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New submitter evolutionary writes: According to FSecure's Chief Research Officer "IoT is unavoidable. If it uses electricity, it will become a computer. If it uses electricity, it will be online. In future, you will only buy IoT appliances, whether you like it or not, whether you know it or not." FSecure's new product to help mitigate data leakage, "Sense", is a IoT Firewall, combining a traditional firewall with a cloud service and uses concepts including behaviourbased blocking and device reputation to figure out whether you have insecure devices.
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Tesla said last night Chris Lattner, the vice president of Autopilot software, has left the company about six months after the electric carmaker hired him away from Apple. From a report: Lattner had led the software development team in charge of Autopilot. Tesla executive Jim Keller is now in charge of Autopilot hardware and software. The company announced it had also hired OpenAI research scientist Andrej Karpathy, who will serve as Tesla's new director of artificial intelligence and Tesla Vision. "Chris just wasn't the right fit for Tesla, and we've decided to make a change," the company told reporters in a statement. "We wish him the best." Lattner tweeted last night, "Turns out that Tesla isn't a good fit for me after all. I'm interested to hear about interesting roles for a seasoned engineering leader!" Lattner is a widely respected figure in the industry. He is the main author of LLVM as well as Apple's Swift programming language. We interviewed him earlier this year.
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The kernel's command line allows the specification of many operating parameters at boot time. A silly bug in commandline parsing was reported by Ilya Matveychikov on May 22; it can be exploited to force a stack buffer overflow with a controlled payload that can overwrite memory. The bug itself stems from a boundschecking error that, while simple, has still been in the Linux kernel source since version 2.6.20. The subsequent disclosure post by Matveychikov in the osssecurity list spawned a discussion on what constitutes a vulnerability, and what is, instead, merely a bug.
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After years of complaints, Uber is rolling out a tipping option for drivers. "Tipping is available in Seattle, Minneapolis and Houston as of today. We're starting with only 3 cities so we can create the best tipping experience for you and your riders. We'll be adding more cities over the next few weeks, and will make tips available to all U.S. drivers, by the end of July 2017," Uber said in an email to drivers. Gizmodo reports: Uber will also roll out a full set of driverfriendly features. The cancellation window will narrow to two minutes (it was previously five) and drivers will get a perminute fee if a rider makes them wait beyond two minutes. Drivers will also get a cut of Uber's "teen fare" which had previously gone exclusively to Uber. Now, drivers will get $2 of the fee. Uber will also offer drivers the option to enroll in injuryprotection insurance. Uber has always argued that it offers a seamless experience and that adding a tip feature into its app would interfere with tha
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Behind the scenes at the White House tech CEO meeting, Apple CEO Tim Cook told President Donald Trump that technology employees are "nervous" about the administration's approach to immigration, CNBC reports, citing a source familiar with the exchange. From the report: The source said the president told the CEOs on Monday that the Senate's healthcare bill needs "more heart." That would be a second known instance of the president criticizing the GOP plan in private meetings. To that, the source said, Cook replied that the immigration approach by the administration also "needs more heart." Cook cited the Deferred Action for Childhood Arrivals program, which is under review by the Trump administration. He also said people in tech and their coworkers were nervous about their status, and added that it "would be great" if the president could "send them a signal." Here's what executives of Amazon, Google, and Microsoft said.
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Lennart Poettering announces casync, a tool for distributing system images. "casync takes inspiration from the popular rsync file synchronization tool as well as the probably even more popular git revision control system. It combines the idea of the rsync algorithm with the idea of gitstyle contentaddressable file systems, and creates a new system for efficiently storing and delivering file system images, optimized for highfrequency update cycles over the Internet. Its current focus is on delivering IoT, container, VM, application, portable service or OS images, but I hope to extend it later in a generic fashion to become useful for backups and home directory synchronization as well."
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One of the largest British retailers in London, M&S, is opting in for laserprinted barcodes to reduce paper waste. "The labels, which are etched onto fruit's skins with lasers instead of stickers, will save 10 tons of paper and five tons of glue every year according to M&S," reports The Telegraph. The labels will be etched into the skins of avocados, but "could soon be introduced to other fruit and vegetables and adopted by other supermarkets which are looking for new waste reduction techniques." The labels themselves include the shop logo, best before date, country of origin and product code for entering at the till. What's more is that the avocado's skin is the only area impacted by the lasers  none of the fruit gets damaged. Bruce66423 writes: Print the information usually on the packaging to reduce waste. Excellent idea  although the Aldi (the radically cheap, all own brand chain) alternative is to leave avocados untouched and get the cashiers to enter the code.
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An anonymous reader quotes a report from TIME: Another study is touting the benefits of yoga  this time, for people with back problems. The new research put yoga headtohead against physical therapy and found the two were equally good at restoring function and reducing the need for pain medication over time. In the new study, published in Annals of Internal Medicine, a group of 320 people did 12 weeks of yoga or physical therapy, or they simply received a book and newsletters about coping with back pain. People in the active treatment groups reported that their pain was less intense than it was at the start of the study and that they were able to physically move more. Some were also able to reduce, or even stop, their pain medications. Those improvements stuck around for a full year after the study was over. This research is unique because the people in the study were racially diverse, and most were from lowincome families. Many had preexisting medical conditions. That's important
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In the August 2017 issue of Consumer Reports magazine, the nonprofit organization ranked internet service providers based off customer satisfaction. According to the report, many consumers still don't like their broadband and television provider, and don't believe they receive a decent value for the high price they pay for service. DSLReports summarizes the findings: The report [...] names Chattanooga municipal broadband provider EPB as the mostliked ISP in the nation. EPB was followed by Google Fiber, Armstrong Cable, Consolidated Cable and RCN as the topranked ISPs in the nation. Google Fiber "was the clear winner for internet service," notes the report, "with the only high score for value." Google Fiber also received high marks for customer support and service. But large, incumbent ISPs continue to be aggressively disliked due to high prices and poor customer service, according to the report. Despite endless annual promises that customer service is the company's priority, Comcast
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Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$adic space group of dimension $d_x=(p1)p^{x1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or equal to $p^{d_x+x}$ have isomorphic mod $p$ cohomology groups. In particular, we show that the cohomology groups of sufficiently large quotients of the unique maximal class pro$p$ group are isomorphic as $\F_p$modules.
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Let C be a smooth projective algebraic curve of genus g over the finite field F_q. A classical result of H. Martens states that the BrillNoether locus of line bundles L in Pic^d C with deg L = d and h^0(L) >= i is of dimension at most d2i+2, under conditions that hold when such an L is both effective and special. We show that the number of such L that are rational over F_q is bounded above by K_g q^(d2i+2), with an explicit constant K_g that grows exponentially with g. Our proof uses the Weil estimates for function fields, and is independent of Martens' theorem. We apply this bound to give a precise lower bound of the form 1  K'_g/q for the probability that a line bundle in (Pic^(g+1) C)(F_q) is base point free. This gives an effective version over finite fields of the usual statement that a general line bundle of degree g+1 is base point free. This is applicable to the author's work on fast Jacobian group arithmetic for typical divisors on curves.
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We give a classification of semisimple and separable algebras in a multifusion category over an arbitrary field in analogy to WedderbenArtin theorem in classical algebras. It turns out that, if the multifusion category admits a semisimple Drinfeld center, the only obstruction to the separability of a semisimple algebra arises from inseparable field extensions as in classical algebras. Among others, we show that a division algebra is separable if and only if it has a nonvanishing dimension.
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Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of nonconsecutive Fibonacci numbers. This theorem induces a binary numeration system for the positive integers known as Fibonacci coding. Fibonacci code is a variablelength prefix code that is robust against insertion and deletion errors and is useful in data transmission and data compression. In this paper, we generalize the theorem of Zeckendorf and prove that every element of a free $\mathbb{Z}$module can be represented as a sum of elements from a Fibonacci sequence of higher order. Immediate applications of these results include a Fibonacci coding for free $\mathbb{Z}$modules, where encoding and decoding algorithms are obtained naturally from the approach of our theorems.
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Let $I, J\subset \mathbb{R}$ be closed intervals, and let $H$ be $C^{3}$ smooth real valued function on $I\times J$ with nonvanishing $H_{x}$ and $H_{y}$. Take any fixed positive numbers $a,b$, and let $d\mu$ be a probability measure with finite moments and absolutely continuous with respect to Lebesgue measure. We show that for the inequality $$ \int_{\mathbb{R}^{n}} \mathrm{ess\,sup}_{y \in \mathbb{R}^{n}}\; H\left( f\left(\frac{xy}{a}\right),g\left(\frac{y}{b}\right)\right)d\mu (x) \geq H\left(\int_{\mathbb{R}^{n}}fd\mu, \int_{\mathbb{R}^{n}}gd\mu \right) $$ to hold for all Borel functions $f,g$ with values in $I$ and $J$ correspondingly it is necessary that $$ a^{2}\frac{H_{xx}}{H_{x}^{2}}+(1a^{2}b^{2})\frac{H_{xy}}{H_{x}H_{y}}+b^{2}\frac{H_{yy}}{H_{y}^{2}}\geq 0, $$ $ab\leq 1$, $a+b\geq 1$ and $\int_{\mathbb{R}^{n}}xd\mu=0$ if $a+b>1$. Moreover, if $d\mu$ is a Gaussian measure then the necessary condition becomes sufficient. This extends Pr\'ekopaLeindler and Ehrhard in
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Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the secret. Thus, secret sharing schemes are systems of variables in which it is very clearly specified which subsets have information about the secret. As such, they provide perfect model systems for information decompositions. However, following this intuition too far leads to an information decomposition with negative partial information terms, which are difficult to interpret. One possible explanation is that the partial information lattice proposed by Williams and Beer is incomplete and has to be extended to incorporate terms corresponding to higher order redundancy. These results put bounds on information decompositions that follow the partial information framework, and they hint at where the partial information lattice needs to be improved.
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The paper introduces nonadditivity parameter transformation group induced by Tsallis entropy. We discuss simple physical applications of a system in the contact with finite heat bath or with temperature fluctuations. With help of the transformation, it is possible to introduce generalized distributive rule in qdeformed algebra. We focus on MaxEnt distributions of Tsallis entropy with rescaled nonadditivity parameter under escort energy constraints. We show that each group element corresponds to one class of qdeformed distributions. Finally, we briefly discuss the application of the transformation to JizbaArimitsu Hybrid entropy and its connection to Average Hybrid entropy.
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A Herglotz function is a holomorphic map from the open complex unit disk into the closed complex right halfplane. A classical Herglotz function has an integral representation against a positive measure on the unit circle. We prove a free analytic analogue of the Herglotz representation and describe how our representations specialize to the free probabilistic case. We also show that the set of representable Herglotz functions arising from noncommutative conditional expectations must be closed in a natural topology.
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In the present paper, the reducibility is derived for linear wave equation of finite smooth and timequasiperiodic potential subject to Dirichlet boundary condition. Moreover, it is proved that the corresponding wave operator possesses the property of pure point spectra and zero Lyapunov exponent.
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In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain complete property. Then, by applying these theorems, we provide some existence and uniqueness of solutions to some integral equations. We also prove the solvability of some equilibrium problems in Banach spaces.
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We consider the dynamics of two layers of incompressible electrically conducting fluid interacting with the magnetic field, which are confined within a 3D horizontally infinite slab and separated by a free internal interface. We assume that the upper fluid is heavier than the lower fluid so that the fluids are susceptible to the RayleighTaylor instability. Yet, we show that the viscous and nonresistive problem around the equilibrium is nonlinearly stable provided that the strength of the vertical component of the steady magnetic field, $\bar B_3$, is greater than the critical value, $\mathcal{M}_c$, which we identify explicitly. We also prove that the problem is nonlinearly unstable if $\bar B_3<\mathcal{M}_c$. Our results indicate that the nonhorizontal magnetic field has strong stabilizing effect on the RayleighTaylor instability but the horizontal one does not have in 3D.
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In this paper, we prove that optimally solving an $n \times n \times n$ Rubik's Cube is NPcomplete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous result that optimally solving an $n \times n \times n$ Rubik's Cube with missing stickers is NPcomplete. We prove this result first for the simpler case of the Rubik's Squarean $n \times n \times 1$ generalization of the Rubik's Cubeand then proceed with a similar but more complicated proof for the Rubik's Cube case.
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In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of at least second order at a nonradial involutive manifold $\Sigma_2$. We shall assume that the Taylor expansion at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$ at the characteristics, but transversal to the symplectic leaves of $\Sigma_2$. We shall also assume that this Taylor expansion is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the NirenbergTreves condition (${\Psi}$). In the case when the sign change of this condition is of infinite order, we also need some conditions on the vanishing of the gradient and the Hessian of the principal symbol at $\Sigma_2$. Under these conditions, we show that $P$ is not solvable.
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In communication through asymmetric channels the capacityachieving input distribution is not uniform in general. Homophonic coding is a framework to invertibly convert a (usually uniform) message into a sequence with some target distribution, and is a promising candidate to generate codewords with the nonuniform target distribution for asymmetric channels. In particular, a VariabletoFixed length (VF) homophonic code can be used as a suitable component for channel codes to avoid decoding error propagation. However, the existing VF homophonic code requires the knowledge of the maximum relative gap of probabilities between two adjacent sequences beforehand, which is an unrealistic assumption for long block codes. In this paper we propose a new VF homophonic code without such a requirement by allowing onesymbol decoding delay. We evaluate this code theoretically and experimentally to verify its asymptotic optimality.
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We consider the group $\mathfrak{X}(G)$ obtained from $G\ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. Deceptively complicated finitely presented groups arise from this construction: $\mathfrak{X}(G)$ is finitely presented if and only if $G$ is finitely presented, but if $F$ is a nonabelian free group of finite rank then $\mathfrak{X}(F)$ has a subgroup of finite index whose third homology is not finitely generated.
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In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in qspace. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multishell schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called Spherical Code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to
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This paper studies a new unmanned aerial vehicle (UAV)enabled wireless power transfer (WPT) system, where a UAVmounted energy transmitter (ET) broadcasts wireless energy to charge distributed energy receivers (ERs) on the ground. In particular, we consider a basic twouser scenario, and investigate how the UAV can optimally exploit its mobility to maximize the amount of energy transferred to the two ERs during a given charging period. We characterize the achievable energy region of the two ERs, by optimizing the UAV's trajectory subject to a maximum speed constraint. We show that when the distance between the two ERs is smaller than a certain threshold, the boundary of the energy region is achieved when the UAV hovers above a fixed location between them for all time; while when their distance is larger than the threshold, to achieve the boundary of the energy region, the UAV in general needs to hover and fly between two different locations above the line connecting them. Numerical re
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This paper is about deriving lower bounds on the error exponents for the twouser interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, etc.). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. Also, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive singleletter formulas for the random coding error exponents. We compare our results with the
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We define a collection of functions $s_i$ on the set of plane trees (or standard Young tableaux). The functions are adapted from transpositions in the representation theory of the symmetric group and almost form a group action. They were motivated by $\textit{local moves}$ in combinatorial biology, which are maps that represent a certain unfolding and refolding of RNA strands. One main result of this study identifies a subset of local moves that we call $s_i$local moves, and proves that $s_i$local moves correspond to the maps $s_i$ acting on standard Young tableaux. We also prove that the graph of $s_i$local moves is a connected, graded poset with unique minimal and maximal elements. We then extend this discussion to functions $s_i^C$ that mimic reflections in the Weyl group of type $C$. The corresponding graph is no longer connected, but we prove it has two connected components, one of symmetric and the other of asymmetric plane trees. We give open questions and possible biological
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We develop the theory of BerezinToeplitz operator on any compact symplectic prequantizable manifold from scratch. Our main inspiration is the Boutet de MonvelGuillemin theory, that we simplify in several ways to obtain a concise exposition. A comparison with the spinc Dirac quantization is also included.
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We study an optimal control problem for a nonautonomous SEIRS model with incidence given by a general function of the infective, the susceptible and the total population, and with vaccination and treatment as control variables. We prove existence and uniqueness results for our problem and, for the case of massaction incidence, we present some simulation results designed to compare an autonomous and corresponding periodic model, as well as the controlled versus uncontrolled models.
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We study optimal finite dimensional approximations of the generally infinitedimensional FokkerPlanckKolmogorov (FPK) equation, finding the curve in a given finitedimensional family that best approximates the exact solution evolution. For a first local approximation we assign a manifold structure to the family and a metric. We then project the vector field of the partial differential equation (PDE) onto the tangent space of the chosen family, thus obtaining an ordinary differential equation for the family parameter. A second global approximation will be based on projecting directly the exact solution from its infinite dimensional space to the chosen family using the nonlinear metric projection. This will result in matching expectations with respect to the exact and approximating densities for particular functions associated with the chosen family, but this will require knowledge of the exact solution of FPK. A first way around this is a localized version of the metric projection bas
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The Bergman minimal model is a dynamic model of plasma glucose concentration with two input variables  insulin delivery and carbohydrate intake. We characterise optimality of bolus insulin inputs by the predicted behaviour of the plasma glucose concentration for a given carbohydrate input. The result is derived subject to the constraints that the plasma glucose concentration must attain but not go below a specified minimum value and the bolus input is rectangular.
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Let $c\in (0, 1]$ be a real number and let $n$ be a sufficiently large integer. We prove that every $n$vertex $c n$regular graph $G$ contains a collection of $\lfloor 1/c \rfloor$ paths whose union covers all but at most $o(n)$ vertices of $G$. The constant $\lfloor 1/c \rfloor$ is best possible when $1/c\notin \mathbb{N}$ and off by $1$ otherwise. Moreover, if in addition $G$ is bipartite, then the number of paths can be reduced to $\lfloor 1/(2c) \rfloor$, which is best possible.
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Brannan showed that a normalized univalent polynomial of the form $P(z)=z+a_2 z^2+\ldots + a_{n1}z^{n1}+\frac{z^n}{n}$ is starlike if and only if $a_2=\ldots=a_{n1}=0$. We give a new and simple proof of his result, showing further that it is also equivalent to the membership of $P$ in the NoshiroWarschawski class of univalent functions whose derivative has positive real part in the disk. Both proofs are based on the Fej\'er lemma for trigonometric polynomials with positive real part.
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In this note, we study the problem of uniqueness of Ricci flow on complete noncompact manifolds. We consider the class of solutions with curvature bounded above by C=t when t > 0 and proved uniqueness if initial curvature is of polynomial growth and Ricci curvature of the ow is relatively small.
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The residual closure of a subgroup $H$ of a group $G$ is the intersection of all virtually normal subgroups of $G$ containing $H$. We show that if $G$ is generated by finitely many cosets of $H$ and if $H$ is commensurated, then the residual closure of $H$ in $G$ is virtually normal. Various applications to separable subgroups, polycyclic groups, residually finite groups, groups acting on trees, lattices in products of trees and justinfinite groups are described.
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In this short note, we consider a system of two rotors, one of which interacts with a Langevin heat bath. We show that the system relaxes to its invariant measure (steady state) no faster than a stretched exponential $\exp(c t^{1/2})$. This indicates that the exponent $1/2$ obtained earlier by the present authors and J.P. Eckmann for short chains of rotors is optimal.
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This paper considers the optimal modification of the likelihood ratio test (LRT) for the equality of two highdimensional covariance matrices. The classical LRT is not well defined when the dimensions are larger than or equal to one of the sample sizes. In this paper, an optimally modified test that works well in cases where the dimensions may be larger than the sample sizes is proposed. In addition, the test is established under the weakest conditions on the moments and the dimensions of the samples. We also present weakly consistent estimators of the fourth moments, which are necessary for the proposed test, when they are not equal to 3. From the simulation results and real data analysis, we find that the performances of the proposed statistics are robust against affine transformations.
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We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradientflow equation of a weak surface FrankOseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finiteelement method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the PoincareHopf theorem and show examples where the energy is decreased by introducing additional orientational defects.
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We prove that the diffraction formula for regular model sets is equivalent to the Poisson Summation Formula for the underlying lattice. This is achieved using Fourier analysis of unbounded measures on locally compact abelian groups as developed by Argabright and de Lamadrid. We also obtain diffraction results for certain classes of nonregular socalled weak model sets.
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An ancient optics problem of Ptolemy, studied later by Alhazen, is discussed. This problem deals with reflection of light in spherical mirrors. Mathematically this reduces to the solution of a quartic equation, which we solve and analyze using a symbolic computation software. Similar problems have been recently studied in connection with raytracing, catadioptric optics, scattering of electromagnetic waves, and mathematical billiards, but we were led to this problem in our study of the socalled triangular ratio metric.
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Iterative decoding and linear programming decoding are guaranteed to converge to the maximumlikelihood codeword when the underlying Tanner graph is cyclefree. Therefore, cycles are usually seen as the culprit of lowdensity paritycheck (LDPC) codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cyclefree Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all paritycheck matrices that are pseudocodewordfree for such class of codes.
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The study of covariances (or positive definite functions) on the sphere (the Earth, in our motivation) goes back to Bochner and Schoenberg (194042) and to the first author (1969, 1973), among others. Extending to the geotemporal case (sphere cross line, for position and time) was for a long time an obstacle to geostatistical modelling. The characterisation question here was raised by the authors and Mijatovi\'c in 2016, and answered by Berg and Porcu in 2017. Extensions to multiple products (of spheres and lines) follows similarly (Guella, Menegatto and Peron, 2016). We survey results of this type, and related applications e.g. in numerical weather prediction.
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We consider probabilistic shaping as a means of increasing the spectral efficiency of fiberoptic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision decoding (HDD). In particular, we extend the probabilistic amplitude shaping (PAS) scheme recently introduced by B\"ocherer \emph{et al.} to a coded modulation (CM) scheme with HDD that uses a staircase code as the forward error correction code. We show that the proposed CM scheme with PAS and staircase codes yields significant gains in spectral efficiency with respect to the baseline scheme using a staircase code and a standard, uniform constellation. Using a single staircase code, the proposed scheme achieves performance within $0.56$$1.55$ dB of the corresponding achievable information rate for a wide range of spectral efficiencies.
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We provide physicsinspired derivations of a number of algorithms for computing the permanent of a matrix. In particular we formulate the computation of the permanent as a Grassmann integral that may be viewed as an interacting manyfermion problem. Applying a discrete HubbardStratonovich decoupling then gives approximation schemes that are equivalent to the familiar determinant Monte Carlo algorithm. This leads to elementary derivations of the wellknown estimators of GodsilGutman and Karmarkar et al. Another straightfoward manipulation of the Grassmann integral, making use of gauge invariance, gives the efficient exact formula of Glynn. In addition to these known results we also give some additional estimators and formulas that are natural in our formulation.
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An n x n permutative matrix is a matrix in which every row is a permutation of the first row. In this paper the result given by Paparella in [Electron. J. Linear Algebra 31 (2016) 306312] is extended to a more general lists of real and complex numbers, and a negative answer to a question posed by him is given.
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Let $\mathbb{M}^{2}$ be a complete non compact orientable surface of non negative curvature. We prove in this paper some theorems involving parabolicity of minimal surfaces in $\mathbb{M}^{2}\times\mathbb{R}$. First, using a characterization of $\delta$parabolicity we prove that under additional conditions on $\mathbb{M}$, an embedded minimal surface with bounded gaussian curvature is proper. The second theorem states that under some conditions on $\mathbb{M}$, if $\Sigma$ is a properly immersed minimal surface with finite topology and one end in $\mathbb{M}\times\mathbb{R}$, which is transverse to a slice $\mathbb{M}\times\{t\}$ except at a finite number of points, and such that $\Sigma\cap(\mathbb{M}\times\{t\})$ contains a finite number of components, then $\Sigma$ is parabolic. In the last result, we assume some conditions on $\mathbb{M}$ and prove that if a minimal surface in $\mathbb{M}\times\mathbb{R}$ has height controlled by a logarithmic function, then it is parabolic and ha
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We give an alternative construction of the Betti realization functor on the derived category of motives of complex algebraic varieties via the category of CW complexes instead of the category of complex analytic spaces. In particular we show that the functor we define via the category of CW complexes coincide with Ayoub's one. We deduce from this construction that Ayoub's realization functor on geometric motives factors trough Nori motives and that the image of this functor on the morphisms between the motive of a point and a shift of a Tate twist of the motive with compact support of a complex algebraic variety coincide with the classical cycle class map on higher Chow groups.
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The problem of cache enabled private information retrieval (PIR) is considered in which a user wishes to privately retrieve one out of $K$ messages, each of size $L$ bits from $N$ distributed databases. The user has a local cache of storage $SL$ bits which can be used to store any function of the $K$ messages. The main contribution of this work is the exact characterization of the capacity of cache aided PIR as a function of the storage parameter $S$. In particular, for a given cache storage parameter $S$, the informationtheoretically optimal download cost $D^{*}(S)/L$ (or the inverse of capacity) is shown to be equal to $(1 \frac{S}{K})\left(1+ \frac{1}{N}+ \ldots + \frac{1}{N^{K1}}\right)$. Special cases of this result correspond to the settings when $S=0$, for which the optimal download cost was shown by Sun and Jafar to be $\left(1+ \frac{1}{N}+ \ldots + \frac{1}{N^{K1}}\right)$, and the case when $S=K$, i.e., cache size is large enough to store all messages locally, for which
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We construct the coarse index class with support condition (as an element of coarse $K$homology) of an equivariant Dirac operator on a complete Riemannian manifold endowed with a proper, isometric action of a group. We further show a coarse relative index theorem and discuss the compatibility of the index with the suspension isomorphism.
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Functional Analysis of Variance (FANOVA) from Hilbertvalued correlated data with spatial rectangular or circular supports is analyzed, when Dirichlet conditions are assumed on the boundary. Specifically, a Hilbertvalued fixed effect model with error term defined from an Autoregressive Hilbertian process of order one (ARH(1) process) is considered, extending the formulation given in RuizMedina (2016). A new statistical test is also derived to contrast the significance of the functional fixed effect parameters. The Dirichlet conditions established at the boundary affect the dependence range of the correlated error term. While the rate of convergence to zero of the eigenvalues of the covariance kernels, characterizing the Gaussian functional error components, directly affects the stability of the generalized leastsquares parameter estimation problem. A simulation study and a realdata application related to fMRI analysis are undertaken to illustrate the performance of the parameter es
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Random constraint satisfaction problems undergo several phase transitions as the ratio between the number of constraints and the number of variables is varied. When this ratio exceeds the satisfiability threshold no more solutions exist; the satisfiable phase, for less constrained problems, is itself divided in an unclustered regime and a clustered one. In the latter solutions are grouped in clusters of nearby solutions separated in configuration space from solutions of other clusters. In addition the rigidity transition signals the appearance of socalled frozen variables in typical solutions: beyond this threshold most solutions belong to clusters with an extensive number of variables taking the same values in all solutions of the cluster. In this paper we refine the description of this phenomenon by estimating the location of the freezing transition, corresponding to the disappearance of all unfrozen solutions (not only typical ones). We also unveil phase transitions for the existen
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The left patience sorting (lPS) monoid, also known in the literature as the Bell monoid, and the right patient sorting (rPS) monoid are introduced by defining certain congruences on words. Such congruences are constructed using insertion algorithms based on the concept of decreasing subsequences. Presentations for these monoids are given. Each finiterank rPS monoid is shown to have polynomial growth and to satisfy a nontrivial identity (dependent on its rank), while the infinite rank rPS monoid does not satisfy a nontrivial identity. The lPS monoids of finite rank have exponential growth and thus do not satisfy nontrivial identities. The complexity of the insertion algorithms is discussed. rPS monoids of finite rank are shown to be automatic and to have recursive complete presentations. When the rank is $1$ or $2$, they are also biautomatic. lPS monoids of finite rank are shown to have finite complete presentations and to be biautomatic.
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