decided I was ready to lead a WordCamp. I originally planned to organize WordCamp Detroit. I was an organizer twice before and the event had missed a year and I […]

The post 5 Critical Lessons Learned Organizing WordCamp Ann Arbor for the Third Time appeared first on Psychology of Web Design | 3.7 Blog.




ni

A set of key visuals for Nike Shanghai

A set of key visuals for Nike Shanghai

AoiroStudioMay 06, 2020

I think this is going to break our visual pattern but this is totally worth it. This is the work from How Wei Zhong who art directed this massive campaign for Nike Shanghai in collaboration with the folks from ILoveDust. It's quite refreshing since first of all it's collaborative participation and obviously the end-result that is just purely vibrant and amazing. To share a little bit of background on this project (in their words). “Qiang Diao” is Chinese for confidence, swagger and game.

And in a city as image and style conscious as Shanghai, Qiang Diao is something many people want for themselves. Nike wanted Shanghai athletes to know that sports can offer you more than fitness. We created OOH celebrating Shanghainese athletes well-known for their strong personalities and, of course, having Qiang Diao.

About How Wei Zhong

How Wei Zhong is an art director at W+K Shanghai based in Kuala Lumpur, Malaysia. You should definitely check his work, it’s filled with incredible works for brands. Give him some love.




ni

Abelardo Morell, Camera Obscura: Early Morning View of the East Side of Midtown Manhattan

Abelardo Morell
Camera Obscura: Early Morning View of the East Side of Midtown Manhattan, , 2014
Website - AbelardoMorell.net

Abelardo Morell was born in Havana, Cuba in 1948. He immigrated to the United States with his parents in 1962. Morell received his undergraduate degree in 1977 from Bowdoin College and an MFA from The Yale University School of Art in 1981. In 1997 he received an honorary degree from Bowdoin College.

His publications include a photographic illustration of Alice’s Adventures in Wonderland (1998) by Dutton Children’s Books, A Camera in a Room (1995) by Smithsonian Press, A Book of Books (2002) and Camera Obscura (2004) by Bulfinch Press and Abelardo Morell (2005), published by Phaidon Press. Recent publications include a limited edition book by The Museum of Modern Art in New York of his Cliché Verre images with a text by Oliver Sacks.

His work has been collected and shown in many galleries, institutions and museums, including the Museum of Modern Art, The Whitney Museum of American Art, the Metropolitan Art Museum in New York, The Chicago Art Institute, The San Francisco Museum of Modern Art, The Houston Museum of Art, The Boston Museum of Fine Art, The Victoria & Albert Museum and over seventy other museums in the United States and abroad. A retrospective of his work organized jointly by the Art Institute of Chicago, The Getty in Los Angeles and The High Museum in Atlanta closed in May 2014 after a year of travel. Abelardo will be having his first show at the Edwynn Houk Gallery in New York opening October 23, 2014 and will run until December 20, 2014 featuring a selection of new pictures.




ni

Using Communities to Further the True Meaning of Resiliency

Service members, veterans, and their caregivers are incredibly resilient, says Adam, but learning to connect with whatever community you are in will only strengthen that resiliency.




ni

Maintaining Relationships with Family and Friends After TBI and PTSD

Adam talks frankly about his challenges keeping up with family and friends since his injury; he has good intentions but following through remains difficult.




ni

Turning Your Life Around After TBI and PTSD

Adam shares an inspiring story about a friend with TBI and PTSD who almost ended his life but instead found the courage to ask for help — even though at the time he may not have known what that help looked like.




ni

BrainLine Military Blogger Adam Anicich Says Thank You and Goodbye for Now

Adam thanks you — his blog viewers and supporters — and encourages you to continue the discussion and awareness raising about TBI and PTSD; the battle does not stop here.





ni

Support Communication During Conversation




ni

Troops to receive Purple Hearts for injuries during Iranian missile barrage on al-Asad airbase in Iraq

There will be Purple Hearts awarded to troops injured during the Jan. 8 Iranian missile barrage on the al-Asad airbase in Iraq, a defense official told Military Times.




ni

Remapping the Neural Pathways of Humanity

The pandemic has changed the daily lives of everyone. How we work, how we shop, and how we interact with each other are all shifting. Comparing life as it is now with how it used to be can lead to sadness or despair and what's called "ambiguous loss."




ni

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




ni

How Coal Country Is Cleaning Up Its Act

By Mason Adams Yes! Magazine A program in eastern Kentucky is retraining miners in industries that help mitigate the environmental impacts of mining on communities. Like many men raised in eastern Kentucky, Frank Morris spent a chunk of his working … Continue reading




ni

Judge Could Hold Up Trump Administration's Bid to Clear Flynn, Legal Experts say

The notoriously independent-minded federal judge who once said he was disgusted by the conduct of Michael Flynn could block the administration's bid to drop criminal charges against the former adviser to President Donald Trump, legal experts said.




ni

Trump Declares, 'I Learned a Lot from Nixon'

During an interview on "Fox and Friends," Trump explained why he chose not to go on a firing spree amid Special Counsel Robert Mueller's Russia investigation a la Nixon's Saturday Night Massacre during the Watergate scandal. "I learned a lot from Richard Nixon: Don't fire people," the President said. "I learned a lot. I study history, and the firing of everybody ... .I should've, in one way," he continued. "But I'm glad I didn't because look at the way it turned out."




ni

Win the Morning. Win the Day with Tim Ferriss

In small, daily actions you’re creating outcomes for yourself and by extension, creating your life. My man Tim Ferriss is a master at deconstructing the work of others and de-stilling it into a working practice. In fact, he wrote his book Tools of Titans as a reference of some of the tactics, routines, and habits of billionaires. In this quick episode, he shares the 3 key themes he’s seen in over 200 hundred people he’s interviewed. Enjoy! FOLLOW TIM: instagram | twitter | website Listen to the Podcast Subscribe   Watch the Episode  This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

The post Win the Morning. Win the Day with Tim Ferriss appeared first on Chase Jarvis Photography.




ni

Harmony > Balance with Jason Calacanis

Today we’re going back to San Francisco with myself and Jason Calacanis on stage during my tour stop for my book Creative Calling. Jason is an investor and long time host of the This Week in Startups podcast. And, of course, Jason wastes no time in our conversation. He goes right to the heart of the matter by getting into failure, venture capitol, knowing when to quit, and when to push through. Enjoy! FOLLOW JASON: facebook | twitter | website Listen to the Podcast Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

The post Harmony > Balance with Jason Calacanis appeared first on Chase Jarvis Photography.




ni

You Are Not Your Ego with Cheri Huber and Ashwini Narayanan

Cheri has been a student and teacher of Zen for over 35 years. She is the author of over 20 books on Zen, and founded the Mountain View Zen Center and the Zen Monastery Peace Center. Cheri also founded a non-profit dedicated to transforming lives and ending suffering, Living Compassion, whose primary work is the Africa Vulnerable Children Project in Zambia. Ashwini co-facilitates and creates workshops with Cheri. She runs the operations of the two nonprofits that Cheri founded. Her eclectic background includes degrees in physics, business, and computer science to working in advertising, an investment bank, a social enterprise, and several technology startups in the Silicon Valley. Cheri and Ashwini have co-written multiple books, including their latest Don’t Suffer, Communicate. Today’s episode isn’t just about awareness practice, it’s about a framework for navigating life. A few highlights: Zen isn’t just the practice of keeping things nicely organized, it’s also a spiritual practice largely focused on awareness and where you direct attention. Self-improvement is an endless diss. The very nature of saying we need improvement implies we’re not enough. Cheri and Ashwini share some useful tools to redirect the attention, such as using a recorder to access the wisdom, love, and compassion that is […]

The post You Are Not Your Ego with Cheri Huber and Ashwini Narayanan appeared first on Chase Jarvis Photography.




ni

Pay Attention to What Ignites You with Jody MacDonald

Imagine this: Your job is good, and safe, but it’s not fueling you anymore. You decide to quit your “real” job and sell all your belongings to live a life of adventure. And just as you are waving your last goodbye, the unthinkable happens and it changes everything. Like most of us, award winning photographer Jody MacDonald didn’t know what her path would be. Yet when her wake up call came, she listened. From train hopping in the Sahara to paragliding in the Himalaya, she’s no stranger to adventure and exploration. Her work blends insightful storytelling, big adventure expeditions and social change in the hopes of promoting the preservation of wild places. Men’s Journal named her “One of the 25 Most Adventures Women in the Past 25 Years and National Geographic said she’s one of the top female adventure photographers pushing the limits. I’ve admired Jody’s work from afar for years. Her life story and career arc is remarkable. It set her on a path to tackle some of the life’s biggest questions and what she has learned is pure gold. In this episode: Why waste your time on things that make you unhappy? What Jody does to tune into […]

The post Pay Attention to What Ignites You with Jody MacDonald appeared first on Chase Jarvis Photography.




ni

The Code of the Extraordinary Mind with Vishen Lakhiani

Join me + bestselling author Vishen Lakhiani LIVE Tuesday April 7 at 6:30pm PST. Vishen Lakhiani is one of today’s most influential minds in the fields of education and human consciousness. He is the founder of Mindvalley University and its 2 million-strong student base and creator of the Quests learning platform: a next-generation method of online learning, which attains an unheard-of 60% completion rate on courses, in an industry where 8% is average. Vishen’s book, The Code of the Extraordinary Mind, made the New York Times Business Best Sellers List, and hit the coveted #1 spot on Amazon five times in 2017. Enjoy! FOLLOW VISHEN: instagram | facebook | website Listen to the Podcast coming soon … Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

The post The Code of the Extraordinary Mind with Vishen Lakhiani appeared first on Chase Jarvis Photography.




ni

Scurry: A Race-To-Finish Scavenger Hunt App

We have a lot of traditions here at Viget, many of which you may have read about - TTT, FLF, Pointless Weekend. There are others, but you have to be an insider for more information on those.

Pointless Weekend is one of our favorite traditions, though. It’s been around over a decade and some pretty fun work has come out of it over the years, like Storyboard, Baby Bookie, and Short Order. At a high level, we take 48 hours to build a tool, experiment, or stunt as a team, across all four of our offices. These projects are entirely separate from our client work and we use them to try out new technologies, explore roles on the team, and stress-test our processes.

The first step for a Pointless Weekend is assembling the teams. We had two teams this year, with a record number of participants. You can read about TrailBuddy, what the other team built, here.

The Scurry team was split between the DC and Durham offices, so all meetings were held via Hangout.

Once we were assembled, we set out to understand the constraints and the goals of our Pointless Project. We went into this weekend with an extra pep in our step, as we were determined to build something for the upcoming Viget 20th anniversary TTT this summer. Here’s what we knew we wanted:

  1. An activity all Vigets could do together, where they could create memories, and share broadly on social
  2. Something that we could use in a spotty network at C Lazy U Ranch in Colorado
  3. A product we can share with others: corporate groups, families and friends, schools, bachelor/ette parties

We landed on a scavenger hunt native app, which we named Scurry (Scavenger + Hurry = Scurry. Brilliant, right?). There are already a few scavenger apps available, so we set out to create something that was

  • Quick and easy to set up hunts
  • Free and intuitive for users
  • A nice combination of trivia and activities
  • Social! We wanted to enable teams to share photos and progress

One of the main reasons we have Pointless Weekends is to test out new technologies and processes. In that vein, we tried out Notion as our central organizing tool - we used it for user journeys, data modeling, and even writing tickets, which we typically use Github for.

We tested out Notion as our primary tool, writing tickets and tracking progress.

When we built the app, we needed to prepare for spotty network service, as internet connectivity isn’t guaranteed at C Lazy U Ranch – where our Viget20 celebration will be. A Progressive Web Application (PWA) didn't make sense for our tech requirements, so we chose the route of creating a native application.

There are a number of options available to build native applications. But, as we were looking to make as much progress as possible in 48-hours, we chose one of our favorite frameworks: React Native. React Native allows developers to build true, cross-platform native applications, using some of our favorite technologies: javascript, the React framework, and a native-specific variant of CSS. We decided on the turn-key solution Expo. Expo has extra tooling allowing for easy development, deployment, and debugging.

This is a snap shot of our app and Expo.

Our frontend developers were able to immediately dive in making screens and styling components, and quickly made the mockups in Whimsical a reality.

On the backend, we used the supported library to connect to the backend datastore, Firebase. Firebase is a hosted solution for data storage, with key features built-in like authentication, realtime updates, and offline support. Our backend developer worked behind the frontend developers hooking those views up to live data.

Both of these tools, Expo and Firebase, were easy to use and allowed us to focus on building a working application quickly, rather than being mired in setup or bespoke solutions to common problems.

Whimsical is one of our favorite tools for building out mockups of an app.

We made impressive progress in our 48-hour sprint, but there’s still some work to do. We have some additional features we hope to add before TTT, which will require additional testing and refining. For now, stay tuned and sign up for our newsletter. We’ll be sure to share when Scurry is ready for the world!



  • News & Culture

ni

5 things to Note in a New Phoenix 1.5 App

Yesterday (Apr 22, 2020) Phoenix 1.5 was officially released ????

There’s a long list of changes and improvements, but the big feature is better integration with LiveView. I’ve previously written about why LiveView interests me, so I was quite excited to dive into this release. After watching this awesome Twitter clone in 15 minutes demo from Chris McCord, I had to try out some of the new features. I generated a new phoenix app with the —live flag, installed dependencies and started a server. Here are five new features I noticed.

1. Database actions in browser

Oops! Looks like I forgot to configure the database before starting the server. There’s now a helpful message and a button in the browser that can run the command for me. There’s a similar button when migrations are pending. This is a really smooth UX to fix a very common error while developing.

2. New Tagline!

Peace-of-mind from prototype to production

This phrase looked unfamiliar, so I went digging. Turns out that the old tagline was “A productive web framework that does not compromise speed or maintainability.” (I also noticed that it was previously “speed and maintainability” until this PR from 2019 was opened on a dare to clarify the language.)

Chris McCord updated the language while adding phx.new —live. I love this framing, particularly for LiveView. I am very excited about the progressive enhancement path for LiveView apps. A project can start out with regular, server rendered HTML templates. This is a very productive way to work, and a great way to start a prototype for just about any website. Updating those templates to work with LiveView is an easier lift than a full rebuild in React. And finally, when you’re in production you have the peace-of-mind that the reliable BEAM provides.

3. Live dependency search

There’s now a big search bar right in the middle of the page. You can search through the dependencies in your app and navigate to the hexdocs for them. This doesn’t seem terribly useful, but is a cool demo of LiveView. The implementation is a good illustration of how compact a feature like this can be using LiveView.

4. LiveDashboard

This is the really cool one. In the top right of that page you see a link to LiveDashboard. Clicking it will take you to a page that looks like this.

This page is built with LiveView, and gives you a ton of information about your running system. This landing page has version numbers, memory usage, and atom count.

Clicking over to metrics brings you to this page.

By default it will tell you how long average queries are taking, but the metrics are configurable so you can define your own custom telemetry options.

The other tabs include process info, so you can monitor specific processes in your system:

And ETS tables, the in memory storage that many apps use for caching:

The dashboard is a really nice thing to get out of the box and makes it free for application developers to monitor their running system. It’s also developing very quickly. I tried an earlier version a week ago which didn’t support ETS tables, ports or sockets. I made a note to look into adding them, but it's already done! I’m excited to follow along and see where this project goes.

5. New LiveView generators

1.5 introduces a new generator mix phx.gen.live.. Like other generators, it will create all the code you need for a basic resource in your app, including the LiveView modules. The interesting part here is that it introduces patterns for organizing LiveView code, which is something I have previously been unsure about. At first glance, the new organization makes sense and feels like a good approach. I look forward to seeing how this works on a real project.

Conclusion

The 1.5 release brings more changes under the hood of course, but these are the first five differences you’ll notice after generating a new Phoenix 1.5 app with LiveView. Congratulations to the entire Phoenix team, but particularly José Valim and Chris McCord for getting this work released.



  • Code
  • Back-end Engineering

ni

An Introduction To React With Ionic

The Ionic Framework is an open-source UI toolkit for building fast, high-quality applications using web technologies with integrations for popular frameworks like Angular and React. Ionic enables cross-platform development using either Cordova or Capacitor, with the latter featuring support for desktop application development using Electron. In this article, we will explore Ionic with the React integration by building an app that displays comics using the Marvel Comics API and allows users to create a collection of their favorites.




ni

A Complete Guide To Mechanical Keyboards

About six years ago, a colleague I’ll call Tom, because that’s his name, forwarded me a link to the ‘WASD CODE’; a keyboard focused on the needs of programmers, designed with the help of Stack Overflow’s Jeff Atwood. I had no idea at the time that there were people actually dedicating themselves to creating keyboards beyond the stock fare shipping with computers. As I read and re-read the blurb, I was smitten.




ni

Nikon has confirmed that their flagship D6 DSLR will start shipping on May 21st

It feels like forever since Nikon announced their newest flagship DSLR; the Nikon D6. It’s actually only been three months, but that hasn’t stopped some people getting anxious. Recently, customers were being told that the D6 would start shipping right about now, but now Nikon has officially come out to announce that the Nikon D6 […]

The post Nikon has confirmed that their flagship D6 DSLR will start shipping on May 21st appeared first on DIY Photography.




ni

eagereyesTV Episode 2: Unit Charts, Dot Plots, ISOTYPE, and What Makes Them Special

Charts usually show values as visual properties, like the length in a bar chart, the location in a scatterplot, the area in a bubble chart, etc. Unit charts show values as multiples instead. One famous example of these charts is called ISOTYPE, and you may have seen them in information graphics as well. They’re an […]




ni

Prolific, the (Much Better) Mechnical Turk Alternative

Prolific is a crowd-sourcing platform for running studies. In contrast to the widely-used Mechanical Turk, it’s specific to studies, has a much better interface, pricing that’s fair to participants, and useful filters to find the right people for your study. Amazon's Mechanical Turk is used for many empirical studies published in the visualization literature, but […]




ni

The Visual Evolution of the “Flattening the Curve” Information Graphic

Communication has been quite a challenge during the COVID-19 pandemic, and data visualization hasn't been the most helpful given the low quality of the data – see Amanda Makulec's plea to think harder about making another coronavirus chart. A great example of how to do things right is the widely-circulated Flatten the Curve information graphic/cartoon. […]




ni

Non-associative Frobenius algebras for simply laced Chevalley groups. (arXiv:2005.02625v1 [math.RA] CROSS LISTED)

We provide an explicit construction for a class of commutative, non-associative algebras for each of the simple Chevalley groups of simply laced type. Moreover, we equip these algebras with an associating bilinear form, which turns them into Frobenius algebras. This class includes a 3876-dimensional algebra on which the Chevalley group of type E8 acts by automorphisms. We also prove that these algebras admit the structure of (axial) decomposition algebras.




ni

On the finiteness of ample models. (arXiv:2005.02613v2 [math.AG] UPDATED)

In this paper, we generalize the finiteness of models theorem in [BCHM06] to Kawamata log terminal pairs with fixed Kodaira dimension. As a consequence, we prove that a Kawamata log terminal pair with $mathbb{R}-$boundary has a canonical model, and can be approximated by log pairs with $mathbb{Q}-$boundary and the same canonical model.




ni

Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations. (arXiv:2005.02311v2 [math.AP] UPDATED)

One proves the existence and uniqueness of a generalized (mild) solution for the nonlinear Fokker--Planck equation (FPE) egin{align*} &u_t-Delta (eta(u))+{mathrm{ div}}(D(x)b(u)u)=0, quad tgeq0, xinmathbb{R}^d, d e2, \ &u(0,cdot)=u_0,mbox{in }mathbb{R}^d, end{align*} where $u_0in L^1(mathbb{R}^d)$, $etain C^2(mathbb{R})$ is a nondecreasing function, $bin C^1$, bounded, $bgeq 0$, $Din(L^2cap L^infty)(mathbb{R}^d;mathbb{R}^d)$ with ${ m div}, Din L^infty(mathbb{R}^d)$, and ${ m div},Dgeq0$, $eta$ strictly increasing, if $b$ is not constant. Moreover, $t o u(t,u_0)$ is a semigroup of contractions in $L^1(mathbb{R}^d)$, which leaves invariant the set of probability density functions in $mathbb{R}^d$. If ${ m div},Dgeq0$, $eta'(r)geq a|r|^{alpha-1}$, and $|eta(r)|leq C r^alpha$, $alphageq1,$ $alpha>frac{d-2}d$, $dgeq3$, then $|u(t)|_{L^infty}le Ct^{-frac d{d+(alpha-1)d}} |u_0|^{frac2{2+(m-1)d}},$ $t>0$, and the existence extends to initial data $u_0$ in the space $mathcal{M}_b$ of bounded measures in $mathbb{R}^d$. The solution map $mumapsto S(t)mu$, $tgeq0$, is a Lipschitz contractions on $mathcal{M}_b$ and weakly continuous in $tin[0,infty)$. As a consequence for arbitrary initial laws, we obtain weak solutions to a class of McKean-Vlasov SDEs with coefficients which have singular dependence on the time marginal laws.




ni

Nonlinear singular problems with indefinite potential term. (arXiv:2005.01789v3 [math.AP] UPDATED)

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator plus an indefinite potential. In the reaction we have the competing effects of a singular term and of concave and convex nonlinearities. In this paper the concave term is parametric. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter $lambda$ varies. This work continues our research published in arXiv:2004.12583, where $xi equiv 0 $ and in the reaction the parametric term is the singular one.




ni

Approximate Two-Sphere One-Cylinder Inequality in Parabolic Periodic Homogenization. (arXiv:2005.00989v2 [math.AP] UPDATED)

In this paper, for a family of second-order parabolic equation with rapidly oscillating and time-dependent periodic coefficients, we are interested in an approximate two-sphere one-cylinder inequality for these solutions in parabolic periodic homogenization, which implies an approximate quantitative propagation of smallness. The proof relies on the asymptotic behavior of fundamental solutions and the Lagrange interpolation technique.




ni

Convergent normal forms for five dimensional totally nondegenerate CR manifolds in C^4. (arXiv:2004.11251v2 [math.CV] UPDATED)

Applying the equivariant moving frames method, we construct convergent normal forms for real-analytic 5-dimensional totally nondegenerate CR submanifolds of C^4. These CR manifolds are divided into several biholomorphically inequivalent subclasses, each of which has its own complete normal form. Moreover it is shown that, biholomorphically, Beloshapka's cubic model is the unique member of this class with the maximum possible dimension seven of the corresponding algebra of infinitesimal CR automorphisms. Our results are also useful in the study of biholomorphic equivalence problem between CR manifolds, in question.




ni

Finite dimensional simple modules of $(q, mathbf{Q})$-current algebras. (arXiv:2004.11069v2 [math.RT] UPDATED)

The $(q, mathbf{Q})$-current algebra associated with the general linear Lie algebra was introduced by the second author in the study of representation theory of cyclotomic $q$-Schur algebras. In this paper, we study the $(q, mathbf{Q})$-current algebra $U_q(mathfrak{sl}_n^{langle mathbf{Q} angle}[x])$ associated with the special linear Lie algebra $mathfrak{sl}_n$. In particular, we classify finite dimensional simple $U_q(mathfrak{sl}_n^{langle mathbf{Q} angle}[x])$-modules.




ni

Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation. (arXiv:2003.04049v2 [math.AP] UPDATED)

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of the fluid and as such determines the variable part of a time changing domain (that is hence a part of the solution) containing the fluid. The uniqueness result is a consequence of a stability estimate where the difference of two solutions is estimated by the distance of the initial values and outer forces. For that we introduce a methodology that overcomes the problem that the two (variable in time) domains of the fluid velocities and pressures are not the same. The estimate holds under the assumption that one of the two weak solutions possesses some additional higher regularity. The additional regularity is exclusively requested for the velocity of one of the solutions resembling the celebrated Ladyzhenskaya-Prodi-Serrin conditions in the framework of variable domains.




ni

The $kappa$-Newtonian and $kappa$-Carrollian algebras and their noncommutative spacetimes. (arXiv:2003.03921v2 [hep-th] UPDATED)

We derive the non-relativistic $c oinfty$ and ultra-relativistic $c o 0$ limits of the $kappa$-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the $kappa$-(A)dS quantum algebra, and quantize the resulting contracted Poisson-Hopf algebras, thus giving rise to the $kappa$-deformation of the Newtonian (Newton-Hooke and Galilei) and Carrollian (Para-Poincar'e, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding $kappa$-Newtonian and $kappa$-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the $kappa$-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter $kappa$, the curvature parameter $eta$ and the speed of light parameter $c$.




ni

Three-point Functions in $mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence. (arXiv:2002.07216v2 [hep-th] UPDATED)

We compute non-extremal three-point functions of scalar operators in $mathcal{N}=4$ super Yang-Mills at tree-level in $g_{YM}$ and at finite $N_c$, using the operator basis of the restricted Schur characters. We make use of the diagrammatic methods called quiver calculus to simplify the three-point functions. The results involve an invariant product of the generalized Racah-Wigner tensors ($6j$ symbols). Assuming that the invariant product is written by the Littlewood-Richardson coefficients, we show that the non-extremal three-point functions satisfy the large $N_c$ background independence; correspondence between the string excitations on $AdS_5 imes S^5$ and those in the LLM geometry.




ni

A stochastic approach to the synchronization of coupled oscillators. (arXiv:2002.04472v2 [nlin.AO] UPDATED)

This paper deals with an optimal control problem associated to the Kuramoto model describing the dynamical behavior of a network of coupled oscillators. Our aim is to design a suitable control function allowing us to steer the system to a synchronized configuration in which all the oscillators are aligned on the same phase. This control is computed via the minimization of a given cost functional associated with the dynamics considered. For this minimization, we propose a novel approach based on the combination of a standard Gradient Descent (GD) methodology with the recently-developed Random Batch Method (RBM) for the efficient numerical approximation of collective dynamics. Our simulations show that the employment of RBM improves the performances of the GD algorithm, reducing the computational complexity of the minimization process and allowing for a more efficient control calculation.




ni

Quasistatic evolution for dislocation-free finite plasticity. (arXiv:1912.10118v2 [math.AP] UPDATED)

We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic strain is the gradient of a plastic deformation map. The total deformation can be then seen as the composition of a plastic and an elastic deformation. This opens the way to an existence theory for the quasistatic evolution problem featuring both Lagrangian and Eulerian variables. A remarkable trait of the result is that it does not require second-order gradients.




ni

Universal Covers of Finite Groups. (arXiv:1910.11453v2 [math.GR] UPDATED)

Motivated by quotient algorithms, such as the well-known $p$-quotient or solvable quotient algorithms, we describe how to compute extensions $ ilde H$ of a finite group $H$ by a direct sum of isomorphic simple $mathbb{Z}_p H$-modules such that $H$ and $ ilde H$ have the same number of generators. Similar to other quotient algorithms, our description will be via a suitable covering group of $H$. Defining this covering group requires a study of the representation module, as introduced by Gasch"utz in 1954. Our investigation involves so-called Fox derivatives (coming from free differential calculus) and, as a by-product, we prove that these can be naturally described via a wreath product construction. An important application of our results is that they can be used to compute, for a given epimorphism $G o H$ and simple $mathbb{Z}_p H$-module $V$, the largest quotient of $G$ that maps onto $H$ with kernel isomorphic to a direct sum of copies of $V$. For this we also provide a description of how to compute second cohomology groups for the (not necessarily solvable) group $H$, assuming a confluent rewriting system for $H$. To represent the corresponding group extensions on the computer, we introduce a new hybrid format that combines this rewriting system with the polycyclic presentation of the module.




ni

Compact manifolds of dimension $ngeq 12$ with positive isotropic curvature. (arXiv:1909.12265v4 [math.DG] UPDATED)

We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $ngeq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a compact quotient manifold of $mathbb{S}^{n-1} imes mathbb{R}$ by diffeomorphisms, or a connected sum of a finite number of such manifolds. This extends a recent work of Brendle, and implies a conjecture of Schoen in dimensions $ngeq 12$. The proof uses Ricci flow with surgery on compact orbifolds with isolated singularities.




ni

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}. ]




ni

Infinite dimensional affine processes. (arXiv:1907.10337v3 [math.PR] UPDATED)

The goal of this article is to investigate infinite dimensional affine diffusion processes on the canonical state space. This includes a derivation of the corresponding system of Riccati differential equations and an existence proof for such processes, which has been missing in the literature so far. For the existence proof, we will regard affine processes as solutions to infinite dimensional stochastic differential equations with values in Hilbert spaces. This requires a suitable version of the Yamada-Watanabe theorem, which we will provide in this paper. Several examples of infinite dimensional affine processes accompany our results.




ni

Representations of the Infinite-Dimensional $p$-Adic Affine Group. (arXiv:1906.08964v2 [math.RT] UPDATED)

We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.




ni

On the Total Curvature and Betti Numbers of Complex Projective Manifolds. (arXiv:1807.11625v2 [math.DG] UPDATED)

We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.




ni

The 2d-directed spanning forest converges to the Brownian web. (arXiv:1805.09399v3 [math.PR] UPDATED)

The two-dimensional directed spanning forest (DSF) introduced by Baccelli and Bordenave is a planar directed forest whose vertex set is given by a homogeneous Poisson point process $mathcal{N}$ on $mathbb{R}^2$. If the DSF has direction $-e_y$, the ancestor $h(u)$ of a vertex $u in mathcal{N}$ is the nearest Poisson point (in the $L_2$ distance) having strictly larger $y$-coordinate. This construction induces complex geometrical dependencies. In this paper we show that the collection of DSF paths, properly scaled, converges in distribution to the Brownian web (BW). This verifies a conjecture made by Baccelli and Bordenave in 2007.




ni

Local Moduli of Semisimple Frobenius Coalescent Structures. (arXiv:1712.08575v3 [math.DG] UPDATED)

We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities and mutual constraints are allowed in the definition of monodromy data, in view of their importance for conjectural relationships between Frobenius manifolds and derived categories. Detailed examples and applications are taken from singularity and quantum cohomology theories. We explicitly compute the monodromy data at points of the Maxwell Stratum of the A3-Frobenius manifold, as well as at the small quantum cohomology of the Grassmannian G(2,4). In the latter case, we analyse in details the action of the braid group on the monodromy data. This proves that these data can be expressed in terms of characteristic classes of mutations of Kapranov's exceptional 5-block collection, as conjectured by one of the authors.




ni

Simulation of Integro-Differential Equation and Application in Estimation of Ruin Probability with Mixed Fractional Brownian Motion. (arXiv:1709.03418v6 [math.PR] UPDATED)

In this paper, we are concerned with the numerical solution of one type integro-differential equation by a probability method based on the fundamental martingale of mixed Gaussian processes. As an application, we will try to simulate the estimation of ruin probability with an unknown parameter driven not by the classical L'evy process but by the mixed fractional Brownian motion.