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Amir Goldstein has a use case for a feature that could be called a "lazy file reflink", he said, though it might also be described as "VFSlevel snapshots". He went through the use case, looking for suggestions, in a session at the 2019 Linux Storage, Filesystem, and MemoryManagement Summit (LSFMM). He has already implemented parts of the solution, but would like to get something upstream, which would mean shifting from the stackedfilesystem approach he has taken so far.
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One thing that is known about using transparent huge pages (THPs) for filesystems is that it is a hard problem to solve, but is there a solid first step that could be taken toward that goal? That is the question Song Liu asked to open his combined filesystem and memorymanagement session at the 2019 Linux Storage, Filesystem, and MemoryManagement Summit (LSFMM). His employer, Facebook, has a solid use case for using THPs on files in the page cache, which may provide a starting point.
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The relationship between SUSE and the openSUSE community is currently under discussion as the community considers different options for how it wants to be organized and governed in the future. Among the options under consideration is the possibility of openSUSE setting up an entirely independent foundation, as it seeks greater autonomy and control over its own future and operations.
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The "guarantees" that existing filesystems make with regard to persistence in the face of a system crash was the subject of a session led by Amir Goldstein at the 2019 Linux Storage, Filesystem, and MemoryManagement Summit (LSFMM). The problem is that filesystem developers are not willing to make much in the way of guarantees unless applications call fsync()—something that is not popular with application developers, who want a cheaper option.
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The cost of fsync() is well known to filesystem developers, which is why there are efforts to provide cheaper alternatives. Ric Wheeler wanted to discuss the longstanding idea of adding an asynchronous version of fsync() in a filesystem session at the 2019 Linux Storage, Filesystem, and MemoryManagement Summit (LSFMM). It turns out that what he wants may already be available via the new io_uring interface.
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The openSUSE project has announced the release of openSUSE Leap 15.1. "Leap releases are scalable and both the desktop and server are equally important for professional’s workloads, which is reflected in the installation menu as well as the amount of packages Leap offers and hardware it supports. Leap is well suited and prepared for usage as a Virtual Machine (VM) or container guest, allowing professional users to efficiently run network services no matter whether it’s a single server or a data center."
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In a combined filesystem and storage session at the 2019 Linux Storage, Filesystem, and MemoryManagement Summit, Avri Altman wanted to discuss the "turbowrite" mode that is coming for Universal Flash Storage (UFS) devices. He wanted to introduce this new feature to assembled developers and to get some opinions on how to support this mode in the kernel.
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Android is now at the point where sRGB color gamut with 8 bits per color channel is not enough to take advantage of the display and camera technology. At Android we have been working to make wide color photography happen endtoend, e.g. more bits and bigger gamuts. This means, eventually users will be able to capture the richness of the scenes, share a wide color pictures with friends and view wide color pictures on their phones. And now with Android Q, it’s starting to get really close to reality: wide color photography is coming to Android. So, it’s very important to applications to be wide color gamut ready. This article will show how you can test your application to see whether it’s wide color gamut ready and wide color gamut capable, and the steps you need to take to be ready for wide color gamut photography.
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Damien Le Moal and Naohiro Aota led a combined storage and filesystem session at the 2019 Linux Storage, Filesystem, and MemoryManagement Summit (LSFMM) on filesystem work that has been done for zoned block devices. These devices have multiple zones with different characteristics; usually there are zones that can only be written in sequential order as well as conventional zones that can be written in random order. The genesis of zoned block devices is shingled magnetic recording (SMR) devices, which were created to increase the capacity of hard disks, but at the cost of some flexibility.
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By the time Linus Torvalds released the 5.2rc1 kernel prepatch and closed the merge window for this development cycle, 12,064 nonmerge changesets had been pulled into the mainline repository — about 3,700 since our summary of the first "half" was written. Thus, as predicted, the rate of change did slow during the latter part of the merge window. That does not mean that no significant changes have been merged, though; read on for a summary of what else has been merged for 5.2.
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The everincreasing complexity of the software stacks we work with has given testing an important role. There was a recent intersection between the automated testing being done by the Yocto Project (YP) and a bug introduced into the Linux kernel that gives some insight into what the future holds and the potential available with this kind of testing.
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A vulnerability in the messaging app WhatsApp has allowed attackers to inject commercial Israeli spyware on to phones, the company and a spyware technology dealer said. WhatsApp, which is used by 1.5bn people worldwide, discovered in early May that attackers were able to install surveillance software on to both iPhones and Android phones by ringing up targets using the app’s phone call function. The malicious code, developed by the secretive Israeli company NSO Group, could be transmitted even if users did not answer their phones, and the calls often disappeared from call logs, said the spyware dealer, who was recently briefed on the WhatsApp hack. I never answer phone calls from telephone numbers I am not familiar with, let alone when the incoming callers his their number blocked. Apparently, though, not even protects you from attacks such as these.
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Researchers have found an explanation for why many drivers act out toward cyclists: They are actually dehumanizing people who ride bikes, according to an April study by Australian researchers in the journal Transportation Research. From a report: And this dehumanization  the belief that a group of people are less than human  correlates to drivers' selfreported aggressive behavior. Since 2010, cyclist fatalities have increased by 25 percent in the US. A total of 777 bicyclists were killed in crashes with drivers in 2017, and 45,000 were injured from crashes in 2015. Data compiled by the League of American Bicyclists also suggests that, in some states, bicyclists are overrepresented in the number of traffic fatalities. "The idea is that if you don't see a group of people as fully human, then you're more likely to be aggressive toward them," said Narelle Haworth, a professor and director of the Centre for Accident Research and Road Safety at Queensland University of Technology, one
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The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product for the fixed points. Since the inverse problem is illposed the regularized differential evolution is applied. For getting the optimized solution of the inverse problem the differential evolution algorithm is paralleled to 32 kernels. Numerical results for different technological levels and errors in measured data are presented and discussed.
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A hyperbolic polynomial (HP) is a real univariate polynomial with all roots real. By Descartes' rule of signs a HP with all coefficients nonvanishing has exactly $c$ positive and exactly $p$ negative roots counted with multiplicity, where $c$ and $p$ are the numbers of sign changes and sign preservations in the sequence of its coefficients. For $c=1$ and $2$, we discuss the question: When the moduli of all the roots of a HP are arranged in the increasing order on the real halfline, at which positions can be the moduli of its positive roots depending on the positions of the sign changes in the sequence of coefficients?
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A deviceindependent dimension test for a Bell experiment aims to estimate the underlying Hilbert space dimension that is required to produce given measurement statistical data without any other assumptions concerning the quantum apparatus. Previous work mostly deals with the twoparty version of this problem. In this paper, we propose a very general and robust approach to test the dimension of any subsystem in a multiparty Bell experiment. Our dimension test stems from the study of a new multiparty scenario which we call prepareanddistribute. This is like the prepareandmeasure scenario, but the quantum state is sent to multiple, noncommunicating parties. Through specific examples, we show that our test results can be tight. Furthermore, we compare the performance of our test to results based on known bipartite tests, and witness remarkable advantage, which indicates that our test is of a true multiparty nature. We conclude by pointing out that with some partial information about
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This research considers the ranking and selection (R&S) problem of selecting the optimal subset from a finite set of alternative designs. Given the total simulation budget constraint, we aim to maximize the probability of correctly selecting the topm designs. In order to improve the selection efficiency, we incorporate the information from across the domain into regression metamodels. In this research, we assume that the mean performance of each design is approximately quadratic. To achieve a better fit of this model, we divide the solution space into adjacent partitions such that the quadratic assumption can be satisfied within each partition. Using the large deviation theory, we propose an approximately optimal simulation budget allocation rule in the presence of partitioned domains. Numerical experiments demonstrate that our approach can enhance the simulation efficiency significantly.
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In this paper we study the drawdown related Parisian ruin problem for spectrally negative L\'{e}vy risk processes. We introduce the drawdown Parisian ruin time and solve the corresponding twosided exit time via excursion theory. We also obtain an expression of the potential measure for the process killed at the drawdown Parisian time. As applications, new results are obtained for spectrally negative L\'{e}vy risk process with dividend barrier and Parisian ruin.
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We prove decay with respect to some Lebesgue norms for a class of Schr\"odinger equations with nonlocal nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain largedata scattering in the energy space for the solutions to the systems of $N$ defocusing Choquard equations with massenergy intercritical nonlinearities in any space dimension and of defocusing HartreeFock equations, for any dimension $d\geq3$.
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We introduce a family of quasiBanach spaces  which we call wave packet smoothness spaces  that includes those function spaces which can be characterised by the sparsity of their expansions in Gabor frames, wave atoms, and many other frame constructions. We construct Banach frames for and atomic decompositions of the wave packet smoothness spaces and study their embeddings in each other and in a few more classical function spaces such as Besov and Sobolev spaces.
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Recently the authors introduced lecture hall tableaux in their study of multivariate little $q$Jacobi polynomials. In this paper, we enumerate bounded lecture hall tableaux. We show that their enumeration is closely related to standard and semistandard Young tableaux. We also show that the number of bounded lecture hall tableaux is the coefficient of the Schur expansion of $s_\lambda(m+y_1,\dots,m+y_n)$. To prove this result, we use two main tools: nonintersecting lattice paths and bijections. In particular we use ideas developed by Krattenthaler to prove bijectively the hook content formula.
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Artin's representation is an injective homomorphism from the braid group $B_n$ on $n$ strands into $\operatorname{Aut}\mathbb{F}_n$, the automorphism group of the free group $\mathbb{F}_n$ on $n$ generators. The representation induces maps $B_n\to\operatorname{Aut}C^*_r(\mathbb{F}_n)$ and $B_n\to\operatorname{Aut}C^*(\mathbb{F}_n)$ into the automorphism groups of the corresponding group $C^*$algebras of $\mathbb{F}_n$. These maps also have natural restrictions to the pure braid group $P_n$. In this paper, we consider twisted versions of the actions by cocycles with values in the circle, and discuss the ideal structure of the associated crossed products. Additionally, we make use of Artin's representation to show that the braid groups $B_\infty$ and $P_\infty$ on infinitely many strands are both $C^*$simple.
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We employ the proximal averaged Newtontype method for optimal control (PANOC) to solve obstacle avoidance problems in real time. We introduce a novel modeling framework for obstacle avoidance which allows us to easily account for generic, possibly nonconvex, obstacles involving polytopes, ellipsoids, semialgebraic sets and generic sets described by a set of nonlinear inequalities. PANOC is particularly wellsuited for embedded applications as it involves simple steps, its implementation comes with a low memory footprint and its fast convergence meets the tight runtime requirements of fast dynamical systems one encounters in modern mechatronics and robotics. The proposed obstacle avoidance scheme is tested on a labscale autonomous vehicle.
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We study the equivariant elliptic characteristic classes of Schubert varieties of the generalized full flag variety $G/B$. For this first we need to twist the notion of elliptic characteristic class of BorisovLibgober by a line bundle, and thus allow the elliptic classes to depend on extra variables. Using the BottSamelson resolution of Schubert varieties we prove a BGGtype recursion for the elliptic classes, and study the Hecke algebra of our elliptic BGG operators. For $G=GL_n(C)$ we find representatives of the elliptic classes of Schubert varieties in natural presentations of the K theory ring of $G/B$, and identify them with the TarasovVarchenko weight function (a.k.a. elliptic stable envelopes for $T^*G/B$). As a byproduct we find another recursion, different from the known Rmatrix recursion for the fixed point restrictions of weight functions. On the other hand the Rmatrix recursion generalizes for arbitrary reductive group $G$.
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We study a wireless adhoc sensor network (WASN) where $N$ sensors gather data from the surrounding environment and transmit their sensed information to $M$ fusion centers (FCs) via multihop wireless communications. This node deployment problem is formulated as an optimization problem to make a tradeoff between the sensing uncertainty and energy consumption of the network. Our primary goal is to find an optimal deployment of sensors and FCs to minimize a Lagrange combination of the sensing uncertainty and energy consumption. To support arbitrary routing protocols in WASNs, the routingdependent necessary conditions for the optimal deployment are explored. Based on these necessary conditions, we propose a routingaware Lloyd algorithm to optimize node deployment. Simulation results show that, on average, the proposed algorithm outperforms the existing deployment algorithms.
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The wellknown plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest PisotVijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the associated control point sets can be described as regular model sets whose windows in twodimensional internal space are Rauzy fractals with a complicated structure. Here, we calculate the resulting pure point diffraction measure via a Fourier matrix cocycle, which admits a closed formula for the Fourier transform of the Rauzy fractals, via a rapidly converging infinite product.
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Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of swarms. As further proof, Gardner's and Carroll's problems have been intensively employed in a number of selection methods and job interviews. Despite the mathematical background, these problems are based on, several solutions and explanations are given in a trivial way. This work proposes a thorough investigation of this framework, as a whole. The results of such study are three mathematical formulations that express the understood mathematical relationship in these wellknown riddles. The proposed formulas are of help in the formalization of the solutions, which have been proven to be less timetaking when compared to the wellknown classic ones, that look more heuristic than rigorous.
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Semianalytic expressions for the static limit of the $T$matrix for electromagnetic scattering are derived for a circular torus, expressed in both a basis of toroidal harmonics and spherical harmonics. The scattering problem for an arbitrary static excitation is solved using toroidal harmonics, and these are then compared to the extended boundary condition method to obtain analytic expressions for auxiliary $Q$ and $P$matrices, from which $\mathbf{T}=\mathbf{P}\mathbf{Q}^{1}$ (in a toroidal basis). By applying the basis transformations between toroidal and spherical harmonics, the quasistatic limit of the $T$matrix block $\mathbf{T}^{22}$ for electricelectric multipole coupling is obtained. For the toroidal geometry there are two similar $T$matrices on a spherical basis, for computing the scattered field both near the origin and in the far field. Static limits of the optical crosssections are computed, and analytic expressions for the limit of a thin ring are derived.
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The aim of this paper is to study the asymptotic properties of the maximum likelihood estimator (MLE) of the drift coefficient for fractional stochastic heat equation driven by an additive spacetime noise. We consider the traditional for stochastic partial differential equations statistical experiment when the measurements are performed in the spectral domain, and in contrast to the existing literature, we study the asymptotic properties of the maximum likelihood (type) estimators (MLE) when both, the number of Fourier modes and the time go to infinity. In the first part of the paper we consider the usual setup of continuous time observations of the Fourier coefficients of the solutions, and show that the MLE is consistent, asymptotically normal and optimal in the meansquare sense. In the second part of the paper we investigate the natural time discretization of the MLE, by assuming that the first N Fourier modes are measured at M time grid points, uniformly spaced over the time inte
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A Deza graph with parameters $(v,k,b,a)$ is a $k$regular graph on $v$ vertices in which the number of common neighbors of two distinct vertices takes two values $a$ or $b$ ($a\leq b$) and both cases exist. In the previous papers Deza graphs with parameters $(v,k,b,a)$ where $kb = 1$ were characterized. In the paper we characterise Deza graphs with $kb = 2$.
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By allowing a mobile device to offload computationintensive tasks to a base station, mobile edge computing (MEC) is a promising solution for saving the mobile device's energy. In real applications, the offloading may span multiple fading blocks. In this paper, we investigate energyefficient offloading over multiple fading blocks with random channel gains. An optimization problem is formulated, which optimizes the amount of data for offloading to minimize the total expected energy consumption of the mobile device. Although the formulated optimization problem is nonconvex, we prove that the objective function of the problem is piecewise convex, and accordingly develop an optimal solution for the problem. Numerical results verify the correctness of our findings and the effectiveness of our proposed method.
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Let $k$ be a field containing an algebraically closed field of characteristic zero. If $G$ is a finite group and $D$ is a division algebra over $k$, finite dimensional over its center, we can associate to a faithful $G$grading on $D$ a normal abelian subgroup $H$, a positive integer $d$ and an element of $Hom(M(H), k^\times)^G$, where $M(H)$ is the Schur multiplier of $H$. Our main theorem is the converse: Given an extension $1\rightarrow H\rightarrow G\rightarrow G/H\rightarrow 1$, where $H$ is abelian, a positive integer $d$, and an element of $Hom(M(H), k^\times)^G$, there is a division algebra with center containing $k$ that realizes these data. We apply this result to classify the $G$simple algebras over an algebraically closed field of characteristic zero that admit a division algebra form over a field containing an algebraically closed field.
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We study the bounded endomorphisms of $\ell_{N}^2(G)=\ell^2(G)\times \dots \times\ell^2(G)$ that commute with translations, where $G$ is a discrete abelian group. It is shown that they form a C*algebra isomorphic to the C*algebra of $N\times N$ matrices with entries in $L^\infty(\widehat{G})$, where $\widehat{G}$ is the dual space of $G$. Characterizations of when these endomorphisms are invertible, and expressions for their norms and for the norms of their inverses, are given. These results allow us to study Riesz systems that arise from the action of $ G $ on a finite set of elements of a Hilbert space.
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Starting today, Microsoft is ending all ebook sales in its Microsoft Store for Windows PCs. "Previously purchased ebooks will be removed from users' libraries in early July," reports The Verge. "Even free ones will be deleted. The company will offer full refunds to users for any books they've purchased or preordered." From the report: Microsoft's "official reason," according to ZDNet, is that this move is part of a strategy to help streamline the focus of the Microsoft Store. It seems that the company no longer has an interest in trying to compete with Amazon, Apple Books, and Google Play Books. It's a bit hard to imagine why anyone would go with Microsoft over those options anyway. If you have purchased ebooks from Microsoft, you can continue accessing them through the Edge browser until everything vanishes in July. After that, customers can expect to automatically receive a refund. According to a newly published Microsoft Store FAQ, "refund processing for eligible customers start rol
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An anonymous reader writes: Microsoft today announced that Visual Studio 2019 for Windows and Mac has hit general availability — you can download it now from visualstudio.microsoft.com/downloads. Visual Studio 2019 includes AIassisted code completion with Visual Studio IntelliCode. Separately, realtime collaboration tool Visual Studio Live Share has also hit general availability, and is now included with Visual Studio 2019.
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At its DataCentric Innovation Day, Intel today announced its Cascade Lake line of Xeon Scalable data center processors. From a report: The secondgeneration lineup of Xeon Scalable processors comes in 53 flavors that span up to 56 cores and 12 memory channels per chip, but as a reminder that Intel company is briskly expanding beyond "just" processors, the company also announced the final arrival of its Optane DC Persistent Memory DIMMs along with a range of new data center SSDs, Ethernet controllers, 10nm Agilex FPGAs, and Xeon D processors. This broad spectrum of products leverages Intel's overwhelming presence in the data center, it currently occupies ~95% of the worlds server sockets, as a springboard to chew into other markets, including its new assault on the memory space with the Optane DC Persistent Memory DIMMs. The longawaited DIMMs open a new market for Intel and have the potential to disrupt the entire memory hierarchy, but also serve as a potentially key component that ca
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This account of Anthem’s development, based on interviews with 19 people who either worked on the game or adjacent to it (all of whom were granted anonymity because they were not authorized to talk about Anthem’s development), is a story of indecision and mismanagement. It’s a story of technical failings, as EA’s Frostbite engine continued to make life miserable for many of BioWare’s developers, and understaffed departments struggled to serve their team’s needs. It’s a story of two studios, one in Edmonton, Alberta, Canada and another in Austin, Texas, that grew resentful toward one another thanks to a tense, lopsided relationship. It’s a story of a video game that was in development for nearly seven years but didn’t enter production until the final 18 months, thanks to big narrative reboots, major design overhauls, and a leadership team said to be unable to provide a consistent vision and unwilling to listen to feedback. Perhaps most alarming, it’s a story about a studio in crisis. Do
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Lego Education, the educationfocused arm of the veteran Denmark company, is making its biggest product debut in three years, unveiling Spike Prime, a new kit that aims to mix the company's familiar bricks with motors, sensors and introductory coding lessons. The company is targeting kids aged between 11 to 14. From a report: Lego Mindstorms have been around for years. The Mindstorms EV3 robotics kit remains a staple of many learning centers and robotics classrooms. Lego's newest kit looks more like Lego Boost, a programmable kit that aimed to win over families in 2017 and was compatible with regular Lego bricks. It's compatible with Lego Boost, Lego Technic sets and classic Lego pieces, but not with Lego's previous Mindstorms accessories. Lego Mindstorms EV3 is remaining alongside Lego Spike Prime in Lego Education's lineup, and looks like it's aiming more at the high school crowd, while Lego Spike Prime could bridge to that higherend projects. The Spike Prime set is created specif
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Two new studies reaffirm every computer dunce's worst fears: IT professionals blame the employees they're bound to help for their computer problems  at least when it comes to security. From a report: One, courtesy of SaaS operations management platform BetterCloud, offers grim reading. 91 percent of the 500 IT and security professionals surveyed admitted they feel vulnerable to insider threats. Which only makes one wonder about the supreme (over)confidence of the other 9 percent. [...] Yet now I've been confronted with another survey. This one was performed by the Ponemon Institute at the behest of securityforyoursecurity company nCipher. Its sampling was depressingly large. 5,856 IT and security professionals from around the world were asked for their views of corporate IT security. They seemed to wail in unison at the lesser and more unwashed. Oh, an objective 30 percent insisted that external hackers were the biggest cause for concern. A teethgritting 54 percent, however, s
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We consider the motion of a point mass in a onedimensional viscous compressible barotropic fluid. The fluidpoint mass system is governed by the barotropic compressible NavierStokes equations and Newton's equation of motion. Our main result concerns the long time behavior of the fluid and the point mass; it gives pointwise convergence estimates of the density and the velocity of the fluid to their equilibrium values. As a corollary, it shows that the fluid velocity $U(x,t)$ and the point mass velocity $V(t)=U(h(t)\pm 0,t)$, where $h(t)$ is the location of the point mass, decay differently as $U(\cdot,t)_{L^{\infty}(\mathbb{R}\backslash \{ h(t) \})}\approx t^{1/2}$ and $V(t)\lesssim t^{3/2}$. This discrepancy between the decay rates of $U(\cdot,t)_{L^{\infty}(\mathbb{R}\backslash \{ h(t) \})}$ and $V(t)=U(h(t)\pm 0,t)$ is due to the hyperbolicparabolic nature of the problem: The fluid velocity decays slower on the characteristics $x=\pm ct$, where $c$ is the speed o
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In this work, we revisit a discrete implementation of the primaldescent dualascent gradient method applied to saddlepoint optimization problems. Through a short proof, we establish linear (exponential) convergence of the algorithm for stronglyconvex cost functions with Lipschitz continuous gradients. Unlike previous studies, we provide explicit upper bounds on the stepsize parameters for stable behavior and on the resulting convergence rate and highlight the importance of having two different primal and dual stepsizes. We also explain the effect of the augmented Lagrangian penalty term on the algorithm stability and performance for the distributed minimization of aggregate cost functions over multiagent networks.
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We introduce a method to improve the tractability of the wellknown Sample Average Approximation (SAA) without compromising important theoretical properties, such as convergence in probability and the consistency of an independent and identically distributed (iid) sample. We consider each scenario as a polyhedron of the mix of firststage and secondstage decision variables. According to John's theorem, the LownerJohn ellipsoid of each polyhedron will be unique which means that different scenarios will have correspondingly different LownerJohn ellipsoids. By optimizing the objective function regarding both feasible regions of the polyhedron and its unique LownerJohn ellipsoid, respectively, we obtain a pair of optimal values, which would be a coordinate on a twodimensional plane. The scenarios, whose coordinates are close enough on the plane, will be treated as one scenario; thus our method reduces the sample size of an iid sample considerably. Instead of using a large iid sample d
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A FogRadio Access Network (FRAN) is studied in which cacheenabled Edge Nodes (ENs) with dedicated fronthaul connections to the cloud aim at delivering contents to mobile users. Using an informationtheoretic approach, this work tackles the problem of quantifying the potential latency reduction that can be obtained by enabling DevicetoDevice (D2D) communication over outofband broadcast links. Following prior work, the Normalized Delivery Time (NDT)  a metric that captures the high signaltonoise ratio worstcase latency  is adopted as the performance criterion of interest. Joint edge caching, downlink transmission, and D2D communication policies based on compressandforward are proposed that are shown to be informationtheoretically optimal to within a constant multiplicative factor of two for all values of the problem parameters, and to achieve the minimum NDT for a number of special cases. The analysis provides insights on the role of D2D cooperation in improving the de
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In order to study gravitational waves in any realistic astrophysical scenario, one must consider geometry perturbations up to second order. Here, we present a general technique for studying linear and quadratic perturbations on a spacetime with torsion. Besides the standard metric mode, a "torsionon" perturbation mode appears. This torsional mode will be able to propagate only in a certain kind of theories.
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It is often necessary to disclose training data to the public domain, while protecting privacy of certain sensitive labels. We use information theoretic measures to develop such privacy preserving data disclosure mechanisms. Our mechanism involves perturbing the data vectors in a manner that strikes a balance in the privacyutility tradeoff. We use maximal information leakage between the output data vector and the confidential label as our privacy metric. We first study the theoretical BernoulliGaussian model and study the privacyutility tradeoff when only the mean of the Gaussian distributions can be perturbed. We show that the optimal solution is the same as the case when the utility is measured using probability of error at the adversary. We then consider an application of this framework to a data driven setting and provide an empirical approximation to the Sibson mutual information. By performing experiments on the MNIST and FERG datasets, we show that our proposed framework a
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We prove linear inviscid damping near a general class of monotone shear flows in a finite channel, in Gevrey spaces. It is an essential step towards proving nonlinear inviscid damping for general shear flows that are not close to the Couette flow, which is a major open problem in 2d Euler equations.
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Some data is linearly additive, other data is not. In this paper, I discuss types of data based on the boundedness of the data and their linearity. 1) Unbounded data can be linear. 2) Oneside bounded data is usually log transformed to be linear. 3) Twoside bounded data is not linear. 4) Untidy data do not fit in these categories. An example of twosided bounded data is probabilities which should be transformed into a linear probability space by taking the logarithm of the odds ratio (log10 odds) which is termed Weight (W). Calculations of means and standard deviation is more accurate when calculated as W values than when calculated as probabilities. A methods to analyze untidy data is discussed.
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In this paper, we construct some families of infinitely many hyperelliptic curves of genus $2$ with exactly two rational points. In the proof, we first show that the MordellWeil ranks of these hyperelliptic curves are $0$ and then determine the sets of rational points by using the LutzNagell type theorem for hyperelliptic curves which was proven by Grant.
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In this paper, we realize polynomial $\H$modules $\Omega(\lambda,\alpha,\beta)$ from irreducible twisted HeisenbergVirasoro modules $\A_{\alpha,\beta}$. It follows from $\H$modules $\Omega(\lambda,\alpha,\beta)$ and $\mathrm{Ind}(M)$ that we obtain a class of natural nonweight tensor product modules $\big(\bigotimes_{i=1}^m\Omega(\lambda_i,\alpha_i,\beta_i)\big)\otimes \mathrm{Ind}(M)$. Then we give the necessary and sufficient conditions under which these modules are irreducible and isomorphic, and also give that the irreducible modules in this class are new.
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This paper considers dilations and translations of lines in the Desargues affine plane. A dilation of a line transforms each line into a parallel line whose length is a multiple of the length of the original line. In addition to the usual Playfair axiom for parallel lines in an affine plane, further conditions are given for distinct lines to be parallel in the Desargues affine plane. This paper introduces the dilation of parallel lines in a finite Desargues affine plane that is a bijection of the lines. Two main results are given in this paper, namely, each dilation in a finite Desarguesian plane is an isomorphism between skew fields constructed over isomorphic lines and each dilation in a finite Desarguesian plane occurs in a Pappian space.
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In this work we compute the Dixmier invariants and bitangents of the plane quartics with 3,6 or 9cyclic automorphisms, we find that a quartic curve with 6cyclic automorphism will have 3 horizontal bitangents which form an asysgetic triple. We also discuss the linear matrix representation problem of such curves, and find a degree 6 equation of 1 variable which solves the symbolic solution of the linear matrix representation problem for the curve with 6cyclic automorphism.
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