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The Bro network security monitoring project has announced a name change to "Zeek". "On the Leadership Team of the Bro Project, we heard clear concerns from the Bro community that the name 'Bro' has taken on strongly negative connotations, such as 'Bro culture'. These send a sharp, antiinclusive  and wholly unintended and undesirable  message to those who might use Bro. The problems were significant enough that during BroCon community sessions, several people have mentioned substantial difficulties in getting their upper management to even consider using opensource software with such a seemingly illchosen, offputting name."
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With $\Fq$ the finite field of $q$ elements, we investigate the following question. If $\gamma$ generates $\Fqn$ over $\Fq$ and $\beta$ is a nonzero element of $\Fqn$, is there always an $a \in \Fq$ such that $\beta(\gamma + a)$ is a primitive element? We resolve this case when $n=3$, thereby proving a conjecture by Cohen. We also improve substantially on what is known when $n=4$.
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The aim of this work is an analysis of distal and nondistal behavior in dense pairs of ominimal structures. A characterization of distal types is given through orthogonality to a generic type in $M^{\operatorname{eq}}$, nondistality is geometrically analyzed through Keisler measures, and a distal expansion for the case of pairs of ordered vector spaces is computed.
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The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the $2M$dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new polynomial identity relating the eigenvalues of such matrices with their matrix { entries} is obtained. In the limit $M\to\infty$ this identity induces some requirements, which should satisfy the scattering data of the resulting infinitedimensional Jacobi operator in the halfline, which super and subdiagonal matrix elements are equal to 1. We obtain such requirements in the simplest case of the discrete Schr\"odinger operator acting in ${l}^2( \mathbb{N})$, which does not have bound and semibound states, and which potential has a compact support.
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This article is based on a talk at the RIEMain in Contact conference in Cagliari, Italy in honor of the 78th birthday of David Blair one of the founders of modern Riemannian contact geometry. The present article is a survey of a special type of Riemannian contact structure known as Sasakian geometry. An ultimate goal of this survey is to understand the moduli of classes of Sasakian structures as well as the moduli of extremal and constant scalar curvature Sasaki metrics, and in particular the moduli of SasakiEinstein metrics.
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We introduce two new measures for the dependence of $n \ge 2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^2$distance of quantities related to the characteristic functions of the underlying random variables. These extend distance covariance (introduced by Sz\'ekely, Rizzo and Bakirov) from pairs of random variables to $n$tuplets of random variables. We show that total distance multivariance can be used to detect the independence of $n$ random variables and has a simple finitesample representation in terms of distance matrices of the sample points, where distance is measured by a continuous negative definite function. Under some mild moment conditions, this leads to a test for independence of multiple random vectors which is consistent against all alternatives.
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For the focusing cubic wave equation, we find an explicit, nontrivial selfsimilar blowup solution $u^*_T$, which is defined on the whole space and exists in all supercritical dimensions $d \geq 5$. For $d=7$, we analyze its stability properties without any symmetry assumptions and prove the existence of a codimension one Lipschitz manifold consisting of initial data whose solutions blowup in finite time and converge asymptotically to $u^*_T$ (modulo spacetime shifts and Lorentz boosts) in the backward lightcone of the blowup point. The underlying topology is strictly above scaling.
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Let $\{T(t)\}_{t\ge 0}$ be a $C_0$semigroup on a separable Hilbert space $H$. We characterize that $T(t)$ is an $m$isometry for every $t$ in terms that the mapping $t\in \Bbb R^+ \rightarrow \T(t)x\^2$ is a polynomial of degree less than $m$ for each $x\in H$. This fact is used to study $m$isometric right translation semigroup on weighted $L^p$spaces. We characterize the above property in terms of conditions on the infinitesimal generator operator or in terms of the cogenerator operator of $\{ T(t)\}_{t\geq 0}$. Moreover, we prove that a nonunitary $2$isometry on a Hilbert space satisfying the kernel condition, that is, $$ T^*T(KerT^*)\subset KerT^*\;, $$ then $T$ can be embedded into a $C_0$semigroup if and only if $dim (KerT^*)=\infty$.
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An anonymous reader quotes a report from The Hill: An Amazon employee is seeking to put new pressure on the company to stop selling its facial recognition technology to law enforcement. An anonymous worker, whose employment at Amazon was verified by Medium, published an oped on that platform on Tuesday criticizing the company's facial recognition work and urging the company to respond to an open letter delivered by a group of employees. The employee wrote that the government has used surveillance tools in a way that disproportionately hurts "communities of color, immigrants, and people exercising their First Amendment rights." "Ignoring these urgent concerns while deploying powerful technologies to government and law enforcement agencies is dangerous and irresponsible," the person wrote. "That's why we were disappointed when Teresa Carlson, vice president of the worldwide public sector of Amazon Web Services, recently said that Amazon 'unwaveringly supports' law enforcement, defense,
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In this paper, we prove a new cohomology theory that is an invariant of a planar trivalent graph with a given perfect matching. This bigraded cohomology theory appears to be very powerful: the graded Euler characteristic of the cohomology is a one variable polynomial (called the 2factor polynomial) that, if nonzero when evaluated at one, implies that the perfect matching is even. This polynomial can be used to construct a polynomial invariant of the graph called the even matching polynomial. We conjecture that the even matching polynomial is positive when evaluated at one for all bridgeless planar trivalent graphs. This conjecture, if true, implies the existence of an even perfect matching for the graph, and thus the trivalent planar graph is 3edgecolorable. This is equivalent to the four color theorema famous conjecture in mathematics that was proven using a computer program in 1970s. While these polynomial invariants may not have enough strength as invariants to prove such a co
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The second eigenvalue of the Robin Laplacian is shown to be maximal for the ball among domains of fixed volume, for negative values of the Robin parameter $\alpha$ in the regime connecting the first nontrivial Neumann and Steklov eigenvalues, and even somewhat beyond the Steklov regime. The result is close to optimal, since the ball is not maximal when $\alpha$ is sufficiently large negative, and the problem admits no maximiser when $\alpha$ is positive.
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In many contemporary optimization problems, such as hyperparameter tuning for deep learning architectures, it is computationally challenging or even infeasible to evaluate an entire function or its derivatives. This necessitates the use of stochastic algorithms that sample problem data, which can jeopardize the guarantees classically obtained through globalization techniques via a trust region or a line search. Using subsampled function values is particularly challenging for the latter strategy, that relies upon multiple evaluations. On top of that all, there has been an increasing interest for nonconvex formulations of datarelated problems. For such instances, one aims at developing methods that converge to secondorder stationary points, which is particularly delicate to ensure when one only accesses subsampled approximations of the objective and its derivatives. This paper contributes to this rapidly expanding field by presenting a stochastic algorithm based on negative curvature a
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A sequence is called $r$sparse if every contiguous subsequence of length $r$ has no repeated letters. A $DS(n, s)$sequence is a $2$sparse sequence with $n$ distinct letters that avoids alternations of length $s+2$. Pettie and Wellman (2018) asked whether there exist $r$sparse $DS(n, s)$sequences of length $\Omega(s n^{2})$ for $s \geq n$ and $r > 2$, which would generalize a result of Roselle and Stanton (1971) for the case $r = 2$. We construct $r$sparse $DS(n, s)$sequences of length $\Omega(s n^{2})$ for $s \geq n$ and $r > 2$. Our construction uses linear hypergraph edgecoloring bounds. We also use the construction to generalize a result of Pettie and Wellman by proving that if $s = \Omega(n^{1/t} (t1)!)$, then there are $r$sparse $DS(n, s)$sequences of length $\Omega(n^{2} s / (t1)!)$ for all $r \geq 2$. In addition, we find related results about the lengths of sequences avoiding $(r, s)$formations.
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In this paper, we study the global dynamics of a general $2\times 2$ competition models with nonsymmetric nonlocal dispersal operators. Our results indicate that local stability implies global stability provided that one of the diffusion rates is sufficiently small. This paper continues the work in \cite{BaiLi2017}, where competition models with symmetric nonlocal operators are considered.
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It is known that fuzzy set theory can be viewed as taking place within a topos. There are several equivalent ways to construct this topos, one is as the topos of \'{e}tal\'{e} spaces over the topological space $Y=[0,1)$ with lower topology. In this topos, the fuzzy subsets of a set $X$ are the subobjects of the constant \'{e}tal\'{e} $X\times Y$ where $X$ has the discrete topology. Here we show that the type2 fuzzy truth value algebra is isomorphic to the complex algebra formed from the subobjects of the constant relational \'{e}tal\'{e} given by the type1 fuzzy truth value algebra $\mathfrak{I}=([0,1],\wedge,\vee,\neg,0,1)$. More generally, we show that if $L$ is the lattice of open sets of a topological space $Y$ and $\mathfrak{X}$ is a relational structure, then the convolution algebra $L^\mathfrak{X}$ is isomorphic to the complex algebra formed from the subobjects of the constant relational \'{e}tal\'{e} given by $\mathfrak{X}$ in the topos of \'{e}tal\'{e} spaces over $Y$.
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Facebook is developing hardware for the TV, news outlet Cheddar reported Tuesday. From the report: The world's largest social network is building a cameraequipped device that sits atop a TV and allows video calling along with entertainment services like Facebook's YouTube competitor, according to people familiar with the matter. The project, internally codenamed "Ripley," uses the same core technology as Facebook's recently announced Portal video chat device for the home. Portal begins shipping next month and uses A.I. to automatically detect and follow people as they move throughout the frame during a video call. Facebook currently plans to announce project Ripley in the spring of 2019, according to a person with direct knowledge of the project. But the device is still in development and the date could be changed.
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In this paper, wireless video transmission to multiple users under total transmission power and minimum required video quality constraints is studied. In order to provide the desired performance levels to the endusers in realtime video transmissions while using the energy resources efficiently, we assume that power control is employed. Due to the presence of interference, determining the optimal power control is a nonconvex problem but can be solved via monotonic optimization framework. However, monotonic optimization is an iterative algorithm and can often entail considerable computational complexity, making it not suitable for realtime applications. To address this, we propose a learningbased approach that treats the input and output of a resource allocation algorithm as an unknown nonlinear mapping and a deep neural network (DNN) is employed to learn this mapping. This learned mapping via DNN can provide the optimal power level quickly for given channel conditions.
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We study Nash equilibria for a twoplayer zerosum optimal stopping game with incomplete and asymmetric information. In our setup, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the other one (asymmetric information feature). We formulate the problem and reduce it to a fully Markovian setup where the uninformed player optimises over stopping times and the informed one uses randomised stopping times in order to hide their informational advantage. Then we provide a general verification result which allows us to find Nash equilibria by solving suitable quasivariational inequalities with some nonstandard constraints. Finally, we study an example with linear payoffs, in which an explicit solution of the corresponding quasivariational inequalities can be obtained.
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We prove that a general complete intersection of dimension $n$, codimension $c$ and type $d_1, \dots, d_c$ in $\mathbb{P}^N$ has ample cotangent bundle if $c \geq 2n2$ and the $d_i$'s are all greater than a bound that is $O(1)$ in $N$ and quadratic in $n$. This degree bound substantially improves the currently bestknown superexponential bound in $N$ by Deng, although our result does not address the case $n \leq c < 2n2$.
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In this paper we propose a combinatorial approach to generalized mathematical derangements and anagrams without fixed letters. In sections 1 and 2 we introduce the functions $P$  the number of generalized derangements of a set, and $P'$  the number of anagrams without fixed letters of a given word. The preliminary observations in these chapters provide the toolbox for developing two recursive algorithms in section 3 for computing $P$ and $P'$. The second algorithm leads to several different inequalities. They allow us to roughly estimate the values of $P$ and $P'$ and partially order them. The final section of this paper is dedicated to some number theoretical properties of $P'.$ The focus is on divisibility and the main technique is partitioning the anagrams into classes of equivalence in different ways. The article ends with a conjecture, which generalizes one of the theorems in the last chapter.
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This paper presents a modified quasireversibility method for computing the exponentially unstable solution of a nonlocal terminalboundary value parabolic problem with noisy data. Based on data measurements, we perturb the problem by the socalled filter regularized operator to design an approximate problem. Different from recently developed approaches that consist in the conventional spectral methods, we analyze this new approximation in a variational framework, where the finite element method can be applied. To see the whole skeleton of this method, our main results lie in the analysis of a semilinear case and we discuss some generalizations where this analysis can be adapted. As is omnipresent in many physical processes, there is likely a myriad of models derived from this simpler case, such as source localization problems for brain tumors and heat conduction problems with nonlinear sinks in nuclear science. With respect to each noise level, we benefit from the FaedoGalerkin meth
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An anonymous reader quotes a report from Recode: Facebook announced Portal last week, its take on the inhome, voiceactivated speaker to rival competitors from Amazon, Google and Apple. Last Monday, we wrote: "No data collected through Portal  even call log data or app usage data, like the fact that you listened to Spotify  will be used to target users with ads on Facebook." We wrote that because that's what we were told by Facebook executives. But Facebook has since reached out to change its answer: Portal doesn't have ads, but data about who you call and data about which apps you use on Portal can be used to target you with ads on other Facebookowned properties. "Portal voice calling is built on the Messenger infrastructure, so when you make a video call on Portal, we collect the same types of information (i.e. usage data such as length of calls, frequency of calls) that we collect on other Messengerenabled devices. We may use this information to inform the ads we show you acr
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We propose an index for gapped quantum lattice systems that conserve a $\mathrm{U}(1)$charge. This index takes integer values and it is therefore stable under perturbations. Our formulation is general, but we show that the index reduces to (i) an index of projections in the noninteracting case, (ii) the filling factor for translational invariant systems, (iii) the quantum Hall conductance in the twodimensional setting without any additional symmetry. Example (ii) recovers the LiebSchultzMattis theorem, (iii) provides a new and short proof of quantization of Hall conductance in interacting manybody systems. Additionally, we provide a new proof of Bloch's theorem on the vanishing of ground state currents.
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At its annual Adobe Max conference, Adobe announced plans to bring a complete version of Photoshop to the iPad in 2019. Photoshop CC for iPad will feature a revamped interface designed specifically for a touch experience, but it will bring the power and functionality people are accustomed to on the desktop. This is the real, full photoshop  the same codebase as the regular Photoshop, but running on the iPad with a touch UI. The Verge's Dami Lee and artist colleagues at The Verge got to test this new version of Photoshop, and they are very clear to stress that the biggest news here isn't even having the "real" Photoshop on the iPad, but the plans Adobe has for the PSD file format. But the biggest change of all is a total rethinking of the classic .psd file for the cloud, which will turn using Photoshop into something much more like Google Docs. Photoshop for the iPad is a big deal, but Cloud PSD is the change that will let Adobe bring Photoshop everywhere. This does se
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Emerging applications of sensor networks for detection sometimes suggest that classical problems ought be revisited under new assumptions. This is the case of binary hypothesis testing with independent  but not necessarily identically distributed  observations under the two hypotheses, a formalism so orthodox that it is used as an opening example in many detection classes. However, let us insert a new element, and address an issue perhaps with impact on strategies to deal with "big data" applications: What would happen if the structure were streamlined such that data flowed freely throughout the system without provenance? How much information (for detection) is contained in the sample values, and how much in their labels? How should decisionmaking proceed in this case? The theoretical contribution of this work is to answer these questions by establishing the fundamental limits, in terms of error exponents, of the aforementioned binary hypothesis test with unlabeled observations draw
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Brinde [Approximating fixed points of weak contractions using the Picard itration, Nonlinear Anal. Forum 9 (2004), 4353] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $\Theta$ contraction mappings and present some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $\Theta$contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided.
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For a polynomial $F(t,A_1,\ldots,A_n)\in\mathbf{F}_p[t,A_1,\ldots,A_n]$ ($p$ being a prime number) we study the decomposition statistics of its specializations $$F(t,a_1,\ldots,a_n)\in\mathbf{F}_p[t]$$ with $(a_1,\ldots,a_n)\in S$, where $S\subset\mathbf{F}_p^n$ is a subset, in the limit $p\to\infty$ and $\deg F$ fixed. We show that for a sufficiently large and regular subset $S\subset\mathbf{F}_p^n$, e.g. a product of $n$ intervals of length $H_1,\ldots,H_n$ with $\prod_{i=1}^nH_n>p^{n1/2+\epsilon}$, the decomposition statistics is the same as for unrestricted specializations (i.e. $S=\mathbf{F}_p^n$) up to a small error. This is a generalization of the wellknown P\'olyaVinogradov estimate of the number of quadratic residues modulo $p$ in an interval.
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This paper deals with the analysis of qualitative properties involved in the dynamics of KellerSegel type systems in which the diffusion mechanisms of the cells are driven by porousmedia fluxsaturated phenomena. We study the regularization inside the support of a solution with jump discontinuity at the boundary of the support. We analyze the behavior of the size of the support and blowup of the solution, and the possible convergence in finite time towards a Dirac mass in terms of the three constants of the system: the mass, the fluxsaturated characteristic speed, and the chemoattractant sensitivity constant. These constants of motion also characterize the dynamics of regular and singular traveling waves.
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In this paper, we investigate exterior and symmetric (co)homology of groups. We give a new approach to symmetric cohomology and also introduce symmetric homology of groups. We compute symmetric homology and exterior (co)homology of some finite groups. Further, we compare the classical, exterior and symmetric (co)homology and introduce some new (co)homologies of groups.
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We study existence of densities for solutions to stochastic differential equations with H\"older continuous coefficients and driven by a $d$dimensional L\'evy process $Z=(Z_{t})_{t\geq 0}$, where, for $t>0$, the density function $f_{t}$ of $Z_{t}$ exists and satisfies, for some $(\alpha_{i})_{i=1,\dots,d}\subset(0,2)$ and $C>0$, \begin{align*} \limsup\limits _{t \to 0}t^{1/\alpha_{i}}\int\limits _{\mathbb{R}^{d}}f_{t}(z+e_{i}h)f_{t}(z)dz\leq Ch,\ \ h\in \mathbb{R},\ \ i=1,\dots,d. \end{align*} Here $e_{1},\dots,e_{d}$ denote the canonical basis vectors in $\mathbb{R}^{d}$. The latter condition covers anisotropic $(\alpha_{1},\dots,\alpha_{d})$stable laws but also particular cases of subordinate Brownian motion. To prove our result we use some ideas taken from \citep{DF13}.
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We study the family of Bethe subalgebras in the Yangian $Y(\mathfrak{g})$ parameterized by the corresponding adjoint Lie group $G$. We describe their classical limits as subalgebras in the algebra of polynomial functions on the formal Lie group $G_1[[t^{1}]]$. In particular we show that, for regular values of the parameter, these subalgebras are free polynomial algebras with the same Poincare series as the Cartan subalgebra of the Yangian. Next, we extend the family of Bethe subalgebras to the De ConciniProcesi wonderful compactification $\overline{G}\supset G$ and describe the subalgebras corresponding to generic points of any stratum in $\overline{G}$ as Bethe subalgebras in the Yangian of the corresponding Levi subalgebra in $\mathfrak{g}$.
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Suppose $G$ is a finite group and $p$ is either a prime number or $0$. For $p$ positive, we say that $G$ is weakly tame at $p$ if $G$ has no nontrivial normal $p$subgroups. By convention we say that every finite group is weakly tame at $0$. Now suppose that $G$ is a finite group which is weakly tame at the residue characteristic of a discrete valuation ring $R$. Our main result shows that the essential dimension of $G$ over the fraction field $K$ of $R$ is at least as large as the essential dimension of $G$ over the residue field $k$. We also prove a more general statement of this type for a class of \'etale gerbes over $R$. As a corollary, we show that, if $G$ is weakly tame at $p$ and $k$ is any field of characteristic $p >0$ containing the algebraic closure of $\mathbb{F}_p$, then the essential dimension of $G$ over $k$ is less than or equal to the essential dimension of $G$ over any characteristic $0$ field. A conjecture of A. Ledet asserts that the essential dimension, $\math
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The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to $Z$transformation directed graph of the graph. A finite distributive lattice is matchable if its Hasse diagram is isomorphic to a $Z$transformation directed graph of a plane weakly elementary bipartite graph, otherwise nonmatchable. We introduce the meetirreducible cell with respect to a perfect matching of a plane (weakly) elementary bipartite graph and give its equivalent characterizations. Using these, we extend a result on nonmatchable distributive lattices, and obtain a class of new nonmatchable distributive lattices.
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The enhanced power graph $\mathcal G_e(\mathbf G)$ of a group $\mathbf G$ is the graph with vertex set $G$ such that two vertices $x$ and $y$ are adjacent if they are contained in a same cyclic subgroup. We prove that finite groups with isomorphic enhanced power graphs have isomorphic directed power graphs. We show that any isomorphism between power graphs of finite groups is an isomorhism between enhanced power graphs of these groups, and we find all finite groups $\mathbf G$ for which $\mathrm{Aut}(\mathcal G_e(\mathbf G)$ is abelian, all finite groups $\mathbf G$ with $\lvert\mathrm{Aut}(\mathcal G_e(\mathbf G)\rvert$ being prime power, and all finite groups $\mathbf G$ with $\lvert\mathrm{Aut}(\mathcal G_e(\mathbf G)\rvert$ being square free. Also we describe enhanced power graphs of finite abelian groups. Finally, we give a characterization of finite nilpotent groups whose enhanced power graphs are perfect, and we present a sufficient condition for a finite group to have weakly pe
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We exhibit a new construction of edgeregular graphs with regular cliques that are not strongly regular. The infinite family of graphs resulting from this construction includes an edgeregular graph with parameters $(24,8,2)$. We also show that edgeregular graphs with $1$regular cliques that are not strongly regular must have at least $24$ vertices.
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Recently, Misanantenaina and Wagner characterized the set of induced $N$free and bowtiefree posets as a certain class of recursively defined subposets which they term "$\mathcal{V}$posets". Here we offer a new characterization of $\mathcal{V}$posets by introducing a property we refer to as \emph{autonomy}. A poset $\mathcal{P}$ is said to be \emph{autonomous} if there exists a directed acyclic graph $D$ (with adjacency matrix $U$) whose transitive closure is $\mathcal{P}$, with the property that any total ordering of the vertices of $D$ so that Gaussian elimination of $U^TU$ proceeds without row swaps is a linear extension of $\mathcal{P}$. Autonomous posets arise from the theory of pressing sequences in graphs, a problem with origins in phylogenetics. The pressing sequences of a graph can be partitioned into families corresponding to posets; because of the interest in enumerating pressing sequences, we investigate when this partition has only one block, that is, when the pressing
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It is shown that the solution of the Cauchy problem for the BBMKP equation converges to the solution of the Cauchy problem for the BBM equation in a suitable function space whenever the initial data for both equations are close as the transverse variable $y \rightarrow \pm \infty$.
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For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. As a consequence, we prove a conjecture of Charles and KerrPearlstein, that zero loci of normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. In particular, this gives a short proof of a special, algebraically motivated case of a result of Saito, BrosnanPearlstein, and Schnell, conjectured by GreenGriffiths, on zero loci of admissible normal functions.
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We introduce a tool for analysing models of $\textnormal{CT}^$, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan's theorem that arithmetical part of models of $\textnormal{PA}$ are recursively saturated. We use this tool to provide a new proof that all models of $\textnormal{CT}^$ carry a partial inductive truth predicate. Finally, we construct a partial truth predicate defined for formulae from a nonstandard cut which cannot be extended to a full truth predicate satisfying $\textnormal{CT}^$.
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We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the righthand side has very few regularity and that the spectral measure can be singular in some directions. The proofs require having good enough estimates for the corresponding heat kernels and their derivatives.
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LQG mean field game systems consisting of a major agent and a large population of minor agents have been addressed in the literature. In this paper, a novel convex analysis approach is utilized to retrieve the best response strategies for the major agent and each individual minor agent which collectively yield an $\epsilon$Nash equilibrium for the entire system.
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We present a unified treatment of the Fourier spectra of spherically symmetric nonlocal diffusion operators. We develop numerical and analytical results for the class of kernels with weak algebraic singularity as the distance between source and target tends to $0$. Rapid algorithms are derived for their Fourier spectra with the computation of each eigenvalue independent of all others. The algorithms are trivially parallelizable, capable of leveraging more powerful compute environments, and the accuracy of the eigenvalues is individually controllable. The algorithms include a Maclaurin series and a full divergent asymptotic series valid for any $d$ spatial dimensions. Using Drummond's sequence transformation, we prove linear complexity recurrence relations for degreegraded sequences of numerators and denominators in the rational approximations to the divergent asymptotic series. These relations are important to ensure that the algorithms are efficient, and also increase the numerical s
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Is it possible to break the hostvector chain of transmission when there is an influx of infectious hosts into a na\"{i}ve population and competent vector? To address this question, a class of vectorborne disease models with an arbitrary number of infectious stages that account for immigration of infective individuals is formulated. The proposed model accounts for forward and backward progression, capturing the mitigation and aggravation to and from any stages of the infection, respectively. The model has a rich dynamic, which depends on the patterns of infected immigrant influx into the host population and connectivity of the transfer between infectious classes. We provide conditions under which the answer of the initial question is positive.
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LiNadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti Geometric Langlands Conjecture of BenZviNadler in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds in the natural generality of reflection groups in Euclidean or hyperbolic space.
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In this paper we generalize the recently introduced concept of fair measure (M. Misiurewicz and A. Rodrigues, Counting preimages. Ergod. Th. & Dynam. Sys. 38 (2018), no. 5, 1837  1856). We study transitive countable state Markov shift maps and extend our results to a particular class of interval maps, Markov and mixing interval maps. Finally, we move beyond the interval and look for fair measures for graph maps.
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When a Stanford researcher removed all the duplicate and fake comments filed with the Federal Communications Commission last year, he found that 99.7 percent of public comments  about 800,000 in all  were pronet neutrality. From a report: "With the fog of fraud and spam lifted from the comment corpus, lawmakers and their staff, journalists, interested citizens and policymakers can use these reports to better understand what Americans actually said about the repeal of net neutrality protections and why 800,000 Americans went further than just signing a petition for a redress of grievances by actually putting their concerns in their own words," Ryan Singel, a media and strategy fellow at Stanford University, wrote in a blog post Monday. Singel released a report [PDF] Monday that analyzed the unique comments  as in, they weren't a copypasta of one or dozens of other letters  filed last year ahead of the FCC's decision to repeal federal net neutrality protections. That's from the
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While global convergence of the DouglasRachford iteration is often observed in applications, proving it is still limited to convex and a handful of other special cases. Lyapunov functions for difference inclusions provide not only global or local convergence certificates, but also imply robust stability, which means that the convergence is still guaranteed in the presence of persistent disturbances. In this work, a global Lyapunov function is constructed by combining known local Lyapunov functions for simpler, local subproblems via an explicit formula that depends on the problem parameters. Specifically, we consider the scenario where one set consists of the union of two lines and the other set is a line, so that the two sets intersect in two distinct points. Locally, near each intersection point, the problem reduces to the intersection of just two lines, but globally the geometry is nonconvex and the DouglasRachford operator multivalued. Our approach is intended to be prototypica
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We study the asymptotic behaviour of the expected cost of the random matching problem on a $2$dimensional compact manifold, improving in several aspects the results of L. Ambrosio, F. Stra and D. Trevisan (A PDE approach to a 2dimensional matching problem). In particular, we simplify the original proof (by treating at the same time upper and lower bounds) and we obtain the coefficient of the leading term of the asymptotic expansion of the expected cost for the random bipartite matching on a general 2dimensional closed manifold. We also sharpen the estimate of the error term given by M. Ledoux (On optimal matching of Gaussian samples II) for the semidiscrete matching. As a technical tool, we develop a refined contractivity estimate for the heat flow on random data that might be of independent interest.
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Let $\Sigma$ be a closed, smooth hypersurface in $\Bbb R^{n + 1}$ which is axially symmetric and is contained inside the unit sphere $\Bbb S^{n}$. For a continuous function $f$, which is defined on $\Bbb S^{n}$, the main goal of this paper is to characterize the support of $f$ in case where its integrals vanish on subspheres obtained by intersecting $\Bbb S^{n}$ with the tangent hyperplanes of a certain subdomain $\mathcal{U}\subset\Sigma$ of $\Sigma$. We show that the support of $f$ can be characterized in case where its integrals also vanish on subspheres obtained by intersecting $\Bbb S^{n}$ with hyperplanes obtained by infinitesimal perturbations of the tangent hyperplanes of $\mathcal{U}$.
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We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshevaccelerated primaldual algorithm to achieve faster ergodic convergence rates. In standard distributed primaldual algorithms, the speed of convergence towards a global optimum (i.e., a saddle point in the corresponding Lagrangian function) is directly influenced by the eigenvalues of the Laplacian matrix representing the communication graph. In this paper, we use Chebyshev matrix polynomials to generate gossip matrices whose spectral properties result in faster convergence speeds, while allowing for a fully distributed implementation. As a result, the proposed algorithm requires fewer gradient updates at the cost of additional rounds of communications between agents. We illustrate the performance of the proposed algorithm in a distributed signal recovery probl
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We deduce from Sageev's results that whenever a group acts locally elliptically on a finite dimensional CAT(0) cube complex, then it must fix a point. As an application, we give an example of a group G such that G does not have property (T), but G and all its finitely generated subgroups can not act without a fixed point on a finite dimensional CAT(0) cube complex, answering a question by Barnhill and Chatterji.
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We demonstrate how selfconcordance of the loss can be exploited to obtain asymptotically optimal rates for Mestimators in finitesample regimes. We consider two classes of losses: (i) canonically selfconcordant losses in the sense of Nesterov and Nemirovski (1994), i.e., with the third derivative bounded with the $3/2$ power of the second; (ii) pseudo selfconcordant losses, for which the power is removed, as introduced by Bach (2010). These classes contain some losses arising in generalized linear models, including logistic regression; in addition, the second class includes some common pseudoHuber losses. Our results consist in establishing the critical sample size sufficient to reach the asymptotically optimal excess risk for both classes of losses. Denoting $d$ the parameter dimension, and $d_{\text{eff}}$ the effective dimension which takes into account possible model misspecification, we find the critical sample size to be $O(d_{\text{eff}} \cdot d)$ for canonically selfconco
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In this note, we consider the backward stochastic differential equation (BSDE) with generator $f(y)z^2,$ where the function $f$ is defined on an open set and locally integral. The existence and uniqueness of solution of such BSDE is explored for bounded or unbounded terminal variables. A comparison theorem and a converse theorem theorem of such BSDEs are obtained.
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Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension $n$, and requiring upto $n$ times fewer iterations. In this paper, we consider greedy updates that are based on subgradients for a class of nonsmooth composite problems, which includes $L1$regularized problems, SVMs and related applications. For these problems we provide (i) the first linear rates of convergence independent of $n$, and show that our greedy update rule provides speedups similar to those obtained in the smooth case. This was previously conjectured to be true for a stronger greedy coordinate selection strategy. Furthermore, we show that (ii) our new selection rule can be mapped to instances of maximum inner product search, allowing to leverage standard nearest neighbor algorithms to speed up the implementation. We dem
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In the present paper, we were mainly concerned with obtaining estimates for the general TaylorMaclaurin coefficients for functions in a certain general subclass of analytic biunivalent functions. For this purpose, we used the Faber polynomial expansions. Several connections to some of the earlier known results are also pointed out.
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The JordanWigner transformation plays an important role in spin models. However, the nonlocality of the transformation implies that a periodic chain of $N$ spins is not mapped to a periodic or an antiperiodic chain of lattice fermions. Since only the $N1$ bond is different, the effect is negligible for large systems, while it is significant for small systems. In this paper, it is interesting to find that a class of periodic spin chains can be exactly mapped to a periodic chain and an antiperiodic chain of lattice fermions without redundancy when the JordanWigner transformation is implemented. For these systems, possible high degeneracy is found to appear in not only the ground state but also the excitation states. Further, we take the onedimensional compass model and a new XYXY model ($\sigma_x\sigma_y\sigma_x\sigma_y$) as examples to demonstrate our proposition. Except for the wellknown onedimensional compass model, we will see that in the XYXY model, the degeneracy also
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We show that elements of control theory, together with an application of Harris' ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of networks of quasiharmonic classical oscillators coupled to heat baths. With the system of oscillators expressed in the form $\mathrm{d} X_t = A X_t \,\mathrm{d} t + F(X_t) \,\mathrm{d} t + B \,\mathrm{d} W_t$ in $\mathbf{R}^d$, where $A$ encodes the harmonic part of the force and $F$ corresponds to the gradient of the anharmonic part of the potential, the hypotheses under which we obtain exponential mixing are the following: $A$ is dissipative, the pair $(A,B)$ satisfies the Kalman condition, $F$ grows sufficiently slowly at infinity (depending on the dimension $d$), and the vector fields in the equation of motion satisfy the weak H\"ormander condition in at least one point of the phase space.
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Variable Stepsize Variable Order (VSVO) methods are the methods of choice to efficiently solve a wide range of ODEs with minimal work and assured accuracy. However, VSVO methods have limited impact in timestepping methods in complex applications due to their computational complexity and the difficulty to implement them in legacy code. We introduce a family of implicit, embedded, VSVO methods that require only one BDF solve at each time step followed by adding linear combinations of the solution at previous time levels. In particular, we construct implicit and linearly implicit VSVO methods of orders two, three and four with the same computational complexity as variable stepsize BDF3. The choice of changing the order of the method is simple and does not require additional solves of linear or nonlinear systems.
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