Mathematics
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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 curvesSubjects: 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 $n2 \geq d \geq \frac{n+1}{2}$.
 [2] arXiv:1801.05838 [pdf, ps, other]

Title: Revisiting the Problem of Recovering Functions in $\Bbb R^{n}$ by Integration on $k$ Dimensional PlanesAuthors: Yehonatan SalmanComments: 22 pagesSubjects: 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 wellposed 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 functionsComments: 11 pagesSubjects: 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 RadiosComments: 6 pages, 4 figures, accepted in WCNC 2018Subjects: Information Theory (cs.IT)
In cellularD2D 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 nthnearest neighbor as the serving node for the receiver of interest, by considering fullduplex (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 selfinterference, FDD2D 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 CodesSubjects: 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 WaveletsComments: 6 pages, 15 figuresSubjects: 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 DitheringComments: 40 pages, 9 figuresSubjects: 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 1bit 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 lowcomplexity signal (e.g., a sparse or compressible signal, or a lowrank 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 lowcomplexity 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 lowcomplexity set.
We finally confirm empirically these observations in several sensing contexts involving sparse signals, lowrank matrices, and compressible signals, with various RIP matrix constructions such as subGaussian random matrices and random partial Discrete Cosine Transform (DCT) matrices.  [8] arXiv:1801.05873 [pdf, other]

Title: Sparse Activity Detection for Massive ConnectivityComments: 15 pages, 7 figures; accepted at TSPSubjects: Information Theory (cs.IT)
This paper considers the massive connectivity application in which a large number of potential devices communicate with a basestation (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 nonorthogonal 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 largescale 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 largescale fading component does not offer tangible benefits. For the multipleantenna case, we employ two different AMP algorithms, namely the AMP with vector denoiser and the parallel AMPMMV, and quantify the benefit of deploying multiple antennas at the BS.
 [9] arXiv:1801.05875 [pdf, other]

Title: An UltraWeak Discontinuous Galerkin Method for Schrödinger Equation in One DimensionSubjects: Numerical Analysis (math.NA)
In this paper, we develop an ultraweak discontinuous Galerkin (DG) method to solve the onedimensional 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 elementwise, facilitating analysis. In most cases, the projection is global, and its analysis depends on the resulting $2\times2$ blockcirculant 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 dimensionsSubjects: 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 narrowstencil 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 Secondorder Linear Elliptic PDEs in Nondivergence FormSubjects: Numerical Analysis (math.NA)
This paper is concerned with continuous and discrete approximations of $W^{2,p}$ strong solutions of secondorder linear elliptic partial differential equations (PDEs) in nondivergence 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 fourthorder PDE is a natural fit for Galerkintype methods unlike the original second order equation since the highest order term is in divergence form. The wellposedness 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 secondorder 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 progressionComments: 19 pagesSubjects: 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 FouvryKowalskiMichel and KowalskiMichelSawin.
 [13] arXiv:1801.05887 [pdf, ps, other]

Title: Uniform Ergodicity for Brownian Motion in a Bounded Convex SetAuthors: Jackson LoperSubjects: Probability (math.PR)
We consider an ndimensional Brownian Motion trapped inside a bounded convex set by normallyreflecting boundaries. It is wellknown that this process is uniformly ergodic. However, the rates of this ergodicity are not wellunderstood, especially in the regime of very highdimensional 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 TransformComments: Submitted to Kinetic and Related ModelsSubjects: 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 mathematiciansAuthors: J.M. LandsbergSubjects: History and Overview (math.HO); Quantum Physics (quantph)
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 MathematiciansSubjects: 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 stateofthe 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 varietiesSubjects: Algebraic Geometry (math.AG); Complex Variables (math.CV)
We prove that quasiprojective 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 twodimensional 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 enumeratorComments: 9 pagesSubjects: 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 groupSubjects: 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 Thirdorder Jacobsthal QuaternionsAuthors: Gamaliel CerdaMoralesComments: 13 pagesSubjects: Rings and Algebras (math.RA)
In 2016, Y\"uce and Torunbalc\i\ Ayd\i n \cite{YucTor} defined dual Fibonacci quaternions. In this paper, we defined the dual thirdorder Jacobsthal quaternions and dual thirdorder JacobsthalLucas quaternions. Also, we investigated the relations between the dual thirdorder Jacobsthal quaternions and thirdorder Jacobsthal numbers. Furthermore, we gave some their quadratic properties, the summations, the Binet's formulas and Cassinilike identities for these quaternions.
 [21] arXiv:1801.05914 [pdf, ps, other]

Title: The De BruijnNewman constant is nonnegativeComments: 44 pages, no figuresSubjects: 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 superexponentially 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 BruijnNewman 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: RateOptimal Streaming Codes for Channels with Burst and Isolated ErasuresComments: shorter version submitted to ISIT 2018Subjects: 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 rateoptimal codes that permit delayconstrained recovery from an erasure burst of length up to $B$. A recent work by Badr et al. extended this result and introduced a slidingwindow channel model $\mathcal{C}(N,B,W)$. Under this model, in a slidingwindow 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 noncontiguous) 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 UstatisticsSubjects: Probability (math.PR)
We present a Rosenthaltype moment bound and a Bernsteintype exponential tail bound for order 1 degenerated matrix Ustatistics in operator norm, with explicit factors on dimension dependencies. We show that the moment bound is tight when the Ustatistics 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 nondegenerated matrix Ustatistics of arbitrary order.
 [24] arXiv:1801.05926 [pdf, ps, other]

Title: The Utility Cost of Robust Privacy GuaranteesSubjects: 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 privacyutility 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 1Authors: Max A. AlekseyevSubjects: 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 nonreversible zerorange processesAuthors: Insuk SeoComments: 63 pages, 1 figureSubjects: Probability (math.PR); Mathematical Physics (mathph)
In this article, we investigate the condensation phenomena for a class of nonreversible zerorange 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 nonreversible processes, we prove that the condensed site of the corresponding zerorange 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 zerorange processes, and that of Landim [22] on totally asymmetric zerorange processes on a onedimensional discrete torus.
 [27] arXiv:1801.05935 [pdf, other]

Title: Computation of the Maximum Likelihood estimator in lowrank Factor AnalysisComments: 22 pages, 4 figuresSubjects: 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 stateoftheart approaches.
 [28] arXiv:1801.05936 [pdf, ps, other]

Title: Gradient Estimates and Ergodicity for SDEs Driven by Multiplicative Lévy Noises via CouplingComments: 34 pagesSubjects: Probability (math.PR)
We consider SDEs driven by multiplicative pure jump L\'{e}vy noises, where L\'evy processes are not necessarily comparable to $\alpha$stablelike 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 EventsComments: This work has been submitted to 2018 IEEE International Conference on Communications Workshops (ICC Workshops): Integrating UAVs into 5GSubjects: 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 (beyond5G) 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.) ABSsupported user equipment and between the ABS and an i.u.d. TBSsupported 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 tradeoff 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 250500 m for the considered setup.
 [30] arXiv:1801.05951 [pdf, other]

Title: Quadratically Constrained Myopic Adversarial ChannelsSubjects: 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 noisetosignal 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 subregime, and at most $\mathcal O(n^2)$ bits in the other subregime) available to the encoderdecoder pair. Our proof techniques involve a novel myopic listdecoding result for achievability and a Plotkintype 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 NSDDEsSubjects: Numerical Analysis (math.NA)
This paper is concerned with strong convergence of the truncated EulerMaruyama 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 IndexAuthors: Niko TratnikSubjects: Combinatorics (math.CO)
In this paper, we generalize the result of Behmaram, YousefiAzari, 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 4cycles 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 ProblemsSubjects: Logic (math.LO); Computational Complexity (cs.CC)
The CSP of a firstorder 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 polynomialtime 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 polynomialtime decidable). We show that for a large class of $\omega$categorical theories $T_1, T_2$ the NelsonOppen conditions are not only sufficient, but also necessary for polynomialtime 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 distributionsComments: 19 pagesSubjects: 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 tnorm is nondivisible, we precisely characterize diagonals between distance distributions, and prove that onestep 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 Rauzytype dynamics II: the labelling method and a second proof of the KZB classification theoremAuthors: Quentin De MourguesComments: 76 pages, 42 figure, 3 tablesSubjects: Combinatorics (math.CO)
Rauzytype 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 Rauzytype 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 powersComments: 6 pagesSubjects: 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 FFTbased algorithm for efficient computation of Green's functions for the Helmholtz and Maxwell's equations in periodic domainsSubjects: 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 quasiperiodic. The quasiperiodic 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 quasiperiodic Green's functions. In this paper, we will introduce a new FFTbased fast algorithm to compute the 2D/3D quasiperiodic 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 KrullGabriel dimension and Galois coveringsAuthors: Grzegorz PastuszakSubjects: Representation Theory (math.RT)
Assume that $K$ is an algebraically closed field, $R$ a locally supportfinite locally bounded $K$category, $G$ a torsionfree admissible group of $K$linear automorphisms of $R$ and $A=R\slash G$. We show that the KrullGabriel dimension $KG(R)$ of $R$ is finite if and only if the KrullGabriel dimension $KG(A)$ of $A$ is finite. In these cases $KG(R)=KG(A)$. We apply this result to determine the KrullGabriel dimension of standard selfinjective algebras of polynomial growth. Finally, we show that there are no superdecomposable pureinjective 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 InterpretationSubjects: 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 QuasiBirthDeath 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 ComplexityAuthors: Siddhartha Kumar, Alexandre Graell i Amat, Iryna Andriyanova, Fredrik Brännström, Eirik RosnesSubjects: 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 twostep 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 improvementComments: 18 pagesSubjects: Numerical Analysis (math.NA)
The direct sampling method (DSM) has been introduced for noniterative 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 RectifiabilitySubjects: 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 $p > n/(n1)$, then $\partial \Omega$ is uniformly rectifiable. Combining our results with those in [HT] (HofmannTapiola) gives us a new characterization of uniform rectifiability which complements the recent results in [HMM] (HofmannMartellMayboroda), [GMT] (GarnettMourgoglouTolsa) and [AGMT] (AzzamGarnettMourgoglouTolsa).
 [43] arXiv:1801.05998 [pdf, other]

Title: A single server queue with batch arrivals and semiMarkov servicesSubjects: Probability (math.PR)
We investigate the transient and stationary queuelength distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semiMarkov 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 steadystate 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 shorttime Fourier transformSubjects: Analysis of PDEs (math.AP)
It is well known that the classical and Sobolev wave fronts were extended into nonequivalent global versions by the use of the shorttime Fourier transform. In this very short paper we give complete characterisations of initial wave front sets via the shorttime 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 pagesSubjects: 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 adventuresComments: 14 pagesSubjects: Number Theory (math.NT); Mathematical Physics (mathph); Classical Analysis and ODEs (math.CA); KTheory 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 threevariable 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 graphsComments: 30 pages, 4 figuresSubjects: 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 cutrank functions provides a rough structural characterization of graphs having no $mK_{1,n}$ vertexminors, which allows us to prove that such graphs have bounded linear rankwidth.
 [48] arXiv:1801.06006 [pdf, ps, other]

Title: Bounds for higher topological complexity of real projective space implied by BPAuthors: Donald M DavisSubjects: Algebraic Topology (math.AT)
We use BrownPeterson 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 mod2 cohomology.
 [49] arXiv:1801.06008 [pdf, ps, other]

Title: Convergence of the solutions of the discounted HamiltonJacobi equation: a counterexampleAuthors: Bruno ZiliottoSubjects: 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 HamiltonJacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1dimensional continuous and coercive Hamiltonian.
 [50] arXiv:1801.06010 [pdf, ps, other]

Title: Divisibility properties of motivic cohomologyAuthors: Bruno KahnComments: 8 pagesSubjects: Algebraic Geometry (math.AG); KTheory and Homology (math.KT)
We extend results of ColliotTh\'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 BlochLichtenbaum spectral sequence for any field containing $k$.
 [51] arXiv:1801.06013 [pdf, ps, other]

Title: Inverse of infinite Hankel moment matricesComments: 62 pagesSubjects: 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_{n1}P_{n1}(x) for a sequence (b_n) such that b_{n1}/b_n\le q<1 for n sufficiently large, hence in particular for eventually logconvex sequences (b_n) such that \sum 1/b_n<\infty. It also holds for certain eventually logconcave 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 birthanddeath process studied by Valent and coauthors, 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_{n1})^2 is defined for any moment problem, while V_n=b_0b_1\ldots b_{n1}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_{n1}/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 problemsSubjects: 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 exponentialtype 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: LiYau inequality for unbounded Laplacian on graphsComments: 19 pagesSubjects: Differential Geometry (math.DG)
In this paper, we derive LiYau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvaturedimension inequality $CDE'(n,K)$, which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of LiYau 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 TandemDuplication ErrorsSubjects: 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 tandemduplication, and utilize the relation to constantweight integer codes in the Manhattan metric. By bounding the intersection of the crosspolytope with hyperplanes, we prove the existence of reconstruction codes with greater capacity than known errorcorrecting 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 groupsAuthors: Wataru YuasaComments: 16 pagesSubjects: 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 halftwist 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 schemesComments: 20 pagesSubjects: 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{CameronLiebler 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 $n \geq 5$, $k, nk \geq 2$ 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 invariantAuthors: J.D. QuigleyComments: 39 pagesSubjects: 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 HigsonRoe sequence for étale groupoids. I. Dual algebras and compatibility with the BC mapComments: 30 pagesSubjects: KTheory and Homology (math.KT); Operator Algebras (math.OA)
We introduce the dual Roe algebras for proper \'{e}tale groupoid actions and deduce the expected HigsonRoe 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 sixterm exact sequence with the BaumConnes map, via a PaschkeHigson map for groupoids. For proper actions on continuous families of manifolds of bounded geometry, we associate with any $G$equivariant Diractype family, a coarse index class which generalizes the Paterson index class and also the MooreSchochet Connes' index class for laminations.
 [59] arXiv:1801.06045 [pdf, ps, other]

Title: Ordered groupvalued probability, positive operators, and integral representationsAuthors: T. KroupaSubjects: 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 wellknown representation theorem of realvalued MValgebraic 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 papersJournalref: Journal of Humanistic Mathematics, Volume 5 Issue 2 (July 2015), pages 186188Subjects: 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 peerreviewed 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 nonmathematical 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 EstimationComments: 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 multiinput multioutput 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 closedloop stability are presented. The performance of the resulting controller relies on a codesign of the system model, the state and disturbance observer, and the controller. Numerical experiments on a firstorder 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 orderComments: 8 pagesSubjects: 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 tnorms. 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 functionsComments: arXiv admin note: text overlap with arXiv:1712.08292Subjects: 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 OperationsAuthors: Ning GuoComments: 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 subalgebra 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 pairsAuthors: Yiqiang LiComments: 49 pagesSubjects: Representation Theory (math.RT); Symplectic Geometry (math.SG)
We study fixedpoint loci of Nakajima varieties under symplectomorphisms and their antisymplectic 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 Steinbergtype variety of the symplectic fixedpoint 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 KraftProcesi row/column removal reductions.
 [66] arXiv:1801.06072 [pdf, other]

Title: On a conjecture about Morita algebrasSubjects: 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 MechanicsComments: 10 pagesSubjects: Mathematical Physics (mathph)
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 complexSubjects: 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 AskeyWilson algebraAuthors: Paul TerwilligerComments: 21 pagesSubjects: 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 AskeyWilson 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 HamiltonJacobi equations I: Cauchy problemSubjects: Analysis of PDEs (math.AP)
We study the representation formulae for the fundamental solutions and viscosity solutions of the HamiltonJacobi 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 RankinSelberg LfunctionsComments: 13 pagesSubjects: Number Theory (math.NT)
We prove an exact formula for the second moment of RankinSelberg $L$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 GaussJacobi Kernel Compression Scheme for Fractional Differential EquationsAuthors: Daniel BaffetSubjects: 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 GaussJacobi 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 GaussJacobi 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 DomainsSubjects: 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 powernon residuesAuthors: Andrea SartoriComments: 15 pages, comments welcomeSubjects: 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 $p1$ does not have small prime factors, but 2.
 [75] arXiv:1801.06112 [pdf, ps, other]

Title: Ideals modulo pSubjects: 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 sigmagood 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 sigmagood 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 categoriesAuthors: Dmitri NikshychComments: 14 pagesSubjects: 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 nondegenerate and grouptheoretical fusion categories.
 [77] arXiv:1801.06127 [pdf, other]

Title: Reduced order models for fluidstructure interaction problems with applications in haemodynamicsSubjects: Numerical Analysis (math.NA)
This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluidstructure 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 fluidstructure interaction problem as a NavierStokes system with nonstandard boundary conditions; second, we employ numerical reduction techniques to further and drastically lower the computational costs. The numerical reduction is obtained coupling two wellknown 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 GopakumarVafa type invariants for CalabiYau 4folds II: Fano 3foldsAuthors: Yalong CaoComments: 15 pagesSubjects: Algebraic Geometry (math.AG); High Energy Physics  Theory (hepth)
In analogy with the GopakumarVafa conjecture on CY 3folds, Klemm and Pandharipande defined GV type invariants on CalabiYau 4folds using GromovWitten 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 3fold $Y$, which reduces to a relation between twisted GW and $\mathrm{DT_3}$ invariants on $Y$. Examples are computed for both compact and noncompact Fano 3folds to support our conjecture.
 [79] arXiv:1801.06143 [pdf, other]

Title: TASEP fluctuations with softshock initial dataSubjects: Probability (math.PR); Mathematical Physics (mathph)
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 spacetime 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 TracyWidom 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 functionSubjects: 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 delaySubjects: Analysis of PDEs (math.AP)
We study the large time asymptotic behavior of the solutions of the linear parabolic equation with delay $(*)$: $u_{t}(t,x) = u_{xx}(t,x)  u(t,x) + \int_{\mathbb{R}} k(xy) \, u (th, y)\, dy$, $x \in \R$, $\ t >0$, 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 RayleighTaylor instability for the Verigin problem with and without phase transitionComments: 28 pages, 1 figureSubjects: Analysis of PDEs (math.AP)
Isothermal incompressible twophase 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 wellposed 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 RayleighTaylor instability.
 [83] arXiv:1801.06162 [pdf, ps, other]

Title: Endomorphisms of nilpotent groups of finite rankAuthors: Hector DurhamSubjects: Group Theory (math.GR)
We obtain sufficient criteria for endomorphisms of torsionfree nilpotent groups of finite rank to be automorphisms, by considering the induced maps on the torsionfree 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 graphComments: 14 pagesSubjects: Combinatorics (math.CO)
Let $G$ be a finite connected simple graph with $d$ vertices and $e$ edges. The cyclomatic number $ed+1$ 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 $c_4(G)  k_4(G) \leq \binom{ed+1}{2}$ if $G$ has at least one odd cycle and that $c_4(G) \leq \binom{ed+2}{2}$ 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 $c_4(G) \leq \binom{ed+1}{2}$.
 [85] arXiv:1801.06171 [pdf, ps, other]

Title: Private Information Retrieval Through Wiretap Channel II: Privacy Meets SecurityComments: Submitted to IEEE Transactions on Information Theory, January 2018Subjects: Information Theory (cs.IT); Cryptography and Security (cs.CR)
We consider the problem of private information retrieval through wiretap channel II (PIRWTCII). In PIRWTCII, a user wants to retrieve a single message (file) privately out of $M$ messages, which are stored in $N$ replicated and noncommunicating 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 PIRWTCII under the combined privacy and security constraints. We obtain a general upper bound for the problem in the form of a maxmin 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 $\boldsymbol{\mu}=(\mu_1, \cdots, \mu_N)$.
Crosslists for Fri, 19 Jan 18
 [86] arXiv:1712.00458 (crosslist from nlin.PS) [pdf, other]

Title: Chimera States in Continuous Media: Existence and DistinctnessComments: Supplemental animation at article webpage: this http URLJournalref: 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 GinzburgLandau 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 (crosslist from quantph) [pdf, ps, other]

Title: Gaussian quantum resource theoriesComments: 6+11 pages, no figuresSubjects: Quantum Physics (quantph); Statistical Mechanics (condmat.statmech); High Energy Physics  Theory (hepth); Mathematical Physics (mathph); Optics (physics.optics)
We develop a general framework characterizing the structure and properties of quantum resource theories for continuousvariable Gaussian states and Gaussian operations, establishing methods for their description and quantification. We show in particular that, under a few intuitive and physicallymotivated 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 (crosslist from grqc) [pdf, ps, other]

Title: Perturbations of Extremal Kerr Spacetime: Analytic Framework and Latetime TailsComments: 31 pagesSubjects: General Relativity and Quantum Cosmology (grqc); High Energy Physics  Theory (hepth); Mathematical Physics (mathph)
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 frequencydomain Green function in terms of infinite series of special functions. As an application, we compute the leading latetime 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 (crosslist from cs.DS) [pdf, ps, other]

Title: Efficient Computation of the 8point DCT via Summation by PartsComments: 13 pages, 4 figures, 2 tablesJournalref: 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 8point discrete cosine transform (DCT) based on the summationbyparts 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 8point 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 (crosslist from nlin.AO) [pdf, ps, other]

Title: Synchronization of electrically coupled resonateandfire neuronsSubjects: Adaptation and SelfOrganizing 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 spikemediated coupling on synchrony in small networks of electrically coupled resonateandfire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete postspike 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 postspike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "resetinduced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phaselocking of symmetrically coupled pairs.
 [91] arXiv:1801.05959 (crosslist from quantph) [pdf, other]

Title: Mapping topological to conformal field theories through strange correlatorsAuthors: Matthias Bal, Dominic J. Williamson, Robijn Vanhove, Nick Bultinck, Jutho Haegeman, Frank VerstraeteSubjects: Quantum Physics (quantph); Statistical Mechanics (condmat.statmech); Strongly Correlated Electrons (condmat.strel); High Energy Physics  Lattice (heplat); Mathematical Physics (mathph)
We extend the concept of strange correlators, defined for symmetryprotected phases in [You et al., Phys. Rev. Lett. 112, 247202 (2014)], to topological phases of matter by taking the inner product between stringnet ground states and product states. The resulting twodimensional partition functions are shown to be either critical or symmetry broken, as the corresponding transfer matrices inherit all matrix product operator symmetries of the stringnet states. For the case of critical systems, those nonlocal 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 stringnet 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/hardhexagon and Ising stringnet. Additionally, we provide a complementary perspective on symmetrypreserving realspace renormalization by showing how known tensor network renormalization methods can be understood as the approximate truncation of an exactly coarsegrained strange correlator.
 [92] arXiv:1801.06014 (crosslist from eess.SP) [pdf, other]

Title: Image Enhancement and Noise Reduction Using Modified DelayMultiplyandSum Beamformer: Application to Medical Photoacoustic ImagingComments: This paper was accepted and presented at Iranian Conference on Electrical Engineering (ICEE) 2017Journalref: Iranian Conference on Electrical Engineering, 24 May 2017Subjects: 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. DelayandSum (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 offaxis signals contribution. To address these problems a new paradigm namely DelayMultiplyandSum (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, twopoint 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 twopoint target. Moreover, levels of sidelobe are reduced for about 25 dB.
 [93] arXiv:1801.06037 (crosslist from grqc) [pdf, other]

Title: The annoying null boundariesComments: 15 pagesSubjects: General Relativity and Quantum Cosmology (grqc); Differential Geometry (math.DG)
We consider a class of globally hyperbolic spacetimes 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 noncompact case.
 [94] arXiv:1801.06046 (crosslist from qbio.NC) [pdf, ps, other]

Title: Conditions for traveling waves in spiking neural networksAuthors: Johanna Senk, Karolína Korvasová, Jannis Schuecker, Espen Hagen, Tom Tetzlaff, Markus Diesmann, Moritz HeliasComments: 42 pages, 12 figuresSubjects: Neurons and Cognition (qbio.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 neuralfield models, phenomenological coarsegrained descriptions of neuralnetwork 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 meanfield theory to reduce a microscopic model of leaky integrateandfire (LIF) neurons with distancedependent connectivity to an effective neuralfield model. In contrast to existing phenomenological descriptions, the dynamics in this neuralfield 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 neuralfield 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 twopopulation networks of excitatory and inhibitory neurons as a combination of delayinduced temporal oscillations and spatial oscillations due to distancedependent connectivity profiles. Finally, we demonstrate quantitative agreement between predictions of the analytically tractable neuralfield model and numerical simulations of both networks of nonlinear ratebased units and networks of LIF neurons.
 [95] arXiv:1801.06069 (crosslist from stat.ME) [pdf, ps, other]

Title: Graphical models for mediation analysisSubjects: 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 socalled pathspecific 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 pathspecific 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 pathspecific effects can be identified under such models, and how this can be done.
 [96] arXiv:1801.06104 (crosslist from cs.CV) [pdf, other]

Title: Invariants of multidimensional time series based on their iteratedintegral signatureSubjects: 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 iteratedintegral signature.
 [97] arXiv:1801.06159 (crosslist 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 (crosslist from quantph) [pdf, other]

Title: Classical simulation of photonic linear optics with lost particlesComments: 26 pages, 14 figures, comments and suggestions are welcomeSubjects: Quantum Physics (quantph); Mathematical Physics (mathph)
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 linearoptical network and is subsequently measured by particlenumber 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 tablesComments: There are some theoretical mistakes. Thus, we would like to withdraw the paperSubjects: Combinatorics (math.CO); Computation (stat.CO)
 [100] arXiv:1307.3965 (replaced) [pdf, ps, other]

Title: The Hyperbolic AxLindemannWeierstrass conjectureComments: The only modification is A.Yafaev'acknowledgement of ERC supportSubjects: Algebraic Geometry (math.AG); Complex Variables (math.CV); Number Theory (math.NT)
 [101] arXiv:1406.2178 (replaced) [pdf, ps, other]

Title: Generalized muordinary Hasse invariantsComments: final version, completely revised, to appearSubjects: 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 3Block ADMM for a Class of Convex Minimization ProblemsSubjects: 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 BoltzmannPoisson Model of Hot Electron Transport by Averaged Empirical Pseudopotential Band StructuresAuthors: Jose MoralesEscalante, Irene M. Gamba, Yingda Cheng, Armando Majorana, ChiWang Shu, James ChelikowskyComments: submission to CMAME (Computer Methods in Applied Mechanics and Engineering) Journal as a reply to the reviewers on February 2017Journalref: Computer Methods in Applied Mechanics and Engineering, Volume 321, 2017, Pages 209234Subjects: Computational Engineering, Finance, and Science (cs.CE); Mesoscale and Nanoscale Physics (condmat.meshall); Numerical Analysis (math.NA)
 [104] arXiv:1512.05648 (replaced) [pdf, ps, other]

Title: Curves in $\mathbb{R}^4$ and tworich pointsComments: 20 pages, 0 figures. v2: fixed an error in Section 5.2Journalref: Discrete. Comput. Geom. 58: 232253, 2017Subjects: Combinatorics (math.CO); Computational Geometry (cs.CG)
 [105] arXiv:1602.03394 (replaced) [pdf, ps, other]

Title: Visibility of quantum graph spectrum from the verticesComments: Substantially revised version; accepted for publication in J. Phys. A: Math. TheorSubjects: Spectral Theory (math.SP); Mathematical Physics (mathph)
 [106] arXiv:1603.02858 (replaced) [pdf, ps, other]

Title: Semiorthogonal decompositions of GIT quotient stacksComments: We now give in certain cases a semiorthogonal decomposition consisting of CalabiYau parts. So it cannot be refined furtherSubjects: Algebraic Geometry (math.AG)
 [107] arXiv:1603.04843 (replaced) [pdf, other]

Title: Approximating faces of marginal polytopes in discrete hierarchical modelsComments: 50 pages, 7 figures, 6 tablesSubjects: Statistics Theory (math.ST)
 [108] arXiv:1604.00711 (replaced) [pdf, ps, other]

Title: Lie algebroids as $L_\infty$ spacesComments: 46 pages, final versionSubjects: 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 SurfacesAuthors: Vladimir MitankinComments: 20 pagesJournalref: Published, J. Lond. Math. Soc. (2), 95(3):1035{1052, 2017Subjects: Number Theory (math.NT)
 [110] arXiv:1605.02408 (replaced) [pdf, ps, other]

Title: Structured Nonconvex and Nonsmooth Optimization: Algorithms and Iteration Complexity AnalysisComments: Section 4.1 is updatedSubjects: 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 structuresSubjects: 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 RootfindingComments: 7 pagesSubjects: 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 treesComments: 19 pages, Colour figuresSubjects: 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 SumAuthors: Brian CloteauxSubjects: Combinatorics (math.CO)
 [115] arXiv:1608.02389 (replaced) [pdf, other]

Title: On $H$Topological Intersection GraphsSubjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)
 [116] arXiv:1608.02415 (replaced) [pdf, other]

Title: Localization of the principal Dirichlet eigenvector in the heavytailed random conductance modelAuthors: Franziska FlegelComments: 40 pages, 3 figures. Revision: Made some arguments mathematically rigorous, made extreme value analysis fit for generalization to higher order eigenvectors, see followup paper arXiv:1801.05684Subjects: Probability (math.PR)
 [117] arXiv:1609.00505 (replaced) [pdf, ps, other]

Title: Topology of scrambled simplicesAuthors: Dmitry N. KozlovComments: 17 pages, 2 figuresSubjects: Algebraic Topology (math.AT); Combinatorics (math.CO)
 [118] arXiv:1609.05395 (replaced) [pdf, ps, other]

Title: Quantum speed limit vs. classical displacement energyComments: Revised version, 56 pagesSubjects: Mathematical Physics (mathph); Symplectic Geometry (math.SG)
 [119] arXiv:1610.08572 (replaced) [pdf, ps, other]

Title: Curve test for enhanced indsheaves and holonomic DmodulesAuthors: Takuro MochizukiSubjects: 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 coefficientsComments: 29 pagesSubjects: 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 CauchySchwarz Inequality for TensorsAuthors: YumTong SiuSubjects: Complex Variables (math.CV)
 [122] arXiv:1701.02573 (replaced) [pdf, ps, other]

Title: Relative singular locus and Balmer spectrum of matrix factorizationsAuthors: Yuki HiranoComments: Title changed, Example 5.10 added. To appear in Transactions of the AMSSubjects: 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 functionComments: 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 elsewhereSubjects: 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 metricsSubjects: Combinatorics (math.CO)
 [125] arXiv:1702.03974 (replaced) [pdf, other]

Title: Knot traces and concordanceComments: 17 pages, 15 figures. This version of the paper has been accepted by the Journal of Topology for publicationSubjects: Geometric Topology (math.GT)
 [126] arXiv:1702.08149 (replaced) [pdf, ps, other]

Title: Conjugate Real Classes in General Linear GroupsComments: minor revision. Fixed minor errorsSubjects: Rings and Algebras (math.RA)
 [127] arXiv:1703.04486 (replaced) [pdf, ps, other]

Title: Euler totient of subfactor planar algebrasAuthors: Sebastien PalcouxComments: 11 pagesSubjects: 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 SubmanifoldsComments: V2: minor changes to address referees' reports, calculations in the local construction have been made more explicit. To appear in Michigan Math. JSubjects: Differential Geometry (math.DG)
 [129] arXiv:1704.02209 (replaced) [pdf, ps, other]

Title: Another proof of the local curvature estimate for the Ricci flowAuthors: ShuYu HsuComments: 11 pages, typos correctedSubjects: 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 RothSubjects: Complex Variables (math.CV); Optimization and Control (math.OC)
 [131] arXiv:1704.07902 (replaced) [pdf, ps, other]

Title: A bijection between the set of nestingsimilarity classes and L & P matchingsComments: 9 pages, 7 figuresJournalref: Discrete Mathematics and Theoretical Computer Science DMTCS vol. 19:2, 2017, #1Subjects: Combinatorics (math.CO)
 [132] arXiv:1705.00560 (replaced) [pdf, ps, other]

Title: Group actions, the Mattila integral and applicationsAuthors: Bochen LiuComments: manuscript updatedSubjects: 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 MotionComments: The current version is a merger of the previous versions with arXiv:1705.04165Subjects: Probability (math.PR); Disordered Systems and Neural Networks (condmat.disnn); Mathematical Physics (mathph)
 [134] arXiv:1705.04165 (replaced) [pdf, ps, other]

Title: The Localization Transition in the Ultrametric EnsembleComments: This article has been merged into arXiv:1705.00923Subjects: Mathematical Physics (mathph); Disordered Systems and Neural Networks (condmat.disnn); Probability (math.PR)
 [135] arXiv:1706.01930 (replaced) [pdf, other]

Title: Square functions and the Hamming cube: DualityComments: 18 pagesSubjects: Analysis of PDEs (math.AP); Probability (math.PR)
 [136] arXiv:1706.04137 (replaced) [pdf, ps, other]

Title: Remarks to the ResonanceDecay Problem in Quantum Mechanics from a mathematical point of viewAuthors: Hellmut BaumgärtelComments: 10 pagesSubjects: Mathematical Physics (mathph)
 [137] arXiv:1706.06431 (replaced) [pdf, ps, other]

Title: Extensions of arcanalytic functionsComments: Published version (corrected). arXiv admin note: text overlap with arXiv:1701.02712Journalref: Math. Ann. (2018)Subjects: Algebraic Geometry (math.AG)
 [138] arXiv:1707.00810 (replaced) [pdf, other]

Title: Rényi Resolvability and Its Applications to the Wiretap ChannelComments: 49 pages. An error in the exponent in Theorem 6 has been fixedSubjects: Information Theory (cs.IT); Cryptography and Security (cs.CR)
 [139] arXiv:1707.03794 (replaced) [pdf, ps, other]

Title: Coupling LoadFollowing Control with OPFComments: This article has been accepted for publication in the IEEE Transactions on Smart GridSubjects: 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 axiomAuthors: Tomasz WitczakComments: 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 bibliographySubjects: Logic (math.LO)
 [141] arXiv:1707.04658 (replaced) [pdf, ps, other]

Title: Multivariate RankinSelberg integrals on $\mathrm{GL}_4$ and $\mathrm{GU}(2,2)$Comments: Final version. To appear in Canad. Math. BullSubjects: Number Theory (math.NT); Representation Theory (math.RT)
 [142] arXiv:1707.04976 (replaced) [pdf, ps, other]

Title: Stochastic NearOptimal Controls for PathDependent SystemsComments: We shorten some of the proofs, the Introduction was updated and a concrete example to Mathematical Finance is presentedSubjects: Probability (math.PR); Optimization and Control (math.OC)
 [143] arXiv:1708.02089 (replaced) [pdf, ps, other]

Title: On the cardinality of the manifold setComments: 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 tSubjects: 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 frequencyComments: 1 figureSubjects: Spectral Theory (math.SP)
 [145] arXiv:1708.09357 (replaced) [pdf, other]

Title: On the quasiAblowitzSegur and quasiHastingsMcLeod solutions of the inhomogeneous Painlevé II equationComments: 13 pages, 2 figures, typos corrected, references addedSubjects: Classical Analysis and ODEs (math.CA)
 [146] arXiv:1709.00742 (replaced) [pdf, ps, other]

Title: The Averaged Kaczmarz Iteration for Solving Inverse ProblemsSubjects: Numerical Analysis (math.NA)
 [147] arXiv:1709.01580 (replaced) [pdf, other]

Title: The rank function of a positroid and noncrossing partitionsComments: 11 pages, 2 figures. v2 : Completely reworked proof. arXiv admin note: text overlap with arXiv:1701.08483Subjects: Combinatorics (math.CO)
 [148] arXiv:1709.04042 (replaced) [pdf, other]

Title: Winding of simple walks on the square latticeAuthors: Timothy BuddComments: 33 pages, 15 figures. Section 4 has been extended and some minor errors have been fixedSubjects: Combinatorics (math.CO); Mathematical Physics (mathph); Probability (math.PR)
 [149] arXiv:1709.04297 (replaced) [pdf, ps, other]

Title: A Discontinuous Ritz Method for a Class of Calculus of Variations ProblemsComments: 17 pages, 1 figure and 4 tablesSubjects: Numerical Analysis (math.NA)
 [150] arXiv:1709.05169 (replaced) [pdf, ps, other]

Title: Nonequilibrium Work Relation from Schroedinger's Unrecognized Probability TheoryAuthors: T. KoideComments: 8 pages, no figure. Typos are corrected, and discussions and references are added. Accepted for publication in J. Phys. CommuSubjects: Statistical Mechanics (condmat.statmech); Mathematical Physics (mathph); Quantum Physics (quantph)
 [151] arXiv:1709.07298 (replaced) [pdf, other]

Title: On the distribution of monochromatic complete subgraphs and arithmetic progressionsComments: Revised version include some heuristic supportSubjects: Combinatorics (math.CO)
 [152] arXiv:1710.02050 (replaced) [pdf, ps, other]

Title: Characterizations of generalized John domains in $\mathbb{R}^n$ via metric dualityComments: 24 pages, 17 figures, substantial changes on the introductionSubjects: 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 GridsComments: 27 pages, 5 figuresSubjects: Probability (math.PR)
 [154] arXiv:1710.09090 (replaced) [pdf, other]

Title: Kernelbased collocation methods for Zakai equationsAuthors: Yumiharu NakanoSubjects: 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 1dimensional Stein spacesAuthors: Jürgen LeitererComments: 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 correctedSubjects: Complex Variables (math.CV)
 [156] arXiv:1711.03524 (replaced) [pdf, other]

Title: Maximal polynomial modulations of singular integralsAuthors: Pavel ZorinKranichComments: v3: 25 pages, Definition (3.19) corrected, other minor corrections madeSubjects: Classical Analysis and ODEs (math.CA)
 [157] arXiv:1711.03578 (replaced) [pdf, ps, other]

Title: ErdősUlam ideals vs. simple density idealsAuthors: Adam KwelaSubjects: Combinatorics (math.CO)
 [158] arXiv:1711.04099 (replaced) [pdf, ps, other]

Title: On aggregation of multitype GaltonWatson branching processes with immigrationComments: 26 pagesSubjects: Probability (math.PR)
 [159] arXiv:1711.05587 (replaced) [pdf, ps, other]

Title: Optimal local wellposedness theory for the kinetic wave equationSubjects: Analysis of PDEs (math.AP)
 [160] arXiv:1711.05589 (replaced) [pdf, other]

Title: Diffeomorphism groups of critical regularityComments: 64 pages, 10 figures. Significant improvement of the main result to include regularities $1\leq\alpha<2$. Most of the arguments are unchangedSubjects: Group Theory (math.GR); Dynamical Systems (math.DS); Geometric Topology (math.GT)
 [161] arXiv:1711.07474 (replaced) [pdf]

Title: XSAT of Linear CNF FormulasAuthors: Bernd. R. SchuhSubjects: 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 boxcounting dimension of the graph of the Weierstrass functionAuthors: Claire DavidSubjects: General Topology (math.GN); Dynamical Systems (math.DS)
 [163] arXiv:1712.00210 (replaced) [pdf, other]

Title: An upper bound on the size of avoidance couplingsComments: 8 pagesSubjects: Probability (math.PR)
 [164] arXiv:1712.00555 (replaced) [pdf, ps, other]

Title: About the equivalence between monads and monadic functorsAuthors: Hadrian HeineSubjects: Category Theory (math.CT)
 [165] arXiv:1712.01737 (replaced) [src]

Title: $uτ$continuous operators on locally solid vector latticesComments: Because of some mistakes in the paper, I would like to withdraw it from arXivSubjects: Functional Analysis (math.FA)
 [166] arXiv:1712.01775 (replaced) [pdf, other]

Title: Estimating linear functionals of a sparse family of Poisson meansSubjects: Statistics Theory (math.ST)
 [167] arXiv:1712.04121 (replaced) [pdf, ps, other]

Title: On relative GromovWitten invariants of projective completions of vector bundlesAuthors: ChengYong DuComments: 14pages; accepted for publication in SCIENCE CHINA MathematicsSubjects: Symplectic Geometry (math.SG); Algebraic Geometry (math.AG)
 [168] arXiv:1712.04905 (replaced) [pdf, ps, other]

Title: Decomposability and MordellWeil ranks of Jacobians using Picard numbersAuthors: Soohyun ParkComments: 14 pages (made some edits and added new material), Comments welcomeSubjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
 [169] arXiv:1712.06512 (replaced) [pdf, ps, other]

Title: Factoriality and class groups of cluster algebrasComments: 31 pages; minor correctionsSubjects: 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 operatorsComments: 37 pages. This updated version contains a section connecting the UALS property and dualitySubjects: Functional Analysis (math.FA)
 [171] arXiv:1712.08520 (replaced) [pdf, other]

Title: Canonical Bases for Permutohedral PlatesAuthors: Nick EarlyComments: New sections; more contextual discussionSubjects: Combinatorics (math.CO); High Energy Physics  Theory (hepth)
 [172] arXiv:1801.02745 (replaced) [pdf, other]

Title: Improved Capacity Upper Bounds for the DiscreteTime Poisson ChannelComments: 11 pages, 3 figures. Fixed some typos in Section 4.2 and added more detailed argument in Section 4.4Subjects: Information Theory (cs.IT)
 [173] arXiv:1801.03481 (replaced) [pdf, ps, other]

Title: Latent Factor Analysis of Gaussian Distributions under Graphical ConstraintsComments: 8 pagesSubjects: Information Theory (cs.IT)
 [174] arXiv:1801.04299 (replaced) [pdf, other]

Title: Belief Propagation Decoding of Polar Codes on Permuted Factor GraphsComments: in IEEE Wireless Commun. and Networking Conf. (WCNC), April 2018Subjects: Information Theory (cs.IT)
 [175] arXiv:1801.04310 (replaced) [pdf, ps, other]

Title: A MultiHop Framework for MultiSource, MultiRelay, AllCast ChannelsComments: In support of a submission to ISIT 2018Subjects: Information Theory (cs.IT)
 [176] arXiv:1801.04420 (replaced) [pdf, ps, other]

Title: LDPC Codes over Gaussian Multiple Access Wiretap ChannelComments: 21 pages, 8 figures, A Revision Submitted to IET CommunicationsSubjects: Information Theory (cs.IT)
 [177] arXiv:1801.04632 (replaced) [pdf, ps, other]

Title: On symmetric matrices associated with oriented link diagramsAuthors: Rinat KashaevComments: 13 pages, Abstract substantially shortened, Lemma 2 and Theorem 1 slightly modifiedSubjects: Geometric Topology (math.GT)
 [178] arXiv:1801.05242 (replaced) [pdf, other]

Title: A Bayesian Conjugate Gradient MethodSubjects: 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 DempsterShafer Evidence TheoryAuthors: Fuyuan XiaoComments: 24 pagesSubjects: Artificial Intelligence (cs.AI); Information Theory (cs.IT)
 [180] arXiv:1801.05768 (replaced) [pdf, other]

Title: The Asymptotic Capacity of Private SearchSubjects: Information Theory (cs.IT); Cryptography and Security (cs.CR); Data Structures and Algorithms (cs.DS)
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