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New submissions

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New submissions for Fri, 18 May 18

[1]  arXiv:1805.06483 [pdf, ps, other]
Title: A new convexity-based inequality, characterization of probability distributions and some free-of-distribution tests
Subjects: Probability (math.PR)

A new inequality between some functional of probability distribution functions is given. The inequality is based on strict convexity of a function used in functional definition. Equality sign in the inequality gives a characteristic property of some probability distributions. This fact together with special character of functional is used to construct free-of-distribution two sample tests.
Key words: convex functions; probability distances; characterization of distributions; Cram\'{e}r - von Mises distance; statistical tests.

[2]  arXiv:1805.06499 [pdf, ps, other]
Title: QoE-Aware Beamforming Design for Massive MIMO Heterogeneous Networks
Comments: Submitted to IEEE Transactions on Vehicular Technology
Subjects: Information Theory (cs.IT); Signal Processing (eess.SP)

One of the main goals of the future wireless networks is improving the users quality of experience (QoE). In this paper, we consider the problem of QoE-based resource allocation in the downlink of a massive multiple-input multiple-output (MIMO) heterogeneous network (HetNet). The network consists of a macro cell with a number of small cells embedded in it. The small cells base stations (BSs) are equipped with a few antennas, while the macro BS is equipped with a massive number of antennas. We consider the two services Video and Web Browsing and design the beamforming vectors at the BSs. The objective is to maximize the aggregated Mean Opinion Score (MOS) of the users under constraints on the BSs powers and the required quality of service (QoS) of the users. We also consider extra constraints on the QoE of users to more strongly enforce the QoE in the beamforming design. To reduce the complexity of the optimization problem, we suggest suboptimal and computationally efficient solutions. Our results illustrate that increasing the number of antennas at the BSs and also increasing the number of small cells antennas in the network leads to a higher user satisfaction.

[3]  arXiv:1805.06507 [pdf, ps, other]
Title: Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain
Comments: 14 pages
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD); Fluid Dynamics (physics.flu-dyn)

We consider the incompressible 2D Euler equations on bounded spatial domain $S$, and study the solution map on the Sobolev spaces $H^k(S)$ ($k > 2$). Through an elaborate geometric construction, we show that for any $T >0$, the time $T$ solution map $u_0 \mapsto u(T)$ is nowhere locally uniformly continuous and nowhere Fr\'echet differentiable.

[4]  arXiv:1805.06512 [pdf, other]
Title: The Broken Stick Project
Authors: P. A. Crowdmath
Comments: 15 pages, 2 figures
Subjects: History and Overview (math.HO)

The broken stick problem is the following classical question.
You have a segment $[0,1]$. You choose two points on this segment at random. They divide the segment into three smaller segments. Show that the probability that the three segments form a triangle is $1/4$.
The MIT PRIMES program, together with Art of Problem Solving, organized a high school research project where participants worked on several variations of this problem. Participants were generally high school students who posted ideas and progress to the Art of Problem Solving forums over the course of an entire year, under the supervision of PRIMES mentors. This report summarizes the findings of this CrowdMath project.

[5]  arXiv:1805.06514 [pdf, ps, other]
Title: Affine Matsuki correspondence for sheaves
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG)

We lift the affine Matsuki correspondence between real and symmetric loop group orbits in affine Grassmannians to an equivalence of derived categories of sheaves. In analogy with the finite-dimensional setting, our arguments depend upon the Morse theory of energy functions obtained from symmetrizations of coadjoint orbits. The additional fusion structures of the affine setting lead to further equivalences with Schubert constructible derived categories of sheaves on real affine Grassmannians.

[6]  arXiv:1805.06515 [pdf, ps, other]
Title: Remote Source Coding under Gaussian Noise : Dueling Roles of Power and Entropy Power
Subjects: Information Theory (cs.IT)

The distributed remote source coding (so-called CEO) problem is studied in the case where the underlying source has finite differential entropy and the observation noise is Gaussian. The main result is a new lower bound for the sum-rate-distortion function under arbitrary distortion measures. When specialized to the case of mean-squared error, it is shown that the bound exactly mirrors a corresponding upper bound, except that the upper bound has the source power (variance) whereas the lower bound has the source entropy power. Bounds exhibiting this pleasing duality of power and entropy power have been well known for direct and centralized source coding since Shannon's work.

[7]  arXiv:1805.06518 [pdf, other]
Title: On displacement of viscous liquid in a system of parallel tubes
Subjects: Classical Analysis and ODEs (math.CA)

An explicitly solvable quasi 1D model of oil displacement is studied. The problem of recovering of the reservoir geometry is solved by means of a fixed point algorithm. The stability of solution is studied in various functional classes.

[8]  arXiv:1805.06519 [pdf]
Title: Hypergeometric expansions of the general Heun function governed by two-term recurrence relations
Subjects: Classical Analysis and ODEs (math.CA)

We show that there exist infinitely many particular choices of parameters for which the three-term recurrence relations governing the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions become two-term. In these cases the coefficients are explicitly written in terms of the gamma functions.

[9]  arXiv:1805.06520 [pdf, ps, other]
Title: $L^p$ norms of the lattice point discrepancy
Comments: 37 pages, 6 figures. arXiv admin note: text overlap with arXiv:1706.04419
Subjects: Classical Analysis and ODEs (math.CA); Analysis of PDEs (math.AP)

We estimate the $L^{p}$ norms of the discrepancy between the volume and the number of integer points in $r\Omega-x$, a dilated by a factor $r$ and translated by a vector $x$ of a convex body $\Omega$ in $\mathbb{R}^{d}$ with smooth boundary with strictly positive curvature, \[ \left\{ {\displaystyle\int_{\mathbb R}}{\displaystyle\int_{\mathbb{T}^{d}}}\left\vert \sum_{k\in\mathbb{Z}^{d}}\chi _{r\Omega-x}(k)-r^{d}\left\vert \Omega\right\vert \right\vert ^{p}dxd\mu(r-R) \right\} ^{1/p}, \] where $\mu$ is a Borel measure compactly supported on the positive real axis and $R\to+\infty$.

[10]  arXiv:1805.06527 [pdf, ps, other]
Title: Inequalities and separation for covariant Schrödinger operators
Subjects: Analysis of PDEs (math.AP)

We consider a differential expression $L^{\nabla}_{V}=\nabla^{\dagger}\nabla+V$, where $\nabla$ is a metric covariant derivative on a Hermitian bundle $E$ over a geodesically complete Riemannian manifold $(M,g)$ with metric $g$, and $V$ is a linear self-adjoint bundle map on $E$. In the language of Everitt and Giertz, the differential expression $L^{\nabla}_{V}$ is said to be separated in $L^p(E)$ if for all $u\in L^p(E)$ such that $L^{\nabla}_{V}u\in L^p(E)$, we have $Vu\in L^p(E)$. We give sufficient conditions for $L^{\nabla}_{V}$ to be separated in $L^2(E)$. We then study the problem of separation of $L^{\nabla}_{V}$ in the more general $L^p$-spaces, and give sufficient conditions for $L^{\nabla}_{V}$ to be separated in $L^p(E)$, when $1<p<\infty$.

[11]  arXiv:1805.06528 [pdf, ps, other]
Title: Pulsating Fronts for a Bistable Lotka-Volterra Competition System with Advection in a Periodic Habitat
Subjects: Analysis of PDEs (math.AP)

This paper is concerned with the following Lotka-Volterra competition system with advection in a periodic habitat \begin{equation*} \begin{cases} \frac{\partial u_1}{\partial t} =d_1(x)\frac{\partial^2 u_1}{\partial x^2}-a_1(x)\frac{\partial u_1}{\partial x}+u_1\left(b_1(x)-a_{11}(x)u_1-a_{12}(x)u_2\right),\\ \frac{\partial u_2}{\partial t} =d_2(x)\frac{\partial^2 u_2}{\partial x^2}-a_2(x)\frac{\partial u_2}{\partial x}+u_2\left(b_2(x)-a_{21}(x)u_1-a_{22}(x)u_2\right), \end{cases} t>0,~x\in\Bbb R, \end{equation*} where $d_i(\cdot)$, $a_i(\cdot)$, $b_i(\cdot)$, $a_{ij}(\cdot)$ $(i,j=1,2)$ are $L$-periodic functions in $C^\nu(\Bbb{R})$ with some $\nu\in(0,1)$. Under certain assumptions, the system admits two periodic locally stable steady states $(u_1^*(x),0)$ and $(0,u_2^*(x))$. In this work, we first establish the existence of the pulsating front $U(x,x+ct)=(U_1(x,x+ct),U_2(x,x+ct))$ connecting two periodic solutions $(0,u_2^*(x))$ and $(u_1^*(x),0)$ at infinities. By using a dynamical method, we confirm further that the pulsating front is asymptotically stable for front-like initial values. As a consequence of the global asymptotically stability, we finally show that the pulsating front is unique up to translation.

[12]  arXiv:1805.06532 [pdf, other]
Title: Beyond 5G with UAVs: Foundations of a 3D Wireless Cellular Network
Subjects: Information Theory (cs.IT)

In this paper, a novel concept of three-dimensional (3D) cellular networks, that integrate drone base stations (drone-BS) and cellular-connected drone users (drone-UEs), is introduced. For this new 3D cellular architecture, a novel framework for network planning for drone-BSs as well as latency-minimal cell association for drone-UEs is proposed. For network planning, a tractable method for drone-BSs' deployment based on the notion of truncated octahedron shapes is proposed that ensures full coverage for a given space with minimum number of drone-BSs. In addition, to characterize frequency planning in such 3D wireless networks, an analytical expression for the feasible integer frequency reuse factors is derived. Subsequently, an optimal 3D cell association scheme is developed for which the drone-UEs' latency, considering transmission, computation, and backhaul delays, is minimized. To this end, first, the spatial distribution of the drone-UEs is estimated using a kernel density estimation method, and the parameters of the estimator are obtained using a cross-validation method. Then, according to the spatial distribution of drone-UEs and the locations of drone-BSs, the latency-minimal 3D cell association for drone-UEs is derived by exploiting tools from optimal transport theory. Simulation results show that the proposed approach reduces the latency of drone-UEs compared to the classical cell association approach that uses a signal-to-interference-plus-noise ratio (SINR) criterion. In particular, the proposed approach yields a reduction of up to 46% in the average latency compared to the SINR-based association. The results also show that the proposed latency-optimal cell association improves the spectral efficiency of a 3D wireless cellular network of drones.

[13]  arXiv:1805.06535 [pdf, ps, other]
Title: Stabilization rates for the damped wave equation with Hölder-regular damping
Authors: Perry Kleinhenz
Subjects: Analysis of PDEs (math.AP)

We study the decay rate of the energy of solutions to the damped wave equation in a setup where the geometric control condition is violated. We consider damping coefficients which are $0$ on a strip and vanish like polynomials, $x^{\beta}$. We prove that the semigroup cannot be stable at rate faster than $1/t^{(\beta+2)/(\beta+3)}$ by producing quasimodes of the associated stationary damped wave equation. This establishes an explicit relation between the rate of vanishing of the damping and rate of decay of solutions. Our result generalizes one of Nonnemacher in which the damping is an indicator function on a strip.

[14]  arXiv:1805.06537 [pdf, ps, other]
Title: Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
Comments: This is a preprint of a paper whose final and definite form is with 'Commun. Nonlinear Sci. Numer. Simul.', ISSN 1007-5704, available at [this http URL]. Submitted 25-March-2018; Accepted for publication 16-May-2018
Subjects: Optimization and Control (math.OC)

This paper presents three direct methods based on Gr\"{u}nwald-Letnikov, trapezoidal and Simpson fractional integral formulas to solve fractional optimal control problems (FOCPs). At first, the fractional integral form of FOCP is considered, then the fractional integral is approximated by Gr\"{u}nwald-Letnikov, trapezoidal and Simpson formulas in a matrix approach. Thereafter, the performance index is approximated either by trapezoidal or Simpson quadrature. As a result, FOCP are reduced to nonlinear programming problems, which can be solved by many well-developed algorithms. To improve the efficiency of the presented method, the gradient of the objective function and the Jacobian of constraints are prepared in closed forms. It is pointed out that the implementation of the methods is simple and, due to the fact that there is no need to derive necessary conditions, the methods can be simply and quickly used to solve a wide class of FOCPs. The efficiency and reliability of the presented methods are assessed by ample numerical tests involving a free final time with path constraint FOCP, a bang-bang FOCP and an optimal control of a fractional-order HIV-immune system.

[15]  arXiv:1805.06551 [pdf, ps, other]
Title: Ground state of a magnetic nonlinear Choquard equation
Comments: 11 pages
Subjects: Analysis of PDEs (math.AP)

We consider the stationary magnetic nonlinear Choquard equation
\[-(\nabla+iA(x))^2u+ V(x)u=\bigg(\frac{1}{|x|^{\alpha}}*F(|u|)\bigg)\frac{f(|u|)}{|u|}{u},\]
where $A: \mathbb{R}^{N}\rightarrow \mathbb{R}^{N}$ is a vector potential, $V$ is a scalar potential, $f\colon\mathbb{R}\to\mathbb{R}$ and $F$ is the primitive of $f$. Under mild hypotheses, we prove the existence of a ground state solution for this problem. We also prove a simple multiplicity result by applying Ljusternik-Schnirelmann methods.

[16]  arXiv:1805.06552 [pdf, ps, other]
Title: Global stability of a multistrain SIS model with superinfection and patch structure
Subjects: Dynamical Systems (math.DS); Classical Analysis and ODEs (math.CA)

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006 7:235-247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters. Finally, we return to the special case of one patch examined in [Math Biosci Eng. 2017 14:421-35] and give a correction to the proof of Theorem 2.2 of that paper.

[17]  arXiv:1805.06554 [pdf, ps, other]
Title: Exponential decay of Rényi divergence under Fokker-Planck equations
Comments: 14 pages
Subjects: Analysis of PDEs (math.AP)

We prove the exponential convergence to the equilibrium, quantified by R\'enyi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictly convex potential. This extends the classical exponential decay result on the relative entropy for the same equation.

[18]  arXiv:1805.06560 [pdf, ps, other]
Title: Extensions of Ramanujan's reciprocity theorem and the Andrews--Askey integral
Authors: Zhi-Guo Liu
Comments: 24 pages
Journal-ref: Journal of mathematical analysis and applications (419) 2014, Pages 1045--1064
Subjects: Combinatorics (math.CO); Classical Analysis and ODEs (math.CA); Number Theory (math.NT); Quantum Algebra (math.QA)

Ramanujan's reciprocity theorem may be considered as a three-variable extension of Jacobi's triple product identity. Using the method of $q$-partial differential equations, we extend Ramanujan's reciprocity theorem to a seven-variable reciprocity formula. The Andrews--Askey integral is a $q$-integral having four parameters with base $q$. Using the same method we extend the Andrews--Askey integral formula to a $q$-integral formula which has seven parameters with base $q$.

[19]  arXiv:1805.06564 [pdf, other]
Title: Kostant-Sekiguchi homeomorphisms
Comments: 44 pages, 2 figures
Subjects: Representation Theory (math.RT)

We lift the Kostant-Sekiguchi correspondence for classical groups to an equivariant homeomorphism between real and symmetric nilpotent cones.

[20]  arXiv:1805.06568 [pdf, ps, other]
Title: Gauss summation and Ramanujan type series for $1/π$
Authors: Zhi-Guo Liu
Comments: 7 pages
Journal-ref: International Journal of Number Theory 8 (2012)289--297
Subjects: Complex Variables (math.CV); Combinatorics (math.CO)

Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce infinitely many Ramanujan type series for $1/\pi$.

[21]  arXiv:1805.06571 [pdf, ps, other]
Title: Caching With Time-Varying Popularity Profiles: A Learning-Theoretic Perspective
Comments: Article published in IEEE Transactions on Communications, 2018
Subjects: Information Theory (cs.IT)

Content caching at the small-cell base stations (sBSs) in a heterogeneous wireless network is considered. A cost function is proposed that captures the backhaul link load called the `offloading loss', which measures the fraction of the requested files that are not available in the sBS caches. As opposed to the previous approaches that consider time-invariant and perfectly known popularity profile, caching with non-stationary and statistically dependent popularity profiles (assumed unknown, and hence, estimated) is studied from a learning-theoretic perspective. A probably approximately correct result is derived, which presents a high probability bound on the offloading loss difference, i.e., the error between the estimated and the optimal offloading loss. The difference is a function of the Rademacher complexity, the $\beta-$mixing coefficient, the number of time slots, and a measure of discrepancy between the estimated and true popularity profiles. A cache update algorithm is proposed, and simulation results are presented to show its superiority over periodic updates. The performance analyses for Bernoulli and Poisson request models are also presented.

[22]  arXiv:1805.06574 [pdf, ps, other]
Title: A canonical decomposition of strong $L^2$-functions
Comments: 51 pages
Subjects: Functional Analysis (math.FA)

In this paper we establish a canonical decomposition of operator-valued strong $L^2$-functions by the aid of the Beurling-Lax-Halmos Theorem which characterizes the shift-invariant subspaces of vector-valued Hardy space. This decomposition reduces to the Douglas-Shapiro-Shields factorization if the flip of the strong $L^2$-function is of bounded type. On the other hand, the kernel of a Hankel operator is shift-invariant. Thus in view of its converse, we may ask whether every shift-invariant subspace is represented by the kernel of a Hankel operator. This question invites us to consider a solution of the equation involved with the unbounded Hankel operators corresponding to the given inner function. In this context, we introduce a notion of the "Beurling degree" for inner functions by employing the canonical decomposition of strong $L^2$-functions induced by the given inner functions. Eventually, we establish a deep connection between the Beurling degree of the given inner function and the spectral multiplicity of the truncated backward shift on the corresponding model space. In addition, we investigate the case of Beurling degree 1.

[23]  arXiv:1805.06575 [pdf, ps, other]
Title: Some inequalities for Garvan's bicrank function of 2-colored partitions
Comments: 27 pages
Subjects: Combinatorics (math.CO); Number Theory (math.NT)

In order to provide a unified combinatorial interpretation of congruences modulo $5$ for 2-colored partition functions, Garvan introduced a bicrank statistic in terms of weighted vector partitions. In this paper, we obtain some inequalities between the bicrank counts $M^{*}(r,m,n)$ for $m=2$, $3$ and $4$ via their asymptotic formulas and some $q$-series techniques. These inequalities are parallel to Andrews and Lewis' results on the rank and crank counts for ordinary partitions.

[24]  arXiv:1805.06578 [pdf, ps, other]
Title: On the edge Szeged index of unicyclic graphs with given diameter
Subjects: Combinatorics (math.CO)

The edge Szeged index of a graph $G$ is defined as $Sz_{e}(G)=\sum\limits_{uv\in E(G)}m_{u}(uv|G)m_{v}(uv|G)$, where $m_{u}(uv|G)$ (resp., $m_{v}(uv|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), respectively. In this paper, we characterize the graph with minimum edge Szeged index among all the unicyclic graphs with given order and diameter.

[25]  arXiv:1805.06579 [pdf, ps, other]
Title: ADMM and Accelerated ADMM as Continuous Dynamical Systems
Comments: accepted at ICML 2018
Subjects: Optimization and Control (math.OC); Dynamical Systems (math.DS)

We derive differential equations that model the continuous limit of the iterate sequence generated by the alternating direction method of multipliers, as well as an accelerated variant. The dynamical system associated with the accelerated variant corresponds to a nonlinear generalization of a damped harmonic oscillator. We employ the direct method of Lyapunov to analyze the stability of critical points and to obtain convergence rates. Our results strengthen the connection between commonly used optimization algorithms and continuous dynamical systems.

[26]  arXiv:1805.06581 [pdf, ps, other]
Title: Classification of Coxeter groups with finitely many elements of $\mathbf{a}$-value 2
Comments: 34 pages; comments welcome
Subjects: Combinatorics (math.CO); Quantum Algebra (math.QA); Representation Theory (math.RT)

We consider Lusztig's $\mathbf{a}$-function on Coxeter groups (in the equal parameter case) and classify all Coxeter groups with finitely many elements of $\mathbf{a}$-value 2 in terms of Coxeter diagrams.

[27]  arXiv:1805.06583 [pdf, other]
Title: Cooperative Limited Feedback Design for Massive Machine-Type Communications
Comments: 11 Pages, 4 figures
Subjects: Information Theory (cs.IT)

Multiuser multiple-input multiple-output (MIMO) systems have been in the spotlight since it is expected to support high connection density in internet of things (IoT) networks. Considering the massive connectivity in IoT networks, the challenge for the multiuser MIMO systems is to obtain accurate channel state information (CSI) at the transmitter in order that the sum-rate throughput can be maximized. However, current communication mechanisms relying upon frequency division duplexing (FDD) might not fully support massive number of machine-type devices due to the rate-constrained limited feedback and complicated time-consuming scheduling. In this paper, we develop a cooperative feedback strategy to maximize the benefits of massive connectivity under limited resource constraint for the feedback link. In the proposed algorithm, two neighboring users form a single cooperation unit to improve the channel quantization performance by sharing some level of channel information. To satisfy the low-latency requirement in IoT networks, the cooperation process is conducted without any transmitter intervention. In addition, we analyze the sum-rate throughput of the multiuser MIMO systems relying upon the proposed feedback strategy to study a cooperation decision-making framework. Based on the analytical studies, we develop a network-adapted cooperation algorithm to turn the user cooperation mode on and off according to network conditions.

[28]  arXiv:1805.06585 [pdf, ps, other]
Title: Iterated circle bundles and infranilmanifolds
Authors: Igor Belegradek
Comments: 4 pages
Subjects: Geometric Topology (math.GT); Differential Geometry (math.DG); Group Theory (math.GR)

We give short proofs of the following two facts: Iterated principal circle bundles are precisely the nilmanifolds. Every iterated circle bundle is almost flat, and hence diffeomorphic to an infranilmanifold.

[29]  arXiv:1805.06586 [pdf, ps, other]
Title: $W^{2,p}$-solutions of parabolic SPDEs in general domains
Authors: Kai Du
Comments: 20 pages
Subjects: Probability (math.PR)

The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of $L^{p}(\Omega\times(0,T),W^{2,p}(G))$-norms of solutions. The H\"older continuity of solutions and their derivatives is also obtained by embedding.

[30]  arXiv:1805.06587 [pdf, ps, other]
Title: Displacement energy of compact Lagrangian submanifold from open subset
Authors: Yong-Geun Oh
Comments: 18 pages
Subjects: Symplectic Geometry (math.SG)

We prove that for any compact Lagrangian submanifold intersecting an open subset $U$ in tame symplectic manifold $(M,\omega)$, the Hofer displacement energy of $L$ from $U$ is positive, provided $L \cap U \neq \emptyset$. We also give an explicitlower bound in terms of an $\epsilon$-regularity type invariant for pseudo-holomorphic curves relative to $L$.

[31]  arXiv:1805.06590 [pdf, ps, other]
Title: Tauvel's height formula for quantum nilpotent algebras
Subjects: Quantum Algebra (math.QA); Rings and Algebras (math.RA)

Tauvel's height formula, which provides a link between the height of a prime ideal and the Gelfand-Kirillov dimension of the corresponding factor algebra, is verified for quantum nilpotent algebras.

[32]  arXiv:1805.06597 [pdf, other]
Title: ARUM: Polar Coded HARQ Scheme based on Incremental Channel Polarization
Subjects: Information Theory (cs.IT)

A hybrid ARQ (HARQ) scheme for polar code, which is called active-bit relocation under masks (ARUM), is proposed. In each transmission, the data bits are encoded and bit-wisely XOR-masked using a binary vector before being transmitted through the channel. The masking process combines multiple transmissions together which forms another step of inter-transmission channel transform. The reliabilities are updated after every transmission, and the less reliable bits in earlier ones are relocated to the more reliable positions at the latest transmitted block. ARUM is a very flexible HARQ scheme which allows each transmission to have a different mother code length and to adopt independent rate-matching scheme with sufficient channel state feedback in HARQ process. Simulation shows that ARUM can obtain near-optimal coding gain.

[33]  arXiv:1805.06601 [pdf, ps, other]
Title: $(t,\ell)$-stability and coherent systems
Comments: 12 pages
Subjects: Algebraic Geometry (math.AG)

Let $X$ be a non-singular irreducible complex projective curve of genus $g\geq 2$. We use $(t,\ell)$-stability to prove the existence of coherent systems over $X$ that are $\alpha$-stable for all allowed $\alpha >0$.

[34]  arXiv:1805.06607 [pdf, other]
Title: Multi-Rate Time Integration on Overset Meshes
Subjects: Numerical Analysis (math.NA)

Overset meshes are an effective tool for the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features. When the maximum allowable timestep on one or more meshes is significantly smaller than on the remaining meshes, standard explicit time integrators impose inefficiencies for time-accurate calculations by requiring that all meshes advance with the smallest timestep. With the targeted use of multi-rate time integrators, separate meshes can be time-marched at independent rates to avoid wasteful computation while maintaining accuracy and stability. This work applies time-explicit multi-rate integrators to the simulation of the compressible Navier-Stokes equations discretized on overset meshes using summation-by-parts (SBP) operators and simultaneous approximation term (SAT) boundary conditions. We introduce a novel class of multi-rate Adams-Bashforth (MRAB) schemes that offer significant stability improvements and computational efficiencies for SBP-SAT methods. We present numerical results that confirm the numerical efficacy of MRAB integrators, outline a number of outstanding implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB. We also investigate the use of our method in the setting of a large-scale distributed-memory parallel implementation where we discuss concerns involving load balancing and communication efficiency.

[35]  arXiv:1805.06613 [pdf, ps, other]
Title: On the matrix harmonic mean
Comments: This article will appear in the Journal of Mathematical Inequalities
Subjects: Functional Analysis (math.FA)

The main goal of this article is to present new types of inequalities refining and reversing inequalities of the harmonic mean of scalars and matrices. Furthermore, implementing the spectral decomposition of positive matrices, we present a new type of inequalities treating certain harmonic matrix perturbation.

[36]  arXiv:1805.06616 [pdf, ps, other]
Title: Construction of type I blowup solutions for a higher order semilinear parabolic equation
Subjects: Analysis of PDEs (math.AP)

We consider the higher-order semilinear parabolic equation $$ \partial_t u = -(-\Delta)^{m} u + u|u|^{p-1}, $$ in the whole space $\mathbb{R}^N$, where $p > 1$ and $m \geq 1$ is an odd integer. We exhibit type I non self-similar blowup solutions for this equation and obtain a sharp description of its asymptotic behavior. The method of construction relies on the spectral analysis of a non self-adjoint linearized operator in an appropriate scaled variables setting. In view of known spectral and sectorial properties of the linearized operator obtained by [Galaktionov, rspa2011], we revisit the technique developed by [Merle-Zaag, duke1997] for the classical case $m = 1$, which consists in two steps: the reduction of the problem to a finite dimensional one, then solving the finite dimensional problem by a classical topological argument based on the index theory. Our analysis provides a rigorous justification of a formal result in [Galaktionov, rspa2011].

[37]  arXiv:1805.06633 [pdf, ps, other]
Title: The blocks and weights of finite special linear and unitary groups
Authors: Zhicheng Feng
Subjects: Representation Theory (math.RT); Group Theory (math.GR)

This paper has two main parts. Firstly, we give a classification of the $\ell$-blocks of finite special linear and unitary groups $SL_n(\epsilon q)$ in the non-defining characteristic $\ell\ge 3$. Secondly, we describe how the $\ell$-weights of $SL_n(\epsilon q)$ can be obtained from the $\ell$-weights of $GL_n(\epsilon q)$ when $\ell\nmid\mathrm{gcd}(n,q-\epsilon)$, and verify the Alperin weight conjecture for $SL_n(\epsilon q)$ under the condition $\ell\nmid\mathrm{gcd}(n,q-\epsilon)$. As a step to establish the Alperin weight conjecture for all finite groups, we prove the inductive blockwise Alperin weight condition for any unipotent $\ell$-block of $SL_n(\epsilon q)$ if $\ell\nmid\mathrm{gcd}(n,q-\epsilon)$.

[38]  arXiv:1805.06640 [pdf, other]
Title: Testing for Conditional Mean Independence with Covariates through Martingale Difference Divergence
Comments: 10 pages, 3 figures
Subjects: Statistics Theory (math.ST); Applications (stat.AP); Computation (stat.CO); Methodology (stat.ME); Machine Learning (stat.ML)

As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, we reformulate an equivalent notion of conditional mean independence through transformation, which is approximated in practice. We apply the martingale difference divergence (Shao and Zhang, 2014) to measure conditional mean dependence, and show that the estimation error from approximation is negligible, as it has no impact on the asymptotic distribution of the test statistic under some regularity assumptions. The implementation of our test is demonstrated by both simulations and a financial data example.

[39]  arXiv:1805.06642 [pdf, ps, other]
Title: The higher rank $q$-deformed Bannai-Ito and Askey-Wilson algebra
Comments: 37 pages
Subjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph)

The $q$-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra $\mathfrak{osp}_q(1\vert 2)$. It turned out to be isomorphic to the Askey-Wilson algebra. In the present paper these results will be extended to higher rank. The rank $n-2$ $q$-Bannai-Ito algebra $\mathcal{A}_n^q$, which by the established isomorphism also yields a higher rank version of the Askey-Wilson algebra, is constructed in the $n$-fold tensor product of $\mathfrak{osp}_q(1\vert 2)$. An explicit realization in terms of $q$-shift operators and reflections is proposed, which will be called the $\mathbb{Z}_2^n$ $q$-Dirac-Dunkl model. The algebra $\mathcal{A}_n^q$ is shown to arise as the symmetry algebra of the constructed $\mathbb{Z}_2^n$ $q$-Dirac-Dunkl operator and to act irreducibly on modules of its polynomial null-solutions. An explicit basis for these modules is obtained using a $q$-deformed $\mathbf{CK}$-extension and Fischer decomposition.

[40]  arXiv:1805.06645 [pdf, ps, other]
Title: Performance Analysis and Optimization of Cooperative Full-Duplex D2D Communication Underlaying Cellular Networks
Comments: 31 pages, 10 figures, submitted to IEEE journal for possible publication
Subjects: Information Theory (cs.IT)

This paper investigates the cooperative full-duplex device-to-device (D2D) communication underlaying cellular network, where the cellular user (CU) acts as a full-duplex relay to assist the D2D communication. To simultaneously support D2D relaying and uplink transmission, superposition coding and successive interference cancellation are adopted at the CU and the D2D receiver, respectively. The achievable rate region and joint outage probability are derived to characterize the performance of the considered system. An optimal power allocation scheme is proposed to maximize the minimum achievable rate. Besides, by analyzing the upper bound of the joint outage probability, we study a suboptimal power allocation to improve the outage performance. The simulation results confirm the theoretical analysis and the advantages of the proposed power allocation schemes.

[41]  arXiv:1805.06650 [pdf, other]
Title: Generalized least square homotopy perturbations for system of fractional partial differential equations
Comments: 20 Pages, 12 Figures
Subjects: Numerical Analysis (math.NA)

In this paper, generalized aspects of least square homotopy perturbations are explored to treat the system of non-linear fractional partial differential equations and the method is called as generalized least square homotopy perturbations (GLSHP). The concept of partial fractional Wronskian is introduced to detect the linear independence of functions depending on more than one variable through Caputo fractional calculus. General theorem related to Wronskian is also proved. It is found that solutions converge more rapidly through GLSHP in comparison to classical fractional homotopy perturbations. Results of this generalization are validated by taking examples from nonlinear fractional wave equations.

[42]  arXiv:1805.06656 [pdf]
Title: Method of improvement of convergence Fourier series and interpoliation polynomials in orthogonal functions
Subjects: Numerical Analysis (math.NA)

There is proposed a method for improving the convergence of Fourier series by function systems, orthogonal at the segment, the application of which allows for smooth functions to receive uniformly convergent series. There is also proposed the method of phantom nodes improving the convergence of interpolation polynomials on systems of orthogonal functions, the application of which in many cases can significantly reduce the interpolation errors of these polynomials. The results of calculations are given at test cases using the proposed methods for trigonometric Fourier series; these calculations illustrate the high efficiency of these methods. Undoubtedly, the proposed method of phantom knots requires further theoretical studies.

[43]  arXiv:1805.06659 [pdf, other]
Title: Positive periodic solutions to an indefinite Minkowski-curvature equation
Comments: 49 pages, 4 PDF figures
Subjects: Classical Analysis and ODEs (math.CA)

We investigate the existence, non-existence, multiplicity of positive periodic solutions, both harmonic (i.e., $T$-periodic) and subharmonic (i.e., $kT$-periodic for some integer $k \geq 2$) to the equation \begin{equation*} \Biggl{(} \dfrac{u'}{\sqrt{1-(u')^{2}}} \Biggr{)}' + \lambda a(t) g(u) = 0, \end{equation*} where $\lambda > 0$ is a parameter, $a(t)$ is a $T$-periodic sign-changing weight function and $g \colon \mathopen{[}0,+\infty\mathclose{[} \to \mathopen{[}0,+\infty\mathclose{[}$ is a continuous function having superlinear growth at zero. In particular, we prove that for both $g(u)=u^{p}$, with $p>1$, and $g(u)= u^{p}/(1+u^{p-q})$, with $0 \leq q \leq 1 < p$, the equation has no positive $T$-periodic solutions for $\lambda$ close to zero and two positive $T$-periodic solutions (a 'small' one and a 'large' one) for $\lambda$ large enough. Moreover, in both cases the 'small' $T$-periodic solution is surrounded by a family of positive subharmonic solutions with arbitrarily large minimal period. The proof of the existence of $T$-periodic solutions relies on a recent extension of Mawhin's coincidence degree theory for locally compact operators in product of Banach spaces, while subharmonic solutions are found by an application of the Poincar\'e--Birkhoff fixed point theorem, after a careful asymptotic analysis of the $T$-periodic solutions for $\lambda \to +\infty$.

[44]  arXiv:1805.06663 [pdf]
Title: Causal Inference from Strip-Plot Designs in a Potential Outcomes Framework
Subjects: Statistics Theory (math.ST)

Strip-plot designs are very useful when the treatments have a factorial structure and the factors levels are hard-to-change. We develop a randomization-based theory of causal inference from such designs in a potential outcomes framework. For any treatment contrast, an unbiased estimator is proposed, an expression for its sampling variance is worked out, and a conservative estimator of the sampling variance is obtained. This conservative estimator has a nonnegative bias, and becomes unbiased under between-block additivity, a condition milder than Neymannian strict additivity. A minimaxity property of this variance estimator is also established. Simulation results on the coverage of resulting confidence intervals lend support to theoretical considerations.

[45]  arXiv:1805.06667 [pdf, other]
Title: A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
Subjects: Numerical Analysis (math.NA)

A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the discrete surface like in {Dziuk's} method, and linearly implicit backward difference formulae for time integration. The proposed method differs from Dziuk's approach in that it discretizes Huisken's evolution equations for the normal vector and mean curvature and uses these evolving geometric quantities in the velocity law projected to the finite element space. This numerical method admits a convergence analysis, which combines stability estimates and consistency estimates to yield optimal-order $H^1$-norm error bounds for the computed surface position, velocity, normal vector and mean curvature. The stability analysis is based on the matrix--vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.

[46]  arXiv:1805.06669 [pdf, ps, other]
Title: R{é}solution du $\partial \bar{\partial}$ pour les formes diff{é}rentielles ayant une valeur au bord au sens des courants d{é}finies dans un domaine contractile fortement pseudoconvexe d'une vari{é}t{é} complexe
Authors: S. Sambou, S. Sambou
Comments: in French
Subjects: Complex Variables (math.CV)

We solve the $\partial \bar{\partial}$-problem for a form with distribution boundary value on a strongly pseudoconvex contractible domain of a complex manifold.

[47]  arXiv:1805.06672 [pdf, ps, other]
Title: Brezis-Gallouet-Wainger type inequality with critical fractional Sobolev space and BMO
Comments: 12 pages, Accepted Paper: Comptes Rendus Mathematique
Subjects: Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA)

In this paper, we prove the Brezis-Gallouet-Wainger type inequality involving the BMO norm, the fractional Sobolev norm, and the logarithmic norm of $\mathcal{\dot{C}}^\eta$, for $\eta\in(0,1)$.

[48]  arXiv:1805.06675 [pdf, other]
Title: Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime
Comments: 20 pages, 12 figures
Subjects: Mathematical Physics (math-ph); Quantum Physics (quant-ph)

The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments remain finite in the limit of large matrix dimensions. Though in this case standard analytical tools are inapplicable, we found that in all considered cases eigenvector distributions are extremely well described by the generalised hyperbolic distribution which differs considerably from the usual Porter-Thomas distribution but shares with it certain universal properties.

[49]  arXiv:1805.06676 [pdf, other]
Title: LQ-optimal Sample-data Control under Stochastic Delays: Gridding Approach for Stabilizability and Detectability
Comments: 28 pages, 3 figures
Subjects: Optimization and Control (math.OC)

We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively solving a Riccati difference equation, provided that a discrete-time Markov jump system equivalent to the sampled-data system is stochastic stabilizable and detectable. Sufficient conditions for these notions are provided in the form of linear matrix inequalities, from which stabilizing controllers and state observers can be constructed.

[50]  arXiv:1805.06679 [pdf, ps, other]
Title: Numerical conservation of energy, momentum and actions for extended RKN methods when applied to nonlinear wave equations via spatial spectral semi-discretizations
Authors: Bin Wang, Xinyuan Wu
Subjects: Numerical Analysis (math.NA)

This paper analyses the long-time behaviour of extended Runge--Kutta--Nystr\"{o}m (ERKN) methods when applied to nonlinear wave equations. It is shown that energy, momentum, and all harmonic actions are approximately preserved over a long time for a one-stage explicit ERKN method when applied to nonlinear wave equations via spectral semi-discretisations. The results are proved by deriving a multi-frequency modulated Fourier expansion of the ERKN method and showing three almost-invariants of the modulation system.

[51]  arXiv:1805.06684 [pdf, other]
Title: The Grothendieck-Teichmueller Lie algebra and Brown's dihedral moduli spaces
Authors: Johan Alm
Comments: 37 pages
Subjects: Quantum Algebra (math.QA); Algebraic Geometry (math.AG)

We prove that the degree zero operadic Hochschild cohomology of the homology operad of Brown's dihedral moduli spaces is the Grothendieck-Teichmueller Lie algebra plus two classes, giving a new perspective on the relationship between the Grothendieck-Teichmueller Lie algebra and (motivic) multiple zeta values.

[52]  arXiv:1805.06688 [pdf, ps, other]
Title: Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations
Comments: 20 pages, 4 figures, 8 tables
Subjects: Numerical Analysis (math.NA)

The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to discretize spatial and temporal derivatives to propagate solutions. Next, we present a non-intrusive time-parallelization and its two-level convergence analysis, where we algorithmically and theoretically generalize the MGRIT to time-dependent fine time-grid propagators. Finally, numerical illustrations show that the obtained numerical scheme possesses the saturation error order, theoretical results of the two-level variant deliver good predictions, and significant speedups can be achieved when compared to parareal and the sequential time-stepping approach.

[53]  arXiv:1805.06700 [pdf]
Title: Solving the linear fractional derivatives ordinary differential equations with constant matrix coefficients
Comments: in Russian
Subjects: Dynamical Systems (math.DS)

The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding solution. On the basis of the obtained results the conditions are given, providing the asymptotic stability of the initial system. The results are illustrated on the numerical example, where it is shown that when the order of the fractional derivative tends to unity, so the solution tends to the corresponding exponential function.

[54]  arXiv:1805.06703 [pdf, other]
Title: Super Ricci flows for weighted graphs
Comments: 40 pages; Comments welcome!
Subjects: Differential Geometry (math.DG); Probability (math.PR)

We present a notion of super Ricci flow for time-dependent finite weighted graphs. A challenging feature is that these flows typically encounter singularities where the underlying graph structure changes. Our notion is robust enough to allow the flow to continue past these singularities. As a crucial tool for this purpose we study the heat flow on such singular time-dependent weighted graphs with changing graph structure. We then give several equivalent characterizations of super Ricci flows in terms of a discrete dynamic Bochner inequality, gradient and transport estimates for the heat flow, and dynamic convexity of the entropy along discrete optimal transport paths. The latter property can be used to show that our notion of super Ricci flow is consistent with classical super Ricci flows for manifolds (or metric measure spaces) in a discrete to continuum limit.

[55]  arXiv:1805.06704 [pdf, ps, other]
Title: Hyers-Ulam Stability of Bessel Equations
Comments: 10 pages
Subjects: Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA)

We analyse different kinds of stabilities for the Bessel equation and for the modified Bessel equation with initial conditions. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, $\sigma$-semi-Hyers-Ulam and Hyers-Ulam stabilities for those equations. Those sufficient conditions are obtained based on the use of integral techniques and majorations.

[56]  arXiv:1805.06706 [pdf, ps, other]
Title: Systematic encoders for generalized Gabidulin codes and the $q$-analogue of Cauchy matrices
Authors: Alessandro Neri
Comments: 26 pages
Subjects: Information Theory (cs.IT)

We characterize the generator matrix in standard form of generalized Gabidulin codes. The parametrization we get for the non-systematic part of this matrix coincides with the $q$-analogue of generalized Cauchy matrices, leading to the definition of generalized rank Cauchy matrices. These matrices can be represented very conveniently and their representation allows to define new interesting subfamilies of generalized Gabidulin codes whose generator matrix is a structured matrix. In particular, as an application, we construct Gabidulin codes whose generator matrix is the concatenation of an identity block and a Toeplitz/Hankel matrix. In addition, our results allow to give a new efficient criterion to verify whether a rank metric code of dimension $k$ and length $n$ is a generalized Gabidulin code. This criterion is only based on the computation of the rank of one matrix and on the verification of the linear independence of two sets of elements and it requires $\mathcal O(k^2n)$ field operations.

[57]  arXiv:1805.06707 [pdf, ps, other]
Title: Diagonal realizability in the Nonnegative Inverse Eigenvalue Problem
Subjects: Spectral Theory (math.SP)

We show that if a list of nonzero complex numbers $\sigma=(\lambda_1,\lambda_2,\ldots,\lambda_k)$ is the nonzero spectrum of a diagonalizable nonnegative matrix, then $\sigma$ is the nonzero spectrum of a diagonalizable nonnegative matrix of order $k+k^2.$

[58]  arXiv:1805.06709 [pdf, ps, other]
Title: Brownian Motions on Metric Graphs with Non-Local Boundary Conditions I: Characterization
Authors: Florian Werner
Subjects: Probability (math.PR)

A classification for Brownian motions on metric graphs, that is, right continuous strong Markov processes which behave like a one-dimensional Brownian motion on the edges and feature effects like Walsh skewness, stickiness and jumps at the vertices, is obtained. The Feller property of these processes is proved, and the boundary conditions of their generators are identified as non-local Feller-Wentzell boundary conditions. By using a technique of successive revivals, a complete description of the generator is achieved for Brownian motions on star graphs.

[59]  arXiv:1805.06713 [pdf, other]
Title: Bounds for the smallest $k$-chromatic graphs of given girth
Comments: 17 pages; submitted for publication
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)

Let $n_g(k)$ denote the smallest order of a $k$-chromatic graph of girth at least $g$. We consider the problem of determining $n_g(k)$ for small values of $k$ and $g$. After giving an overview of what is known about $n_g(k)$, we provide some new lower bounds based on exhaustive searches, and then obtain several new upper bounds using computer algorithms for the construction of witnesses, and for the verification of their correctness. We also present the first examples of reasonably small order for $k = 4$ and $g > 5$. In particular, the new bounds include: $n_4(7) \leq 77$, $26 \leq n_6(4) \leq 66$, $30 \leq n_7(4) \leq 171$.

[60]  arXiv:1805.06716 [pdf, other]
Title: Gabor phase retrieval is severely ill-posed
Comments: 16 pages
Subjects: Functional Analysis (math.FA)

The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous [2]. On the other hand, the problem is always stable in finite-dimensional settings. A prominent example of such a phase retrieval problem is the recovery of a signal from the modulus of its Gabor transform. In this paper, we study Gabor phase retrieval and ask how the stability degrades on a natural family of finite-dimensional subspaces of the signal domain $L^2(\mathbb{R})$. We prove that the stability constant scales at least quadratically exponentially in the dimension of the subspaces. Our construction also shows that typical priors such as sparsity or smoothness promoting penalties do not constitute regularization terms for phase retrieval.

[61]  arXiv:1805.06717 [pdf, ps, other]
Title: Density for solutions to stochastic differential equations with unbounded drift
Authors: C. Olivera, C. Tudor
Journal-ref: Brazilian Journal of Probability and Statistics 2018
Subjects: Probability (math.PR)

Via a special transform and by using the techniques of the Malliavin calculus, we analyze the density of the solution to a stochastic differential equation with unbounded drift.

[62]  arXiv:1805.06719 [pdf, ps, other]
Title: Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics
Subjects: Probability (math.PR); Dynamical Systems (math.DS)

We consider Perron-Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations, and establish their Fr\'{e}chet differentiability with respect to the drift. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron-Frobenius and Koopman operators.

[63]  arXiv:1805.06720 [pdf, ps, other]
Title: Geometry of Orlicz spaces equipped with norms generated by some lattice norms in $\mathbb{R}^{2}$
Subjects: Functional Analysis (math.FA)

In Orlicz spaces generated by convex Orlicz functions a family of norms generated by some lattice norms in $\mathbb{R}^{2}$ are defined and studied. This family of norms includes the family of the p-Amemiya norms ($1\leq p\leq\infty$) studied in [10-11], [14-15] and [20]. Criteria for strict monotonicity, lower and upper local uniform monotonicities and uniform monotonicities of Orlicz spaces and their subspaces of order continuous elements, equipped with these norms, are given in terms of the generating Orlicz functions, and the lattice norm in $\mathbb{R}^{2}$. The problems of strict convexity and of the existence of order almost isometric as well as of order isometric copies in these spaces are also discussed.

[64]  arXiv:1805.06727 [pdf, ps, other]
Title: Realization of a graph as the Reeb graph of a Morse function on a manifold
Subjects: Geometric Topology (math.GT)

We investigate the problem of the realization of a given graph as the Reeb graph $\mathcal{R}(f)$ of a smooth function $f\colon M\rightarrow \mathbb{R}$ with finitely many critical points, where $M$ is a closed manifold. We show that for any $n\geq2$ and any graph $\Gamma$ admitting the so called good orientation there exist an $n$-manifold $M$ and a Morse function $f\colon M\rightarrow \mathbb{R} $ such that its Reeb graph $\mathcal{R}(f)$ is isomorphic to $\Gamma$, extending previous results of Sharko and Masumoto-Saeki. We prove that Reeb graphs of simple Morse functions maximize the number of cycles. Furthermore, we provide a complete characterization of graphs which can arise as Reeb graphs of surfaces.

[65]  arXiv:1805.06729 [pdf, ps, other]
Title: Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets
Subjects: Optimization and Control (math.OC); Systems and Control (cs.SY)

In this note, we present a data-driven approach for ambiguous or distributionally robust chance constrained optimization problems. We consider the case where the decision-maker has access to a finite number of samples or realizations of the uncertainty. The chance constraint is then required to hold for all distributions that are close to the empirical distribution constructed from the samples (where the distance between two distributions are defined via the Wasserstein distance). When the feasibility set of the chance constraint program is replaced by its convex inner approximation (following the framework of [Nemirovski and Shapiro 2006]), we present a convex reformulation of the ambiguous chance constraint program under the Wasserstein ambiguity set. We then show that the feasibility set of the original problem and that of its convex inner approximation are identical when the constraint function is concave in the uncertainty parameter. Finally, we present a tractable convex reformulation of the ambiguous chance constraint program when the constraint function is affine in uncertainty.

[66]  arXiv:1805.06732 [pdf, ps, other]
Title: The descriptive complexity of the set of all closed zero-dimensional subsets of a Polish space
Subjects: Logic (math.LO)

Given a space $X$ we investigate the descriptive complexity class $\G_X$ of the set $\FF_0(X)$ of all its closed zero-dimensional subsets, viewed as a subset of the hyperspace $\FF(X)$ of all closed subsets of $X$. We prove that
$\max \{ \G_X; \ X \text{ analytic } \}=\pca $ and
$\sup \{ \G_X; \ X \text{ Borel } \borm \xi\} \supseteq \Game \bora \xi$ for any countable ordinal $\xi\geq1$. In particular we prove that there exists a one-dimensional Polish subpace of $2^\wo\times \R^2$ for which $\FF_0(X)$ is not in the smallest non trivial pointclass closed under complementation and the Souslin operation $\mathcal A\,$.

[67]  arXiv:1805.06733 [pdf, ps, other]
Title: On a probabilistic Nyman-Beurling criterion for the Riemann hypothesis
Comments: 22 pages, 3 figures
Subjects: Number Theory (math.NT); Probability (math.PR)

The Riemann hypothesis can be expressed through the Nyman-Beurling criterion as an approximation problem in the space of square integrable functions on $(0,\infty)$. This involves dilation of the fractional part function by factors $\theta_k\in(0,1)$, $k\ge1$. We develop a probabilistic extension of the Nyman-Beurling criterion by considering these $\theta_k$ as random: this yields new structures and criteria, which have some relationships with the general strong B\'aez-Duarte criterion (gBD). We start here the study of these criteria, with a special focus on exponential and gamma distributions. By means of our probabilistic point of view, we partially solve an open problem raised by B\'aez-Duarte for gBD. Finally, considering random variables with $(0,\infty)$-support induces a regularization effect that we illustrate, for exponential laws, with the elimination of an arithmetical complexity within the Vasyunin formula. The involved reciprocity formula for cotangent sums is of independent interest.

[68]  arXiv:1805.06743 [pdf, ps, other]
Title: $C^*$-simplicity and representations of topological full groups of groupoids
Comments: 13 pages
Subjects: Operator Algebras (math.OA); Group Theory (math.GR)

Given an ample groupoid $G$ with compact unit space, we study the canonical representation of the topological full group $[[G]]$ in the full groupoid $C^*$-algebra $C^*(G)$. In particular, we show that the image of this representation generates $C^*(G)$ if and only if $C^*(G)$ admits no tracial state. The techniques that we use include the notion of groups covering groupoids. As an application, we provide sufficient conditions for $C^*$-simplicity of certain topological full groups, including those associated with topologically free and minimal actions of non-amenable and countable groups on the Cantor set.

[69]  arXiv:1805.06744 [pdf, ps, other]
Title: On the Motion of a Body with a Cavity Filled with Compressible Fluid
Subjects: Analysis of PDEs (math.AP)

We study the motion of the system, S, constituted by a rigid body, B, containing in its interior a viscous compressible fluid, and moving in absence of external forces. Our main objective is to characterize the long time behavior of the coupled system body-fluid. Under suitable assumptions on the "mass distribution" of S, and for sufficiently "small" Mach number and initial data, we show that every corresponding motion (in a suitable regularity class) must tend to a steady state where the fluid is at rest with respect to B. Moreover, S, as a whole, performs a uniform rotation around an axis parallel to the (constant) angular momentum of S, and passing through its center of mass.

[70]  arXiv:1805.06746 [pdf, ps, other]
Title: A Proof of the Riemann Hypothesis Through the Nicolas Inequality
Comments: 3 pages
Subjects: General Mathematics (math.GM)

A work by Nicolas has shown that if it can be proven that a certain inequality holds for all $n$, the Riemann hypothesis is true. This inequality is associated with the Mertens theorem, and hence the Euler totient at $\prod_{k=1}^n p_k$, where $n$ is any integer. We shall show that indeed the Nicolas inequality holds for all $n$.

[71]  arXiv:1805.06748 [pdf, ps, other]
Title: Automorphism group of universal Coxeter group
Authors: Olga Varghese
Comments: 7 pages
Subjects: Group Theory (math.GR)

We study algebraic and geometric properties of the automorphism group of universal Coxeter group of rank $n\geq 4$, Aut$(W_n)$. In particular, we prove that whenever Aut$(W_n)$ acts by isometries on complete $d$-dimensional CAT(0) space with $d<\lfloor\frac{n}{2}\rfloor$, then it must fix a point. We also prove that Aut$(W_n)$ does not have Kazhdan's property (T) and is not amenable. Further, strong restrictions are obtained on homomorphisms of Aut$(W_n)$ to groups that do not contain a copy of Sym(n).

[72]  arXiv:1805.06754 [pdf, ps, other]
Title: On wellposedness of generalized neural field equations with delay
Comments: this http URL
Subjects: Analysis of PDEs (math.AP); Functional Analysis (math.FA)

We obtain conditions for existence of unique global or maximally extended solutions to generalized neural field equations. We also study continuous dependence of these solutions on the spatiotemporal integration kernel, delay effects, firing rate and prehistory functions.

[73]  arXiv:1805.06755 [pdf, ps, other]
Title: Laplace transforms based some novel integrals via hypergeometric technique
Comments: 22 pages, 0 figure
Subjects: Classical Analysis and ODEs (math.CA)

In this paper, we obtain the analytical solutions of Laplace transforms based some novel integrals with suitable convergence conditions, by using hypergeometric approach (some algebraic properties of Pochhammer symbol and classical summation theorems of hypergeometric series ${}_{2}F_{1}(1)$, ${}_{2}F_{1}(-1)$ , ${}_{4}F_{3}(-1)$) . Also, we obtain the Laplace transforms of arbitrary powers of some finite series containing hyperbolic sine and cosine functions having different arguments, in terms of hypergeometric and Beta functions. Moreover, Laplace transforms of even and odd positive integral powers of sine and cosine functions with different arguments, and their combinations of the product (taking two, three, four functions at a time), are obtained. In addition, some special cases are yield from the main results.

[74]  arXiv:1805.06760 [pdf, ps, other]
Title: Topology and Higher Concurrencies
Authors: Nils A. Baas
Subjects: General Mathematics (math.GM)

We formulate a general approach to higher concurrencies in general and neural codes in particular, and suggest how the higher order aspects may be dealt with in using topology.

[75]  arXiv:1805.06761 [pdf]
Title: Fractional order (an)-isotropic total variation in image processing: Gamma-convergence and bilevel training scheme
Authors: Pan Liu, Xin Yang Lu
Subjects: Analysis of PDEs (math.AP)

New fractional $s$-order seminorms, $TV^s$, with $s\in(0,1)$ and defined via the Riemann-Liouville fractional derivative, are proposed in the multi-dimensional setting, as a generalization of the integer order $TV$-seminorms. A bilevel training scheme, which simultaneously optimizes both the parameters and the order of derivation, is proposed. The existence of solutions to the bilevel training scheme is proved by $\Gamma$--convergence. Finally, a finite grid approximation for numerically solving such training scheme is proposed, in which the approximation error is made explicit.

[76]  arXiv:1805.06762 [pdf, ps, other]
Title: On certain new means generated by $p$-functions
Comments: 16
Subjects: Classical Analysis and ODEs (math.CA)

In this paper authors generalize logarithmic mean $L$, Neuman-S\'andor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these generalized means are established.

[77]  arXiv:1805.06763 [pdf, ps, other]
Title: The $Σ_1$-Provability Logic of HA*
Comments: arXiv admin note: substantial text overlap with arXiv:1409.5699
Subjects: Logic (math.LO)

For the Heyting Arithmetic HA, HA* is defined as the theory $\{A\mid {\sf HA}\vdash A^{\Box}\}$, where $A^{\Box}$ is called the box translation of $A$. We characterize the $\Sigma_1$-provability logic of HA* as a modal theory ${\sf iH}_\sigma^*$.

[78]  arXiv:1805.06765 [pdf, ps, other]
Title: Identities for second order recurrence sequences
Authors: Kunle Adegoke
Comments: 17 pages, no figures, no tables
Subjects: General Mathematics (math.GM)

We derive several identities for arbitrary homogeneous second order recurrence sequences with constant coefficients. The results are then applied to present a unified study of six well known integer sequences, namely the Fibonacci sequence, the sequence of Lucas numbers, the Jacobsthal sequence, the Jacobsthal-Lucas sequence, the Pell sequence and the Pell-Lucas sequence.

[79]  arXiv:1805.06767 [pdf, ps, other]
Title: Model theory of Steiner triple systems
Subjects: Logic (math.LO)

A Steiner triple system is a set $S$ together with a collection $\mathcal{B}$ of subsets of $S$ of size 3 such that any two elements of $S$ belong to exactly one element of $\mathcal{B}$. It is well known that the class of finite Steiner triple systems has a Fra\"{\i}ss\'e limit $M_{\mathrm{F}}$. Here we show that the theory $T^\ast_\mathrm{Sq}$ of $M_{\mathrm{F}}$ is the model completion of the theory of Steiner triple systems. We also prove that $T^\ast_\mathrm{Sq}$ has quantifier elimination, it is not small and has $\mathrm{TP}_2$ and $\mathrm{NSOP}_1$.

[80]  arXiv:1805.06769 [pdf, ps, other]
Title: Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity
Comments: 23 pages
Subjects: Analysis of PDEs (math.AP)

In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow 'wave-like'. A Strauss type critical exponent is determined as the upper bound for the exponent in the nonlinearity in the main theorems. Two blow-up results are obtained for the sub-critical case and for the critical case, respectively. In both cases, an upper bound lifespan estimate is given.

[81]  arXiv:1805.06772 [pdf]
Title: A few results on the infimum of regular polygons equal-size split line
Authors: Yuyang Zhu
Comments: 11 pages, 9 figures
Subjects: General Mathematics (math.GM)

If an n-side unit regular polygon is divided into m equal sized parts, then what is the minimum length of the split line ${l_{m,n}}$? This problem has its practical application in real world. This paper proved that ${l_{2,3}} = \sqrt {\frac{{\sqrt 3 \pi }}{{12}}} $, ${l_{3,3}} = \frac{{\sqrt 3 }}{2}$, and $\frac{1}{2}\sqrt {n\pi {\rm{ctan}}\frac{\pi }{n}} \le \mathop {\lim }\limits_{m \to \infty } \frac{{{l_{m,n}}}}{{\sqrt m }} \le \sqrt {\frac{{\sqrt 3 }}{2}n{\rm{ctan}}\frac{\pi }{{\rm{n}}}} $

[82]  arXiv:1805.06773 [pdf, other]
Title: R2-based hypervolume contribution approximation in multi-objective optimization
Subjects: Optimization and Control (math.OC)

In this paper, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Compared with the traditional method which is based on the R2 contribution to approximate the hypervolume contribution, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method and a simple method are compared through numerical experiments. Our experimental results show the overwhelming superiority of the new method over the other two methods, where the new method achieves the best performances for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution. \keywords{Hypervolume contribution, R2 indicator, Multi-objective optimization}

[83]  arXiv:1805.06775 [pdf, other]
Title: Circularly Pulse-Shaped Precoding for OFDM: A New Waveform and Its Optimization Design for 5G New Radio
Comments: 15 pages, 21 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible
Subjects: Information Theory (cs.IT)

A new circularly pulse-shaped (CPS) precoding orthogonal frequency division multiplexing (OFDM) waveform, or CPS-OFDM for short, is proposed in this paper. CPS-OFDM, characterized by user-specific precoder flexibility, possesses the advantages of both low out-of-subband emission (OSBE) and low peak-to-average power ratio (PAPR), which are two major desired physical layer signal properties for various scenarios in 5G New Radio (NR), including fragmented spectrum access, new types of user equipments (UEs), and communications at high carrier frequencies. As opposed to most of existing waveform candidates using windowing or filtering techniques, CPS-OFDM prevents block extension that causes extra inter-block interference (IBI) and envelope fluctuation unfriendly to signal reception and power amplifier (PA) efficiency, respectively. An optimization problem of the prototype shaping vector built in the CPS precoder is formulated to minimize the variance of instantaneous power (VIP) with controllable OSBE power (OSBEP) and noise enhancement penalty (NEP). In order to solve the optimization problem involving a quartic objective function, the majorization-minimization (MM) algorithmic framework is exploited. By proving the convexity of the proposed problem, the globally optimal solution invariant of coming data is guaranteed to be attained via numbers of iterations. Simulation results demonstrate the advantages of the proposed scheme in terms of detection reliability and spectral efficiency for practical 5G cases such as asynchronous transmissions and mixed numerologies.

[84]  arXiv:1805.06778 [pdf, ps, other]
Title: Characterizations of almost greedy and partially greedy bases
Comments: 18 pages
Subjects: Functional Analysis (math.FA)

We shall present new characterizations of partially greedy and almost greedy bases. A new class of basis (which we call reverse partially greedy basis) arises naturally from these characterizations of partially greedy bases. We also give characterizations for $1$-partially greedy and $1$-reverse partially greedy bases.

[85]  arXiv:1805.06783 [pdf, ps, other]
Title: Screen Transversal Lightlike Submanifolds of Golden Semi-Riemannian Manifolds
Comments: 15 page. arXiv admin note: substantial text overlap with arXiv:1804.03600
Subjects: Differential Geometry (math.DG)

The main purpose of the present paper is to study the geometry of screen transversal lightlike submanifolds and radical screen transversal lightlike submanifolds and screen transversal anti-invariant lightlike submanifolds of Golden Semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be metric connection. We also obtain characterization of screen transversal anti-invariant lightlike submanifolds of Golden Semi- Riemannian manifolds. Finally, we give two examples.

[86]  arXiv:1805.06785 [pdf, ps, other]
Title: On the Geometry of Lightlike Submanifolds in Metallic Semi-Riemannian Manifolds
Comments: 19 pages. arXiv admin note: substantial text overlap with arXiv:1804.01355
Subjects: Differential Geometry (math.DG)

In the present paper, we introduce screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds with its subclasses, namely screen transversal anti-invariant, radical screen transversal and isotropic screen transversal lightlike submanifolds, and give an example. We show that there do not exist co-isotropic and totally screen transversal type of screen transversal anti-invariant lightlike submanifolds of a metallic semi-Riemannian manifold. We investigate the geometry of distributions involved in the definition of such submanifolds and the conditions for the induced connection to be a metric connection. Furthermore, we give a necessary and sufficient condition for an isotropic screen transversal lightlike submanifold to be totally geodesic.

[87]  arXiv:1805.06787 [pdf, other]
Title: Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II
Subjects: Numerical Analysis (math.NA)

The present work is the second part of a pair of papers, considering Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity. The first part mainly dealt with presenting a robust analysis with respect to the mesh size $h$ and the introduction of a reconstruction operator to restore divergence-conformity and pressure robustness using a non conforming right hand side. The aim of this part is the presentation of a high order polynomial robust analysis for the relaxed $H(\operatorname{div})$-conforming Hybrid Discontinuous Galerkin discretization of the two dimensional Stokes problem. It is based on the recently proven polynomial robust LBB-condition for BDM elements [P. L. Lederer, J. Sch\"oberl, IMA Journal of Numerical Analysis, 2017] and is derived by a direct approach instead of using a best approximation C\'{e}a like result. We further treat the impact of the reconstruction operator on the $hp$ analysis and present a numerical investigation considering polynomial robustness. We conclude the paper presenting an efficient operator splitting time integration scheme for the Navier--Stokes equations which is based on the methods recently presented in [C. Lehrenfeld, J. Sch\"oberl, \emph{Comp. Meth. Appl. Mech. Eng.}, 361 (2016)] and includes the ideas of the reconstruction operator.

[88]  arXiv:1805.06789 [pdf, other]
Title: Arithmeticity of the monodromy of some Kodaira fibrations
Comments: 44 pages, 9 figures
Subjects: Geometric Topology (math.GT); Algebraic Geometry (math.AG); Group Theory (math.GR)

A question of Griffiths-Schmid asks when the monodromy group of an algebraic family of complex varieties is arithmetic. We resolve this in the affirmative for the class of algebraic surfaces known as Atiyah-Kodaira manifolds, which have base and fibers equal to complete algebraic curves. Our methods are topological in nature and involve an analysis of the "geometric" monodromy, valued in the mapping class group of the fiber.

[89]  arXiv:1805.06791 [pdf, ps, other]
Title: John and uniform domains in generalized Siegel boundaries
Subjects: Metric Geometry (math.MG)

Given the pair of vector fields $X=\partial_x+|z|^{2m}y\partial_t$ and $ Y=\partial_y-|z|^{2m}x \partial_t,$ where $(x,y,t)= (z,t)\in\mathbb{R}^3=\mathbb{C}\times\mathbb{R}$, we give a condition on a bounded domain $\Omega\subset\mathbb{R}^3$ which ensures that $\Omega$ is an $(\epsilon,\delta)$-domain for the Carnot-Carath\'eodory metric. We also analyze the Ahlfors regularity of the natural surface measure induced at the boundary by the vector fields.

[90]  arXiv:1805.06796 [pdf, ps, other]
Title: The horizontal heat kernel on the quaternionic anti de-Sitter spaces and related twistor spaces
Subjects: Differential Geometry (math.DG); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)

The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel formula is explicit enough to derive small time asymptotics. Related twistor spaces and corresponding heat kernels are also discussed and the connection to the quaternionic magnetic Laplacian is done.

[91]  arXiv:1805.06800 [pdf, other]
Title: Adaptive Discrete Second Order Sliding Mode Control with Application to Nonlinear Automotive Systems
Comments: 12 pages, 7 figures, 1 table
Journal-ref: Journal of Dynamic Systems, Measurement, and Control, 2018
Subjects: Optimization and Control (math.OC)

Sliding mode control (SMC) is a robust and computationally efficient model-based controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. However, the implementation of the conventional continuous-time SMC on digital computers is limited, due to the imprecisions caused by data sampling and quantization, and the chattering phenomena, which results in high frequency oscillations. One effective solution to minimize the effects of data sampling and quantization imprecisions is the use of higher order sliding modes. To this end, in this paper, a new formulation of an adaptive second order discrete sliding mode control (DSMC) is presented for a general class of multi-input multi-output (MIMO) uncertain nonlinear systems. Based on a Lyapunov stability argument and by invoking the new Invariance Principle, not only the asymptotic stability of the controller is guaranteed, but also the adaptation law is derived to remove the uncertainties within the nonlinear plant dynamics. The proposed adaptive tracking controller is designed and tested in real-time for a highly nonlinear control problem in spark ignition combustion engine during transient operating conditions. The simulation and real-time processor-in-the-loop (PIL) test results show that the second order single-input single-output (SISO) DSMC can improve the tracking performances up to 90%, compared to a first order SISO DSMC under sampling and quantization imprecisions, in the presence of modeling uncertainties. Moreover, it is observed that by converting the engine SISO controllers to a MIMO structure, the overall controller performance can be enhanced by 25%, compared to the SISO second order DSMC, because of the dynamics coupling consideration within the MIMO DSMC formulation.

[92]  arXiv:1805.06803 [pdf, other]
Title: Supplier Cooperation in Drone Delivery
Comments: 5 pages, 3 figures, 1 table, Vehicular Technology Conference (VTC Fall), 2018 IEEE 88th
Subjects: Optimization and Control (math.OC)

Recently, unmanned aerial vehicles (UAVs), also known as drones, has emerged as an efficient and cost-effective solution for package delivery. Especially, drones are expected to incur lower cost, and achieve fast and environment friendly delivery. While most of existing drone research concentrates on surveillance applications, few works studied the drone package delivery planning problem. Even so, the previous works only focus on the drone delivery planning of a single supplier. In this paper, thus we propose the supplier cooperation in drone delivery (CoDD) framework. The framework considers jointly package assignment, supplier cooperation, and cost management. The objective of the framework is to help suppliers minimize and achieve fair share of the cost as well as reach a stable cooperation. The trade-off between using drones and outsourcing package delivery to a carrier is also investigated. The performance evaluation of the CoDD framework is conducted by using the Solomon benchmark suite and a real Singapore dataset which evidently confirms the practical findings.

[93]  arXiv:1805.06805 [pdf, ps, other]
Title: Counting Gallai 3-colorings of complete graphs
Comments: 17 pages, 9 pages of appendix, 7 figures
Subjects: Combinatorics (math.CO)

An edge coloring of the n-vertex complete graph K_n is a Gallai coloring if it does not contain any rainbow triangle, that is, a triangle whose edges are colored with three distinct colors. We prove that the number of Gallai colorings of K_n with at most three colors is at most 7(n+1)*2^{n choose 2}, which improves the best known upper bound of \frac{3}{2} * (n-1)! * 2^{(n-1) choose 2} in [Discrete Mathematics, 2017].

[94]  arXiv:1805.06810 [pdf, ps, other]
Title: Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. III
Comments: 16 pages
Subjects: Combinatorics (math.CO)

We present statistics on the decompositions (with respect to a distinguished symmetric 2t-cycle) of vertices of the hypercube graph, whose negative parts are regarded as disjoint unions of two subsets of the ground set {1,...,t} of the corresponding oriented matroid.

[95]  arXiv:1805.06811 [pdf, other]
Title: Recursive parameter estimation in a Riemannian manifold
Comments: first draft of research report
Subjects: Statistics Theory (math.ST)

This report states and proves a set of propositions concerning the convergence, rate of convergence, and asymptotic normality and efficiency, of recursive parameter estimates in a Riemannian manifold.

[96]  arXiv:1805.06812 [pdf, other]
Title: Open canals flow with fluvial to torrential phase transitions on networks
Subjects: Numerical Analysis (math.NA)

Network flows and specifically open canal flows can be modeled by systems of balance laws defined on topological graphs. The shallow water or Saint-Venant system of balance laws is one of the most used model and present two phases: fluvial or sub-critical and torrential or super critical. Phase transitions may occur within the same canal but transitions related to networks are less investigated. In this paper we provide a complete characterization of possible phase transitions for a simple network with two canals and one junction. Our analysis allows the study of more complicate scenarios. Moreover, we provide some numerical simulations to show the theory at work.

[97]  arXiv:1805.06813 [pdf, ps, other]
Title: Strong time-periodic solutions to the bidomain equations with arbitrary large forces
Subjects: Analysis of PDEs (math.AP)

We prove the existence of strong time-periodic solutions to the bidomain equations with arbitrary large forces. We construct weak time-periodic solutions by a Galerkin method combined with Brouwer's fixed point theorem and a priori estimate independent of approximation. We then show their regularity so that our solution is a strong time-periodic solution in $L^2$ spaces. Our strategy is based on the weak-strong uniqueness method.

[98]  arXiv:1805.06815 [pdf, ps, other]
Title: Artificial compressibility method for the Navier-Stokes-Maxwell-Stefan system
Subjects: Analysis of PDEs (math.AP)

The Navier-Stokes-Maxwell-Stefan system describes the dynamics of an incompressible gaseous mixture in isothermal condition. In this paper we set up an artificial compressibility type approximation. In particular we focus on the existence of solution for the approximated system and the convergence to the incompressible case. The existence of the approximating system is proved by means of semidiscretization in time and by estimating the fractional time derivative.

[99]  arXiv:1805.06817 [pdf, other]
Title: On stringy Euler characteristics of Clifford non-commutative varieties
Comments: 34 pages, 2 figures
Subjects: Algebraic Geometry (math.AG)

It was shown by Kuznetsov that complete intersections of $n$ generic quadrics in ${\mathbb P}^{2n-1}$ are related by Homological Projective Duality to certain non-commutative (Clifford) varieties which are in some sense birational to double covers of ${\mathbb P}^{n-1}$ ramified over symmetric determinantal hypersurfaces. Mirror symmetry predicts that the Hodge numbers of the complete intersections of quadrics must coincide with the appropriately defined Hodge numbers of these double covers. We observe that these numbers must be different from the well-known Batyrev's stringy Hodge numbers, else the equality fails already at the level of Euler characteristics. We define a natural modification of stringy Hodge numbers for the particular class of Clifford varieties, and prove the corresponding equality of Euler characteristics in arbitrary dimension.

[100]  arXiv:1805.06827 [pdf, ps, other]
Title: Mahavier Products, Idempotent Relations, and Condition $Γ$
Subjects: General Topology (math.GN)

Clearly, a generalized inverse limit of metrizable spaces indexed by $\mathbb N$ is metrizable, as it is a subspace of a countable product of metrizable spaces. The authors previously showed that all idempotent, upper semi-continuous, surjective, continuum-valued bonding functions on $[0,1]$ (besides the identity) satisfy a certain Condition $\Gamma$; it follows that only in trivial cases can a generalized inverse limit of copies of ([0,1]) indexed by an uncountable ordinal be metrizable. The authors show that Condition $\Gamma$ is in fact guaranteed by much weaker criteria, proving a more general metrizability theorem for certain Mahavier Products.

[101]  arXiv:1805.06831 [pdf, ps, other]
Title: Relating log-tangent integrals with the Riemann zeta function
Comments: 20 pages
Subjects: Number Theory (math.NT)

We show that integrals involving log-tangent function, with respect to certain square-integrable functions on $(0, \pi/2)$, can be evaluated by some series involving the harmonic number. Then we use this result to establish many closed forms relating to the Riemann zeta function at odd positive integers. In addition, we show that the log-tangent integral with respect to the Hurwitz zeta function defines a meromorphic function and that its values depend on the Dirichlet series $\zeta_h(s) :=\sum_{n = 1}^\infty h_n n^{-s}$, where $h_n = \sum_{k=1}^n(2k-1)^{-1}$.

[102]  arXiv:1805.06833 [pdf, other]
Title: An extension of the Plancherel measure
Comments: 10 pages + 13pages of figures, figures are contained in 3 pdf files, the first one contains the 11 pages of Figure 1
Subjects: Statistics Theory (math.ST)

Given a distribution in the unite square and having iid sample from it the first question what a statistician might do to test the hypothesis that the sample is iid. For this purpose an extension of the Plancherel measure is introduced. Recent literature on asymptotic behavior of Plancherel measure is discussed with extension to the new set up. Models for random permutations are described and the power of different tests is compared.

[103]  arXiv:1805.06838 [pdf, ps, other]
Title: Sums of Weighted Differentiation Composition Operators
Comments: 13 pages
Subjects: Complex Variables (math.CV); Functional Analysis (math.FA)

We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions of unit norm. The solution obtained has norm bounded by a constant independent of the points chosen. As a direct application, we obtain a characterization of the order-boundedness of a sum of products of weighted composition and differentiation operators acting between weighted Bergman spaces. We also characterize the compactness of such operators that map a weighted Bergman space into the space of bounded analytic functions.

[104]  arXiv:1805.06840 [pdf, other]
Title: Extending functions from a neighborhood of the sphere to the ball
Comments: 56 pages, comments are welcome
Subjects: Differential Geometry (math.DG)

In this article, we are interested in the problem of extending the germ of a smooth function $\tilde{f}$ defined along the standard sphere of dimension $n$ to a function defined on the ball which has no critical points. The article gives a necessary condition using the Morse chain complex associated to the function $f$, restriction of $\tilde{f}$ to the sphere $\mathbb{S}^n$, which is assumed to be a Morse function.

[105]  arXiv:1805.06844 [pdf, ps, other]
Title: Time Fractional Schroödinger Equation
Authors: Arnaud Rougirel (LMA-Poitiers), Hassan Emamirad
Subjects: Analysis of PDEs (math.AP)

We propose a time fractional extension of the Schr{\"o}dinger equation that keeps the main mechanical and quantum properties of the classical Schr{\"o}dinger equation. This extension is shown to be equivalent to another well identified time first order PDE with fractional hamiltonian.

[106]  arXiv:1805.06847 [pdf, ps, other]
Title: Quantitative structure of stable sets in finite abelian groups
Authors: C. Terry, J. Wolf
Subjects: Logic (math.LO); Combinatorics (math.CO)

We prove an arithmetic regularity lemma for stable subsets of finite abelian groups, generalising our previous result for high-dimensional vector spaces over finite fields of prime order. A qualitative version of this generalisation was recently obtained by the first author in joint work with Conant and Pillay, using model-theoretic techniques. In contrast, the approach in the present paper is highly quantitative and relies on several key ingredients from arithmetic combinatorics.

[107]  arXiv:1805.06848 [pdf, ps, other]
Title: Edge-statistics on large graphs
Comments: 22 pages
Subjects: Combinatorics (math.CO); Probability (math.PR)

The inducibility of a graph $H$ measures the maximum number of induced copies of $H$ a large graph $G$ can have. Generalizing this notion, we study how many induced subgraphs of fixed order $k$ and size $\ell$ a large graph $G$ on $n$ vertices can have. Clearly, this number is $\binom{n}{k}$ for every $n$, $k$ and $\ell \in \left \{0, \binom{k}{2} \right\}$. We conjecture that for every $n$, $k$ and $0 < \ell < \binom{k}{2}$ this number is at most $\left(1/e + o_k(1) \right) \binom{n}{k}$. If true, this would be tight for $\ell \in \{1, k-1\}$.
In support of our `Edge-statistics conjecture' we prove that the corresponding density is bounded away from $1$ by an absolute constant. Furthermore, for various ranges of the values of $\ell$ we establish stronger bounds. In particular, we prove that for `almost all' pairs $(k, \ell)$ only a polynomially small fraction of the $k$-subsets of $V(G)$ has exactly $\ell$ edges, and prove an upper bound of $(1/2 + o_k(1))\binom{n}{k}$ for $\ell = 1$.
Our proof methods involve probabilistic tools, such as anti-concentration results relying on fourth moment estimates and Brun's sieve, as well as graph-theoretic and combinatorial arguments such as Zykov's symmetrization, Sperner's theorem and various counting techniques.

[108]  arXiv:1805.06852 [pdf, ps, other]
Title: Saddle Point Least Squares Preconditioning of Mixed Methods
Comments: Submitted to CAMWA on 5/17/18
Subjects: Numerical Analysis (math.NA)

We present a simple way to discretize and precondition mixed variational formulations. Our theory connects with, and takes advantage of, the classical theory of symmetric saddle point problems and the theory of preconditioning symmetric positive definite operators. Efficient iterative processes for solving the discrete mixed formulations are proposed and choices for discrete spaces that are always compatible are provided. For the proposed discrete spaces and solvers, a basis is needed only for the test spaces and assembly of a global saddle point system is avoided. We prove sharp approximation properties for the discretization and iteration errors and also provide a sharp estimate for the convergence rate of the proposed algorithm in terms of the condition number of the elliptic preconditioner and the discrete $\inf-\sup$ and $\sup-\sup$ constants of the pair of discrete spaces.

[109]  arXiv:1805.06854 [pdf, ps, other]
Title: Free $(\mathbb{Z}/p)^n$-complexes and $p$-DG modules
Comments: 29 pages
Subjects: Algebraic Topology (math.AT); Commutative Algebra (math.AC); Representation Theory (math.RT)

We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring $\mathbb{F}_p[G]$ of an elementary abelian $p$-group $G$ in terms of commutative algebra. This extends results of Carlsson for $p=2$ to all primes. As an intermediate step, we construct an embedding of the derived category of perfect chain complexes over $\mathbb{F}_p[G]$ into the derived category of $p$-DG modules over a polynomial ring.

[110]  arXiv:1805.06856 [pdf, ps, other]
Title: Projections with fixed difference: a Hopf-Rinow theorem
Subjects: Functional Analysis (math.FA)

The set $D_{A_0}$, of pairs of orthogonal projections $(P,Q)$ in generic position with fixed difference $P-Q=A_0$, is shown to be a homogeneus smooth manifold: it is the quotient of the unitary group of the commutant $\{A_0\}'$ divided by the unitary subgroup of the commutant $\{P_0, Q_0\}'$, where $(P_0,Q_0)$ is any fixed pair in $D_{A_0}$. Endowed with a natural reductive structure (a linear connection) and the quotient Finsler metric of the operator norm, it behaves as a classic Riemannian space: any two pairs in $D_{A_0}$ are joined by a geodesic of minimal length. Given a base pair $(P_0,Q_0)$, pairs in an open dense subset of $D_{A_0}$ can be joined to $(P_0,Q_0)$ by a {\it unique} minimal geodesic.

[111]  arXiv:1805.06859 [pdf, ps, other]
Title: On the total volume of the double hyperbolic space
Authors: Lizhao Zhang
Comments: 23 pages
Subjects: Metric Geometry (math.MG)

Let the double hyperbolic space $\mathbb{DH}^n$, proposed in this paper as an extension of the hyperbolic space $\mathbb{H}^n$ and homeomorphic to the standard unit $n$-sphere $\mathbb{S}^n$, contain both the two sheets of the two-sheeted hyperboloid (but with the geodesics in the lower sheet $\mathbb{H}^n_{-}$ negatively \emph{valued}, and so is the associated volume element of $\mathbb{H}^n_{-}$ if $n$ is odd), which are connected at the boundary at infinity by identifying $\partial\mathbb{H}^n=\partial\mathbb{H}^n_{-}$ projectively. We propose to extend the volume of the polytopes in $\mathbb{H}^n$ to polytopes in $\mathbb{DH}^n$, where the volume can possibly be complex valued. With a proper interpretation and choice of the extension in each dimension, we prove a Schl\"{a}fli differential formula for $\mathbb{DH}^n$, and show that the total volume of $\mathbb{DH}^n$ is equal to $i^n V_n(\mathbb{S}^n)$, for both even and odd dimensions. A Schl\"{a}fli differential formula for $\partial\mathbb{H}^n$ is also explored when $n$ is odd. As a dual of $\mathbb{DH}^n$, an extension of the de Sitter space is proposed, which is compact without boundary and homeomorphic to $\mathbb{S}^{n-1}\times\mathbb{S}^1$.

[112]  arXiv:1805.06860 [pdf, other]
Title: Quantum Transport in a Low-Density Periodic Potential: Homogenisation via Homogeneous Flows
Comments: 42 pages, 1 figure
Subjects: Mathematical Physics (math-ph); Dynamical Systems (math.DS)

We show that the time evolution of a quantum wavepacket in a periodic potential converges in a combined high-frequency/Boltzmann-Grad limit, up to second order in the coupling constant, to terms that are compatible with the linear Boltzmann equation. This complements results of Eng and Erd\"os for low-density random potentials, where convergence to the linear Boltzmann equation is proved in all orders. We conjecture, however, that the linear Boltzmann equation fails in the periodic setting for terms of order four and higher. Our proof uses Floquet-Bloch theory, multi-variable theta series and equidistribution theorems for homogeneous flows. Compared with other scaling limits traditionally considered in homogenisation theory, the Boltzmann-Grad limit requires control of the quantum dynamics for longer times, which are inversely proportional to the total scattering cross section of the single-site potential.

[113]  arXiv:1805.06863 [pdf, ps, other]
Title: A remark on constant scalar curvature Kähler metrics on minimal models
Comments: 8 pages. All comments are welcome!
Subjects: Differential Geometry (math.DG)

In this short note, we prove the existence of constant scalar curvature K\"ahler metrics on compact K\"ahler manifolds with semi-ample canonical bundles.

[114]  arXiv:1805.06866 [pdf, ps, other]
Title: On the projections of mutual multifractal spectra
Subjects: Metric Geometry (math.MG)

The aim of this article is to study the behaviour of the relative multifractal spectrum under projections. First of all, we depict a relationship between the mutual multifractal spectra of a couple of measures $(\mu, \nu)$ and its orthogonal projections in Euclidean space. As an application, we improve Svetova's result (Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 11 (2004), 41-46) and study the mutual multifractal analysis of the projections of measures.

[115]  arXiv:1805.06873 [pdf, ps, other]
Title: Modular forms invariant under non-split Cartan subgroups
Subjects: Number Theory (math.NT)

In this paper we describe a method for computing a basis for the space of weight $2$ cusp forms invariant under a non-split Cartan subgroup of prime level $p$. As an application we compute, for certain small values of $p$, explicit equations over $\bf Q$ for the canonical embeddings of the associated modular curves.

Cross-lists for Fri, 18 May 18

[116]  arXiv:1712.08837 (cross-list from stat.ME) [pdf, other]
Title: Optimization and Testing in Linear Non-Gaussian Component Analysis
Comments: 33 pages, 3 tables, 8 figures
Subjects: Methodology (stat.ME); Statistics Theory (math.ST); Applications (stat.AP); Computation (stat.CO); Machine Learning (stat.ML)

Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model to a linear latent factor model with any number of both non-Gaussian components (signals) and Gaussian components (noise), where observations are linear combinations of independent components. Although the individual Gaussian components are not identifiable, the Gaussian subspace is identifiable. We introduce an estimator along with its optimization approach in which non-Gaussian and Gaussian components are estimated simultaneously, maximizing the discrepancy of each non-Gaussian component from Gaussianity while minimizing the discrepancy of each Gaussian component from Gaussianity. When the number of non-Gaussian components is unknown, we develop a statistical test to determine it based on resampling and the discrepancy of estimated components. Through a variety of simulation studies, we demonstrate the improvements of our estimator over competing estimators, and we illustrate the effectiveness of the test to determine the number of non-Gaussian components. Further, we apply our method to real data examples and demonstrate its practical value.

[117]  arXiv:1805.06467 (cross-list from hep-th) [pdf, other]
Title: Top Down Approach to 6D SCFTs
Comments: 121 pages, 4 figures
Subjects: High Energy Physics - Theory (hep-th); Algebraic Geometry (math.AG); Representation Theory (math.RT)

Six-dimensional superconformal field theories (6D SCFTs) occupy a central place in the study of quantum field theories encountered in high energy theory. This article reviews the top down construction and study of this rich class of quantum field theories, in particular, how they are realized by suitable backgrounds in string / M- / F-theory. We review the recent F-theoretic classification of 6D SCFTs, explain how to calculate physical quantities of interest such as the anomaly polynomial of 6D SCFTs, and also explain recent progress in understanding renormalization group flows for deformations of such theories. Additional topics covered by this review include some discussion on the (weighted and signed) counting of states in these theories via superconformal indices. We also include several previously unpublished results as well as a new variant on the swampland conjecture for general quantum field theories decoupled from gravity. The aim of the article is to provide a point of entry into this growing literature rather than an exhaustive overview.

[118]  arXiv:1805.06489 (cross-list from quant-ph) [pdf, ps, other]
Title: Deterministic transformations of coherent states under incoherent operations
Comments: 16 pages, 8 figures, accepted for publication in PRA
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)

It is well known that majorization condition is the necessary and sufficient condition for the deterministic transformations of both pure bipartite entangled states by local operations and coherent states under incoherent operations. In this paper, we present two explicit protocols for these transformations. We first present a permutation-based protocol which provides a method for the single step transformation of $d$-dimensional coherent states. We also obtain generalized solutions of this protocol for some special cases of $d$-level systems. Then, we present an alternative protocol where we use $d'$-level ($d' < d$) subspace solutions of the permutation-based protocol to achieve the complete transformation as a sequence of coherent state transformations. We show that these two protocols also provide solutions for deterministic transformations of pure bipartite entangled states.

[119]  arXiv:1805.06498 (cross-list from q-fin.MF) [pdf, ps, other]
Title: Utility maximization with proportional transaction costs under model uncertainty
Subjects: Mathematical Finance (q-fin.MF); Optimization and Control (math.OC)

We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a semi-static utility maximization for the case of exponential utility preference. Using randomization techniques recently developed in \cite{BDT17}, we can transform the original problem into a frictionless market framework, however, with the extra probability uncertainty on an enlarged space. This allows us to prove all together the existence of the optimal strategy, the auxiliary dynamic programming principle as well as the convex duality theorem in our context with transaction costs. As an application of the duality representation, some important features of utility indifference prices are investigated in the robust setting.

[120]  arXiv:1805.06506 (cross-list from physics.soc-ph) [pdf, other]
Title: Emergence of Benford's Law in Classical Music
Comments: 5 pages, 5 figures
Subjects: Physics and Society (physics.soc-ph); Probability (math.PR)

We analyzed a large selection of classical musical pieces composed by Bach, Beethoven, Mozart, Schubert and Tchaikovsky, and found a surprising connection with mathematics. For each composer, we extracted the time intervals each note was played in each piece and found that the corresponding data sets are Benford distributed. Remarkably, the logarithmic distribution is not only present for the leading digits, but for all digits.

[121]  arXiv:1805.06516 (cross-list from nlin.CD) [pdf, ps, other]
Title: Dependence upon initial conditions
Authors: Y. Charles Li
Subjects: Chaotic Dynamics (nlin.CD); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Atmospheric and Oceanic Physics (physics.ao-ph); Fluid Dynamics (physics.flu-dyn)

This article discusses dependence on initial conditions in natural and social sciences with focus on physical science. The main focus is on the newly discovered rough dependence on initial data.

[122]  arXiv:1805.06523 (cross-list from cs.LG) [pdf, other]
Title: End-to-end Learning of a Convolutional Neural Network via Deep Tensor Decomposition
Comments: 29 pages, 12 figures
Subjects: Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML)

In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an algorithm for simultaneously learning all the kernels from the training data. Our approach dubbed Deep Tensor Decomposition (DeepTD) is based on a rank-1 tensor decomposition. We theoretically investigate DeepTD under a realizable model for the training data where the inputs are chosen i.i.d. from a Gaussian distribution and the labels are generated according to planted convolutional kernels. We show that DeepTD is data-efficient and provably works as soon as the sample size exceeds the total number of convolutional weights in the network. We carry out a variety of numerical experiments to investigate the effectiveness of DeepTD and verify our theoretical findings.

[123]  arXiv:1805.06562 (cross-list from cs.PL) [pdf, other]
Title: Efficient compilation of array probabilistic programs
Subjects: Programming Languages (cs.PL); Probability (math.PR)

Probabilistic programming languages are valuable because they allow us to build, run, and change concise probabilistic models that elide irrelevant details. However, current systems are either inexpressive, failing to support basic features needed to write realistic models, or inefficient, taking orders of magnitude more time to run than hand-coded inference. Without resolving this dilemma, model developers are still required to manually rewrite their high-level models into low-level code to get the needed performance.
We tackle this dilemma by presenting an approach for efficient probabilistic programming with arrays. Arrays are a key element of almost any realistic model. Our system extends previous compilation techniques from scalars to arrays. These extensions allow the transformation of high-level programs into known efficient algorithms. We then optimize the resulting code by taking advantage of the domain-specificity of our language. We further JIT-compile the final product using LLVM on a per-execution basis. These steps combined lead to significant new opportunities for specialization. The resulting performance is competitive with manual implementations of the desired algorithms, even though the original program is as concise and expressive as the initial model.

[124]  arXiv:1805.06604 (cross-list from cs.NA) [pdf, other]
Title: Accelerating Nonnegative Matrix Factorization Algorithms using Extrapolation
Comments: 19 pages, 6 figures, 6 tables
Subjects: Numerical Analysis (cs.NA); Optimization and Control (math.OC); Machine Learning (stat.ML)

In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the two-block coordinate descent algorithms tackling the non-convex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms, namely, accelerated hierarchical alternating least squares (A-HALS) and alternating nonnegative least squares (ANLS), using synthetic, image and document data sets.

[125]  arXiv:1805.06611 (cross-list from eess.SP) [pdf, other]
Title: Antenna Switching Sequence Design for Channel Sounding in a Fast Time-varying Channel
Comments: 6 pages, accepted to IEEE International Conference on Communications (ICC)
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT)

This paper investigates the impact of array switching patterns on the accuracy of parameter estimation of multipath components for a time division multiplexed (TDM) channel sounder. To measure fast time-varying channels, the conventional uniform array switching pattern poses a fundamental limit of the number of antennas that a TDM channel sounder can utilize. We propose a method, which is based on the simulated annealing algorithm, to find non-uniform array switching patterns for realistic antenna arrays, so that we can extend the Doppler estimation range of the channel sounder by suppressing the high sidelobes in the spatio-temporal ambiguity function. Monte Carlo simulations demonstrate that the optimal switching sequence leads to significantly smaller root mean square errors of both direction of departure and Doppler. Results can be applied in both vehicle-to-vehicle and mobile millimeter wave MIMO channel measurements.

[126]  arXiv:1805.06639 (cross-list from stat.ME) [pdf, other]
Title: Independent Component Analysis via Energy-based and Kernel-based Mutual Dependence Measures
Comments: 11 pages, 4 figures
Subjects: Methodology (stat.ME); Statistics Theory (math.ST); Applications (stat.AP); Computation (stat.CO); Machine Learning (stat.ML)

We apply both distance-based (Jin and Matteson, 2017) and kernel-based (Pfister et al., 2016) mutual dependence measures to independent component analysis (ICA), and generalize dCovICA (Matteson and Tsay, 2017) to MDMICA, minimizing empirical dependence measures as an objective function in both deflation and parallel manners. Solving this minimization problem, we introduce Latin hypercube sampling (LHS) (McKay et al., 2000), and a global optimization method, Bayesian optimization (BO) (Mockus, 1994) to improve the initialization of the Newton-type local optimization method. The performance of MDMICA is evaluated in various simulation studies and an image data example. When the ICA model is correct, MDMICA achieves competitive results compared to existing approaches. When the ICA model is misspecified, the estimated independent components are less mutually dependent than the observed components using MDMICA, while they are prone to be even more mutually dependent than the observed components using other approaches.

[127]  arXiv:1805.06693 (cross-list from cs.NI) [pdf, other]
Title: Hierarchical Beamforming: Resource Allocation, Fairness and Flow Level Performance
Comments: 34 pages
Subjects: Networking and Internet Architecture (cs.NI); Information Theory (cs.IT); Performance (cs.PF); Systems and Control (cs.SY)

We consider hierarchical beamforming in wireless networks. For a given population of flows, we propose computationally efficient algorithms for fair rate allocation including proportional fairness and max-min fairness. We next propose closed-form formulas for flow level performance, for both elastic (with either proportional fairness and max-min fairness) and streaming traffic. We further assess the performance of hierarchical beamforming using numerical experiments. Since the proposed solutions have low complexity compared to conventional beamforming, our work suggests that hierarchical beamforming is a promising candidate for the implementation of beamforming in future cellular networks.

[128]  arXiv:1805.06739 (cross-list from hep-th) [pdf, other]
Title: Octonions, exceptional Jordan algebra and the role of the group F_4 in particle physics
Comments: 37 pages, 2 figures; extended version of lectures presented by I.T. at the Institute for Nuclear Research and Nuclear Energy, Sofia
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

Normed division rings are reviewed in the more general framework of composition algebras that include the split (indefinite metric) case. The Jordan - von Neumann - Wigner classification of finite dimensional Jordan algebras is outlined with special attention to the 27 dimensional exceptional Jordan algebra J. The automorphism group F_4 of J and its maximal Borel - de Siebenthal subgroups are studied in detail and applied to the classification of fundamental fermions and gauge bosons. Their intersection in F_4 is demonstrated to coincide with the gauge group of the Standard Model of particle physics.

[129]  arXiv:1805.06753 (cross-list from stat.ML) [pdf, other]
Title: Interpolatron: Interpolation or Extrapolation Schemes to Accelerate Optimization for Deep Neural Networks
Subjects: Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Learning (cs.LG); Optimization and Control (math.OC)

In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for convex optimization, but it does not work well for nonconvex optimization typically. Alternatively, we propose an interpolation scheme to accelerate nonconvex optimization and call the method Interpolatron. We explain motivation behind Interpolatron and conduct a thorough empirical analysis. Empirical results on DNNs of great depths (e.g., 98-layer ResNet and 200-layer ResNet) on CIFAR-10 and ImageNet show that Interpolatron can converge much faster than the state-of-the-art methods such as the SGD with momentum and Adam. Furthermore, Anderson's acceleration, in which mixing coefficients are computed by least-squares estimation, can also be used to improve the performance. Both Interpolatron and Anderson's acceleration are easy to implement and tune. We also show that Interpolatron has linear convergence rate under certain regularity assumptions.

[130]  arXiv:1805.06780 (cross-list from cs.CG) [pdf, other]
Title: The Crossing Number of Single-Pair-Seq-Shellable Drawings of Complete Graphs
Comments: arXiv admin note: substantial text overlap with arXiv:1803.07515
Subjects: Computational Geometry (cs.CG); Combinatorics (math.CO)

The Harary-Hill Conjecture states that for $n\geq 3$ every drawing of $K_n$ has at least \begin{align*} H(n) := \frac{1}{4}\Big\lfloor\frac{n}{2}\Big\rfloor\Big\lfloor\frac{n-1}{2}\Big\rfloor\Big\lfloor\frac{n-2}{2}\Big\rfloor\Big\lfloor\frac{n-3}{2}\Big\rfloor \end{align*} crossings. In general the problem remains unsolved, however there has been some success in proving the conjecture for restricted classes of drawings. The most recent and most general of these classes is seq-shellability. In this work, we improve these results and introduce the new class of single-pair-seq-shellable drawings. We prove the Harary-Hill Conjecture for this new class using novel results on triple cumulated $k$-edges. So far, all approaches for proving the Harary-Hill Conjecture for specific classes rely on a globally fixed reference face. We successfully apply new techniques in order to loosen this restriction, which enables us to select different reference faces when considering subdrawings. Furthermore, we introduce the notion of $k$-deviations as the difference between an optimal and the actual number of $k$-edges. Using $k$-deviations, we gain interesting insights into the essence of $k$-edges, and we further relax the necessity of a fixed reference face.

[131]  arXiv:1805.06828 (cross-list from cs.DM) [pdf, ps, other]
Title: On two consequences of Berge-Fulkerson conjecture
Comments: 3 pages
Subjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)

The classical Berge-Fulkerson conjecture states that any bridgeless cubic graph $G$ admits a list of six perfect matchings such that each edge of $G$ belongs to two of the perfect matchings from the list. In this short note, we discuss two statements that are consequences of this conjecture. We show that the first statement is equivalent to Fan-Raspaud conjecture. We also show that the smallest counter-example to the second one is a cyclically $4$-edge-connected cubic graph.

[132]  arXiv:1805.06834 (cross-list from cs.LG) [pdf, other]
Title: Subspace Estimation from Incomplete Observations: A High-Dimensional Analysis
Comments: 13 pages, 6 figures
Subjects: Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Information Theory (cs.IT); Machine Learning (stat.ML)

We present a high-dimensional analysis of three popular algorithms, namely, Oja's method, GROUSE and PETRELS, for subspace estimation from streaming and highly incomplete observations. We show that, with proper time scaling, the time-varying principal angles between the true subspace and its estimates given by the algorithms converge weakly to deterministic processes when the ambient dimension $n$ tends to infinity. Moreover, the limiting processes can be exactly characterized as the unique solutions of certain ordinary differential equations (ODEs). A finite sample bound is also given, showing that the rate of convergence towards such limits is $\mathcal{O}(1/\sqrt{n})$. In addition to providing asymptotically exact predictions of the dynamic performance of the algorithms, our high-dimensional analysis yields several insights, including an asymptotic equivalence between Oja's method and GROUSE, and a precise scaling relationship linking the amount of missing data to the signal-to-noise ratio. By analyzing the solutions of the limiting ODEs, we also establish phase transition phenomena associated with the steady-state performance of these techniques.

[133]  arXiv:1805.06842 (cross-list from physics.flu-dyn) [pdf, ps, other]
Title: Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations
Authors: Yue Pu (CNA), Robert Pego (CNA), Denys Dutykh (LAMA), Didier Clamond (JAD)
Comments: 25 pages, 4 figures, 23 references. Accepted to Comm. Math. Sci. Other author's papers can be downloaded at this http URL
Subjects: Fluid Dynamics (physics.flu-dyn); Analysis of PDEs (math.AP); Numerical Analysis (math.NA)

We study a regularization of the classical Saint-Venant (shallow-water) equations, recently introduced by D. Clamond and D. Dutykh (Commun. Nonl. Sci. Numer. Simulat. 55 (2018) 237-247). This regularization is non-dispersive and formally conserves mass, momentum and energy. We show that for every classical shock wave, the system admits a corresponding non-oscillatory traveling wave solution which is continuous and piecewise smooth, having a weak singularity at a single point where energy is dissipated as it is for the classical shock. The system also admits cusped solitary waves of both elevation and depression.

[134]  arXiv:1805.06865 (cross-list from cs.PF) [pdf, other]
Title: Optimal Scheduling and Exact Response Time Analysis for Multistage Jobs
Subjects: Performance (cs.PF); Optimization and Control (math.OC)

Scheduling to minimize mean response time in an M/G/1 queue is a classic problem. The problem is usually addressed in one of two scenarios. In the perfect-information scenario, the scheduler knows each job's exact size, or service requirement. In the zero-information scenario, the scheduler knows only each job's size distribution. The well-known shortest remaining processing time (SRPT) policy is optimal in the perfect-information scenario, and the more complex Gittins index policy is optimal in the zero-information scenario.
In real systems the scheduler often has partial but incomplete information about each job's size. We introduce a new job model, that of multistage jobs, to capture the partial-information scenario. A multistage job consists of a sequence of stages, where both the sequence of stages and stage sizes are unknown, but the scheduler always knows which stage of a job is in progress.
We give an optimal algorithm for scheduling multistage jobs and an exact response time analysis of our algorithm. As a special case of our analysis, we obtain the first closed-form expression for mean response time under the Gittins index policy in the M/G/1 queue.

Replacements for Fri, 18 May 18

[135]  arXiv:1211.4892 (replaced) [pdf, ps, other]
Title: Confusion of Tagged Perturbations in Forward Automatic Differentiation of Higher-Order Functions
Subjects: Symbolic Computation (cs.SC); Mathematical Software (cs.MS); Differential Geometry (math.DG)
[136]  arXiv:1305.1798 (replaced) [pdf, other]
Title: Highly symmetric fundamental domains for lattices in R^2 and R^3
Comments: Completely rewritten version, two additional authors (JD, ML) of this new version. 18 pages, 15 figures
Subjects: Combinatorics (math.CO); Metric Geometry (math.MG)
[137]  arXiv:1504.03782 (replaced) [pdf, ps, other]
Title: A Ratio of Alternants Formula for Loop Schur Functions
Authors: Gabriel Frieden
Comments: 12 pages. (v2) Added a denominator formula (Corollary 3.2) and an alternative ratio of alternants formula (Theorem 3.3); improved the exposition; changed notational conventions for $h_k^{(r)}$ and alternants
Subjects: Combinatorics (math.CO)
[138]  arXiv:1508.06267 (replaced) [pdf, ps, other]
Title: Nucleation and growth in two dimensions
Comments: 35 pages, Section 6 updated
Subjects: Probability (math.PR); Combinatorics (math.CO)
[139]  arXiv:1512.07445 (replaced) [pdf, other]
Title: Smooth estimation of a monotone hazard and a monotone density under random censoring
Subjects: Statistics Theory (math.ST)
[140]  arXiv:1607.06545 (replaced) [pdf, other]
Title: On two arithmetic theta lifts
Comments: 55 pages; accepted for publication in Compositio Math
Subjects: Number Theory (math.NT)
[141]  arXiv:1608.03081 (replaced) [pdf, other]
Title: On Hodges' Superefficiency and Merits of Oracle Property in Model Selection
Authors: Xianyi Wu, Xian Zhou
Comments: 29 pages, 1 fiture
Journal-ref: Annals of the Institute of Statistical Mathematics, 2018
Subjects: Statistics Theory (math.ST)
[142]  arXiv:1609.00984 (replaced) [pdf, ps, other]
Title: Atiyah classes of strongly homotopy Lie pairs
Comments: 30 pages; final version. To appear in Algebra Colloquium
Subjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph); Differential Geometry (math.DG)
[143]  arXiv:1609.06617 (replaced) [pdf, other]
Title: Smoothed isotonic estimators of a monotone baseline hazard in the Cox model
Subjects: Statistics Theory (math.ST)
[144]  arXiv:1609.08646 (replaced) [pdf, ps, other]
Title: Squared chromatic number without claws or large cliques
Comments: 13 pages; v2 corrects for a subtlety in the original derivation of Thm 1.2; v3 accepted to Canadian Mathematical Bulletin
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
[145]  arXiv:1610.03883 (replaced) [pdf, ps, other]
Title: A method for obtaining Fibonacci identities
Journal-ref: Integers, Vol. 18 (2018), #A42
Subjects: Number Theory (math.NT); Information Theory (cs.IT); Numerical Analysis (math.NA); Rings and Algebras (math.RA)
[146]  arXiv:1611.01506 (replaced) [pdf, other]
Title: Isotonized smooth estimators of a monotone baseline hazard in the Cox model
Comments: arXiv admin note: text overlap with arXiv:1609.06617
Subjects: Statistics Theory (math.ST)
[147]  arXiv:1611.01681 (replaced) [pdf, other]
Title: Excited Random Walk in a Markovian Environment
Authors: Nicholas Travers
Comments: Final published copy, 60 pages, no figures. Corrects Assumption (A) to assume explicitly that the reversed stack sequence $(R_k)$ is a uniformly ergodic Markov chain, as well as the original stack sequence $(S_k)$. Also adds an analysis of the limiting distribution in the case $\delta = 2$
Subjects: Probability (math.PR)
[148]  arXiv:1612.00434 (replaced) [pdf, other]
Title: Stationary random walks on the lattice
Comments: Shortened to 18 pages, fixed several typos. Entropy results moved to forthcoming paper. Removed a false statement claiming that completely positive entropy implies finite-energy
Subjects: Probability (math.PR); Dynamical Systems (math.DS)
[149]  arXiv:1704.02942 (replaced) [pdf, ps, other]
Title: The Boolean SATisfiability Problem in Clifford algebra
Authors: Marco Budinich
Comments: 16 pages, better formalization and simpler proofs
Subjects: Mathematical Physics (math-ph); Computational Complexity (cs.CC)
[150]  arXiv:1704.06962 (replaced) [pdf, ps, other]
Title: Coherent multiple-antenna block-fading channels at finite blocklength
Subjects: Information Theory (cs.IT)
[151]  arXiv:1705.03299 (replaced) [pdf, ps, other]
Title: Collapsing hyperkähler manifolds
Comments: 38 pages; v4 main result improved
Subjects: Differential Geometry (math.DG); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Metric Geometry (math.MG)
[152]  arXiv:1705.03792 (replaced) [pdf, ps, other]
Title: The free energy in the Derrida--Retaux recursive model
Authors: Yueyun Hu (LAGA), Zhan Shi (LPMA)
Subjects: Probability (math.PR)
[153]  arXiv:1705.04029 (replaced) [pdf, ps, other]
Title: Super-linear propagation for a general, local cane toads model
Subjects: Analysis of PDEs (math.AP)
[154]  arXiv:1705.07235 (replaced) [pdf, ps, other]
Title: Proof of the Sendov conjecture for polynomials of degree nine
Authors: Zaizhao Meng
Subjects: Complex Variables (math.CV)
[155]  arXiv:1705.10223 (replaced) [pdf, other]
Title: On the smallest non-trivial quotients of mapping class groups
Comments: 18 pages, 2 figures; v.2: Section 2 (on projective representations of mapping class groups) completely rewritten
Subjects: Group Theory (math.GR)
[156]  arXiv:1706.05147 (replaced) [pdf, other]
Title: Spectral Domain Sampling of Graph Signals
Authors: Yuichi Tanaka
Comments: accepted to IEEE Transactions on Signal Processing
Subjects: Information Theory (cs.IT)
[157]  arXiv:1706.05173 (replaced) [pdf, ps, other]
Title: The distance between a naive cumulative estimator and its least concave majorant
Subjects: Statistics Theory (math.ST)
[158]  arXiv:1706.05366 (replaced) [pdf, ps, other]
Title: General Variational Formulas for Abelian Differentials
Comments: 40 pages. To appear on International Mathematics Research Notices
Subjects: Algebraic Geometry (math.AG)
[159]  arXiv:1707.04981 (replaced) [pdf, ps, other]
Title: The Optimal Equilibrium for Time-Inconsistent Stopping Problems -- the Discrete-Time Case
Subjects: Optimization and Control (math.OC); Mathematical Finance (q-fin.MF)
[160]  arXiv:1707.05484 (replaced) [pdf, ps, other]
Title: Sparse domination via the helicoidal method
Comments: 60 pages
Subjects: Classical Analysis and ODEs (math.CA)
[161]  arXiv:1708.01195 (replaced) [pdf, ps, other]
Title: Properads and Homotopy Algebras Related to Surfaces
Comments: 26 pages. Composition in the open Frobenius properad fixed. Discussion of the Euler characteristic adapted accordingly
Subjects: Algebraic Topology (math.AT); Mathematical Physics (math-ph)
[162]  arXiv:1708.03145 (replaced) [pdf, ps, other]
Title: Chow motives associated to certain algebraic Hecke characters
Comments: 20 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[163]  arXiv:1708.04632 (replaced) [pdf, other]
Title: On Almost Well-Covered Graphs of Girth at Least 6
Subjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)
[164]  arXiv:1708.06928 (replaced) [pdf, other]
Title: Filling systems on surfaces
Comments: Previous title has changed, Theorem 1.1 and Theorem 1.2 in the previous version are generalized, 17 pages, 8 figures
Subjects: Geometric Topology (math.GT)
[165]  arXiv:1708.08517 (replaced) [pdf, other]
Title: Universal edge transport in interacting Hall systems
Comments: 63 pages, 2 figures. Proof adapted to a larger class of hopping Hamiltonians. Minor corrections, typos fixed. Accepted for publication on Comm. Math. Phys
Subjects: Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el)
[166]  arXiv:1708.09583 (replaced) [pdf, ps, other]
Title: Quermassintegral preserving curvature flow in Hyperbolic space
Authors: Ben Andrews, Yong Wei
Comments: 22 pages, minor revision, accepted by GAFA
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)
[167]  arXiv:1709.04050 (replaced) [src]
Title: A formula for a bounded point derivation on $R^p(X)$
Comments: There is an error in the use of Green's theorem in the proof of Lemma 2.1
Subjects: Complex Variables (math.CV)
[168]  arXiv:1710.00563 (replaced) [pdf, ps, other]
Title: Algebraic independence for values of integral curves
Authors: Tiago J. Fonseca
Comments: 51 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[169]  arXiv:1710.02547 (replaced) [pdf, other]
Title: An isogeometric finite element formulation for phase transitions on deforming surfaces
Comments: Restructured Sec. 2 - Sec. 5; refined and updated the computational results; added appendix A, B and C
Subjects: Numerical Analysis (math.NA)
[170]  arXiv:1710.08080 (replaced) [pdf, ps, other]
Title: Recovery and the Data Processing Inequality for quasi-entropies
Journal-ref: IEEE Transactions on Information Theory (2018)
Subjects: Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[171]  arXiv:1711.03413 (replaced) [pdf, ps, other]
Title: Stability of the tangent bundles of complete intersections and effective restriction
Authors: Jie Liu
Comments: 21 pages. The paper is significantly rewritten. More results on complete intersections in Hermitian symmetric spaces are included. Any comments are welcome
Subjects: Algebraic Geometry (math.AG)
[172]  arXiv:1711.04085 (replaced) [pdf, ps, other]
Title: Symmetric weighted odd-power variations of fractional Brownian motion and applications
Comments: 23 pages. arXiv admin note: text overlap with arXiv:1604.03157
Subjects: Probability (math.PR)
[173]  arXiv:1711.05485 (replaced) [pdf, ps, other]
Title: Prüfer intersection of valuation domains of a field of rational functions
Comments: to appear in J. Algebra. All comments are welcome. Keywords: Pr\"ufer domain, pseudo-convergent sequence, pseudo-limit, residually transcendental extension, integer-valued polynomial
Subjects: Commutative Algebra (math.AC); Rings and Algebras (math.RA)
[174]  arXiv:1711.05823 (replaced) [pdf, ps, other]
Title: The holomorphic bosonic string
Comments: Fixed typos and clarified exposition. Modified Section 5
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)
[175]  arXiv:1711.06849 (replaced) [pdf, ps, other]
Title: Closed form expressions for derivatives of Bessel functions with respect to the order
Subjects: Classical Analysis and ODEs (math.CA)
[176]  arXiv:1712.00938 (replaced) [pdf, ps, other]
Title: Algebraic Soft Decoding of Reed-Solomon Codes Using Module Minimization
Comments: 30 pages, 4 figures
Subjects: Information Theory (cs.IT)
[177]  arXiv:1712.04262 (replaced) [pdf, ps, other]
Title: Vandermonde determinantal ideals
Comments: 6 pages, simplified the proof of the main result. To appear in Math. Scand
Subjects: Commutative Algebra (math.AC)
[178]  arXiv:1712.06705 (replaced) [pdf, ps, other]
Title: Boundary behavior of solutions of elliptic operators in divergence form with a BMO anti-symmetric part
Subjects: Analysis of PDEs (math.AP)
[179]  arXiv:1712.07801 (replaced) [pdf, other]
Title: Density Estimation with Contaminated Data: Minimax Rates and Theory of Adaptation
Authors: Haoyang Liu, Chao Gao
Subjects: Statistics Theory (math.ST); Methodology (stat.ME)
[180]  arXiv:1801.02545 (replaced) [pdf, ps, other]
Title: Quasiregular semigroups with examples
Authors: A. Fletcher
Subjects: Dynamical Systems (math.DS); Complex Variables (math.CV)
[181]  arXiv:1801.08590 (replaced) [pdf, other]
Title: Individual testing is optimal for nonadaptive group testing in the linear regime
Authors: Matthew Aldridge
Comments: 4 pages, 1 figure
Subjects: Information Theory (cs.IT); Combinatorics (math.CO); Probability (math.PR)
[182]  arXiv:1801.09311 (replaced) [pdf, ps, other]
Title: On the combinatorics of faces of trees and anodyne extensions of dendroidal sets
Authors: Matija Bašić
Comments: 26 pages
Journal-ref: Glasnik Matematicki, Vol. 53, No. 2, 2018
Subjects: Algebraic Topology (math.AT)
[183]  arXiv:1801.10071 (replaced) [pdf, ps, other]
Title: The Helicoidal Method
Comments: expository paper, 47 pages
Subjects: Classical Analysis and ODEs (math.CA)
[184]  arXiv:1801.10479 (replaced) [pdf, ps, other]
Title: Identities about level 2 Eisenstein series
Authors: Ce Xu
Subjects: Number Theory (math.NT)
[185]  arXiv:1802.00417 (replaced) [pdf, ps, other]
Title: On torus actions of higher complexity
Comments: 36 pages
Subjects: Algebraic Geometry (math.AG)
[186]  arXiv:1802.01148 (replaced) [pdf, other]
Title: Spectral Characterizations of Solvability and Stability for Delay Differential-Algebraic Equations
Authors: Phi Ha
Subjects: Dynamical Systems (math.DS)
[187]  arXiv:1802.01545 (replaced) [pdf, other]
Title: Solution for a bipartite Euclidean traveling-salesman problem in one dimension
Comments: 9 pages, 5 figures
Journal-ref: Phys. Rev. E 97, 052109, 2018
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Combinatorics (math.CO)
[188]  arXiv:1802.04227 (replaced) [pdf, ps, other]
Title: On a conjecture of Erdős on locally sparse Steiner triple systems
Comments: updated references and corrected a typo in Section 6 (thanks to Zur Luria for pointing this out)
Subjects: Combinatorics (math.CO)
[189]  arXiv:1802.06027 (replaced) [pdf, other]
Title: Inverter Probing for Power Distribution Network Topology Processing
Subjects: Optimization and Control (math.OC)
[190]  arXiv:1802.06735 (replaced) [pdf, ps, other]
Title: When are permutation invariants Cohen-Macaulay over all fields?
Comments: 30 pages, 5 figures. Rewrote the statement and proof of Lemma 3.7 in response to a referee report, and correspondingly updated later material relying on Lemma 3.7 such as Proposition 3.11 (formerly 3.8) statement and proof, and the proof of Proposition 4.2. Also, added a few remarks after the new proof of Lemma 3.7
Subjects: Commutative Algebra (math.AC); Combinatorics (math.CO)
[191]  arXiv:1802.09411 (replaced) [pdf, other]
Title: Principles of Bayesian Inference using General Divergence Criteria
Subjects: Statistics Theory (math.ST)
[192]  arXiv:1802.10340 (replaced) [pdf, ps, other]
Title: On a singular limit for stratified compressible fluids
Subjects: Analysis of PDEs (math.AP)
[193]  arXiv:1803.00561 (replaced) [pdf, ps, other]
Title: Initial conditions and degrees of freedom of non-local gravity
Comments: 1+29+16 pages, 2 figures, 8 appendices. v2: Hamiltonian formalism clarified, section on causality added
Journal-ref: JHEP 05 (2018) 087
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
[194]  arXiv:1803.06034 (replaced) [pdf, ps, other]
Title: Multistage stochastic programs with a random number of stages: dynamic programming equations, solution methods, and application to portfolio selection
Authors: Vincent Guigues
Subjects: Optimization and Control (math.OC)
[195]  arXiv:1803.06363 (replaced) [pdf, ps, other]
Title: Geometric Adaptive Control for a Quadrotor UAV with Wind Disturbance Rejection
Subjects: Optimization and Control (math.OC)
[196]  arXiv:1803.06477 (replaced) [pdf, ps, other]
Title: On the homotopy types of $\mathrm{Sp}(n)$ gauge groups
Comments: 9 pages
Subjects: Algebraic Topology (math.AT)
[197]  arXiv:1803.10847 (replaced) [pdf, ps, other]
Title: Algebraic Semantics for Nelson's Logic S
Comments: 16 pages
Subjects: Logic (math.LO)
[198]  arXiv:1804.01360 (replaced) [pdf, other]
Title: Skew Braces and Hopf-Galois Structures of Heisenberg Type
Comments: Final version submitted to the Journal of Algebra
Subjects: Quantum Algebra (math.QA); Group Theory (math.GR); Number Theory (math.NT)
[199]  arXiv:1804.02654 (replaced) [pdf, ps, other]
Title: Ribbonness of a stable-ribbon surface-link
Authors: Akio Kawauchi
Comments: Many (essential or inessential) errors are corrected. Welcome your comments
Subjects: Geometric Topology (math.GT)
[200]  arXiv:1804.03095 (replaced) [pdf, other]
Title: Exact non-Markovian dynamics of Gaussian quantum channels: Finite-time and asymptotic regimes
Comments: 9 pages, 2 figures. The present work supersedes and replaces arXiv:1609.00917
Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph); Optics (physics.optics)
[201]  arXiv:1804.03195 (replaced) [pdf, ps, other]
Title: Contextual Search via Intrinsic Volumes
Subjects: Data Structures and Algorithms (cs.DS); Learning (cs.LG); Metric Geometry (math.MG)
[202]  arXiv:1804.03206 (replaced) [pdf, other]
Title: Merging joint distributions via causal model classes with low VC dimension
Authors: Dominik Janzing
Comments: 21 pages, two errors in V1 corrected
Subjects: Statistics Theory (math.ST)
[203]  arXiv:1804.04321 (replaced) [pdf, ps, other]
Title: Spectral decomposition of normal absolutely minimum attaining operators
Authors: Neeru Bala, G. Ramesh
Comments: The hypothesis in Theorem 4.7 is changed and hence the title of the article
Subjects: Functional Analysis (math.FA); Spectral Theory (math.SP)
[204]  arXiv:1804.04799 (replaced) [pdf, ps, other]
Title: Families of not perfectly straight knots
Authors: Nicholas Owad
Comments: 10 pages, 6 figures, Comments and suggestions welcome. Minor grammatical corrections, added two questions
Subjects: Geometric Topology (math.GT)
[205]  arXiv:1804.05247 (replaced) [pdf, ps, other]
Title: Weak Siegel-Weil formula for M_2(Q) and arithmetic on quaternions
Authors: Tuoping Du
Subjects: Number Theory (math.NT)
[206]  arXiv:1804.06334 (replaced) [pdf, other]
Title: On $f$-Divergences: Integral Representations, Local Behavior, and Inequalities
Authors: Igal Sason
Comments: Final edits before publication. To appear in the Entropy journal, special issue on Entropy and Information Inequalities, May 2018
Subjects: Information Theory (cs.IT); Probability (math.PR)
[207]  arXiv:1804.09702 (replaced) [pdf, ps, other]
Title: On Short Sums Involving Fourier Coefficients of Maass Forms
Authors: Jesse Jääsaari
Comments: Typos corrected, assumption regarding the Ramanujan-Petersson conjecture removed from Theorem 1
Subjects: Number Theory (math.NT)
[208]  arXiv:1805.00884 (replaced) [pdf, other]
Title: Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media
Comments: 39 pages
Subjects: Mathematical Physics (math-ph); Materials Science (cond-mat.mtrl-sci); Functional Analysis (math.FA); Spectral Theory (math.SP)
[209]  arXiv:1805.01303 (replaced) [pdf, ps, other]
Title: Lorentzian elasticity
Comments: Extra appendix added + minor edits
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Analysis of PDEs (math.AP); Differential Geometry (math.DG)
[210]  arXiv:1805.01683 (replaced) [pdf, ps, other]
Title: Poles of the complex zeta function of a plane curve
Authors: Guillem Blanco
Comments: 36 pages. Corrected typos. Some remarks added. Changes in the statements of Conjecture (sec. 2), Theorem 6.8 and Corollary 6.9. Arguments and results unchanged
Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV)
[211]  arXiv:1805.02405 (replaced) [pdf, ps, other]
Title: A Combinatorial Game and an Efficiently Computable Shift Rule for the Prefer Max De Bruijn Sequence
Subjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)
[212]  arXiv:1805.02913 (replaced) [pdf, ps, other]
Title: Level curves of rational functions and unimodular points on rational curves
Subjects: Number Theory (math.NT)
[213]  arXiv:1805.03201 (replaced) [pdf, other]
Title: Ordinary Complex Differential Equations with Applications in Science and Engineering
Authors: Ali K. Joohy
Comments: 152 pages
Subjects: Mathematical Physics (math-ph); Complex Variables (math.CV); Quantum Physics (quant-ph)
[214]  arXiv:1805.03431 (replaced) [pdf, ps, other]
Title: Ergodicity for Neutral Type SDEs with Infinite Length of Memory
Subjects: Probability (math.PR)
[215]  arXiv:1805.03998 (replaced) [pdf, ps, other]
Title: Proximal Vortex Cycles and Vortex Nerves. Non-Concentric, Nesting, Possibly Overlapping Homology Cell Complexes
Authors: J.F. Peters
Comments: 10 figures, 25 pages
Subjects: Geometric Topology (math.GT)
[216]  arXiv:1805.04799 (replaced) [pdf, ps, other]
Title: Horizontal and vertical mutation fans
Authors: Kiyoshi Igusa
Comments: 23 pages, 10 figures, presented at Workshop on Cluster Algebras and Related Topics held at the Chern Institute of Mathematics, Nankai University, China, July 10-13, 2017, accepted for publication in SCIENCE CHINA Mathematics, v2: minor corrections
Subjects: Representation Theory (math.RT)
[217]  arXiv:1805.04973 (replaced) [pdf, ps, other]
Title: Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach
Comments: 19 pages, 11 figures
Subjects: Optimization and Control (math.OC)
[218]  arXiv:1805.05788 (replaced) [pdf, other]
Title: How to discover dissipative PDEs from particles? Particle fluctuations determine evolution operator
Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); Dynamical Systems (math.DS)
[219]  arXiv:1805.06134 (replaced) [pdf, ps, other]
Title: A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lift of half-integral weight
Comments: 31 pages
Subjects: Number Theory (math.NT)
[220]  arXiv:1805.06231 (replaced) [pdf, ps, other]
Title: Local curvature estimates for the Laplacian flow
Authors: Yi Li
Comments: add some references
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)
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