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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.




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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.




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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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Support Communication During Conversation




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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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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




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How To Get UN-STUCK From Anything in Life That’s Got You Down [with Lewis Howes]

Ever felt STUCK with something in your life? Blocked, like you can’t get past this mental state, this hurdle, this creative block, this bad habit, this… Wait a minute. Why am I even asking that question? Of course you’ve been stuck before. We’ve literally ALL been stuck before. And by extension we all know how much it sucks to be in this state of mind. AND – on the flipside – how amazing it is when you can reclaim your life and get back to the things you want to be thinking, doing, and becoming. I’m obsessed with overcoming the mental blockers that try to keep me down – and I think it’s been a big piece of my personal success. Which is why I thought this little nugget might help. ENTER: Lewis Howes. My good friend Lewis Howes was in the studio shooting his newest CreativeLive course last week and I was able to snag him for a few minutes to chat about his new book and his amazingly simple, yet powerful process for reclaiming our lives and live our biggest dreams. In this episode, Lewis shares a powerful experience from his life and how- on reflection – it helped […]

The post How To Get UN-STUCK From Anything in Life That’s Got You Down [with Lewis Howes] appeared first on Chase Jarvis Photography.




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Resilience and Going Untouchable with Neil Pasricha

Neil Pasricha is a bestselling author and podcaster whose work focuses on topics core to all of our lives: gratitude, happiness, failure, resilience, and trust. He’s the author of six books including The Book of Awesome, The Happiness Equation, Awesome Is Everywhere, and his latest book: You Are Awesome.  In this episode: We are too thin skinned. No matter how great our achievements, we’re crushed by the simplest things. Neil shares some practical advice to navigate through pain and build resiliency Always do something you’re learning… Or as I like to say, how to give yourself permission to suck There’s a reason why they call something a “practice”. We get into how to let go and allow yourself to be human. and much more Enjoy! FOLLOW NEIL: 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 […]

The post Resilience and Going Untouchable with Neil Pasricha appeared first on Chase Jarvis Photography.




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My Favorite Gifts For Photographers Under $100(ish)

Every holiday season, I get an influx of DMs, tweets, texts and messages from followers, friends and family asking for my photo gear recommendations. This year, rather than putting together a list of all the high-tech cameras and lenses that come with high-price tags to match – I wanted share some affordable add-ons that thrifty photographers should have in their arsenal. As I like to say, the best camera is the one you have with you and most of the time that’s the one in your pocket ????  If you are looking for gift ideas for the photographer on your list these are my go-tos under $100(ish).   Moment Lens  These pocket size lenses will transform your mobile device into a lightweight DSLR. With a variety of lenses from fisheye to macro, Moment add-ons are durable, easy-to-use and have incredible clarity. Compatible with almost every smartphone, these compact lens take the camera in your pocket up a notch.          Shure Mic Shure has transformed mobile audio with its line of mobile mics. Regardless of your price point, the audio company creates options that will take your sound from distorted to crystal clear. As a photographer and podcaster […]

The post My Favorite Gifts For Photographers Under $100(ish) appeared first on Chase Jarvis Photography.




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Getting Comfortable with Being Uncomfortable

Being uncomfortable isn’t usually fun. In fact, we’re probably more likely to try to avoid uncomfortable situations than actually run toward them. Yet, it is a valuable skill. Not only in dealing with adversity but giving us confidence and trust in ourselves to recover quickly from failure, manage our fears, and explore the unknown. In today’s episode, we dive a big deeper into this topic and I share a few ways we can all practice getting comfortable with being uncomfortable. Enjoy! FOLLOW CHASE: instagram | 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 Getting Comfortable with Being Uncomfortable appeared first on Chase Jarvis Photography.




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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

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Unsolved Zoom Mysteries: Why We Have to Say “You’re Muted” So Much

Video conference tools are an indispensable part of the Plague Times. Google Meet, Microsoft Teams, Zoom, and their compatriots are keeping us close and connected in a physically distanced world.

As tech-savvy folks with years of cross-office collaboration, we’ve laughed at the sketches and memes about vidconf mishaps. We practice good Zoomiquette, including muting ourselves when we’re not talking.

Yet even we can’t escape one vidconf pitfall. (There but for the grace of Zoom go I.) On nearly every vidconf, someone starts to talk, and then someone else says: “Oop, you’re muted.” And, inevitably: “Oop, you’re still muted.”

That’s right: we’re trying to follow Zoomiquette by muting, but then we forget or struggle to unmute when we do want to talk.

In this post, I’ll share my theories for why the You’re Muted Problems are so pervasive, using Google Meet, Microsoft Teams, and Zoom as examples. Spoiler alert: While I hope this will help you be more mindful of the problem, I can’t offer a good solution. It still happens to me. All. The. Time.

Skip the why and go straight to the vidconf app keyboard shortcuts you should memorize right now.

Why we don't realize we’re muted before talking

Why does this keep happening?!?

Simply put: UX and design decisions make it harder to remember that you’re muted before you start to talk.

Here’s a common scenario: You haven’t talked for a bit, so you haven’t interacted with the Zoom screen for a few seconds. Then you start to talk — and that’s when someone tells you, “You’re muted.”

We forget so easily in these scenarios because when our mouse has been idle for a few seconds, the apps hide or downplay the UI elements that tell us we’re muted.

Zoom and Teams are the worst offenders:

  • Zoom hides both the toolbar with the main in-app controls (the big mute button) and the mute status indicator on your video pane thumbnail.
  • Teams hides the toolbar, and doesn't show a mute status indicator on your video thumbnail in the first place.

Meet is only slightly better:

  • Meet hides the toolbar, and shows only a small mute status icon in your video thumbnail.

Even when our mouse is active, the apps’ subtle approach to muted state UI can make it easy to forget that we’re muted:

Teams is the worst offender:

  • The mute button is an icon rather than words.
  • The muted-state icon's styling could be confused with unmuted state: Teams does not follow the common pattern of using red to denote muted state.
  • The mute button is not differentiated in visual hierarchy from all the other controls.
  • As mentioned above, Teams never shows a secondary mute status indicator.

Zoom is a bit better, but still makes it pretty easy to forget that you’re muted:

  • Pros:
    • Zoom is the only app to use words on the mute button, in this case to denote the button action (rather than the muted state).
    • The muted-state icon’s styling (red line) is less likely to be confused with the unmuted-state icon.
  • Cons:
    • The mute button’s placement (bottom left corner of the page) is easy to overlook.
    • The mute button is not differentiated in visual hierarchy from the other toolbar buttons — and Zoom has a lot of toolbar buttons, especially when logged in as host.
    • The secondary mute status indicator is a small icon.
    • The mute button’s muted-state icon is styled slightly differently from the secondary mute status indicator.
  • Potential Cons:
    • While words denote the button action, only an icon denotes the muted state.

Meet is probably the clearest of the three apps, but still has pitfalls:

  • Pros:
    • The mute button is visually prominent in the UI: It’s clearly differentiated in the visual hierarchy relative to other controls (styled as a primary button); is a large button; and is placed closer to the center of the controls bar.
    • The muted-state icon’s styling (red fill) is less likely to be confused with the unmuted-state icon.
  • Cons:
    • Uses only an icon rather than words to denote the muted state.
  • Unrelated Con:
    • While the mute button is visually prominent, it’s also placed next to the hang-up button. So in Meet’s active state you might be less likely to forget you’re muted … but more likely to accidentally hang up when trying to unmute. 😬

I know modern app design leans toward minimalism. There’s often good rationale to use icons rather than words, or to de-emphasize controls and indicators when not in use.

But again: This happens on basically every call! Often multiple times per call!! And we’re supposed to be tech-savvy!!! Imagine what it’s like for the tens of millions of vidconf newbs.

I would argue that “knowing your muted state” has turned out to be a major vidconf user need. At this point, it’s certainly worth rethinking UX patterns for.

Why we keep unsuccessfully unmuting once we realize we’re muted

So we can blame the You’re Muted Problem on UX and design. But what causes the You’re Still Muted Problem? Once we know we’re muted, why do we sometimes fail to unmute before talking again?

This one is more complicated — and definitely more speculative. To start making sense of this scenario, here’s the sequence I’m guessing most commonly plays out (I did this a couple times before I became aware of it):

The crucial part is when the person tries to unmute by pressing the keyboard Volume On/Off key.

If that’s in fact what’s happening (again, this is just a hypothesis), I’m guessing they did that because when someone says “You’re muted” or “I can’t hear you,” our subconscious thought process is: “Oh, Audio is Off. Press the keyboard key that I usually press when I want to change Audio Off to Audio On.”

There are two traps in this reflexive thought process:

First, the keyboard volume keys control the speaker volume, not the microphone volume. (More specifically, they control the system sound output settings, rather than the system sound input settings or the vidconf app’s sound input settings.)

In fact, there isn’t a keyboard key to control the microphone volume. You can’t unmute your mic via a dedicated keyboard key, the way that you can turn the speaker volume on/off via a keyboard key while watching a movie or listening to music.

Second, I think we reflexively press the keyboard key anyway because our mental model of the keyboard audio keys is just: Audio. Not microphone vs. speaker.

This fuzzy mental model makes sense: There’s only one set of keyboard keys related to audio, so why would I think to distinguish between microphone and speaker? 

So my best guess is hardware design causes the You’re Still Muted Problem. After all, keyboard designs are from a pre-Zoom era, when the average person rarely used the computer’s microphone.

If that is the cause, one potential solution is for hardware manufacturers to start including dedicated keys to control microphone volume:

Video conference keyboard shortcuts you should memorize right now

Let me know if you have other theories for the You’re Still Muted Problem!

In the meantime, the best alternative is to learn all of the vidconf app keyboard shortcuts for muting/unmuting:

  • Meet
    • Mac: Command(⌘) + D
    • Windows: Control + D
  • Teams
    • Mac: Command(⌘) + Shift + M
    • Windows: Ctrl + Shift + M
  • Zoom
    • Mac: Command(⌘) + Shift + A
    • Windows: Alt + A
    • Hold Spacebar: Temporarily unmute

Other vidconf apps not included in my analysis:

  • Cisco Webex Meetings
    • Mac: Ctrl + Alt + M
    • Windows: Ctrl + Shift + M
  • GoToMeeting

Bonus protip from Jackson Fox: If you use multiple vidconf apps, pick a keyboard shortcut that you like and manually change each app’s mute/unmute shortcut to that. Then you only have to remember one shortcut!




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Mirage JS Deep Dive: Understanding Mirage JS Models And Associations (Part 1)

Mirage JS is helping simplify modern front-end development by providing the ability for front-end engineers to craft applications without relying on an actual back-end service. In this article, I’ll be taking a framework-agnostic approach to show you Mirage JS models and associations. If you haven’t heard of Mirage JS, you can read my previous article in which I introduce it and also integrate it with the progressive framework Vue.js.




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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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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 […]




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ISOTYPE Book: Young, Prager, There’s Work for All

This book from 1945 contains a very interesting mix of different charts made by the ISOTYPE Institute, some classic and some quite unusual. As a book about labor and unemployment, it also makes extensive use of Gerd Arntz’s famous unemployed man icon. Michael Young and Theodor Prager’s There’s Work for All is part of a […]




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Corners Picks *** Sunday *** 17 September 2017

We have a new preview on https://www.007soccerpicks.com/sunday-matches/corners-picks-sunday-17-september-2017/

Corners Picks *** Sunday *** 17 September 2017

MATCH CORNERS PICKS To return: ??? USD Odds: 1.55 Stake: 100 USD   Starting in   Teams   Our Prediction Odds Chelsea - Arsenal Soccer: Premier League OVER 9.5 CORNERS 1.55




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Half Time Picks *** Sunday *** 17 September 2017

We have a new preview on https://www.007soccerpicks.com/sunday-matches/half-time-picks-sunday-17-september-2017/

Half Time Picks *** Sunday *** 17 September 2017

HALF TIME PICKS To return: ??? USD Odds: 7.43 Stake: 100 USD   Starting in   Teams   Half Time Our Pick Odds Alaves - Villarreal Soccer: Spain - LaLiga HALF TIME X 2.01 Zenit Petersburg - Ufa Soccer: Russia -…




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Goals Scored Picks *** Sunday *** 17 September 2017

We have a new preview on https://www.007soccerpicks.com/sunday-matches/goals-scored-picks-sunday-17-september-2017/

Goals Scored Picks *** Sunday *** 17 September 2017

MATCH GOALS PICKS To return: ??? USD Odds: 6.44 Stake: 100 USD   Starting in   Teams   Our Prediction Odds Amiens - Marseille Soccer: France - Ligue 1 UNDER 2.5 1.85 AC Milan - Udinese Soccer: Italy - Serie A…




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Fulltime Result Picks *** Sunday *** 17 September 2017

We have a new preview on https://www.007soccerpicks.com/sunday-matches/fulltime-result-picks-sunday-17-september-2017/

Fulltime Result Picks *** Sunday *** 17 September 2017

FULLTIME PICKS To return: ??? USD Odds: 3.88 Stake: 100 USD   Starting in   Teams   Our Prediction Odds Waregem - Mouscron Soccer: Belgium - Jupiler League 1 1.61 Sassuolo - Juventus Soccer: Italy - Serie…




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Double Chance Picks *** Sunday *** 17 September 2017

We have a new preview on https://www.007soccerpicks.com/sunday-matches/double-chance-picks-sunday-17-september-2017/

Double Chance Picks *** Sunday *** 17 September 2017

DOUBLE CHANCE PICKS To return: ??? USD Odds: 2.80 Stake: 100 USD   Starting in   Teams   Our Prediction Odds Las Palmas - Ath Bilbao Soccer: Spain - LaLiga X2 1.45 Chievo - Atalanta Soccer: Italy - Serie…




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Both teams to score Picks *** Sunday *** 17 September 2017

We have a new preview on https://www.007soccerpicks.com/sunday-matches/teams-score-picks-sunday-17-september-2017/

Both teams to score Picks *** Sunday *** 17 September 2017

BOTH TEAMS TO SCORE To return: ??? USD Odds: 5.36 Stake: 100 USD   Starting in   Teams   BTS Our Pick Odds Tosno - Spartak Moscow Soccer: Russia - Premier League Both to score NO 1.53 Chelsea - Arsenal Soccer:…



  • both teams to score picks
  • both teams to score tips
  • Both teams to score
  • Sunday Matches

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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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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.




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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.




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Willems' Fundamental Lemma for State-space Systems and its Extension to Multiple Datasets. (arXiv:2002.01023v2 [math.OC] UPDATED)

Willems et al.'s fundamental lemma asserts that all trajectories of a linear system can be obtained from a single given one, assuming that a persistency of excitation condition holds. This result has profound implications for system identification and data-driven control, and has seen a revival over the last few years. The purpose of this paper is to extend Willems' lemma to the situation where multiple (possibly short) system trajectories are given instead of a single long one. To this end, we introduce a notion of collective persistency of excitation. We will then show that all trajectories of a linear system can be obtained from a given finite number of trajectories, as long as these are collectively persistently exciting. We will demonstrate that this result enables the identification of linear systems from data sets with missing data samples. Additionally, we show that the result is of practical significance in data-driven control of unstable systems.




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Unbounded Kobayashi hyperbolic domains in $mathbb C^n$. (arXiv:1911.05632v2 [math.CV] UPDATED)

We first give a sufficient condition, issued from pluripotential theory, for an unbounded domain in the complex Euclidean space $mathbb C^n$ to be Kobayashi hyperbolic. Then, we construct an example of a rigid pseudoconvex domain in $mathbb C^3$ that is Kobayashi hyperbolic and has a nonempty core. In particular, this domain is not biholomorphic to a bounded domain in $mathbb C^3$ and the mentioned above sufficient condition for Kobayashi hyperbolicity is not necessary.




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Locally equivalent Floer complexes and unoriented link cobordisms. (arXiv:1911.03659v4 [math.GT] UPDATED)

We show that the local equivalence class of the collapsed link Floer complex $cCFL^infty(L)$, together with many $Upsilon$-type invariants extracted from this group, is a concordance invariant of links. In particular, we define a version of the invariants $Upsilon_L(t)$ and $ u^+(L)$ when $L$ is a link and we prove that they give a lower bound for the slice genus $g_4(L)$. Furthermore, in the last section of the paper we study the homology group $HFL'(L)$ and its behaviour under unoriented cobordisms. We obtain that a normalized version of the $upsilon$-set, introduced by Ozsv'ath, Stipsicz and Szab'o, produces a lower bound for the 4-dimensional smooth crosscap number $gamma_4(L)$.




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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.




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Khintchine-type theorems for values of subhomogeneous functions at integer points. (arXiv:1910.02067v2 [math.NT] UPDATED)

This work has been motivated by recent papers that quantify the density of values of generic quadratic forms and other polynomials at integer points, in particular ones that use Rogers' second moment estimates. In this paper we establish such results in a very general framework. Namely, given any subhomogeneous function (a notion to be defined) $f: mathbb{R}^n o mathbb{R}$, we derive a necessary and sufficient condition on the approximating function $psi$ for guaranteeing that a generic element $fcirc g$ in the $G$-orbit of $f$ is $psi$-approximable; that is, $|fcirc g(mathbf{v})| le psi(|mathbf{v}|)$ for infinitely many $mathbf{v} in mathbb{Z}^n$. We also deduce a sufficient condition in the case of uniform approximation. Here, $G$ can be any closed subgroup of $operatorname{ASL}_n(mathbb{R})$ satisfying certain axioms that allow for the use of Rogers-type estimates.




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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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On boundedness, gradient estimate, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop. (arXiv:1909.04587v4 [math.AP] UPDATED)

In this work, we study dynamic properties of classical solutions to a homogenous Neumann initial-boundary value problem (IBVP) for a two-species and two-stimuli chemotaxis model with/without chemical signalling loop in a 2D bounded and smooth domain. We successfully detect the product of two species masses as a feature to determine boundedness, gradient estimates, blow-up and $W^{j,infty}(1leq jleq 3)$-exponential convergence of classical solutions for the corresponding IBVP. More specifically, we first show generally a smallness on the product of both species masses, thus allowing one species mass to be suitably large, is sufficient to guarantee global boundedness, higher order gradient estimates and $W^{j,infty}$-convergence with rates of convergence to constant equilibria; and then, in a special case, we detect a straight line of masses on which blow-up occurs for large product of masses. Our findings provide new understandings about the underlying model, and thus, improve and extend greatly the existing knowledge relevant to this model.




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Integrability of moduli and regularity of Denjoy counterexamples. (arXiv:1908.06568v4 [math.DS] UPDATED)

We study the regularity of exceptional actions of groups by $C^{1,alpha}$ diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first derivatives that are continuous with concave modulus of continuity $alpha$. Let $G$ be a finitely generated group admitting a $C^{1,alpha}$ action $ ho$ with a free orbit on the circle, and such that the logarithms of derivatives of group elements are uniformly bounded at some point of the circle. We prove that if $G$ has spherical growth bounded by $c n^{d-1}$ and if the function $1/alpha^d$ is integrable near zero, then under some mild technical assumptions on $alpha$, there is a sequence of exceptional $C^{1,alpha}$ actions of $G$ which converge to $ ho$ in the $C^1$ topology. As a consequence for a single diffeomorphism, we obtain that if the function $1/alpha$ is integrable near zero, then there exists a $C^{1,alpha}$ exceptional diffeomorphism of the circle. This corollary accounts for all previously known moduli of continuity for derivatives of exceptional diffeomorphisms. We also obtain a partial converse to our main result. For finitely generated free abelian groups, the existence of an exceptional action, together with some natural hypotheses on the derivatives of group elements, puts integrability restrictions on the modulus $alpha$. These results are related to a long-standing question of D. McDuff concerning the length spectrum of exceptional $C^1$ diffeomorphisms of the circle.




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Study of fractional Poincar'e inequalities on unbounded domains. (arXiv:1904.07170v2 [math.AP] UPDATED)

The central aim of this paper is to study (regional) fractional Poincar'e type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non existence type results are established depending on various conditions on domains and on the range of $s in (0,1)$. The best constant in both regional fractional and fractional Poincar'e inequality is characterized for strip like domains $(omega imes mathbb{R}^{n-1})$, and the results obtained in this direction are analogous to those of the local case. This settles one of the natural questions raised by K. Yeressian in [ extit{Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89, (2014), no 1-2}].




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Diophantine Equations Involving the Euler Totient Function. (arXiv:1902.01638v4 [math.NT] UPDATED)

We deal with various Diophantine equations involving the Euler totient function and various sequences of numbers, including factorials, powers, and Fibonacci sequences.




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Optimal construction of Koopman eigenfunctions for prediction and control. (arXiv:1810.08733v3 [math.OC] UPDATED)

This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to construct a rich set of eigenfunctions such that the state (or any other observable quantity of interest) is in the span of these eigenfunctions and hence predictable in a linear fashion. The eigenfunction construction is optimization-based with no dictionary selection required. Once a predictor for the uncontrolled part of the system is obtained in this way, the incorporation of control is done through a multi-step prediction error minimization, carried out by a simple linear least-squares regression. The predictor so obtained is in the form of a linear controlled dynamical system and can be readily applied within the Koopman model predictive control framework of [12] to control nonlinear dynamical systems using linear model predictive control tools. The method is entirely data-driven and based purely on convex optimization, with no reliance on neural networks or other non-convex machine learning tools. The novel eigenfunction construction method is also analyzed theoretically, proving rigorously that the family of eigenfunctions obtained is rich enough to span the space of all continuous functions. In addition, the method is extended to construct generalized eigenfunctions that also give rise Koopman invariant subspaces and hence can be used for linear prediction. Detailed numerical examples with code available online demonstrate the approach, both for prediction and feedback control.




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A Class of Functional Inequalities and their Applications to Fourth-Order Nonlinear Parabolic Equations. (arXiv:1612.03508v3 [math.AP] UPDATED)

We study a class of fourth order nonlinear parabolic equations which include the thin-film equation and the quantum drift-diffusion model as special cases. We investigate these equations by first developing functional inequalities of the type $ int_Omega u^{2gamma-alpha-eta}Delta u^alphaDelta u^eta dx geq cint_Omega|Delta u^gamma |^2dx $, which seem to be of interest on their own right.




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On the zeros of the Riemann zeta function, twelve years later. (arXiv:0806.2361v7 [math.GM] UPDATED)

The paper proves the Riemann Hypothesis.




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The Fourier Transform Approach to Inversion of lambda-Cosine and Funk Transforms on the Unit Sphere. (arXiv:2005.03607v1 [math.FA])

We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained for totally geodesic Funk transforms on the sphere and the correpsonding lambda-cosine transforms.




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A reaction-diffusion system to better comprehend the unlockdown: Application of SEIR-type model with diffusion to the spatial spread of COVID-19 in France. (arXiv:2005.03499v1 [q-bio.PE])

A reaction-diffusion model was developed describing the spread of the COVID-19 virus considering the mean daily movement of susceptible, exposed and asymptomatic individuals. The model was calibrated using data on the confirmed infection and death from France as well as their initial spatial distribution. First, the system of partial differential equations is studied, then the basic reproduction number, R0 is derived. Second, numerical simulations, based on a combination of level-set and finite differences, shown the spatial spread of COVID-19 from March 16 to June 16. Finally, scenarios of unlockdown are compared according to variation of distancing, or partially spatial lockdown.




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Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces. (arXiv:2005.03494v1 [math.CA])

We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent problems from this class, we prove a constructive criterion for their solutions to be continuous in the Sobolev space with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem.




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On completion of unimodular rows over polynomial extension of finitely generated rings over $mathbb{Z}$. (arXiv:2005.03485v1 [math.AC])

In this article, we prove that if $R$ is a finitely generated ring over $mathbb{Z}$ of dimension $d, dgeq2, frac{1}{d!}in R$, then any unimodular row over $R[X]$ of length $d+1$ can be mapped to a factorial row by elementary transformations.




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Characteristic Points, Fundamental Cubic Form and Euler Characteristic of Projective Surfaces. (arXiv:2005.03481v1 [math.DG])

We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. of those domains). These relations determine the possible coexistences of projective umbilics and godrons on the surface. Our study is based on a "fundamental cubic form" for which we provide a closed simple expression.