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In 1933, G\"{o}del introduced a provability interpretation of the propositional intuitionistic logic to establish a formalization for the BHK interpretation. He used the modal system, $\mathbf{S4}$, as a formalization of the intuitive concept of provability and then translated $\mathbf{IPC}$ to $\mathbf{S4}$. His work suggested the problem to find a concrete provability interpretation of the modal logic $\mathbf{S4}$. In this paper, we will try to answer this problem. In fact, we will generalize Solovay's provability interpretation of the modal logic $\mathbf{GL}$ to capture other modal logics such as $\mathbf{K4}$, $\mathbf{KD4}$ and $\mathbf{S4}$. Then we will use these results to find a formalization for the BHK interpretation and we will show that with different interpretations of the BHK interpretation, we can capture some of the propositional logics such as Intuitionistic logic, minimal logic and VisserRuitenburg's basic logic. Moreover, we will show that there is no provability
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In this paper, we study polynomial norms, i.e. norms that are the $d^{\text{th}}$ root of a degree$d$ homogeneous polynomial $f$. We first show that a necessary and sufficient condition for $f^{1/d}$ to be a norm is for $f$ to be strictly convex, or equivalently, convex and positive definite. Though not all norms come from $d^{\text{th}}$ roots of polynomials, we prove that any norm can be approximated arbitrarily well by a polynomial norm. We then investigate the computational problem of testing whether a form gives a polynomial norm. We show that this problem is strongly NPhard already when the degree of the form is 4, but can always be answered by testing feasibility of a semidefinite program (of possibly large size). We further study the problem of optimizing over the set of polynomial norms using semidefinite programming. To do this, we introduce the notion of rsosconvexity and extend a result of Reznick on sum of squares representation of positive definite forms to positive d
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This paper is devoted to the analysis of a simple LotkaVolterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen `17 where we have characterized the persistence and extinction of such a food chain under the assumption that there is no intraspecific competition among predators. In the current paper we focus on the case when all the species experience intracompetition. The food chain we analyze consists of one prey and $n1$ predators. The $j$th predator eats the $j1$th species and is eaten by the $j+1$th predator; this way each species only interacts with at most two other species  the ones that are immediately above or below it in the trophic chain. We show that one can classify, based on the invasion rates of the predators (which we can determine from the interaction coefficients of the system via an algorithm), which species go extinct and which converge to their unique invariant probability measure. We obtain stronger res
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We prove, under some assumptions, the existence of correctors for the stochastic homogenization of of " viscous " possibly degenerate HamiltonJacobi equations in stationary ergodic media. The general claim is that, assuming knowledge of homogenization in probability, correctors exist for all extreme points of the convex hull of the sublevel sets of the effective Hamiltonian. Even when homogenization is not a priori known, the arguments imply existence of correctors and, hence, homogenization in some new settings. These include positively homogeneous Hamiltonians and, hence, geometrictype equations including motion by mean curvature, in radially symmetric environments and for all directions. Correctors also exist and, hence, homogenization holds for many directions for non convex Hamiltonians and general stationary ergodic media.
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In this paper we extend the approach of orthogonal polynomials for extreme value calculations of Hermitian random matrices, developed by Nadal and Majumdar [1102.0738], to normal random matrices and 2D Coulomb gases in general. Firstly, we show that this approach provides an alternative derivation of results in the literature. More precisely, we show convergence of the rescaled eigenvalue with largest modulus of a Ginibre ensemble to a Gumbel distribution, as well as universality for an arbitrary radially symmetric potential. Secondly, it is shown that this approach can be generalised to obtain convergence of the eigenvalue with smallest modulus and its universality for ring distributions. Furthermore, the here presented techniques can be used to compute finite N expressions of the above distributions, which is important for practical applications given the slow convergence.
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Bounded weak solutions of Burgers' equation $\partial_tu+\partial_x(u^2/2)=0$ that are not entropy solutions need in general not be $BV$. Nevertheless it is known that solutions with finite entropy productions have a $BV$like structure: a rectifiable jump set of dimension one can be identified, outside which $u$ has vanishing mean oscillation at all points. But it is not known whether all points outside this jump set are Lebesgue points, as they would be for $BV$ solutions. In the present article we show that the set of nonLebesgue points of $u$ has Hausdorff dimension at most one. In contrast with the aforementioned structure result, we need only one particular entropy production to be a finite Radon measure, namely $\mu=\partial_t (u^2/2)+\partial_x(u^3/3)$. We prove H\"older regularity at points where $\mu$ has finite $(1+\alpha)$dimensional upper density for some $\alpha>0$. The proof is inspired by a result of De Lellis, Westdickenberg and the second author : if $\mu_+$ has
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In this paper we study the spherical convexity of quadratic functions on spherically convex sets. In particular, conditions characterizing the spherical convexity of quadratic functions on spherical convex sets associated to the positive orthants, Lorentz and circular cones are given.
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Let $H_1, H_2$ be complex Hilbert spaces and $T$ be a densely defined closed linear operator from its domain $D(T)$, a dense subspace of $H_1$, into $H_2$. Let $N(T)$ denote the null space of $T$ and $R(T)$ denote the range of $T$. Recall that $C(T) := D(T) \cap N(T)^{\perp}$ is called the {\it carrier space of} $T$ and the {\it reduced minimum modulus } $\gamma(T)$ of $T$ is defined as: $$ \gamma(T) := \inf \{\T(x)\ : x \in C(T), \x\ = 1 \} .$$ Further, we say that $T$ {\it attains its reduced minimum modulus} if there exists $x_0 \in C(T) $ such that $\x_0\ = 1$ and $\T(x_0)\ = \gamma(T)$. We discuss some properties of operators that attain reduced minimum modulus. In particular, the following results are proved.
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The proliferation of mobile Internet and connected devices, offering a variety of services at different levels of performance, represents a major challenge for the fifth generation wireless networks and beyond. This requires a paradigm shift towards the development of key enabling techniques for the next generation wireless networks. In this respect, visible light communication (VLC) has recently emerged as a new communication paradigm that is capable of providing ubiquitous connectivity by complementing radio frequency communications. One of the main challenges of VLC systems, however, is the low modulation bandwidth of the lightemittingdiodes, which is in the megahertz range. This article presents a promising technology, referred to as "optical nonorthogonal multiple access (ONOMA)", which is envisioned to address the key challenges in the next generation of wireless networks. We provide a detailed overview and analysis of the stateoftheart integration of ONOMA in VLC networ
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The smart meter (SM) privacy problem is addressed together with the cost of energy for the consumer. It is assumed that a storage device, e.g., an electrical battery, is available to the consumer, which can be utilized both to achieve privacy and to reduce the energy cost by modifying the energy consumption profile. Privacy is measured via the squarederror distortion between the SM readings, which are reported to the utility provider (UP), and a target profile, whereas timeofuse pricing is considered for energy cost calculation. Extensive numerical results are presented to evaluate the performance of the proposed strategy. The tradeoff between the achievable privacy and the energy cost is studied by taking into account the limited capacity of the battery as well as the capability to sell energy to the UP.
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We propose an optimal transportation aproach to price European options under the SteinStein stochastic volatility model by using the flow that transports the set of particles from prior to the posterior distribution. We also propose to direct the flow to a rarely corners of the state space by using a mutation and reweighing algorithm. We demonstrate the efficiency of our approach on a simple example for which the closed form formula is available. This methods shows the advantage of having low variance and bias and contrasts to other filtering schemes recently developed in signalprocessing literature, including particle filter technique.
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We revisit closedloop performance guarantees for Model Predictive Control in the deterministic and stochastic cases, which extend to novel performance results applicable to receding horizon control of Partially Observable Markov Decision Processes. While performance guarantees similar to those achievable in deterministic Model Predictive Control can be obtained even in the stochastic case, the presumed stochastic optimal control law is intractable to obtain in practice. However, this intractability relaxes for a particular instance of stochastic systems, namely Partially Observable Markov Decision Processes, provided reasonable problem dimensions are taken. This motivates extending available performance guarantees to this particular class of systems, which may also be used to approximate general nonlinear dynamics via gridding of state, observation, and control spaces. We demonstrate applicability of the novel closedloop performance results on a particular example in healthcare decis
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Risk contagion concerns any entity dealing with large scale risks. Suppose (X,Y) denotes a risk vector pertaining to two components in some system. A relevant measurement of risk contagion would be to quantify the amount of influence of high values of Y on X. This can be measured in a variety of ways. In this paper, we study two such measures: the quantity E[max(Xt,0)Y > t] called Marginal Mean Excess (MME) as well as the related quantity E[XY > t] called Marginal Expected Shortfall (MES). Both quantities are indicators of risk contagion and useful in various applications ranging from finance, insurance and systemic risk to environmental and climate risk. We work under the assumptions of multivariate regular variation, hidden regular variation and asymptotic tail independence for the risk vector (X,Y). Many broad and useful model classes satisfy these assumptions. We present several examples and derive the asymptotic behavior of both MME and MES as the threshold t tends to inf
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An $(n,k,l)$ MDS array code of length $n,$ dimension $k=nr$ and subpacketization $l$ is formed of $l\times n$ matrices over a finite field $F,$ with every column of the matrix stored on a separate node in a distributed storage system and viewed as a coordinate of the codeword. Repair of a failed node can be performed by accessing a set of $d\le n1$ helper nodes. The code is said to have the optimal access property if the amount of data accessed at each of the helper nodes meets a lower bound on this quantity. For optimalaccess MDS codes with $d=n1,$ the subpacketization $l$ satisfies the bound $l\ge r^{(k1)/r}.$ In our previous work, for any $n$ and $r,$ we presented an explicit construction of optimalaccess MDS codes with subpacketization $l=r^{n1}.$ In this paper we take up the question of reducing the subpacketization value $l$ to make it approach the lower bound. We construct an explicit family of optimalaccess codes with $l=r^{\lceil n/r\rceil},$ which differs from the
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A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of this method is between the total degree bound and the mixed volume bound and can be easily computed. The new algorithm has been implemented as a program called LPH using C++. Our experiments show its efficiency compared to the polyhedral or other homotopies on such systems. As an application, the algorithm can be used to find witness points on each connected component of a real variety.
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Multiple antennas have been exploited for spatial multiplexing and diversity transmission in a wide range of communication applications. However, most of the advances in the design of high speed wireless multipleinput multiple output (MIMO) systems are based on informationtheoretic principles that demonstrate how to efficiently transmit signals conforming to Gaussian distribution. Although the Gaussian signal is capacityachieving, signals conforming to discrete constellations are transmitted in practical communication systems. As a result, this paper is motivated to provide a comprehensive overview on MIMO transmission design with discrete input signals. We first summarize the existing fundamental results for MIMO systems with discrete input signals. Then, focusing on the basic pointtopoint MIMO systems, we examine transmission schemes based on three most important criteria for communication systems: the mutual information driven designs, the mean square error driven designs, and
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This paper considers the problem of decentralized optimization with a composite objective containing smooth and nonsmooth terms. To solve the problem, a proximalgradient scheme is studied. Specifically, the smooth and nonsmooth terms are dealt with by gradient update and proximal update, respectively. The studied algorithm is closely related to a previous decentralized optimization algorithm, PGEXTRA [37], but has a few advantages. First of all, in our new scheme, agents use uncoordinated stepsizes and the stable upper bounds on stepsizes are independent from network topology. The stepsizes depend on local objective functions, and they can be as large as that of the gradient descent. Secondly, for the special case without nonsmooth terms, linear convergence can be achieved under the strong convexity assumption. The dependence of the convergence rate on the objective functions and the network are separated, and the convergence rate of our new scheme is as good as one of the two c
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In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the Dirichlet to Neumann mapping can be used to reconstruct impenetrable subregions via a sampling method. We also propose a noniterative method to reconstruct the impedance parameter using the reconstructed boundary of the inclusion from the knowledge of multiple Cauchy pairs which can be computed from Dirichlet to Neumann mapping. Some numerical reconstructions are presented in two space dimensions.
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We propose a $\lambda$calculusstyle formal language, called the $\mu$syntax, as a lightweight representation of the structure of cyclic operads. We illustrate the rewriting methods behind the formalism by giving a complete stepbystep proof of the equivalence between the unbiased and biased definitions of cyclic operads.
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We present a novel hybrid numericalasymptotic boundary element method for transmission problems describing high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. We demonstrate by means of a range of numerical experiments that our boundary element method can achieve a fixed accuracy of approximation using only a relatively small, frequencyindependent number of degrees of freedom. Our numerical approximation space, which can be applied in the context of any direct boundary integral equation formulation, approximates the unknown boundary solution as a sum of the classical geometrical optics approximation, computed by a beam tracing algorithm, plus a contribution due to diffraction, computed by a boundary element method using oscillatory basis functions chosen to efficiently capture the high frequency behaviour. For the scattering scenarios we consider, we show that the inclusion of the diffraction term provides an order of magnitude improveme
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In this article we prove exactness of the homotopy sequence of overconvergent $p$adic fundamental groups for a smooth and projective morphism in characteristic $p$. We do so by first proving a corresponding result for rigid analytic varieties in characteristic $0$, following dos Santos in the algebraic case. In characteristic $p$, we then proceed by a series of reductions to the case of a liftable family of curves, where we can apply the rigid analytic result.
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The proofs of Oka's Coherence Theorems are based on Weierstrass' Preparation (division) Theorem. Here we observe that a Weak Coherence of Oka proved without Weierstrass' Preparation (division) Theorem, but only with \textit{power series expansions} is sufficient to prove Oka's J\^okuIk\^o and hence Cousin I, II, holomorphic extensions, and Levi's Problem, as far as the domain spaces are nonsingular. The proof of the Weak Coherence of Oka is almost of linear algebra. We will present some new or simplified arguments in the proofs.
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Security updates have been issued by Arch Linux (firefox and weechat), Debian (chicken, firefoxesr, libcroco, libreoffice, and tiff), Fedora (backintime, bind, firefox, libarchive, libnl3, pcre2, phppearCAS, and pythondjango), Mageia (icu and proftpd), openSUSE (mozillanss and wireshark), Red Hat (java1.6.0sun, java1.7.0oracle, and java1.8.0oracle), Scientific Linux (firefox and java1.8.0openjdk), Slackware (mozilla, ntp, and proftpd), and Ubuntu (firefox).
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The main aim of this paper is to prove $R$triviality for simple, simply connected algebraic groups with Tits index $E_{8,2}^{78}$ or $E_{7,1}^{78}$, defined over a field $k$ of arbitrary characteristic. Let $G$ be such a group. We prove that there exists a quadratic extension $K$ of $k$ such that $G$ is $R$trivial over $K$, i.e., for any extension $F$ of $K$, $G(F)/R=\{1\}$, where $G(F)/R$ denotes the group of $R$equivalence classes in $G(F)$, in the sense of Manin (see \cite{M}). As a consequence, it follows that the variety $G$ is retract $K$rational and that the KneserTits conjecture holds for these groups over $K$. Moreover, $G(L)$ is projectively simple as an abstract group for any field extension $L$ of $K$. In their monograph (\cite{TW}) J. Tits and Richard Weiss conjectured that for an Albert division algebra $A$ over a field $k$, its structure group $Str(A)$ is generated by scalar homotheties and its $U$operators. This is known to be equivalent to the KneserTits conject
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We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a normally hyperbolic invariant manifold. The information on the outer dynamics is encoded by a geometrically defined map, referred to as the `scattering map'. We find pseudoorbits of the scattering map that keep advancing in some privileged direction. Then we use the recurrence property of the `inner dynamics', restricted to the normally hyperbolic invariant manifold, to return to those pseudoorbits. Finally, we apply topological methods to show the existence of true orbits that follow the successive applications of the two dynamics. This method differs, in several crucial aspects, from earlier works. Unlike the well known `twodynamics' approach, the method we present relies on the outer dynamics alone. There are virtually no assumptions on the inner
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We prove that a function given by Pistorius relating to Riemann zeta function $\zeta (s)$ and a SturmLiouville eigenvalue problem is meaningful in a strip domain in $\mathbb{C}$ which leads to that nontrivial zeros of $\zeta (s)$ all have real part equal to $\frac{1}{2}$ by using classical results of eigenvalue problem.
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We introduce a hybridizable discontinuous Galerkin method for the incompressible NavierStokes equations for which the approximate velocity field is pointwise divergencefree. The method proposed here builds on the method presented by Labeur and Wells [SIAM J. Sci. Comput., vol. 34 (2012), pp. A889A913]. We show that with simple modifications of the function spaces in the method of Labeur and Wells that it is possible to formulate a simple method with pointwise divergencefree velocity fields, and which is both momentum conserving and energy stable. Theoretical results are verified by two and threedimensional numerical examples and for different orders of polynomial approximation.
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Let $p$ be an odd prime, $n$ a positive integer and $g$ a primitive root of $p^n$. Suppose $D_i^{(p^n)}=\{g^{2s+i}s=0,1,2,\cdots,\frac{(p1)p^{n1}}{2}\}$, $i=0,1$, is the generalized cyclotomic classes with $Z_{p^n}^{\ast}=D_0\cup D_1$. In this paper, we prove that Gauss periods based on $D_0$ and $D_1$ are both equal to 0 for $n\geq2$. As an application, we determine a lower bound on the 2adic complexity of a class of DingHelleseth generalized cyclotomic sequences of period $p^n$. The result shows that the 2adic complexity is at least $p^np^{n1}1$, which is larger than $\frac{N+1}{2}$, where $N=p^n$ is the period of the sequence.
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We derive a lower bound on the differential entropy of a logconcave random variable $X$ in terms of the $p$th absolute moment of $X$. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds on the ratedistortion function and the channel capacity. Specifically, we study the ratedistortion function for logconcave sources and distortion measure $ x  \hat x^r$, and we establish that the difference between the rate distortion function and the Shannon lower bound is at most $\log(2 \sqrt{\pi e}) \approx 2.5$ bits, independently of $r$ and the target distortion $d$. For meansquare error distortion, the difference is at most $\log (\sqrt{2 \pi e}) \approx 2$ bits, regardless of $d$. The bounds can be further strengthened if the source, in addition to being logconcave, is symmetric. In particular, we establish that for meansquare error distortion, the difference is at most $\log (\sqrt{\pi e}) \approx 1.5$ bits, regardless of $d$. We als
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An alternating sign matrix, or ASM, is a $(0, \pm 1)$matrix where the nonzero entries in each row and column alternate in sign. We generalize this notion to hypermatrices: an $n\times n\times n$ hypermatrix $A=[a_{ijk}]$ is an {\em alternating sign hypermatrix}, or ASHM, if each of its planes, obtained by fixing one of the three indices, is an ASM. Several results concerning ASHMs are shown, such as finding the maximum number of nonzeros of an $n\times n\times n$ ASHM, and properties related to Latin squares. Moreover, we investigate completion problems, in which one asks if a subhypermatrix can be completed (extended) into an ASHM. We show several theorems of this type.
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We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric HawkDove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their stability and derive the Nash equilibria. We also give a detailed account of the local bifurcations that the system exhibits based on choices of the typical HawkDove parameters and . We also give details on the connections between the results found in this work and those of the standard twostrategy HawkDove game. We conclude the paper with some examples of numerical simulations that further illustrate some global behaviours of the system.
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A balancing domain decomposition by constraints (BDDC) algorithm with adaptive primal constraints in variational form is introduced and analyzed for highorder mortar discretization of twodimensional elliptic problems with high varying and random coefficients. Some vectorvalued auxiliary spaces and operators with essential properties are defined to describe the variational algorithm, and the coarse space is formed by using a transformation operator on each interface. Compared with the adaptive BDDC algorithms for conforming Galerkin approximations, our algorithm is more simple, because there is not any continuity constraints at subdomain vertices in the mortar method involved in this paper. The condition number of the preconditioned system is proved to be bounded above by a userdefined tolerance and a constant which is dependent on the maximum number of interfaces per subdomain, and independent of the mesh size and the contrast of the given coefficients. Numerical results show the r
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A string theoretic framework is constructed relating the cohomology of wild character varieties to refined stable pair theory and torus link invariants. Explicit conjectural formulas are derived for wild character varieties with a unique irregular point on the projective line. For this case the string theoretic construction leads to a conjectural colored generalization of existing results of Hausel, Mereb and Wong as well as Shende, Treumann and Zaslow.
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A pseudocircle is a simple closed curve on some surface. Arrangements of pseudocircles were introduced by Gr\"unbaum, who defined them as collections of pseudocircles that pairwise intersect in exactly two points, at which they cross. There are several variations on this notion in the literature, one of which requires that no three pseudocircles have a point in common. Working under this definition, Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size at most $4$ are embeddable into the sphere. Ortner asked if an analogous result held for embeddability into a compact orientable surface $\Sigma_g$ of genus $g>0$. In this paper we answer this question, under an even more general definition of an arrangement, in which the pseudocircles in the collection are not required to intersect each other, or that the intersections are crossings: it suffices to have one pseudocircle that intersects all other pseudocircle
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In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for $n>3$, $\Aut(P_n)$ is generated by the subgroup $\Aut_c(P_n)$ of central automorphisms of $P_n$, the subgroup $\Aut(B_n)$ of restrictions of automorphisms of $B_n$ on $P_n$ and one extra automorphism $w_n$. We also investigate the lifting and extension problem for automorphisms of some wellknown exact sequences arising from braid groups, and prove that that answers are negative in most cases. Specifically, we prove that no nontrivial central automorphism of $P_n$ can be extended to an automorphism of $B_n$.
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We describe absolutely ordered $p$normed spaces, for $1 \le p \le \infty$ which presents a model for "noncommutative" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of {\it absolute compatibility} among positive elements in absolute order unit spaces and relate it to symmetrized product in the case of a C$^{\ast}$algebra. In the latter case, whenever one of the elements is a projection, the elements are absolutely compatible if and only if they commute. We develop an order theoretic prototype of the results. For this purpose, we introduce the notion of {\it order projections} and extend the results related to projections in a unital C$^{\ast}$algebra to order projections in an absolute order unit space. As an application, we describe spectral decomposition theory for elements of an absolute order unit space.
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Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a nontrivial shape when heated or cooled. In this paper, we start from a variational formulation for the entropic elastic energy of liquid crystal elastomers and we derive an effective twodimensional metric constraint, which links the deformation and the heterogeneous director field. Our main results show that satisfying the metric constraint is both necessary and sufficient for the deformation to be an approximate minimizer of the energy. We include several examples which show that the class of deformations satisfying the metric constraint is quite rich.
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An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residualtype and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and elementwise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive coplanar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh postprocessing.
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We exhibit a nonvarying phenomenon for the counting problem of cylinders, weighted by their area, passing through two marked (regular) Weierstrass points of a translation surface in a hyperelliptic connected component $\mathcal{H}^{hyp}(2g2)$ or $\mathcal{H}^{hyp}(g1,g1)$, $g > 1$. As an application, we obtain the nonvarying phenomenon for the counting problem of (weighted) periodic trajectories on the classical windtree model, a billiard in the plane endowed with $\mathbb{Z}^2$periodically located identical rectangular obstacles.
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Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. We present a number of techniques to improve the robustness and efficiency of this algorithm. We show that our approach consistently and significantly outperforms previous competing approaches in both stability and speed. We also present a robust convergence criterion which is backward stable.
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We prove that the ground space projections of a subspace of energy operators in a matrix *algebra are the greatest projections of the algebra under certain operator cone constraints. The lattice of ground space projections being coatomistic, we also discuss its maximal elements as building blocks. We demonstrate the results with (commutative) twolocal threebit Hamiltonians. We expect the variation principle to be useful also for noncommutative Hamiltonians.
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Several authors have studied convergence in distribution to the Brownian web under diffusive scaling of Markovian random walks. In a paper by R. Roy, K. Saha and A. Sarkar, convergence to the Brownian web is proved for a system of coalescing random paths  the Random Directed Forest which are not Markovian. Paths in the Random Directed Forest do not cross each other before coalescence. Here we study a generalization of the nonMarkovian Random Directed Forest where paths can cross each other and prove convergence to the Brownian web. This provides an example of how the techniques to prove convergence to the Brownian web for systems allowing crossings can be applied to nonMarkovian systems.
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This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle. On the other hand, we prove that the domains given by Dittrich, Exner and \v{S}eba [Dirac operators with a spherically symmetric $\delta$shell interaction, J. Math. Phys. 30.12 (1989), 28752882] and by Arrizabalaga, Mas and Vega [Shell interactions for Dirac operators, J. Math. Pures et Appl. 102.4 (2014), 617639] for the realization of an electrostatic spherical shell interaction coincide. Finally, we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support, improving previous results in the spherical case.
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An anonymous reader writes: A Wall Street engineer was arrested for planting credentialslogging malware on his company's servers. According to an FBI affidavit, the engineer used these credentials to log into fellow employees' accounts. The engineer claims he did so only because he heard rumors of an acquisition and wanted to make sure he wouldn't be let go. In reality, the employee did look at archived email inboxes, but he also stole encryption keys needed to access the protected source code of his employer's trading platform and trading algorithms. Using his access to the company's Unix network (which he gained after a promotion last year), the employee then rerouted traffic through backup servers in order to avoid the company's traffic monitoring solution and steal the company's source code. The employee was caught after he kept intruding and disconnecting another employee's RDP session. The employee understood someone hacked his account and logged the attacker's unique identifier
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theodp quotes today's New York Times profile of Uber CEO Travis Kalanick: For months, Mr. Kalanick had pulled a fast one on Apple by directing his employees to help camouflage the ridehailing app from Apple's engineers. The reason? So Apple would not find out that Uber had secretly been tracking iPhones even after its app had been deleted from the devices, violating Apple's privacy guidelines. Uber told TechCrunch this afternoon that it still uses a form of this device fingerprinting, saying they need a way to identify those devices which committed fraud in the past  especially in China, where Uber drivers used stolen iPhones to request dozens of rides from themselves to increase their pay rate. It's been modified to comply with Apple's rules, and "We absolutely do not track individual users or their location if they've deleted the app..." an Uber spokesperson said. "Being able to recognize known bad actors when they try to get back onto our network is an important security measure
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Not quite promptly at six o’clock on Saturday morning, two dozen scientists whose fields of study can’t be summarized in a sentence boarded a bus at the Institute for Advanced Study, in Princeton, New Jersey, and headed south, bound for the March for Science, in Washington, D.C. “I hope it doesn’t rain,” Ed Witten, the first and only theoretical physicist ever to win the Fields Medal, the Academy Award of mathematics, said. Witten, who is in his sixties, is tall even when seated and speaks in a measured, almost sheepish tone. He was reading a book about the First World War on his Kindle, a device that, he conceded, he hadn’t yet mastered. The sky, still pale, was cloudy, and the forecast did indeed call for rain.
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Selfmade billionaire, Alibaba chairman Jack Ma warned on Monday that society could see decades of pain thanks to disruption caused by the internet and new technologies to different areas of the economy. From a report: In a speech at a China Entrepreneur Club event, the billionaire urged governments to bring in education reform and outlined how humans need to work with machines. "In the coming 30 years, the world's pain will be much more than happiness, because there are many more problems that we have come across," Ma said in Chinese, speaking about potential job disruptions caused by technology. [...] Ma also spoke about the rise of robots and artificial intelligence (AI) and said that this technology will be needed to process the large amount of data being generated today, something that a human brain can't do. But machines shouldn't replace what humans can do, Ma said, but instead the technology community needs to look at making machines do what humans cannot. This would make the m
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An anonymous reader quotes the BBC: A group of aurora enthusiasts have found a new type of light in the night sky and named it Steve. Eric Donovan from the University of Calgary in Canada spotted the feature in photos shared on a Facebook group. He did not recognise it as a catalogued phenomenon and although the group were calling it a proton arc, he knew proton auroras were not visible. Testing showed it appeared to be a hot stream of fastflowing gas in the higher reaches of the atmosphere. The European Space Agency sent electric field instruments to measure it 300km (190 miles) above the surface of the Earth and found the temperature of the air was 3,000C (5,400F) hotter inside the gas stream than outside it. Inside, the 25kmwide ribbon of gas was flowing at 6 km/s (13,000mph), 600 times faster than the air on either side. One official at the European Space Agency made sure to thank the "army of citizen scientists" who helped with the discovery, saying "It turns out that Steve is
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Amazon said on Monday it is launching a platform for companies with subscription services  from newspapers, magazines to TV streaming. The "Subscribe with Amazon" marketplace allows consumers to buy subscriptions to products like SlingTV streaming, Headspace meditation, Dropbox Plus, as well as workout videos, online classes, meal plans and even matchmakers. The marketplace also features more traditional subscriptions, similar to those that have become popular on Amazon's Kindle tablets, including the Chicago Tribune, LA Times, Wall Street Journal and New Yorker.
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Startup Eternime, founded by MIT fellow Marius Ursache, is still working on "immortal avatars" that, after your death, will continue interacting with your loves ones from beyond the grave. An anonymous reader quotes CNET: Give Eternime access to your social media profiles and the startup's algorithms will scrape your posts and interactions to build a profile... The algorithms will study your memories and mannerisms. They'll learn how to be "you"... Eternime was announced in 2014 after Ursache developed the idea during the MIT Entrepreneurship Development Program. He wasn't entirely sure if he should develop the project further and wanted to get a sense of public reaction. In the first four days, 3,000 people signed up at Eterni.me, the company's website, for a private beta. Then, Urasche received an email from a man dying of terminal cancer. "Eternime, he wrote, was the last chance to leave something behind for friends and family," Urasche told me. "That was the moment I decided that t
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Can a humorless show be great? My bias has long been that truly ambitious dramas are also funny, however submerged or black their jokes. And yet John Ridley’s “American Crime,” on ABC, which is currently ending its third season (and likely its last, given the ratings), breaks that rule and is still a keeper. An astringent outlier in a dizzy age, it has none of the ironic pop songs and retro homages that dominate so many modern cable dramas. It’s serious in an oldfashioned sense: sincere, thoughtful, and heartbreaking.
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Rod Dreher was fortyfour when his little sister died. At the time, he was living in Philadelphia with his wife and children. His sister, Ruthie, lived in their Louisiana home town, outside St. Francisville (pop. 1,712). Dreher’s family had been there for generations, but he had never fit in. As a teenager, when his father and sister went hunting he stayed in his room and listened to the Talking Heads; he read “A Moveable Feast” and dreamed of Paris. He left as soon as he could, becoming a television critic for the Washington Times and then a film critic for the New York Post. He was living in Cobble Hill on 9/11, and watched the South Tower fall. He walked with his wife in Central Park. He wrote a book, “Crunchy Cons,” about how conservatives like him—“Birkenstocked Burkeans” and “hip homeschooling mamas”—might change America. Ruthie never left. She was a middleschool teacher, and her husband was a firefighter. She could give a damn about Edmund Burke and the New York Post. She was
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Bette Midler is such an incredible selfcreation—an artist like no other—that finding roles that can harness her enormous energy while allowing room for her wit and her extraordinary skill as a balladeer must have long been a nightmare for her agents. Early in her now more than fiftyyear career, Midler did happen upon a part that tapped into her many talents. In 1979, she starred in “The Rose,” a fictional film portrait of a Janis Joplinlike singer, which moved a lot of people, not least because the script reflected aspects of Midler’s own life: her camaraderie with her gay fans and the distance she may have felt from her parents. (Her father wasn’t supportive of her aspirations and saw her perform only once.) Although “The Rose” was a milestone in Midler’s wildly diverse career—in addition to acting onstage and onscreen, she makes records, performs solo shows, and runs a charity that helps transform vacant lots into gardens and public spaces—it was just one of many. As recently as 2
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An anonymous reader quotes Help Net Security: Researchers from several German universities have checked the PHP codebases of over 64,000 projects on GitHub, and found 117 vulnerabilities that they believe have been introduced through the use of code from popular but insufficiently reviewed tutorials. The researchers identified popular tutorials by inputting search terms such as "mysql tutorial", "php search form", "javascript echo user input", etc. into Google Search. The first five results for each query were then manually reviewed and evaluated for SQLi and XSS vulnerabilities by following the Open Web Application Security Project's Guidelines. This resulted in the discovery of 9 tutorials containing vulnerable code (6 with SQLi, 3 with XSS). The researchers then checked for the code in GitHub repositories, and concluded that "there is a substantial, if not causal, link between insecure tutorials and web application vulnerabilities." Their paper is titled "Leveraging Flawed Tutoria
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