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Is UX Certification worth it?

BCS launched their Foundation Certificate in User Experience 3 years ago. We thought this was an opportune time to review its effectiveness. We contacted candidates who had taken (and passed) the certificate through Userfocus and asked, 'What impact has attaining the BCS Foundation Certificate in UX had on your job?' Ten key themes emerged.




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'And the award goes to...' How to avoid winning a Procrustes Award for bad UX

We're familiar with awarding prizes for excellence, from the Oscars to The International Design Awards. But what if we started giving prizes to shame bad examples of design? Enter the Procrustes Awards.




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The future of UX research is automated, and that's a problem

If you compare the UX research methods we use today with the methods we used 16 years ago, something interesting emerges. We see that UX research is becoming increasingly remote and increasingly unmoderated. In other words, we're moving to a world where UX research is becoming automated. We can learn a lot from automated research. But it comes at the price of understanding our users.




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Transitioning from academic research to UX research

Doing UX research in a university is very different to doing UX research in a business setting. If you're an academic making the leap, what are the main differences you need to keep in mind?




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Why Your Website Doesn’t Generate Leads (and how to fix it)

You’re homepage is beautifully designed. It’s clear all the ways you can help. You’ve articulated why someone should hire you. You’ve validated your claims through case studies and testimonials, yet… You’re not getting the volume of leads you need. Sure they trickle in every month, but it’s not enough to grow your business. What are […]

The post Why Your Website Doesn’t Generate Leads (and how to fix it) appeared first on Psychology of Web Design | 3.7 Blog.




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It’s A Living Mural for X-Games China & Innersect

It’s A Living Mural for X-Games China & Innersect

AoiroStudioMay 05, 2020

I think Fabio and I are on a challenge to keep the ABDZ homepage in color tones of 'pastel visuals'. It's perfect because I stumbled across the new project from It's A Living aka Ricardo Gonzalez for X-Games China & Innersect 2019 in Shanghai, China. I don't know if you are familiar or not by Ricardo's distinct lettering style but it's just plain beautiful and vibrant. INNERSECT is the biggest street culture convention in China, a street fashion project founded by celebrity icon Edison Chen in 2017. Feast your eyes!

About It’s A Living

AKA Ricardo Gonzalez is an incredible artist who has worked through many collaborations and his lettering style is so unique. Make sure to check out his links.




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Best Alexa Skills That Will Actually Surprise You

Technology has changed the way we live. A few decades back, we couldn’t even imagine making a video call to a person sitting in another corner of the world. With every technological advancement, mankind is treading towards greater development. From smart gadgets to machines, every invention has leveraged the human lifestyle.  There’s no doubt in […]

Original post: Best Alexa Skills That Will Actually Surprise You

The post Best Alexa Skills That Will Actually Surprise You appeared first on Daily Blog Tips.





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Website Inspiration: CleanShot X

What a brilliant Landing Page for the latest CleanShot X release by MakeTheWeb. This is a good reference to the new Landing Page direction I want to take One Page Love. Slightly more lenient on links to other meta pages (changelog, terms) as long as the Single Page presents everything a customer would want to […]





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Could you get PTSD from your pandemic experience? The long-term mental health effects of coronavirus

Experiencing intense flashbacks, nightmares, irritability, anger, and fear? In the face of a traumatic event like the Covid-19 pandemic, it’s common to feel this way.




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Children’s Exposure to Secondhand Smoke May Be Vastly Underestimated by Parents

Tel Aviv University Press Release Smoking parents misperceive where and when their kids are exposed to cigarette smoke, Tel Aviv University researchers say Four out of 10 children in the US are exposed to secondhand smoke, according to the American … Continue reading




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Federal Watchdog Backs Reinstating Ousted Vaccine Expert

A federal watchdog is recommending that ousted vaccine expert Rick Bright be reinstated while it investigates whether the Trump administration retaliated against his whistleblower complaints when it removed him from a key post overseeing the coronavirus response, Bright's lawyers said Friday.




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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.




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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."




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the quest for personal style (with pal Alex Strohl)

One of the most common questions I get is about how to stand out + how to develop personal style. So when fellow photographer Alex Strohl stopped by the studio, I wanted to get his take on this ever-popular question. If you’re not familiar with Alex’s work, a quick spin on instagram will fill in the blanks. He’s a photographer that tells stories through pictures and film. And when you see his work, there is a distinct thumbprint on it. Developing a personal style is critical. It’s the reason why someone would seek you out vs someone else. It’s the thing that differentiates your work from everyone else. There’s a thousand ways to develop your personal style. In our conversation, Alex shares some of his insights he’s gained along the way. Though each of us may take a different path to get there, there is one constant, and that’s doing a lot of work. So take a listen and then get back to work. ???? Enjoy and subscribe to the podcast below if you dig.  Please give Alex a shout on social @alexstrohl ???? FOLLOW ALEX: twitter | instagram | website Listen to the Podcast Subscribe   Watch the Episode  […]

The post the quest for personal style (with pal Alex Strohl) appeared first on Chase Jarvis Photography.




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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.




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A Viget Exploration: How Tech Can Help in a Pandemic

Viget Explorations have always been the result of our shared curiosities. They’re usually a spontaneous outcome of team downtime and a shared problem we’ve experienced. We use our Explorations to pursue our diverse interests and contribute to the conversations about building a better digital world.

As the COVID-19 crisis emerged, we were certainly experiencing a shared problem. As a way to keep busy and manage our anxieties, a small team came together to dive into how technology has helped, and, unfortunately, hindered the community response to the current pandemic.

We started by researching the challenges we saw: information overload, a lack of clarity, individual responsibility, and change. Then we brainstormed possible technical solutions that could further improve how communities respond to a pandemic. Click here to see our Exploration on some possible ways to take the panic out of pandemics.

While we aren’t currently pursuing the solutions outlined in the Exploration, we’d love to hear what you think about these approaches, as well as any ideas you have for how technology can help address the outlined challenges.

Please note, this Exploration doesn’t provide medical information. Visit the Center for Disease Control’s website for current information and COVID-19, its symptoms, and treatments.

At Viget, we’re adjusting to this crisis for the safety of our clients, our staff, and our communities. If you’d like to hear from Viget's co-founder, Brian Williams, you can read his article on our response to the situation.



  • News & Culture

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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

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Should you use Userbase for your next static site?

During the winter 2020 Pointless Weekend, we built TrailBuddy (working app coming soon). Our team consisted of four developers, two project managers, two front-end developers, a digital-analyst, a UXer, and a designer. In about 48 hours, we took an idea from Jeremy Field’s head to a (mostly) working app. We broke up the project in two parts:. First, a back-end that crunches trail, weather, and soil data. That data is exposed via a GraphQL API for a web app to consume.

While developers built the API, I built a static front end using Next.js. Famously, static front-ends don’t have a database, or a concept of “users.” A bit of functionality I wanted to add was saving favorite trails. I didn’t want to be hacky about it, I needed some way to add users and a database. I knew it’d be hard for the developers to set this up as part of the API, they had their hands full with all the #soil-soil-soil-soil-soil (a slack channel dedicated solely to figuring out our soil data problem—those were plentiful.) I had been looking for an excuse to use Userbase, and this seemed like as good a time as any.

A textbook Userbase use case

“When would I use it?” The Usebase site lists these reasons:

  • If you want to build a web app without writing any backend code.
  • If you never want to see your users' data.
  • If you're tired of dealing with databases.
  • If you want to radically simplify your GDPR compliance.
  • And if you want to keep things really simple.

This was a perfect fit for my problem. I didn’t want to write any more backend code for this. I didn’t want to see our user’s data, I don’t care to know anyone’s favorite trails.* A nice bonus to not having users in our backend was not having to worry about keeping their data safe. We don’t have their data at all, it’s end-to-end encrypted by Userbase. We can offer a reasonable amount of privacy for free (well for the price of using Userbase: $49 a year.) I am not tired of dealing with databases, but I’d rather not. I don’t think anyone doesn’t want to simplify their GDPR compliance. Finally, given our tight timeline I wanted nothing more than to keep things really simple.

A sign up form that I didn't have to write a back-end for

Using Userbase

Userbase can be tried for free, so I set aside thirty minutes or so to do a quick proof of concept to make sure this would work out for us. I made an account and followed their Quickstart. Userbase is a fundamentally easy tool to use, but their quickstart is everything I’d want out of a quickstart:

  • Written in the most vanilla way possible (just HTML and vanilla JS). This means I can adapt it to my needs, in this case React using Next.js
  • Easy to follow, it does the most barebones tour of the functionality you can expect to get out of the SDK (software development kit.) In other words it is quick and it is a start
  • It has a live demo and code samples you can download and run yourself

It didn’t take long after that to integrate Userbase into our app with more help from their great docs. I debated whether to add code samples of what we did here, and I didn’t because any reader would be better off using the great quickstart and docs Userbase provides—they are that clear, and that good. Depending on your use case you’ll need to adapt the examples to your needs, for us the trickiest things were creating a top level authentication context to manage users in the app, and a custom hook to encapsulate all the logic for setting, updating, and deleting favourite trails in the app. Userbase’s SDK worked seamlessly for us.

A log in form that I didn't have to write a back-end for

Is Userbase for you?

Maybe. I am definitely a fan, so much so that this blog post probably reads like an advert. Userbase saved me a ton of time in this project. It reminded me of “The All Powerful Front End Developer” talk by Chris Coyer. I don’t fully subscribe to all the ideas in that talk, but it is nice to have “serverless” tools like Userbase, and all the new JAMstacky things. There are limits to the Userbase serverless experience in terms of scale, and control. Obviously relying on a third party for something always carries some (probably small) risk—it’s worth noting Usebase includes a note on their pricing page that says “You can host it yourself always under your control, or we can run it for you for a full serverless experience”—Still, I wouldn’t hesitate this to use in future projects.

One of the great things about Viget and Pointless Weekend is the opportunity to try new things. For me that was Next.js and Userbase for Trailbuddy. It doesn’t always work out (in fact this is my first pointless weekend where a risk hasn’t blown up in my face) but it is always fun. Getting to try out Userbase and beginning to think about how we may use it in the future made the weekend worthwhile for me, and it made my job on this project much more enjoyable.

*I will write a future post about privacy conscious analytics in TrailBuddy when I’ve figured that out. I am looking into Fathom Analytics for that.



  • Code
  • Front-end Engineering

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Wix Video — a great marketing tool for any website.

Increases time on page and boosts engagement with your site Thanks to the ever-increasing internet speeds, videos are in high demand. Right now, video is everywhere on social media, websites, and apps. We are watching them on all our screens, desktops, tablets, phones and smart TVs. It is expected a growth in video content up …

Wix Video — a great marketing tool for any website. Read More »




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First impressions of the Fuji X-Pro2 (and the Fujinon 100-400mm lens)

Fuji released their new flagship camera this month, the X-Pro2. It is the first X-series camera to feature a 24MP sensor (compared to 16MP before) and it has a very interesting hybrid optical & electronic view finder. When I first […]




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Exploring Node.js Internals

Since the introduction of Node.js by Ryan Dahl at the European JSConf on 8 November 2009, it has seen wide usage across the tech industry. Companies such as Netflix, Uber, and LinkedIn give credibility to the claim that Node.js can withstand a high amount of traffic and concurrency. Armed with basic knowledge, beginner and intermediate developers of Node.js struggle with many things: “It’s just a runtime!” “It has event loops!




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Getting Started With Nuxt

Web developers build a lot of Single Page Applications using JavaScript frameworks (Angular, React, Vue). SPAs dynamically populate the contents of their pages on load which means by the time google crawls their site, the important content is yet to be injected into the site. Part of this problem can be solved by pre-rendering your application’s content. This is where server-side applications come in, and for Vuejs developers, we can build server-side applications using Nuxt.




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Join Our New Online Workshops On CSS, Accessibility, Performance, And UX

It has been a month since we launched our first online workshop and, to be honest, we really didn’t know whether people would enjoy them — or if we would enjoy running them. It was an experiment, but one we are so glad we jumped into! I spoke about the experience of taking my workshop online on a recent episode of the Smashing podcast. As a speaker, I had expected it to feel very much like I was presenting into the empty air, with no immediate feedback and expressions to work from.




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Aputure announces new LS-60D daylight and LX-60X bicolour LED lights

Aputure’s been coming pretty thick and fast on the announcements lately, and now they’ve announced their new Light Storm 60D daylight and 60X bi-colour adjustable focusing LED lights. As the name suggests, these are 60 Watt LEDs, and everything is built inside the head, meaning there’s no external control unit to have to deal with. […]

The post Aputure announces new LS-60D daylight and LX-60X bicolour LED lights appeared first on DIY Photography.




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Google Lens now copies handwritten text and pastes it straight to your computer

Are there still folks among you who, like me, prefer handwriting to typing? If you’re in this group, you’ll love this new feature on Google Lens. The app now lets you scan your handwritten notes, copy them, and paste them straight to your computer. I gave it a spin, and I bring you my impressions […]

The post Google Lens now copies handwritten text and pastes it straight to your computer appeared first on DIY Photography.




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Watch YouTube’s most informed sock puppet teach you how to shoot with manual exposure

For those who’ve never seen TheCrafsMan SteadyCraftin on YouTube, you’re in for a treat – even if you already understand everything contained within this 25-minute video. For those who have, you know exactly what to expect. I’ve been following this rather unconventional channel for a while now. It covers a lot of handy DIY and […]

The post Watch YouTube’s most informed sock puppet teach you how to shoot with manual exposure appeared first on DIY Photography.




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Godox’s new SL150/SL200 Mark II LED lights offer fanless “silent mode” operation

The Godox SL series LED lights have proven to be extremely popular due to their low cost. Two of the models in that range, the SL150 and SL200 have seen a Mark II update today, according to an email that Godox has been sending out today. One of the features of the new SL150II and […]

The post Godox’s new SL150/SL200 Mark II LED lights offer fanless “silent mode” operation appeared first on DIY Photography.




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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.




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The entropy of holomorphic correspondences: exact computations and rational semigroups. (arXiv:2004.13691v1 [math.DS] CROSS LISTED)

We study two notions of topological entropy of correspondences introduced by Friedland and Dinh-Sibony. Upper bounds are known for both. We identify a class of holomorphic correspondences whose entropy in the sense of Dinh-Sibony equals the known upper bound. This provides an exact computation of the entropy for rational semigroups. We also explore a connection between these two notions of entropy.




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Regular Tur'an numbers of complete bipartite graphs. (arXiv:2005.02907v2 [math.CO] UPDATED)

Let $mathrm{rex}(n, F)$ denote the maximum number of edges in an $n$-vertex graph that is regular and does not contain $F$ as a subgraph. We give lower bounds on $mathrm{rex}(n, F)$, that are best possible up to a constant factor, when $F$ is one of $C_4$, $K_{2,t}$, $K_{3,3}$ or $K_{s,t}$ when $t>s!$.




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A Marstrand type slicing theorem for subsets of $mathbb{Z}^2 subset mathbb{R}^2$ with the mass dimension. (arXiv:2005.02813v2 [math.CO] UPDATED)

We prove a Marstrand type slicing theorem for the subsets of the integer square lattice. This problem is the dual of the corresponding projection theorem, which was considered by Glasscock, and Lima and Moreira, with the mass and counting dimensions applied to subsets of $mathbb{Z}^{d}$. In this paper, more generally we deal with a subset of the plane that is $1$ separated, and the result for subsets of the integer lattice follow as a special case. We show that the natural slicing question in this setting is true with the mass dimension.




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On the affine Hecke category. (arXiv:2005.02647v2 [math.RT] UPDATED)

We give a complete (and surprisingly simple) description of the affine Hecke category for $ ilde{A}_2$ in characteristic zero. More precisely, we calculate the Kazhdan-Lusztig polynomials, give a recursive formula for the projectors defining indecomposable objects and, for each coefficient of a Kazhdan-Lusztig polynomial, we produce a set of morphisms with such a cardinality.




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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.




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Arthur packets for $G_2$ and perverse sheaves on cubics. (arXiv:2005.02438v2 [math.RT] UPDATED)

This paper begins the project of defining Arthur packets of all unipotent representations for the $p$-adic exceptional group $G_2$. Here we treat the most interesting case by defining and computing Arthur packets with component group $S_3$. We also show that the distributions attached to these packets are stable, subject to a hypothesis. This is done using a self-contained microlocal analysis of simple equivariant perverse sheaves on the moduli space of homogeneous cubics in two variables. In forthcoming work we will treat the remaining unipotent representations and their endoscopic classification and strengthen our result on stability.




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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.




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Almost invariant subspaces of the shift operator on vector-valued Hardy spaces. (arXiv:2005.02243v2 [math.FA] UPDATED)

In this article, we characterize nearly invariant subspaces of finite defect for the backward shift operator acting on the vector-valued Hardy space which is a vectorial generalization of a result of Chalendar-Gallardo-Partington (C-G-P). Using this characterization of nearly invariant subspace under the backward shift we completely describe the almost invariant subspaces for the shift and its adjoint acting on the vector valued Hardy space.




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Cameron-Liebler sets in Hamming graphs. (arXiv:2005.02227v2 [math.CO] UPDATED)

In this paper, we discuss Cameron-Liebler sets in Hamming graphs, obtain several equivalent definitions and present all classification results.




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Some Quot schemes in tilted hearts and moduli spaces of stable pairs. (arXiv:2005.02202v2 [math.AG] UPDATED)

For a smooth projective variety $X$, we study analogs of Quot functors in hearts of non-standard $t$-structures of $D^b(mathrm{Coh}(X))$. The technical framework is that of families of $t$-structures, as studied in arXiv:1902.08184. We provide several examples and suggest possible directions of further investigation, as we reinterpret moduli spaces of stable pairs, in the sense of Thaddeus (arXiv:alg-geom/9210007) and Huybrechts-Lehn (arXiv:alg-geom/9211001), as instances of Quot schemes.




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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.




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Entropy and Emergence of Topological Dynamical Systems. (arXiv:2005.01548v2 [math.DS] UPDATED)

A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace.

We introduce a concept for these two spaces, which is called entropy order, and prove that it coincides with topological entropy of $(X,f)$. We also consider the entropy order of an invariant measure and a variational principle is established.




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Resonances as Viscosity Limits for Exponentially Decaying Potentials. (arXiv:2005.01257v2 [math.SP] UPDATED)

We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to the case of exponentially decaying potentials. That means that the eigenvalues of $-Delta + V - iepsilon x^2$, $|V(x)|leq e^{-2gamma |x|}$ converge, as $ epsilon o 0+ $, to the poles of the meromorphic continuation of $ ( -Delta + V -lambda^2 )^{-1} $ uniformly on compact subsets of $ extrm{Re},lambda>0$, $ extrm{Im},lambda>-gamma$, $arglambda > pi/8$.




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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.




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Solving an inverse problem for the Sturm-Liouville operator with a singular potential by Yurko's method. (arXiv:2004.14721v2 [math.SP] UPDATED)

An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution, and obtain necessary and sufficient conditions of solvability for the inverse problem in the self-adjoint and the non-self-adjoint cases




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An embedding of the Morse boundary in the Martin boundary. (arXiv:2004.14624v2 [math.GR] UPDATED)

We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona's work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic.




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Complete reducibility: Variations on a theme of Serre. (arXiv:2004.14604v2 [math.GR] UPDATED)

In this note, we unify and extend various concepts in the area of $G$-complete reducibility, where $G$ is a reductive algebraic group. By results of Serre and Bate--Martin--R"{o}hrle, the usual notion of $G$-complete reducibility can be re-framed as a property of an action of a group on the spherical building of the identity component of $G$. We show that other variations of this notion, such as relative complete reducibility and $sigma$-complete reducibility, can also be viewed as special cases of this building-theoretic definition, and hence a number of results from these areas are special cases of more general properties.




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Lagrangian geometry of matroids. (arXiv:2004.13116v2 [math.CO] UPDATED)

We introduce the conormal fan of a matroid M, which is a Lagrangian analog of the Bergman fan of M. We use the conormal fan to give a Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M. This allows us to express the h-vector of the broken circuit complex of M in terms of the intersection theory of the conormal fan of M. We also develop general tools for tropical Hodge theory to prove that the conormal fan satisfies Poincar'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. The Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M, when combined with the Hodge-Riemann relations for the conormal fan of M, implies Brylawski's and Dawson's conjectures that the h-vectors of the broken circuit complex and the independence complex of M are log-concave sequences.




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On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations. (arXiv:2004.12660v3 [math.AP] UPDATED)

In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we give some new results for the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.




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Differentiating through Log-Log Convex Programs. (arXiv:2004.12553v2 [math.OC] UPDATED)

We show how to efficiently compute the derivative (when it exists) of the solution map of log-log convex programs (LLCPs). These are nonconvex, nonsmooth optimization problems with positive variables that become convex when the variables, objective functions, and constraint functions are replaced with their logs. We focus specifically on LLCPs generated by disciplined geometric programming, a grammar consisting of a set of atomic functions with known log-log curvature and a composition rule for combining them. We represent a parametrized LLCP as the composition of a smooth transformation of parameters, a convex optimization problem, and an exponential transformation of the convex optimization problem's solution. The derivative of this composition can be computed efficiently, using recently developed methods for differentiating through convex optimization problems. We implement our method in CVXPY, a Python-embedded modeling language and rewriting system for convex optimization. In just a few lines of code, a user can specify a parametrized LLCP, solve it, and evaluate the derivative or its adjoint at a vector. This makes it possible to conduct sensitivity analyses of solutions, given perturbations to the parameters, and to compute the gradient of a function of the solution with respect to the parameters. We use the adjoint of the derivative to implement differentiable log-log convex optimization layers in PyTorch and TensorFlow. Finally, we present applications to designing queuing systems and fitting structured prediction models.