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New submissions

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New submissions for Fri, 19 Jan 18

[1]  arXiv:1801.05834 [pdf, ps, other]
Title: Positivity Results for spaces of rational curves
Subjects: Algebraic Geometry (math.AG)

Let $X$ be a very general hypersurface of degree $d$ in $\mathbb{P}^n$. We investigate positivity properties of the spaces $R_e(X)$ of degree $e$ rational curves in $X$. We show that for small $e$, $R_e(X)$ has no rational curves meeting the locus of smooth embedded curves. We show that for $n \leq d$, there are no rational curves in the locus $Y \subset X$ swept out by lines. And we exhibit differential forms on a smooth compactification of $R_e(X)$ for every $e$ and $n-2 \geq d \geq \frac{n+1}{2}$.

[2]  arXiv:1801.05838 [pdf, ps, other]
Title: Revisiting the Problem of Recovering Functions in $\Bbb R^{n}$ by Integration on $k$ Dimensional Planes
Authors: Yehonatan Salman
Comments: 22 pages
Subjects: Analysis of PDEs (math.AP)

The aim of this paper is to present inversion methods for the classical Radon transform which is defined on a family of $k$ dimensional planes in $\Bbb R^{n}$ where $1\leq k\leq n - 2$. For these values of $k$ the dimension of the set $\mathcal{H}(n,k)$, of all $k$ dimensional planes in $\Bbb R^{n}$, is greater than $n$ and thus in order to obtain a well-posed problem one should choose proper subsets of $\mathcal{H}(n,k)$. We present inversion methods for some prescribed subsets of $\mathcal{H}(n,k)$ which are of dimension $n$.

[3]  arXiv:1801.05842 [pdf, ps, other]
Title: Lipschitz contact equivalence and real analytic functions
Comments: 11 pages
Subjects: Metric Geometry (math.MG)

We study the properties of the a complete invariant of the analytic function of two variables with respect to the Lipschitz contact equivalence. This invariant is called pizza. We prove that the pizza of real analytic functions has some continuity properties.

[4]  arXiv:1801.05844 [pdf, ps, other]
Title: Performance Analysis of Joint Pairing and Mode Selection in D2D Communications with FD Radios
Comments: 6 pages, 4 figures, accepted in WCNC 2018
Subjects: Information Theory (cs.IT)

In cellular-D2D networks, users can select the communication mode either direct and form D2D links or indirect and communicate with BS. In former case, users should perform pairing selection and choose their pairs. The main focus in this paper is proposing an analytical framework by using tools from stochastic geometry to address these two issues, i.e. i) mode selection for the user devices to be established in either cellular or D2D mode, which is done based on received power from BS influenced by a bias factor, and ii) investigation of choosing nth-nearest neighbor as the serving node for the receiver of interest, by considering full-duplex (FD) radios as well as half- duplex (HD) in the D2D links. The analytic and simulation results demonstrate that even though the bias factor determines the throughput of each mode, it does not have any influence on the system sum throughput. Furthermore, we demonstrate that despite of suffering from self-interference, FD-D2D results in higher system sum throughput as well as higher coverage probability in comparison to its counterpart, namely purely HD- D2D network.

[5]  arXiv:1801.05848 [pdf, ps, other]
Title: Random Construction of Partial MDS Codes
Subjects: Information Theory (cs.IT)

This work deals with partial MDS (PMDS) codes, a special class of locally repairable codes, used for distributed storage system. We first show that a known construction of these codes, using Gabidulin codes, can be extended to use any maximum rank distance code. Then we define a standard form for the generator matrices of PMDS codes and use this form to give an algebraic description of PMDS generator matrices. This implies that over a sufficiently large finite field a randomly chosen generator matrix in PMDS standard form generates a PMDS code with high probability. This also provides sufficient conditions on the field size for the existence of PMDS codes.

[6]  arXiv:1801.05859 [pdf, other]
Title: A Kotel'nikov Representation for Wavelets
Comments: 6 pages, 15 figures
Subjects: Classical Analysis and ODEs (math.CA); Signal Processing (eess.SP); Numerical Analysis (math.NA); Methodology (stat.ME)

This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an analysis with a filter bank of constant quality factor is revisited on these bases. It is shown that if the wavelet spectral support is limited into the band $[f_m,f_M]$, then an orthogonal analysis is guaranteed provided that $f_M \leq 3f_m$, a quite simple result, but that invokes some parallel with the Nyquist rate. Nevertheless, in cases of orthogonal wavelets whose spectrum does not verify this condition, it is shown how to construct an "equivalent" filter bank with no spectral overlapping.

[7]  arXiv:1801.05870 [pdf, other]
Title: Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering
Comments: 40 pages, 9 figures
Subjects: Information Theory (cs.IT)

In Compressive Sensing theory and its applications, quantization of signal measurements, as integrated into any realistic sensing model, impacts the quality of signal reconstruction. In fact, there even exist incompatible combinations of quantization functions (e.g., the 1-bit sign function) and sensing matrices (e.g., Bernoulli) that cannot lead to an arbitrarily low reconstruction error when the number of observations increases.
This work shows that, for a scalar and uniform quantization, provided that a uniform random vector, or "random dithering", is added to the compressive measurements of a low-complexity signal (e.g., a sparse or compressible signal, or a low-rank matrix) before quantization, a large class of random matrix constructions known to respect the restricted isometry property (RIP) are made "compatible" with this quantizer. This compatibility is demonstrated by the existence of (at least) one signal reconstruction method, the "projected back projection" (PBP), whose reconstruction error is proved to decay when the number of quantized measurements increases.
Despite the simplicity of PBP, which amounts to projecting the back projection of the compressive observations (obtained from their multiplication by the adjoint sensing matrix) onto the low-complexity set containing the observed signal, we also prove that given a RIP matrix and for a single realization of the dithering, this reconstruction error decay is also achievable uniformly for the sensing of all signals in the considered low-complexity set.
We finally confirm empirically these observations in several sensing contexts involving sparse signals, low-rank matrices, and compressible signals, with various RIP matrix constructions such as sub-Gaussian random matrices and random partial Discrete Cosine Transform (DCT) matrices.

[8]  arXiv:1801.05873 [pdf, other]
Title: Sparse Activity Detection for Massive Connectivity
Comments: 15 pages, 7 figures; accepted at TSP
Subjects: Information Theory (cs.IT)

This paper considers the massive connectivity application in which a large number of potential devices communicate with a base-station (BS) in a sporadic fashion. The detection of device activity pattern together with the estimation of the channel are central problems in such a scenario. Due to the large number of potential devices in the network, the devices need to be assigned non-orthogonal signature sequences. The main objective of this paper is to show that by using random signature sequences and by exploiting sparsity in the user activity pattern, the joint user detection and channel estimation problem can be formulated as a compressed sensing single measurement vector (SMV) problem or multiple measurement vector (MMV) problem, depending on whether the BS has a single antenna or multiple antennas, and be efficiently solved using an approximate message passing (AMP) algorithm. This paper proposes an AMP algorithm design that exploits the statistics of the wireless channel and provides an analytical characterization of the probabilities of false alarm and missed detection by using the state evolution. We consider two cases depending on whether the large-scale component of the channel fading is known at the BS and design the minimum mean squared error (MMSE) denoiser for AMP according to the channel statistics. Simulation results demonstrate the substantial advantage of exploiting the statistical channel information in AMP design; however, knowing the large-scale fading component does not offer tangible benefits. For the multiple-antenna case, we employ two different AMP algorithms, namely the AMP with vector denoiser and the parallel AMP-MMV, and quantify the benefit of deploying multiple antennas at the BS.

[9]  arXiv:1801.05875 [pdf, other]
Title: An Ultra-Weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension
Subjects: Numerical Analysis (math.NA)

In this paper, we develop an ultra-weak discontinuous Galerkin (DG) method to solve the one-dimensional nonlinear Schr\"odinger equation. Stability conditions and error estimates are derived for the scheme with a general class of numerical fluxes. The error estimates are based on detailed analysis of the projection operator associated with each individual flux choice. Depending on the parameters, we find out that in some cases, the projection can be defined element-wise, facilitating analysis. In most cases, the projection is global, and its analysis depends on the resulting $2\times2$ block-circulant matrix structures. For a large class of parameter choices, optimal $\textit{a priori}$ $L^2$ error estimates can be obtained. Numerical examples are provided verifying theoretical results.

[10]  arXiv:1801.05877 [pdf, other]
Title: Nonstandard local discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic equations in high dimensions
Subjects: Numerical Analysis (math.NA)

This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity solutions of these fully nonlinear PDEs. The proposed LDG methods are natural extensions of a narrow-stencil finite difference framework recently proposed by the authors for approximating viscosity solutions. The idea of the methodology is to use multiple approximations of first and second order derivatives as a way to resolve the potential low regularity of the underlying viscosity solution. Consistency and generalized monotonicity properties are proposed that ensure the numerical operator approximates the differential operator. The resulting algebraic system has several linear equations coupled with only one nonlinear equation that is monotone in many of its arguments. The structure can be explored to design nonlinear solvers. This paper also presents and analyzes numerical results for several numerical test problems in two dimensions which are used to gauge the accuracy and efficiency of the proposed LDG methods.

[11]  arXiv:1801.05879 [pdf, other]
Title: Analysis of the Vanishing Moment Method and its Finite Element Approximations for Second-order Linear Elliptic PDEs in Non-divergence Form
Subjects: Numerical Analysis (math.NA)

This paper is concerned with continuous and discrete approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form. The continuous approximation of these equations is achieved through the Vanishing Moment Method (VMM) which adds a small biharmonic term to the PDE. The structure of the new fourth-order PDE is a natural fit for Galerkin-type methods unlike the original second order equation since the highest order term is in divergence form. The well-posedness of the weak form of the perturbed fourth order equation is shown as well as error estimates for approximating the strong solution of the original second-order PDE. A $C^1$ finite element method is then proposed for the fourth order equation, and its existence and uniqueness of solutions as well as optimal error estimates in the $H^2$ norm are shown. Lastly, numerical tests are given to show the validity of the method.

[12]  arXiv:1801.05880 [pdf, ps, other]
Title: Sums of Kloosterman sums over primes in an arithmetic progression
Comments: 19 pages
Subjects: Number Theory (math.NT)

For $q$ prime, $X \geq 1$ and coprime $u,v \in \mathbb{N}$ we estimate the sums \begin{equation*} \sum_{\substack{p \leq X \substack p \equiv u \hspace{-0.25cm} \mod{v} p \text{ prime}}} \text{Kl}_2(p;q), \end{equation*} where $\text{Kl}_2(p;q)$ denotes a normalised Kloosterman sum with modulus $q$. This is a sparse analogue of a recent theorem due to Blomer, Fouvry, Kowalski, Michel and Mili\'cevi\'c showing cancellation amongst sums of Kloosterman sums over primes in short intervals. We use an optimisation argument inspired by Fouvry, Kowalski and Michel. Our argument compares three different bounds for bilinear forms involving Kloosterman sums. The first input in this method is a bilinear bound we prove using uniform asymptotics for oscillatory integrals due to Petrow, Kiral and Young. In contrast with the case when the sum runs over all primes, we exploit cancellation over a sum of stationary phase integrals that result from a Voronoi type summation. The second and third inputs are deep bilinear bounds for Kloosterman sums due to Fouvry-Kowalski-Michel and Kowalski-Michel-Sawin.

[13]  arXiv:1801.05887 [pdf, ps, other]
Title: Uniform Ergodicity for Brownian Motion in a Bounded Convex Set
Authors: Jackson Loper
Subjects: Probability (math.PR)

We consider an n-dimensional Brownian Motion trapped inside a bounded convex set by normally-reflecting boundaries. It is well-known that this process is uniformly ergodic. However, the rates of this ergodicity are not well-understood, especially in the regime of very high-dimensional sets. Here we present new bounds on these rates for convex sets with a given diameter. Our bounds do not depend upon the smoothness of the boundary nor the value of the ambient dimension, n.

[14]  arXiv:1801.05892 [pdf, other]
Title: Evaluating High Order Discontinuous Galerkin Discretization of the Boltzmann Collision Integral in $O(N^2)$ Operations Using the Discrete Fourier Transform
Comments: Submitted to Kinetic and Related Models
Subjects: Numerical Analysis (math.NA)

We present a numerical algorithm for evaluating the Boltzmann collision operator with $O(N^2)$ operations based on high order discontinuous Galerkin discretizations in the velocity variable. To formulate the approach, Galerkin projection of the collision operator is written in the form of a bilinear circular convolution. An application of the discrete Fourier transform allows to rewrite the six fold convolution sum as a three fold weighted convolution sum in the frequency space. The new algorithm is implemented and tested in the spatially homogeneous case, and results in a considerable improvement in speed as compared to the direct evaluation. Simultaneous and separate evaluations of the gain and loss terms of the collision operator were considered. Less numerical error was observed in the conserved quantities with simultaneous evaluation.

[15]  arXiv:1801.05893 [pdf, ps, other]
Title: A very brief introduction to quantum computing and quantum information theory for mathematicians
Authors: J.M. Landsberg
Subjects: History and Overview (math.HO); Quantum Physics (quant-ph)

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references.

[16]  arXiv:1801.05894 [pdf, other]
Title: Deep Learning: An Introduction for Applied Mathematicians
Subjects: History and Overview (math.HO); Learning (cs.LG); Numerical Analysis (math.NA); Machine Learning (stat.ML)

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very brief introduction to the basic ideas that underlie deep learning from an applied mathematics perspective. Our target audience includes postgraduate and final year undergraduate students in mathematics who are keen to learn about the area. The article may also be useful for instructors in mathematics who wish to enliven their classes with references to the application of deep learning techniques. We focus on three fundamental questions: what is a deep neural network? how is a network trained? what is the stochastic gradient method? We illustrate the ideas with a short MATLAB code that sets up and trains a network. We also show the use of state-of-the art software on a large scale image classification problem. We finish with references to the current literature.

[17]  arXiv:1801.05898 [pdf, ps, other]
Title: Brody hyperbolicity of base spaces of certain families of varieties
Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV)

We prove that quasi-projective base spaces of smooth families of minimal varieties of general type with maximal variation do not admit Zariski dense entire curves. We deduce the fact that moduli stacks of polarized varieties of this sort are Brody hyperbolic, answering a special case of a question of Viehweg and Zuo. For two-dimensional bases, we show analogous results in the more general case of families of varieties admitting a good minimal model.

[18]  arXiv:1801.05899 [pdf, ps, other]
Title: On the cycle index and the weight enumerator
Comments: 9 pages
Subjects: Combinatorics (math.CO); Group Theory (math.GR)

In this paper, we introduce the concept of the complete cycle index and discuss a relation with the complete weight enumerator in coding theory. This work was motivated by Cameron's lecture note "Polynomial aspects of codes, matroids and permutation groups."

[19]  arXiv:1801.05907 [pdf, ps, other]
Title: On the constant scalar curvature Kähler metrics, general automorphism group
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)

In this paper, we derive estimates for scalar curvature type equations with more singular right hand side. As an application, we prove Donaldson's conjecture on the equivalence between geodesic stability and existence of cscK when $Aut_0(M,J)\neq0$. Moreover, we also show that when $Aut_0(M,J)\neq0$, the properness of $K$-energy with respect to a suitably defined distance implies the existence of cscK.

[20]  arXiv:1801.05910 [pdf, ps, other]
Title: Dual Third-order Jacobsthal Quaternions
Comments: 13 pages
Subjects: Rings and Algebras (math.RA)

In 2016, Y\"uce and Torunbalc\i\ Ayd\i n \cite{Yuc-Tor} defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jacobsthal-Lucas quaternions. Also, we investigated the relations between the dual third-order Jacobsthal quaternions and third-order Jacobsthal numbers. Furthermore, we gave some their quadratic properties, the summations, the Binet's formulas and Cassini-like identities for these quaternions.

[21]  arXiv:1801.05914 [pdf, ps, other]
Title: The De Bruijn-Newman constant is non-negative
Comments: 44 pages, no figures
Subjects: Number Theory (math.NT)

For each $t \in {\bf R}$, define the entire function $$ H_t(x) := \int_0^\infty e^{tu^2} \Phi(u) \cos(xu)\ du$$ where $\Phi$ is the super-exponentially decaying function $$ \Phi(u) := \sum_{n=1}^\infty (2\pi^2 n^4 e^{9u} - 3\pi n^2 e^{5u} ) \exp(-\pi n^2 e^{4u} ).$$ Newman showed that there exists a finite constant $\Lambda$ (the \emph{de Bruijn-Newman constant}) such that the zeroes of $H_t$ are all real precisely when $t \geq \Lambda$. The Riemann hypothesis is the equivalent to the assertion $\Lambda \leq 0$, and Newman conjectured the complementary bound $\Lambda \geq 0$.
In this paper we establish Newman's conjecture. The argument proceeds by assuming for contradiction that $\Lambda < 0$, and then analyzing the dynamics of zeroes of $H_t$ (building on the work of Csordas, Smith, and Varga) to obtain increasingly strong control on the zeroes of $H_t$ in the range $\Lambda < t \leq 0$, until one establishes that the zeroes of $H_0$ are in local equilibrium, in the sense that locally behave (on average) as if they were equally spaced in an arithmetic progression, with gaps staying close to the global average gap size. But this latter claim is inconsistent with the known results about the local distribution of zeroes of the Riemann zeta function, such as the pair correlation estimates of Montgomery.

[22]  arXiv:1801.05919 [pdf, other]
Title: Rate-Optimal Streaming Codes for Channels with Burst and Isolated Erasures
Comments: shorter version submitted to ISIT 2018
Subjects: Information Theory (cs.IT)

Recovery of data packets from packet erasures in a timely manner is critical for many streaming applications. An early paper by Martinian and Sundberg introduced a framework for streaming codes and designed rate-optimal codes that permit delay-constrained recovery from an erasure burst of length up to $B$. A recent work by Badr et al. extended this result and introduced a sliding-window channel model $\mathcal{C}(N,B,W)$. Under this model, in a sliding-window of width $W$, one of the following erasure patterns are possible (i) a burst of length at most $B$ or (ii) at most $N$ (possibly non-contiguous) arbitrary erasures. Badr et al. obtained a rate upper bound for streaming codes that can recover with a time delay $T$, from any erasure patterns permissible under the $\mathcal{C}(N,B,W)$ model. However, constructions matching the bound were absent, except for a few parameter sets. In this paper, we present an explicit family of codes that achieves the rate upper bound for all feasible parameters $N$, $B$, $W$ and $T$.

[23]  arXiv:1801.05921 [pdf, ps, other]
Title: Operator Norm Moment and Exponential Inequalities for Matrix U-statistics
Subjects: Probability (math.PR)

We present a Rosenthal-type moment bound and a Bernstein-type exponential tail bound for order 1 degenerated matrix U-statistics in operator norm, with explicit factors on dimension dependencies. We show that the moment bound is tight when the U-statistics is of order 2, in which case a matching lower bound can be obtained. Underlying both of these inequalities is a tight expected operator norm bound for matrix Rademacher chaos with a weak logarithm dependency on the dimension and a matching lower bound. Based on the two inequalities, we obtain moment and tail bounds for non-degenerated matrix U-statistics of arbitrary order.

[24]  arXiv:1801.05926 [pdf, ps, other]
Title: The Utility Cost of Robust Privacy Guarantees
Subjects: Information Theory (cs.IT); Cryptography and Security (cs.CR)

Consider a data publishing setting for a data set with public and private features. The objective of the publisher is to maximize the amount of information about the public features in a revealed data set, while keeping the information leaked about the private features bounded. The goal of this paper is to analyze the performance of privacy mechanisms that are constructed to match the distribution learned from the data set. Two distinct scenarios are considered: (i) mechanisms are designed to provide a privacy guarantee for the learned distribution; and (ii) mechanisms are designed to provide a privacy guarantee for every distribution in a given neighborhood of the learned distribution. For the first scenario, given any privacy mechanism, upper bounds on the difference between the privacy-utility guarantees for the learned and true distributions are presented. In the second scenario, upper bounds on the reduction in utility incurred by providing a uniform privacy guarantee are developed.

[25]  arXiv:1801.05928 [pdf, ps, other]
Title: On partitions into squares of distinct integers whose reciprocals sum to 1
Authors: Max A. Alekseyev
Subjects: Number Theory (math.NT); Discrete Mathematics (cs.DM)

In 1963, Graham proved that all integers greater than 77 (but not 77 itself) can be partitioned into distinct positive integers whose reciprocals sum to 1. He further conjectured that for any sufficiently large integer, it can be partitioned into squares of distinct positive integers whose reciprocals sum to 1. In this study, we establish the exact bound for existence of such representations by proving that 8542 is the largest integer with no such partition.

[26]  arXiv:1801.05934 [pdf, other]
Title: Condensation of non-reversible zero-range processes
Authors: Insuk Seo
Comments: 63 pages, 1 figure
Subjects: Probability (math.PR); Mathematical Physics (math-ph)

In this article, we investigate the condensation phenomena for a class of nonreversible zero-range processes on a fixed finite set. By establishing a novel inequality bounding the capacity between two sets, and by developing a robust framework to perform quantitative analysis on the metastability of non-reversible processes, we prove that the condensed site of the corresponding zero-range processes approximately behaves as a Markov chain on the underlying graph whose jump rate is proportional to the capacity with respect to the underlying random walk. The results presented in the current paper complete the generalization of the work of Beltran and Landim [4] on reversible zero-range processes, and that of Landim [22] on totally asymmetric zero-range processes on a one-dimensional discrete torus.

[27]  arXiv:1801.05935 [pdf, other]
Title: Computation of the Maximum Likelihood estimator in low-rank Factor Analysis
Comments: 22 pages, 4 figures
Subjects: Optimization and Control (math.OC); Computation (stat.CO); Machine Learning (stat.ML)

Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood (ML) principle, which seeks to maximize the likelihood under the assumption that the positive definite covariance matrix can be decomposed as the sum of a low rank positive semidefinite matrix and a diagonal matrix with nonnegative entries. This leads to a challenging rank constrained nonconvex optimization problem. We reformulate the low rank ML Factor Analysis problem as a nonlinear nonsmooth semidefinite optimization problem, study various structural properties of this reformulation and propose fast and scalable algorithms based on difference of convex (DC) optimization. Our approach has computational guarantees, gracefully scales to large problems, is applicable to situations where the sample covariance matrix is rank deficient and adapts to variants of the ML problem with additional constraints on the problem parameters. Our numerical experiments demonstrate the significant usefulness of our approach over existing state-of-the-art approaches.

[28]  arXiv:1801.05936 [pdf, ps, other]
Title: Gradient Estimates and Ergodicity for SDEs Driven by Multiplicative Lévy Noises via Coupling
Comments: 34 pages
Subjects: Probability (math.PR)

We consider SDEs driven by multiplicative pure jump L\'{e}vy noises, where L\'evy processes are not necessarily comparable to $\alpha$-stable-like processes. By assuming that the SDE has a unique solution, we obtain gradient estimates of the associated semigroup when the drift term is locally H\"{o}lder continuous, and we establish the ergodicity of the process both in the $L^1$-Wasserstein distance and the total variation, when the coefficients are dissipative for large distances. The proof is based on a new explicit Markov coupling for SDEs driven by multiplicative pure jump L\'{e}vy noises, which is derived for the first time in this paper.

[29]  arXiv:1801.05948 [pdf, other]
Title: Uplink Coverage Performance of an Underlay Drone Cell for Temporary Events
Comments: This work has been submitted to 2018 IEEE International Conference on Communications Workshops (ICC Workshops): Integrating UAVs into 5G
Subjects: Information Theory (cs.IT)

Using a drone as an aerial base station (ABS) to provide coverage to users on the ground is envisaged as a promising solution for beyond fifth generation (beyond-5G) wireless networks. While the literature to date has examined downlink cellular networks with ABSs, we consider an uplink cellular network with an ABS. Specifically, we analyze the use of an underlay ABS to provide coverage for a temporary event, such as a sporting event or a concert in a stadium. Using stochastic geometry, we derive the analytical expressions for the uplink coverage probability of the terrestrial base station (TBS) and the ABS. The results are expressed in terms of (i) the Laplace transforms of the interference power distribution at the TBS and the ABS and (ii) the distance distribution between the ABS and an independently and uniformly distributed (i.u.d.) ABS-supported user equipment and between the ABS and an i.u.d. TBS-supported user equipment. The accuracy of the analytical results is verified by Monte Carlo simulations. Our results show that varying the ABS height leads to a trade-off between the uplink coverage probability of the TBS and the ABS. In addition, assuming a quality of service of 90% at the TBS, an uplink coverage probability of the ABS of over 85% can be achieved, with the ABS deployed at or below its optimal height of typically between 250-500 m for the considered setup.

[30]  arXiv:1801.05951 [pdf, other]
Title: Quadratically Constrained Myopic Adversarial Channels
Subjects: Information Theory (cs.IT)

We study communication in the presence of a jamming adversary where quadratic power constraints are imposed on the transmitter and the jammer. The jamming signal is assumed to be a function of the codebook, and a noncausal but noisy observation of the transmitted codeword. For a certain range of the noise-to-signal ratios (NSRs) of the transmitter and the jammer, we are able to characterize the capacity of this channel under deterministic encoding. For the remaining NSR regimes, we determine the capacity under the assumption of a small amount of common randomness (at most $\mathcal O(\log(n))$ bits in one sub-regime, and at most $\mathcal O(n^2)$ bits in the other sub-regime) available to the encoder-decoder pair. Our proof techniques involve a novel myopic list-decoding result for achievability and a Plotkin-type push attack for the converse in a subregion of the NSRs, which may be of independent interest.

[31]  arXiv:1801.05952 [pdf, ps, other]
Title: Convergence rates of truncated EM scheme for NSDDEs
Authors: Li Tan, Chenggui Yuan
Subjects: Numerical Analysis (math.NA)

This paper is concerned with strong convergence of the truncated Euler-Maruyama scheme for neutral stochastic differential delay equations driven by Brownian motion and pure jumps respectively. Under local Lipschitz condition, convergence rates of the truncated EM scheme are given.

[32]  arXiv:1801.05963 [pdf, ps, other]
Title: Formula for Calculating the Wiener Polarity Index
Authors: Niko Tratnik
Subjects: Combinatorics (math.CO)

In this paper, we generalize the result of Behmaram, Yousefi-Azari, and Ashrafi proved in 2012 for calculating the Wiener polarity index of a graph. An important advantage of our generalization is that it can be used for graphs that contain 4-cycles and also for graphs whose different cycles have more than one common edge. In addition, using the main result a closed formula for the Wiener polarity index is derived for phenylenes and recalculated for catacondensed benzenoid graphs.

[33]  arXiv:1801.05965 [pdf, ps, other]
Title: Complexity of Combinations of Qualitative Constraint Satisfaction Problems
Subjects: Logic (math.LO); Computational Complexity (cs.CC)

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures. Nelson and Oppen presented conditions that imply decidability (or polynomial-time decidability) of $\mathrm{CSP}(T_1 \cup T_2)$ under the assumption that $\mathrm{CSP}(T_1)$ and $\mathrm{CSP}(T_2)$ are decidable (or polynomial-time decidable). We show that for a large class of $\omega$-categorical theories $T_1, T_2$ the Nelson-Oppen conditions are not only sufficient, but also necessary for polynomial-time tractability of $\mathrm{CSP}(T_1 \cup T_2)$ (unless P=NP).

[34]  arXiv:1801.05966 [pdf, ps, other]
Title: Towards probabilistic partial metric spaces: Diagonals between distance distributions
Comments: 19 pages
Subjects: General Topology (math.GN); Category Theory (math.CT)

The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the quantaloid of diagonals between distance distributions, which is expected to establish the categorical foundation of probabilistic partial metric spaces. Observing that the quantale of distance distributions w.r.t. an arbitrary continuous t-norm is non-divisible, we precisely characterize diagonals between distance distributions, and prove that one-step functions are the only distance distributions on which the set of diagonals coincides with the generated down set.

[35]  arXiv:1801.05973 [pdf, other]
Title: A combinatorial approach to Rauzy-type dynamics II: the labelling method and a second proof of the KZB classification theorem
Comments: 76 pages, 42 figure, 3 tables
Subjects: Combinatorics (math.CO)

Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example (the Rauzy dynamics) concerns an action on permutations, associated to interval exchange transformations (IET) for the Poincar\'e map on compact orientable translation surfaces. The equivalence classes on the objects induced by the group action have been classified by Kontsevich and Zorich, and by Boissy through methods involving both combinatorics algebraic geometry, topology and dynamical systems. Our first paper proposed an ad hoc combinatorial proof of this classification. In this paper we define a general method, called the labelling method, which allows one to classify Rauzy-type dynamics in a much more systematic way. We apply the method to the Rauzy dynamics and obtain a second combinatorial proof of the classification.

[36]  arXiv:1801.05975 [pdf, ps, other]
Title: Groups whose elements are not conjugate to their powers
Comments: 6 pages
Subjects: Group Theory (math.GR)

We call a finite group irrational if none of its elements is conjugate to a distinct power of itself. We prove that those groups are solvable and describe certain classes of these groups, where the above property is only required for $p$-elements, for $p$ from a prescribed set of primes.

[37]  arXiv:1801.05977 [pdf, ps, other]
Title: An FFT-based algorithm for efficient computation of Green's functions for the Helmholtz and Maxwell's equations in periodic domains
Subjects: Numerical Analysis (math.NA)

The integral equation method is widely used in numerical simulations of 2D/3D acoustic and electromagnetic scattering problems, that needs a large number of values of the Green's functions. A significant topic is the scattering problems in periodic domains, that the corresponding Green's functions are quasi-periodic. The quasi-periodic Green's functions are defined by series that converge too slowly to be used for calculations. Many mathematicians have developed several efficient numerical methods to calculate quasi-periodic Green's functions. In this paper, we will introduce a new FFT-based fast algorithm to compute the 2D/3D quasi-periodic Green's functions for both Helmholtz equations and Maxwell's equations. The convergence results and error estimates are also investigated in this paper. At the end of this paper, the numerical examples will be given to show that when large number of values are needed, the new algorithm is very competitive.

[38]  arXiv:1801.05979 [pdf, ps, other]
Title: On Krull-Gabriel dimension and Galois coverings
Subjects: Representation Theory (math.RT)

Assume that $K$ is an algebraically closed field, $R$ a locally support-finite locally bounded $K$-category, $G$ a torsion-free admissible group of $K$-linear automorphisms of $R$ and $A=R\slash G$. We show that the Krull-Gabriel dimension $KG(R)$ of $R$ is finite if and only if the Krull-Gabriel dimension $KG(A)$ of $A$ is finite. In these cases $KG(R)=KG(A)$. We apply this result to determine the Krull-Gabriel dimension of standard selfinjective algebras of polynomial growth. Finally, we show that there are no super-decomposable pure-injective modules over standard selfinjective algebras of domestic type.

[39]  arXiv:1801.05981 [pdf, other]
Title: Doubling Algorithms for Stationary Distributions of Fluid Queues: A Probabilistic Interpretation
Subjects: Probability (math.PR); Numerical Analysis (math.NA)

Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the literature as the matrix $\Psi$. Here, we present a probabilistic interpretation of the family of algorithms known as \emph{doubling}, which are currently the most effective algorithms for computing the return probability matrix $\Psi$.
To this end, we first revisit the links described in \cite{ram99, soares02} between fluid queues and Quasi-Birth-Death processes; in particular, we give new probabilistic interpretations for these connections. We generalize this framework to give a probabilistic meaning for the initial step of doubling algorithms, and include also an interpretation for the iterative step of these algorithms. Our work is the first probabilistic interpretation available for doubling algorithms.

[40]  arXiv:1801.05989 [pdf, ps, other]
Title: Code Constructions for Distributed Storage With Low Repair Bandwidth and Low Repair Complexity
Subjects: Information Theory (cs.IT)

We present the construction of a family of erasure correcting codes for distributed storage systems that achieve low repair bandwidth and low repair complexity. The construction is based on two classes of codes, where the primary goal of the first class of codes is to achieve a good fault tolerance, while the second class of codes aims at reducing the repair bandwidth and the repair complexity. The repair procedure is a two-step procedure where parts of the failed node are repaired in the first step using the first code. The downloaded symbols during the first step are cached in the memory and used to repair the remaining erased data symbols at no additional read cost during the second step of the repair process. The first class of codes is based on maximum distance separable (MDS) codes modified using piggybacks, while the second class of codes is designed to reduce the number of additional symbols that need to be downloaded to repair the remaining erased symbols. We show that the proposed codes achieve better repair bandwidth compared to MDS, Piggyback, and local reconstruction codes, while a better repair complexity is achieved when compared to MDS, Zigzag, and Piggyback codes.

[41]  arXiv:1801.05993 [pdf, ps, other]
Title: Direct sampling method for imaging small dielectric inhomogeneities: analysis and improvement
Comments: 18 pages
Subjects: Numerical Analysis (math.NA)

The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis of the behavior of the DSM has not been provided yet. Such an analysis is proposed here within the framework of the asymptotic hypothesis in the 2D case leading to the expression of the DSM indicator function in terms of the Bessel function of order zero and the sizes, shapes and permittivities of the inhomogeneities. Thanks to this analytical expression the limitations of the DSM method when one of the inhomogeneities is smaller and/or has lower permittivity than the others is exhibited and illustrated. An improved DSM is proposed to overcome this intrinsic limitation in the case of multiple incident waves. Then we show that both the traditional and improved DSM are closely related to a normalized version of the Kirchhoff migration. The theoretical elements of our proposal are supported by various results from numerical simulations with synthetic and experimental data.

[42]  arXiv:1801.05996 [pdf, ps, other]
Title: $\varepsilon$-Approximability of Harmonic Functions in $L^p$ Implies Uniform Rectifiability
Subjects: Analysis of PDEs (math.AP)

Suppose that $\Omega \subset \mathbb{R}^{n+1}$, $n \ge 2$, is an open set satisfying the corkscrew condition with an $n$-dimensional ADR boundary, $\partial \Omega$. In this note, we show that if harmonic functions are $\varepsilon$-approximable in $L^p$ for any $p > n/(n-1)$, then $\partial \Omega$ is uniformly rectifiable. Combining our results with those in [HT] (Hofmann-Tapiola) gives us a new characterization of uniform rectifiability which complements the recent results in [HMM] (Hofmann-Martell-Mayboroda), [GMT] (Garnett-Mourgoglou-Tolsa) and [AGMT] (Azzam-Garnett-Mourgoglou-Tolsa).

[43]  arXiv:1801.05998 [pdf, other]
Title: A single server queue with batch arrivals and semi-Markov services
Subjects: Probability (math.PR)

We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and serves as a vehicle to display our results. The sequence of service times is governed by a modulating process $J(t)$. The state of $J(\cdot)$ at a service initiation time determines the joint distribution of the subsequent service duration and the state of $J(\cdot)$ at the next service initiation.
Several earlier works have imposed technical conditions, on the zeros of a matrix determinant arising in the analysis, that are required in the computation of the stationary queue length probabilities. The imposed conditions in several of these articles are difficult or impossible to verify. Without such assumptions, we determine both the transient and the steady-state joint distribution of the number of customers immediately after a departure and the state of the process $J(t)$ at the start of the next service.
We numerically investigate how the mean queue length is affected by variability in the number of customers that arrive during a single service time. Our main observations here are that increasing variability may {\em reduce} the mean queue length, and that the Markovian dependence of service times can lead to large queue lengths, even if the system is not in heavy traffic.

[44]  arXiv:1801.05999 [pdf, ps, other]
Title: On the characterisations of wave front sets via the short-time Fourier transform
Subjects: Analysis of PDEs (math.AP)

It is well known that the classical and Sobolev wave fronts were extended into non-equivalent global versions by the use of the short-time Fourier transform. In this very short paper we give complete characterisations of initial wave front sets via the short-time Fourier transform.

[45]  arXiv:1801.06001 [pdf, ps, other]
Title: Generalized power central group identities in almost subnormal subgroups of $\GL_n(D)$
Comments: 12 pages
Subjects: Rings and Algebras (math.RA)

In this paper, we study almost subnormal subgroups of the general linear group $\GL_n(D)$ of degree $n\ge 1$ over a division ring $D$ that satisfy a generalized power central group identity.

[46]  arXiv:1801.06002 [pdf, ps, other]
Title: Short walk adventures
Comments: 14 pages
Subjects: Number Theory (math.NT); Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA); K-Theory and Homology (math.KT); Probability (math.PR)

We review recent development of short uniform random walks, with a focus on its connection to (zeta) Mahler measures and modular parametrisation of the density functions. Furthermore, we extend available "probabilistic" techniques to cover a variation of random walks and reduce some three-variable Mahler measures, which are conjectured to evaluate in terms of $L$-values of modular forms, to hypergeometric form.

[47]  arXiv:1801.06004 [pdf, ps, other]
Title: Scattered classes of graphs
Comments: 30 pages, 4 figures
Subjects: Combinatorics (math.CO)

For a class $\mathcal C$ of graphs $G$ equipped with functions $f_G$ defined on subsets of $E(G)$ or $V(G)$, we say that $\mathcal{C}$ is $k$-scattered with respect to $f_G$ if there exists a constant $\ell$ such that for every graph $G\in \mathcal C$, the domain of $f_G$ can be partitioned into subsets of size at most $k$ so that the union of every collection of the subsets has $f_G$ value at most $\ell$. We present structural characterizations of graph classes that are $k$-scattered with respect to several graph connectivity functions. In particular, our theorem for cut-rank functions provides a rough structural characterization of graphs having no $mK_{1,n}$ vertex-minors, which allows us to prove that such graphs have bounded linear rank-width.

[48]  arXiv:1801.06006 [pdf, ps, other]
Title: Bounds for higher topological complexity of real projective space implied by BP
Authors: Donald M Davis
Subjects: Algebraic Topology (math.AT)

We use Brown-Peterson cohomology to obtain lower bounds for the higher topological complexity, TC_k(RP^n), of real projective spaces, which are often much stronger than those implied by ordinary mod-2 cohomology.

[49]  arXiv:1801.06008 [pdf, ps, other]
Title: Convergence of the solutions of the discounted Hamilton-Jacobi equation: a counterexample
Authors: Bruno Ziliotto
Subjects: Analysis of PDEs (math.AP); Optimization and Control (math.OC)

This paper provides a counterexample about the asymptotic behavior of the solutions of a discounted Hamilton-Jacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1-dimensional continuous and coercive Hamiltonian.

[50]  arXiv:1801.06010 [pdf, ps, other]
Title: Divisibility properties of motivic cohomology
Authors: Bruno Kahn
Comments: 8 pages
Subjects: Algebraic Geometry (math.AG); K-Theory and Homology (math.KT)

We extend results of Colliot-Th\'el\`ene and Raskind on the $\mathcal{K}_2$-cohomology of smooth projective varieties over a separably closed field $k$ to the \'etale motivic cohomology of smooth, not necessarily projective, varieties over $k$. Some consequences are drawn, such as the degeneration of the Bloch-Lichtenbaum spectral sequence for any field containing $k$.

[51]  arXiv:1801.06013 [pdf, ps, other]
Title: Inverse of infinite Hankel moment matrices
Comments: 62 pages
Subjects: Classical Analysis and ODEs (math.CA)

A Hamburger moment sequence (s_n) is characterized by positive definiteness of the infinite Hankel matrix \mathcal H=\{s_{m+n}\}. In the indeterminate case, where different measures have the same moments, there exists an infinite symmetric matrix \mathcal A=\{a_{j,k}\} given by the reproducing kernel K(z,w)=\sum_{n=0}^\infty P_n(z)P_n(w)=\sum_{j,k=0}^\infty a_{j,k}z^jw^k, defined in terms of the orthonormal polynomials P_n(z). We say that the matrix product \mathcal A\mathcal H is absolutely convergent, if all elements of \mathcal A\mathcal H are defined by absolutely convergent series. We study the question if the matrix product \mathcal A\mathcal H is absolutely convergent and yields the identity matrix \mathcal I.
We prove that this is always the case, when the moment problem is symmetric and xP_n(x)=b_nP_{n+1}(x)+b_{n-1}P_{n-1}(x) for a sequence (b_n) such that b_{n-1}/b_n\le q<1 for n sufficiently large, hence in particular for eventually log-convex sequences (b_n) such that \sum 1/b_n<\infty. It also holds for certain eventually log-concave sequences (b_n) including b_n=(n+1)^c, c>3/2. The latter is based on new estimates for the symmetrized version of a cubic birth-and-death process studied by Valent and co-authors, and in this case \mathcal A\mathcal H is not absolutely convergent.
The general results of the paper are based on a study of two scale invariant sequences (U_n) and (V_n). Here, U_n=s_{2n}/(b_0b_1\ldots b_{n-1})^2 is defined for any moment problem, while V_n=b_0b_1\ldots b_{n-1}c_n only makes sense for indeterminate moment problems, because c_n:=\sqrt{a_{n,n}}. A major result is that (U_n) and (V_n) are bounded for symmetric indeterminate moment problems for which b_{n-1}/b_n\le q<1 for n sufficiently large.

[52]  arXiv:1801.06016 [pdf, other]
Title: On improving the numerical convergence of highly nonlinear elasticity problems
Subjects: Numerical Analysis (math.NA)

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and loads are restricted to small load step sizes. In this work, we present a new method to transform the discretized governing equations so that the transformed problem has significantly reduced nonlinearity and, therefore, Newton solvers exhibit improved convergence properties. We study exponential-type nonlinearity in soft tissues and geometric nonlinearity in compression, and propose different formulations for the two problems. We test the new formulations in several numerical examples and show an improvement in convergence, even when extremely large load steps are applied. The proposed framework is generic and can be applied to other types of nonlinearities as well.

[53]  arXiv:1801.06021 [pdf, ps, other]
Title: Li-Yau inequality for unbounded Laplacian on graphs
Comments: 19 pages
Subjects: Differential Geometry (math.DG)

In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature-dimension inequality $CDE'(n,K)$, which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, heat kernel bounds and Cheng's eigenvalue estimate. These are first kind of results on this direction for unbounded Laplacian on graphs.

[54]  arXiv:1801.06022 [pdf, ps, other]
Title: Reconstruction Codes for DNA Sequences with Uniform Tandem-Duplication Errors
Subjects: Information Theory (cs.IT)

DNA as a data storage medium has several advantages, including far greater data density compared to electronic media. We propose that schemes for data storage in the DNA of living organisms may benefit from studying the reconstruction problem, which is applicable whenever multiple reads of noisy data are available. This strategy is uniquely suited to the medium, which inherently replicates stored data in multiple distinct ways, caused by mutations. We consider noise introduced solely by uniform tandem-duplication, and utilize the relation to constant-weight integer codes in the Manhattan metric. By bounding the intersection of the cross-polytope with hyperplanes, we prove the existence of reconstruction codes with greater capacity than known error-correcting codes, which we can determine analytically for any set of parameters.

[55]  arXiv:1801.06026 [pdf, other]
Title: On power subgroups of Dehn twists in hyperelliptic mapping class groups
Authors: Wataru Yuasa
Comments: 16 pages
Subjects: Geometric Topology (math.GT); Group Theory (math.GR); Quantum Algebra (math.QA)

This paper contains two topics, the index of a power subgroup in the mapping class group $\mathcal{M}(0,2n)$ of a $2n$-punctured sphere and in the hyperelliptic mapping class group $\Delta(g,0)$ of an oriented closed surface of genus $g$. The main tool is a projective representation of $\mathcal{M}(0,2n)$ obtained through the Kauffman bracket skein module. For $\mathcal{M}(0,2n)$, we prove that the normal closure of the fifth power of a half-twist has infinite index. This is the remaining case of a Masbaum's work. For $\Delta(g,0)$, we consider the normal closure of $m$-th powers of Dehn twists along all symmetric simple closed curves. We show the subgroup has infinite index if $m\geq 5$ and $m\neq 6$ for any $g\geq 2$.

[56]  arXiv:1801.06034 [pdf, ps, other]
Title: Boolean degree 1 functions on some classical association schemes
Comments: 20 pages
Subjects: Combinatorics (math.CO)

We investigate Boolean degree 1 functions for several classical association schemes, including Johnson graphs, Grassmann graphs, graphs from polar spaces, and bilinear forms graphs, as well as some other domains such as multislices (Young subgroups of the symmetric group). In some settings, Boolean degree 1 functions are also known as \textit{completely regular strength 0 codes}, \textit{Cameron--Liebler line classes}, and \textit{tight sets}.
We classify all Boolean degree $1$ functions on the multislice. On the Grassmann scheme $J_q(n, k)$ we show that all Boolean degree $1$ functions are trivial for $n \geq 5$, $k, n-k \geq 2$ and $q \in \{ 2, 3, 4 \}$, and that for general $q$, the problem can be reduced to classifying all Boolean degree $1$ functions on $J_q(n, 2)$. We also consider polar spaces and the bilinear forms graphs, giving evidence that all Boolean degree $1$ functions are trivial for appropriate choices of the parameters.

[57]  arXiv:1801.06035 [pdf, other]
Title: The motivic Mahowald invariant
Authors: J.D. Quigley
Comments: 39 pages
Subjects: Algebraic Topology (math.AT)

The classical Mahowald invariant is a method for producing nonzero classes in the stable homotopy groups of spheres from classes in lower stems. We study the Mahowald invariant in the setting of motivic stable homotopy theory over $Spec(\mathbb{C})$. We compute a motivic version of the $C_2$-Tate construction for various motivic spectra, and show that this construction produces "blueshift" in these cases. We use these computations to show that the Mahowald invariant of $\eta^i$, $i \geq 1$, is the first element in Adams filtration $i$ of the $w_1$-periodic families constructed by Andrews ~\cite{And14}. This provides an exotic periodic analog of Mahowald and Ravenel's computation ~\cite{MR93} that the classical Mahowald invariant of $2^i$, $i \geq 1$, is the first element in Adams filtration $i$ of the $v_1$-periodic families constructed by Adams ~\cite{Ada66}.

[58]  arXiv:1801.06040 [pdf, ps, other]
Title: The Higson-Roe sequence for étale groupoids. I. Dual algebras and compatibility with the BC map
Comments: 30 pages
Subjects: K-Theory and Homology (math.KT); Operator Algebras (math.OA)

We introduce the dual Roe algebras for proper \'{e}tale groupoid actions and deduce the expected Higson-Roe short exact sequence. When the action is cocompact, we show that the Roe $C^*$-ideal of locally compact operators is Morita equivalent to the reduced $C^*$-algebra of our groupoid, and we further identify the boundary map of the associated periodic six-term exact sequence with the Baum-Connes map, via a Paschke-Higson map for groupoids. For proper actions on continuous families of manifolds of bounded geometry, we associate with any $G$-equivariant Dirac-type family, a coarse index class which generalizes the Paterson index class and also the Moore-Schochet Connes' index class for laminations.

[59]  arXiv:1801.06045 [pdf, ps, other]
Title: Ordered group-valued probability, positive operators, and integral representations
Authors: T. Kroupa
Subjects: Functional Analysis (math.FA); Logic (math.LO)

Probability maps are additive and normalised maps taking values in the unit interval of a lattice ordered Abelian group. They appear in theory of affine representations and they are also a semantic counterpart of Hajek's probability logic. In this paper we obtain a correspondence between probability maps and positive operators between certain Riesz spaces, which extends the well-known representation theorem of real-valued MV-algebraic states by positive linear functionals. When the codomain algebra contains all continuous functions, the set of all probability maps is convex, and we prove that its extreme points coincide with homomorphisms. We also show that probability maps can be viewed as a collection of states indexed by maximal ideals of a codomain algebra and we characterise this collection in special cases.

[60]  arXiv:1801.06056 [pdf, ps, other]
Title: The user's guide project: giving experiential context to research papers
Journal-ref: Journal of Humanistic Mathematics, Volume 5 Issue 2 (July 2015), pages 186-188
Subjects: History and Overview (math.HO)

This paper was written in 2015, and published in the Journal of Humanistic Mathematics. This paper announces the first issue (2015) of Enchiridion: Mathematics User's Guides, a project to produce peer-reviewed User's Guides as companions to published papers. These User's Guides are meant to explain the key insights and organizing principles in their companion papers, the metaphors and imagery used by the authors, the story of the development of the companion papers, and a colloquial summary appropriate for a non-mathematical audience. Examples of User's Guides can be found at https://mathusersguides.com/

[61]  arXiv:1801.06058 [pdf, other]
Title: Output Feedback Control Based on State and Disturbance Estimation
Comments: 10 pages, 3 figures, journal (accepted for publication)
Subjects: Optimization and Control (math.OC)

Recently developed control methods with strong disturbance rejection capabilities provide a useful option for control design. The key lies in a general concept of disturbance and effective ways to estimate and compensate the disturbance. This work extends the concept of disturbance as the mismatch between a system model and the true dynamics, and estimates and compensates the disturbance for multi-input multi-output linear/nonlinear systems described in a general form. The results presented do not need to assume the disturbance to be independent of the control inputs or satisfy a certain matching condition, and do not require the system to be expressible in an integral canonical form as required by algorithms previously described in literature. The estimator and controller are designed under a state tracking framework, and sufficient conditions for the closed-loop stability are presented. The performance of the resulting controller relies on a co-design of the system model, the state and disturbance observer, and the controller. Numerical experiments on a first-order system and an inverted pendulum under uncertainties are used to illustrate the control design method and demonstrate its efficacy.

[62]  arXiv:1801.06060 [pdf, ps, other]
Title: Flat ideals in the unit interval with the canonical fuzzy order
Comments: 8 pages
Subjects: General Mathematics (math.GM)

A characterization of flat ideals in the unit interval with the canonical fuzzy order is obtained with the help of the ordinal sum decomposition of continuous t-norms. This characterization will be useful in the study of topological and domain theoretic properties of fuzzy orders.

[63]  arXiv:1801.06064 [pdf, ps, other]
Title: Characterizations of the compactness of commutators associated with Lipschitz functions
Comments: arXiv admin note: text overlap with arXiv:1712.08292
Subjects: Classical Analysis and ODEs (math.CA)

We first give some characterizations of the the compact iterated commutators associated with Lipschitzs functions. Our results are even new in the unweighted setting for the first order commutators.

[64]  arXiv:1801.06065 [pdf, other]
Title: Wildly Compatible Systems and Six Operations
Authors: Ning Guo
Comments: 16 pages, comments welcomed !
Subjects: Algebraic Geometry (math.AG)

Let $S$ be an excellent regular scheme and let $X$ be a scheme separated and of finite type over $S$. Let $K_c(X, \mathbb{F}_{\lambda})$ be the Grothendieck ring of $\mathbb{F}_{\lambda}$-constructible sheaves on $X$, where $\mathbb{F}_{\lambda}$ is the finite field with $\lambda$ elements. Given an index set $I$ and for certain $\mathbb{Q}$-vector subspaces $V\subset \prod_{i\in I}\mathbb{Q}_{\lambda_i}$, we define wildly compatible systems of virtual constructible sheaves on $X$. The main result is that for $\dim S \leq 1$, wildly compatible systems are preserved by Grothendieck's six operations and Verdier's duality, with further assumption that $V$ is a sub-algebra for derived Hom and tensor product. Finally, when $X$ is a curve over a finite field we prove all $\ell$-adic compatible systems will give wildly compatible systems.

[65]  arXiv:1801.06071 [pdf, ps, other]
Title: Quiver varieties and symmetric pairs
Authors: Yiqiang Li
Comments: 49 pages
Subjects: Representation Theory (math.RT); Symplectic Geometry (math.SG)

We study fixed-point loci of Nakajima varieties under symplectomorphisms and their anti-symplectic cousins, which are compositions of a diagram automorphism, a reflection functor and a transpose defined by certain bilinear forms. These subvarieties provide a natural home for geometric representation theory of symmetric pairs. In particular, the cohomology of a Steinberg-type variety of the symplectic fixed-point subvarieties is conjecturally related to the universal enveloping algebra of the subalgebra in a symmetric pair. The latter symplectic subvarieties are further used to construct geometrically an action of a twisted Yangian on torus equivariant cohomology of Nakajima varieties. In type $A$ case, these subvarieties provide a quiver model for partial Springer resolutions of nilpotent Slodowy slices of classical groups and associated symmetric spaces, which leads to a rectangular symmetry and a refinement of Kraft-Procesi row/column removal reductions.

[66]  arXiv:1801.06072 [pdf, other]
Title: On a conjecture about Morita algebras
Subjects: Representation Theory (math.RT)

We give an example of a Morita algebra $A$ with a tilting module $T$ such that the algebra $End_A(T)$ has dominant dimension at least two but is not a Morita algebra. This provides a counterexample to a conjecture by Chen and Xi from \cite{CX}.

[67]  arXiv:1801.06076 [pdf, ps, other]
Title: Commutativity in Lagrangian and Hamiltonian Mechanics
Comments: 10 pages
Subjects: Mathematical Physics (math-ph)

The main result of this note is a characterization of the Poisson commutativity of Hamilton functions in terms of their principal action functions.

[68]  arXiv:1801.06078 [pdf, ps, other]
Title: Noncrossing partitions, Bruhat order and the cluster complex
Subjects: Combinatorics (math.CO)

We introduce two order relations on finite Coxeter groups which refine the absolute and the Bruhat order, and establish some of their main properties. In particular we study the restriction of these orders to noncrossing partitions and show that the intervals for these orders can be enumerated in terms of the cluster complex. The properties of our orders permit to revisit several results in Coxeter combinatorics, such as the Chapoton triangles and how they are related, the enumeration of reflections with full support, the bijections between clusters and noncrossing partitions.

[69]  arXiv:1801.06083 [pdf, ps, other]
Title: The $q$-Onsager algebra and the universal Askey-Wilson algebra
Authors: Paul Terwilliger
Comments: 21 pages
Subjects: Quantum Algebra (math.QA)

Recently Pascal Baseilhac and Stefan Kolb obtained a PBW basis for the $q$-Onsager algebra $\mathcal O_q$. They defined the PBW basis elements recursively, and it is obscure how to express them in closed form. To mitigate the difficulty, we bring in the universal Askey-Wilson algebra $\Delta_q$. There is a natural algebra homomorphism $\natural :\mathcal O_q \to \Delta_q$. We apply $\natural $ to the above PBW basis, and express the images in closed form. Our results make heavy use of the Chebyshev polynomials of the second kind.

[70]  arXiv:1801.06088 [pdf, ps, other]
Title: On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem
Authors: Kai Zhao, Wei Cheng
Subjects: Analysis of PDEs (math.AP)

We study the representation formulae for the fundamental solutions and viscosity solutions of the Hamilton-Jacobi equations of contact type. We also obtain a vanishing contact structure result for relevant Cauchy problems which can be regarded as an extension to the vanishing discount problem.

[71]  arXiv:1801.06089 [pdf, ps, other]
Title: Level Reciprocity in the twisted second moment of Rankin-Selberg L-functions
Comments: 13 pages
Subjects: Number Theory (math.NT)

We prove an exact formula for the second moment of Rankin-Selberg $L$-functions $L(1/2,f \times g)$ twisted by $\lambda_f(p)$, where $g$ is a fixed holomorphic cusp form and $f$ is summed over automorphic forms of a given level $q$. The formula is a reciprocity relation that exchanges the twist parameter $p$ and the level $q$. The method involves the Bruggeman/Kuznetsov trace formula on both ends; finally the reciprocity relation is established by an identity of sums of Kloosterman sums.

[72]  arXiv:1801.06095 [pdf, ps, other]
Title: A Gauss-Jacobi Kernel Compression Scheme for Fractional Differential Equations
Authors: Daniel Baffet
Subjects: Numerical Analysis (math.NA)

A scheme for approximating the kernel $w$ of the fractional $\alpha$-integral by a linear combination of exponentials is proposed and studied. The scheme is based on the application of a composite Gauss-Jacobi quadrature rule to an integral representation of $w$. This results in an approximation which converges rapidly in the number $J$ of quadrature nodes associated with each interval of the composite rule. Using error analysis for Gauss-Jacobi quadratures for analytic functions, an estimate of the relative pointwise error is obtained. The estimate shows that the number of terms required for the approximation to satisfy a prescribed error tolerance is bounded for all $\alpha\in(0,1)$, and that $J$ is bounded uniformly for $\alpha\in(0,1)$, $T>0$, and $

[73]  arXiv:1801.06103 [pdf, other]
Title: Cut Finite Elements for Convection in Fractured Domains
Subjects: Numerical Analysis (math.NA)

We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$ dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem can be formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is based on using a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.

[74]  arXiv:1801.06110 [pdf, other]
Title: Least primitive root and simultaneous power-non residues
Authors: Andrea Sartori
Comments: 15 pages, comments welcome
Subjects: Number Theory (math.NT)

Let $p$ be a prime and let $g(p)$ be the least primitive root modulo $p$. We prove that for any $\epsilon>0$ \begin{align} g(p)\ll p^{\frac{1}{4\sqrt{e}}+\epsilon} \nonumber \end{align} for most large enough primes $p$ such that $p-1$ does not have small prime factors, but 2.

[75]  arXiv:1801.06112 [pdf, ps, other]
Title: Ideals modulo p
Subjects: Commutative Algebra (math.AC)

The main focus of this paper is on the problem of relating an ideal I in the polynomial ring Q[x_1,..., x_n] to a corresponding ideal in F_p[x_1, ..., x_n] where p is a prime number; in other words, the reduction modulo p of I. We define a new notion of sigma-good prime for I which depends on the term ordering sigma, and show that all but finitely many primes are good for all term orderings. We relate our notion of sigma-good primes to some other similar notions already in the literature. One characteristic of our approach is that enables us to detect some bad primes, a distinct advantage when using modular methods.

[76]  arXiv:1801.06125 [pdf, ps, other]
Title: Classifying braidings on fusion categories
Authors: Dmitri Nikshych
Comments: 14 pages
Subjects: Quantum Algebra (math.QA); Representation Theory (math.RT)

We show that braidings on a fusion category $\mathcal{C}$ correspond to certain fusion subcategories of the center of $\mathcal{C}$ transversal to the canonical Lagrangian algebra. This allows to classify braidings on non-degenerate and group-theoretical fusion categories.

[77]  arXiv:1801.06127 [pdf, other]
Title: Reduced order models for fluid-structure interaction problems with applications in haemodynamics
Subjects: Numerical Analysis (math.NA)

This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical discretisation. The resulting method is both accurate and computationally cheap. This goal is achieved by means of two levels of reduction: first, we describe the model equations with a reduced mathematical formulation which allows to write the fluid-structure interaction problem as a Navier-Stokes system with non-standard boundary conditions; second, we employ numerical reduction techniques to further and drastically lower the computational costs. The numerical reduction is obtained coupling two well-known techniques: the proper orthogonal decomposition and the reduced basis method, in particular the greedy algorithm. We start by reducing the numerical dimension of the problem at hand with a proper orthogonal decomposition and we measure the system energy with specific norms; this allows to take into account the different orders of magnitude of the state variables, the velocity and the pressure. Then, we introduce a strategy based on a greedy procedure which aims at enriching the reduced discretization space with low offline computational costs. As application, we consider a realistic haemodynamics problem with a perturbation in the boundary conditions and we show the good performances of the reduction techniques presented in the paper. The gains obtained in term of CPU time are of three orders of magnitude.

[78]  arXiv:1801.06130 [pdf, ps, other]
Title: Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds II: Fano 3-folds
Authors: Yalong Cao
Comments: 15 pages
Subjects: Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th)

In analogy with the Gopakumar-Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi-Yau 4-folds using Gromov-Witten theory and conjectured their integrality. In a joint work with Maulik and Toda, the author conjectured their genus zero invariants are $\mathrm{DT_4}$ invariants of one dimensional stable sheaves. In this paper, we study this conjecture on the total space of canonical bundle of a Fano 3-fold $Y$, which reduces to a relation between twisted GW and $\mathrm{DT_3}$ invariants on $Y$. Examples are computed for both compact and non-compact Fano 3-folds to support our conjecture.

[79]  arXiv:1801.06143 [pdf, other]
Title: TASEP fluctuations with soft-shock initial data
Subjects: Probability (math.PR); Mathematical Physics (math-ph)

The totally asymmetric simple exclusion process (TASEP) has a persistent shock (jump discontinuity) in its macroscopic particle density if the initial density is an appropriate step function. It serves as a microscopic model of shocks in Burgers' equation.
This paper studies fluctuations of the shock in KPZ setting, or soft shock, whereby the step size is tuned with time in KPZ space-time scaling. In the double limit of large time followed by step size, the fluctuation of a particle at the soft shock converges to the maximum of two independent GOE Tracy-Widom random variables. More generally, joint fluctuations of particles near the soft shock are aptly combined maxima of these two random variables.
The fluctuations of the hard shock are expectedly the same and will be subject of future work. Proofs rely on determinantal formulae for TASEP and the KPZ fixed point.

[80]  arXiv:1801.06148 [pdf, ps, other]
Title: Characterization of probability distribution convergence in Wasserstein distance by $L^{p}$-quantization error function
Subjects: Probability (math.PR)

We establish the condition for probability measure characterization by $L^{p}$-quantization error function in $\mathbb{R}^{d}$. There are two types of characterization: the static characterization for the identity of two probability measures, and the characterization for the convergence of probability measure sequence for the Wasserstein distance of order $p$. We show that the general probability measure characterization for any order $p$ with any norm on $\mathbb{R}^{d}$ can be established with a finite level $N$ by a geometrical approach based on the Vorono\"i diagram. We also show that in the case of order $p=2$ for a separable Hilbert space equipped with Hilbert norm, the condition of probability measure characterization on the level $N$ can be reduced to $N=2$ and this condition can be reduced further in dimension 1.

[81]  arXiv:1801.06151 [pdf, ps, other]
Title: An estimation of level sets for non local KPP equations with delay
Subjects: Analysis of PDEs (math.AP)

We study the large time asymptotic behavior of the solutions of the linear parabolic equation with delay $(*)$: $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + \int_{\mathbb{R}} k(x-y) \, u (t-h, y)\, dy$, $x \in \R$, $\ t >0$, and $k(x) \in L^1(\R)$. As an application we get estimates on the measure of level sets of non local KPP type equations with delay. For this type of nonlinear equations we prove that, in contrast with the classical case, the solution to the initial value problem with data of compact support may not be persistent.

[82]  arXiv:1801.06156 [pdf, other]
Title: The Rayleigh-Taylor instability for the Verigin problem with and without phase transition
Comments: 28 pages, 1 figure
Subjects: Analysis of PDEs (math.AP)

Isothermal incompressible two-phase flows in a capillary are modeled with and without phase transition in the presence of gravity, employing Darcy's law for the velocity field. It is shown that the resulting systems are thermodynamically consistent in the sense that the available energy is a strict Lyapunov functional. In both cases, the equilibria with flat interface are identified. It is shown that the problems are well-posed in an $L_p$-setting and generate local semiflows in the proper state manifolds. The main result concerns the stability of equilibria with flat interface, i.e. the Rayleigh-Taylor instability.

[83]  arXiv:1801.06162 [pdf, ps, other]
Title: Endomorphisms of nilpotent groups of finite rank
Authors: Hector Durham
Subjects: Group Theory (math.GR)

We obtain sufficient criteria for endomorphisms of torsion-free nilpotent groups of finite rank to be automorphisms, by considering the induced maps on the torsion-free abelianisation and the centre. Whilst these results are known in the finitely generated case removing this assumption introduces several difficulties.

[84]  arXiv:1801.06169 [pdf, ps, other]
Title: The number of $4$-cycles and the cyclomatic number of a finite simple graph
Comments: 14 pages
Subjects: Combinatorics (math.CO)

Let $G$ be a finite connected simple graph with $d$ vertices and $e$ edges. The cyclomatic number $e-d+1$ of $G$ is the dimension of the cycle space of $G$. Let $c_4(G)$ denote the number of $4$-cycles of $G$ and $k_4(G)$ that of $K_4$, the complete graph with $4$ vertices. Via certain techniques of commutative algebra, if follows that $c_4(G) - k_4(G) \leq \binom{e-d+1}{2}$ if $G$ has at least one odd cycle and that $c_4(G) \leq \binom{e-d+2}{2}$ if $G$ is bipartite. In the present paper, it will be proved that every finite connected simple graph $G$ with at least one odd cycle satisfies the inequality $c_4(G) \leq \binom{e-d+1}{2}$.

[85]  arXiv:1801.06171 [pdf, ps, other]
Title: Private Information Retrieval Through Wiretap Channel II: Privacy Meets Security
Comments: Submitted to IEEE Transactions on Information Theory, January 2018
Subjects: Information Theory (cs.IT); Cryptography and Security (cs.CR)

We consider the problem of private information retrieval through wiretap channel II (PIR-WTC-II). In PIR-WTC-II, a user wants to retrieve a single message (file) privately out of $M$ messages, which are stored in $N$ replicated and non-communicating databases. An external eavesdropper observes a fraction $\mu_n$ (of its choice) of the traffic exchanged between the $n$th database and the user. In addition to the privacy constraint, the databases should encode the returned answer strings such that the eavesdropper learns absolutely nothing about the \emph{contents} of the databases. We aim at characterizing the capacity of the PIR-WTC-II under the combined privacy and security constraints. We obtain a general upper bound for the problem in the form of a max-min optimization problem, which extends the converse proof of the PIR problem under asymmetric traffic constraints. We propose an achievability scheme that satisfies the security constraint by encoding a secret key, which is generated securely at each database, into an artificial noise vector using an MDS code. The user and the databases operate at one of the corner points of the achievable scheme for the PIR under asymmetric traffic constraints such that the retrieval rate is maximized under the imposed security constraint. The upper bound and the lower bound match for the case of $M=2$ and $M=3$ messages, for any $N$, and any $\boldsymbol{\mu}=(\mu_1, \cdots, \mu_N)$.

Cross-lists for Fri, 19 Jan 18

[86]  arXiv:1712.00458 (cross-list from nlin.PS) [pdf, other]
Title: Chimera States in Continuous Media: Existence and Distinctness
Comments: Supplemental animation at article webpage: this http URL
Journal-ref: Phys. Rev. Lett. 119, 244101 (2017)
Subjects: Pattern Formation and Solitons (nlin.PS); Dynamical Systems (math.DS)

The defining property of chimera states is the coexistence of coherent and incoherent domains in systems that are structurally and spatially homogeneous. The recent realization that such states might be common in oscillator networks raises the question of whether an analogous phenomenon can occur in continuous media. Here, we show that chimera states can exist in continuous systems even when the coupling is strictly local, as in many fluid and pattern forming media. Using the complex Ginzburg-Landau equation as a model system, we characterize chimera states consisting of a coherent domain of a frozen spiral structure and an incoherent domain of amplitude turbulence. We show that in this case, in contrast with discrete network systems, fluctuations in the local coupling field play a crucial role in limiting the coherent regions. We suggest these findings shed light on new possible forms of coexisting order and disorder in fluid systems.

[87]  arXiv:1801.05450 (cross-list from quant-ph) [pdf, ps, other]
Title: Gaussian quantum resource theories
Comments: 6+11 pages, no figures
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Optics (physics.optics)

We develop a general framework characterizing the structure and properties of quantum resource theories for continuous-variable Gaussian states and Gaussian operations, establishing methods for their description and quantification. We show in particular that, under a few intuitive and physically-motivated assumptions on the set of free states, no Gaussian quantum resource can be distilled with Gaussian free operations, even when an unlimited supply of the resource state is available. This places fundamental constraints on state transformations in all such Gaussian resource theories. Our methods rely on the definition of a general Gaussian resource quantifier whose value does not change when multiple copies are considered. We discuss in particular the applications to quantum entanglement, where we extend previously known results by showing that Gaussian entanglement cannot be distilled even with Gaussian operations preserving the positivity of the partial transpose, as well as to other Gaussian resources such as steering and optical nonclassicality. A unified semidefinite programming representation of all these resources is provided.

[88]  arXiv:1801.05830 (cross-list from gr-qc) [pdf, ps, other]
Title: Perturbations of Extremal Kerr Spacetime: Analytic Framework and Late-time Tails
Comments: 31 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

We develop a complete and systematic analytical approach to field perturbations of the extreme Kerr spacetime based on the formalism of Mano, Suzuki, and Takasugi (MST) for the Teukolsky equation. We give analytical expressions for the radial solutions and frequency-domain Green function in terms of infinite series of special functions. As an application, we compute the leading late-time behavior due to the branch point at zero frequency of scalar, gravitational, and electromagnetic field perturbations on and off the event horizon.

[89]  arXiv:1801.05832 (cross-list from cs.DS) [pdf, ps, other]
Title: Efficient Computation of the 8-point DCT via Summation by Parts
Comments: 13 pages, 4 figures, 2 tables
Journal-ref: J Sign Process Syst (2017)
Subjects: Data Structures and Algorithms (cs.DS); Numerical Analysis (cs.NA); Numerical Analysis (math.NA); Computation (stat.CO); Methodology (stat.ME)

This paper introduces a new fast algorithm for the 8-point discrete cosine transform (DCT) based on the summation-by-parts formula. The proposed method converts the DCT matrix into an alternative transformation matrix that can be decomposed into sparse matrices of low multiplicative complexity. The method is capable of scaled and exact DCT computation and its associated fast algorithm achieves the theoretical minimal multiplicative complexity for the 8-point DCT. Depending on the nature of the input signal simplifications can be introduced and the overall complexity of the proposed algorithm can be further reduced. Several types of input signal are analyzed: arbitrary, null mean, accumulated, and null mean/accumulated signal. The proposed tool has potential application in harmonic detection, image enhancement, and feature extraction, where input signal DC level is discarded and/or the signal is required to be integrated.

[90]  arXiv:1801.05874 (cross-list from nlin.AO) [pdf, ps, other]
Title: Synchronization of electrically coupled resonate-and-fire neurons
Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Dynamical Systems (math.DS)

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical coupling have been shown to exhibit resonant properties, and the subthreshold fluctuations arising from resonance are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete post-spike reset. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuity in the dynamics. We find that both spikes and resonant subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs.

[91]  arXiv:1801.05959 (cross-list from quant-ph) [pdf, other]
Title: Mapping topological to conformal field theories through strange correlators
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); Mathematical Physics (math-ph)

We extend the concept of strange correlators, defined for symmetry-protected phases in [You et al., Phys. Rev. Lett. 112, 247202 (2014)], to topological phases of matter by taking the inner product between string-net ground states and product states. The resulting two-dimensional partition functions are shown to be either critical or symmetry broken, as the corresponding transfer matrices inherit all matrix product operator symmetries of the string-net states. For the case of critical systems, those non-local matrix product operator symmetries are the lattice remnants of topological conformal defects in the field theory description. Following [Aasen et al., J. Phys. A 49, 354001 (2016)], we argue that the different conformal boundary conditions can be obtained by applying the strange correlator concept to the different topological sectors of the string-net obtained from Ocneanu's tube algebra. This is demonstrated by calculating the conformal field theory spectra on the lattice in the different topological sectors for the Fibonacci/hard-hexagon and Ising string-net. Additionally, we provide a complementary perspective on symmetry-preserving real-space renormalization by showing how known tensor network renormalization methods can be understood as the approximate truncation of an exactly coarse-grained strange correlator.

[92]  arXiv:1801.06014 (cross-list from eess.SP) [pdf, other]
Title: Image Enhancement and Noise Reduction Using Modified Delay-Multiply-and-Sum Beamformer: Application to Medical Photoacoustic Imaging
Comments: This paper was accepted and presented at Iranian Conference on Electrical Engineering (ICEE) 2017
Journal-ref: Iranian Conference on Electrical Engineering, 2-4 May 2017
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT)

Photoacoustic imaging (PAI) is an emerging biomedical imaging modality capable of providing both high contrast and high resolution of optical and UltraSound (US) imaging. When a short duration laser pulse illuminates the tissue as a target of imaging, tissue induces US waves and detected waves can be used to reconstruct optical absorption distribution. Since receiving part of PA consists of US waves, a large number of beamforming algorithms in US imaging can be applied on PA imaging. Delay-and-Sum (DAS) is the most common beamforming algorithm in US imaging. However, make use of DAS beamformer leads to low resolution images and large scale of off-axis signals contribution. To address these problems a new paradigm namely Delay-Multiply-and-Sum (DMAS), which was used as a reconstruction algorithm in confocal microwave imaging for breast cancer detection, was introduced for US imaging. Consequently, DMAS was used in PA imaging systems and it was shown this algorithm results in resolution enhancement and sidelobe degrading. However, in presence of high level of noise the reconstructed image still suffers from high contribution of noise. In this paper, a modified version of DMAS beamforming algorithm is proposed based on DAS inside DMAS formula expansion. The quantitative and qualitative results show that proposed method results in more noise reduction and resolution enhancement in expense of contrast degrading. For the simulation, two-point target, along with lateral variation in two depths of imaging are employed and it is evaluated under high level of noise in imaging medium. Proposed algorithm in compare to DMAS, results in reduction of lateral valley for about 19 dB followed by more distinguished two-point target. Moreover, levels of sidelobe are reduced for about 25 dB.

[93]  arXiv:1801.06037 (cross-list from gr-qc) [pdf, other]
Title: The annoying null boundaries
Comments: 15 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); Differential Geometry (math.DG)

We consider a class of globally hyperbolic space-times with "expanding singularities". Under suitable assumptions we show that no $C^0$-extensions across a compact boundary exist, while the boundary must be null wherever differentiable (which is almost everywhere) in the non-compact case.

[94]  arXiv:1801.06046 (cross-list from q-bio.NC) [pdf, ps, other]
Title: Conditions for traveling waves in spiking neural networks
Comments: 42 pages, 12 figures
Subjects: Neurons and Cognition (q-bio.NC); Dynamical Systems (math.DS)

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and uniqueness of different types of waves or bumps of activity using neural-field models, phenomenological coarse-grained descriptions of neural-network dynamics. But it remains unclear how these insights can be transferred to more biologically realistic networks of spiking neurons, where individual neurons fire irregularly. Here, we employ mean-field theory to reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with distance-dependent connectivity to an effective neural-field model. In contrast to existing phenomenological descriptions, the dynamics in this neural-field model depends on the mean and the variance in the synaptic input, both determining the amplitude and the temporal structure of the resulting effective coupling kernel. For the neural-field model we derive conditions for the existence of spatial and temporal oscillations and periodic traveling waves using linear stability analysis. We first prove that periodic traveling waves cannot occur in a single homogeneous population of neurons, irrespective of the form of distance dependence of the connection probability. Compatible with the architecture of cortical neural networks, traveling waves emerge in two-population networks of excitatory and inhibitory neurons as a combination of delay-induced temporal oscillations and spatial oscillations due to distance-dependent connectivity profiles. Finally, we demonstrate quantitative agreement between predictions of the analytically tractable neural-field model and numerical simulations of both networks of nonlinear rate-based units and networks of LIF neurons.

[95]  arXiv:1801.06069 (cross-list from stat.ME) [pdf, ps, other]
Title: Graphical models for mediation analysis
Subjects: Methodology (stat.ME); Statistics Theory (math.ST)

Mediation analysis seeks to infer how much of the effect of an exposure on an outcome can be attributed to specific pathways via intermediate variables or mediators. This requires identification of so-called path-specific effects. These express how a change in exposure affects those intermediate variables (along certain pathways), and how the resulting changes in those variables in turn affect the outcome (along subsequent pathways). However, unlike identification of total effects, adjustment for confounding is insufficient for identification of path-specific effects because their magnitude is also determined by the extent to which individuals who experience large exposure effects on the mediator, tend to experience relatively small or large mediator effects on the outcome. This chapter therefore provides an accessible review of identification strategies under general nonparametric structural equation models (with possibly unmeasured variables), which rule out certain such dependencies. In particular, it is shown which path-specific effects can be identified under such models, and how this can be done.

[96]  arXiv:1801.06104 (cross-list from cs.CV) [pdf, other]
Title: Invariants of multidimensional time series based on their iterated-integral signature
Subjects: Computer Vision and Pattern Recognition (cs.CV); Representation Theory (math.RT)

We introduce a novel class of features for multidimensional time series, that are invariant with respect to transformations of the ambient space. The general linear group, the group of rotations and the group of permutations of the axes are considered. The starting point for their construction is Chen's iterated-integral signature.

[97]  arXiv:1801.06159 (cross-list from stat.ML) [pdf, other]
Title: When Does Stochastic Gradient Algorithm Work Well?
Subjects: Machine Learning (stat.ML); Learning (cs.LG); Optimization and Control (math.OC)

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a fixed, large step size and propose a novel assumption on the objective function, under which this method has the improved convergence rates (to a neighborhood of the optimal solutions). We then empirically demonstrate that these assumptions hold for logistic regression and standard deep neural networks on classical data sets. Thus our analysis helps to explain when efficient behavior can be expected from the SGD method in training classification models and deep neural networks.

[98]  arXiv:1801.06166 (cross-list from quant-ph) [pdf, other]
Title: Classical simulation of photonic linear optics with lost particles
Comments: 26 pages, 14 figures, comments and suggestions are welcome
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)

We explore the possibility of efficient classical simulation of linear optics experiments under the effect of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an $n$-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in the $m$ output modes. We examine two models of losses. In the first model a fixed number of particles is lost. We prove that in this scenario the output statistics can be well approximated by an efficient classical simulation, provided that the number of photons that is left grows slower than $\sqrt{n}$. In the second loss model, every time a photon passes through a beamsplitter in the network, it has some probability of being lost. For this model the relevant parameter is $s$, the smallest number of beamsplitters that any photon traverses as it propagates through the network. We prove that it is possible to approximately simulate the output statistics already if $s$ grows logarithmically with $m$, regardless of the geometry of the network. The latter result is obtained by proving that it is always possible to commute $s$ layers of uniform losses to the input of the network regardless of its geometry, which could be a result of independent interest. We believe that our findings put strong limitations on future experimental realizations of quantum computational supremacy proposals based on boson sampling.

Replacements for Fri, 19 Jan 18

[99]  arXiv:1111.6518 (replaced) [src]
Title: Semigroups and sequential importance sampling for multiway tables
Comments: There are some theoretical mistakes. Thus, we would like to withdraw the paper
Subjects: Combinatorics (math.CO); Computation (stat.CO)
[100]  arXiv:1307.3965 (replaced) [pdf, ps, other]
Title: The Hyperbolic Ax-Lindemann-Weierstrass conjecture
Comments: The only modification is A.Yafaev'acknowledgement of ERC support
Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV); Number Theory (math.NT)
[101]  arXiv:1406.2178 (replaced) [pdf, ps, other]
Title: Generalized mu-ordinary Hasse invariants
Comments: final version, completely revised, to appear
Subjects: Algebraic Geometry (math.AG); Group Theory (math.GR); Number Theory (math.NT)
[102]  arXiv:1505.04252 (replaced) [pdf, ps, other]
Title: Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems
Subjects: Optimization and Control (math.OC); Learning (cs.LG); Machine Learning (stat.ML)
[103]  arXiv:1512.05403 (replaced) [pdf, other]
Title: Discontinuous Galerkin Deterministic Solvers for a Boltzmann-Poisson Model of Hot Electron Transport by Averaged Empirical Pseudopotential Band Structures
Comments: submission to CMAME (Computer Methods in Applied Mechanics and Engineering) Journal as a reply to the reviewers on February 2017
Journal-ref: Computer Methods in Applied Mechanics and Engineering, Volume 321, 2017, Pages 209-234
Subjects: Computational Engineering, Finance, and Science (cs.CE); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Numerical Analysis (math.NA)
[104]  arXiv:1512.05648 (replaced) [pdf, ps, other]
Title: Curves in $\mathbb{R}^4$ and two-rich points
Comments: 20 pages, 0 figures. v2: fixed an error in Section 5.2
Journal-ref: Discrete. Comput. Geom. 58: 232--253, 2017
Subjects: Combinatorics (math.CO); Computational Geometry (cs.CG)
[105]  arXiv:1602.03394 (replaced) [pdf, ps, other]
Title: Visibility of quantum graph spectrum from the vertices
Comments: Substantially revised version; accepted for publication in J. Phys. A: Math. Theor
Subjects: Spectral Theory (math.SP); Mathematical Physics (math-ph)
[106]  arXiv:1603.02858 (replaced) [pdf, ps, other]
Title: Semi-orthogonal decompositions of GIT quotient stacks
Comments: We now give in certain cases a semi-orthogonal decomposition consisting of Calabi-Yau parts. So it cannot be refined further
Subjects: Algebraic Geometry (math.AG)
[107]  arXiv:1603.04843 (replaced) [pdf, other]
Title: Approximating faces of marginal polytopes in discrete hierarchical models
Comments: 50 pages, 7 figures, 6 tables
Subjects: Statistics Theory (math.ST)
[108]  arXiv:1604.00711 (replaced) [pdf, ps, other]
Title: Lie algebroids as $L_\infty$ spaces
Comments: 46 pages, final version
Subjects: Differential Geometry (math.DG); Algebraic Geometry (math.AG); Quantum Algebra (math.QA)
[109]  arXiv:1604.08510 (replaced) [pdf, ps, other]
Title: Failures of the Integral Hasse Principle for Affine Quadric Surfaces
Comments: 20 pages
Journal-ref: Published, J. Lond. Math. Soc. (2), 95(3):1035{1052, 2017
Subjects: Number Theory (math.NT)
[110]  arXiv:1605.02408 (replaced) [pdf, ps, other]
Title: Structured Nonconvex and Nonsmooth Optimization: Algorithms and Iteration Complexity Analysis
Comments: Section 4.1 is updated
Subjects: Optimization and Control (math.OC); Learning (cs.LG); Machine Learning (stat.ML)
[111]  arXiv:1605.08288 (replaced) [pdf, other]
Title: A counterexample to Thiagarajan's conjecture on regular event structures
Subjects: Formal Languages and Automata Theory (cs.FL); Discrete Mathematics (cs.DM); Combinatorics (math.CO)
[112]  arXiv:1606.01396 (replaced) [pdf, ps, other]
Title: Implicit Deflation for Univariate Polynomial Root-finding
Comments: 7 pages
Subjects: Numerical Analysis (math.NA); Numerical Analysis (cs.NA)
[113]  arXiv:1606.02926 (replaced) [pdf, ps, other]
Title: A counterexample to the reconstruction conjecture for locally finite trees
Comments: 19 pages, Colour figures
Subjects: Combinatorics (math.CO)
[114]  arXiv:1607.03836 (replaced) [pdf, ps, other]
Title: A Sufficient Condition for Graphic Sequences with Given Largest and Smallest Entries, Length, and Sum
Authors: Brian Cloteaux
Subjects: Combinatorics (math.CO)
[115]  arXiv:1608.02389 (replaced) [pdf, other]
Title: On $H$-Topological Intersection Graphs
Subjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)
[116]  arXiv:1608.02415 (replaced) [pdf, other]
Title: Localization of the principal Dirichlet eigenvector in the heavy-tailed random conductance model
Authors: Franziska Flegel
Comments: 40 pages, 3 figures. Revision: Made some arguments mathematically rigorous, made extreme value analysis fit for generalization to higher order eigenvectors, see follow-up paper arXiv:1801.05684
Subjects: Probability (math.PR)
[117]  arXiv:1609.00505 (replaced) [pdf, ps, other]
Title: Topology of scrambled simplices
Authors: Dmitry N. Kozlov
Comments: 17 pages, 2 figures
Subjects: Algebraic Topology (math.AT); Combinatorics (math.CO)
[118]  arXiv:1609.05395 (replaced) [pdf, ps, other]
Title: Quantum speed limit vs. classical displacement energy
Comments: Revised version, 56 pages
Subjects: Mathematical Physics (math-ph); Symplectic Geometry (math.SG)
[119]  arXiv:1610.08572 (replaced) [pdf, ps, other]
Title: Curve test for enhanced ind-sheaves and holonomic D-modules
Authors: Takuro Mochizuki
Subjects: Complex Variables (math.CV); Algebraic Geometry (math.AG)
[120]  arXiv:1612.00950 (replaced) [pdf, ps, other]
Title: A limiting absorption principle for the Helmholtz equation with variable coefficients
Comments: 29 pages
Subjects: Analysis of PDEs (math.AP)
[121]  arXiv:1701.02404 (replaced) [pdf, ps, other]
Title: Skoda's Ideal Generation from Vanishing Theorem for Semipositive Nakano Curvature and Cauchy-Schwarz Inequality for Tensors
Authors: Yum-Tong Siu
Subjects: Complex Variables (math.CV)
[122]  arXiv:1701.02573 (replaced) [pdf, ps, other]
Title: Relative singular locus and Balmer spectrum of matrix factorizations
Authors: Yuki Hirano
Comments: Title changed, Example 5.10 added. To appear in Transactions of the AMS
Subjects: Algebraic Geometry (math.AG); Category Theory (math.CT); Representation Theory (math.RT)
[123]  arXiv:1701.06842 (replaced) [pdf, ps, other]
Title: Pseudomoments of the Riemann zeta function
Comments: Following the advice of a referee, the original version of this submission "Hardy space of Dirichlet series and pseudomoment of the Riemann zeta function" has been split into two papers; the present submission deals with pseudomoments, while another submission, titled "Linear space properties of $H^p$ spaces of Dirichlet series", will appear elsewhere
Subjects: Functional Analysis (math.FA); Complex Variables (math.CV); Number Theory (math.NT)
[124]  arXiv:1702.00190 (replaced) [pdf, other]
Title: Reconstructing unrooted phylogenetic trees from symbolic ternary metrics
Subjects: Combinatorics (math.CO)
[125]  arXiv:1702.03974 (replaced) [pdf, other]
Title: Knot traces and concordance
Comments: 17 pages, 15 figures. This version of the paper has been accepted by the Journal of Topology for publication
Subjects: Geometric Topology (math.GT)
[126]  arXiv:1702.08149 (replaced) [pdf, ps, other]
Title: Conjugate Real Classes in General Linear Groups
Comments: minor revision. Fixed minor errors
Subjects: Rings and Algebras (math.RA)
[127]  arXiv:1703.04486 (replaced) [pdf, ps, other]
Title: Euler totient of subfactor planar algebras
Comments: 11 pages
Subjects: Operator Algebras (math.OA); Combinatorics (math.CO); Group Theory (math.GR); Representation Theory (math.RT)
[128]  arXiv:1703.09240 (replaced) [pdf, ps, other]
Title: Random Manifolds have no Totally Geodesic Submanifolds
Comments: V2: minor changes to address referees' reports, calculations in the local construction have been made more explicit. To appear in Michigan Math. J
Subjects: Differential Geometry (math.DG)
[129]  arXiv:1704.02209 (replaced) [pdf, ps, other]
Title: Another proof of the local curvature estimate for the Ricci flow
Authors: Shu-Yu Hsu
Comments: 11 pages, typos corrected
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)
[130]  arXiv:1704.07418 (replaced) [pdf, ps, other]
Title: Is there a Teichmüller principle in higher dimensions?
Authors: Oliver Roth
Subjects: Complex Variables (math.CV); Optimization and Control (math.OC)
[131]  arXiv:1704.07902 (replaced) [pdf, ps, other]
Title: A bijection between the set of nesting-similarity classes and L & P matchings
Comments: 9 pages, 7 figures
Journal-ref: Discrete Mathematics and Theoretical Computer Science DMTCS vol. 19:2, 2017, #1
Subjects: Combinatorics (math.CO)
[132]  arXiv:1705.00560 (replaced) [pdf, ps, other]
Title: Group actions, the Mattila integral and applications
Authors: Bochen Liu
Comments: manuscript updated
Subjects: Classical Analysis and ODEs (math.CA); Combinatorics (math.CO)
[133]  arXiv:1705.00923 (replaced) [pdf, ps, other]
Title: The Phase Transition in the Ultrametric Ensemble and Local Stability of Dyson Brownian Motion
Comments: The current version is a merger of the previous versions with arXiv:1705.04165
Subjects: Probability (math.PR); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mathematical Physics (math-ph)
[134]  arXiv:1705.04165 (replaced) [pdf, ps, other]
Title: The Localization Transition in the Ultrametric Ensemble
Comments: This article has been merged into arXiv:1705.00923
Subjects: Mathematical Physics (math-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Probability (math.PR)
[135]  arXiv:1706.01930 (replaced) [pdf, other]
Title: Square functions and the Hamming cube: Duality
Comments: 18 pages
Subjects: Analysis of PDEs (math.AP); Probability (math.PR)
[136]  arXiv:1706.04137 (replaced) [pdf, ps, other]
Title: Remarks to the Resonance-Decay Problem in Quantum Mechanics from a mathematical point of view
Comments: 10 pages
Subjects: Mathematical Physics (math-ph)
[137]  arXiv:1706.06431 (replaced) [pdf, ps, other]
Title: Extensions of arc-analytic functions
Comments: Published version (corrected). arXiv admin note: text overlap with arXiv:1701.02712
Journal-ref: Math. Ann. (2018)
Subjects: Algebraic Geometry (math.AG)
[138]  arXiv:1707.00810 (replaced) [pdf, other]
Title: Rényi Resolvability and Its Applications to the Wiretap Channel
Comments: 49 pages. An error in the exponent in Theorem 6 has been fixed
Subjects: Information Theory (cs.IT); Cryptography and Security (cs.CR)
[139]  arXiv:1707.03794 (replaced) [pdf, ps, other]
Title: Coupling Load-Following Control with OPF
Comments: This article has been accepted for publication in the IEEE Transactions on Smart Grid
Subjects: Optimization and Control (math.OC); Systems and Control (cs.SY)
[140]  arXiv:1707.03859 (replaced) [pdf, other]
Title: Intuitionistic modal logic based on neighborhood semantics without superset axiom
Authors: Tomasz Witczak
Comments: We have discussed some classical cases with two kinds of necessity - for minimal and maximal neighborhoods. We proved translation result between intuitionistic and classical version of our system. Also we removed some minor mistakes (e.g. typos) and added certain new references to bibliography
Subjects: Logic (math.LO)
[141]  arXiv:1707.04658 (replaced) [pdf, ps, other]
Title: Multivariate Rankin-Selberg integrals on $\mathrm{GL}_4$ and $\mathrm{GU}(2,2)$
Comments: Final version. To appear in Canad. Math. Bull
Subjects: Number Theory (math.NT); Representation Theory (math.RT)
[142]  arXiv:1707.04976 (replaced) [pdf, ps, other]
Title: Stochastic Near-Optimal Controls for Path-Dependent Systems
Comments: We shorten some of the proofs, the Introduction was updated and a concrete example to Mathematical Finance is presented
Subjects: Probability (math.PR); Optimization and Control (math.OC)
[143]  arXiv:1708.02089 (replaced) [pdf, ps, other]
Title: On the cardinality of the manifold set
Comments: 23 pages. Added smooth versions of the main theorems. Improved exposition. Corrected the mistake from the first version in definition of r_k in section 3, current display (3.2), where we omitted factor t
Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT)
[144]  arXiv:1708.02670 (replaced) [pdf, other]
Title: Hölder continuity of the integrated density of states for Extended Harper's Model with Liouville frequency
Comments: 1 figure
Subjects: Spectral Theory (math.SP)
[145]  arXiv:1708.09357 (replaced) [pdf, other]
Title: On the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painlevé II equation
Authors: Dan Dai, Weiying Hu
Comments: 13 pages, 2 figures, typos corrected, references added
Subjects: Classical Analysis and ODEs (math.CA)
[146]  arXiv:1709.00742 (replaced) [pdf, ps, other]
Title: The Averaged Kaczmarz Iteration for Solving Inverse Problems
Subjects: Numerical Analysis (math.NA)
[147]  arXiv:1709.01580 (replaced) [pdf, other]
Title: The rank function of a positroid and non-crossing partitions
Comments: 11 pages, 2 figures. v2 : Completely reworked proof. arXiv admin note: text overlap with arXiv:1701.08483
Subjects: Combinatorics (math.CO)
[148]  arXiv:1709.04042 (replaced) [pdf, other]
Title: Winding of simple walks on the square lattice
Authors: Timothy Budd
Comments: 33 pages, 15 figures. Section 4 has been extended and some minor errors have been fixed
Subjects: Combinatorics (math.CO); Mathematical Physics (math-ph); Probability (math.PR)
[149]  arXiv:1709.04297 (replaced) [pdf, ps, other]
Title: A Discontinuous Ritz Method for a Class of Calculus of Variations Problems
Comments: 17 pages, 1 figure and 4 tables
Subjects: Numerical Analysis (math.NA)
[150]  arXiv:1709.05169 (replaced) [pdf, ps, other]
Title: Nonequilibrium Work Relation from Schroedinger's Unrecognized Probability Theory
Authors: T. Koide
Comments: 8 pages, no figure. Typos are corrected, and discussions and references are added. Accepted for publication in J. Phys. Commu
Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[151]  arXiv:1709.07298 (replaced) [pdf, other]
Title: On the distribution of monochromatic complete subgraphs and arithmetic progressions
Comments: Revised version include some heuristic support
Subjects: Combinatorics (math.CO)
[152]  arXiv:1710.02050 (replaced) [pdf, ps, other]
Title: Characterizations of generalized John domains in $\mathbb{R}^n$ via metric duality
Comments: 24 pages, 17 figures, substantial changes on the introduction
Subjects: General Topology (math.GN); Algebraic Topology (math.AT); Classical Analysis and ODEs (math.CA)
[153]  arXiv:1710.08991 (replaced) [pdf, other]
Title: An Extended Mean Field Game for Storage in Smart Grids
Comments: 27 pages, 5 figures
Subjects: Probability (math.PR)
[154]  arXiv:1710.09090 (replaced) [pdf, other]
Title: Kernel-based collocation methods for Zakai equations
Authors: Yumiharu Nakano
Subjects: Numerical Analysis (math.NA); Optimization and Control (math.OC); Probability (math.PR)
[155]  arXiv:1710.10969 (replaced) [pdf, ps, other]
Title: Similarity of holomorphic matrices on 1-dimensional Stein spaces
Authors: Jürgen Leiterer
Comments: This is a revised version of a part a preprint from Sep 2016, later (Mar 2017) posted as arXiv:1703.09524. Changes in this version, v2, from 18 Jan 2018 are: a "Note added in proof" and a reference are added, some redactional changes are carried out (not changing the results), typos corrected
Subjects: Complex Variables (math.CV)
[156]  arXiv:1711.03524 (replaced) [pdf, other]
Title: Maximal polynomial modulations of singular integrals
Comments: v3: 25 pages, Definition (3.19) corrected, other minor corrections made
Subjects: Classical Analysis and ODEs (math.CA)
[157]  arXiv:1711.03578 (replaced) [pdf, ps, other]
Title: Erdős-Ulam ideals vs. simple density ideals
Authors: Adam Kwela
Subjects: Combinatorics (math.CO)
[158]  arXiv:1711.04099 (replaced) [pdf, ps, other]
Title: On aggregation of multitype Galton-Watson branching processes with immigration
Comments: 26 pages
Subjects: Probability (math.PR)
[159]  arXiv:1711.05587 (replaced) [pdf, ps, other]
Title: Optimal local well-posedness theory for the kinetic wave equation
Subjects: Analysis of PDEs (math.AP)
[160]  arXiv:1711.05589 (replaced) [pdf, other]
Title: Diffeomorphism groups of critical regularity
Comments: 64 pages, 10 figures. Significant improvement of the main result to include regularities $1\leq\alpha&lt;2$. Most of the arguments are unchanged
Subjects: Group Theory (math.GR); Dynamical Systems (math.DS); Geometric Topology (math.GT)
[161]  arXiv:1711.07474 (replaced) [pdf]
Title: XSAT of Linear CNF Formulas
Authors: Bernd. R. Schuh
Subjects: Computational Complexity (cs.CC); Logic (math.LO)
[162]  arXiv:1711.10349 (replaced) [pdf, ps, other]
Title: Bypassing dynamical systems : A simple way to get the box-counting dimension of the graph of the Weierstrass function
Authors: Claire David
Comments: arXiv admin note: substantial text overlap with arXiv:1703.06839, arXiv:1703.03371
Subjects: General Topology (math.GN); Dynamical Systems (math.DS)
[163]  arXiv:1712.00210 (replaced) [pdf, other]
Title: An upper bound on the size of avoidance couplings
Comments: 8 pages
Subjects: Probability (math.PR)
[164]  arXiv:1712.00555 (replaced) [pdf, ps, other]
Title: About the equivalence between monads and monadic functors
Authors: Hadrian Heine
Subjects: Category Theory (math.CT)
[165]  arXiv:1712.01737 (replaced) [src]
Title: $uτ$-continuous operators on locally solid vector lattices
Comments: Because of some mistakes in the paper, I would like to withdraw it from arXiv
Subjects: Functional Analysis (math.FA)
[166]  arXiv:1712.01775 (replaced) [pdf, other]
Title: Estimating linear functionals of a sparse family of Poisson means
Subjects: Statistics Theory (math.ST)
[167]  arXiv:1712.04121 (replaced) [pdf, ps, other]
Title: On relative Gromov--Witten invariants of projective completions of vector bundles
Authors: Cheng-Yong Du
Comments: 14pages; accepted for publication in SCIENCE CHINA Mathematics
Subjects: Symplectic Geometry (math.SG); Algebraic Geometry (math.AG)
[168]  arXiv:1712.04905 (replaced) [pdf, ps, other]
Title: Decomposability and Mordell-Weil ranks of Jacobians using Picard numbers
Authors: Soohyun Park
Comments: 14 pages (made some edits and added new material), Comments welcome
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[169]  arXiv:1712.06512 (replaced) [pdf, ps, other]
Title: Factoriality and class groups of cluster algebras
Comments: 31 pages; minor corrections
Subjects: Commutative Algebra (math.AC); Rings and Algebras (math.RA)
[170]  arXiv:1712.07638 (replaced) [pdf, ps, other]
Title: Joint spreading models and uniform approximation of bounded operators
Comments: 37 pages. This updated version contains a section connecting the UALS property and duality
Subjects: Functional Analysis (math.FA)
[171]  arXiv:1712.08520 (replaced) [pdf, other]
Title: Canonical Bases for Permutohedral Plates
Authors: Nick Early
Comments: New sections; more contextual discussion
Subjects: Combinatorics (math.CO); High Energy Physics - Theory (hep-th)
[172]  arXiv:1801.02745 (replaced) [pdf, other]
Title: Improved Capacity Upper Bounds for the Discrete-Time Poisson Channel
Comments: 11 pages, 3 figures. Fixed some typos in Section 4.2 and added more detailed argument in Section 4.4
Subjects: Information Theory (cs.IT)
[173]  arXiv:1801.03481 (replaced) [pdf, ps, other]
Title: Latent Factor Analysis of Gaussian Distributions under Graphical Constraints
Comments: 8 pages
Subjects: Information Theory (cs.IT)
[174]  arXiv:1801.04299 (replaced) [pdf, other]
Title: Belief Propagation Decoding of Polar Codes on Permuted Factor Graphs
Comments: in IEEE Wireless Commun. and Networking Conf. (WCNC), April 2018
Subjects: Information Theory (cs.IT)
[175]  arXiv:1801.04310 (replaced) [pdf, ps, other]
Title: A Multi-Hop Framework for Multi-Source, Multi-Relay, All-Cast Channels
Comments: In support of a submission to ISIT 2018
Subjects: Information Theory (cs.IT)
[176]  arXiv:1801.04420 (replaced) [pdf, ps, other]
Title: LDPC Codes over Gaussian Multiple Access Wiretap Channel
Comments: 21 pages, 8 figures, A Revision Submitted to IET Communications
Subjects: Information Theory (cs.IT)
[177]  arXiv:1801.04632 (replaced) [pdf, ps, other]
Title: On symmetric matrices associated with oriented link diagrams
Authors: Rinat Kashaev
Comments: 13 pages, Abstract substantially shortened, Lemma 2 and Theorem 1 slightly modified
Subjects: Geometric Topology (math.GT)
[178]  arXiv:1801.05242 (replaced) [pdf, other]
Title: A Bayesian Conjugate Gradient Method
Subjects: Methodology (stat.ME); Numerical Analysis (cs.NA); Numerical Analysis (math.NA); Statistics Theory (math.ST)
[179]  arXiv:1801.05707 (replaced) [pdf, ps, other]
Title: A Generalized Dempster--Shafer Evidence Theory
Authors: Fuyuan Xiao
Comments: 24 pages
Subjects: Artificial Intelligence (cs.AI); Information Theory (cs.IT)
[180]  arXiv:1801.05768 (replaced) [pdf, other]
Title: The Asymptotic Capacity of Private Search
Subjects: Information Theory (cs.IT); Cryptography and Security (cs.CR); Data Structures and Algorithms (cs.DS)
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