solidot新版网站常见问题,请点击这里查看。
solidot此次改版内容包括服务器更新、编程语言、网站后台管理的优化、页面和操作流程的优化等。

信息流

  • We show that the theory of De Morgan algebras has a model completion and axiomatise it.

    发表评论 查看更多 翻译此文

    收起

  • Let $S=\{x^2+c_1, x^2+c_2,\dots, x^2+c_s\}$ be a set of quadratic polynomials with rational coefficients, and let $P$ be a rational basepoint. We classify the pairs $(S,P)$ for which $P$ has finite orbit for $S$, assuming that the maximum period length for each individual polynomial is at most three (conjectured by Poonen). In particular, under these hypotheses we prove that if $s\geq4$, then there are no points $P$ with finite orbit for $S$. Moreover, we use this perspective to formulate an analog of the Morton-Silverman Conjecture for sets of polynomials.

    发表评论 查看更多 翻译此文

    收起

  • The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous (and therefore Hall) but not locally extensible are constructed. Some open questions are also mentioned.

    发表评论 查看更多 翻译此文

    收起

  • We show that any free product of finite-dimensional von Neumann algebras equipped with non-tracial states is isomorphic to a free Araki-Woods factor with its free quasi-free state possibly direct sum a finite-dimensional von Neumann algebra. This gives a complete answer to questions posed by Dykema and Shlyakhtenko, which had been partially answered by work of Houdayer and work of Ueda. We also extend this to suitable infinite-dimensional von Neumann algebras with almost periodic states.

    发表评论 查看更多 翻译此文

    收起

  • For a given positive random variable $V>0$ and a given $Z\sim N(0,1)$ independent of $V$, we compute the scalar $t_0$ such that the distance between $Z\sqrt{V}$ and $Z\sqrt{t_0},$ in the $L^2(\R)$ sense, is minimal. We also consider the same problem in several dimensions. \textsc{Keywords:} Normal approximation, Gaussian scale mixture, Plancherel theorem.

    发表评论 查看更多 翻译此文

    收起

  • Drawdown/regret times feature prominently in optimal stopping problems, in statistics (CUSUM procedure) and in mathematical finance (Russian options). Recently it was discovered that a first passage theory with general drawdown times, which generalize classic ruin times, may be explicitly developed for spectrally negative L\'evy processes -- see Avram, Vu, Zhou(2017), Li, Vu, Zhou(2017). In this paper, we further examine general drawdown related quantities for taxed time-homogeneous Markov processes, using the pathwise connection between general drawdown and tax.

    发表评论 查看更多 翻译此文

    收起

  • In this note we study some basic properties of general fractional derivatives induced by weighted Bergman kernels. As an application we demonstrate a method for generating pre-images of analytic functions under weighted Bergman projections. This approach is useful for proving the surjectivity of weighted Bergman projections in cases when the target space is not a subspace of the domain space (such situations arise often when dealing with Bloch and Besov spaces). We also discuss a fractional Littlewood-Paley formula.

    发表评论 查看更多 翻译此文

    收起

  • bestweasel writes: The Hollywood Reporter highlights an academic paper which finds that half of the criticism aimed at director Rian Johnson over Star Wars: The Last Jedi was politically motivated. From the report: [Researcher Morten Bay's paper] titled Weaponizing The Haters: The Last Jedi and the strategic politicization of pop culture through social media manipulation, examines the online response to the movie that has come to be considered controversial amongst the larger fanbase of the franchise. Bay suggests that reputation may not be earned, and instead "finds evidence of deliberate, organized political influence measures disguised as fan arguments." He continues, "The likely objective of these measures is increasing media coverage of the fandom conflict, thereby adding to and further propagating a narrative of widespread discord and dysfunction in American society. Persuading voters of this narrative remains a strategic goal for the U.S. alt-right movement, as well as the Russi

    发表评论 查看更多 翻译此文

    收起

  • Donna Strickland is first woman to win physics prize since 1963 and third ever to win.

    发表评论 查看更多 翻译此文

    收起

  • A Gentle Introduction to Markov Chain Monte Carlo (2012)

    发表评论 查看更多 翻译此文

    收起

  • ARM releases free Cortex-M processor cores for FPGAs

    发表评论 查看更多 翻译此文

    收起

  • Academic Grievance Studies and the Corruption of Scholarship

    发表评论 查看更多 翻译此文

    收起

  • Mike Bouma shares the announcement from Hyperior Entertainment, which holds exclusive rights to AmigaOS: The new, cleaned-up, polished Amiga operating system for your 68K machine fixes all the small annoyances that have piled up over the years. Originally intended as a bug-fix release, it also modernizes many system components previously upgraded in OS 3.9. Contrary to its modest revision number, AmigaOS 3.1.4 is arguably as large an upgrade as OS 3.9 was, and surpasses it in stability and robustness. Over 320K of release notes cover almost every aspect of your favorite classic AmigaOS -- from bootmenu to datatypes. Some of the highlights mentioned include: Over 20 Kickstart ROM modules and many more disk-based core OS components were fixed, updated, or added; Support for large hard disks; A modernized Workbench; and A colorful, professionally designed icon set is included, along with the traditional four-color icons.

    发表评论 查看更多 翻译此文

    收起

  • The new, cleaned-up, polished Amiga operating system for your 68K machine fixes all the small annoyances that have piled up over the years. Originally intended as a bug-fix release, it also modernizes many system components previously upgraded in OS 3.9. Contrary to its modest revision number, AmigaOS 3.1.4 is arguably as large an upgrade as OS 3.9 was, and surpasses it in stability and robustness. Over 320K of release notes cover almost every aspect of your favourite classic AmigaOS - from bootmenu to datatypes. This is not AmigaOS 4 - just making that clear here - but an updated version of AmigaOS 3 for classic 68K-based Amigas.

    发表评论 查看更多 翻译此文

    收起

  •  

    An Open Source Pipelined FFT Generator

    10-03 Hacker News 2890

    An Open Source Pipelined FFT Generator

    发表评论 查看更多 翻译此文

    收起

  •  

    Announcing flicker-free boot for Fedora 29

    10-03 Hacker News 2864

    Announcing flicker-free boot for Fedora 29

    发表评论 查看更多 翻译此文

    收起

  •  

    Arcan 0.5.5, Durden 0.5 released

    10-03 OSnews 2884

    More than three quarters of a year has gone by since last time, but the Arcan project has squeezed out a new release of the 'multimedia server' or 'desktop engine' Arcan and its related subproject, the Durden desktop environment. For those unaware of the project as such, it might be worthwhile to skim through a recent summary that can be found in the article "Revisiting the Arcan Project" - but suffice to say that it is an ambitious attempt at replacing large swaths (terminal emulators, display server, audio server, and so on) of the normal user-facing parts of the BSD and Linux userspace, with a single compact and coherently scriptable component.

    发表评论 查看更多 翻译此文

    收起

  • We chat up quantitative psychologist Dan Hoffman about how your mind lies to you.

    发表评论 查看更多 翻译此文

    收起

  • OpenSourceAllTheWay writes: As someone who grew up with 1980s and 1990s computers and electronics and still has whole boxes of lovingly prepared printed computer, peripheral, game and software manuals from that era, I am continually surprised by how just many products ship without a proper printed manual these days. Case in point would be things like Android phones. Android has quite a few not-entirely-obvious functions built into it. And a lot of people aren't even aware they exist. No Android phone I've bought has ever had a printed manual included in its little product box. Not even a small one. Even expensive laptops ranging in price from 2,000 to 5,000 Dollars often come only with a few sheets of printed paper in the box -- warranty card, where to register the device, URL for downloading drivers and so on. Why is this? It can't be environmental concern -- the electronics devices themselves, when thrown away, are a hundred times (if not worse) more harmful to the environment than a

    发表评论 查看更多 翻译此文

    收起

  • The White House should worry less about China’s progress and invest heavily in artificial intelligence breakthroughs, according to Kai-Fu Lee.

    发表评论 查看更多 翻译此文

    收起

  • Bill to ban bots inpersonating people for telemarketing and influencing election

    发表评论 查看更多 翻译此文

    收起

  • Black holes ruled out as universe’s missing dark matter

    发表评论 查看更多 翻译此文

    收起

  •  

    Bonus Daily Cartoon: Tuesday, October 2nd

    10-03 THE NEW YORKER 2790

    In Barry Blitt’s Bonus Daily Cartoon, Kanye and Kavanaugh rep some favorite beverages.

    发表评论 查看更多 翻译此文

    收起

  •  

    CirnOS: new Lua-based OS

    10-03 OSnews 2558

    CirnOS is an operating system for the Raspberry Pi built for the purpose of usability and simplicity. It provides a simple environment for running Lua scripts on Raspberry Pi. It has no kernel or time management - it is single threaded. You run your code on the device, and that is it. CirnOS has only been tested on the Raspberry Pi Zero, but should work on the original Raspberry Pi and the Zero W.

    发表评论 查看更多 翻译此文

    收起

  •  

    Concatenative and stack languages

    10-03 Hacker News 2790

    Concatenative and stack languages

    发表评论 查看更多 翻译此文

    收起

  • Child-porn case in Ohio reveals how some law enforcement are trying to thwart Face ID.

    发表评论 查看更多 翻译此文

    收起

  • dmoberhaus writes: DARPA just awarded a $1.3 million contract to an international team of researchers to study quantized inertia or QI. This is a controversial theory that many physicists think is pseudoscience, but according to the physicist that created it, QI may be the foundation for light-powered space travel that could open the door for interstellar travel. Motherboard looks at the fact and fiction of QI, its relationship to the 'impossible' EmDrive being developed by NASA and how these physicists are going to create experimental light-powered engines. Quantized inertia (QI) is an alternative theory of inertia, a property of matter that describes an object's resistance to acceleration. QI was first proposed by University of Plymouth physicist Mike McCulloch in 2007, but it is still considered a fringe theory by many, if not most, physicists today. McCulloch has used the theory to explain galactic rotation speeds without the need for dark matter, but he believes it may one day pro

    发表评论 查看更多 翻译此文

    收起

  •  

    Data Factories

    10-03 Hacker News 2475

    Data Factories

    发表评论 查看更多 翻译此文

    收起

  • Plus 50% off Kindle and Hulu subscriptions, Anker accessory discounts, and more.

    发表评论 查看更多 翻译此文

    收起

  • Astronomers have discovered a dwarf planet, dubbed "the Goblin," in the outer reaches of the Solar System that never gets any closer to the Sun than 6 billion miles. Some experts say its orbital configuration points to the existence of Planet Nine, a hypothetical planet in our Solar System that is estimated to be about 10 times the mass of Earth. Gizmodo reports: The Goblin, or 2015 TG38 as it's more formally called, is what's known as an extreme trans-Neptunian object, or ETNO. As the moniker implies, these objects, of which there are potentially thousands, are located well beyond the orbit of Neptune. The researchers who discovered the object, a team led by Scott Sheppard from the Carnegie Institution for Science and Chadwick Trujillo from Northern Arizona University, estimate that the Goblin is around 185 miles (300 kilometers) in diameter. At this size, it could very well be sphere-like in shape. Its mean distance from the Sun is about 80 astronomical units (AU), where 1 AU is the

    发表评论 查看更多 翻译此文

    收起

  • John Cassidy writes about the new United States-Mexico-Canada Agreement and its likely impact on the U.S. automobile industry.

    发表评论 查看更多 翻译此文

    收起

  • Op-ed: Secret rulings should not force tech companies to build backdoors.

    发表评论 查看更多 翻译此文

    收起

  • Fastai for PyTorch: Fast and accurate neural nets using modern best practices

    发表评论 查看更多 翻译此文

    收起

  • It's not enough to play nicely with others—you also have to be seen playing nicely

    发表评论 查看更多 翻译此文

    收起

  •  

    Frederick Wiseman at The New Yorker Festival

    10-03 THE NEW YORKER 2812

    Richard Brody will interview the documentary filmmaker Frederick Wiseman on Saturday, October 6, 2018, as part of The New Yorker Festival.

    发表评论 查看更多 翻译此文

    收起

  • Generative Coding – “The Nature of Code” Ported to Three.js

    发表评论 查看更多 翻译此文

    收起

  • Streaming media has transformed the way we consume music and video, making it easy to instantly access your favorite content. It's a technically complex process that has come a long way in a few short years, but the next technical frontier for streaming will be much more demanding than video. We've been working on Project Stream, a technical test to solve some of the biggest challenges of streaming. For this test, we're going to push the limits with one of the most demanding applications for streaming - a blockbuster video game. Google's trying their hands at game streaming - in the case of this test, Assassin's Creed Odyssey (which I happen to have just started on my PS4 Pro). If one company has the hardware to actually pull this off properly and consistently, it's Google.

    发表评论 查看更多 翻译此文

    收起

  • Company plans stricter rules for developers and greater control for users.

    发表评论 查看更多 翻译此文

    收起

  • An anonymous reader quotes a report from The Washington Post: A unit of Google's parent company Alphabet is proposing to turn a rundown part of Toronto's waterfront into what may be the most wired community in history -- to "fundamentally refine what urban life can be." Sidewalk Labs has partnered with a government agency known as Waterfront Toronto with plans to erect mid-rise apartments, offices, shops and a school on a 12-acre (4.9-hectare) site -- a first step toward what it hopes will eventually be a 800-acre (325-hectare) development. High-level interest is clear: Prime Minister Justin Trudeau and Alphabet's then-Executive Chairman Eric Schmidt appeared together to announce the plan in October. But some Canadians are rethinking the privacy implications (Warning: source may be paywalled; alternative source) of giving one of the most data-hungry companies on the planet the means to wire up everything from street lights to pavement. And some want the public to get a cut of the reven

    发表评论 查看更多 翻译此文

    收起

  • darthcamaro writes: Though Justin Trudeau is the envy of many world leaders for his likeability, the head of of the Canadian Centre for Cyber Security at the Canadian Security Establishment (CSE), which helps to protect federal government networks says that his agency is trying to make Canada less attractive -- to hackers. Speaking at the SecTor conference in Toronto Scott Jones said:"By doing the basics, you're making the adversaries that come after you deploy more advanced tools and techniques, and you just might not be worth the expense," Jones said. "My ultimate goal is to make Canada unattractive to cyber-criminals and data hackers, because our community is vigilant and engaged so much so that threat actors aren't enticed to even attack us."

    发表评论 查看更多 翻译此文

    收起

  • Ross Goodwin, a former ghostwriter for the Obama administration, uses neural networks to generate poetry, screenplays, and, now, literary travel fiction. The Atlantic tells the story of how Goodwin used a custom machine to write a "novel" narrating its own cross-country road trip. Slashdot reader merbs shares an excerpt from the report: On March 25, 2017, a black Cadillac with a white-domed surveillance camera attached to its trunk departed Brooklyn for New Orleans. An old GPS unit was fastened atop the roof. Inside, a microphone dangled from the ceiling. Wires from all three devices fed into Ross Goodwin's Razer Blade laptop, itself hooked up to a humble receipt printer. This, Goodwin hoped, was the apparatus that was going to produce the next American road-trip novel. The aim was to use the road as a conduit for narrative experimentation, in the tradition of Kerouac, Wolfe, and Kesey, but with the vehicle itself as the artist. He chose the New York-to-NOLA route as a nod to the famou

    发表评论 查看更多 翻译此文

    收起

  • An analysis of all known decentralized exchanges

    发表评论 查看更多 翻译此文

    收起

  • Jeremy Horwitz, writing for VentureBeat: An obscure feature in Apple's Xcode development software enabled Apple Watch apps to make an instant transition from 32-bit to 64-bit last month, an unheralded win for Apple Watch developers inside and outside the company. The "Enable Bitcode" feature was introduced to developers three years ago, but the Accidental Tech Podcast suggests that it was quietly responsible for the smooth launch of software for the Apple Watch Series 4 last month. Support for Bitcode was originally added to Xcode 7 in November 2015, subsequently becoming optional for iOS apps but mandatory for watchOS and tvOS apps. Bitcode is an "intermediate representation" halfway between human-written app code and machine code. Rather than the developer sending a completely compiled app to the App Store, enabling Bitcode provides Apple with a partially compiled app that it can then finish compiling for whatever processors it wants to support. The report suggests that this change a

    发表评论 查看更多 翻译此文

    收起

  • Matt Doyle takes on the voice of the Pied Piper in a piece satirizing the false innocence of those participating in child separation.

    发表评论 查看更多 翻译此文

    收起

  • Ask HN: What are good projects to understand CUDA and GPU Programming?

    发表评论 查看更多 翻译此文

    收起

  • Bill Gates: “I never said '640K should be enough for anybody'”

    发表评论 查看更多 翻译此文

    收起

  • Brendan Eich Writes to the US Senate: We Need a GDPR for the United States

    发表评论 查看更多 翻译此文

    收起

  • China Censors Bad Economic News Amid Signs of Slower Growth

    发表评论 查看更多 翻译此文

    收起

  • Long time reader theodp writes: Facebook last week announced the launch of CodeFWD, "a free online education program created in partnership with [robotic toy maker] Sphero to increase the amount of underrepresented and female students interested in studying computer science." Sphero and CodeFWD are offering a free Sphero BOLT Power Pack (a classroom set of 15 robots valued at $2,499) for a select number of accepted applicants through the program. So, what do you need to begin CodeFWD by Facebook? "No experience necessary. No experience preferred ," explains the website. However, that's not to say CodeFWD is for all. "CodeFWD is intended for educators who are credentialed K-12 teachers or 501(c)(3) non-profit staff members in the United States," the website makes clear, adding that "given the limited supply of robots, we will evaluate the information you've provided and prioritize those applications that help us achieve the goal of expanding access to computer programming opportunities.

    发表评论 查看更多 翻译此文

    收起

  • Study: appealing to pleasure made people more likely to eat mealworm truffles

    发表评论 查看更多 翻译此文

    收起

  • Last year, Apple co-founder Steve Wozniak announced a coding program called Woz U that's designed with the goal of offering an affordable education. "Our goal is to educate and train people in employable digital skills without putting them into years of debt," Wozniak said last fall. "People often are afraid to choose a technology-based career because they think they can't do it. I know they can, and I want to show them how." Now that a round of students have been through the 33-week program, a number of problems have appeared. Former student, Bill Duerr, called the program "broken," and that "lots of times there's just hyperlinks to Microsoft documents, to Wikipedia." 9to5Mac reports: "Duerr said typos in course content were one of many problems. So-called 'live lectures' were pre-recorded and out of date, student mentors were unqualified, and at one point, one of his courses didn't even have an instructor," reports CBS. CBS heard from over 24 current and former students and employees

    发表评论 查看更多 翻译此文

    收起

  • "A decade ago, internet users who grew up with Web 1.0 bid a fond farewell to Sunset Strip, Rodeo Drive, Colosseum, and other 'neighborhoods' on web-hosting service GeoCities, when Yahoo announced it was shutting the main site down," writes Isabella Steger for Quartz. "Now Japanese GeoCities fans will face the same fate." From the report: Yahoo Japan announced today (Oct. 1) that it will shut down (link in Japanese) its GeoCities service in March 2019, 22 years after its launch. The company said in a statement that it was hard to encapsulate in one word the reason for the shut down, but that profitability and technological issues were primary factors. It added that it was full of "regret" for the fate of the immense amount of information that would be lost as a result of the service's closure. Japan is the only country where the web hosting service remained in operation. Like the main GeoCities, the Japanese service was also organized around different themed neighborhoods. For example,

    发表评论 查看更多 翻译此文

    收起

  • Google DeepMind Founder Demis Hassabis: Three Truths about AI

    发表评论 查看更多 翻译此文

    收起

  • Earlier this year, we heard rumors that Google was working on a game-streaming service. It looks like those rumors were true. From a report: The company today unveiled "Project Stream," and while Google calls this a "technical test" to see how well game streaming to Chrome works, it's clear that this is the foundational technology for a game-streaming service. To sweeten the pot, Google is launching this test in partnership with Ubisoft and giving a limited number of players free access to Assassin's Creed Odyssey for the duration of the test. You can sign up for the test now; starting on October 5, Google will invite a limited number of participants to play the game for free in Chrome. As Google notes, the team wanted to work with a AAA title because that's obviously far more of a challenge than working with a less graphics-intense game. And for any game-streaming service to be playable, the latency has to be minimal and the graphics can't be worse than on a local machine.

    发表评论 查看更多 翻译此文

    收起

  • Play Assassin's Creed Odyssey through a desktop-class Chrome browser, starting October 5.

    发表评论 查看更多 翻译此文

    收起

  • schwit1 shares a report from the Brookings Institution: Something of enormous global significance is happening almost without notice. For the first time since agriculture-based civilization began 10,000 years ago, the majority of humankind is no longer poor or vulnerable to falling into poverty. By our calculations, as of this month, just over 50 percent of the world's population, or some 3.8 billion people, live in households with enough discretionary expenditure to be considered "middle class" or "rich." About the same number of people are living in households that are poor or vulnerable to poverty. So September 2018 marks a global tipping point. After this, for the first time ever, the poor and vulnerable will no longer be a majority in the world. Barring some unfortunate global economic setback, this marks the start of a new era of a middle-class majority. In most countries, there is a clear relationship between the fate of the middle class and the happiness of the population. Acc

    发表评论 查看更多 翻译此文

    收起

  • It's a smart form factor, and the unusual materials are more than just a gimmick.

    发表评论 查看更多 翻译此文

    收起

  • In El Chapo’s Trial, Extraordinary Steps to Keep Witnesses Alive

    发表评论 查看更多 翻译此文

    收起

  • Let $K$ be a local field of characteristic $p$. We consider the local Langlands correspondence for tori, and construct examples for which depth is not preserved.

    发表评论 查看更多 翻译此文

    收起

  •  

    MAC address age tracking

    10-02 Hacker News 2484

    MAC address age tracking

    发表评论 查看更多 翻译此文

    收起

  •  

    Mega Man 11 review: Switching gears

    10-02 Ars Technica 2617

    Nostalgic run-and-gun action is equal parts familiar and strange.

    发表评论 查看更多 翻译此文

    收起

  • More than 9M broken links on Wikipedia are now rescued

    发表评论 查看更多 翻译此文

    收起

  •  

    On the Attack

    10-02 THE NEW YORKER 2393

    Margaret Talbot writes about how Christine Blasey Ford’s experience was just as bad as Anita Hill’s—maybe worse.

    发表评论 查看更多 翻译此文

    收起

  • We introduce a ${\mathbb Z}_2$-index for time reversal invariant Hamiltonians with unique gapped ground state on quantum spin chains. We show this is an invariant of a $C^1$-classification of gapped Hamiltonians.

    发表评论 查看更多 翻译此文

    收起

  • The maximal commutative subalgebras containing only Toeplitz matrices have been identified as generalized circulants. A similar simple description cannot be obtained for block Toeplitz matrices. We introduce and investigate certain families of maximal commutative algebras of block Toeplitz matrices.

    发表评论 查看更多 翻译此文

    收起

  • This paper is concerned with the Fourier-Bessel method for the boundary value problems of the Helmholtz equation in a smooth simply connected domain. Based on the denseness of Fourier-Bessel functions, the problem can be approximated by determining the unknown coefficients in the linear combination. By the boundary conditions, an operator equation can be obtained. We derive a lower bound for the smallest singular value of the operator, and obtain a stability and convergence result for the regularized solution with a suitable choice of the regularization parameter. Numerical experiments are also presented to show the effectiveness of the proposed method.

    发表评论 查看更多 翻译此文

    收起

  • Given a family of continuous real functions $\mathcal{G}$, let $R_\mathcal{G}$ be a binary relation defined as follows: a continuous function $f\colon\mathbb{R}\to\mathbb{R}$ is in the relation with a closed set $E\subseteq\mathbb{R}$ if and only if there exists $g\in\mathcal{G}$ such that $f\upharpoonright E = g\upharpoonright E$. We consider a Galois connection between families of continuous functions and hereditary families of closed sets of reals naturally associated to $R_\mathcal{G}$. We study complete lattices determined by this connection and prove several results showing the dependence of the properties of these lattices on the properties of $\mathcal{G}$. In some special cases we obtain exact description of these lattices.

    发表评论 查看更多 翻译此文

    收起

  • We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials $\mathbf V$ of Coulomb type: we characterise its eigenvalues in terms of the Birman-Schwinger principle and we bound its discrete spectrum from below, showing that the \emph{ground-state energy} is reached if and only if $\mathbf V$ verifies some {rigidity} conditions. In the particular case of an electrostatic potential, these imply that $\mathbf V$ is the Coulomb potential.

    发表评论 查看更多 翻译此文

    收起

  • We are interested in the following problem of covering the plane with congruent circular discs with a constraint on the distance between "consecutive" discs. Let $(D_n)_{n \in \mathbb N}$ be a sequence of unit circular discs such that $\cup_{n \in \mathbb{N}} D_n = \mathbb {R}^2$ with the condition that for $n \ge 2$, centre of the disc $D_n$ lies in $D_{n-1}$. What is a "most economical" or an optimal way of placing $D_n$ for all $n \in \mathbb{N}$? We answer this question in the case where no "sharp" turn is allowed, i.e. if $C_n$ is the centre of the disc $D_n$, then for all $n \ge 2$, smaller of the angles $\angle C_{n-1}C_nC_{n+1}$ is not very small. Next we consider a closely related problem. We wish to find out an optimal way to cover the plane with unit circular discs with the constraint that each disc contains the centres of at least two other discs. We find out the answer in the case when centres of the discs form a two-dimensional lattice.

    发表评论 查看更多 翻译此文

    收起

  • In this paper, we study the computation and communication costs in decentralized distributed optimization and give a sharp complexity analysis for the proposed distributed accelerated gradient methods. We present two algorithms based on the framework of the accelerated penalty method with increasing penalty parameters. Our first algorithm achieves the $O\left(\left(\epsilon\sqrt{1-\sigma_2(W)}\right)^{-1}\right)$ complexities for both computation and communication, which match the communication complexity lower bound for non-smooth distributed optimization, where $\sigma_2(W)$ denotes the second largest singular value of the weight matrix $W$ associated to the network. Our second algorithm employs a double-loop and obtains the near optimal $O\left(\sqrt{L/\left(\epsilon(1-\sigma_2(W))\right)}\log\epsilon^{-1}\right)$ communication complexity and the optimal $O\left(\sqrt{L/\epsilon}\right)$ computation complexity for $L$-smooth distributed optimization. When the problem is $\mu$-strong

    发表评论 查看更多 翻译此文

    收起

  • We introduce and investigate an infinite family of functions which are shown to have generalised quantum modular properties. We realise their "companions" in the lower half plane both as double Eichler integrals and as non-holomorphic theta functions with coefficients given by double error functions. Further, we view these Eichler integrals in a modular setting as parts of certain weight two indefinite theta series.

    发表评论 查看更多 翻译此文

    收起

  • During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information. In this work we propose a direct least-squares approach conceptually similar to the limited memory quasi-Newton methods, but that computes the search direction in a slightly different way. This is achieved in a fast and numerically robust manner by maintaining a Cholesky factor of low dimension. This is combined with a stochastic line search relying upon fulfilment of the Wolfe condition in a backtracking manner, where the step length is adaptively modified with respect to the optimisation progress. We support our new algorithm by providing several theoretical results guaranteeing its performance. The performance is demonstrated on real-world benchmark problems which shows improved results in comparison with already established methods.

    发表评论 查看更多 翻译此文

    收起

  • We discuss a framework for constructing large subsets of $\mathbb{R}^n$ and $K^n$ for non-archimedean local fields $K$. This framework is applied to obtain new estimates for the Hausdorff dimension of angle-avoiding sets and to provide a counterexample to a limiting version of the Capset problem.

    发表评论 查看更多 翻译此文

    收起

  • The main goal of group testing with inhibitors (GTI) is to identify a small number of defective items and inhibitor items in a large set of items. A test on a subset of items is positive if it satisfies some specific property. Inhibitor items cancel the effects of positive items, which often make the outcome of a test containing defective items negative. Different GTI models can be formulated by considering how specific properties have different cancellation effects. This work introduces generalized GTI (GGTI) in which a new type of items is added, i.e., hybrid items. A hybrid item plays the roles of both defectives items and inhibitor items. Since the number of GGTI models is large (at least 96), we introduce a framework for classifying all types of items non-adaptively, i.e., all tests are designed in advanced. We then explain how GGTI can be used to classify neurons in neuroscience. Finally, we optimize the construction of disjunct matrices, which are an important tool in GTI.

    发表评论 查看更多 翻译此文

    收起

  • This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error equation. The geometric assumptions, which are necessary for the optimal order of the conforming VEM error estimate in the $H^1$-seminorm, are relaxed for that in a bilinear form-induced energy norm.

    发表评论 查看更多 翻译此文

    收起

  • On a smooth projective threefold, we construct an essentially surjective functor $\mathcal{F}$ from a category of two-term complexes to a category of quotients of coherent sheaves, and describe the fibers of this functor. Under a coprime assumption on rank and degree, the domain of $\mathcal{F}$ coincides with the category of higher-rank PT stable objects, which appear on one side of Toda's higher-rank DT/PT correspondence formula. The codomain of $\mathcal{F}$ is the category of objects that appear on one side of another correspondence formula by Gholampour-Kool, between the generating series of topological Euler characteristics of two types of quot schemes.

    发表评论 查看更多 翻译此文

    收起

  • In this paper, we present an extension of Uzawa's algorithm and apply it to build approximating sequences of mean field games systems. We prove that Uzawa's iterations can be used in a more general situation than the one in it is usually used. We then present some numerical results of those iterations on discrete mean field games systems of optimal stopping, impulse control and continuous control.

    发表评论 查看更多 翻译此文

    收起

  • We propose a new heuristic approach to integral moments of L-functions over function fields, which we demonstrate in the case of Dirichlet characters ramified at one place (the function field analogue of the moments of the Riemann zeta function, where we think of the character n^{it} as ramified at the infinite place). We represent the moment as a sum of traces of Frobenius on cohomology groups associated to irreducible representations. Conditional on a hypothesis on the vanishing of some of these cohomology groups, we calculate the moments of the L-function and they match the predictions of the Conrey-Farmer-Keating-Rubinstein-Snaith recipe. In this case, the decomposition into irreducible representations seems to separate the main term and error term, which are mixed together in the long sums obtained from the approximate functional equation, even when it is dyadically decomposed. This makes our heuristic statement relatively simple, once the geometric background is set up. We hope t

    发表评论 查看更多 翻译此文

    收起

  • Let $V_1,V_2,V_3$ be a triple of even dimensional vector spaces over a number field $F$ equipped with nondegenerate quadratic forms $\mathcal{Q}_1,\mathcal{Q}_2,\mathcal{Q}_3$, respectively. Let \begin{align*} Y \subset \prod_{i=1}V_i \end{align*} be the closed subscheme consisting of $(v_1,v_2,v_3)$ on which $\mathcal{Q}_1(v_1)=\mathcal{Q}_2(v_2)=\mathcal{Q}_3(v_3)$. Motivated by conjectures of Braverman and Kazhdan and related work of Lafforgue, Ng\^o, and Sakellaridis we prove an analogue of the Poisson summation formula for certain functions on this space.

    发表评论 查看更多 翻译此文

    收起

  • We address the variational problem for the generalized principal eigenvalue on $\mathbb{R}^d$ of linear and semi-linear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the Collatz-Wielandt formula for potentials that vanish at infinity under minimal hypotheses, and also for general potentials under blanket geometric ergodicity assumptions. We also present associated results having the flavor of a refined maximum principle.

    发表评论 查看更多 翻译此文

    收起