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We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar or embedded on the torus. The set of positive face weights on the graph gives a set of global coordinates on the space of circle patterns with embedded dual. Under this correspondence, which extends the previously known isoradial case, the urban renewal (local move for dimer models) is equivalent to the Miquel move (local move for circle patterns). As a consequence the Miquel dynamics on circle patterns is governed by the octahedron recurrence. As special cases of these circle pattern embeddings, we recover harmonic embeddings for resistor networks and sembeddings for the Ising model.
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In this paper, we present a distributionally robust optimization (DRO) approach for the transmission expansion planning (TEP) problem, considering both long and shortterm uncertainties on the system load and renewable generation. Longterm uncertainty is represented on two interrelated levels. At the first level, as is customary in industry applications, the deep uncertainty faced in economic, political, environmental, and technological development is addressed based on plausible visions of longterm future scenarios (trends), traced by current experts beliefs. Subsequently, uncertaintyrelated parameters defining the probability distributions of the uncertain factors are partially refined for each longterm scenario, thereby inducing an ambiguity set. Finally, for each longterm scenario and induced ambiguity set, the inherent risk model for the shortterm uncertainty is described by means of conditional probability distributions. The mathematical problem is formulated as a distribu
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We investigate the asymptotic behavior of eigenfunctions of the Laplacian on Riemannian manifolds. We show that BenjaminiSchramm convergence provides a unified language for the level and eigenvalue aspects of the theory. As a result, we present a mathematically precise formulation of Berry's conjecture for a compact negatively curved manifold and formulate a Berrytype conjecture for sequences of locally symmetric spaces. We prove some weak versions of these conjectures. Using ergodic theory, we also analyze the connections of these conjectures to Quantum Unique Ergodicity.
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We study the energy distribution of harmonic 1forms on a compact hyperbolic Riemann surface $S$ that has a small separating closed geodesic. The result is applied to the question how close the Jacobian torus of $S$ comes to a torus that splits. The aim is to answer this and related questions in terms of geometric data of $S$ such as its injectivity radius and the lengths of geodesics that form a homology basis. This is version 1 of an extended paper in which also non separating small geodesics are considered.
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Local and categorytheoretical entropies associated with an endomorphism of finite length (i.e., with zerodimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to categorytheoretical entropy. The two entropies are shown to be equal when the ring is regular, and also for the Frobenius endomorphism of a complete local ring of positive characteristic. Furthermore, given a flat morphism of CohenMacaulay local rings endowed with compatible endomorphisms of finite length, it is shown that local entropy is "additive". Finally, over a ring that is a homomorphic image of a regular local ring, a formula for local entropy in terms of an asymptotic partial Euler characteristic is given.
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Adinkras are combinatorial objects developed to study supersymmetry representations. Gates et al. introduced the "gadget" as a function of pairs of adinkras, obtaining some mysterious results for $(n=4, k=1)$ adinkras with computeraided computation. Specifically, very few values of the gadget actually appear, suggesting a great deal of symmetry in these objects. In this paper, we compute gadgets symbolically and explain some of these observed phenomena with group theory and combinatorics. Guided by this work, we give some suggestions for generalizations of the gadget to other values of the $n$ and $k$ parameters.
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We consider a family of higherdimensional noncommutative tori, which are twisted analogues of the algebras of continuous functions on ordinary tori, and their Toeplitz extensions. Just as solenoids are inverse limits of tori, our Toeplitz noncommutative solenoids are direct limits of the Toeplitz extensions of noncommutative tori. We consider natural dynamics on these Toeplitz algebras, and compute the equilibrium states for these dynamics. We find a large simplex of equilibrium states at each positive inverse temperature, parametrised by the probability measures on an (ordinary) solenoid.
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In contrast with many other convex optimization classes, stateoftheart semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel proximal algorithm for solving general semidefinite programming problems. The proposed methodology, based on the primaldual hybrid gradient method, allows the presence of linear inequalities without the need of adding extra slack variables and avoids solving a linear system at each iteration. More importantly, it does simultaneously compute the dual variables associated with the linear constraints. The main contribution of this work is to achieve a substantial speedup by effectively adjusting the proposed algorithm in order to exploit the lowrank property inherent to several semidefinite programming problems. This proposed modification is the key element that allows the operator splitting method to efficiently scale to larger instances. Convergence guaran
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We give a partial solution to a question by Alas, Junqueria and Wilson by proving that under PFA the onepoint compactification of a locally compact, discretely generated and countably tight space is also discretely generated. After this, we study the cardinal number given by the smallest possible character of remote and far sets of separable metrizable spaces. Finally, we prove that in some cases a countable space has far points.
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If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$ is explicitly described as a subgroup of the canonical semidirect product of groups ${\rm GL} (m, \, k) \rtimes {\rm M}_{n\times m} (k)$. An Artin type theorem for Lie algebras is proved: if a group $G$ whose order isinvertible in $k$ acts as automorphisms on a Lie algebra $\mathfrak{h}$, then $\mathfrak{h}$ is isomorphic to a skew crossed product $\mathfrak{h}^G \, \#^{\bullet} \, V$, where $\mathfrak{h}^G$ is the subalgebra of invariants and $V$ is the kernel of the Reynolds operator. The Galois group ${\rm Gal} \,(\mathfrak{h}/\mathfrak{h}^G)$ is also computed, highlighting the difference from the classical Galois theory of fields where the corresponding group is $G$. The counterpart for Lie algebras of Hilbert's Theorem 90 is proved and based on
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D. Bennequin and P. Baudot introduced a cohomological construction adapted to information theory, called 'information cohomology', that characterizes Shannon entropy through a cocycle condition. This text develops the relation between information cohomology and topos theory. We also introduce several new constructions and results. First, we define generalized information structures, as categories of finite random variables related by a notion of extension or refinement; classical and quantum probability spaces appear as models (representations) for these general structures. Generalized information structures form a category with finite products and coproducts. We prove that information cohomology is invariant under isomorphisms of generalized structures. Secondly, we prove that the relativelyfree bar construction gives a projective object for the computation of cohomology. Thirdly, we provide detailed computations of $H^1$ for classical probabilities and describe the degenerate cases.
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For a smooth projective curve, the cycles of subordinate or, more generally, secant divisors to a given linear series are among some of the most studied objects in classical enumerative geometry. We consider the intersection of two such cycles corresponding to secant divisors of two different linear series on the same curve and investigate the validity of the enumerative formulas counting the number of divisors in the intersection. We study some interesting cases, with unexpected transversality properties, and establish a general method to verify when this intersection is empty.
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In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known endALE, ALF, ALG or ALH. 2.In ALG and ALHnonsplitting cases, it must be biholomorphic to a compact complex elliptic surface minus a divisor. Thus, we confirm a longstanding question of Yau in ALG and ALH cases. 3.In ALFD_k case, it must have an O(4)multiplet.
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We analyze the optimal harvesting problem for an ecosystem of species that experience environmental stochasticity. Our work generalizes the current literature significantly by taking into account nonlinear interactions between species, statedependent prices, and species injections. The key generalization is making it possible to not only harvest, but also `seed' individuals into the ecosystem. This is motivated by how fisheries and certain endangered species are controlled. The harvesting problem becomes finding the optimal harvestingseeding strategy that maximizes the expected total income from the harvest minus the lost income from the species injections. Our analysis shows that new phenomena emerge due to the possibility of species injections. It is wellknown that multidimensional harvesting problems are very hard to tackle. We are able to make progress, by characterizing the value function as a viscosity solution of the associated HamiltonJacobiBellman (HJB) equations. Moreov
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This paper deals with the MonteCarlo methods for evaluating expectations of functionals of solutions to McKeanVlasov Stochastic Differential Equations (MVSDE) with drifts of superlinear growth. We assume that the MVSDE is approximated in the standard manner by means of an interacting particle system and propose two importance sampling (IS) techniques to reduce the variance of the resulting Monte Carlo estimator. In the \emph{complete measure change} approach, the IS measure change is applied simultaneously in the coefficients and in the expectation to be evaluated. In the \emph{decoupling} approach we first estimate the law of the solution in a first set of simulations without measure change and then perform a second set of simulations under the importance sampling measure using the approximate solution law computed in the first step. For both approaches, we use large deviations techniques to identify an optimisation problem for the candidate measure change. The decoupling approac
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The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size. Two graphs are said to be \textit{independence equivalent} if they have equivalent independence polynomials. We extend previous work by showing that independence equivalence class of every odd path has size 1, while the class can contain arbitrarily many graphs for even paths. We also prove that the independence equivalence class of every even cycle consists of two graphs when $n\ge 2$ except the independence equivalence class of $C_6$ which consists of three graphs. The odd case remains open, although, using irreducibility results from algebra, we were able show that for a prime $p \geq 5$ and $n\ge 1$ the independence equivalence class of $C_{p^n}$ consists of only two graphs.
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In this paper, we provide an accessible introduction to the theory of locally convex supermanifolds in the categorical approach. In this setting, a supermanifold is a functor $\mathcal{M}\colon\mathbf{Gr}\to\mathbf{Man}$ from the category of Grassmann algebras to the category of locally convex manifolds that has certain local models, forming something akin to an atlas. We give a mostly selfcontained, concrete definition of supermanifolds along these lines, closing several gaps in the literature on the way. If $\Lambda_n\in\mathbf{Gr}$ is the Grassmann algebra with $n$ generators, we show that $\mathcal{M}_{\Lambda_n}$ has the structure of a so called multilinear bundle over the base manifold $\mathcal{M}_\mathbb{R}$. We use this fact to show that the projective limit $\varprojlim_n\mathcal{M}_{\Lambda_n}$ exists in the category of manifolds. In fact, this gives us a faithful functor $\varprojlim\colon\mathbf{SMan}\to\mathbf{Man}$ from the category of supermanifolds to the category of
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Infinitesimal bialgebras were introduced by Joni and Rota. An infinitesimal bialgebra is at the same time an algebra and coalgebra, in such a way that the comultiplication is a derivation. Twenty years after Joni and Rota, Aguiar introduced the concept of an infinitesimal (nonunitary) Hopf algebra. In this paper we study infinitesimal unitary bialgebras and infinitesimal unitary Hopf algebras, in contrary to Aguiar's approach. Using an infinitesimal version of the Hochschild 1cocycle condition, we prove respectively that a class of decorated planar rooted forests is the free cocycle infinitesimal unitary bialgebra and free cocycle infinitesimal unitary Hopf algebra on a set. As an application, we obtain that the planar rooted forests is the free cocycle infinitesimal unitary Hopf algebra on the empty set.
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Generalising a construction of Falconer, we consider classes of $G_\delta$subsets of $\mathbb{R}^d$ with the property that sets belonging to the class have large Hausdorff dimension and the class is closed under countable intersections. We relate these classes to some inhomogeneous potentials and energies, thereby providing some useful tools to determine if a set belongs to one of the classes. As applications of this theory, we calculate, or at least estimate, the Hausdorff dimension of randomly generated limsupsets, and sets that appear in the setting of shrinking targets in dynamical systems. For instance, we prove that for $\alpha \geq 1$, \[ \mathrm{dim}_\mathrm{H}\, \{ \, y :  T_a^n (x)  y < n^{\alpha} \text{ infinitely often} \, \} = \frac{1}{\alpha}, \] for almost every $x \in [1a,1]$, where $T_a$ is a quadratic map with $a$ in a set of parameters described by Benedicks and Carleson.
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In this paper, we construct a theory of integration of Voevodsky motives over a perfect field $k$, and show that it circumvents some of the complications of motivic integration, leading to new arithmetic and geometric results concerning Kequivalent $k$varieties. One main application is that up to direct summing a common Chow motive, Kequivalent smooth projective $k$varieties have the same $\mathbb{Z}[1/p]$Chow motives ($p$ is the characteristic exponent of $k$), partially answering a conjecture of ChinLung Wang. In addition to generalizing a theorem of Kontsevich on the equality of Hodge numbers of Kequivalent smooth projective complex varieties, we show that such varieties have isomorphic \textit{integral} singular cohomology groups. On the arithmetic side, we show that Kequivalent smooth $k$varieties have isomorphic $\ell$adic Galois representations up to semisimplification. Furthermore, we connect this theory of integration of Voevodsky motives to the existence of motivic
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In this paper, we study an interference alignment (IA) scheme with finite time extension and beamformer selection method with low computational complexity for X channel. An IA scheme with a chain structure by the Latin square is proposed for Kx3 multipleinput multipleoutput (MIMO) X channel. Since the proposed scheme can have a larger set of possible beamformers than the conventional schemes, its performance is improved by the efficient beamformer selection for a given channel. Also, we propose a condition number (CN) based beamformer selection method with low computational complexity and its performance improvement is numerically verified.
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In this paper, we study a new notion of scaled minimaxity for sparse estimation in highdimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on existing results. We recover sharp results for the global minimaxity as a consequence of our study. Fixing the scale of the signaltonoise ratio, we prove that the estimation error can be much smaller than the global minimax error. We construct a new optimal estimator for the scaled minimax sparse estimation. An optimal adaptive procedure is also described.
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In systems and synthetic biology, much research has focused on the behavior and design of single pathways, while, more recently, experimental efforts have focused on how crosstalk (coupling two or more pathways) or inhibiting molecular function (isolating one part of the pathway) affects systemslevel behavior. However, the theory for tackling these larger systems in general has lagged behind. Here, we analyze how joining networks (e.g., crosstalk) or decomposing networks (e.g., inhibition or knockouts) affects three properties that reaction networks may possessidentifiability (recoverability of parameter values from data), steadystate invariants (relationships among species concentrations at steady state, used in model selection), and multistationarity (capacity for multiple steady states, which correspond to multiple cell decisions). Specifically, we prove results that clarify, for a network obtained by joining two smaller networks, how properties of the smaller networks can b
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We prove a compactness theorem for full Booleanvalued models. As an application, we show that if $T$ is a complete countable theory and $\mathcal{B}$ is a complete Boolean algebra, then $\lambda^+$saturated $\mathcal{B}$valued models of $T$ exist. Moreover, if $\mathcal{U}$ is an ultrafilter on $T$ and $\mathbf{M}$ is a $\lambda^+$saturated $\mathcal{B}$valued model of $T$, then whether or not $\mathbf{M}/\mathcal{U}$ is $\lambda^+$saturated just depends on $\mathcal{U}$ and $T$; we say that $\mathcal{U}$ $\lambda^+$saturates $T$ in this case. We show that Keisler's order can be formulated as follows: $T_0 \trianglelefteq T_1$ if and only if for every cardinal $\lambda$, for every complete Boolean algebra $\mathcal{B}$ with the $\lambda^+$c.c., and for every ultrafilter $\mathcal{U}$ on $\mathcal{B}$, if $\mathcal{U}$ $\lambda^+$saturates $T_1$, then $\mathcal{U}$ $\lambda^+$saturates $T_0$.
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In this paper we consider the large genus asymptotics for two classes of SiegelVeech constants associated with an arbitrary connected stratum $\mathcal{H} (\alpha)$ of Abelian differentials. The first is the saddle connection SiegelVeech constant $c_{\text{sc}}^{m_i, m_j} \big( \mathcal{H} (\alpha) \big)$ counting saddle connections between two distinct, fixed zeros of prescribed orders $m_i$ and $m_j$, and the second is the area SiegelVeech constant $c_{\text{area}} \big( \mathcal{H}(\alpha) \big)$ counting maximal cylinders weighted by area. By combining a combinatorial analysis of explicit formulas of EskinMasurZorich that express these constants in terms of MasurVeech strata volumes, with a recent result for the large genus asymptotics of these volumes, we show that $c_{\text{sc}}^{m_i, m_j} \big( \mathcal{H} (\alpha) \big) = (m_i + 1) (m_j + 1) \big( 1 + o(1) \big)$ and $c_{\text{area}} \big( \mathcal{H}(\alpha) \big) = \frac{1}{2} + o(1)$, both as $\alpha = 2g  2$ tends
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Consider a chordal random curve model on a planar graph, in the scaling limit when a finemesh graph approximates a simplyconnected planar domain. The wellknown precompactness conditions of Kemppainen and Smirnov show that certain "crossing estimates" guarantee the subsequential weak convergence of the random curves in the topology of unparametrized curves, as well as in a topology inherited from curves on the unit disc via conformal maps. We complement this result by proving that proceeding to weak limit commutes with changing topology, i.e., limits of conformal images are conformal images of limits, without imposing any boundary regularity assumptions on the domains where the random curves lie. Treating such rough boundaries becomes necessary, e.g., in convergence proofs to multiple SLEs. The result in this generality has not been explicated before and is not trivial, which we demonstrate by giving warning examples and deducing strong consequences.
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FasterthanNyquist (FTN) signaling is a promising nonorthogonal physical layer transmission technique to improve the spectral efficiency of future communication systems but at the expense of intersymbolinterference (ISI). In this paper, we investigate the detection problem of FTN signaling and formulate the sequence estimation problem of any $M$ary phase shift keying (PSK) FTN signaling as an optimization problem that turns out to be nonconvex and nondeterministic polynomial time (NP)hard to solve. We propose a novel algorithm, based on concepts from semidefinite relaxation (SDR) and Gaussian randomization, to detect any $M$ary PSK FTN signaling in polynomial time complexity regardless of the constellation size $M$ or the ISI length. Simulation results show that the proposed algorithm strikes a balance between the achieved performance and the computational complexity. Additionally, results show the merits of the proposed algorithm in improving the spectral efficiency when compar
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Motivated by problems in percolation theory, we study the following 2player positional game. Let $\Lambda_{m \times n}$ be a rectangular gridgraph with $m$ vertices in each row and $n$ vertices in each column. Two players, Maker and Breaker, play in alternating turns. On each of her turns, Maker claims $p$ (asyet unclaimed) edges of the board $\Lambda_{m \times n}$, while on each of his turns Breaker claims $q$ (asyet unclaimed) edges of the board and destroys them. Maker wins the game if she manages to claim all the edges of a crossing path joining the lefthand side of the board to its righthand side, otherwise Breaker wins. We call this game the $(p,q)$crossing game on $\Lambda_{m \times n}$. Given $m,n\in \mathbb{N}$, for which pairs $(p,q)$ does Maker have a winning strategy for the $(p,q)$crossing game on $\Lambda_{m \times n}$? The $(1,1)$case corresponds exactly to the popular game of Bridgit, which is well understood due to it being a special case of the older Shannon
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We obtain limit theorems for $\Phi(A^p)^{1/p}$ and $(A^p\sigma B)^{1/p}$ as $p\to\infty$ for positive matrices $A,B$, where $\Phi$ is a positive linear map between matrix algebras (in particular, $\Phi(A)=KAK^*$) and $\sigma$ is an operator mean (in particular, the weighted geometric mean), which are considered as certain reciprocal LieTrotter formulas and also a generalization of Kato's limit to the supremum $A\vee B$ with respect to the spectral order.
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We present a sample path dependent measure of causal influence between time series. The proposed causal measure is a random sequence, a realization of which enables identification of specific patterns that give rise to high levels of causal influence. We show that these patterns cannot be identified by existing measures such as directed information (DI). We demonstrate how sequential prediction theory may be leveraged to estimate the proposed causal measure and introduce a notion of regret for assessing the performance of such estimators. We prove a finite sample bound on this regret that is determined by the worst case regret of the sequential predictors used in the estimator. Justification for the proposed measure is provided through a series of examples, simulations, and application to stock market data. Within the context of estimating DI, we show that, because joint Markovicity of a pair of processes does not imply the marginal Markovicity of individual processes, commonly used pl
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Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved phase reconstruction. Computationally, ptychography is extremely expensive, as ptychographic microscopes allow for large fields to be imaged at high resolution. In this work, we propose a multigridbased optimization framework to reduce the computational burdens of largescale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the stateoftheart method in the optics community.
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Nonconcave maximization has been the subject of much recent study in the optimization and machine learning communities, specifically in deep learning. Recent papers ((Ge \etal 2015, Lee \etal 2017) and references therein) indicate that first order methods work well and avoid saddles points. Results as in (Lee \etal 2017), however, are limited to the \textit{unconstrained} case or for cases where the critical points are in the interior of the feasibility set, which fail to capture some of the most interesting applications. In this paper we focus on \textit{constrained} nonconcave maximization. We analyze a variant of a wellestablished algorithm in machine learning called Multiplicative Weights Update (MWU) for the maximization problem $\max_{\mathbf{x} \in D} P(\mathbf{x})$, where $P$ is nonconcave, twice continuously differentiable and $D$ is a product of simplices. We show that MWU converges almost always for small enough stepsizes to critical points that satisfy the second order
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Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an effective question in real algebraic geometry, it is in general difficult to determine whether a given network can give rise to a multistationary system, and if so, to identify witnesses to multistationarity, that is, specific parameter values for which the system exhibits multiple steady states. Here we investigate both problems. First, we build on work of Conradi, Feliu, Mincheva, and Wiuf, who showed that for certain reaction networks whose steady states admit a positive parametrization, multistationarity is characterized by whether a certain "critical function" changes sign. Here, we allow for more general parametrizations, which make it much easier to determine the existence of a sign change. This is particularly simple when the steadystate equations
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The contribution of this paper is twofold: First, we prove existence and uniqueness of the weighted maximum likelihood estimator of the multivariate Student$t$ distribution and propose an efficient algorithm for its computation that we call generalized multivariate myriad filter (GMMF). Second, we use the GMMF in a nonlocal framework for the denoising of images corrupted by different kinds of noise. The resulting method is very flexible and can handle very heavytailed noise such as Cauchy noise, but also also Gaussian or wrapped Cauchy noise.
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An anonymous reader quotes a report from Bloomberg: Amazon is sweetening the pay for some of its longtime warehouse workers after employees criticized the loss of bonuses and stock awards as part of the company's pledge to boost all wages to at least $15 an hour. The world's largest online retailer grabbed headlines last week with its minimumpay pledge  followed by concerns from veteran workers who feared their compensation would actually decline because the company also eliminated bonuses and stock awards. Amazon said any workers already earning $15 would get raises of $1 per hour. Now, some of those employees are learning their hourly raises will actually be $1.25 an hour. Additionally, Amazon is introducing a new cash bonus of $1,500 to $3,000 for tenure milestones at five, 10, 15 and 20 years. Workers with good attendance in the month of December will also get a $100 bonus, according to the company. "All hourly Operations and Customer Service employees will see an increase in th
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Jeffrey Dastin, reporting for Reuters: Amazon's machinelearning specialists uncovered a big problem: their new recruiting engine did not like women. The team had been building computer programs since 2014 to review job applicants' resumes with the aim of mechanizing the search for top talent, five people familiar with the effort told Reuters. Automation has been key to Amazon's ecommerce dominance, be it inside warehouses or driving pricing decisions. The company's experimental hiring tool used artificial intelligence to give job candidates scores ranging from one to five stars  much like shoppers rate products on Amazon, some of the people said. "Everyone wanted this holy grail," one of the people said. "They literally wanted it to be an engine where I'm going to give you 100 resumes, it will spit out the top five, and we'll hire those." But by 2015, the company realized its new system was not rating candidates for software developer jobs and other technical posts in a genderneut
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Apple is planning a new digital video service that will provide original content free to its device owners, CNBC reported Wednesday. From the report: Apple is preparing a new digital video service that will marry original content and subscription services from legacy media companies, according to people familiar with the matter. Owners of Apple devices, such as the iPhone, iPad and Apple TV will find the stillintheworks service in the preinstalled "TV" application, said the people, who asked not to be named because the details of the project are private. The product will include Appleowned content, which will be free to Apple device owners, and subscription "channels" which will allow customers to sign up for onlineonly services, such as those from HBO and Starz. Apple plans to debut the revamped app early next year, the people said. As Bloomberg reported in May, the subscription channels will essentially copy Amazon's Prime Video Channel Subscriptions. Customers will be able to
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From a report: Within the past four years, Apple has managed to "dramatically reduce" the rate of iPhonerelated repair fraud in its retail stores in China, according to The Information's Wayne Ma. The report is based on interviews with more than a dozen former Apple employees who spoke on condition of anonymity. In 2013, Apple is said to have discovered a highly sophisticated fraud scheme in which organized thieves would buy or steal iPhones, remove valuable components like the processor or logic board, swap in fake components, and return the "broken" iPhones to receive replacements they could resell. From the report: "Thieves would stand outside stores with suitcases full of iPhones with some of the original components stripped out and replaced with inferior parts, two of the people said. The fraudsters would hire people to pretend to be customers to return them, each taking a device to stand in line at the Genius Bar, the people said. Once the phones were swapped, the actors would p
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Japanese retailer Uniqlo in Tokyo's Ariake district has managed to cut 90% of its staff and replace them with robots that are capable of inspecting and sorting the clothing housed there. The automation also allows them to operate 24 hours a day. Quartz reports: The company recently remodeled the existing warehouse with an automated system created in partnership with Daifuku, a provider of material handling systems. Now that the system is running, the company revealed during a walkthrough of the new facility, Uniqlo has been able to cut staff at the warehouse by 90%. The Japan News described how the automation works: "The robotic system is designed to transfer products delivered to the warehouse by truck, read electronic tags attached to the products and confirm their stock numbers and other information. When shipping, the system wraps products placed on a conveyor belt in cardboard and attaches labels to them. Only a small portion of work at the warehouse needs to be done by employees,
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The BBC had to replace live broadcasts with recorded material on its TV news channels for about an hour on Wednesday following a technical glitch. BBC News reports: The News at Six was also presented from the BBC's Millbank studio instead of its usual home of New Broadcasting House. The issue affected OpenMedia, a new computer system rolled out across BBC News outlets over the past six months. OpenMedia supplier Annova has been helping to investigate the fault. Engineers believe they have now addressed the problem. BBC News Home Editor Mark Easton shared on social media that he was rushing across London to the Millbank studio.
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The Android Developers Blog describes the controlflow integrity work that is shipping on the Pixel 3 handset. "LLVM's CFI implementation adds a check before each indirect branch to confirm that the target address points to a valid function with a correct signature. This prevents an indirect branch from jumping to an arbitrary code location and even limits the functions that can be called. As C compilers do not enforce similar restrictions on indirect branches, there were several CFI violations due to function type declaration mismatches even in the core kernel that we have addressed in our CFI patch sets for kernels 4.9 and 4.14."
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During a hearing in front of the Senate Homeland Security Committee on Wednesday, FBI Director Christopher Wray told senators to "be careful what you read," when asked about a recent story involving spy chips from China being secretly embedded into servers owned by Apple, Amazon and other big companies. From a report: Senator Ron Johnson, RWis., chairman of the committee, asked Wray when his agency found out about the chips that server manufacturer Super Micro implanted into server hardware, as reported last week by Bloomberg Businessweek. "I would say to the newspaper article or, I mean, the magazine article, I would say be careful what you read," Wray replied. "Especially in this context." Johnson called on Wray to speak to the accuracy of the story, telling the FBI director that, "We don't want false information out there." Wray said he couldn't offer much detail because the agency has a policy of not confirming or denying that an investigation is underway. "I do want to be careful
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We discuss the constant $\sigma_{2}$ problem for conic 4spheres. Based on earlier works of ChangHanYang and HanLiTeixeira, we are able to find a necessary condition for the existence problem. In particular, when the condition is sharp, we have the uniqueness result similar to that of Troyanov in dimension 2. It indicates that the boundary of the moduli of all conic 4spheres with constant $\sigma_{2}$ metrics consists of conic spheres with 2 conic points and rotational symmetry.
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Let $S$ be a smooth, totally real, compact immersion in $\mathbb{C}^n$ of real dimension $m \leq n$, which is locally polynomially convex and it has finitely many points where it selfintersects finitely many times, transversely or nontransversely. We prove that $S$ is rationally convex if and only if it is isotropic with respect to a "degenerate" K\"ahler form in $\mathbb{C}^n$.
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This paper presents a theoretical analysis of numerical integration based on interpolation with a Stein kernel. In particular, the case of integrals with respect to a posterior distribution supported on a general Riemannian manifold is considered and the asymptotic convergence of the estimator in this context is established. Our results are considerably stronger than those previously reported, in that the optimal rate of convergence is established under a basic Sobolevtype assumption on the integrand. The theoretical results are empirically verified on $\mathbb{S}^2$.
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We introduce a direct, linear sampling approach to imaging in an acoustic waveguide with sound hard walls. The waveguide terminates at one end and has unknown geometry due to compactly supported wall deformations. The goal of imaging is to determine these deformations and to identify localized scatterers in the waveguide, using a remote array of sensors that emits time harmonic probing waves and records the echoes. We present a theoretical analysis of the imaging approach and illustrate its performance with numerical simulations.
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In this paper, we introduce the concept of the Tutte polynomials of genus $g$ and discuss some of its properties. We note that the Tutte polynomials of genus one are wellknown Tutte polynomials. The Tutte polynomials are matroid invariants, and we claim that the Tutte polynomials of genus $g$ are also matroid invariants. The main result of this paper and the forthcoming paper declares that the Tutte polynomials of genus $g$ are complete matroid invariants.
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This paper concerns a FokkerPlanck equation on the positive real line modeling nucleation and growth of clusters. The main feature of the equation is the dependence of the driving vector field and boundary condition on a nonlocal order parameter related to the excess mass of the system. The first main result concerns the wellposedness and regularity of the Cauchy problem. The wellposedness is based on a fixed point argument, and the regularity on Schauder estimates. The first a priori estimates yield H\"older regularity of the nonlocal order parameter, which is improved by an iteration argument. The asymptotic behavior of solutions depends on some order parameter $\rho$ depending on the initial data. The system shows different behavior depending on a value $\rho_s>0$, determined from the potentials and diffusion coefficient. For $\rho \leq \rho_s$, there exists an equilibrium solution $c^{\text{eq}}_{(\rho)}$. If $\rho\le\rho_s$ the solution converges strongly to $c^{\text{eq}}
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The purpose of this note is to prove the $G$equivariant Sarkisov program for a connected algebraic group $G$ following the proof of the Sarkisov program by Hacon and McKernan. As a consequence, we obtain a characterisation of connected subgroups of $Bir(Z)$ acting rationally on $Z$.
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For any rational prime $p$, we define a certain $p$stabilization of holomorphic Siegel Eisenstein series for the symplectic group ${\rm Sp}(2n)_{/\mathbb{Q}}$ of an arbitrary genus $n \ge 1$. In addition, we derive an explicit formula for the Fourier coefficients and conclude their $p$adic interpolation problems. Consequently, for any odd prime $p$, we deduce the existence of a $\Lambda$adic form (in the sense of A. Wiles, H. Hida and R.L. Taylor) such that after taking a suitable constant multiple, it interpolates $p$adic analytic families of the abovementioned $p$stabilized Siegel Eisenstein series with nebentypus characters locally trivial at $p$ and Siegel Eisenstein series with nebentypus characters locally nontrivial at $p$ simultaneously. This can be viewed as a quite natural generalization of the ordinary $\Lambda$adic Eisenstein series for ${\rm GL}(2)$.
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We study a basic linear elliptic equation on a lower dimensional rectifiable set $S$ in $\mathbb{R}^N$ with the Neumann boundary data. Set $S$ is a support of a finite Borel measure $\mu$. We will use the measure theoretic tools to interpret the equation and the Neumann boundary condition. For this purpose we recall the Sobolevtype space dependent on the measure $\mu$. We establish existence and uniqueness of weak solutions provided that an appropriate source term is given.
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We obtain fundamental imbeddings for the fractional Sobolev space with variable exponent that is a generalization of wellknown fractional Sobolev spaces. As an application, we obtain apriori bounds and multiplicity of solutions to some nonlinear elliptic problems involving the fractional $p(\cdot)$Laplacian.
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The analyses of cellular network performance based on stochastic geometry generally ignore the traffic dynamics in the network. This restricts the proper evaluation and dimensioning of the network from the perspective of a mobile operator. To address the effect of dynamic traffic, recently, the mean cell approach has been introduced, which approximates the average network load by the zero cell load. However, this is not a realistic characterization of the network load, since a zero cell is statistically larger than a random cell drawn from the population of cells, i.e., a typical cell. In this paper, we analyze the load of a noiselimited network characterized by high signal to noise ratio (SNR). The noiselimited assumption can be applied to a variety of scenarios, e.g., millimeter wave networks with efficient interference management mechanisms. First, we provide an analytical framework to obtain the cumulative density function of the load of the typical cell. Then, we obtain two appr
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Starting from the observation that a flying saucer is a nonholonomic mechanical system whose 5dimensional configuration space is a contact manifold, we show how to enrich this space with a number of geometric structures by imposing further nonlinear restrictions on the saucer's velocity. These restrictions define certain `manoeuvres' of the saucer, which we call `attacking,' `landing,' or `G2 mode' manoeuvres, and which equip its configuration space with three kinds of flat parabolic geometry in five dimensions. The attacking manoeuvre corresponds to the flat Legendrean contact structure, the landing manoeuvre corresponds to the flat hypersurface type CR structure with Levi form of signature (1,1), and the most complicated G2 manoeuvre corresponds to the contact Engel structure with split real form of the exceptional Lie group G2 as its symmetries. A celebrated double fibration relating the two nonequivalent flat 5dimensional parabolic G2 geometries is used to construct a `G2 joystic
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We identify various structures on the configuration space C of a flying saucer, moving in a threedimensional smooth manifold M. Always C is a fivedimensional contact manifold. If M has a projective structure, then C is its twistor space and is equipped with an almost contact Legendrean structure. Instead, if M has a conformal structure, then the saucer moves according to a CR structure on C. With yet another structure on M, the contact distribution in C is equipped with a cone over a twisted cubic. This defines a certain type of Cartan geometry on C (more specifically, a type of `parabolic geometry') and we provide examples when this geometry is `flat,' meaning that its symmetries comprise the split form of the exceptional Lie algebra G2.
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Generation expansion planning (GEP) models have been useful aids for longterm planning. Recent growth in intermittent renewable generation has increased the need to represent the capability for nonrenewables to respond to rapid changes in daily loads, leading research to bring unit commitment (UC) features into GEPs. Such GEP+UC models usually contain discrete variables which, along with many details, make computation times impractically long for analysts who need to develop, debug, modify and use the GEP for many alternative runs. We propose a GEP with generation aggregated by technology type, and with the minimal UC content necessary to represent the limitations on generation to respond to rapid changes in demand, i.e., rampup and rampdown constraints, with ramp limits estimated from historical data on maximum rates of change of each generation type. We illustrate with data for the province of Ontario in Canada; the GEP is a large scale linear program that solves in less than one
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Given a rational map $f:\overline{\mathbb C}\to \overline{\mathbb C}$ and a finite graph $G\subset \overline{\mathbb C}$ such that $f(G)\subset G$ and $f$ is expanding on some neighbourhood of $G$, we show that there is another finite graph $G'\subset \bigcup _{n\ge 0}f^{n}(G)$ in an arbitrarily small neighbourhood of $G$ such that $f^N(G')\subset G'$ for some integer $N$ but $\bigcup _{i=0}^{N1}f^{i}(G')$ contains accumulating {\em{plaits}} and {\em{nests}}
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In this article, we analyse a stabilised equalorder finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a subdomain, for example along the boundary of the domain, with the only condition that a maximum angle is fulfilled in each element.This discretisation is motivated by applications on moving domains as arising e.g. in fluidstructure interaction or multiphaseflow problems. To deal with the anisotropies, we define a modification of the original Continuous Interior Penalty stabilisation approach. We show analytically the discrete stability of the method and convergence of order ${\cal O}(h^{3/2})$ in the energy norm and ${\cal O}(h^{5/2})$ in the $L^2$norm of the velocities. We present numerical examples for a linear Stokes problem and for a nonlinear fluidstructure interaction problem, that substantiate the analytical results and show the capabilities of the approach.
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In noisy evolutionary optimization, sampling is a common strategy to deal with noise. By the sampling strategy, the fitness of a solution is evaluated multiple times (called \emph{sample size}) independently, and its true fitness is then approximated by the average of these evaluations. Previous studies on sampling are mainly empirical. In this paper, we first investigate the effect of sample size from a theoretical perspective. By analyzing the (1+1)EA on the noisy LeadingOnes problem, we show that as the sample size increases, the running time can reduce from exponential to polynomial, but then return to exponential. This suggests that a proper sample size is crucial in practice. Then, we investigate what strategies can work when sampling with any fixed sample size fails. By two illustrative examples, we prove that using parent or offspring populations can be better. Finally, we construct an artificial noisy example to show that when using neither sampling nor populations is effecti
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