# Mathematics

## New submissions

[ total of 249 entries: 1-249 ]
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### New submissions for Fri, 17 Nov 17

[1]
Title: First and second $K$-groups of an elliptic curve over a global field of positive characteristic
Comments: This paper will appear at Annales de l'Institut Fourier
Subjects: K-Theory and Homology (math.KT)

In this paper, we show that the maximal divisible subgroup of groups $K_1$ and $K_2$ of an elliptic curve $E$ over a function field is uniquely divisible. Further those $K$-groups modulo this uniquely divisible subgroup are explicitly computed. We also calculate the motivic cohomology groups of the minimal regular model of $E$, which is an elliptic surface over a finite field.

[2]
Title: Spaces of Types in Positive Model Theory
Authors: Levon Haykazyan
Subjects: Logic (math.LO)

We introduce a notion of the space of types in positive model theory based on Stone duality for distributive lattices. We show that this space closely mirrors the Stone space of types in first-order model theory. We use this to generalise some classical results on countable models from first-order model theory to positive model theory.

[3]
Title: Scaled Boundary Parametrizations in Isogeometric Analysis
Subjects: Numerical Analysis (math.NA)

This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational domain is available. The idea goes back to the Scaled Boundary Finite Element Method (SB-FEM), which has recently been extended to IGA. We take here a different viewpoint and study these parametrizations as bivariate or trivariate B-spline functions that are directly suitable for standard Galerkin-based IGA. Our main results are first a general framework for this class of parametrizations, including aspects such as smoothness and regularity as well as generalizations to domains that are not star-shaped. Second, using the Poisson equation as example, we explain the relation between standard Galerkin-based IGA and the Scaled Boundary IGA by means of the Laplace-Beltrami operator. Further results concern the separation of integrals in both approaches and an analysis of the singularity in the scaling center. Among the computational examples we present a planar rotor geometry that stems from a screw compressor machine and compare different parametrization strategies.

[4]
Title: Random gradient extrapolation for distributed and stochastic optimization
Authors: Guanghui Lan, Yi Zhou
Subjects: Optimization and Control (math.OC); Computational Complexity (cs.CC); Learning (cs.LG); Machine Learning (stat.ML)

In this paper, we consider a class of finite-sum convex optimization problems defined over a distributed multiagent network with $m$ agents connected to a central server. In particular, the objective function consists of the average of $m$ ($\ge 1$) smooth components associated with each network agent together with a strongly convex term. Our major contribution is to develop a new randomized incremental gradient algorithm, namely random gradient extrapolation method (RGEM), which does not require any exact gradient evaluation even for the initial point, but can achieve the optimal ${\cal O}(\log(1/\epsilon))$ complexity bound in terms of the total number of gradient evaluations of component functions to solve the finite-sum problems. Furthermore, we demonstrate that for stochastic finite-sum optimization problems, RGEM maintains the optimal ${\cal O}(1/\epsilon)$ complexity (up to a certain logarithmic factor) in terms of the number of stochastic gradient computations, but attains an ${\cal O}(\log(1/\epsilon))$ complexity in terms of communication rounds (each round involves only one agent). It is worth noting that the former bound is independent of the number of agents $m$, while the latter one only linearly depends on $m$ or even $\sqrt m$ for ill-conditioned problems. To the best of our knowledge, this is the first time that these complexity bounds have been obtained for distributed and stochastic optimization problems. Moreover, our algorithms were developed based on a novel dual perspective of Nesterov's accelerated gradient method.

[5]
Title: Reconstructing general plane quartics from their inflection lines
Subjects: Algebraic Geometry (math.AG)

Let $C$ be a general plane quartic and let ${\rm Fl}(C)$ denote the configuration of inflection lines of $C$. We show that if $D$ is any plane quartic with the same configuration of inflection lines ${\rm Fl}(C)$, then the quartics $C$ and $D$ coincide. To formalize this result, we extend the notion of inflection lines to singular quartics, using a degeneration argument. We then perform a detailed analysis to show that the configurations associated to singular quartics do not arise as configurations of general quartics.

[6]
Title: On the values of unipotent characters in bad characteristic
Authors: Meinolf Geck
Subjects: Representation Theory (math.RT)

Let $G(q)$ be a Chevalley group over a finite field $F_q$. By Lusztig's and Shoji's work, the problem of computing the values of the unipotent characters of $G(q)$ is solved, in principle, by the theory of character sheaves; one issue in this solution is the determination of certain scalars relating two types of class functions on $G(q)$. We show that this issue can be reduced to the case where $q$ is a prime, which opens the way to use computer algebra methods. Here, and in a sequel to this article, we use this approach to solve a number of cases in groups of exceptional type which seemed hitherto out of reach.

[7]
Title: Integral Formulas for Higher Order Higher Spin Conformally Invariant Differential Operators
Authors: Chao Ding
Subjects: Representation Theory (math.RT); Complex Variables (math.CV)

In this paper, we establish higher order Borel-Pompeiu formulas for arbitrary order conformally invariant differential operators in higher spin theory, and that is the theory of functions on $m$-dimensional Euclidean space taking values in arbitrary irreducible representations of the Spin group. These conformally invariant differential operators, named as fermionic operators when the orders are odd and bosonic operators when the orders are even. As applications, we provide higher order Cauchy integral formulas for fermionic operators and higher order Green's type integral formulas for bosonic operators. This continues the work of building up basic integral formulas for conformally invariant differential operators in higher spin theory.

[8]
Title: A Parameter Estimation Method Using Linear Response Statistics: Numerical Scheme
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Data Analysis, Statistics and Probability (physics.data-an)

This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift diffusions as a nonlinear least-square problem. To avoid solving the model repeatedly when using an iterative scheme in solving the resulting least-square problems, a polynomial surrogate model is employed on appropriate response statistics with smooth dependence on the parameters. An analysis for the convergence of the Gauss-Newton algorithm for the surrogate model will be presented. The efficacy of the method is demonstrated on two prototypical examples that belong to classes of models with wide range of applications, including the Langevin dynamics and the stochastically forced gradient flows. Several important practical issues, such as the selection of the appropriate response operator to ensure the identifiability of the parameters and the reduction of the parameter space, are discussed. From the numerical experiments, it is found that the proposed approach is superior compared to the conventional approach that uses equilibrium statistics to determine the parameters.

[9]
Title: On the proximity of large primes
Subjects: Number Theory (math.NT)

By a sphere-packing argument, we show that there are infinitely many pairs of primes that are close to each other for some metrics on the integers. In particular, for any numeration basis $q$, we show that there are infinitely many pairs of primes the base $q$ expansion of which differ in at most two digits. Likewise, for any fixed integer $t,$ there are infinitely many pairs of primes, the first $t$ digits of which are the same. In another direction, we show that, there is a constant $c$ depending on $q$ such that for infinitely many integers $m$ there are at least $c\log \log m$ primes which differ from $m$ by at most one base $q$ digit.

[10]
Title: A rank 18 Waring decomposition of $sM_{\langle 3\rangle}$ with 432 symmetries
Authors: Austin Conner
Subjects: Representation Theory (math.RT)

The recent discovery that the exponent of matrix multiplication is determined by the rank of the symmetrized matrix multiplication tensor has invigorated interest in better understanding symmetrized matrix multiplication. I present an explicit rank 18 Waring decomposition of $sM_{\langle 3\rangle}$ and describe its symmetry group.

[11]
Title: The residual finiteness of (hyperbolic) automorphism-induced HNN-extensions
Authors: Alan D. Logan
Subjects: Group Theory (math.GR)

We classify finitely generated, residually finite automorphism-induced HNN-extensions in terms of the residual separability of a single associated subgroup. This classification yields a general method to construct automorphism-induced HNN-extensions which are not residually finite. We prove that this construction can never yield a "new" counter-example to Gromov's conjecture on the residual finiteness of hyperbolic groups.

[12]
Title: Schwartz functions on quasi-Nash varieties
Authors: Boaz Elazar
Subjects: Algebraic Geometry (math.AG)

We introduce a new category called Quasi-Nash, unifying Nash manifolds and algebraic varieties. We define Schwartz functions, tempered functions and tempered distributions in this category. We show that properties that hold on affine spaces, Nash manifolds and algebraic varieties, also hold in this category.

[13]
Title: Set complexity of construction of a regular polygon
Authors: Eugene Kogan
Subjects: Number Theory (math.NT); Computational Complexity (cs.CC)

Given a subset of $\mathbb C$ containing $x,y$, one can add $x + y$ or $x - y$ or $xy$ or (when $y\ne0$) $x/y$ or any $z$ such that $z^2=x$. Let $p$ be a prime Fermat number. We prove that it is possible to obtain from $\{1\}$ a set containing all the $p$-th roots of 1 by $16 p^2$ above operations. This problem is different from the standard estimation of complexity of an algorithm computing the $p$-th roots of 1.

[14]
Title: Completeness of the list of spinor regular ternary quadratic forms
Subjects: Number Theory (math.NT)

Extending the notion of regularity introduced by Dickson in 1939, a positive definite ternary integral quadratic form is said to be spinor regular if it represents all the positive integers represented by its spinor genus (that is, all positive integers represented by any form in its spinor genus). Jagy conducted an extensive computer search for primitive ternary quadratic forms that are spinor regular, but not regular, resulting in a list of 29 such forms. In this paper, we will prove that there are no additional forms with this property.

[15]
Title: Global convergence rates of augmented Lagrangian methods for constrained convex programming
Authors: Yangyang Xu
Subjects: Optimization and Control (math.OC); Data Structures and Algorithms (cs.DS); Numerical Analysis (math.NA)

Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Its convergence and local convergence speed have been extensively studied. However, its global convergence rate is still open for problems with nonlinear inequality constraints. In this paper, we work on general constrained convex programs. For these problems, we establish the global convergence rate of ALM and its inexact variants.
We first assume exact solution to each subproblem in the ALM framework and establish an $O(1/k)$ ergodic convergence result, where $k$ is the number of iterations. Then we analyze an inexact ALM that approximately solves the subproblems. Assuming summable errors, we prove that the inexact ALM also enjoys $O(1/k)$ convergence if smaller stepsizes are used in the multiplier updates. Furthermore, we apply the inexact ALM to a constrained composite convex problem with each subproblem solved by Nesterov's optimal first-order method. We show that $O(\varepsilon^{-\frac{3}{2}-\delta})$ gradient evaluations are sufficient to guarantee an $\varepsilon$-optimal solution in terms of both primal objective and feasibility violation, where $\delta$ is an arbitrary positive number. Finally, for constrained smooth problems, we modify the inexact ALM by adding a proximal term to each subproblem and improve the iteration complexity to $O(\varepsilon^{-1}|\log\varepsilon|)$.

[16]
Title: Python Implementation and Construction of Finite Abelian Groups
Subjects: Group Theory (math.GR); Mathematical Software (cs.MS)

Here we present a working framework to establish finite abelian groups in python. The primary aim is to allow new A-level students to work with examples of finite abelian groups using open source software. We include the code used in the implementation of the framework. We also prove some useful results regarding finite abelian groups which are used to establish the functions and help show how number theoretic results can blend with computational power when studying algebra. The groups established are based modular multiplication and addition. We include direct products of cyclic groups meaning the user has access to all finite abelian groups.

[17]
Title: Fronthaul-Aware Group Sparse Precoding and Signal Splitting in SWIPT C-RAN
Comments: Accepted by IEEE Globecom 2017
Subjects: Information Theory (cs.IT)

We investigate the precoding, remote radio head (RRH) selection and signal splitting in the simultaneous wireless information and power transferring (SWIPT) cloud radio access networks \mbox{(C-RANs)}. The objective is to minimize the power consumption of the SWIPT C-RAN. Different from the existing literature, we consider the nonlinear fronthaul power consumption and the multiple antenna RRHs. By switching off the unnecessary RRHs, the group sparsity of the precoding coefficients is introduced, which indicates that the precoding process and the RRH selection are coupled. In order to overcome these issues, a group sparse precoding and signal splitting algorithm is proposed based on the majorization-minimization framework, and the convergence behavior is established. Numerical results are used to verify our proposed studies.

[18]
Title: The holomorphic bosonic string
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)

We present a holomorphic version of the bosonic string in the formalism of quantum field theory developed by Costello and collaborators. In this paper we focus on the case in which space-time is flat and construct a one-loop exact quantization. Starting from first principles, we arrive at the critical dimension as an obstruction to satisfying the quantum master equation. Moreover, we show how the factorization algebra recovers the BRST cohomology of the string and give another construction of the Gerstenhaber structure. Finally, we show how the factorization homology along closed manifolds encodes the determinant line bundle over the moduli space of Riemann surfaces.

[19]
Title: On the Duflot filtration for Equivariant Cohomology Rings
Authors: James C. Cameron
Subjects: Algebraic Topology (math.AT)

We give a systemization of the structure induced on Borel equivariant cohomology by the Duflot filtration, and apply this to give new proofs of results about depth, associated primes, and detection on subgroups for the cohomology rings of classifying spaces of compact Lie groups that were previously only known for the cohomology of finite groups. We also apply our framework to yield computations for the top several local cohomology modules of the cohomology of a $p$-Sylow of $S_{p^n}$, giving vanishing and nonvanishing results for these modules that are stronger than those dictated by the general theory.

[20]
Title: Least informative distributions in Maximum q-log-likelihood estimation
Subjects: Statistics Theory (math.ST)

We use the Maximum $q$-log-likelihood estimation for Least informative distributions (LID) in order to estimate the parameters in probability density functions (PDFs) efficiently and robustly when data include outlier(s). LIDs are derived by using convex combinations of two PDFs, $f_\epsilon=(1-\epsilon)f_0+\epsilon f_1$. A convex combination of two PDFs is considered as a contamination $f_1$ as outlier(s) to underlying $f_0$ distributions and $f_\epsilon$ is a contaminated distribution. The optimal criterion is obtained by minimizing the change of Maximum q-log-likelihood function when the data have slightly more contamination. In this paper, we make a comparison among ordinary Maximum likelihood, Maximum q-likelihood estimations, LIDs based on $\log_q$ and Huber M-estimation. Akaike and Bayesian information criterions (AIC and BIC) based on $\log_q$ and LID are proposed to assess the fitting performance of functions. Real data sets are applied to test the fitting performance of estimating functions that include shape, scale and location parameters.

[21]
Title: On monotonicity of some functionals with variable exponent under symmetrization
Subjects: Optimization and Control (math.OC); Analysis of PDEs (math.AP)

We give necessary and sufficient conditions for the P\'olya--Szeg\"o type inequality with variable exponent of summability.

[22]
Title: Evaluation of Certain Hypergeometric Functions over Finite Fields
Subjects: Number Theory (math.NT)

For an odd prime $p$, let $\phi$ denote the quadratic character of the multiplicative group $\mathbb F_p^\times$, where $\mathbb F_p$ is the finite field of $p$ elements. In this paper, we will obtain evaluations of the hypergeometric functions $${}_2F_1\left(\begin{array}{cc} \phi\psi& \psi & \phi \end{array};x\right), \quad x\in \mathbb F_p, \,x\neq 0, 1$$ over $\mathbb F_p$ in terms of Hecke character attached to CM Elliptic curves for characters $\psi$ of $\mathbb F_p^\times$ of order $3$, $4$, $6$, $8$, and $12$.

[23]
Authors: Nima Hoda
Subjects: Group Theory (math.GR)

Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize 2-dimensional CAT(0) cube complexes and are a square analog of systolic complexes. We introduce and study the basic properties of these complexes. We then prove a form of dismantlability for the 1-skeleta of finite quadric complexes and use it to show that every finite group acting on a quadric complex stabilizes a complete bipartite subgraph of its 1-skeleton. Finally, we prove that C(4)-T(4) small cancellation groups act on quadric complexes.

[24]
Title: Trace spaces of counterexamples to Naimark's Problem
Authors: Andrea Vaccaro
Subjects: Operator Algebras (math.OA); Logic (math.LO)

A counterexample to Naimark's Problem is a $C^\ast$-algebra with a unique unitary equivalence class of irreducible representations which is not isomorphic to the algebra of compact operators. We prove, assuming the extra set-theoretic axiom known as Diamond Principle, the existence of a counterexample to Naimark's Problem whose trace space is nonseparable and, for every metrizable Choquet simplex $X$, the existence of a counterexample to Naimark's Problem whose trace space is homeomorphic to $X$.

[25]
Title: Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)

We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in an algorithm to compute the rational points on a curve of genus $g \ge 2$ over the rationals whose Jacobian has Mordell-Weil rank $g$ and Picard number greater than one, and which satisfies some additional conditions. This algorithm is then applied to the modular curve $X_{s}(13)$, completing the classification of non-CM elliptic curves over $\mathbf{Q}$ with split Cartan level structure due to Bilu-Parent and Bilu-Parent-Rebolledo.

[26]
Title: Local eigenvalue statistics of one-dimensional random non-selfadjoint pseudo-differential operators
Subjects: Spectral Theory (math.SP); Analysis of PDEs (math.AP); Probability (math.PR)

We study a class of one-dimensional non-selfadjoint semiclassical elliptic pseudo-differential operators subject to small random perturbations. We compare two types of random perturbation: random potential and random matrix. It is known by recent works of Sj\"ostrand and Hager that, under suitable conditions on the law of the perturbation, the eigenvalues of the perturbed operator contained in the interior of the pseudospectrum will follow Weyl-asymptotics with probability close to one. We show that in the limit of the semiclassical parameter $h\to 0$, the local statistics of the eigenvalues of the perturbed operator in the interior of the pseudospectrum is universal in the sense that it only depends on the type of random perturbation and the principal symbol of the unperturbed operator. It is, however, independent of the law of the perturbation.

[27]
Title: Logarithmic Kodaira dimension and zeros of holomorphic log-one-forms
Authors: Chuanhao Wei
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG)

In this paper, we prove that the zero-locus of any global holomorphic log-one-form on a projective log-smooth pair $\left(X,D\right)$ of log-general type must be non-empty. Applying this result, we give an answer to the algebraic hyperbolicity part of Shafarevich's conjecture, with the generic fiber being Kawamata-log-terminal (klt) and of log-general type.

[28]
Title: Geburtstage, Wuerfel, Produkte und Karten
Authors: Edgar M. E. Wermuth (Technische Hochschule Nuernberg, Germany)
Comments: 30 pages, in German, 21 figures
Subjects: History and Overview (math.HO)

This article, based on a talk, treats some elementary, but not completely simple examples from probability. They concern multiple birthday coincidences, throwing dice, the combinatorics of the German card game "Doppelkopf", and the properties of products of uniformly distributed random numbers. The material, a lot of which was not taken from or found in other sources, should be of interest to all those who lecture or plan to lecture on probability, especially on an elementary or introductory level, and are looking for challenging examples or problems.

[29]
Title: Large time behavior of entropy solutions to 1-d unipolar hydrodynamic model for semiconductor devices
Subjects: Analysis of PDEs (math.AP)

We are concerned with the global existence and large time behavior of entropy solutions to the one dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval.In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space $x$ and time $t$ by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy solution converges to the corresponding unique stationary solution exponentially in time. No any smallness condition is assumed on the initial data and doping profile.

[30]
Title: A new characterization of the dual polar graphs
Subjects: Combinatorics (math.CO)

In this paper we give a new characterization of the dual polar graphs, extending the work of Brouwer and Wilbrink on regular near polygons. Also as a consequence of our characterization we confirm a conjecture of the authors on non-bipartite distance-regular graphs with smallest eigenvalue at most $-k/2$, where $k$ is the valency of the distance-regular graph, in case of $c_2 \geq3$ and $a_1 =1$.

[31]
Title: Packing nearly optimal Ramsey R(3,t) graphs
Authors: He Guo, Lutz Warnke
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM); Probability (math.PR)

In 1995 Kim famously proved the Ramsey bound R(3,t) \ge c t^2/\log t by constructing an n-vertex graph that is triangle-free and has independence number at most C \sqrt{n \log n}. We extend this celebrated result, which is best possible up to the value of the constants, by approximately decomposing the complete graph K_n into a packing of such nearly optimal Ramsey R(3,t) graphs.
More precisely, for any \epsilon>0 we find an edge-disjoint collection (G_i)_i of n-vertex graphs G_i \subseteq K_n such that (a) each G_i is triangle-free and has independence number at most C_\epsilon \sqrt{n \log n}, and (b) the union of all the G_i contains at least (1-\epsilon)\binom{n}{2} edges. Our algorithmic proof proceeds by sequentially choosing the graphs G_i via a semi-random (i.e., Rodl nibble type) variation of the triangle-free process.
As an application, we prove a conjecture in Ramsey theory by Fox, Grinshpun, Liebenau, Person, and Szabo (concerning a Ramsey-type parameter introduced by Burr, Erdos, Lovasz in 1976). Namely, denoting by s_r(H) the smallest minimum degree of r-Ramsey minimal graphs for H, we close the existing logarithmic gap for H=K_3 and establish that s_r(K_3) = \Theta(r^2 \log r).

[32]
Title: Efficient D-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems
Subjects: Numerical Analysis (math.NA)

We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the infinite-dimensional limit. The optimal design is obtained by solving an optimization problem that involves repeated evaluation of the log-determinant of high-dimensional operators along with their derivatives. Forming and manipulating these operators is computationally prohibitive for large-scale problems. Our methods exploit the low-rank structure in the inverse problem in three different ways, yielding efficient algorithms. Our main approach is to use randomized estimators for computing the D-optimal criterion, its derivative, as well as the Kullback--Leibler divergence from posterior to prior. Two other alternatives are proposed based on a low-rank approximation of the prior-preconditioned data misfit Hessian, and a fixed low-rank approximation of the prior-preconditioned forward operator. Detailed error analysis is provided for each of the methods, and their effectiveness is demonstrated on a model sensor placement problem for initial state reconstruction in a time-dependent advection-diffusion equation in two space dimensions.

[33]
Title: Convergence of iterative methods based on Neumann series for composite materials: theory and practice
Subjects: Numerical Analysis (math.NA)

Iterative Fast Fourier Transform methods are very useful for calculating the fields in composite materials and their macroscopic response, and are now widely applied. In essence the differential constraints are satisfied by going to Fourier space, and the constitutive law by going to real space, and so by iterating back and forth both the constitutive law and the differential constraints are effectively both satisfied. The methods correspond to Neumann series expansions of appropriate operators. For composites containing two or more components there is also a link with series expansions for the effective tensor as a function of the component moduli and it is shown that the singularity structure of this function can shed much light on the convergence properties of the various Iterative Fast Fourier Transform methods. Here we look at a model example of the conductivity of a periodic array of conducting squares at 25\% volume fraction for which there is an exact formula for the effective conductivity due Obnosov. Interestingly some of the methods converge when the squares have zero conductivity and even when they have negative conductivity. On the other hand the numerics show that often accuracy is lost after relatively few iterations, of the order of twenty in some cases. There is little point in iterating beyond this. On the other hand accuracy does improve when the grid size is reduced, as one might expect.

[34]
Title: Solution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained $\ell_1$ Minimization
Subjects: Optimization and Control (math.OC)

In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems incorporates many important polyhedral constrained $\ell_1$ recovery problems arising from sparse optimization, such as basis pursuit, LASSO, and basis pursuit denoising, as well as polyhedral gauge recovery. By leveraging the max-formulation of convex piecewise affine functions and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches; these conditions are applied to a wide range of $\ell_1$ minimization problems under possible polyhedral constraints. An effective linear program based scheme is proposed to verify solution uniqueness conditions. The results obtained in this paper not only recover the known solution uniqueness conditions in the literature by removing restrictive assumptions but also yield new uniqueness conditions for much broader constrained $\ell_1$-minimization problems.

[35]
Title: Hybrid Normed Ideal Perturbations of n-tuples of Operators I
Subjects: Operator Algebras (math.OA); Spectral Theory (math.SP)

In hybrid normed ideal perturbations of $n$-tuples of operators, the normed ideal is allowed to vary with the component operators. We begin extending to this setting the machinery we developed for normed ideal perturbations based on the modulus of quasicentral approximation and an adaptation of our non-commutative generalization of the Weyl--von~Neumann theorem. For commuting $n$-tuples of hermitian operators, the modulus of quasicentral approximation remains essentially the same when $\cC_n^-$ is replaced by a hybrid $n$-tuple $\cC_{p_1,\dots}^-,\dots,\cC^-_{p_n}$, $p_1^{-1} + \dots + p_n^{-1} = 1$. The proof involves singular integrals of mixed homogeneity.

[36]
Title: On the Computation of Certain Weighted Colimits
Authors: Michael Lambert
Subjects: Category Theory (math.CT)

The present paper gives computations of weighted pseudo-colimits of pseudo-functors on 1-categories valued in certain 2-categories, such as the 2-category of contravariant pseudo-functors on a 1-category. The main result is a generalization of the well-known result of SGA 4 that shows how to compute conical colimits of certain cloven fibrations. Concluding discussions give an computation of bicolimits of certain pseudo-functors and colimits in reflective sub 2-categories.

[37]
Title: Instability of solitons in the 2d cubic Zakharov-Kuznetsov equation
Subjects: Analysis of PDEs (math.AP)

We consider the two dimensional generalization of the Korteweg-de Vries equation, the generalized Zakharov-Kuznetsov (ZK) equation, $u_t + \partial_{x_1}(\Delta u + u^p) = 0, (x_1,x_2) \in \mathbb{R}^2$. It is known that solitons are stable for nonlinearities $p < 3$ and unstable for $p > 3$, which was established by Anne de Bouard in [5] generalizing the arguments of Bona-Souganidis-Strauss in [1] for the gKdV equation. The $L^2$-critical case with $p=3$ has been open and in this paper we prove that solitons are unstable in the cubic ZK equation. This matches the situation with the critical gKdV equation, proved in 2001 by Martel and Merle in [22]. While the general strategy follows [22], the two dimensional case creates several difficulties and to deal with them, we design a new virial-type quantity, revisit monotonicity properties and, most importantly, develop new pointwise decay estimates, which can be useful in other contexts.

[38]
Title: Consistency of Hill Estimators in a Linear Preferential Attachment Model
Subjects: Probability (math.PR)

Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Practical analyses on the tail exponent of the power-law degree distribution use the Hill estimator as one of the key summary statistics, whose consistency is justified mostly for iid data. The major goal in this paper is to answer the question whether the Hill estimator is still consistent when applied to non-iid network data. To do this, we first derive the asymptotic behavior of the degree sequence via embedding the degree growth of a fixed node into a birth immigration process. We also need to show the convergence of the tail empirical measure, from which the consistency of Hill estimators is obtained. This step requires checking the concentration of degree counts. We give a proof for a particular linear preferential attachment model and use simulation results as an illustration in other choices of models.

[39]
Title: On Channel Reciprocity to Activate Uplink Channel Training for Downlink Data Transmission
Comments: 6 pages, 3 figures, submitted to IEEE Int. Conf. Commun. (ICC) 2018
Subjects: Information Theory (cs.IT)

We determine, for the first time, the requirement on channel reciprocity to activate uplink channel training, instead of downlink channel training, to achieve a higher data rate for the downlink transmission from a multi-antenna base station to a single-antenna user. To this end, we first derive novel closed-form expressions for the lower bounds on the data rates achieved by these two channel training strategies by considering the impact of finite blocklength. The performance comparison result of these two strategies is determined by the amount of channel reciprocity that is utilized in the uplink channel training. We then derive an approximated but analytical expression for the minimum channel reciprocity that enables the uplink channel training to outperform the downlink channel training. Through numerical results, we demonstrate that this minimum channel reciprocity decreases as the blocklength decreases or the number of transmit antennas increases, which shows the necessity and benefits of activating the uplink channel training for shortpacket communications with massive transmit antennas. This work provides pivotal and unprecedented guidelines on choosing channel training strategies and channel reciprocity calibrations in practice.

[40]
Title: Maximization of the Fundamental Tone on the Klein Bottle
Subjects: Spectral Theory (math.SP); Differential Geometry (math.DG)

In this expository paper we provide a complete proof of the fact that the first non-zero eigenvalue of the Laplacian on a Klein bottle is maximized by the bipolar Lawson surface \tau_{3,1}. While this result follows from the earlier work of Jakobson-Nadirashvili-Polterovich, El Soufi-Giacomini-Jazar, Nadirashvili-Sire and Petrides, its proof has never been written up in full. The goal of this note is to close this gap in the literature. In particular, we generalize certain results of El Soufi and Ilias regarding conformal volume to metrics with conical singularities and prove continuity of the k-conformal eigenvalue functional with respect to conformal classes.

[41]
Title: Optimal Load Balancing in Millimeter Wave Cellular Heterogeneous Networks
Comments: 7 pages, 5 figures, submitted to ICC 2018
Subjects: Information Theory (cs.IT)

In this paper, we propose a novel and effective approach to optimizing the load balancing in a millimeter wave (mmWave) cellular heterogeneous network (HetNet) with a macro-tier and a micro-tier. The unique characteristics of mmWave transmission are incorporated into the network by adopting the Poisson point process (PPP) for base station (BS) location, the line-of-sight (LoS) ball model for mmWave links, the sectored antenna model for key antenna array characteristics, and Nakagami-$m$ fading for wireless channels. To reduce the load of macro-tier BSs, we consider a bias factor $A_{s}$ in the network for offloading user equipments (UEs) to micro-tier BSs. For this network, we first analyze the loads of macro- and micro-tier BSs. Then we derive a new expression for the rate coverage probability of the network, based on which the optimal $A_{s}$ maximizing the rate coverage probability is found. Through numerical results, we demonstrate the correctness of our analysis and the validity of the optimal $A_{s}$. Importantly, the optimal $A_{s}$ can bring a profound improvement in the rate coverage probability relative to a fixed $A_{s}$. Furthermore, we evaluate the impact of various network parameters, e.g., the densities and the beamwidths of BSs, on the rate coverage probability and the optimal $A_{s}$, offering valuable guidelines into practical mmWave HetNet design.

[42]
Title: Using p-Refinement to Increase Boundary Derivative Convergence Rates
Subjects: Numerical Analysis (math.NA)

Many important physical problems, such as fluid structure interaction or conjugate heat transfer, require numerical methods that compute boundary derivatives or fluxes to high accuracy. This paper proposes a novel alternative to calculating accurate approximations of boundary derivatives of elliptic problems: instead of postprocessing, we describe a new continuous finite element method based on p-refinement of cells adjacent to the boundary to increase the approximation order of the derivative on the boundary itself. We prove that the order of the approximation on the p-refined cells is, in 1D, determined by the rate of convergence at the knot connecting the higher and lower order cells and that this idea can be extended, in some simple settings, to 2D problems. We verify this rate of convergence numerically with a series of experiments in both 1D and 2D.

[43]
Title: Improving an inequality for the divisor function
Authors: Jeffrey P.S. Lay
Subjects: Number Theory (math.NT)

We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.

[44]
Title: A variational problem associated to a hyperbolic Caffarelli--Kohn--Nirenberg inequality
Subjects: Analysis of PDEs (math.AP)

We prove a Caffarelli--Kohn--Nirenberg inequality in the hyperbolic space. For a semilinear elliptic equation involving the associated weighted Laplace--Beltrami operator, we establish variationally the existence of positive radial solutions in the subcritical regime. We also show a non-existence result in star-shaped domains when the exponent is supercritical.

[45]
Title: $A_2$ Skein Representations of Pure Braid Groups
Authors: Wataru Yuasa
Comments: 13 pages, many TikZ pictures
Subjects: Geometric Topology (math.GT); Group Theory (math.GR); Quantum Algebra (math.QA)

We define a family of representations $\{\rho_n\}_{n\geq 0}$ of a pure braid group $P_{2k}$. These representations are obtained from an action of $P_{2k}$ on a certain type of $A_2$ web space with color $n$. The $A_2$ web space is a generalization of the Kauffman bracket skein module of a disk with marked points on its boundary. We also introduce a triangle-free basis of such an $A_2$ web space and calculate matrix representations of $\rho_n$ about the standard generators of $P_{2k}$.

[46]
Title: The Schur multiplier of central product of groups
Comments: 10 pages, to appear in Journal of Pure and Applied Algebra
Subjects: Group Theory (math.GR)

Let $G$ be a central product of two groups $H$ and $K$. We study second cohomology group of $G$, having coefficients in a divisible abelian group $D$ with trivial $G$-action, in terms of the second cohomology groups of certain quotients of $H$ and $K$. In particular, for $D = \mathbb{C}^{*}$, some of our results provide a refinement of results from [Some groups with non-trivial multiplicators, Math. Z. {\bf 120 } (1971), 307-308] and [On the Schur multiplicator of a central quotient of a direct product of groups, J. Pure Appl. Algebra {\bf 3} (1973), 73-82].

[47]
Title: The Critical Point Equation And Contact Geometry
Comments: In the published version there was a sign error in Eq. (1.3). We have fixed it here
Journal-ref: Journal of Geometry 108, 185-194 (2017)
Subjects: Differential Geometry (math.DG)

In this paper, we consider the CPE conjecture in the frame-work of $K$-contact and $(\kappa, \mu)$-contact manifolds. First, we prove that if a complete $K$-contact metric satisfies the CPE is Einstein and is isometric to a unit sphere $S^{2n+1}$. Next, we prove that if a non-Sasakian $(\kappa, \mu)$-contact metric satisfies the CPE, then $M^{3}$ is flat and for $n > 1$, $M^{2n+1}$ is locally isometric to $E^{n+1}\times S^{n}(4)$.

[48]
Title: Pattern of Zeros
Subjects: Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el)

In this paper, we provide a set of definitions upon which one can prove in a rigorous way most of the main results achieved in the pattern of zeros classification of fractional quantum Hall states.

[49]
Title: Residues formulas for the push-forward in K-theory, the case of G2/P
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG)

We study residue formulas for push-forward in K-theory of homogeneous spaces. First we review formulas for classical groups, which we derive from a formula for the classical Grassmannian case. Next we consider the homogeneous spaces for G2. One of them embeds in the Grassmannian Gr(2,7). We find its fundamental class in the equivariant K-theory and obtain the residue formula for the push-forward. This formula is valid for G2/B as well.

[50]
Title: Partial-Approximate Controllability of Nonlocal Fractional Evolution Equations via Approximating Method
Authors: N. I. Mahmudov
Subjects: Dynamical Systems (math.DS)

In this paper we study partial-approximate controllability of semilinear nonlocal fractional evolution equations in Hilbert spaces. By using fractional calculus, variational approach and approximating technique, we give the approximate problem of the control system and get the compactness of approximate solution set. Then new sufficient conditions for the partial-approximate controllability of the control system are obtained when the compactness conditions or Lipschitz conditions for the nonlocal function are not required. Finally, we apply our abstract results to the parial-approximate controllability of the semilinear heat equation and delay equation.

[51]
Title: A three-field formulation of the Poisson problem with Nitsche approach
Subjects: Numerical Analysis (math.NA)

We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirichlet boundary condition but still preserves the optimal convergence. We use the biorthogonal system for efficient numerical computation and introduce a stabilisation term so that the problem is coercive on the whole space. Numerical examples are presented to verify the algebraic formulation of the problem.

[52]
Title: Overview of (pro-)Lie group structures on Hopf algebra character groups
Comments: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spain
Subjects: Group Theory (math.GR)

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.

[53]
Title: Construction of Nikulin configurations on some Kummer surfaces and applications
Subjects: Algebraic Geometry (math.AG)

A Nikulin configuration is the data of $16$ disjoint smooth rational curves on a K3 surface. According to a well known result of Nikulin, if a K3 surface contains a Nikulin configuration $\mathcal{C}$, then $X$ is a Kummer surface $X=Km(B)$ where $B$ is an Abelian surface determined by $\mathcal{C}$. Let $B$ be a generic Abelian surface having a polarization $M$ with $M^{2}=k(k+1)$ (for $k>0$ an integer) and let $X=Km(B)$ be the associated Kummer surface. To the natural Nikulin configuration $\mathcal{C}$ on $X=Km(B)$, we associate another Nikulin configuration $\mathcal{C}'$; we denote by $B'$ the Abelian surface associated to $\mathcal{C}'$, so that we have also $X=Km(B')$. For $k\geq2$ we prove that $B$ and $B'$ are not isomorphic. We then construct an infinite order automorphism of the Kummer surface $X$ that occurs naturally from our situation. Associated to the two Nikulin configurations $\mathcal{C},$ $\mathcal{C}'$, there exists a natural bi-double cover $S\to X$, which is a surface of general type. We study this surface which is a Lagrangian surface in the sense of Bogomolov-Tschinkel, and for $k=2$ is a Schoen surface.

[54]
Title: Physical-Layer Schemes for Wireless Coded Caching
Comments: 25 pages, 14 figures. This manuscript is the extended journal version of the ISIT 2017 conference article available at arXiv:1701.02979 [cs.IT]
Subjects: Information Theory (cs.IT); Networking and Internet Architecture (cs.NI)

We investigate the potentials of applying the coded caching paradigm in wireless networks. In order to do this, we investigate physical layer schemes for downlink transmission from a multiantenna transmitter to several cache-enabled users. As the baseline scheme we consider employing coded caching on top of max-min fair multicasting, which is shown to be far from optimal at high SNR values. Our first proposed scheme, which is near-optimal in terms of DoF, is the natural extension of multiserver coded caching to Gaussian channels. As we demonstrate, its finite SNR performance is not satisfactory, and thus we propose a new scheme in which the linear combination of messages is implemented in the finite field domain, and the one-shot precoding for the MISO downlink is implemented in the complex field. While this modification results in the same near-optimal DoF performance, we show that this leads to significant performance improvement at finite SNR. Finally, we extend our scheme to the previously considered cache-enabled interference channels, and moreover, we provide an Ergodic rate analysis of our scheme. Our results convey the important message that although directly translating schemes from the network coding ideas to wireless networks may work well at high SNR values, careful modifications need to be considered for acceptable finite SNR performance.

[55]
Title: On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables
Authors: Liyu Liu
Subjects: Rings and Algebras (math.RA)

Homological smoothness and twisted Calabi-Yau property of generalized Weyl algebras over polynomial algebras in two variables is studied. A necessary and sufficient condition to be homologically smooth is given. The Nakayama automorphisms of such algebras are also computed in terms of the Jacobian determinants of defining automorphisms.

[56]
Title: On the Problem of Fair Division in Saturated Measure Spaces with Vectorized Preferences
Authors: Nobusumi Sagara
Subjects: Functional Analysis (math.FA)

The purpose of this paper is twofold. First, we axiomatize preference relations on $\sigma$-algebras to vectorize them in a Banach space and furnish a utility representation in terms of a nonadditive measure satisfying the appropriate requirement of continuity and convexity. Second, we investigate the fair division problems in which each individual has vectorized preferences on a $\sigma$-algebra. We show the existence of individually rational Pareto optimal partitions, Walrasian equilibria, core partitions, and Pareto optimal envy-free partitions.

[57]
Title: Optimal Selection of Interconnections in Composite Systems for Structural Controllability
Subjects: Optimization and Control (math.OC)

In this paper, we study structural controllability of a linear time invariant (LTI) composite system consisting of several subsystems. We assume that the neighbourhood of each subsystem is unconstrained, i.e., any subsystem can interact with any other subsystem. The interaction links between subsystems are referred as interconnections. We assume the composite system to be structurally controllable if all possible interconnections are present, and our objective is to identify the minimum set of interconnections required to keep the system structurally controllable. We consider structurally identical subsystems, i.e., the zero/non-zero pattern of the state matrices of the subsystems are the same, but dynamics can be different. We present a polynomial time optimal algorithm to identify the minimum cardinality set of interconnections that subsystems must establish to make the composite system structurally controllable.

[58]
Title: The boundary value problem for Yang--Mills--Higgs fields
Subjects: Differential Geometry (math.DG)

We show the existence of Yang--Mills--Higgs (YMH) fields over a Riemann surface with boundary where a free boundary condition is imposed on the section and a Neumann boundary condition on the connection. In technical terms, we study the convergence and blow-up behavior of a sequence of Sacks-Uhlenbeck type $\alpha$-YMH fields as $\alpha\to 1$. For $\alpha>1$, each $\alpha$-YMH field is shown to be smooth up to the boundary under some gauge transformation. This is achieved by showing a regularity theorem for more general coupled systems, which extends the classical results of Ladyzhenskaya-Ural'ceva and Morrey.

[59]
Title: Beltrami's theorem via parabolic geometry
Authors: Michael Eastwood
Subjects: Differential Geometry (math.DG)

We use Beltrami's theorem as an excuse to present some arguments from parabolic differential geometry without any of the parabolic machinery.

[60]
Title: Maximum modulus principle for "holomorphic functions" on the quantum matrix ball
Subjects: Operator Algebras (math.OA)

We describe the Shilov boundary ideal for a q-analog of the algebra of holomorphic functions on the unit ball in the space of $n\times n$ matrices and show that its $C^*$-envelope is isomorphic to the $C^*$-algebra of continuous functions on the quantum unitary group $U_q(n)$.

[61]
Title: Gamma-positivity in combinatorics and geometry
Subjects: Combinatorics (math.CO)

Gamma-positivity is an elementary property that polynomials with symmetric coefficients may have, which directly implies their unimodality. The idea behind it stems from work of Foata, Sch\"utzenberger and Strehl on the Eulerian polynomials; it was revived independently by Br\"and\'en and Gal in the course of their study of poset Eulerian polynomials and face enumeration of flag simplicial spheres, respectively, and has found numerous applications since then. This paper surveys some of the main results and open problems on gamma-positivity, appearing in various combinatorial or geometric contexts, as well as some of the diverse methods that have been used to prove it.

[62]
Title: A kind of orthogonal polynomials and related identities II
Authors: Zhi-Hong Sun
Subjects: Classical Analysis and ODEs (math.CA); Combinatorics (math.CO)

Let $\{d_n^{(r)}(x)\}$ and $\{D_n^{(r)}(x)\}$ be given by $d_n^{(r)}(x) = \sum_{k=0}^n \binom{x+r+k}k\binom{x-r}{n-k} \ (n\ge 0)$, $D_0^{(r)}(x)=1,\ D_1^{(r)}(x)=x$ and $D_{n+1}^{(r)}(x) =xD_n^{(r)}(x)-n(n+2r)D_{n-1}^{(r)}(x)\ (n\ge 1).$ In this paper we illustrate the connection between $\{d_n^{(r)}(x)\}$ and Meixner polynomials and the connection between $\{D_n^{(r)}(x)\}$ and Meixner-Pollaczek polynomials. New formulas and recurrence relations for $d_n^{(r)}(x)$ are obtained, and a new proof of the formula for $d_n^{(r)}(x)^2$ is also given.

[63]
Title: On the stable Andreadakis problem
Authors: Jacques Darné (LPP)
Subjects: Algebraic Topology (math.AT); Group Theory (math.GR)

Let $F\_n$ be the free group on $n$ generators. Consider the group $IA\_n$ of automorpisms of $F\_n$ acting trivially on its abelianization. There are two canonical filtrations on $IA\_n$: the first one is its lower central series $\Gamma\_*$; the second one is the Andreadakis filtration $\mathcal A\_*$, defined from the action on $F\_n$. In this paper, we establish that the canonical morphism between the associated graded Lie rings ${\mathcal L}(\Gamma\_*)$ and ${\mathcal L}(\mathcal A\_*)$ is stably surjective. We then investigate a $p$-restricted version of the Andreadakis problem. A calculation of the Lie algebra of the classical congruence group is also included.

[64]
Title: The duals of the 2-modular irreducible modules of the alternating groups
Authors: John Murray
Subjects: Representation Theory (math.RT)

We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2

[65]
Title: A Law of Large Numbers in the Supremum Norm for a Multiscale Stochastic Spatial Gene Network
Authors: Arnaud Debussche (IPSO, IRMAR), Mac Jugal Nguepedja Nankep (IRMAR)
Subjects: Analysis of PDEs (math.AP); Probability (math.PR)

We study the asymptotic behavior of multiscale stochastic spatial gene networks. Multiscaling takes into account the difference of abundance between molecules , and captures the dynamic of rare species at a mesoscopic level. We introduce an assumption of spatial correlations for reactions involving rare species and a new law of large numbers is obtained. According to the scales, the whole system splits into two parts with different but coupled dynamics. The high scale component converges to the usual spatial model which is the solution of a partial differential equation, whereas, the low scale component converges to the usual homogeneous model which is the solution of an ordinary differential equation. Comparisons are made in the supremum norm.

[66]
Title: Stability of optimal spherical codes
Subjects: Information Theory (cs.IT)

For many extremal configurations of points on a sphere, the linear programming approach can be used to show their optimality. In this paper we establish the general framework for showing stability of such configurations and use this framework to prove the stability of the two spherical codes formed by minimal vectors of the lattice $E_8$ and of the Leech lattice.

[67]
Title: Semiconductor Boltzmann-Dirac-Benny equation with BGK-type collision operator: existence of solutions vs. ill-posedness
Authors: Marcel Braukhoff
Subjects: Analysis of PDEs (math.AP)

A semiconductor Boltzmann equation with a non-linear BGK-type collision operator is analyzed for a cloud of ultracold atoms in an optical lattice:
$\partial_t f + \nabla_p\epsilon(p)\cdot\nabla_x f - \nabla_x n_f\cdot\nabla_p f = n_f(1- n_f)(\mathcal{F}_f-f), \quad x\in\mathbb{R}^d, p\in\mathbb{T}^d, t>0.$
This system contains an interaction potential $n_f(x,t):=\int_{\mathbb{T}^d}f(x,p,t)dp$ being significantly more singular than the Coulomb potential, which is used in the Vlasov-Poisson system. This causes major structural difficulties in the analysis. Furthermore, $\epsilon(p) = -\sum_{i=1}^d$ $\cos(2\pi p_i)$ is the dispersion relation and $\mathcal{F}_f$ denotes the Fermi-Dirac equilibrium distribution, which depends non-linearly on $f$ in this context.
In a dilute plasma - without collisions (r.h.s$.=0$) - this system is closely related to the Vlasov-Dirac-Benney equation. It is shown for analytic initial data that the semiconductor Boltzmann equation possesses a local, analytic solution. Here, we exploit the techniques of Mouhout and Villani by using Gevrey-type norms which vary over time. In addition, it is proved that this equation is locally ill-posed in Sobolev spaces close to some Fermi-Dirac equilibrium distribution functions.

[68]
Title: A generalized Levi condition for weakly hyperbolic Cauchy problems with coefficients low regular in time and smooth in space
Subjects: Analysis of PDEs (math.AP)

We consider the Cauchy problem for weakly hyperbolic $m$-th order partial differential equations with coefficients low-regular in time and smooth in space. It is well-known that in general one has to impose Levi conditions to get $C^\infty$ or Gevrey well-posedness even if the coefficients are smooth. We use moduli of continuity to describe the regularity of the coefficients with respect to time, weight sequences for the characterization of their regularity with respect to space and weight functions to define the solution spaces. Furthermore, we propose a generalized Levi condition that models the influence of multiple characteristics more freely. We establish sufficient conditions for the well-posedness of the Cauchy problem, that link the Levi condition as well as the modulus of continuity and the weight sequence of the coefficients to the weight function of the solution space. Additionally, we obtain that the influences of the Levi condition and the low regularity of coefficients on the weight function of the solution space are independent of each other.

[69]
Title: Orbispaces, orthogonal spaces, and the universal compact Lie group
Authors: Stefan Schwede
Subjects: Algebraic Topology (math.AT)

This paper identifies the homotopy theories of topological stacks and orbispaces with unstable global homotopy theory. At the same time, we provide a new perspective by interpreting it as the homotopy theory of spaces with an action of the universal compact Lie group'. The upshot is a novel way to construct and study genuine cohomology theories on stacks, orbifolds, and orbispaces, defined from stable global homotopy types represented by orthogonal spectra.
The universal compact Lie group (which is neither compact nor a Lie group) is a well known object, namely the topological monoid $\mathcal L$ of linear isometric self-embeddings of $\mathbb R^\infty$. The underlying space of $\mathcal L$ is contractible, and the homotopy theory of $\mathcal L$-spaces with respect to underlying weak equivalences is just another model for the homotopy theory of spaces. However, the monoid $\mathcal L$ contains copies of all compact Lie groups in a specific way, and we define global equivalences of $\mathcal L$-spaces by testing on corresponding fixed points. We establish a global model structure on the category of $\mathcal L$-spaces and prove it to be Quillen equivalent to the global model category of orthogonal spaces, and to the category of orbispaces, i.e., presheaves of spaces on the global orbit category.

[70]
Title: Probabilities of incidence between lines and a plane curve over finite fields
Subjects: Combinatorics (math.CO)

We study the probability for a random line to intersect a given plane curve, defined over a finite field, in a given number of points. In particular, we focus on the limits of these probabilities under successive finite field extensions. The main tools we use are the Lang-Weil bound for the number of rational points of an algebraic variety and a geometric interpretation of the Galois group of a curve. Supposing absolute irreducibility for the curve, we prove the existence of these limits, and under a mildly stronger condition we provide an explicit formula for them, depending only on the degree of the curve.

[71]
Title: Homogenization of the discrete diffusive coagulation-fragmentation equations in perforated domains
Subjects: Mathematical Physics (math-ph)

The asymptotic behavior of the solution of an infinite set of Smoluchowski's discrete coagulation-fragmentation-diffusion equations with non-homogeneous Neumann boundary conditions, defined in a periodically perforated domain, is analyzed. Our homogenization result, based on Nguetseng-Allaire two-scale convergence, is meant to pass from a microscopic model (where the physical processes are properly described) to a macroscopic one (which takes into account only the effective or averaged properties of the system). When the characteristic size of the perforations vanishes, the information given on the microscale by the non-homogeneous Neumann boundary condition is transferred into a global source term appearing in the limiting (homogenized) equations. Furthermore, on the macroscale, the geometric structure of the perforated domain induces a correction in the diffusion coefficients.

[72]
Title: Utility maximization via decoupling fields
Subjects: Probability (math.PR)

We consider the utility maximization problem for a general class of utility functions defined on the real line. We rely on existing results which reduce the problem to a coupled forward-backward stochastic differential equation (FBSDE) and concentrate on showing existence and uniqueness of solution processes to this FBSDE. We use the method of decoupling fields for strongly coupled, multi-dimensional and possibly non-Lipschitz systems as the central technique in conducting the proofs.

[73]
Title: Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson--Nernst--Planck Equations
Journal-ref: Communications in Computational Physics 2017
Subjects: Numerical Analysis (math.NA)

The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective model for the description of ionic transport in ion channels. It is observed that an ion channel exhibits voltage-dependent switching between open and closed states. Different conductance states of a channel imply that the ssPNP equations probably have multiple solutions with different level of currents. We propose numerical approaches to study multiple solutions to the ssPNP equations with multiple ionic species. To find complete current-voltage (I-V ) and current-concentration (I-C) curves, we reformulate the ssPNP equations into four different boundary value problems (BVPs). Numerical continuation approaches are developed to provide good initial guesses for iteratively solving algebraic equations resulting from discretization. Numerical continuations on V , I, and boundary concentrations result in S-shaped and double S-shaped (I-V and I-C) curves for the ssPNP equations with multiple species of ions. There are five solutions to the ssPNP equations with five ionic species, when an applied voltage is given in certain intervals. Remarkably, the current through ion channels responds hysteretically to varying applied voltages and boundary concentrations, showing a memory effect. In addition, we propose a useful computational approach to locate turning points of an I-V curve. With obtained locations, we are able to determine critical threshold values for hysteresis to occur and the interval for V in which the ssPNP equations have multiple solutions. Our numerical results indicate that the developed numerical approaches have a promising potential in studying hysteretic conductance states of ion channels.

[74]
Title: Permutations sorted by a finite and an infinite stack in series
Comments: 12 pages, 8 figures, 1 table
Subjects: Combinatorics (math.CO)

An antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable. Pattern-avoidance is a partial order on the set of all finite permutations. We prove that the set of permutations sorted by a stack of depth $t \geq 3$ and an infinite stack in series has infinite basis, by constructing an infinite antichain. This answers an open question on identifying the breakpoint for the basis to change from finite to infinite in a sorting process with two stacks in series.

[75]
Title: Norms of truncated Toeplitz operators and numerical radii of restricted shifts
Subjects: Functional Analysis (math.FA); Complex Variables (math.CV)

This paper gives a new approach to the calculation of the numerical radius of a restricted shift operator by linking it to the norm of a truncated Toeplitz operator (TTO), which can be be calculated by various methods. Further results on the norm of a TTO are derived, and a conjecture on the existence of continuous symbols for compact TTO is resolved.

[76]
Title: A faithful 2TQFT
Subjects: Rings and Algebras (math.RA)

It has been shown in this paper that the commutative Frobenius algebra $QZ_5\otimes Z(QS_3)$ provides a complete invariant for two-dimensional cobordisms, i.e., that the corresponding two-dimensional quantum field theory is faithful. The essential role in the proof of this result plays Zsigmondy's Theorem.

[77]
Title: Linear structure in certain subsets of quasi-Banach sequence spaces
Authors: Daniel Tomaz
Subjects: Functional Analysis (math.FA)

For $0<p<1,$ we prove that there is a $\mathfrak{c}$-dimensional subspace of $\mathcal{L}\left( \ell_{p},\ell_{p}\right)$ such that, except for the null vector, all of its vectors fail to be absolutely $(r,s)$-summing regardless of the real numbers $r,s$, with $1\leq s\leq r<\infty$. This extends a result proved by Maddox in 1987. Moreover, the result is sharp in the sense that it is not valid for $p\geq1.$

[78]
Title: New integration methods for perturbed ODEs based on symplectic implicit Runge-Kutta schemes with application to solar system simulations
Subjects: Numerical Analysis (math.NA)

We propose a family of integrators, Flow-Composed Implicit Runge-Kutta (FCIRK) methods, for perturbations of nonlinear ordinary differential equations, consisting of the composition of flows of the unperturbed part alternated with one step of an implicit Runge-Kutta (IRK) method applied to a transformed system. The resulting integration schemes are symplectic when both the perturbation and the unperturbed part are Hamiltonian and the underlying IRK scheme is symplectic. In addition, they are symmetric in time (resp. have order of accuracy $r$) if the underlying IRK scheme is time-symmetric (resp. of order $r$). The proposed new methods admit mixed precision implementation that allows us to efficiently reduce the effect of round-off errors. We particularly focus on the potential application to long-term solar system simulations, with the equations of motion of the solar system rewritten as a Hamiltonian perturbation of a system of uncoupled Keplerian equations. We present some preliminary numerical experiments with a simple point mass Newtonian 10-body model of the solar system (with the sun, the eight planets, and Pluto) written in canonical heliocentric coordinates.

[79]
Title: Linear response, and consequences for differentiability of statistical quantities and Multifractal Analysis
Subjects: Dynamical Systems (math.DS)

In this article we initially fix ourselves to smooth expanding dynamical systems. We prove the differentiability of the topological pressure, equilibrium states and their densities with respect to smooth expanding dynamical systems and any smooth potential. This is done by proving the regularity of the dominant eigenvalue of the transfer operator with respect to dynamics and potential. From that, we obtain strong consequences on the regularity of the dynamical system statistical properties, that apply in more general contexts. Indeed, we prove that the average and variance obtained from the central limit theorem vary $C^{r-1}$ with respect to the $C^{r}-$expanding dynamics and $C^{r}-$potential, and also, there is a large deviations principle with its rate $C^{r-1}$ in relation the dynamics and potential. An application for multifractal analysis is given.

[80]
Title: On the critical densities of minor-closed classes
Subjects: Combinatorics (math.CO)

Given a minor-closed class $\mathcal{A}$ of graphs, let $\beta_{\mathcal{A}}$ denote the supremum over all graphs in $\mathcal{A}$ of the ratio of edges to vertices. We investigate the set $B$ of all such values $\beta_{\mathcal{A}}$, taking further the project begun by Eppstein. Amongst other results, we determine the small values in $B$ (those up to 2); we show that $B$ is asymptotically dense'; and we answer some questions posed by Eppstein.

[81]
Title: Dynamical characterization of combinatorially rich sets near zero
Subjects: Dynamical Systems (math.DS); Combinatorics (math.CO)

Hindman and Leader first introduced the notion of Central sets near zero for dense subsemigroups of $((0,\infty),+)$ and proved a powerful combinatorial theorem about such sets. Using the algebraic structure of the Stone-$\breve{C}$ech compactification, Bayatmanesh and Tootkabani generalized and extended this combinatorial theorem to the central theorem near zero. Algebraically one can define quasi-central set near zero for dense subsemigroup of $((0,\infty),+)$, and they also satisfy the conclusion of central sets theorem near zero. In a dense subsemigroup of $((0,\infty),+)$, C-sets near zero are the sets, which satisfies the conclusions of the central sets theorem near zero. Like discrete case, we shall produce dynamical characterizations of these combinatorically rich sets near zero.

[82]
Title: Finding exact formulas for the $L_2$ discrepancy of digital $(0,n,2)$-nets via Haar functions
Authors: Ralph Kritzinger
Subjects: Number Theory (math.NT)

We use the Haar function system in order to study the $L_2$ discrepancy of a class of digital $(0,n,2)$-nets. Our approach yields exact formulas for this quantity, which measures the irregularities of distribution of a set of points in the unit interval. We will obtain such formulas not only for the classical digital nets, but also for shifted and symmetrized versions thereof. The basic idea of our proofs is to calculate all Haar coefficents of the discrepancy function exactly and insert them into Parseval's identity. We will also discuss reasons why certain (symmetrized) digital nets fail to achieve the optimal order of $L_2$ discrepancy and use the Littlewood-Paley inequality in order to obtain results on the $L_p$ discrepancy for all $p\in (1,\infty)$.

[83]
Title: On the vector bundles from Chang and Ran's proof of the unirationality of $\mathcal{M}_g$, $g \leq 13$
Subjects: Algebraic Geometry (math.AG)

We combine the idea of Chang and Ran [Invent. Math. 76 (1984), 41-54] of using monads of vector bundles on the projective 3-space to prove the unirationality of the moduli spaces of curves of low genus with our classification of globally generated vector bundles with small first Chern class $c_1$ on the projective 3-space to get an alternative argument for the unirationality of the moduli spaces of curves of degree at most 13 (based on the general framework of Chang and Ran).

[84]
Title: Variational time discretization of Riemannian splines
Subjects: Numerical Analysis (math.NA)

We investigate a generalization of cubic splines to Riemannian manifolds. Spline curves are defined as minimizers of the spline energy - a combination of the Riemannian path energy and the time integral of the squared covariant derivative of the path velocity - under suitable interpolation conditions. A variational time discretization for the spline energy leads to a constrained optimization problem over discrete paths on the manifold. Existence of continuous and discrete spline curves is established using the direct method in the calculus of variations. Furthermore, the convergence of discrete spline paths to a continuous spline curve follows from the $\Gamma$-convergence of the discrete to the continuous spline energy. Finally, selected example settings are discussed, including splines on embedded finite-dimensional manifolds, on a high-dimensional manifold of discrete shells with applications in surface processing, and on the infinite-dimensional shape manifold of viscous rods.

[85]
Title: Mourre Theory For Time-Periodic Magnetic Fields
Authors: Masaki Kawamoto
Subjects: Mathematical Physics (math-ph)

We study the Mourre theory for the Floquet Hamiltonian $\hat{H} = -i \partial_t + H(t)$ generated by the time-periodic Hamiltonian $H(t)$ with $H(t+T) =H(t)$, which describes the Schr\"{o}dinger equations with general time-periodic magnetic fields.

[86]
Title: Sharp geometric condition for null-controllability of the heat equation on $\mathbb{R}^d$ and consistent estimates on the control cost
Subjects: Analysis of PDEs (math.AP)

In this note we study the control problem for the heat equation on $\mathbb{R}^d$, $d\geq 1$, with control set $\omega\subset\mathbb{R}^d$. We provide a necessary and sufficient condition (called $(\gamma, a)$-\emph{thickness}) on $\omega$ such that the heat equation is null-controllable in any positive time. We give an estimate of the control cost with explicit dependency on the characteristic geometric parameters of the control set. Finally, we derive a control cost estimate for the heat equation on cubes with periodic, Dirichlet, or Neumann boundary conditions, where the control sets are again assumed to be thick. We show that the control cost estimate is consistent with the $\mathbb{R}^d$ case.

[87]
Title: Extensions of the Hitsuda-Skorokhod integral
Authors: Peter Parczewski
Subjects: Probability (math.PR)

We present alternative definitions of the stochastic integral introduced by Ayew and Kuo and of the Hitsuda-Skorokhod integral extended to domains in $L^p$-spaces, $p \geq 1$. Our approach is motivated by the S-transform characterization of the Hitsuda-Skorokhod integral and based on simple processes of stochastic exponential type. We prove that the new stochastic integral extends the mentioned stochastic integrals above and we outline their connection.

[88]
Title: Homogenization in magnetic-shape-memory polymer composites
Subjects: Analysis of PDEs (math.AP); Numerical Analysis (math.NA)

Magnetic-shape-memory materials (e.g. specific NiMnGa alloys) react with a large change of shape to the presence of an external magnetic field. As an alternative for the difficult to manifacture single crystal of these alloys we study composite materials in which small magnetic-shape-memory particles are embedded in a polymer matrix. The macroscopic properties of the composite depend strongly on the geometry of the microstructure and on the characteristics of the particles and the polymer.
We present a variational model based on micromagnetism and elasticity, and derive via homogenization an effective macroscopic model under the assumption that the microstructure is periodic. We then study numerically the resulting cell problem, and discuss the effect of the microstructure on the macroscopic material behavior. Our results may be used to optimize the shape of the particles and the microstructure.

[89]
Title: An optimal adaptive wavelet method for First Order System Least Squares
Subjects: Numerical Analysis (math.NA)

In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet solver in optimal computational complexity. The applications that are considered are second order elliptic PDEs with general inhomogeneous boundary conditions, and the stationary Navier-Stokes equations.

[90]
Title: The fractional Calderón problem
Authors: Mikko Salo
Comments: 9 pages, 1 figure, to appear in the proceedings of Journ\'ees EDP (Roscoff, June 2017)
Subjects: Analysis of PDEs (math.AP)

We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness and approximation properties, which turn out to yield strong results in related inverse problems.

[91]
Title: Gorenstein homological properties of tensor rings
Authors: Xiao-Wu Chen, Ming Lu
Subjects: Rings and Algebras (math.RA); Representation Theory (math.RT)

Let $R$ be a two-sided noetherian ring and $M$ be a nilpotent $R$-bimodule, which is finitely generated on both sides. We study Gorenstein homological properties of the tensor ring $T_R(M)$. Under certain conditions, the ring $R$ is Gorenstein if and only if so is $T_R(M)$. We characterize Gorenstein projective $T_R(M)$-modules in terms of $R$-modules.

[92]
Title: On first exit times and their means for Brownian bridges
Subjects: Probability (math.PR)

For a Brownian bridge from $0$ to $y$ we prove that the mean of the first exit time from interval $(-h,h), \,\, h>0,$ behaves as $O(h^2)$ when $h \downarrow 0.$ Similar behavior is seen to hold also for the 3-dimensional Bessel bridge. For Brownian bridge and 3-dimensional Bessel bridge this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to prove in detail an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.

[93]
Title: Equivalence classes of exact module categories over graded tensor categories
Subjects: Quantum Algebra (math.QA); Category Theory (math.CT)

We describe equivalence classes of exact indecomposable module categories over a finite graded tensor category. When applied to a pointed fusion category, our results coincide with the ones obtained in [S. Natale, On the equivalence of module categories over a group-theoretical fusion category, SIGMA, Symmetry Integrability Geom. Methods Appl. 13 Paper 042, 9 p. (2017)].

[94]
Title: A uniform open image theorem for l-adic representations in positive characteristic
Authors: Emiliano Ambrosi
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)

Let $k$ be a finitely generated field of characteristic $p > 0$ and $\ell$ a prime. Let $X$ be a smooth, separated, geometrically connected curve of finite type over $k$ and $\rho: \pi_1(X)\rightarrow GL_r(\mathbb Z_{\ell})$ a continuous representation of the \etale fundamental group of $X$ with image $G$. Any $k$-rational point $x:Spec(k)\rightarrow X$ induces a local representation $\rho_x: \pi_1(Spec(k)) \rightarrow \pi_1(X) \rightarrow GL_r(\mathbb Z_{\ell})$ with image $G_x$. The goal of this paper is to study how $G_x$ varies with $x\in X(k)$. In particular we prove that if $\ell\neq p$ and every open subgroup of $\rho(\pi_1(X_{\overline k}))$ has finite abelianization, then the set $X_{\rho}^{ex}(k)$ of $k$-rational points such that $G_x$ is not open in $G$ is finite and there exists a constant $C\geq 0$ such that $[G:G_x]\leq C$ for all $x\in X(k)-X_{\rho}^{ex}(k)$. This result can be applied to obtain uniform bounds for the $\ell$-primary torsion of groups theoretic invariants in one dimensional families of varieties. For example, torsion of abelian varieties and the Galois invariants of the geometric Brauer group. This extends to positive characteristic previous results of Anna Cadoret and Akio Tamagawa in characteristic 0.

[95]
Title: Switch chain mixing times through triangle counts
Comments: 7 pages, 8 figures in the main article. 2 pages, 2 figures in the supplementary material
Subjects: Probability (math.PR); Physics and Society (physics.soc-ph)

Sampling uniform simple graphs with power-law degree distributions with degree exponent $\tau\in(2,3)$ is a non-trivial problem. We propose a method to sample uniform simple graphs that uses a constrained version of the configuration model together with a Markov Chain switching method. We test the convergence of this algorithm numerically in the context of the presence of small subgraphs. We then compare the number of triangles in uniform random graphs with the number of triangles in the erased configuration model. Using simulations and heuristic arguments, we conjecture that the number of triangles in the erased configuration model is larger than the number of triangles in the uniform random graph, provided that the graph is sufficiently large.

[96]
Title: An introduction to Lorenzen's "Algebraic and logistic investigations on free lattices" (1951)
Subjects: Logic (math.LO); History and Overview (math.HO)

This article proposes an historical and mathematical introduction to Lorenzen's "Algebraische und logistische Untersuchungen \"uber freie Verb\"ande". These "Investigations" appeared in 1951 in The journal of symbolic logic. They have immediately been recognised as a landmark in the history of infinitary proof theory, but their approach and method of proof have not been incorporated into the corpus of proof theory. More precisely, the admissibility of cut is proved by double induction, on the cut formula and on the complexity of the derivations, without using any ordinal assignment, contrary to the presentation of cut elimination in most standard texts on proof theory.
We propose a translation (arXiv:1710.08138) and this introduction with the intent of giving a new impetus to their reception. We also propose a translation of a preliminary manuscript, "A preorder-theoretic proof of consistency", with the kind permission of Lorenzen's daughter, Jutta Reinhardt.
The "Investigations" are best known for providing a constructive proof of consistency for ramified type theory without axiom of reducibility. Lorenzen does so by showing that it is a part of a trivially consistent "inductive calculus" that describes our knowledge of arithmetic without detour. The proof resorts only to the inductive definition of formulas and theorems. He proposes furthermore a definition of a semilattice, of a distributive lattice, of a pseudocomplemented semilattice, and of a countably complete boolean lattice as deductive calculuses, and shows how to present them for constructing the respective free object over a given preordered set. This work illustrates that lattice theory is a bridge between algebra and logic.
The preliminary manuscript, given as an appendix, contains already the main ideas and applies them to a constructive proof of consistency for elementary number theory.

[97]
Title: Gossez's approximation theorems in the Musielak-Orlicz-Sobolev spaces
Subjects: Functional Analysis (math.FA)

We prove the density of smooth functions in the modular topology in the Musielak-Orlicz-Sobolev spaces essentially extending the results of Gossez \cite{GJP2} obtained in the Orlicz-Sobolev setting. We impose new systematic regularity assumption on $M$ which allows to study the problem of density unifying and improving the known results in the Orlicz-Sobolev spaces, as well as the variable exponent Sobolev spaces.
We confirm the precision of the method by showing the lack of the Lavrentiev phenomenon in the double-phase case. Indeed, we get the modular approximation of $W^{1,p}_0(\Omega)$ functions by smooth functions in the double-phase space governed by the modular function $H(x,s)=s^p+a(x)s^q$ with $a\in C^{0,\alpha}(\Omega)$ excluding the Lavrentiev phenomenon within the sharp range $q/p\leq 1+\alpha/N$. See \cite[Theorem~4.1]{min-double-reg1} for the sharpness of the result.

[98]
Title: Average size of 2-Selmer groups of Jacobians of hyperelliptic curves over function fields
Authors: Van Thinh Dao
Subjects: Algebraic Geometry (math.AG)

In this paper, we are going to compute the average size of 2-Selmer groups of two families of hyperelliptic curves with marked points over function fields. The result will be obtained by a geometric method which could be considered as a generalization of the one that was used previously by Q.P. Ho, V.B. Le Hung, and B.C. Ngo to obtain the average size of 2-Selmer groups of elliptic curves.

[99]
Title: Polish Topologies for Graph Products of Groups
Subjects: Logic (math.LO)

We give strong necessary conditions on the admissibility of a Polish group topology for an arbitrary graph product of groups $G(\Gamma, G_a)$, and use them to give a characterization modulo a finite set of nodes. As a corollary, we give a complete characterization in case all the factor groups $G_a$ are countable.

[100]
Title: Limiting absorption principle and radiation condition for repulsive Hamiltonians
Authors: Kyohei Itakura
Comments: 22 pages. arXiv admin note: substantial text overlap with arXiv:1602.07488 by other authors
Subjects: Mathematical Physics (math-ph); Functional Analysis (math.FA)

For spherically symmetric repulsive Hamiltonians we prove the Besov bound, the radiation condition bounds and the limiting absorption principle. The Sommerfeld uniqueness result also follows as a corollary of these. In particular, the Hamiltonians considered in this paper cover the case of inverted harmonic oscillator. In the proofs of our theorems, we mainly use a commutator argument invented recently by Ito and Skibsted. This argument is simple and elementary, and dose not employ energy cut-offs or the microlocal analysis.

[101]
Title: The Class of Countable Projective Planes is Borel Complete
Authors: Gianluca Paolini
Subjects: Logic (math.LO)

We observe that Hall's free projective extension $P \mapsto F(P)$ of partial planes is a Borel map, and use a modification of the construction introduced in [9] to conclude that the class of countable non-Desarguesian projective planes is Borel complete. In the process, we also rediscover the main result of [7] on the realizability of every group as the group of collineations of some projective plane. Finally, we use classical results of projective geometry to prove that the class of countable Pappian projective planes is Borel complete.

[102]
Title: Joint Power Control and Beamforming for Uplink Non-Orthogonal Multiple Access in 5G Millimeter-Wave Communications
Comments: 12 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1711.01380
Subjects: Information Theory (cs.IT)

In this paper, we investigate the combination of two key enabling technologies for the fifth generation (5G) wireless mobile communication, namely millimeter-wave (mmWave) communications and non-orthogonal multiple access (NOMA). In particular, we consider a typical 2-user uplink mmWave-NOMA system, where the base station (BS) equips an analog beamforming structure with a single RF chain and serves 2 NOMA users. An optimization problem is formulated to maximize the achievable sum rate of the 2 users while ensuring a minimal rate constraint for each user. The problem turns to be a joint power control and beamforming problem, i.e., we need to find the beamforming vectors to steer to the two users simultaneously subject to an analog beamforming structure, and meanwhile control appropriate power on them. As direct search for the optimal solution of the non-convex problem is too complicated, we propose to decompose the original problem into two sub-problems that are relatively easy to solve: one is a power control and beam gain allocation problem, and the other is an analog beamforming problem under a constant-modulus constraint. The rational of the proposed solution is verified by extensive simulations, and the performance evaluation results show that the proposed sub-optimal solution achieve a close-to-bound uplink sum-rate performance.

[103]
Title: A breakdown of injectivity for weighted ray transforms in multidimensions
Authors: Fedor Goncharov (1), Roman Novikov (1) ((1) CMAP)
Subjects: Functional Analysis (math.FA); Classical Analysis and ODEs (math.CA)

We consider weighted ray-transforms $P\_W$ (weighted Radon transforms along straight lines) in $R^d , d \geq 2$, with strictly positive weights $W$. We construct an example of such a transform with non-trivial kernel in the space of infinitely smooth compactly supported functions on $R^d$. In addition, the constructed weight W is rotation-invariant continuous and is infinitely smooth almost everywhere on $R^d \times S^{d--1}$. In particular, by this construction we give counterexamples to some well-known injectivity results for weighted ray transforms for the case when the regularity of W is slightly relaxed.

[104]
Title: Quasidensity: a survey and some examples
Authors: Stephen Simons
Subjects: Functional Analysis (math.FA)

In three previous papers, we discussed quasidense multifunctions from a Banach space into its dual, or, equivalently, quasidense subsets of the product of a Banach space and its dual. In this paper, we survey (without proofs) some of the main results about quasidensity, and give some simple limiting examples in Hilbert spaces, reflexive Banach spaces, and nonreflexive Banach spaces.

[105]
Title: A Family of Virtual Element Methods for Plane Elasticity Problems Based on the Hellinger-Reissner Principle
Subjects: Numerical Analysis (math.NA)

A family of Virtual Element schemes based on the Hellinger-Reissner variational principle is presented. A convergence and stability analysis is rigorously developed. Numerical tests confirming the theoretical predictions are performed.

[106]
Title: Infinity-tilting theory
Comments: LaTeX 2e with pb-diagram and xy-pic, 33 pages, 4 figures
Subjects: Category Theory (math.CT); Representation Theory (math.RT)

We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between $\infty$-tilting objects in complete, cocomplete abelian categories with an injective cogenerator and $\infty$-cotilting objects in complete, cocomplete abelian categories with a projective generator is constructed. We also introduce $\infty$-tilting pairs, consisting of an $\infty$-tilting object and its $\infty$-tilting class, and obtain a bijective correspondence between $\infty$-tilting and $\infty$-cotilting pairs. Finally, we discuss the related derived equivalences and t-structures.

[107]
Title: Linear differential equations with solutions in weighted Fock spaces
Subjects: Complex Variables (math.CV)

This research is concerned with the nonhomogeneous linear complex differential equation $$f^{(k)}+A_{k-1}f^{(k-1)}+\cdots+A_{1}f'+A_{0}f=A_{k}$$ in the complex plane. In the higher order case, the mutual relations between coefficients and solutions in weighted Fock spaces are discussed, respectively. In particular, sufficient conditions for the solutions of the second order case $$f"+Af=0$$ to be in some weighted Fock space are given by Bergman reproducing kernel and coefficient $A$.

[108]
Title: A novel low-rank matrix completion approach to estimate missing entries in Euclidean distance matrices
Comments: This paper has 12 pages, 1 figure and 5 tables
Subjects: Optimization and Control (math.OC)

A Euclidean Distance Matrix (EDM) is a table of distance-square between points on a k- dimensional Euclidean space, with applications in many fields (e.g. engineering, geodesy, economics, genetics, biochemistry, psychology). A problem that often arises is the absence (or uncertainty) of some EDM elements. In many situations, only a subset of all pairwise distances is available and it is desired to have some procedure to estimate the missing distances. In this paper, we address the problem of missing data in EDM through low-rank matrix completion techniques. We exploit the fact that the rank of a EDM is at most k+2 and does not depend on the number of points, which is, in general, much bigger then k. We use a Singular Value Decomposition approach that considers the rank of the matrix to be completed and computes, in each iteration, a parameter that controls the convergence of the method. After performing a number of computational experiments, we could observe that our proposal was able to recover, with high precision, random EDMs with more than one thousand points and up to 98 percent of missing data in few minutes. Additionally, our method required a smaller number of iterations when compared to other competitive state-of-art technique.

[109]
Title: Regularity of solutions to space--time fractional wave equations: a PDE approach
Subjects: Analysis of PDEs (math.AP); Numerical Analysis (math.NA)

We consider an evolution equation involving the fractional powers, of order $s \in (0,1)$, of a symmetric and uniformly elliptic second order operator and Caputo fractional time derivative of order $\gamma \in (1,2]$. Since it has been shown useful for the design of numerical techniques for related problems, we also consider a quasi--stationary elliptic problem that comes from the realization of the spatial fractional diffusion as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi--infinite cylinder. We provide existence and uniqueness results together with energy estimates for both problems. In addition, we derive regularity estimates both in time and space; the time--regularity results show that the usual assumptions made in the numerical analysis literature are problematic

[110]
Title: On the Hilbert function of general fat points in $\mathbb{P}^1 \times \mathbb{P}^1$
Subjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG)

We study the bi-graded Hilbert function of ideals of general fat points with same multiplicity in $\mathbb{P}^1\times\mathbb{P}^1$. Our first tool is the multiprojective-affine-projective method introduced by the second author in previous works with A.V. Geramita and A. Gimigliano where they solved the case of double points. In this way, we compute the Hilbert function when the smallest entry of the bi-degree is at most the multiplicity of the points. Our second tool is the differential Horace method introduced by J. Alexander and A. Hirschowitz to study the Hilbert function of sets of fat points in standard projective spaces. In this way, we compute the entire bi-graded Hilbert function in the case of triple points.

[111]
Title: A Low-Rank Rounding Heuristic for Semidefinite Relaxation of Hydro Unit Commitment Problems
Comments: Submitted to IEEE Power and Energy Society General Meeting 2018
Subjects: Optimization and Control (math.OC)

Hydro unit commitment is the problem of maximizing water use efficiency while minimizing start-up costs in the daily operation of multiple hydro plants, subject to constraints on short-term reservoir operation, and long-term goals. A low-rank rounding heuristic is presented for the semidefinite relaxation of the mixed-integer quadratic-constrained formulation of this problem. In addition to limits on reservoir and generator operation, transmission constraints are represented by an approximate AC power flow model. In our proposed method, the mathematical program is equivalently formulated as a QCQP problem solved by convex relaxation based on semidefinite programming, followed by a MILP solution of undefined unit commitment schedules. Finally, a rank reduction procedure is applied. Effectiveness of the proposed heuristic is compared to branch-and-bound solutions for numerical case studies of varying sizes of the generation and transmission systems.

[112]
Title: Subdiffusive discrete time random walks via Monte Carlo and subordination
Subjects: Numerical Analysis (math.NA)

A class of discrete time random walks has recently been introduced to provide a stochastic process based numerical scheme for solving fractional order partial differential equations, including the fractional subdiffusion equation. Here we develop a Monte Carlo method for simulating discrete time random walks with Sibuya power law waiting times, providing another approximate solution of the fractional subdiffusion equation. The computation time scales as a power law in the number of time steps with a fractional exponent simply related to the order of the fractional derivative. We also provide an explicit form of a subordinator for discrete time random walks with Sibuya power law waiting times. This subordinator transforms from an operational time, in the expected number of random walk steps, to the physical time, in the number of time steps.

[113]
Title: Stationary states of boundary driven exclusion processes with nonreversible boundary dynamics
Subjects: Probability (math.PR); Statistical Mechanics (cond-mat.stat-mech)

We prove a law of large numbers for the empirical density of one-dimensional, boundary driven, symmetric exclusion processes with different types of non-reversible dynamics at the boundary. The proofs rely on duality techniques.

[114]
Title: Power Diagram Detection with Applications to Information Elicitation
Subjects: Optimization and Control (math.OC)

Power diagrams, a type of weighted Voronoi diagrams, have many applications throughout operations research. We study the problem of power diagram detection: determining whether a given finite partition of $\mathbb{R}^d$ takes the form of a power diagram. This detection problem is particularly prevalent in the field of information elicitation, where one wishes to design contracts to incentivize self-minded agents to provide honest information.
We devise a simple linear program to decide whether a polyhedral cell decomposition can be described as a power diagram. Further, we discuss applications to property elicitation, peer prediction, and mechanism design, where this question arises. Our model is able to efficiently decide the question for decompositions of $\mathbb{R}^d$ or of a restricted domain in $\mathbb{R}^d$. The approach is based on the use of an alternative representation of power diagrams, and invariance of a power diagram under uniform scaling of the parameters in this representation.

[115]
Title: Entropy and finiteness of groups with acylindrical splittings
Subjects: Metric Geometry (math.MG); Differential Geometry (math.DG); Geometric Topology (math.GT)

We prove that there exists a positive, explicit function $F(k, E)$ such that, for any group $G$ admitting a $k$-acylindrical splitting and any generating set $S$ of $G$ with $\mathrm{Ent}(G,S)<E$, we have $|S| \leq F(k, E)$. We deduce corresponding finiteness results for classes of groups possessing acylindrical splittings and acting geometrically with bounded entropy: for instance, $D$-quasiconvex $k$-malnormal amalgamated products acting on $\delta$-hyperbolic spaces or on $CAT(0)$-spaces with entropy bounded by $E$. A number of finiteness results for interesting families of Riemannian or metric spaces with bounded entropy and diameter also follow: CAT(0)-groups with negatively curved splittings, Riemannian 2-orbifolds, ramified coverings, cusp-decomposable manifolds.

[116]
Title: Weak square and stationary reflection
Subjects: Logic (math.LO)

It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if $\mu^{\mathrm{cf}(\lambda)} < \lambda$ for all $\mu < \lambda$, then $\square^*_\lambda$ entails the existence of a non-reflecting stationary subset of $E^{\lambda^+}_{\mathrm{cf}(\lambda)}$ in the forcing extension for adding a single Cohen subset of $\lambda^+$. It follows that indestructible forms of simultaneous stationary reflection entail the failure of weak square. We demonstrate this by settling a question concerning the subcomplete forcing axiom (SCFA), proving that SCFA entails the failure of $\square^*_\lambda$ for every singular cardinal $\lambda$ of countable cofinality.

[117]
Title: A prismatic classifying space
Authors: J. Scott Carter (University of South Alabama), Victoria Lebed (Trinity College Dublin), Seung Yeop Yang (University of Denver)
Subjects: Geometric Topology (math.GT)

A qualgebra $G$ is a set having two binary operations that satisfy compatibility conditions which are modeled upon a group under conjugation and multiplication. We develop a homology theory for qualgebras and describe a classifying space for it. This space is constructed from $G$-colored prisms (products of simplices) and simultaneously generalizes (and includes) simplicial classifying spaces for groups and cubical classifying spaces for quandles. Degenerate cells of several types are added to the regular prismatic cells; by duality, these correspond to "non-rigid" Reidemeister moves and their higher dimensional analogues. Coupled with $G$-coloring techniques, our homology theory yields invariants of knotted trivalent graphs in $\mathbb{R}^3$ and knotted foams in $\mathbb{R}^4$. We re-interpret these invariants as homotopy classes of maps from $S^2$ or $S^3$ to the classifying space of $G$.

[118]
Title: On the probability of nonexistence in binomial subsets
Subjects: Combinatorics (math.CO)

Let $\Gamma$ be a hypergraph with vertex set $\Omega$, let $p \colon \Omega \to [0,1]$, and let $\Omega_p$ be a random set formed by including every $\omega\in\Omega$ independently with probability $p(\omega)$. We investigate the general question of deriving fine (asymptotic) estimates for the probability that $\Omega_p$ is an independent set in $\Gamma$, which is an omnipresent problem in probabilistic combinatorics. Our main result provides a sequence of lower and uppe r bounds on this quantity, each of which can be evaluated explicitly. Under certain natural conditions, we obtain an explicit closed formula that is asymptotic to this probability. We demonstrate the applicability of our results with two concrete examples: subgraph containment in random graphs and arithmetic progressions in random subsets of the integers.

[119]
Title: The indeterminacy locus of the Voisin map
Subjects: Algebraic Geometry (math.AG)

Beauville and Donagi proved that the variety of lines $F(Y)$ of a smooth cubic fourfold $Y$ is a hyperK\"{a}hler variety. Recently, C. Lehn, M.Lehn, Sorger and van Straten proved that one can naturally associate a hyperK\"{a}hler variety $Z(Y)$ to the variety of twisted cubics on $Y$. Then, Voisin defined a degree 6 rational map $\psi:F(Y)\times F(Y)\dashrightarrow Z(Y)$. We will show that the indeterminacy locus of $\psi$ is the locus of intersecting lines.

[120]
Title: Fine properties of branch point singularities: Dirichlet energy minimizing multi-valued functions
Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)

In the early 1980's Almgren developed a theory of Dirichlet energy minimizing multi-valued functions, proving that the Hausdorff dimension of the singular set (including branch points) of such a function is at most $(n-2),$ where $n$ is the dimension of its domain. Almgren used this result in an essential way to show that the same upper bound holds for the dimension of the singular set of an area minimizing $n$-dimensional rectifiable current of arbitrary codimension. In either case, the dimension bound is sharp. We develop estimates to study the asymptotic behaviour of a multi-valued Dirichlet energy minimizer on approach to its singular set. Our estimates imply that a Dirichlet energy minimizer at ${\mathcal H}^{n-2}$ a.e. point of its singular set has a unique set of homogeneous multi-valued cylindrical tangent functions (blow-ups) to which the minimizer, modulo a set of single-valued harmonic functions, decays exponentially fast upon rescaling. A corollary is that the singular set is countably $(n-2)$-rectifiable. Our work is inspired by the work of L. Simon on the analysis of singularities of minimal submanifolds in multiplicity 1 classes, and uses some new estimates and strategies together with techniques from Wickramasekera's prior work to overcome additional difficulties arising from higher multiplicity and low regularity of the minimizers in the presence of branch points. The results described here were announced in earlier work of the authors where the special case of two-valued Dirichlet minimizing functions was treated.

[121]
Title: Theorem of Existence and Uniqueness of Solution for Differential Equation of Fractional Order
Authors: M.V.Kukushkin
Subjects: Functional Analysis (math.FA)

In this paper we proved a theorems of existence and uniqueness of solutions of differential equation of second order with fractional derivative in the Kipriyanov sense in lower terms. As a domain of definition of the functions we consider the n --- dimensional Euclidean space. By a simple reduction of Kipriyanov operator to the operator of fractional differentiation in the sense of Marchaud these results can be considered valid for the operator of fractional differentiation in the sense of Riemann-Liouville, because of known fact coincidence of these operators on the classes of functions representable by the fractional integral.

[122]
Title: Boolean Extremes and Dagum Distributions
Subjects: Functional Analysis (math.FA); Probability (math.PR)

We study the max-convolution and max-stable laws for Boolean independence and prove that these are Dagum distributions (also known as log-logistical distributions).

[123]
Title: Congruences for coefficients of modular functions in genus zero levels
Subjects: Number Theory (math.NT)

We prove congruences for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight $0$ and levels $6, 10, 12, 18$ with poles only at the cusp at infinity. In addition, we show that these Fourier coefficients satisfy Zagier duality in all weights, and give a general formula for the generating functions of such canonical bases for all genus zero levels.

[124]
Title: Deceptiveness of internet data for disease surveillance
Subjects: Information Theory (cs.IT); Social and Information Networks (cs.SI); Populations and Evolution (q-bio.PE); Applications (stat.AP)

Quantifying how many people are or will be sick, and where, is a critical ingredient in reducing the burden of disease because it helps the public health system plan and implement effective outbreak response. This process of disease surveillance is currently based on data gathering using clinical and laboratory methods; this distributed human contact and resulting bureaucratic data aggregation yield expensive procedures that lag real time by weeks or months. The promise of new surveillance approaches using internet data, such as web event logs or social media messages, is to achieve the same goal but faster and cheaper. However, prior work in this area lacks a rigorous model of information flow, making it difficult to assess the reliability of both specific approaches and the body of work as a whole.
We model disease surveillance as a Shannon communication. This new framework lets any two disease surveillance approaches be compared using a unified vocabulary and conceptual model. Using it, we describe and compare the deficiencies suffered by traditional and internet-based surveillance, introduce a new risk metric called deceptiveness, and offer mitigations for some of these deficiencies. This framework also makes the rich tools of information theory applicable to disease surveillance. This better understanding will improve the decision-making of public health practitioners by helping to leverage internet-based surveillance in a way complementary to the strengths of traditional surveillance.

[125]
Title: Methods for constructing elliptic and hyperelliptic curves with rational points
Authors: Kirti Joshi
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)

I provide methods of constructing elliptic and hyperelliptic curves over global fields with interesting rational points over the given fields or over large field extensions. I also provide a elliptic curves defined over any given number field equipped with a rational point, (resp. with two rational points) of infinite order over the given number field, and elliptic curves over the rationals with two rational points over `simplest cubic fields.' I also provide hyperelliptic curves of genus exceeding any given number over any given number fields with points (over the given number field) which span a subgroup of rank at least $g$ in the group of rational points of the Jacobian of this curve. I also provide a method of constructing hyperelliptic curves over rational function fields with rational points defined over field extensions with large finite simple Galois groups, such as the Mathieu group $M_{24}$.

[126]
Title: Irreducible polynomials over a finite field with restricted coefficients
Authors: Sam Porritt
Subjects: Number Theory (math.NT)

We prove a function field analogue of Maynard's result about primes with restricted digits. That is, for certain ranges of parameters n and q, we prove an asymptotic formula for the number of irreducible polynomials of degree n over a finite field F_q whose coefficients are restriced to lie in a given subset of F_q.

[127]
Title: Pre-Plactic Algebra and Snakes
Authors: Todor Popov
Subjects: Quantum Algebra (math.QA)

We study a factor Hopf algebra $\mathfrak{PP}$ of the Malvenuto-Reutenauer convolution algebra of functions on symmetric groups ${\mathfrak{S}}=\oplus_{n\geq 0} \mathbb C[{\mathfrak{S}}_n]$ that we coined pre-plactic algebra. The pre-plactic algebra admits the Poirier-Reutenauer algebra based on Standard Young Tableaux as a factor and it is closely related to the quantum pseudo-plactic algebra introduced by Krob and Thibon in the non-commutative character theory of quantum group comodules. The connection between the quantum pseudo-plactic algebra and the pre-plactic algebra is similar to the connection between the Lascoux-Sch\"utzenberger plactic algebra and the Poirier-Reutenauer algebra. We show that the dimensions of the pre-plactic algebra are given by the numbers of alternating permutations (coined snakes after V.I. Arnold). Pre-plactic algebra is instrumental in calculating the Hilbert-Poincar\'e series of the quantum pseudo-plactic algebra.

[128]
Title: Motivic Landweber Exact Theories and Étale Cohomology
Subjects: Algebraic Geometry (math.AG)

Thomason's \'{e}tale descent theorem for Bott periodic algebraic $K$-theory is generalized to any motivic Landweber exact theory, for essentially smooth schemes over a perfect field. This is achieved by amplifying the effects from the case of motivic cohomology, using the slice spectral sequence in the case of the universal example of algebraic cobordism. As applications, we construct an \'etale descent spectral sequence converging to Bott-inverted motivic Landweber exact theories, prove cellularity and effectivity of the \'{e}tale versions of these motivic spectra, and describe their module categories.

### Cross-lists for Fri, 17 Nov 17

[129]  arXiv:1704.02796 (cross-list from cs.DM) [pdf, ps, other]
Title: Backtracking and Commutative Algorithms for the LLL
Authors: Fotis Iliopoulos
Subjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO); Probability (math.PR)

Following the groundbreaking works of Moser and Tardos~\cite{M,MT} that made the Lov\'asz Local Lemma (LLL) constructive, a series of works have exploited key ideas of their analysis to come up with a plethora of results.
A first line of works employs the entropy compression method to analyze stochastic search algorithm similar to the Moser-Tardos algorithm but without explicitly referring to a specific version of the LLL. Such an example is a class of backtracking algorithms for Constraint Satisfaction Problems (CSPs) introduced by Grytczuk, Kozik and Micek~\cite{djm}, and later approached more systematically by the work of Esperet and Parraeu~\cite{ac}, which have found applications in a wide variety of problems.
A different series of works exploit a key ingredient of the original analysis of Moser and Tardos, the witness tree lemma, in order to: derive deterministic and parallel algorithms for the LLL, to estimate the entropy of the output distribution, to partially avoid bad events and to deal with super-polynomially many bad events. Unfortunately, these results do not extend to the most general algorithmic LLL frameworks~\cite{AI,HV}. Mainly, this is because the witness tree lemma, provably, no longer holds.
Our first contribution is to extend the framework of Achlioptas and Iliopoulos~\cite{AI} and provide a Local Lemma criterion that can capture every application of backtracking algorithms we are aware of and more. Our second contribution is to show that for commutative algorithms, a class recently introduced by Kolmogorov, the witness tree lemma holds. Armed with this fact, we extend the main result of Haeupler, Saha, and Srinivasan~\cite{HSS} to commutative algorithms, establishing that the output of such algorithms well-approximates the LLL-distribution. Moreover, we define a class of commutative backtracking algorithms and show that we can get similar results.

[130]  arXiv:1711.05753 (cross-list from hep-th) [pdf, other]
Title: Thomas Precession for Dressed Particles
Authors: Blagoje Oblak
Subjects: High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); General Relativity and Quantum Cosmology (gr-qc); Representation Theory (math.RT); Quantum Physics (quant-ph)

We consider a particle dressed with boundary gravitons in three-dimensional Minkowski space. The existence of BMS transformations implies that the particle's wavefunction picks up a Berry phase when subjected to changes of reference frames that trace a closed path in the asymptotic symmetry group. We evaluate this phase and show that, for BMS superrotations, it provides a gravitational generalization of Thomas precession. In principle, such phases are observable signatures of asymptotic symmetries.

[131]  arXiv:1711.05817 (cross-list from cs.LG) [pdf]
Subjects: Learning (cs.LG); Optimization and Control (math.OC)

Most algorithms for reinforcement learning work by estimating action-value functions. Here we present a method that uses Lagrange multipliers, the costate equation, and multilayer neural networks to compute policy gradients. We show that this method can find solutions to time-optimal control problems, driving nonlinear mechanical systems quickly to a target configuration. On these tasks its performance is comparable to that of deep deterministic policy gradient, a recent action-value method.

[132]  arXiv:1711.05869 (cross-list from stat.ML) [pdf, other]
Title: Predictive Independence Testing, Predictive Conditional Independence Testing, and Predictive Graphical Modelling
Subjects: Machine Learning (stat.ML); Learning (cs.LG); Statistics Theory (math.ST); Methodology (stat.ME)

Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art workflows suffer from the need for heuristic or subjective manual choices, high computational complexity, or strong parametric assumptions.
We address these problems by establishing a theoretical link between multivariate/conditional independence testing, and model comparison in the multivariate predictive modelling aka supervised learning task. This link allows advances in the extensively studied supervised learning workflow to be directly transferred to independence testing workflows - including automated tuning of machine learning type which addresses the need for a heuristic choice, the ability to quantitatively trade-off computational demand with accuracy, and the modern black-box philosophy for checking and interfacing.
As a practical implementation of this link between the two workflows, we present a python package 'pcit', which implements our novel multivariate and conditional independence tests, interfacing the supervised learning API of the scikit-learn package. Theory and package also allow for straightforward independence test based learning of graphical model structure.
We empirically show that our proposed predictive independence test outperform or are on par to current practice, and the derived graphical model structure learning algorithms asymptotically recover the 'true' graph. This paper, and the 'pcit' package accompanying it, thus provide powerful, scalable, generalizable, and easy-to-use methods for multivariate and conditional independence testing, as well as for graphical model structure learning.

[133]  arXiv:1711.05893 (cross-list from cs.LG) [pdf, other]
Title: On Communication Complexity of Classification Problems
Subjects: Learning (cs.LG); Computational Complexity (cs.CC); Information Theory (cs.IT)

This work introduces a model of distributed learning in the spirit of Yao's communication complexity model. We consider a two-party setting, where each of the players gets a list of labelled examplesand they communicate in order to jointly perform some learning task. To naturally fit into the framework of learning theory, we allow the players to send each other labelled examples, where each example costs one unit of communication. This model can also be thought of as a distributed version of sample compression schemes.
We study several fundamental questions in this model. For example, we define the analogues of the complexity classes P, NP and coNP, and show that in this model P equals the intersection of NP and coNP. The proof does not seem to follow from the analogous statement in classical communication complexity; in particular, our proof uses different techniques, including boosting and metric properties of VC classes.
This framework allows to prove, in the context of distributed learning, unconditional separations between various learning contexts, like realizable versus agnostic learning, and proper versus improper learning. The proofs here are based on standard ideas from communication complexity as well as learning theory and geometric constructions in Euclidean space. As a corollary, we also obtain lower bounds that match the performance of algorithms from previous works on distributed classification.

[134]  arXiv:1711.05895 (cross-list from stat.ME) [pdf, other]
Title: Linear-Cost Covariance Functions for Gaussian Random Fields
Subjects: Methodology (stat.ME); Numerical Analysis (math.NA)

Gaussian random fields (GRF) are a fundamental stochastic model for spatiotemporal data analysis. An essential ingredient of GRF is the covariance function that characterizes the joint Gaussian distribution of the field. Commonly used covariance functions give rise to fully dense and unstructured covariance matrices, for which required calculations are notoriously expensive to carry out for large data. In this work, we propose a construction of covariance functions that result in matrices with a hierarchical structure. Empowered by matrix algorithms that scale linearly with the matrix dimension, the hierarchical structure is proved to be efficient for a variety of random field computations, including sampling, kriging, and likelihood evaluation. Specifically, with $n$ scattered sites, sampling and likelihood evaluation has an $O(n)$ cost and kriging has an $O(\log n)$ cost after preprocessing, particularly favorable for the kriging of an extremely large number of sites (e.g., predicting on more sites than observed). We demonstrate comprehensive numerical experiments to show the use of the constructed covariance functions and their appealing computation time. Numerical examples on a laptop include simulated data of size up to one million, as well as a climate data product with over two million observations.

[135]  arXiv:1711.05958 (cross-list from hep-th) [pdf, other]
Title: $E_8$ spectral curves
Authors: Andrea Brini
Comments: 87 pages, 5 figures. Raw binaries containing spectral curve data available with an accompanying Mathematica notebook at this https URL (180Mb ZIP archive; beware this currently unpacks to 912Mb)
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Exactly Solvable and Integrable Systems (nlin.SI)

I provide an explicit construction of spectral curves for the affine $\mathrm{E}_8$ relativistic Toda chain. Their closed form expression is obtained by determining the full set of character relations in the representation ring of $\mathrm{E}_8$ for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of both integrals of motion and the action-angle map for the resulting integrable system.
I consider two main areas of applications of these constructions. On the one hand, I consider the resulting family of spectral curves in the context of the correspondences between Toda systems, 5d Seiberg-Witten theory, Gromov-Witten theory of orbifolds of the resolved conifold, and Chern-Simons theory to establish a version of the B-model Gopakumar-Vafa correspondence for the $\mathrm{sl}_N$ L\^e-Murakami-Ohtsuki invariant of the Poincar\'e integral homology sphere to all orders in $1/N$. On the other, I consider a degenerate version of the spectral curves and prove a 1-dimensional Landau-Ginzburg mirror theorem for the Frobenius manifold structure on the space of orbits of the extended affine Weyl group of type $\mathrm{E}_8$ introduced by Dubrovin-Zhang (equivalently, the orbifold quantum cohomology of the type-$\mathrm{E}_8$ polynomial $\mathbb{C} P^1$ orbifold). This leads to closed-form expressions for the flat co-ordinates of the Saito metric, the prepotential, and a higher genus mirror theorem based on the Chekhov-Eynard-Orantin recursion. I will also show how the constructions of the paper lead to a generalisation of a conjecture of Norbury-Scott to ADE $\mathbb{P}^1$-orbifolds, and a mirror of the Dubrovin-Zhang construction for all Weyl groups and choices of marked roots.

[136]  arXiv:1711.05967 (cross-list from hep-th) [pdf, other]
Title: A Renormalizable SYK-type Tensor Field Theory
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)

In this paper we introduce a simple field theoretic version of the Carrozza-Tanasa-Klebanov-Tarnopolsky (CTKT) "uncolored" holographic tensor model. It gives a more familiar interpretation to the previously abstract modes of the SYK or CTKT models in terms of momenta. We choose for the tensor propagator the usual Fermionic propagator of condensed matter, with a spherical Fermi surface, but keep the CTKT interactions. Hence our field theory can also be considered as an ordinary condensed matter model with a non-local and non-rotational invariant interaction. Using a multiscale analysis we prove that this field theory is just renormalizable to all orders of perturbation theory in the ultraviolet regime.

[137]  arXiv:1711.06063 (cross-list from cs.CR) [pdf, ps, other]
Title: On error linear complexity of new generalized cyclotomic binary sequences of period $p^2$
Subjects: Cryptography and Security (cs.CR); Number Theory (math.NT)

We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the sequences (Designs, Codes and Cryptography, 2017, https://doi.org/10.1007/s10623-017-0408-7). More exactly, we determine the values of $k$-error linear complexity over $\mathbb{F}_2$ for almost $k>0$ in terms of the theory of Fermat quotients. Results indicate that such sequences have good stability.

[138]  arXiv:1711.06111 (cross-list from hep-th) [pdf, ps, other]
Title: Kinematical Lie algebras via deformation theory
Subjects: High Energy Physics - Theory (hep-th); Representation Theory (math.RT)

We present a deformation theory approach to the classification of kinematical Lie algebras in 3+1 dimensions and present calculations leading to the classifications of all deformations of the static kinematical Lie algebra and of its universal central extension, up to isomorphism. In addition we determine which of these Lie algebras admit an invariant symmetric inner product. Among the new results, we find some deformations of the centrally extended static kinematical Lie algebra which are extensions (but not central) of deformations of the static kinematical Lie algebra. This paper lays the groundwork for two companion papers which present similar classifications in dimension D + 1 for all D>3 and in dimension 2+1.

[139]  arXiv:1711.06123 (cross-list from cond-mat.mes-hall) [pdf, other]
Title: Direct reconstruction of two-dimensional currents in thin films from magnetic field measurements
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph)

Accurate determination of microscopic transport and magnetization currents is of central importance for the study of the electric properties of low dimensional materials and interfaces, of superconducting thin films and of electronic devices. Current distribution is usually derived from the measurement of the perpendicular component of the magnetic field above the surface of the sample, followed by numerical inversion of the Biot-Savart law. The inversion is commonly obtained by deriving the current stream function $g$, which is then differentiated in order to obtain the current distribution. However, this two-step procedure requires filtering at each step and, as a result, oversmoothes the solution. To avoid this oversmoothing we develop a direct procedure for inversion of the magnetic field that avoids use of the stream function. This approach provides enhanced accuracy of current reconstruction over a wide range of noise levels. We further introduce a reflection procedure that allows for the reconstruction of currents that cross the boundaries of the measurement window. The effectiveness of our approach is demonstrated by several numerical examples.

[140]  arXiv:1711.06150 (cross-list from hep-th) [pdf, other]
Title: 3d Expansions of 5d Instanton Partition Functions
Subjects: High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)

We propose a set of novel expansions of Nekrasov's instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on $\mathbb{C}^2_{q,t^{-1}} \times \mathbb{S}^1$, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces $\mathbb{C}_{q} \times \mathbb{S}^1$, $\mathbb{C}_{t^{-1}} \times \mathbb{S}^1$ and their intersection along $\mathbb{S}^1$. These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with $W_{q,t}$ correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.

[141]  arXiv:1711.06154 (cross-list from cs.NI) [pdf, other]
Title: Reliable Video Streaming over mmWave with Multi Connectivity and Network Coding
Comments: To be presented at the 2017 IEEE International Conference on Computing, Networking and Communications (ICNC), March 2017, Maui, Hawaii, USA (invited paper). 6 pages, 4 figures
Subjects: Networking and Internet Architecture (cs.NI); Information Theory (cs.IT)

The next generation of multimedia applications will require the telecommunication networks to support a higher bitrate than today, in order to deliver virtual reality and ultra-high quality video content to the users. Most of the video content will be accessed from mobile devices, prompting the provision of very high data rates by next generation (5G) cellular networks. A possible enabler in this regard is communication at mmWave frequencies, given the vast amount of available spectrum that can be allocated to mobile users; however, the harsh propagation environment at such high frequencies makes it hard to provide a reliable service. This paper presents a reliable video streaming architecture for mmWave networks, based on multi connectivity and network coding, and evaluates its performance using a novel combination of the ns-3 mmWave module, real video traces and the network coding library Kodo. The results show that it is indeed possible to reliably stream video over cellular mmWave links, while the combination of multi connectivity and network coding can support high video quality with low latency.

[142]  arXiv:1711.06209 (cross-list from gr-qc) [pdf, other]
Title: Horizon quantum fuzziness for non-singular black holes
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein's field equations according to the formalism known as Horizon Quantum Mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.

### Replacements for Fri, 17 Nov 17

[143]  arXiv:1012.0781 (replaced) [pdf, ps, other]
Title: Correlation between Angle and Side
Authors: Steven R. Finch
Subjects: Probability (math.PR); Classical Analysis and ODEs (math.CA)
[144]  arXiv:1111.2680 (replaced) [pdf, ps, other]
Title: Bivariate least squares linear regression: towards a unified analytic formalism. II. Extreme structural models
Authors: R. Caimmi
Comments: 55 pages, 5 tables, and 3 figures. Added references, corrected typos, new appendix F. arXiv admin note: substantial text overlap with arXiv:1103.0628
Journal-ref: Applied Mathematical Sciences 2017 vol. 11, 2393
Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); Statistics Theory (math.ST)
[145]  arXiv:1307.4164 (replaced) [pdf, ps, other]
Title: Approximating Minimum Cost Connectivity Orientation and Augmentation
Subjects: Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM); Combinatorics (math.CO)
[146]  arXiv:1503.01023 (replaced) [pdf, other]
Title: Cylindrical confinement of semiflexible polymers
Journal-ref: Phys. Rev. E 91, 063203 (2015)
Subjects: Soft Condensed Matter (cond-mat.soft); Mathematical Physics (math-ph)
[147]  arXiv:1503.03461 (replaced) [pdf, ps, other]
Title: Skew polynomial rings over abelian and idempotent reflexive rings
Authors: Mohamed Louzari
Subjects: Rings and Algebras (math.RA)
[148]  arXiv:1507.06616 (replaced) [pdf, ps, other]
Title: Robust Monotone Submodular Function Maximization
Comments: Preliminary version in IPCO 2016
Subjects: Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM); Optimization and Control (math.OC)
[149]  arXiv:1509.08349 (replaced) [pdf, ps, other]
Title: Global well-posedness of an initial-boundary value problem for viscous non-resistive MHD systems
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
[150]  arXiv:1510.00502 (replaced) [pdf, other]
Title: Bicovariograms and Euler characteristic of random fields excursions
Authors: Raphaël Lachièze-Rey (MAP5 - UMR 8145), Raphaëllachì Eze-Rey
Subjects: Probability (math.PR)
[151]  arXiv:1510.03246 (replaced) [pdf, other]
Title: Entropy of embedded surfaces in quasi-fuchsian manifolds
Authors: Olivier Glorieux
Subjects: Differential Geometry (math.DG)
[152]  arXiv:1511.02000 (replaced) [pdf, ps, other]
Title: Integrable mappings and the notion of anticonfinement
Subjects: Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
[153]  arXiv:1512.02155 (replaced) [pdf, ps, other]
Title: Limit theorems for Markovian Hawkes processes with a large initial intensity
Subjects: Probability (math.PR)
[154]  arXiv:1602.00878 (replaced) [pdf, ps, other]
Title: On Properties of the Support of Capacity-Achieving Distributions for Additive Noise Channel Models with Input Cost Constraints
Comments: Accepted for publication in the IEEE Transactions on Information Theory with minor modifications on the current version
Subjects: Information Theory (cs.IT)
[155]  arXiv:1602.03614 (replaced) [pdf, ps, other]
Title: The free-boundary Brakke flow
Authors: Nick Edelen
Comments: fixed some details, references; accepted to Crelle
Subjects: Differential Geometry (math.DG)
[156]  arXiv:1602.05819 (replaced) [pdf, ps, other]
Title: Constraint satisfaction problems for reducts of homogeneous graphs
Subjects: Logic in Computer Science (cs.LO); Computational Complexity (cs.CC); Logic (math.LO)
[157]  arXiv:1603.04937 (replaced) [pdf, other]
Title: Julia sets of Orthogonal polynomials
Subjects: Complex Variables (math.CV)
[158]  arXiv:1603.06544 (replaced) [pdf, ps, other]
Title: Nearest Points on Toric Varieties
Subjects: Algebraic Geometry (math.AG); Symbolic Computation (cs.SC); Optimization and Control (math.OC)
[159]  arXiv:1605.05159 (replaced) [pdf, ps, other]
Title: Restriction and induction of indecomposable modules over the Temperley-Lieb algebras
Subjects: Mathematical Physics (math-ph); Representation Theory (math.RT)
[160]  arXiv:1606.07370 (replaced) [pdf, other]
Title: Almost balanced biased graph representations of frame matroids
Subjects: Combinatorics (math.CO)
[161]  arXiv:1607.06921 (replaced) [pdf, other]
Title: Estimation and Prediction using generalized Wendland Covariance Functions under fixed domain asymptotics
Subjects: Statistics Theory (math.ST)
[162]  arXiv:1608.01986 (replaced) [pdf, other]
Title: Measurement uncertainty relations for discrete observables: Relative entropy formulation
Comments: 45 pages, 3 figures. The structure of the paper has been revised
Subjects: Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[163]  arXiv:1608.02336 (replaced) [pdf, ps, other]
Title: The Vlasov-Poisson equation in $\mathbb{R}^3$ with infinite charge and velocities
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
[164]  arXiv:1608.04813 (replaced) [pdf, other]
Title: Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions
Comments: Extended version of the work presented in FOGA 2017
Subjects: Optimization and Control (math.OC)
[165]  arXiv:1608.05999 (replaced) [pdf, other]
Title: Strongly dissipative surface diffeomorphisms
Subjects: Dynamical Systems (math.DS)
[166]  arXiv:1610.01116 (replaced) [pdf, ps, other]
Title: Forced Edges and Graph Structure
Authors: Brian Cloteaux
Subjects: Combinatorics (math.CO)
[167]  arXiv:1610.09238 (replaced) [pdf, ps, other]
Title: Strata of $k$-differentials
Comments: corrected and updated; final version, to appear in Algebraic Geometry
Subjects: Algebraic Geometry (math.AG); Dynamical Systems (math.DS); Geometric Topology (math.GT)
[168]  arXiv:1611.04323 (replaced) [pdf, ps, other]
Title: Central Limit Theorem and bootstrap procedure for Wasserstein's variations with application to structural relationships between distributions
Subjects: Statistics Theory (math.ST)
[169]  arXiv:1612.02542 (replaced) [pdf, other]
Title: Minimum Rates of Approximate Sufficient Statistics
Comments: To appear in the IEEE Transactions on Information Theory
Subjects: Information Theory (cs.IT); Statistics Theory (math.ST)
[170]  arXiv:1612.05152 (replaced) [pdf, ps, other]
Title: Properness of nilprogressions and the persistence of polynomial growth of given degree
Comments: 34 pages. Added Theorem 1.16 (a Bilu-type result for an arbitrary abelian group)
Subjects: Group Theory (math.GR); Combinatorics (math.CO)
[171]  arXiv:1701.00027 (replaced) [pdf, ps, other]
Title: Betti numbers and pseudoeffective cones in 2-Fano varieties
Subjects: Algebraic Geometry (math.AG)
[172]  arXiv:1701.00992 (replaced) [pdf, ps, other]
Title: Viscous displacement in porous media: the Muskat problem in 2D
Comments: 42 pages, to appear in Trans. Amer. Math. Soc
Subjects: Analysis of PDEs (math.AP)
[173]  arXiv:1701.01215 (replaced) [pdf, ps, other]
Title: On stationary Navier-Stokes flows around a rotating obstacle in two-dimensions
Subjects: Analysis of PDEs (math.AP)
[174]  arXiv:1701.04839 (replaced) [pdf, ps, other]
Title: A non-Archimedean Ohsawa-Takegoshi extension theorem
Comments: 20 pages. There was an error in the proof of Theorem 3.1 in the first version, which is corrected in this version after putting additional hypotheses on the ground field. To this end, Lemma 2.1 and the sequence of lemmas in section 3 have been added and/or modified
Subjects: Algebraic Geometry (math.AG)
[175]  arXiv:1701.05705 (replaced) [pdf, ps, other]
Title: Construction and nonexistence of strong external difference families
Comments: 24 pages. Minor modifications to version 2 to simplify two proofs
Subjects: Combinatorics (math.CO)
[176]  arXiv:1702.02114 (replaced) [pdf, ps, other]
Title: A remark on spaces of flat metrics with cone singularities of constant sign curvatures
Subjects: Differential Geometry (math.DG)
[177]  arXiv:1702.04458 (replaced) [pdf, other]
Title: Decentralized Baseband Processing for Massive MU-MIMO Systems
Comments: 16 pages; to appear in the IEEE Journal on Emerging and Selected Topics in Circuits and Systems (JETCAS)
Subjects: Information Theory (cs.IT)
[178]  arXiv:1702.04632 (replaced) [pdf, other]
Title: Squaring operations in the $RO(C_2)$-graded and real motivic Adams spectral sequences
Authors: Sean Tilson
Comments: Results extended from previous version to cover the real motivic Adams spectral sequence
Subjects: Algebraic Topology (math.AT)
[179]  arXiv:1702.08193 (replaced) [pdf, other]
Title: Modularisation of Sequent Calculi for Normal and Non-normal Modalities
Subjects: Logic in Computer Science (cs.LO); Logic (math.LO)
[180]  arXiv:1704.01361 (replaced) [pdf, other]
Title: Applications of position-based coding to classical communication over quantum channels
Comments: v3: 40 pages, v3 includes an inequality relating Petz-Renyi relative entropy to hypothesis testing relative entropy and a new simultaneous decoding achievable rate region in terms of conditional collision quantum entropies
Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT)
[181]  arXiv:1704.07458 (replaced) [pdf, other]
Title: A robust and efficient implementation of LOBPCG
Subjects: Numerical Analysis (math.NA)
[182]  arXiv:1705.03289 (replaced) [pdf, ps, other]
Title: Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales
Subjects: Numerical Analysis (math.NA)
[183]  arXiv:1705.04195 (replaced) [pdf, ps, other]
Title: Improved Bounds for the Greedy Strategy in Optimization Problems with Curvature
Comments: The manuscript was submitted to Discrete Applied Mathematics. arXiv admin note: text overlap with arXiv:1605.03628
Subjects: Optimization and Control (math.OC)
[184]  arXiv:1705.04930 (replaced) [pdf, ps, other]
Title: The homotopy category of flat functors
Subjects: Algebraic Geometry (math.AG)
[185]  arXiv:1705.06995 (replaced) [pdf, other]
Title: Nearly second-order asymptotic optimality of sequential change-point detection with one-sample updates
Subjects: Statistics Theory (math.ST); Learning (cs.LG)
[186]  arXiv:1705.08678 (replaced) [pdf, other]
Title: Automatic alignment for three-dimensional tomographic reconstruction
Subjects: Numerical Analysis (math.NA)
[187]  arXiv:1705.10580 (replaced) [pdf, other]
Title: Extremal rays in the Hermitian eigenvalue problem
Authors: Prakash Belkale
Comments: 25 pages, comments are welcome. In v2, small changes. Thoroughly revised in v3, introduction expanded, with changes in notation
Subjects: Algebraic Geometry (math.AG); Representation Theory (math.RT)
[188]  arXiv:1705.10607 (replaced) [pdf, ps, other]
Title: Automorphism groups of quandles and related groups
Subjects: Group Theory (math.GR); Geometric Topology (math.GT)
[189]  arXiv:1705.10676 (replaced) [pdf, ps, other]
Title: Statistical Mechanics of the Uniform Electron Gas
Comments: Final version to appear in J. Ec. polytech. Math
Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); Chemical Physics (physics.chem-ph)
[190]  arXiv:1706.00991 (replaced) [pdf, ps, other]
Title: Linear response and moderate deviations: hierarchical approach. II
Authors: Boris Tsirelson
Comments: 15 pages. Minor corrections in: (1.2); proof of 2.6 (first paragraph); proof of 2.4 (first paragraph); Lemma 3.16 (formulation); and proof of 3.6
Subjects: Probability (math.PR)
[191]  arXiv:1706.02452 (replaced) [pdf, other]
Title: An HMM--ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media
Subjects: Numerical Analysis (math.NA)
[192]  arXiv:1706.03727 (replaced) [pdf, ps, other]
Title: Elliptic equations with transmission and Wentzell boundary conditions and an application to steady water waves in the presence of wind
Authors: Hung Le
Subjects: Analysis of PDEs (math.AP)
[193]  arXiv:1706.04901 (replaced) [pdf, ps, other]
Title: Diagonal Multilinear Operators on Köthe Sequence Spaces
Subjects: Functional Analysis (math.FA)
[194]  arXiv:1706.06639 (replaced) [pdf, other]
Title: Transition of EMRIs through resonance: corrections to higher order in the on-resonance flux modification
Comments: 72 pages, 39 figures, 1 table. Presented at the poster session of the American Physical Society April Meeting 2017
Journal-ref: Journal of Mathematical Physics 58, 112501 (2017)
Subjects: General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
[195]  arXiv:1706.08391 (replaced) [pdf, other]
Title: Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions
Subjects: Analysis of PDEs (math.AP)
[196]  arXiv:1707.01122 (replaced) [pdf, ps, other]
Title: Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
Comments: Latex, 34 pages, no figure, Added Material, Discussions and References, Version to appear in Annals of Physics
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[197]  arXiv:1707.02969 (replaced) [pdf, other]
Title: Upper and Lower Bounds on the Speed of a One Dimensional Excited Random Walk
Subjects: Probability (math.PR)
[198]  arXiv:1707.04343 (replaced) [pdf, other]
Title: Stable processes, self-similarity and the unit ball
Subjects: Probability (math.PR)
[199]  arXiv:1707.05021 (replaced) [pdf, ps, other]
Title: Strong Local Nondeterminism of Spherical Fractional Brownian Motion
Subjects: Statistics Theory (math.ST)
[200]  arXiv:1707.06870 (replaced) [pdf, ps, other]
Title: New Wilson-like theorems arising from Dickson polynomials
Comments: 28 pages. Results of this article were presented at the Mathematical Congress of the Americas, MCA2017. Version 2 is a major revision, containing new theorems, simplified proofs of some lemmas, and corrections. Warning: numbering of theorems etc. is different between V1 and V2. Also, the definition of deterministic square root was changed
Subjects: Number Theory (math.NT)
[201]  arXiv:1707.07308 (replaced) [pdf, other]
Title: On Certain Degenerate Whittaker Models for Cuspidal Representations of $\mathrm{GL}_{k\cdot n}\left(\mathbb{F}_q\right)$
Subjects: Number Theory (math.NT); Combinatorics (math.CO); Representation Theory (math.RT)
[202]  arXiv:1707.07828 (replaced) [pdf, ps, other]
Title: On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
Subjects: Probability (math.PR)
[203]  arXiv:1707.09335 (replaced) [pdf, other]
Title: Macroscopic loops in the loop $O(n)$ model at Nienhuis' critical point
Comments: 26 pages, 9 figures; Theorem 2 now includes uniqueness of the Gibbs measure
Subjects: Probability (math.PR); Mathematical Physics (math-ph)
[204]  arXiv:1708.00602 (replaced) [pdf, other]
Title: Phase Retrieval From Binary Measurements
Subjects: Information Theory (cs.IT)
[205]  arXiv:1708.02308 (replaced) [pdf, ps, other]
Title: Non-Archimedean pseudodifferential operators and Feller Semigroups
Comments: The title was shortened. A technical mistake was corrected
Subjects: Probability (math.PR)
[206]  arXiv:1708.06620 (replaced) [pdf, ps, other]
Title: Integration of Modules: Exponentials and Stability
Comments: Version 2: Some changes in terminology. Examples of over-restricted modules are added. Version 3: Mistakes in tables are corrected
Subjects: Representation Theory (math.RT); Group Theory (math.GR); Rings and Algebras (math.RA)
[207]  arXiv:1708.07896 (replaced) [pdf, ps, other]
Title: Bounds of the rank of the Mordell-Weil group of jacobians of hyperelliptic curves
Subjects: Number Theory (math.NT)
[208]  arXiv:1708.08109 (replaced) [pdf, ps, other]
Title: On the notions of energy tensors in tetrad-affine gravity
Authors: Daniel Canarutto
Comments: 7 pages, accepted version to appear on Gravitation & Cosmology
Subjects: General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
[209]  arXiv:1708.09822 (replaced) [src]
Title: The Structure of Hopf Algebras Acting on Galois Extensions with Dihedral Groups
Comments: 22 pages; incorrect example (Example 5)
Subjects: Number Theory (math.NT)
[210]  arXiv:1709.02351 (replaced) [pdf, other]
Title: Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator
Subjects: Numerical Analysis (math.NA)
[211]  arXiv:1709.02979 (replaced) [pdf, ps, other]
Title: Clusters of Integers with Equal Total Stopping Times in the 3x + 1 Problem
Subjects: Number Theory (math.NT)
[212]  arXiv:1709.05287 (replaced) [pdf, other]
Title: Sampling of probability measures in the convex order and approximation of Martingale Optimal Transport problems
Subjects: Probability (math.PR); Computational Finance (q-fin.CP)
[213]  arXiv:1710.00357 (replaced) [pdf, ps, other]
Title: A New Property of Random Regular Bipartite Graphs
Authors: Paul Federbush
Comments: 9 pages, improved result to include all k &lt;10, some changes in Section 9
Subjects: Combinatorics (math.CO); Mathematical Physics (math-ph)
[214]  arXiv:1710.00528 (replaced) [pdf, ps, other]
Title: Plethysm and fast matrix multiplication
Authors: Tim Seynnaeve
Subjects: Representation Theory (math.RT); Computational Complexity (cs.CC)
[215]  arXiv:1710.02021 (replaced) [pdf, ps, other]
Title: Stable arithmetic regularity in the finite-field model
Authors: C. Terry, J. Wolf
Subjects: Logic (math.LO); Combinatorics (math.CO)
[216]  arXiv:1710.02307 (replaced) [pdf, other]
Title: A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media
Subjects: Numerical Analysis (math.NA)
[217]  arXiv:1710.02663 (replaced) [pdf, other]
Title: A mixed finite element method for a sixth order elliptic problem
Subjects: Numerical Analysis (math.NA)
[218]  arXiv:1710.06022 (replaced) [pdf, ps, other]
Title: Global exact controllability of the bilinear Schroedinger potential type models on quantum graphs
Authors: Alessandro Duca
Subjects: Optimization and Control (math.OC)
[219]  arXiv:1710.06030 (replaced) [pdf, other]
Title: Linear Regression with Sparsely Permuted Data
Subjects: Statistics Theory (math.ST); Methodology (stat.ME); Machine Learning (stat.ML)
[220]  arXiv:1710.06775 (replaced) [pdf, other]
Title: Crystalline Evolutions in Chessboard-like Microstructures
Comments: 17 pages, 10 figures. arXiv admin note: text overlap with arXiv:1707.03342
Subjects: Analysis of PDEs (math.AP)
[221]  arXiv:1710.06887 (replaced) [pdf, ps, other]
Title: Finite torsors over strongly $F$-regular singularities
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
[222]  arXiv:1710.07534 (replaced) [pdf, other]
Title: New hyperbolic 4-manifolds of low volume
Comments: 21 pages, 7 figures, proofs of the main theorems are now in a separate section. Added the Coxeter diagrams of the commensurability classes of the manifolds. New and better proof of Lemma 2.2
Subjects: Geometric Topology (math.GT)
[223]  arXiv:1710.07676 (replaced) [pdf, ps, other]
Title: On the two dimensional Radon transform with data on an arc
Subjects: Analysis of PDEs (math.AP)
[224]  arXiv:1710.08063 (replaced) [pdf, other]
Title: Cluster algebras and Jones polynomials
Comments: 35 pages, 12 Figures, v2 minor changes
Subjects: Geometric Topology (math.GT); Combinatorics (math.CO); Rings and Algebras (math.RA)
[225]  arXiv:1710.08743 (replaced) [pdf, ps, other]
Title: Quantum Mechanics on Periodic and Non-Periodic Lattices and Almost Unitary Schwinger Operators
Subjects: Mathematical Physics (math-ph)
[226]  arXiv:1710.10040 (replaced) [pdf, ps, other]
Title: Contact real hypersurfaces in the complex hyperbolic quadric
Comments: Extensive revision of the first version. The Introduction has been rewritten completely, in particular including a reference to an earlier proof of the classification. Section 2 has been rewritten to replace the incorrect model of the complex hyperbolic quadric from v1 with a correct one. Sections 4 and 5 have also been revised to make the arguments clearer and easier to understand. 24 pages
Subjects: Differential Geometry (math.DG)
[227]  arXiv:1710.10148 (replaced) [pdf, ps, other]
Title: The Schrödinger Formalism of Electromagnetism and Other Classical Waves --- How to Make Quantum-Wave Analogies Rigorous
Comments: 58 pages, updated version incorporates suggestions from the community
Subjects: Optics (physics.optics); Mathematical Physics (math-ph)
[228]  arXiv:1710.10156 (replaced) [pdf, ps, other]
Title: Sums of arctangents and sums of products of arctangents
Subjects: Number Theory (math.NT)
[229]  arXiv:1710.10597 (replaced) [pdf, ps, other]
Title: A Study of Generalized Covariant Hamilton Systems With Connection On Manifold
Authors: Gen Wang, Daoyi Peng
Subjects: Dynamical Systems (math.DS)
[230]  arXiv:1710.11298 (replaced) [pdf, ps, other]
Title: Effective Tensor Sketching via Sparsification
Authors: Dong Xia, Ming Yuan
Subjects: Methodology (stat.ME); Information Theory (cs.IT); Numerical Analysis (cs.NA); Machine Learning (stat.ML)
[231]  arXiv:1711.01240 (replaced) [pdf, ps, other]
Title: Simple stably projectionless C*-algebras with generalized tracial rank one
Comments: This is a part of the merging of arXiv:1611.0440 and arXiv:1611.05159
Subjects: Operator Algebras (math.OA)
[232]  arXiv:1711.01938 (replaced) [pdf, other]
Title: Single-Carrier Modulation versus OFDM for Millimeter-Wave Wireless MIMO
Comments: accepted for publication on IEEE Transactions on Communications
Subjects: Information Theory (cs.IT); Networking and Internet Architecture (cs.NI)
[233]  arXiv:1711.02424 (replaced) [pdf, other]
Title: Hybrid stochastic kinetic description of two-dimensional traffic dynamics
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP); Adaptation and Self-Organizing Systems (nlin.AO)
[234]  arXiv:1711.02453 (replaced) [pdf, other]
Title: Bounded operators on mixed norm Lebesgue spaces
Subjects: Functional Analysis (math.FA); Classical Analysis and ODEs (math.CA)
[235]  arXiv:1711.02755 (replaced) [pdf, ps, other]
Title: Lévy-Khintchine decompositions for generating functionals on universal CQG-algebras
Subjects: Quantum Algebra (math.QA)
[236]  arXiv:1711.03520 (replaced) [pdf, ps, other]
Title: Projected and near-projected embeddings
Comments: 19 pages. v2: improved exposition
Subjects: Geometric Topology (math.GT)
[237]  arXiv:1711.04242 (replaced) [pdf, other]
Title: Higher dimensional electrical circuits and the matroid dual of a nonplanar graph
Subjects: Combinatorics (math.CO)
[238]  arXiv:1711.04287 (replaced) [pdf, other]
Title: Analysis and Synthesis of MIMO Multi-Agent Systems Using Network Optimization
Subjects: Optimization and Control (math.OC)
[239]  arXiv:1711.04337 (replaced) [pdf, ps, other]
Title: An inverse theorem for an inequality of Kneser
Authors: Terence Tao
Comments: 25 pages, no figures. Submitted, Proceedings of the Steklov Institute of Mathematics. Some references (and the title) corrected
Subjects: Combinatorics (math.CO)
[240]  arXiv:1711.04363 (replaced) [pdf, ps, other]
Title: On k-Total Dominating Graphs
Comments: 20 pages plus appendix, one figure
Subjects: Combinatorics (math.CO)
[241]  arXiv:1711.04535 (replaced) [pdf, ps, other]
Title: Minimal threefolds which are birationally fibred by (1,2)-surfaces
Authors: Meng Chen, Yong Hu
Comments: 11 pages, incorrect argument in Example 3.1 and Example 3.2 are revised
Subjects: Algebraic Geometry (math.AG)
[242]  arXiv:1711.04572 (replaced) [pdf, ps, other]
Title: Haar systems, KMS states on von Neumann algebras and $C^*$-algebras on dynamically defined groupoids and Noncommutative Integration
Subjects: Dynamical Systems (math.DS); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Functional Analysis (math.FA); Operator Algebras (math.OA)
[243]  arXiv:1711.04786 (replaced) [pdf, ps, other]
Title: Strongly γ-deformed N=4 SYM as an integrable CFT
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[244]  arXiv:1711.05147 (replaced) [pdf, other]
Title: Restoration by Compression
Subjects: Information Theory (cs.IT)
[245]  arXiv:1711.05211 (replaced) [pdf, ps, other]
Title: Invariant Hermitean Metric Generated By Reproducing Kernel Hilbert Spaces
Subjects: Functional Analysis (math.FA); Complex Variables (math.CV)
[246]  arXiv:1711.05222 (replaced) [pdf, ps, other]
Title: Continuity and Holomorphicity of Symbols of Weighted Composition Operators
Subjects: Functional Analysis (math.FA); Complex Variables (math.CV); General Topology (math.GN)
[247]  arXiv:1711.05485 (replaced) [pdf, ps, other]
Title: Prüfer intersection of valuation domains of a field of rational functions