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The bootstrap algebraic multigrid framework allows for the adaptive construction of algebraic multigrid methods in situations where geometric multigrid methods are not known or not available at all. While there has been some work on adaptive coarsening in this framework in terms of algebraic distances, coarsening is the part of the adaptive bootstrap setup that is least developed. In this paper we try to close this gap by introducing an adaptive coarsening scheme that views interpolation as a local regression problem. In fact the bootstrap algebraic multigrid setup can be understood as a machine learning ansatz that learns the nature of smooth error by local regression. In order to turn this idea into a practical method we modify least squares interpolation to both avoid overfitting of the data and to recover a sparse response that can be used to extract information about the coupling strength amongst variables like in classical algebraic multigrid. In order to improve the sofound coa
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We consider a class of nonlocal reactiondiffusion problems, referred to as replicatormutator equations in evolutionary genetics. For a confining fitness function, we prove wellposedness and write the solution explicitly, via some underlying Schr\"odinger spectral elements (for which we provide new and nonstandard estimates). As a consequence, the long time behaviour is determined by the principal eigenfunction or ground state. Based on this, we discuss (rigorously and via numerical explorations) the conditions on the fitness function and the mutation rate for evolutionary branching to occur.
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We give new examples of compact, negatively curved Einstein manifolds of dimension $4$. These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of 4manifolds $(X_k)$ previously considered by Gromov and Thurston. The construction begins with a certain sequence $(M_k)$ of hyperbolic 4manifolds, each containing a totally geodesic surface $\Sigma_k$ which is nullhomologous and whose normal injectivity radius tends to infinity with $k$. For a fixed choice of natural number $l$, we consider the $l$fold cover $X_k \to M_k$ branched along $\Sigma_k$. We prove that for any choice of $l$ and all large enough $k$ (depending on $l$), $X_k$ carries an Einstein metric of negative sectional curvature. The first step in the proof is to find an approximate Einstein metric on $X_k$, which is done by interpolating between a model Einstein metric near the branch locus and the pullback of the hyperbolic metric from $M_k$. The second step in t
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We give a rigorous proof of existence for solitary waves of a peridynamics model in one space dimension recently investigated by Silling (J. Mech. Phys. Solids 96:121132, 2016). We adapt the variational framework developed by Friesecke and Wattis (Comm. Math Phys. 161:391418, 1994) for the FermiPastaUlamTsingou lattice equations to treat a truncated problem which cuts off shortrange interactions, then pass to the limit.
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Let $A$ be an Artin algebra, $M$ be a Gorenstein projective $A$module and $B =$ End$_A M$, then $M$ is a $A$$B$bimodule. We use the restricted flat dimension of $M_B$ to give a characterization of the homological dimensions of $A$ and $B$, and obtain the following main results: (1) if $A$ is a CMfinite algebra with $\cal GP$($A$) = add$_AE$ and fin.dim $A \geq 2,$ then ${\rm fin.dim}\ B \leq {\rm fin.dim}\ A + {\rm rfd}(M_B) +{\rm pd}_B{\rm Hom}_A(M, E);$ (2) If $A$ is a CMfinite $n$Gorenstein algebra with $\cal GP$($A$) = add$_AE$ and $n \geq 2$, then gl.dim $B \leq n + {\rm pd}_B{\rm Hom}_A(M, E).$
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This article is devoted to the expansion of multiple Stratonovich stochastic integrals of fifth multiplicity, based on the method of generalized multiple Fourier series. We consider the expansion of multiple Ito stochastic integrals of fifth multiplicity (based on generalized multiple Fourier series) as the tool of the proof of the expansion for multiple Stratonovich stochastic integrals. As it turned out, expansions of multiple Stratonovich stochastic integrals are essentially simpler than expansions of multiple Ito stochastic integrals. The multiple Stratonovich stochastic integrals are the part of the TaylorStratonovich expansion. That is why the results of the article can be useful for numerical integrations of Ito or Stratonovich stochastic differential equations.
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We derive explicit upper bounds for various functions counting primes in arithmetic progressions. By way of example, if $q$ and $a$ are integers with $\gcd(a,q)=1$ and $3 \leq q \leq 10^5$, and $\theta(x;q,a)$ denotes the sum of the logarithms of the primes $p \equiv a \pmod{q}$ with $p \leq x$, we show that $$ \bigg \theta (x; q, a)  \frac{x}{\phi (q)} \bigg < \frac1{3600} \frac q{\phi(q)} \frac{x}{\log x}, $$ for all $x \geq 7.94 \cdot 10^9$ (with sharper constants obtained for individual such moduli $q$). We establish inequalities of the same shape for the other standard primecounting functions $\pi(x;q,a)$ and $\psi(x;q,a)$, as well as inequalities for the $n$th prime congruent to $a\pmod q$ when $q\le4500$. For moduli $q>10^5$, we find even stronger explicit inequalities, but only for much larger values of $x$. Along the way, we also derive an improved explicit lower bound for $L(1,\chi)$ for quadratic characters $\chi$, and an improved explicit upper bound for exception
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Consider an oriented fourdimensional Lorentzian manifold $(\widetilde{M}^{3, 1}, \widetilde{g})$ and an oriented sevendimensional Riemannian manifold $(M^{7}, g)$. We describe a class of decomposable elevendimensional supergravity backgrounds on the product manifold $({\mathcal{M}}^{10, 1}=\widetilde{M}^{3,1} \times M^7, g_{{\mathcal{M}}}=\widetilde{g}+g)$, endowed with a flux form given in terms of the volume form on $\widetilde{M}^{3, 1}$ and a closed $4$form $F^{4}$ on $M^{7}$. We show that the Maxwell equation for such a flux form can be read in terms of the coclosed 3form $\phi=\star_{7}F^{4}$. Moreover, the supergravity equation reduces to the condition that $(\widetilde{M}^{3,1},\widetilde{g})$ is an Einstein manifold with negative Einstein constant and $(M^7, g, F)$ is a Riemannian manifold which satisfies the Einstein equation with a stressenergy tensor associated to the 3form $\phi$. Whenever this 3form is generic, the Maxwell equation induces a weak ${\rm G}_2$stru
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In this paper we survey a recent progress on continuous frames inspired by the solution of the KadisonSinger problem by Marcus, Spielman, and Srivastava. We present an extension of Lyapunov's theorem for discrete frames due to Akemann and Weaver and a similar extension for continuous frames by the author. We also outline a solution of the discretization problem, which was originally posed by Ali, Antoine, and Gazeau, and recently solved by Freeman and Speegle.
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We extend our techniques developed in our manuscript mentioned in the subtitle to obtain a deterministic polynomial time algorithm for computing the noncommutative rank together with certificates of linear spaces of matrices over sufficiently large base fields. The key new idea is a reduction procedure that keeps the blowup parameter small, and there are two methods to implement this idea: the first one is a greedy argument that removes certain rows and columns, and the second one is an efficient algorithmic version of a result of Derksen and Makam. Both methods rely crucially on the regularity lemma in the aforementioned manuscript, and in this note we improve that lemma by removing a coprime condition there. arXiv:1508.00690
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Sequential attack detection in a distributed estimation system is considered, where each sensor successively produces onebit quantized samples of a desired deterministic scalar parameter corrupted by additive noise. The unknown parameters in the preattack and postattack models, namely the desired parameter to be estimated and the injected malicious data at the attacked sensors pose a significant challenge for designing a computationally efficient scheme for each sensor to detect the occurrence of attacks by only using local communication with neighboring sensors. The generalized Cumulative Sum (GCUSUM) algorithm is considered, which replaces the unknown parameters with their maximum likelihood estimates in the CUSUM test statistic. For the problem under consideration, a sufficient condition is provided under which the expected false alarm period of the GCUSUM can be guaranteed to be larger than any given value. Next, we consider the distributed implementation of the GCUSUM. We first
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We continue the study of strong, weak, and $dc$weak eigenforms introduced by Chen, Kiming, and Wiese. We completely determine all systems of Hecke eigenvalues of level $1$ modulo $128$, showing there are finitely many. This extends results of Hatada and can be considered as evidence for the more general conjecture formulated by the author together with Kiming and Wiese on finiteness of systems of Hecke eigenvalues modulo prime powers at any fixed level. We also discuss the finiteness of systems of Hecke eigenvalues of level $1$ modulo $9$, reducing the question to the finiteness of a single eigenvalue. Furthermore, we answer the question of comparing weak and $dc$weak eigenforms and provide the first known examples of nonweak $dc$weak eigenforms.
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We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear to offer protection to a standard trial multiplication attack.
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We consider an energy harvesting transmitter sending status updates to a receiver over an erasure channel, where each status update is of length $k$ symbols. The energy arrivals and the channel erasures are independent and identically distributed (i.i.d.) and Bernoulli distributed in each slot. In order to combat the effects of the erasures in the channel and the uncertainty in the energy arrivals, we use channel coding to encode the status update symbols. We consider two types of channel coding: maximum distance separable (MDS) codes and rateless erasure codes. For each of these models, we study two achievable schemes: besteffort and saveandtransmit. In the besteffort scheme, the transmitter starts transmission right away, and sends a symbol if it has energy. In the saveandtransmit scheme, the transmitter remains silent in the beginning in order to save some energy to minimize energy outages in future slots. We analyze the average age of information (AoI) under each of these pol
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We say that a planar set $A$ has the Kakeya property if there exist two different positions of $A$ such that $A$ can be continuously moved from the first position to the second within a set of arbitrarily small area. We prove that if $A$ is closed and has the Kakeya property, then the union of the nontrivial connected components of $A$ can be covered by a null set which is either the union of parallel lines or the union of concentric circles. In particular, if $A$ is closed, connected and has the Kakeya property, then $A$ can be covered by a line or a circle.
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We show that an arbitrary factor map $\pi:X \to Y$ on an irreducible subshift of finite type is a composition of a finitetoone factor code and a class degree one factor code. Using this structure theorem on infinitetoone factor codes, we then prove that any equilibrium state $\nu$ on $Y$ for a potential function of sufficient regularity lifts to a unique measure of maximal relative entropy on $X$. This answers a question raised by Boyle and Petersen (for lifts of Markov measures) and generalizes the earlier known special case of finitetoone factor codes.
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Abstract coarse structures were introduced by J.Ro. Subsequently, equivalent structures, called large scale structures were introduced by J.Dydak and C.Hoffland. This paper is devoted to a much simpler definition of majority of useful coarse structures. Namely, they are equivalence relations on the set of simple ends of sets equipped with a bounded structure. As an application we show that Gromov boundary of every hyperbolic space is an example of a Higson corona and each Freundenthal compactification is an example of a Higson compactification.
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We consider Homogeneous Algebraic Riccati Equations in the general situation when the matrix of the dynamics can be "mixed". We show that in this case the equation may have infinitely many families of solutions. An analysis of these families is carried over and explicit formulas are derived. We also derive sufficient conditions under which the union of the families covers the whole set of solutions.
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Various problems in manifold estimation make use of a quantity called the reach, denoted by $\tau\_M$, which is a measure of the regularity of the manifold. This paper is the first investigation into the problem of how to estimate the reach. First, we study the geometry of the reach through an approximation perspective. We derive new geometric results on the reach for submanifolds without boundary. An estimator $\hat{\tau}$ of $\tau\_{M}$ is proposed in a framework where tangent spaces are known, and bounds assessing its efficiency are derived. In the case of i.i.d. random point cloud $\mathbb{X}\_{n}$, $\hat{\tau}(\mathbb{X}\_{n})$ is showed to achieve uniform expected loss bounds over a $\mathcal{C}^3$like model. Finally, we obtain upper and lower bounds on the minimax rate for estimating the reach.
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Essential  the phone company led by Android cofounder Andy Rubin  has had some difficulty in getting a stable 8.0 Oreo update released. After three beta releases, the company is not quite satisfied that the update is ready for general release. Because of these protracted issues, Essential has announced plans to skip the 8.0 release entirely in favor of 8.1, which will "push the public release back a couple weeks," according to the company. Not even a phone with close to stock Android, built by the very same person who developed Android in the first place, can be updated to a newer Android release without delays, stability issues, and general problems  to the point where they're skipping a version altogether. Android is a mess.
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For any $C^\infty$, areapreserving Anosov diffeomorphism $f$ of a surface, we show that a suspension flow over $f$ is $C^\infty$conjugate to a constanttime suspension flow of a hyperbolic automorphism of the two torus if and only if the volume measure is the measure with maximal entropy. We also show that the the metric entropy with respect to the volume measure and the topological entropy of suspension flow over Anosov diffeomorphisms on torus achieve all possible values. Our results fit into two programs related to entropy rigidity and flexibility of Anosov systems.
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In this paper, we study a multiuser multipleinputmultipleoutput secrecy simultaneous wireless information and power transfer (SWIPT) channel which consists of one transmitter, one cooperative jammer (CJ), multiple energy receivers (potential eavesdroppers, ERs), and multiple colocated receivers (CRs). We exploit the dual of artificial noise (AN) generation for facilitating efficient wireless energy transfer and secure transmission. Our aim is to maximize the minimum harvested energy among ERs and CRs subject to secrecy rate constraints for each CR and total transmit power constraint. By incorporating normbounded channel uncertainty model, we propose a iterative algorithm based on sequential parametric convex approximation to find a nearoptimal solution. Finally, simulation results are presented to validate the performance of the proposed algorithm outperforms that of the conventional ANaided scheme and CJaided scheme.
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We investigate elliptic boundaryvalue problems for which the maximum of the orders of the boundary operators is equal to or greater than the order of the elliptic differential equation. We prove that the operator corresponding to an arbitrary problem of this kind is bounded and Fredholm between appropriate Hilbert spaces which form certain twosided scales and are built on the base of isotropic H\"ormander spaces. The differentiation order for these spaces is given by an arbitrary real number and positive function which varies slowly at infinity in the sense of Karamata. We establish a local a priori estimate for the generalized solutions to the problem and investigate their local regularity (up to the boundary) on these scales. As an application, we find sufficient conditions under which the solutions have continuous classical derivatives of a given order.
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We analyze the weak solution concept for the FornbergWhitham equation in case of traveling waves with a piecewise smooth profile function. The existence of discontinuous weak traveling wave solutions is shown by means of analysis of a corresponding planar dynamical system and appropriate patching of disconnected orbits.
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We construct the generalized LebesgueBochner spaces $L^p(\mu,\varPi)$ for positive measures $\mu$ and for suitable real or complex topological vector spaces $\varPi$ so that for $1<p<+\infty$ and Banachable $\varPi$ with separable topology the strong dual of the classical Bochner space $L^p(\mu,\varPi)$ becomes canonically represented by $L^{p^*}(\mu,\varPi_\sigma')\,$. Hence we need no separability assumption of the norm topology of the strong dual $\varPi_\beta'$ of $\varPi$. For $p=1$ and for suitably restricted positive measures $\mu$ we even get a similar result without any separability of the norm topology of the target space $\varPi$. For positive Radon measures on locally compact topological spaces these results are essentially contained on pages 588606 in R. E. Edwards' classical Functional Analysis.
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Deep learning involves a difficult nonconvex optimization problem with a large number of weights between any two adjacent layers of a deep structure. To handle large data sets or complicated networks, distributed training is needed, but the calculation of function, gradient, and Hessian is expensive. In particular, the communication and the synchronization cost may become a bottleneck. In this paper, we focus on situations where the model is distributedly stored, and propose a novel distributed Newton method for training deep neural networks. By variable and featurewise data partitions, and some careful designs, we are able to explicitly use the Jacobian matrix for matrixvector products in the Newton method. Some techniques are incorporated to reduce the running time as well as the memory consumption. First, to reduce the communication cost, we propose a diagonalization method such that an approximate Newton direction can be obtained without communication between machines. Second, w
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We consider a distributed computing framework where the distributed nodes have different communication capabilities, motivated by the heterogeneous networks in data centers and mobile edge computing systems. Following the structure of MapReduce, this framework consists of Map computation phase, Shuffle phase, and Reduce computation phase. The Shuffle phase allows distributed nodes to exchange intermediate values, in the presence of heterogeneous communication bottlenecks for different nodes (heterogeneous communication load constraints). Focusing on twonode and threenode (K=2, 3) distributed computing systems with heterogeneous communication load constraints, in this work we characterize the minimum total computation load, as well as the minimum worstcase computation load for some cases. The worstcase computation load depends on the computation load of a node with the heaviest job. Therefore, by minimizing the worstcase computation load it could potentially minimize the system lat
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We present a new proof of the dimensionless $L^p$ boundedness of the Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion, namely that of a new dimensionless weighted $L^p$ estimate with optimal exponent. Other than previous arguments, only a small part of our proof is based on special auxiliary functions, the core of the argument is a weak type estimate and a sparse decomposition of the stochastic process by X.D. Li, whose projection is the Riesz vector.
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Coisiche shared this story from the Guardian: Sensitive information about the location and staffing of military bases and spy outposts around the world has been revealed by a fitness tracking company. The details were released by Strava in a data visualisation map that shows all the activity tracked by users of its app, which allows people to record their exercise and share it with others. The map, released in November 2017, shows every single activity ever uploaded to Strava  more than 3 trillion individual GPS data points, according to the company. The app can be used on various devices including smartphones and fitness trackers like Fitbit to see popular running routes in major cities, or spot individuals in more remote areas who have unusual exercise patterns. However, over the weekend military analysts noticed that the map is also detailed enough that it potentially gives away extremely sensitive information about a subset of Strava users: military personnel on active service..
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Longtime Slashdot reader drinkypoo writes: Last week, Neoen's and Tesla's massive battery was paid up to $1000/MWh to charge itself and now it could have earned up to 1 million AUD in the last few days by selling the power back to the grid to cover a coal plant outage. Unlike other forms of power storage, battery systems can be switched between states (charging, discharging, or idle) effectively instantly, which permits a stabilizing effect on the grid. "What we are seeing here," writes Fred Lambert at Electrek.co, "is the Powerpack system enabling Neoen to sell electricity at up to $14,000 AUD per MWh and charging itself at almost no cost during overproduction."
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An anonymous reader writes: "I will be short. I've got an order to kill you," the note said, demanding $2,800 in U.S. dollars or Bitcoin. "I switched from being upset about it to, 'I need to get the word out'," one of its targets told a local newscaster. They filed a report through the FBI's web site. "If only 1% of people send money  there's no overhead for them; that's money in the bank," one FBI agent tells the news team. A quick Google search finds recent reports of two nearly identical threats using the same text. "I have been thinking for a long time whether it is worth sending this notice, and decided that you still have the right to know... I've got an order to kill you, because some of your activity causes trouble to several people... I decided to break some rules, as this will be my final order... As soon as I receive the funds, I will forward you the name of the man [this] order came from, and all other information I have."
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The article is devoted to comparison of the Milstein expansion of multiple stochastic integrals with the method of expansion of multiple stochastic integrals, based on generalized multiple Fourier series. We consider some practical material connected with expansions of multiple Stratonovich stochastic integrals from the TaylorStratonovich expansion, based on multiple trigonometric Fourier series. The comparison of effectiveness of the FourierLegendre series as well as the trigonomertic Fourier series for expansion of multiple Stratonovich stochastic integrals is considered.
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This paper deals with two related problems, namely distancepreserving binary embeddings and quantization for compressed sensing . First, we propose fast methods to replace points from a subset $\mathcal{X} \subset \mathbb{R}^n$, associated with the Euclidean metric, with points in the cube $\{\pm 1\}^m$ and we associate the cube with a pseudometric that approximates Euclidean distance among points in $\mathcal{X}$. Our methods rely on quantizing fast JohnsonLindenstrauss embeddings based on bounded orthonormal systems and partial circulant ensembles, both of which admit fast transforms. Our quantization methods utilize noiseshaping, and include SigmaDelta schemes and distributed noiseshaping schemes. The resulting approximation errors decay polynomially and exponentially fast in $m$, depending on the embedding method. This dramatically outperforms the current decay rates associated with binary embeddings and Hamming distances. Additionally, it is the first such binary embedding r
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We present an eventtriggered control strategy for stabilizing a scalar, continuoustime, timeinvariant, linear system over a digital communication channel having bounded delay, and in the presence of bounded system disturbance. We propose an encodingdecoding scheme, and determine lower bounds on the packet size and on the information transmission rate which are sufficient for stabilization. We show that for small values of the delay, the timing information implicit in the triggering events is enough to stabilize the system with any positive rate. In contrast, when the delay increases beyond a critical threshold, the timing information alone is not enough to stabilize the system and the transmission rate begins to increase. Finally, large values of the delay require transmission rates higher than what prescribed by the classic datarate theorem. The results are numerically validated using a linearized model of an inverted pendulum.
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The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi linear operators. In the present paper we push this subject further, by proving Hardy Littlewood inequalities for multipolynomials and, en passant, a variant of the Kahane SalemZygmund inequality in this framework.
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In this paper, we introduce a clustered millimeter wave network with nonorthogonal multiple access (NOMA), where the base station (BS) is located at the center of each cluster and all users follow a Poisson Cluster Process. To provide a realistic directional beamforming, an actual antenna pattern is deployed at all BSs. We provide a nearestrandom scheme, in which near user is the closest node to the corresponding BS and far user is selected at random, to appraise the coverage performance and universal throughput of our system. Novel closedform expressions are derived under a loose network assumption. Moreover, we present several Monte Carlo simulations and numerical results, which show that: 1) NOMA outperforms orthogonal multiple access regarding the system rate; 2) the coverage probability is proportional to the number of possible NOMA users and a negative relationship with the variance of intracluster receivers; and 3) an optimal number of the antenna elements is existed for max
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For semisimple Lie groups, moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. In many cases, natural topological invariants label connected components of the moduli spaces. Hitchin representations into split real forms, and maximal representations into Hermitian Lie groups, are the only previously know cases where natural invariants do not fully distinguish connected components. In this note we announce the existence of new such exotic components in the moduli spaces for the groups $\mathrm{SO}(p,q)$ with $2<p<q$. These groups lie outside formerly know classes of groups associated with exotic components.
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Correlated random fields are a common way to model dependence struc tures in highdimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp totic variance which adds up all autocovariances in the temporal and spatial domain. Especially, it arises in the standardization of test statistics based on partial sums of random fields and thus the construction of tests requires its estimation. In this paper we propose consistent estimators for this parameter for strictly stationary {\phi}mixing random fields with arbitrary dimension of the domain and taking values in a Euclidean space of arbitrary dimension, thus allowing for multivariate random fields. We establish consistency, provide cen tral limit theorems and show that distributional approximations of related test statistics based on sample autocovariances of random fields can be obtained by the subsampling approach. As in applications the spatialtemporal c
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We develop the construction of the fractional powers of singular (pointlike) perturbations of the Laplacian, and the construction of singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and nonlinear Schr\"odinger equations for the corresponding operators we outline a programme of relevant questions that deserve being investigated.
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For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential nonuniform convergence in total variation norm to a quasistationary distribution. We also characterize a subset of its domain of attraction by an integrability condition, prove the existence of a right eigenvector for the semigroup of the process and the existence and exponential ergodicity of the Qprocess. These results are applied to onedimensional and multidimensional diffusion processes, to pure jump continuous time processes, to reducible processes with several communication classes, to perturbed dynamical systems and discrete time processes evolving in discrete state spaces.
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The HalesJewett theorem states that for any $m$ and $r$ there exists an $n$ such that any $r$colouring of the elements of $[m]^n$ contains a monochromatic combinatorial line. We study the structure of the wildcard set $S \subseteq [n]$ which determines this monochromatic line, showing that when $r$ is odd there are $r$colourings of $[3]^n$ where the wildcard set of a monochromatic line cannot be the union of fewer than $r$ intervals. This is tight, as for $n$ sufficiently large there are always monochromatic lines whose wildcard set is the union of at most $r$ intervals.
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Let $X$ be a smooth projective variety over a field of characteristic $0$ and $L$ an ample divisor. In this paper we study the Weak Lefschetz conjecture for Chow groups using the technique employed by Grothendieck in his study of the problem for Picard groups, and using Bloch's formula to interpret Chow groups in terms of Milnor $K$ theory we prove the infinitesimal part of the conjecture.
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We consider a particle system with weights and the scaling limits derived from its occupation time. We let the particles perform independent recurrent L\'evy motions and we assume that their initial positions and weights are given by a Poisson point process. In the limit we obtain a number of recently discovered stationary stable selfsimilar processes recently studied in [SAM1] and [SAM2]. We also observe very different limit processes depending on whether the function, whose occupation time is considered, integrates to zero or not.
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We consider nonadaptive probabilistic group testing in the linear regime, where each of n items is defective independently with probability p in (0,1), where p is a constant independent of n. We show that testing each item individually is optimal, in the sense that with fewer than n tests the error probability is bounded away from zero.
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A new finite blocklength converse for the Slepian Wolf coding problem is presented which significantly improves on the best known converse for this problem, due to Miyake and Kanaya [2]. To obtain this converse, an extension of the linear programming (LP) based framework for finite blocklength point topoint coding problems from [3] is employed. However, a direct application of this framework demands a complicated analysis for the SlepianWolf problem. An analytically simpler approach is presented wherein LPbased finite blocklength converses for this problem are synthesized from pointtopoint lossless source coding problems with perfect sideinformation at the decoder. New finite blocklength metaconverses for these pointtopoint problems are derived by employing the LPbased framework, and the new converse for SlepianWolf coding is obtained by an appropriate combination of these converses.
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Since there is no hyperbolic Dehn filling theorem in higher dimensions, it is difficult to construct concrete hyperbolic manifolds of small volume in dimension at least four. We build up a census of closed hyperbolic 4manifolds of volume $\frac{34\pi^2}{3}\cdot 16$ by using small cover theory over the rightangled 120cell. In particular, we classify all the orientable 4dimensional small covers over the 120cell and obtain exactly 56 many up to homeomorphism. All of them have even intersection forms.
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In this paper, we investigate a general nonlinear model of opinion dynamics in which both statedependent susceptibility to persuasion and antagonistic interactions are considered. According to the existing literature and sociopsychological theories, we examine three specializations of statedependent susceptibility, that is, stubborn positives scenario, stubborn neutrals scenario, and stubborn extremists scenario. Interactions among agents form a signed graph, in which positive and negative edges represent friendly and antagonistic interactions, respectively. Based on PerronFrobenius property of eventually positive matrices and LaSalle invariance principle, we conduct a comprehensive theoretical analysis of the generalized nonlinear opinion dynamics. We obtain some sufficient conditions such that the states of all agents converge into the subspace spanned by the right positive eigenvector of an eventually positive matrix. When there exists at least one entry of the right positive ei
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In late November 2016, CNN purchased YouTube star Casey Neistat's videosharing app Beme for $25 million. The news network purchased the app in a bid to harness Neistat's (at the time) 6 million subscribers, with the hopes of turning the company into an independently operated daily online news show and a core part of CNN's offerings that would appeal to a younger demographic. Today, CNN has shut down Beme because Neistat was unable to figure out a viable strategy due to creative differences and sluggish process. He will be departing from CNN. The Verge reports: "I couldn't find answers. I would sort of disappear, and I would hide, and I would make YouTube videos for my channel because at least I would be able to yield something," Neistat told Buzzfeed News. "I don't think I'm giving CNN what I want to give them, and I don't think they're getting value from me." When CNN bought Beme, it said Neistat's company would focus on "timely and topical video and empowering content creators to us
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In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birthanddeath chains and GaltonWatson forests. Using these ideas, we establish limit theorems showing that if the first $n$ boxes are occupied independently with probability $p\in(0,1)$, then the number of solitons is of order $n$ for all $p$, and the length of the longest soliton is of order $\log n$ for $p<1/2$, order $\sqrt{n}$ for $p=1/2$, and order $n$ for $p>1/2$. Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed $j\geq 1$, the top $j$ soliton lengths have the same order as the longest for $p\leq 1/2$, whereas all but the longest have order at most $\log n$ for $p>1/2$. As an application, we obtain scaling limits for the lengths of the $k^{\text{th}}$ longest increasing and
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Google on Thursday pushed an update to its marquee Web browser Chrome, now at v64, which offers a handful of new features including an improved ad blocker. From a report: Most of the new features included with Chrome 64 are meant to improve the browser's support for the everchanging web standards that drive the modern Internet. For example, Chrome 64 is choke full of support for new browser APIs, new CSS properties, new JavaScript (ECMAScript) features, and changes to Chrome's V8 JavaScript engine. [...] Other big changes that shipped with Chrome 64 are on the browser's security side. For starters, Chrome 64 includes mitigations against the webexploitable Spectre flaw. Further, Chrome 64 also comes with a bolstered popup blocker that can now block tabunder behavior, being much more efficient at blocking malvertising redirects.
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