# Mathematics

## New submissions

[ total of 249 entries: 1-249 ]
[ showing up to 2000 entries per page: fewer | more ]

### New submissions for Fri, 23 Feb 18

[1]
Title: Pointwise a posteriori error bounds for blow-up in the semilinear heat equation
Subjects: Numerical Analysis (math.NA)

This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for the semilinear heat equation with a general local Lipschitz reaction term whose solution may blow-up in finite time. More specifically, conditional a posteriori error bounds are derived in the $L^{\infty}L^{\infty}$ norm for a first order in time, implicit-explicit (IMEX), conforming finite element method in space discretization of the problem. Numerical experiments applied to both blow-up and non blow-up cases highlight the generality of our approach and complement the theoretical results.

[2]
Title: Decompositions of Bernstein-Sato polynomials and slices
Comments: 31 pages. arXiv admin note: text overlap with arXiv:1310.3691
Subjects: Representation Theory (math.RT)

Let $G$ be a linearly reductive group acting on a vector space $V$, and $f$ a (semi-)invariant polynomial on $V$. In this paper we study systematically decompositions of the Bernstein-Sato polynomial of $f$ in parallel with some representation-theoretic properties of the action of $G$ on $V$. We provide a technique based on a multiplicity one property, that we use to compute the Bernstein-Sato polynomials of several classical invariants in an elementary fashion. Furthermore, we derive a "slice method" which shows that the decomposition of $V$ as a representation of $G$ can induce a decomposition of the Bernstein-Sato polynomial of $f$ into a product of two Bernstein-Sato polynomials - that of an ideal and that of a semi-invariant of smaller degree. Using the slice method, we compute Bernstein-Sato polynomials for a large class of semi-invariants of quivers.

[3]
Title: A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces
Subjects: Classical Analysis and ODEs (math.CA)

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space $%H_{p}$ to the Lebesgue space $L_{p}$ for all $0<p\leq 1.$ We also prove that the result is sharp in a particular sense.

[4]
Title: The fundamental Laplacian eigenvalue of the ellipse with Dirichlet boundary conditions
Comments: 6 pages
Subjects: Numerical Analysis (math.NA)

In this project, I examine the lowest Dirichlet eigenvalue of the Laplacian within the ellipse as a function of eccentricity. Two existing analytic expansions of the eigenvalue are extended: Close to the circle (eccentricity near zero) three terms are added to the Maclaurin series; and near the infinite strip (eccentricity near unity) four terms are added to the asymptotic expansion. In the past, other methods, such as boundary variation techniques, have been used to work on this problem, but I use a different approach -- which not only offers independent confirmation of existing results, but extends them. My starting point is a high precision computation of the eigenvalue for many values of eccentricity (from zero to unity). These data are then fit to polynomials in appropriate parameters yielding high-precision coefficients that are fed into an LLL integer-relation algorithm with forms guided by prior results.

[5]
Title: The Lattice of subracks is atomic
Comments: 15 pages, 10 figures
Subjects: Combinatorics (math.CO); Commutative Algebra (math.AC)

A rack is a set together with a self-distributive bijective binary operation. In this paper, we give a positive answer to a question due to Heckenberger, Shareshian and Welker. Indeed, we prove that the lattice of subracks of a rack is atomic. Further, by using the atoms, we associate certain quandles to racks. We also show that the lattice of subracks of a rack is isomorphic to the lattice of subracks of a quandle. Moreover, we show that the lattice of subracks of a rack is distributive if and only if its corresponding quandle is trivial. Finally, applying our corresponding quandles, we provide a coloring of certain knot diagrams.

[6]
Title: Counting Motifs with Graph Sampling
Subjects: Statistics Theory (math.ST); Discrete Mathematics (cs.DM); Machine Learning (stat.ML)

Applied researchers often construct a network from a random sample of nodes in order to infer properties of the parent network. Two of the most widely used sampling schemes are subgraph sampling, where we sample each vertex independently with probability $p$ and observe the subgraph induced by the sampled vertices, and neighborhood sampling, where we additionally observe the edges between the sampled vertices and their neighbors.
In this paper, we study the problem of estimating the number of motifs as induced subgraphs under both models from a statistical perspective. We show that: for any connected $h$ on $k$ vertices, to estimate $s=\mathsf{s}(h,G)$, the number of copies of $h$ in the parent graph $G$ of maximum degree $d$, with a multiplicative error of $\epsilon$, (a) For subgraph sampling, the optimal sampling ratio $p$ is $\Theta_{k}(\max\{ (s\epsilon^2)^{-\frac{1}{k}}, \; \frac{d^{k-1}}{s\epsilon^{2}} \})$, achieved by Horvitz-Thompson type of estimators. (b) For neighborhood sampling, we propose a family of estimators, encompassing and outperforming the Horvitz-Thompson estimator and achieving the sampling ratio $O_{k}(\min\{ (\frac{d}{s\epsilon^2})^{\frac{1}{k-1}}, \; \sqrt{\frac{d^{k-2}}{s\epsilon^2}}\})$. This is shown to be optimal for all motifs with at most $4$ vertices and cliques of all sizes.
The matching minimax lower bounds are established using certain algebraic properties of subgraph counts. These results quantify how much more informative neighborhood sampling is than subgraph sampling, as empirically verified by experiments on both synthetic and real-world data. We also address the issue of adaptation to the unknown maximum degree, and study specific problems for parent graphs with additional structures, e.g., trees or planar graphs.

[7]
Title: Quaternionic hyperbolic lattices of minimal covolume
Comments: 21 pages (11pt)
Subjects: Metric Geometry (math.MG); Geometric Topology (math.GT)

For any n>1 we determine the uniform and nonuniform lattices of the smallest covolume in the Lie group Sp(n,1). We explicitly describe them in terms of the ring of Hurwitz integers in the nonuniform case with n even, respectively, of the icosian ring in the uniform case for all n>1.

[8]
Title: On the polar Orlicz-Minkowski problems and the $p$-capacitary Orlicz-Petty bodies
Comments: This paper has been accepted by Indiana University Mathematics Journal
Subjects: Metric Geometry (math.MG)

In this paper, we propose and study the polar Orlicz-Minkowski problems: under what conditions on a nonzero finite measure $\mu$ and a continuous function $\varphi:(0,\infty)\rightarrow(0,\infty)$, there exists a convex body $K\in\mathcal{K}_0$ such that $K$ is an optimizer of the following optimization problems: \begin{equation*} \inf/\sup \bigg\{\int_{S^{n-1}}\varphi\big( h_L \big) \,d \mu: L \in \mathcal{K}_{0} \ \text{and}\ |L^\circ|=\omega_{n}\bigg\}. \end{equation*} The solvability of the polar Orlicz-Minkowski problems is discussed under different conditions. In particular, under certain conditions on $\varphi,$ the existence of a solution is proved for a nonzero finite measure $\mu$ on $S^{n-1}$ which is not concentrated on any hemisphere of $S^{n-1}.$ Another part of this paper deals with the $p$-capacitary Orlicz-Petty bodies. In particular, the existence of the $p$-capacitary Orlicz-Petty bodies is established and the continuity of the $p$-capacitary Orlicz-Petty bodies is proved.

[9]
Title: Proving ergodicity via divergence of ergodic sums
Authors: Zemer Kosloff
Comments: 22 pages, 0 figures
Subjects: Dynamical Systems (math.DS); Probability (math.PR)

A classical fact in ergodic theory is that ergodicity is equivalent to almost everywhere divergence of ergodic sums of all nonnegative integrable functions which are not identically zero. We show two methods, one in the measure preserving case and one in the nonsingular case, which enable one to prove this criteria by checking it on a dense collection of functions and then extending it to all nonnegative functions. The first method is then used in a new proof of a folklore criterion for ergodicity of Poisson suspensions which does not make any reference to Fock spaces. The second method which involves the double tail relation is used to show that a large class of nonsingular Bernoulli and inhomogeneous Markov shifts are ergodic if and only if they are conservative. In the last section we discuss an extension of the Bernoulli shift result to other countable groups including $\mathbb{Z}^{d},\ d\geq 2$ and discrete Heisenberg groups.

[10]
Title: On uniqueness of weak solutions of the incompressible Navier-Stokes equations in 3-dimensional case
Comments: 28 pages
Subjects: Analysis of PDEs (math.AP)

In this article we study the uniqueness of the weak solution of the incompressible Navier-Stokes Equation in the 3-dimensional case with use of different approach. Here the uniqueness of the obtained by Leray of weak solution is proved in the case, when datums from spaces that are densely contained into spaces of datums for which was proved the existence of the weak solution. Moreover we investigate the solvability and uniqueness of the weak solutions of problems associated with investigation of the main problem.28 p

[11]
Title: Partial Franel sums
Authors: Rogelio Tomas
Comments: 12 pages
Subjects: Number Theory (math.NT)

Analytical expressions are derived for the position of Farey fractions in the Farey sequence $F_N$ of order $N$ for a particular choice of $N$. The asymptotic behaviour is derived obtaining a lower error bound than in previous results when these fractions are in the vicinity of $0/1$, $1/2$ or $1/1$. Franel's famous formulation of Riemann's hypothesis uses the summation of distances between Farey fractions and evenly spaced points in $[0,1]$. A partial Franel sum is defined here as a summation of these distances over a subset of fractions in $F_N$. The partial Franel sum in the range $[0, i/N]$, with $N={\rm lcm}([2,i])$ is shown here to behave as $O(\log N)$. Other partial Franel sums are also explored.

[12]
Title: Optimal Multi-User Scheduling of Buffer-Aided Relay Systems
Comments: Accepted by IEEE ICC 2018, Kansas City,USA
Subjects: Information Theory (cs.IT)

Multi-User scheduling is a challenging problem under the relaying scenarios. Traditional schemes, which are based on the instantaneous signal-to-interference-plus-noises ratios (SINRs), cannot solve the inherent disparities of the qualities between different links. Hence, the system performance is always limited by the weaker links. In this paper, from the whole system throughput view, we propose an optimal multi-user scheduling scheme for the multi-user full-duplex (FD) buffer aided relay systems. We first formulate the throughput maximization problem. Then, according to the characteristics of the Karush-Kuhn-Tucker conditions, we obtain the optimal decision functions and the optimal weighted factors of different links of the proposed scheme. Simulation results show that the proposed scheme not only solves the disparities of the qualities between $S_i$-$R$ and $R$-$D_i$ links, but also that between different $S_{i}$-$R$ or $D_{i}$-$R$ links, which can be used as guidance in the design of the practical systems.

[13]
Title: A New Hybrid Half-Duplex/Full-Duplex Relaying System with Antenna Diversity
Comments: 13 pages, 7 figures
Subjects: Information Theory (cs.IT)

The hybrid half-duplex/full-duplex (HD/FD) relaying scheme is an effective paradigm to overcome the negative effects of the self-interference incurred by the full-duplex (FD) mode. However, traditional hybrid HD/FD scheme does not consider the diversity gain incurred by the multiple antennas of the FD node when the system works in the HD mode, leading to the waste of the system resources. In this paper, we propose a new hybrid HD/FD relaying scheme, which utilizes both the antennas of the FD relay node for reception and transmission when the system works in the HD mode. With multiple antennas, the maximum ratio combining/maximum ratio transmission is adopted to process the signals at the relay node. Based on this scheme, we derive the exact closed-form system outage probability and conduct various numerical simulations. The results show that the proposed scheme remarkably improves the system outage performance over the traditional scheme, and demonstrate that the proposed scheme can more effectively alleviate the adverse effects of the residual self-interference.

[14]
Title: Universal Quadratic Forms and Indecomposables over Biquadratic Fields
Comments: 14 pages, comments are welcome
Subjects: Number Theory (math.NT)

The aim of this article is to study (additively) indecomposable algebraic integers $\mathcal O_K$ of biquadratic number fields $K$ and universal totally positive quadratic forms with coefficients in $\mathcal O_K$. There are given sufficient conditions for an indecomposable element of a quadratic subfield to remain indecomposable in the biquadratic number field $K$. Furthermore, estimates are proven which enable algorithmization of the method of escalation over $K$. These are used to prove, over two particular biquadratic number fields $\mathbb{Q}(\sqrt{2}, \sqrt{3})$ and $\mathbb{Q}(\sqrt{6}, \sqrt{19})$, a lower bound on the number of variables of a universal quadratic forms, verifying Kitaoka's conjecture.

[15]
Title: Permanental processes with kernels that are not equivalent to a symmetric matrix
Subjects: Probability (math.PR)

Kernels of $\alpha$-permanental processes of the form
$v(x,y)=u(x,y)+f(y),\qquad x,y\in S,$
in which $u(x,y)$ is symmetric, and $f$ is an excessive function for the Borel right process with potential densities $u(x,y)$, are considered. Conditions are given that determine whether $\{v(x,y);x,y\in S\}$ is symmetrizable or asymptotically symmetrizable.

[16]
Title: An upper bound for the representation dimension of group algebras for groups with an elementary abelian Sylow $p$-subgroup
Authors: Simon F. Peacock
Subjects: Representation Theory (math.RT)

Linckelmann showed in 2011 that a group algebra is separably equivalent to the group algebra of its Sylow p-subgroups. In this article we use this relationship, together with Mackey decomposition, to demonstrate that a group algebra of a group with an elementary abelian Sylow $p$-subgroup $P$, has representation dimension at most $|P|$.

[17]
Title: A new extension of Hurwitz-Lerch Zeta function
Comments: 10 pages
Subjects: Classical Analysis and ODEs (math.CA)

The main objective of this paper is to introduce a new extension of Hurwitz-Lerch Zeta function in terms of extended beta function. We then investigate its important properties such as integral representations, differential formulas, Mellin transform and certain generating relations. Also, some important special cases of the main results are pointed out.

[18]
Title: Phase transition for infinite systems of spiking neurons
Subjects: Probability (math.PR)

We prove the existence of a phase transition for a stochastic model of interacting neurons. The spiking activity of each neuron is represented by a point process having rate $1$ whenever its membrane potential is larger than a threshold value. This membrane potential evolves in time and integrates the spikes of all {\it presynaptic neurons} since the last spiking time of the neuron. When a neuron spikes, its membrane potential is reset to $0$ and simultaneously, a constant value is added to the membrane potentials of its postsynaptic neurons. Moreover, each neuron is exposed to a leakage effect leading to an abrupt loss of potential occurring at random times driven by an independent Poisson point process of rate $\gamma > 0 .$ For this process we prove the existence of a value $\gamma_c$ such that the system has one or two extremal invariant measures according to whether $\gamma > \gamma_c$ or not.

[19]
Title: Open manifolds with non-homeomorphic positively curved souls
Comments: 19 pages
Subjects: Differential Geometry (math.DG)

We extend two known existence results to simply connected manifolds with positive sectional curvature: we show that there exist pairs of simply connected positively-curved manifolds that are tangentially homotopy equivalent but not homeomorphic, and we deduce that an open manifold may admit a pair of non-homeomorphic simply connected and positively-curved souls. Examples of such pairs are given by explicit pairs of Eschenburg spaces. To deduce the second statement from the first, we extend our earlier work on the stable converse soul question and show that it has a positive answer for a class of spaces that includes all Eschenburg spaces.

[20]
Title: Equivelar toroids with few flag-orbits
Subjects: Combinatorics (math.CO)

An $(n+1)$-toroid is a quotient of a tessellation of the $n$-dimensional Euclidean space with a lattice group. Toroids are generalizations of maps in the torus on higher dimensions and also provide examples of abstract polytopes. Equivelar toroids are those that are induced by regular tessellations. In this paper we present a classification of equivelar $(n+1)$-toroids with at most $n$ flag-orbits; in particular, we discuss a classification of $2$-orbit toroids of arbitrary dimension.

[21]
Title: Concise Complexity Analyses for Trust-Region Methods
Comments: 10 pages
Subjects: Optimization and Control (math.OC)

Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain control over the choice of trust region radius after any successful iteration. The analyses highlight the essential algorithm components required to obtain certain complexity bounds. In addition, a new update strategy for the trust region radius is proposed that offers a second-order complexity bound.

[22]
Title: Fast Ewald summation for Green's functions of Stokes flow in a half-space
Comments: Submitted to Research in the Mathematical Sciences
Subjects: Numerical Analysis (math.NA)

Recently, Gimbutas et al derived an elegant representation for the Green's functions of Stokes flow in a half-space. We present a fast summation method for sums involving these half-space Green's functions (stokeslets, stresslets and rotlets) that consolidates and builds on the work by Klinteberg et al for the corresponding free-space Green's functions. The fast method is based on two main ingredients: The Ewald decomposition and subsequent use of FFTs. The Ewald decomposition recasts the sum into a sum of two exponentially decaying series: one in real-space (short-range interactions) and one in Fourier-space (long-range interactions) with the convergence of each series controlled by a common parameter. The evaluation of short-range interactions is accelerated by restricting computations to neighbours within a specified distance, while the use of FFTs accelerates the computations in Fourier-space thus accelerating the overall sum. We demonstrate that while the method incurs extra costs for the half-space in comparison to the free-space evaluation, greater computational savings is also achieved when compared to their respective direct sums.

[23]
Title: Data Privacy for a $ρ$-Recoverable Function
Subjects: Information Theory (cs.IT)

A user's data is represented by a finite-valued random variable. Given a function of the data, a querier is required to recover, with at least a prescribed probability, the value of the function based on a query response provided by the user. The user devises the query response, subject to the recoverability requirement, so as to maximize privacy of the data from the querier. Privacy is measured by the probability of error incurred by the querier in estimating the data from the query response. We analyze single and multiple independent query responses, with each response satisfying the recoverability requirement, that provide maximum privacy to the user. Achievability schemes with explicit randomization mechanisms for query responses are given and their privacy compared with converse upper bounds.

[24]
Title: On the Super Mumford Form in the Presence of Ramond and Neveu-Schwarz Punctures
Authors: Daniel Diroff
Subjects: Mathematical Physics (math-ph)

We generalize a known result to give an expression for the super Mumford form $\mu$ on the moduli spaces of super Riemann surfaces with Ramond and Neveu-Schwarz punctures in the limit where the number of punctures is large compared to the genus. In the case of Neveu-Schwarz punctures we consider the super Mumford form over the component of the moduli space corresponding to an odd spin structure. The super Mumford form $\mu$ can be used to create a measure whose integral computes scattering amplitudes of superstring theory. We express $\mu$ in terms of local bases of $H^0(\Sigma, \omega^j)$ for $\omega$ the Berezinian line bundle of a family of super Riemann surfaces.

[25]
Title: Regularity of biased 1D random walks in random environment
Comments: 27 pages, 1 figure
Subjects: Probability (math.PR)

We study the asymptotic properties of nearest-neighbor random walks in 1d random environment under the influence of an external field of intensity $\lambda\in\mathbb{R}$. For shift-invariant environments, we show that the limiting velocity $v(\lambda)$ is always increasing and that it is everywhere analytic except at most in two points $\lambda_-$ and $\lambda_+$. When $\lambda_-$ and $\lambda_+$ are distinct, $v(\lambda)$ might fail to be continuous. We refine the assumptions in \cite{Z} for having a recentered CLT with diffusivity $\sigma^2(\lambda)$ and give explicit conditions for $\sigma^2(\lambda)$ to be analytic. For the conductance model we show that, in contrast with the deterministic case, $\sigma^2$ is not always decreasing in $\lambda$ and that it is not differentiable at $\lambda=0$. For this model, we also prove the Einstein Relation extending the result of \cite{LD16}.

[26]
Title: Reflection Positivity Then and Now
Authors: Arthur Jaffe
Comments: 12 pages
Subjects: History and Overview (math.HO); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

We review the discovery of reflection positivity. We also explain a new geometric approach and proof of the reflection positivity property.

[27]
Title: A New Design of Binary MDS Array Codes with Asymptotically Weak-Optimal Repair
Subjects: Information Theory (cs.IT)

Binary maximum distance separable (MDS) array codes are a special class of erasure codes for distributed storage that not only provide fault tolerance with minimum storage redundancy but also achieve low computational complexity. They are constructed by encoding $k$ information columns into $r$ parity columns, in which each element in a column is a bit, such that any $k$ out of the $k+r$ columns suffice to recover all information bits. In addition to providing fault tolerance, it is critical to improve repair performance in practical applications. If one column of an MDS code is failed, it is known that we need to download at least $1/(d-k+1)$ fraction of the data stored in each of $d$ healthy columns. If this lower bound is achieved for the repair of the failure column from accessing arbitrary $d$ healthy columns, we say that the MDS code has optimal repair. However, if such lower bound is only achieved by $d$ specific healthy columns, then we say the MDS code has weak-optimal repair. Existing binary MDS array codes that achieve high data rate (i.e., $k/(k+r)>1/2$) and optimal repair of information column only support double fault tolerance (i.e., $r=2$), which is insufficient for failure-prone distributed storage environments in practice. This paper fills the void by proposing two explicit constructions of binary MDS array codes with more parity columns (i.e., $r\geq 3$) that achieve asymptotically weak-optimal repair, where $k+1\leq d\leq k+\lfloor(r-1)/2\rfloor$. Codes in the first construction have odd number of parity columns and asymptotically weak-optimal repair for any one information failure, while codes in the second construction have even number of parity columns and asymptotically weak-optimal repair for any one column failure.

[28]
Title: Symmetry of maximals for fractional ideals of curves
Authors: Delphine Pol
Comments: 12 pages, comments are welcome
Subjects: Algebraic Geometry (math.AG)

The purpose of this paper is to extend the symmetry of maximals of the ring of a germ of reducible plane curve proved by Delgado to a relation between the relative maximals of a fractional ideal and the absolute maximals of its dual for any admissible ring. In particular, it includes the case of germs of reduced reducible curve of any codimension. We then apply this symmetry to characterize the elements in the set of values of a fractional ideal from some of its projections and the irreducible absolute maximals of the dual ideal.

[29]
Title: On the implementation of a primal-dual algorithm for second order time-dependent mean field games with local couplings
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)

We study a numerical approximation of a time-dependent Mean Field Game (MFG) system with local couplings. The discretization we consider stems from a variational approach described in [Briceno-Arias, Kalise, and Silva, SIAM J. Control Optim., 2017] for the stationary problem and leads to the finite difference scheme introduced by Achdou and Capuzzo-Dolcetta in [SIAM J. Numer. Anal., 48(3):1136-1162, 2010]. In order to solve the finite dimensional variational problems, in [Briceno-Arias, Kalise, and Silva, SIAM J. Control Optim., 2017] the authors implement the primal-dual algorithm introduced by Chambolle and Pock in [J. Math. Imaging Vision, 40(1):120-145, 2011], whose core consists in iteratively solving linear systems and applying a proximity operator. We apply that method to time-dependent MFG and, for large viscosity parameters, we improve the linear system solution by replacing the direct approach used in [Briceno-Arias, Kalise, and Silva, SIAM J. Control Optim., 2017] by suitable preconditioned iterative algorithms.

[30]
Title: Safety-Aware Optimal Control of Stochastic Systems Using Conditional Value-at-Risk
Comments: Extended version of a 2018 ACC paper
Subjects: Optimization and Control (math.OC); Systems and Control (cs.SY)

In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set distance to formulate a safety risk-constrained optimal control problem. Our reformulation method using an extremal representation of the safety risk measure provides a computationally tractable dynamic programming solution. A useful byproduct of the proposed solution is the notion of a risk-constrained safe set, which is a new stochastic safety verification tool. We also establish useful connections between the risk-constrained safe sets and the popular probabilistic safe sets. The tradeoff between the risk tolerance and the mean performance of our controller is examined through an inventory control problem.

[31]
Title: Class groups of imaginary quadratic fields of $3$-rank at least $2$
Comments: 5 Pages
Subjects: Number Theory (math.NT)

We produce an infinite family of imaginary quadratic fields whose ideal class groups have $3$-rank at least $2$.

[32]
Title: Exploiting Inter-User Interference for Secure Massive Non-Orthogonal Multiple Access
Journal-ref: IEEE Journal on Seleted Areas in Communications, 2018
Subjects: Information Theory (cs.IT)

This paper considers the security issue of the fifth-generation (5G) wireless networks with massive connections, where multiple eavesdroppers aim to intercept the confidential messages through active eavesdropping. To realize secure massive access, non-orthogonal channel estimation (NOCE) and non-orthogonal multiple access (NOMA) techniques are combined to enhance the signal quality at legitimate users, while the inter-user interference is harnessed to deliberately confuse the eavesdroppers even without exploiting artificial noise (AN). We first analyze the secrecy performance of the considered secure massive access system and derive a closed-form expression for the ergodic secrecy rate. In particular, we reveal the impact of some key system parameters on the ergodic secrecy rate via asymptotic analysis with respect to a large number of antennas and a high transmit power at the base station (BS). Then, to fully exploit the inter-user interference for security enhancement, we propose to optimize the transmit powers in the stages of channel estimation and multiple access. Finally, extensive simulation results validate the effectiveness of the proposed secure massive access scheme.

[33]
Title: Asynchronous stochastic approximations with asymptotically biased errors and deep multi-agent learning
Subjects: Optimization and Control (math.OC); Dynamical Systems (math.DS); Machine Learning (stat.ML)

Asynchronous stochastic approximations are an important class of model-free algorithms that are readily applicable to multi-agent reinforcement learning (RL) and distributed control applications. When the system size is large, the aforementioned algorithms are used in conjunction with function approximations. In this paper, we present a complete analysis, including stability (almost sure boundedness) and convergence, of asynchronous stochastic approximations with asymptotically bounded biased errors, under easily verifiable sufficient conditions. As an application, we analyze the Policy Gradient algorithms and the more general Value Iteration based algorithms with noise. These are popular reinforcement learning algorithms due to their simplicity and effectiveness. Specifically, we analyze the asynchronous approximate counterpart of policy gradient (A2PG) and value iteration (A2VI) schemes. It is shown that the stability of these algorithms remains unaffected when the approximation errors are guaranteed to be asymptotically bounded, although possibly biased. Regarding convergence of A2VI, it is shown to converge to a fixed point of the perturbed Bellman operator when balanced step-sizes are used. Further, a relationship between these fixed points and the approximation errors is established. A similar analysis for A2PG is also presented.

[34]
Title: Two theorems on distribution of Gaussian quadratic forms
Comments: Problems of Information Transmission, v. 53, no. 3, pp. 3--15, 2017
Subjects: Information Theory (cs.IT); Probability (math.PR)

New results on comparison of distributions of Gaussian quadratic forms are presented

[35]
Title: On detection of Gaussian stochastic sequences
Comments: Problems of Information Transmission, vol. 53, no. 4, pp. 47--66, 2017
Subjects: Information Theory (cs.IT)

The problem of minimax detection of Gaussian random signal vector in White Gaussian additive noise is considered. It is supposed that an unknown vector $\boldsymbol{\sigma}$ of the signal vector intensities belong to the given set ${\mathcal E}$. It is investigated when it is possible to replace the set ${\mathcal E}$ by a smaller set ${\mathcal E}_{0}$ without loss of quality (and, in particular, to replace it by a single point $\boldsymbol{\sigma}_{0}$).

[36]
Title: Exceptional Legendrian torus knots
Comments: 24 pages, 10 figures
Subjects: Symplectic Geometry (math.SG); Geometric Topology (math.GT)

We present classification results for exceptional Legendrian realisations of torus knots. These are the first results of that kind for non-trivial topological knot types. Enumeration results of Ding-Li-Zhang concerning tight contact structures on certain Seifert fibred manifolds with boundary allow us to place upper bounds on the number of tight contact structures on the complements of torus knots; the classification of exceptional realisations of these torus knots is then achieved by exhibiting sufficiently many realisations in terms of contact surgery diagrams. We also discuss a couple of general theorems about the existence of exceptional Legendrian knots.

[37]
Title: Densities and stability via factorization homology
Authors: Q.P. Ho
Subjects: Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Number Theory (math.NT)

Using factorization homology, we develop a uniform and conceptual approach for treating homological stability, homological densities, and arithmetic densities in algebraic geometry. This categorifies and generalizes the coincidences appearing in the work of Farb-Wolfson-Wood, and in fact, provides a conceptual understanding of these coincidences. Our computation of the stable homological densities also yields rational homotopy types which answer a question posed by Vakil-Wood. Our approach hinges on the study of homological stability of cohomological Chevalley complexes, which is of independent interest.

[38]
Title: The maximal abelian dimension of a Lie algebra, Rentschler's property and Milovanov's conjecture
Authors: Alfons I. Ooms
Comments: 49 pages
Subjects: Representation Theory (math.RT)

A finite dimensional Lie algebra L with magic number c(L) is said to satisfy Rentschler's property if it admits an abelian Lie subalgebra H of dimension at least c(L) - 1. We study the occurrence of this new property in various Lie algebras, such as nonsolvable, solvable, nilpotent, metabelian and filiform Lie algebras. Under some mild condition H gives rise to a complete Poisson commutative subalgebra of the symmetric algebra S(L). Using this, we show that Milovanov's conjecture holds for the filiform Lie algebras of type Ln, Qn, Rn, Wn and also for all filiform Lie algebras of dimension at most eight. For the latter the Poisson center of these Lie algebras is determined.

[39]
Title: Solutions to the affine quasi-Einstein equation for homogeneous surfaces
Comments: 5 figures
Subjects: Differential Geometry (math.DG)

We examine the space of solutions to the affine quasi--Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitions, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descriptions of these solution spaces. We use the dimension of the space of affine Killing vector fields to structure our discussion as this provides a convenient organizational framework.

[40]
Title: Well-posedness to the continuous coagulation processes with collision-induced multiple fragmentation
Subjects: Analysis of PDEs (math.AP)

An existence result on weak solutions to the continuous coagulation equation with collision-induced multiple fragmentation is established for certain classes of unbounded coagulation, collision and breakup kernels. In this model, a pair of particles can coagulate into a larger one if their confrontation is a completely inelastic collision; otherwise, one of them will split into many smaller particles due to a destructive collision. In the present work, both coagulation and fragmentation processes are considered to be intrinsically nonlinear. The breakup kernel may have a possibility to attain a singularity at the origin. The proof is based on the classical weak L^1 compactness method applied to suitably chosen approximating equations. In addition, we study the uniqueness of weak solutions under additional growth conditions on collision and breakup kernels which mainly relies on the integrability of higher moments. Finally, it is obtained that the unique weak solution is mass-conserving.

[41]
Title: The continuous coagulation and nonlinear multiple fragmentation equation
Subjects: Analysis of PDEs (math.AP)

The present paper deals with the existence and uniqueness of global classical solutions to the continuous coagulation and nonlinear multiple fragmentation equations for large classes of unbounded coagulation, collision and breakup kernels. In addition, it is shown that solutions are mass conserving. The coagulation and breakup kernels may have singularities on both the co-ordinate axes whereas the collision kernel grows up to bilinearity.

[42]
Title: The exterior derivative of the Lee form of almost Hermitian manifolds
Comments: 15 pages
Subjects: Differential Geometry (math.DG)

The exterior derivative $d \theta$ of the Lee form $\theta$ of almost Hermitian manifolds is studied. If $\omega$ is the K\"ahler two-form, it is proved that the $\mathbb{R}\omega$-component of $d\theta$ is always zero. expressions for the other components, in $[\lambda_0^{1,1}]$ and in $[[ \lambda^{2,0} ]]$, of $d\theta$ are also obtained. They are given in terms of the intrinsic torsion. Likewise, it is described some interrelations between the Lee form and $U(n)$-components of the Riemannian curvature tensor.

[43]
Title: On higher dimensional singularities for the fractional Yamabe problem: a non-local Mazzeo-Pacard program
Subjects: Analysis of PDEs (math.AP)

We consider the problem of constructing solutions to the fractional Yamabe problem that are singular at a given smooth sub-manifold, and we establish the classical gluing method of Mazzeo and Pacard for the scalar curvature in the fractional setting. This proof is based on the analysis of the model linearized operator, which amounts to the study of an ODE, and thus our main contribution here is the development of new methods coming from conformal geometry and scattering theory for the study of non-local ODEs. No traditional phase-plane analysis is available here. Instead, first, we provide a rigorous construction of radial fast-decaying solutions by a blow-up argument and a bifurcation method. Second, we use conformal geometry to rewrite this non-local ODE, giving a hint of what a non-local phase-plane analysis should be. Third, for the linear theory, we examine a fractional Schr\"{o}dinger equation with a Hardy type critical potential. We construct its Green's function, deduce Fredholm properties, and analyze its asymptotics at the singular points in the spirit of Frobenius method. Surprisingly enough, a fractional linear ODE may still have a two-dimensional kernel as in the second order case.

[44]
Title: Cambrian acyclic domains: counting $c$-singletons
Comments: 24 pages, 11 figures
Subjects: Combinatorics (math.CO)

We study the size of certain acyclic domains that arise from geometric and combinatorial constructions. These acyclic domains consist of all permutations visited by commuting equivalence classes of maximal reduced decompositions if we consider the symmetric group and, more generally, of all c-singletons of a Cambrian lattice associated to the weak order of a finite Coxeter group. For this reason, we call these sets Cambrian acyclic domains. Extending a closed formula of Galambos--Reiner for a particular acyclic domain called Fishburn's alternating scheme, we provide explicit formulae for the size of any Cambrian acyclic domain and characterize the Cambrian acyclic domains of minimum or maximum size.

[45]
Title: A Version of $κ$-Miller Forcing
Subjects: Logic (math.LO)

Let $\kappa$ be a regular uncountable cardinal such that $2^{<\kappa} = \kappa$ or just $2^{(\kappa^{<\kappa})} = 2^\kappa$ and there is a $\kappa$-mad family of size $2^\kappa$. We show under these assumptions the forcing order $\kappa$-Miller with club many splitting nodes collapses $2^\kappa$ to $\omega$ and adds a $\kappa$-Cohen real.

[46]
Title: Invariant surfaces in Euclidean space with a log-linear density
Authors: Rafael López
Comments: 26 pages, 7 figures
Subjects: Differential Geometry (math.DG)

A $\lambda$-translating soliton with density vector $\vec{v}$ is a surface in Euclidean space whose mean curvature $H$ satisfies $2H=2\lambda+\langle N,\vec{v}\rangle$, where $N$ is the Gauss map. We classify all $\lambda$-translating solitons that are invariant by a one-parameter group of translations and a one-parameter group of rotations.

[47]
Title: Joint Antenna Selection and Phase-Only Beamforming Using Mixed-Integer Nonlinear Programming
Comments: to be presented at WSA 2018
Subjects: Optimization and Control (math.OC); Information Theory (cs.IT)

In this paper, we consider the problem of joint antenna selection and analog beamformer design in downlink single-group multicast networks. Our objective is to reduce the hardware costs by minimizing the number of required phase shifters at the transmitter while fulfilling given distortion limits at the receivers. We formulate the problem as an L0 minimization problem and devise a novel branch-and-cut based algorithm to solve the resulting mixed-integer nonlinear program to optimality. We also propose a suboptimal heuristic algorithm to solve the above problem approximately with a low computational complexity. Computational results illustrate that the solutions produced by the proposed heuristic algorithm are optimal in most cases. The results also indicate that the performance of the optimal methods can be significantly improved by initializing with the result of the suboptimal method.

[48]
Title: Decomposition of a graph into two disjoint odd subgraphs
Subjects: Combinatorics (math.CO)

An odd (resp. even) subgraph in a multigraph is its subgraph in which every vertex has odd (resp. even) degree. We say that a multigraph can be decomposed into two odd subgraphs if its edge set can be partitioned into two sets so that both form odd subgraphs. In this paper we give a necessary and sufficient condition for the decomposability of a multigraph into two odd subgraphs. We also present a polynomial time algorithm for finding such a decomposition or showing its non-existence. We also deal with the case of the decomposability into an even subgraph and an odd subgraph.

[49]
Title: Rodin's formula in arbitrary codimension
Comments: 10 pages
Subjects: Classical Analysis and ODEs (math.CA)

We extend the Rodin's formula for $p$--modulus of the family of curves in $\mathbb{R}^n$ to arbitrary codimension. The proof relies on the formula for the $p$--modulus of family of level sets of a submersion and an algebraic lemma relating Jacobi matrices of considered maps. We state appropriate examples.

[50]
Title: Compact $λ$-translating solitons with boundary
Authors: Rafael López
Comments: 14 pages, no figures
Subjects: Differential Geometry (math.DG)

A $\lambda$-translating soliton with density vector $\vec{v}$ is a surface $\Sigma$ in Euclidean space ${\mathbb R}^3$ whose mean curvature $H$ satisfies $2H=2\lambda+\langle N,\vec{v}\rangle$, where $N$ is the Gauss map of $\Sigma$. In this article we study the shape of a compact $\lambda$-translating soliton in terms of its boundary. If $\Gamma$ is a given closed curve, we deduce under what conditions on $\lambda$ there exists a compact $\lambda$-translating soliton $\Sigma$ with boundary $\Gamma$ and we provide estimates of the surface area in relation with the height of $\Sigma$. Finally we study the shape of $\Sigma$ related with the one of $\Gamma$, in particular, we give conditions that assert that $\Sigma$ inherits the symmetries of its boundary $\Gamma$.

[51]
Title: Multidimensional multiscale scanning in Exponential Families: Limit theory and statistical consequences
Subjects: Probability (math.PR); Statistics Theory (math.ST); Methodology (stat.ME)

In this paper we consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\{Y_i\}_{i \in \left\{1,...,n\right\}^d}$, each distributed according to a one-dimensional natural exponential family $\mathcal F = \left\{F_\theta\right\}_{\theta \in\Theta}$. Given some baseline parameter $\theta_0 \in\Theta$, the field is scanned using local likelihood ratio tests to detect from a (large) given system of regions $\mathcal{R}$ those regions $R \subset \left\{1,...,n\right\}^d$ with $\theta_i \neq \theta_0$ for some $i \in R$. We provide a unified methodology which controls the overall family wise error (FWER) to make a wrong detection at a given error rate.
Fundamental to our method is a Gaussian approximation of the asymptotic distribution of the underlying multiscale scanning test statistic with explicit rate of convergence. From this, we obtain a weak limit theorem which can be seen as a generalized weak invariance principle to non identically distributed data and is of independent interest. Furthermore, we give an asymptotic expansion of the procedures power, which yields minimax optimality in case of Gaussian observations.

[52]
Title: Robust estimators in a generalized partly linear regression model under monotony constraints
Subjects: Statistics Theory (math.ST)

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and nonparametrically on an univariate regressor in such a way that the nonparametric component is assumed to be a monotone function. A class of robust estimates for the monotone nonparametric component and for the regression parameter, related to the linear one, is defined. The robust estimators are based on a spline approach combined with a score function which bounds large values of the deviance. As an application, we consider the isotonic partly linear log--Gamma regression model. Through a Monte Carlo study, we investigate the performance of the proposed estimators under a partly linear log--Gamma regression model with increasing nonparametric component.

[53]
Title: On the permanent of Sylvester-Hadamard matrices
Authors: Ulysse Chabaud
Comments: 2 pages
Subjects: Combinatorics (math.CO)

We prove a conjecture due to Wanless about the permanent of Hadamard matrices in the particular case of Sylvester-Hadamard matrices. Namely we show that for all n greater or equal to 2, the dyadic valuation of the permanent of the Sylvester-Hadamard matrix of order n is equal to the dyadic valuation of n!. As a consequence, the permanent of the Sylvester-Hadamard matrix of order n doesn't vanish for n greater or equal to 2.

[54]
Title: The use of sampling weights in the M-quantile random-effects regression: an application to PISA mathematics scores
Subjects: Statistics Theory (math.ST)

M-quantile random-effects regression represents an interesting approach for modelling multilevel data when the interest of researchers is focused on the conditional quantiles. When data are based on complex survey designs, sampling weights have to be incorporate in the analysis. A pseudo-likelihood approach for accommodating sampling weights in the M-quantile random-effects regression is presented. The proposed methodology is applied to the Italian sample of the "Program for International Student Assessment 2015" survey in order to study the gender gap in mathematics at various quantiles of the conditional distribution. Findings offer a possible explanation of the low share of females in "Science, Technology, Engineering and Mathematics" sectors.

[55]
Title: Spanned lines and Langer's inequality
Authors: Frank de Zeeuw
Subjects: Combinatorics (math.CO)

We collect some results in combinatorial geometry that follow from an inequality of Langer in algebraic geometry. Langer's inequality gives a lower bound on the number of incidences between a point set and its spanned lines, and was recently used by Han to improve the constant in the weak Dirac conjecture. Here we observe that this inequality also leads to improved constants in Beck's theorem, which states that a finite point set in the real or complex plane has many points on a line or spans many lines. Most of the proofs that we use are not original, and the goal of this note is mainly to carefully record the quantitative results in one place. We also include some discussion of possible further improvements to these statements.

[56]
Title: On the classification of almost contact metric manifolds
Comments: 15 pages
Subjects: Differential Geometry (math.DG)

On connected manifolds of dimension higher than three, the non-existence of $132$ Chinea and Gonz\'alez-D\'avila types of almost contact metric structures is proved. This is a consequence of some interrelations among components of the intrinsic torsion of an almost contact metric structure. Such interrelations allow to describe the exterior derivatives of some relevant forms in the context of almost contact metric geometry.

[57]
Title: Structure and Supersaturation for Intersecting Families
Comments: 28 pages
Subjects: Combinatorics (math.CO)

The extremal problems regarding the maximum possible size of intersecting families of various combinatorial objects have been extensively studied. In this paper, we investigate supersaturation extensions, which in this context ask for the minimum number of disjoint pairs that must appear in families larger than the extremal threshold. We study the minimum number of disjoint pairs in families of permutations and in $k$-uniform set families, and determine the structure of the optimal families. Our main tool is a removal lemma for disjoint pairs. We also determine the typical structure of $k$-uniform set families without matchings of size $s$ when $n \ge 2sk + 38s^4$, and show that almost all $k$-uniform intersecting families on vertex set $[n]$ are trivial when $n\ge (2+o(1))k$.

[58]
Title: Approximate controllabilty from the exterior of space-time fractional diffusion equations with the fractional Laplacian
Authors: Mahamadi Warma
Subjects: Analysis of PDEs (math.AP)

Let $\Om\subset\RR^N$ a bounded domain with a Lipschitz continuous boundary. We study the controllability of the space-time fractional diffusion equation \begin{equation*} \begin{cases} \mathbb D_t^\alpha u+(-\Delta)^su=0\;\;&\mbox{ in }\;(0,T)\times\Omega\\ u=g &\mbox{ in }\;(0,T)\times(\RR^N\setminus\Omega)\\ u(0,\cdot)=u_0&\mbox{ in }\;\Omega, \end{cases} \end{equation*} where $u=u(t,x)$ is the state to be controlled and $g=g(t,x)$ is the control function which is localized in a subset $\mathcal O$ of $\Omc$. Here, $0<\alpha\le 1$, $0<s<1$ and $T>0$ be real numbers. After giving an explicit representation of solutions, we show that the system is always approximately controllable for every $T>0$, $u_0\in L^2(\Omega)$ and $g\in \mathcal D((0,T)\times\mathcal O)$ where $\mathcal O\subset(\RR^N\setminus\bOm)$ is any open set. The results obtained are sharp in the sense that such a system is never null controllable if $0<\alpha<1$. The proof of our result is based on a new unique continuation principle for the eigenvalues problem associated with the fractional Laplace operator subject to the zero exterior boundary condition that we have established.

[59]
Title: The tangent bundle of a model category
Comments: Formerly part of arXiv:1612.02607
Subjects: Algebraic Topology (math.AT)

This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category $\mathcal{M}$ satisfying suitable conditions, we construct a relative model category $\mathcal{TM} \to \mathcal{M}$, called the tangent bundle, whose fibers are models for spectra in the various over-categories of $\mathcal{M}$, and which presents the $\infty$-categorical tangent bundle. Moreover, the tangent bundle $\mathcal{TM}$ inherits an enriched model structure when such a structure exists on $\mathcal{M}$. This additional structure is used in subsequent work to identify the tangent bundles of algebras over an operad and of enriched categories.

[60]
Title: Stabilizing discrete-time linear systems
Comments: 18 pages
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)

In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$ is stable if and only if it can be written as $A=S^{-1}UBS$, where $S$ is positive definite, $U$ is orthogonal, and $B$ is a positive semidefinite contraction (that is, the singular values of $B$ are less or equal 1). This characterization results in an equivalent optimization problem with a feasible set on which it is easy to project. We propose a very efficient fast projected gradient method to solve the problem in variables $(S,U,B)$. We show the effectiveness of the proposed method compared to other approaches.

[61]
Title: Pseudo-Harmonic Maps From Complete Noncompact Pseudo-Hermitian Manifolds To Regular Balls
Comments: 24 pages
Subjects: Differential Geometry (math.DG)

In this paper, we give an estimate of sub-Laplacian of Riemannian distance functions in pseudo-Hermitian manifolds which plays a similar role as Laplacian comparison theorem, and deduce a prior horizontal gradient estimate of pseudo-harmonic maps from pseudo-Hermitian manifolds to regular balls of Riemannian manifolds. As an application, Liouville theorem will be established under the conditions of nonnegative pseudo-Hermitian Ricci curvature and vanishing pseudo-Hermitian torsion. Moreover, we obtain the existence of pseudo-harmonic maps from complete noncompact pseudo-Hermitian manifolds to regular balls of Riemannian manifolds.

[62]
Title: Horizontal Gradient Estimate of Positive Pseudo-Harmonic Functions on Complete Noncompact Pseudo-Hermitian Manifolds
Authors: Yibin Ren
Comments: 16 pages
Subjects: Differential Geometry (math.DG)

In this paper, we will give a horizontal gradient estimate of positive solutions of $\Delta_b u = - \lambda u$ on complete noncompact pseudo-Hermitian manifolds. As a consequence, we recapture the Liouville theorem of positive pseudo-harmonic functions on Sasakian manifolds with nonnegative pseudo-Hermitian Ricci curvature.

[63]
Title: A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation
Subjects: Analysis of PDEs (math.AP)

In general, the non-conservative approximation of coagulation-fragmentation equations (CFEs) may lead to the occurrence of gelation phenomenon. In this article, it is shown that the non-conservative approximation of CFEs can also provide the existence of mass conserving solutions to CFEs for large classes of unbounded coagulation and fragmentation kernels.

[64]
Title: 2VRP: a benchmark problem for small but rich VRPs
Comments: 40 pages
Subjects: Optimization and Control (math.OC)

We consider a 2-vehicle routing problem (2VRP) which can be viewed as a building block for the variety of vehicle routing problems (VRP). As a simplified version of the 2VRP, we consider a 2-period balanced travelling salesman problem (2TSP) and describe a polynomially solvable case of this NP-hard problem. For the 2VRP with general settings, we suggest a framework based on the Held and Karp dynamic programming algorithm. Our algorithms based on this framework show an exceptionally good performance on the published test data. Our approach can be easily extended to a variety of constraints/attributes in the VRP, hence the wording "small but rich" in the title of our paper. We also introduce a new methodological approach: we use easy solvable special cases for generating test instances and then use these instances in computational experiments.

[65]
Title: Quillen cohomology of $(\infty,2)$-categories
Subjects: Algebraic Topology (math.AT)

In this paper we study the homotopy theory of parameterized spectrum objects in the $\infty$-category of $(\infty, 2)$-categories, as well as the Quillen cohomology of an $(\infty, 2)$-category with coefficients in such a parameterized spectrum. More precisely, we construct an analogue of the twisted arrow category for an $(\infty,2)$-category $\mathbb{C}$, which we call its twisted 2-cell $\infty$-category. We then establish an equivalence between parameterized spectrum objects over $\mathbb{C}$, and diagrams of spectra indexed by the twisted 2-cell $\infty$-category of $\mathbb{C}$. Under this equivalence, the Quillen cohomology of $\mathbb{C}$ with values in such a diagram of spectra is identified with the two-fold suspension of its inverse limit spectrum. As an application, we provide an alternative, obstruction-theoretic proof of the fact that adjunctions between $(\infty,1)$-categories are uniquely determined at the level of the homotopy $(3, 2)$-category of $\mathrm{Cat}_{\infty}$.

[66]
Title: Seidel's conjectures in hyperbolic 3-space
Comments: 22 pages, 4 figures
Subjects: Differential Geometry (math.DG)

We prove, in the case of hyperbolic 3-space, a couple of conjectures raised by J. J. Seidel in "On the volume of a hyperbolic simplex", Stud. Sci. Math. Hung. 21, 243-249, 1986. These conjectures concern expressing the volume of an ideal hyperbolic tetrahedron as a monotonic function of algebraic maps. More precisely, Seidel's first conjecture states that the volume of an ideal tetrahedron in hyperbolic 3-space is determined by (the permanent and the determinant of) the doubly stochastic Gram matrix $G$ of its vertices; Seidel's fourth conjecture claims that the mentioned volume is a monotonic function of both the permanent and the determinant of $G$.

[67]
Title: Abel's Lemma and Dirichlet's Test Incorrectly Determine that a Trigonometric Version of the Dirichlet Series $ζ(s)=\sum n^{-s}$ is Convergent Throughout the Critical Strip at $t\ne0$
Authors: Ayal Sharon
Comments: 17 pages, 2 figures
Subjects: General Mathematics (math.GM)

Euler's formula is used to derive a trigonometric version of the Dirichlet series $\zeta(s)=\sum n^{-s}$, which is divergent in the half-plane $\sigma \le 1$, wherein $s \in \mathbb{C}$ and $s=\sigma +it$. Abel's lemma and Dirichlet's test incorrectly hold that trigonometric $\zeta(s)$ is convergent in the critical strip $0<\sigma \le 1$ at $t\ne0$, because they fail to consider a divergent series with monotonically decreasing terms (e.g. the harmonic series) in combination with a bounded oscillating function having an increasing half-period duration, such as $f(t, n) = \sin(t \cdot \ln(n))$.

[68]
Title: On monotonicity of FIFO-diverging junctions
Subjects: Dynamical Systems (math.DS)

This technical note concerns the dynamics of FIFO-diverging junctions in compartmental models for traffic networks. Many strong results on the dynamical behavior of such traffic networks rely on monotonicity of the underlying dynamics. In road traffic modeling, a common model for diverging junctions is based on the First-in, first-out principle. These type of junctions pose a problem in the analysis of traffic dynamics, since their dynamics are not monotone with respect to the positive orthant. However, this technical note demonstrates that they are in fact monotone with respect to the partial ordering induced by a particular, polyhedral cone.

[69]
Title: Symmetry preserving degenerations of the generic symmetric matrix
Comments: 33 pages. arXiv admin note: text overlap with arXiv:1610.07681
Subjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG)

One considers certain degenerations of the generic symmetric matrix over a field $k$ of characteristic zero and the main structures related to the determinant $f$ of the matrix, such as the ideal generated by its partial derivatives, the polar map defined by these derivatives and its image $V(f)$, the Hessian matrix, the ideal and the map given by the cofactors, and the dual variety of $V(f)$.

[70]
Title: Octonions, triality, the exceptional Lie algebra F4, and polar actions on the Cayley hyperbolic plane
Authors: Andreas Kollross
Comments: 24 pages; comments are welcome
Subjects: Differential Geometry (math.DG); Rings and Algebras (math.RA)

Using octonions and the triality property of Spin(8), we find explicit formulae for the Lie brackets of the exceptional simple real Lie algebras $\mathfrak{f}_4$ and $\mathfrak{f}^*_4$, i.e. the Lie algebras of the isometry groups of the Cayley projective plane and the Cayley hyperbolic plane. As an application, we classify polar actions on the Cayley hyperbolic plane which leave a totally geodesic subspace invariant.

[71]
Title: Expansion Trees with Cut
Comments: arXiv admin note: text overlap with arXiv:1308.0428
Subjects: Logic (math.LO)

Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view, it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information of which instances have been chosen for which quantifiers.
This compact representation is known in the literature as Miller's expansion tree proof. It is inherently analytic and hence corresponds to a cut-free sequent calculus proof. Recently several extensions of such proof representations to proofs with cuts have been proposed. These extensions are based on graphical formalisms similar to proof nets and are limited to prenex formulas.
In this paper we present a new syntactic approach that directly extends Miller's expansion trees by cuts and covers also non-prenex formulas. We describe a cut-elimination procedure for our expansion trees with cut that is based on the natural reduction steps and show that it is weakly normalizing.

[72]
Title: Distributions of countable models of quite o-minimal Ehrenfeucht theories
Subjects: Logic (math.LO)

We describe Rudin-Keisler preorders and distribution functions of numbers of limit models for quite o-minimal Ehrenfeucht theories. Decomposition formulas for these distributions are found.

[73]
Title: A gradient flow approach to relaxation rates for the multi-dimensional Cahn-Hilliard equation
Subjects: Analysis of PDEs (math.AP)

The aim of this paper is to study relaxation rates for the Cahn-Hilliard equation in dimension larger than one. We follow the approach of Otto and Westdickenberg based on the gradient flow structure of the equation and establish differential and algebraic relationships between the energy, the dissipation, and the squared $H^{--1}$ distance to a kink. This leads to a scale separation of the dynamics into two different stages: a first fast phase of the order $t^{ -- 1/2}$ where one sees convergence to some kink, followed by a slow relaxation phase with rate $t^{-- 1/ 4}$ where convergence to the centered kink is observed.

[74]
Title: Applications of Optimal Control of a Nonconvex Sweeping Process to Optimization of the Planar Crowd Motion Model
Comments: 22 pages, 8 figures
Subjects: Optimization and Control (math.OC)

This paper concerns optimal control of a nonconvex perturbed sweeping process and its applications to optimization of the planar crowd motion model of traffic equilibria. The obtained theoretical results allow us to investigate a dynamic optimization problem for the microscopic planar crown motion model with finitely many participants and completely solve it analytically in the case of two participants.

[75]
Title: On relative separability in hypergraphs of models of theories
Subjects: Logic (math.LO)

In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general case and for almost countably categorical quite o-minimal theories are established.

[76]
Title: Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem
Authors: Andre Wibisono
Comments: 44 pages
Subjects: Optimization and Control (math.OC); Information Theory (cs.IT); Learning (cs.LG); Machine Learning (stat.ML)

We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in discrete time, and consider how to remove or reduce the bias. We point out the difficulty is that the heat flow is exactly solvable, but neither its forward nor backward method is implementable in general, except for Gaussian data. We propose the symmetrized Langevin algorithm (SLA), which should have a smaller bias than ULA, at the price of implementing a proximal gradient step in space. We show SLA is in fact consistent for Gaussian target measure, whereas ULA is not. We also illustrate various algorithms explicitly for Gaussian target measure, including gradient descent, proximal gradient, and Forward-Backward, and show they are all consistent.

[77]
Title: Fano threefolds as equivariant compactifications of the vector group
Comments: 36 pages + Appendix of 15 pages. Comments are very welcome!
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)

In this article, we determine all equivariant compactifications of the three-dimensional vector group $\mathbf{G}_a^3$ which are smooth Fano threefolds with Picard number greater or equal than two.

[78]
Title: On structures in hypergraphs of models of a theory
Subjects: Logic (math.LO)

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types of models of a theory, are given.

[79]
Title: SO(p,q)-Higgs bundles and higher Teichmüller components
Comments: 55 pages. Comments welcome
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG); Geometric Topology (math.GT)

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such exotic' components in moduli spaces of SO(p,q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO(p,q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO(2,q), with q> 3).

[80]
Title: On freedom and independence in hypergraphs of models of theories
Subjects: Logic (math.LO)

Notions of freedom and independence for hypergraphs of models of a theory are defined. Properties of these notions and their applications to some natural classes of theories are studied.

[81]
Title: Mapping Borel sets onto balls and self-similar sets by Lipschitz and nearly Lipschitz maps
Authors: Ondřej Zindulka
Subjects: Classical Analysis and ODEs (math.CA)

If $X$ is an analytic metric space satisfying a very mild doubling condition, then for any finite Borel measure $\mu$ on $X$ there is a set $N\subseteq X$ such that $\mu(N)>0$, an ultrametric space $Z$ and a Lipschitz bijection $\phi:N\to Z$ whose inverse is nearly Lipschitz, i.e., $\beta$-H\"older for all $\beta<1$. As an application it is shown that a Borel set in a Euclidean space maps onto $[0,1]^n$ by a nearly Lipschitz map if and only if it cannot be covered by countably many sets of Hausdorff dimension strictly below $n$. The argument extends to analytic metric spaces satisfying the mild condition. Further generalization replaces cubes with self-similar sets, nearly Lipschitz maps with nearly H\"older maps and integer dimension with arbitrary finite dimension.

[82]
Title: On residual categories for Grassmannians
Subjects: Algebraic Geometry (math.AG)

We define and discuss some general properties of residual categories of Lefschetz decompositions in triangulated categories. In the case of the derived category of coherent sheaves on the Grassmannian $\text{G}(k,n)$ we conjecture that the residual category associated with Fonarev's Lefschetz exceptional collection is generated by a completely orthogonal exceptional collection. We prove this conjecture for $k = p$, a prime number, modulo completeness of Fonarev's collection (and for $p = 3$ we check this completeness).

[83]
Title: Bloch functions on the unit ball of a Banach space
Subjects: Functional Analysis (math.FA)

The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch space considering the boundness of $(1-\|x\|^2) \|f'(x)\|$ on $B_E$ and by preserving the invariance of the correspondiing seminorm when we compose with automorphisms $\phi$ of $B_E$. We study the connection between these spaces proving that they are different in general and prove that all bounded analytic functions on $B_{E}$ are Bloch functions in both ways.

[84]
Title: Homotopical Quantum Field Theory
Authors: Donald Yau
Comments: 302 pages
Subjects: Mathematical Physics (math-ph); Algebraic Topology (math.AT); Category Theory (math.CT)

Algebraic quantum field theory and prefactorization algebra are two mathematical approaches to quantum field theory. In this monograph, using a new coend definition of the Boardman-Vogt construction of a colored operad, we define homotopy algebraic quantum field theories and homotopy prefactorization algebras and investigate their homotopy coherent structures. Homotopy coherent diagrams, homotopy inverses, A-infinity-algebras, E-infinity-algebras, and E-infinity-modules arise naturally in this context. In particular, each homotopy algebraic quantum field theory has the structure of a homotopy coherent diagram of A-infinity-algebras and satisfies a homotopy coherent version of the causality axiom. When the time-slice axiom is defined for algebraic quantum field theory, a homotopy coherent version of the time-slice axiom is satisfied by each homotopy algebraic quantum field theory. Over each topological space, every homotopy prefactorization algebra has the structure of a homotopy coherent diagram of E-infinity-modules over an E-infinity-algebra. To compare the two approaches, we construct a comparison morphism from the colored operad for (homotopy) prefactorization algebras to the colored operad for (homotopy) algebraic quantum field theories and study the induced adjunctions on algebras.

[85]
Title: Linear complexity of Ding-Helleseth generalized cyclotomic sequences of order eight
Comments: 18 pages, 7 tables
Subjects: Number Theory (math.NT); Cryptography and Security (cs.CR)

During the last two decades, many kinds of periodic sequences with good pseudo-random properties have been constructed from classical and generalized cyclotomic classes, and used as keystreams for stream ciphers and secure communications. Among them are a family DH-GCS$_{d}$ of generalized cyclotomic sequences on the basis of Ding and Helleseth's generalized cyclotomy, of length $pq$ and order $d=\mathrm{gcd}(p-1,q-1)$ for distinct odd primes $p$ and $q$. The linear complexity (or linear span), as a valuable measure of unpredictability, is precisely determined for DH-GCS$_{8}$ in this paper. Our approach is based on Edemskiy and Antonova's computation method with the help of explicit expressions of Gaussian classical cyclotomic numbers of order $8$. Our result for $d=8$ is compatible with Yan's low bound $(pq-1)/2$ of the linear complexity for any order $d$, which means high enough to resist security attacks of the Berlekamp-Massey algorithm. Finally, we include SageMath codes to illustrate the validity of our result by examples.

[86]
Title: Greedy kernel methods for accelerating implicit integrators for parametric ODEs
Subjects: Numerical Analysis (math.NA)

We present a novel acceleration method for the solution of parametric ODEs by single-step implicit solvers by means of greedy kernel-based surrogate models. In an offline phase, a set of trajectories is precomputed with a high-accuracy ODE solver for a selected set of parameter samples, and used to train a kernel model which predicts the next point in the trajectory as a function of the last one. This model is cheap to evaluate, and it is used in an online phase for new parameter samples to provide a good initialization point for the nonlinear solver of the implicit integrator. The accuracy of the surrogate reflects into a reduction of the number of iterations until convergence of the solver, thus providing an overall speedup of the full simulation. Interestingly, in addition to providing an acceleration, the accuracy of the solution is maintained, since the ODE solver is still used to guarantee the required precision. Although the method can be applied to a large variety of solvers and different ODEs, we will present in details its use with the Implicit Euler method for the solution of the Burgers equation, which results to be a meaningful test case to demonstrate the method's features.

[87]
Title: Adaptive synchronisation of unknown nonlinear networked systems with prescribed performance
Comments: arXiv admin note: text overlap with arXiv:1802.07253
Journal-ref: International Journal of Systems Science 48, no. 4 (2017): 885-898
Subjects: Optimization and Control (math.OC); Systems and Control (cs.SY); Dynamical Systems (math.DS)

This paper proposes an adaptive tracking control with prescribed performance function for distributive cooperative control of highly nonlinear multi-agent systems. The use of such approach confines the tracking error within a large predefined set to a predefined smaller set. The key idea is to transform the constrained system into unconstrained one through the transformation of the output error. Agents' dynamics are assumed unknown, and the controller is developed for a strongly connected structured network. The proposed controller allows all agents to follow the trajectory of the leader node, while satisfying the necessary dynamic requirements. The proposed approach guarantees uniform ultimate boundedness for the transformed error as well as a bounded adaptive estimate of the unknown parameters and dynamics. Simulations include two examples to validate the robustness and smoothness of the proposed controller against highly nonlinear heterogeneous multi-agent system with uncertain time-variant parameters and external disturbances.

[88]
Title: Topological spaces of persistence modules and their properties
Comments: 30 pages
Subjects: Algebraic Topology (math.AT); General Topology (math.GN)

Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules, including many of those that have been previously studied, and describe the relationships between them. In the cases where these classes are sets, interleaving distance induces a topology. We undertake a systematic study the resulting topological spaces and their basic topological properties.

[89]
Title: The topological chiral homology of the spherical category
Authors: Dario Beraldo
Comments: 16 pages, preliminary version (the treatment of higher category theory needs improvements)
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG); Category Theory (math.CT); Quantum Algebra (math.QA)

We consider the spherical DG category $Sph_G$ attached to an affine algebraic group $G$. By definition, $Sph_G := IndCoh(LS_G(S^2))$ consists of ind-coherent sheaves of the stack of $G$-local systems on the $2$-sphere $S^2$. The $3$-dimensional version of the pair of pants endows $Sph_G$ with an $E_3$-monoidal structure. More generally, for an algebraic stack $Y$ (satisfying some mild conditions) and $n \geq -1$, we can look at the $E_{n+1}$-monoidal DG category $Sph(Y,n) := IndCoh_0((Y^{S^n})^\wedge_Y)$, where $IndCoh_0$ is the sheaf theory introduced in [AG2] and [centerH]. % The case of $Sph_G$ is recovered by setting $Y =BG$ and $n=2$.
The cobordism hypothesis associates to $Sph(Y,n)$ an $(n+1)$-dimensional TQFT, whose value of a manifold $M^d$ of dimension $d \leq n+1$ (possibly with boundary) is given by the {topological chiral homology} $\int_{M^d} Sph(Y,n)$. % In this paper, we compute such homology (in virtually all cases): we have the Stokes style formula $$\int_{M^d} Sph(Y,n) \simeq IndCoh_0 ( (Y^{\partial(M^d \times D^{n+1-d})})^\wedge _{Y^M} ) ,$$ where the formal completion is constructed using the obvious projection $\partial(M^d \times D^{n+1-d}) \to M^d$.
The most interesting instance of this formula is for $Sph_G \simeq Sph(BG,2)$, the original spherical category, and $X$ a Riemann surface. In this case, we obtain a monoidal equivalence $\int_X Sph_G \simeq H(LS_G^{Betti}(X))$, where $LS_G^{Betti}(X)$ is the stack of $G$-local systems on the topological space underlying $X$ and $H$ is the sheaf theory introduced in [centerH].

[90]
Title: Time-parallel iterative solvers for parabolic evolution equations
Subjects: Numerical Analysis (math.NA)

We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of parabolic problems, we show that the standard nonsymmetric time-global system can be equivalently reformulated as an original symmetric saddle-point system that remains inf-sup stable with respect to the same natural parabolic norms. We then propose and analyse an efficient and readily implementable parallel-in-time preconditioner to be used with an inexact Uzawa method. The proposed preconditioner is non-intrusive and easy to implement in practice, and also features the key theoretical advantages of robust spectral bounds, leading to convergence rates that are independent of the number of time-steps, final time, or spatial mesh sizes, and also a theoretical parallel complexity that grows only logarithmically with respect to the number of time-steps. Numerical experiments with large-scale parallel computations show the effectiveness of the method, along with its good weak and strong scaling properties.

[91]
Title: Mapping Analytic sets onto cubes by little Lipschitz functions
Subjects: Classical Analysis and ODEs (math.CA)

A mapping $f:X\to Y$ between metric spaces is called \emph{little Lipschitz} if the quantity $$\operatorname{lip}(f(x)=\liminf_{r\to0}\frac{\operatorname{diam} f(B(x,r))}{r}$$ is finite for every $x\in X$.
We prove that if a compact (or, more generally, analytic) metric space has packing dimension greater than $n$, then $X$ can be mapped onto an $n$-dimensional cube by a little Lipschitz function.
The result requires two facts that are interesing in their own right. First, an analytic metric space $X$ contains, for any $\varepsilon>0$, a compact subset $S$ that embeds into an ultrametric space by a Lipschitz map, and $\dim_P S\geq\dim_P X-\varepsilon$. Second, a little Lipschitz function on a closed subset admits a little Lipschitz extension.

[92]
Title: The moduli space of Fano manifolds with Kaehler-Ricci solitons
Authors: Eiji Inoue
Comments: 48 pages
Subjects: Differential Geometry (math.DG); Algebraic Geometry (math.AG)

We construct a canonical Hausdorff complex analytic moduli space of Fano manifolds with Kaehler-Ricci solitons. This naturally enlarges the moduli space of Fano manifolds with Kaehler-Einstein metrics, which was constructed by Odaka and Li-Wang-Xu. We discover a moment map picture for Kaehler-Ricci solitons, and give complex analytic charts on the topological space consisting of Kaehler-Ricci solitons, by studying differential geometric aspects of this infinite dimensional moment map. Some stacky words and arguments on Gromov-Hausdorff convergence help to glue them together in the holomorphic manner.

[93]
Title: Reducibility for wave equations of finitely smooth potential with periodic boundary conditions
Comments: arXiv admin note: text overlap with arXiv:1706.06713
Subjects: Dynamical Systems (math.DS)

In the present paper, the reducibility is derived for the wave equations with finitely smooth and time-quasi-periodic potential subjects to periodic boundary conditions. More exactly, the linear wave equation $u_{tt}-u_{xx}+Mu+\varepsilon (V_0(\omega t)u_{xx}+V(\omega t, x)u)=0,\;x\in \mathbb{R}/2\pi \mathbb{Z}$ can be reduced to a linear Hamiltonian system of a constant coefficient operator which is of pure imaginary point spectrum set, where $V$ is finitely smooth in $(t, x)$, quasi-periodic in time $t$ with Diophantine frequency $\omega\in \mathbb{R}^{n},$ and $V_0$ is finitely smooth and quasi-periodic in time $t$ with Diophantine frequency $\omega\in \mathbb{R}^{n},$ Moreover, it is proved that the corresponding wave operator possesses the property of pure point spectra and zero Lyapunov exponent.

[94]
Title: Scaling limits of discrete snakes with stable branching
Authors: Cyril Marzouk
Comments: 27 pages, 3 figures (hopefully more to come)
Subjects: Probability (math.PR)

We consider so-called discrete snakes obtained from size-conditioned critical Bienaym\'e-Galton-Watson trees by assigning to each node a random spatial position in such a way that the increments along each edge are i.i.d. When the offspring distribution belongs to the domain of attraction of a stable law with index $\alpha \in (1,2]$, we give a necessary and sufficient condition on the tail distribution of the spatial increments for this spatial tree to converge, in a functional sense, towards the Brownian snake driven by the $\alpha$-stable L\'evy tree. We also study the case of heavier tails, and apply our result to study the number of inversions of a uniformly random permutation indexed by the tree.

[95]
Title: Stability and Optimal Control of Switching PDE-Dynamical Systems
Authors: Falk M. Hante
Subjects: Optimization and Control (math.OC); Analysis of PDEs (math.AP); Dynamical Systems (math.DS)

Selected results for the stability and optimal control of abstract switched systems in Banach and Hilbert space are reviewed. The dynamics are typically given in a piecewise sense by a family of nonlinearly perturbed evolutions of strongly continuous semigroups. Stability refers to characterizations of asymptotic decay of solutions that holds uniformly for certain classes of switching signals for time going to infinity. Optimal control refers to the minimization of costs associated to solutions by appropriately selecting switching signals. Selected numerical results verify and visualize some of the available theory.

[96]
Title: A note on friezes of type $Λ_4$ and $Λ_6$
Authors: Lukas Andritsch
Comments: 8 pages, 7 figures
Subjects: Combinatorics (math.CO)

We point out a certain connection between Conway-Coxeter friezes of triangulations and $p$-angulated generalisation of frieze patterns recently introduced by Holm and J{\o}rgensen: the friezes of type $\Lambda_p$ coincide with Conway-Coxeter friezes of certain triangulations for $p=4$ and $p=6$ in every odd row.

[97]
Title: The global geometry of surfaces with prescribed mean curvature in $\mathbb{R}^3$
Comments: 60 pages, 16 figures
Subjects: Differential Geometry (math.DG)

We develop a global theory for complete hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. This theory extends the usual one of constant mean curvature hypersurfaces in $\mathbb{R}^{n+1}$, and also that of self-translating solitons of the mean curvature flow. Among other topics, we will study existence and geometric properties of compact examples, existence and classification of rotational hypersurfaces, and stability properties. For the particular case $n=2$, we will obtain results regarding a priori height and curvature estimates, non-existence of complete stable surfaces, and classification of properly embedded surfaces with at most one end.

[98]
Title: Models of affine curves and Ga-actions
Authors: Kevin Langlois
Comments: To appear in the Proceeding Schemas des arcs et singularites
Subjects: Algebraic Geometry (math.AG)

Using the approach of Barkatou and El Kaoui, we classify certain affine curves over discrete valuation rings having a free additive group action. Our classification generalizes results of Miyanishi in equi-characteristic 0.

[99]
Title: An homogenization approach for the inverse spectral problem of periodic Schrödinger operators
Authors: Lorenzo Zanelli
Subjects: Mathematical Physics (math-ph)

We study the inverse spectral problem for periodic Schr\"odinger opera\-tors of kind $- \frac{1}{2} \hbar^2 \Delta_x + V(x)$ on the flat torus $\Bbb T^n := (\Bbb R / 2 \pi \Bbb Z)^n$ with potentials $V \in C^{\infty} (\Bbb T^n)$. We show that if two operators are isospectral for any $0 < \hbar \le 1$ then they have the same effective Hamiltonian given by the periodic homogenization of Hamilton-Jacobi equation. This result provides a necessary condition for the isospectrality of these Schr\"odinger operators. We also provide a link between our result and the spectral limit of quantum integrable systems.

[100]
Title: New Results on Finite-Time Stability: Geometric Conditions and Finite-Time Controllers
Comments: 2018 American Control Conference, Milwaukee, Wisconsin, June 2018
Subjects: Dynamical Systems (math.DS); Systems and Control (cs.SY)

This paper presents a novel controller that yields finite-time stability for linear systems. We first present a necessary and sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers based on vector fields and barrier functions to demonstrate the utility of this geometric condition. We also consider the general class of linear controllable systems, and present a continuous feedback control law to stabilize the origin of the system in finite time. Finally, we present simulation results for each of these controllers, showing the efficacy of the designed control laws.

[101]
Title: From Vectors to Geometric Algebra
Comments: 26 pages, 23 figures, also available in Spanish
Subjects: General Mathematics (math.GM)

Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous Pythagorean theorem. Synthetic proofs of theorems in Euclidean geometry can then be replaced by powerful algebraic proofs. Whereas we largely limit our attention to 2 and 3 dimensions, geometric algebra is applicable in any number of dimensions, and in both Euclidean and non-Euclidean geometries.

[102]
Title: Topological Hochschild Homology of H(Z/p^k)
Authors: Nitu Kitchloo
Subjects: Algebraic Topology (math.AT)

In this short note we study the topological Hoschschild homology of Eilenberg-MacLane spectra for finite cyclic groups. In particular, we show that the Eilenberg-MacLane spectrum H(Z/p^k) is a Thom spectrum for any prime p (except, possibly, when p=k=2) and we also compute its topological Hoschshild homology. This yields a short proof of the results obtained by Brun, except for the anomalous case p=k=2.

[103]
Title: A counterexample to Herzog's Conjecture on the number of involutions
Authors: Mohammad Zarrin
Comments: 2 pages
Subjects: Group Theory (math.GR)

In 1979, Herzog put forward the following conjecture: if two simple groups have the same number of involutions, then they are of the same order. We give a counterexample to this conjecture.

[104]
Title: Two flat structures on minimal surfaces
Authors: Hojoo Lee
Comments: Comments welcome
Subjects: Differential Geometry (math.DG)

In this expository article, we illustrate how two independent flat structures on minimal surfaces induce a harmonic function, which captures the uniqueness of Enneper's surface.

[105]
Title: Web spaces and worldwide web spaces: topological aspects of domain theory
Authors: Marcel Erné
Comments: 36 pages, 1 figure, 8 diagrams. arXiv admin note: text overlap with arXiv:1607.04721
Subjects: General Topology (math.GN)

Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology with a second topology having the dual specialization order; these patch spaces possess good convexity and separation properties and determine the original web spaces. The category of C-spaces is concretely isomorphic to the category of fan spaces; these are certain quasi-ordered spaces having neighborhood bases of fans, obtained by deleting a finite number of principal filters from a principal filter. Our approach has useful consequences for domain theory, because the T$_0$ web spaces are exactly the generalized Scott spaces of locally approximating ideal extensions, and the T$_0$ C-spaces are exactly the generalized Scott spaces of globally approximating and interpolating ideal extensions. We extend the characterization of continuous lattices as meet- continuous lattices with T$_2$ Lawson topology and the Fundamental Theorem of Compact Semilattices to non-complete posets. Finally, we investigate cardinal invariants like density and weight of the involved objects.

[106]
Title: Cocommutative Com-PreLie bialgebras
Authors: Loïc Foissy (LMPA)
Comments: arXiv admin note: text overlap with arXiv:1501.06375
Subjects: Rings and Algebras (math.RA)

A Com-PreLie bialgebra is a commutative bialgebra with an extra preLie product satisfying some compatibilities with the product and coproduct. We here give a classification of connected, cocommutative Com-PreLie bialgebras over a field of characteristic zero: we obtain a main family of symmetric algebras on a space V of any dimension, and another family available only if V is one-dimensional. We also explore the case of Com-PreLie bialgebras over a group algebra and over a tensor product of a group algebra and of a symmetric algebra.

[107]
Title: On Completely Solvable Lie Foliation
Authors: Ameth Ndiaye
Subjects: Differential Geometry (math.DG)

In this paper we try to generalize the Haefliger theorem on completly solvable Lie foliations. We prove that: every completely solvable Lie foliation on a compact manifold is the inverse image of a homogenus foliation. Every manifold in this paper is compact and our Lie group G is connexe and simply connexe.

[108]
Title: p-Blocks Relative to a Character of a Normal Subgroup
Authors: Noelia Rizo
Subjects: Representation Theory (math.RT); Group Theory (math.GR)

Let G be a finite group, let N be a normal subgroup of G, and let theta in Irr(N) be a G-invariant character. We fix a prime p, and we introduce a canonical partition of Irr(G|theta) relative to p. We call each member B_theta of this partition a theta-block, and to each theta-block B_theta we naturally associate a conjugacy class of p-subgroups of G/N, which we call the theta-defect groups of B_theta. If N is trivial, then the theta-blocks are the Brauer p-blocks. Using theta-blocks, we can unify the Gluck-Wolf-Navarro-Tiep theorem and Brauer's Height Zero conjecture in a single statement, which, after work of B. Sambale, turns out to be equivalent to the the Height Zero conjecture. We also prove that the k(B)-conjecture is true if and only if every theta-block B_theta has size less than or equal the size of any of its theta-defect groups, hence bringing normal subgroups to the k(B)-conjecture.

[109]
Title: Algebra and geometry of tensors for modeling rater agreement data
Comments: 24 pages, 8 figures
Subjects: Statistics Theory (math.ST)

We study three different quasi-symmetry models and three different mixture models of $n\times n\times n$ tensors for modeling rater agreement data. For these models we give a geometric description of the associated varieties and we study their invariants distinguishing between the case $n=2$ and the case $n>2$. Finally, for the two models for pairwise agreement we state some results about the pairwise Cohen's $\kappa$ coefficients.

[110]
Title: Algebroid Structures on Para-Hermitian Manifolds
Authors: David Svoboda
Comments: 31 pages
Subjects: Differential Geometry (math.DG); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

We present a global construction of a so-called D-bracket appearing in the physics literature of Double Field Theory (DFT) and show that if certain integrability criteria are satisfied, it can be seen as a sum of two Courant algebroid brackets. In particular, we show that the local picture of the extended space-time used in DFT fits naturally in the geometrical framework of the para-Hermitian manifolds and that the data of an (almost) para-Hermitian manifold is sufficient to construct the D-bracket. Moreover, the twists of the bracket appearing in DFT can be interpreted in this framework geometrically as a consequence of certain deformations of the underlying para-Hermitian structure.

[111]
Title: On quaternion algebras over quadratic and biquadratic fields
Subjects: Number Theory (math.NT)

Let p and q be two positive primes. In this paper we obtain a complete characterization of quaternion division algebras H_K(p,q) over quadratic and biquadratic number fields K.

[112]
Title: Schrödinger-Koopman quasienergy states of quantum systems driven by a classical flow
Subjects: Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD); Quantum Physics (quant-ph)

We study the properties of the quasienergy states of a quantum system driven by a classical dynamical systems. The quasienergies are defined in a same manner as in light-matter interaction but where the Floquet approach is generalized by the use of the Koopman approach of dynamical systems. We show how the properties of the classical flow (fixed and cyclic points, ergodicity, chaos) influence the driven quantum system. This approach of the Schr\"odinger-Koopman quasienergies can be applied to quantum control, quantum information in presence of noises, and dynamics of mixed classical-quantum systems. We treat the example of a spin ensemble kicked following discrete classical flow as the Arnold's cat map and the Chirikov standard map.

[113]
Title: A Logic of Strong Contact between Polytopes
Comments: Master thesis of Tsvetlin Marinov under the supervision of Tinko Tinchev. 33 pages
Subjects: Logic (math.LO)

We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are in strong contact if a small enough object can pass from one of them to the other while remaining in their union. In the first half of the paper we prove that this relation is indeed a contact relation between polytopes, which turns out not to be the case for arbitrary regular closed in Euclidean spaces sets. In the second half we study the universal fragments of the logics of the resultant contact algebras. We prove that they all coincide with the set of theorems of a standard quantifier-free formal system for connected contact algebras, which also coincides with the universal fragments of the logics of a variety of (classes of) contact algebras of interest.

[114]
Title: The spatial Lambda-Fleming-Viot process with fluctuating selection
Subjects: Probability (math.PR)

We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just two genetic types. Short bursts of selection acting in opposing directions drive to maintain both types at intermediate frequencies, while the fluctuations due to 'genetic drift' work to eliminate variation in the population.
We consider first a population with no spatial structure, modelled by an adaptation of the Lambda (or generalised) Fleming-Viot process, and derive a stochastic differential equation as a scaling limit. This amounts to a limit result for a Lambda-Fleming-Viot process in a rapidly fluctuating random environment. We then extend to a population that is distributed across a spatial continuum, which we model through a modification of the spatial Lambda-Fleming-Viot process with selection. In this setting we show that the scaling limit is a stochastic partial differential equation. As is usual with spatially distributed populations, in dimensions greater than one, the 'genetic drift' disappears in the scaling limit, but here we retain some stochasticity due to the fluctuations in the environment, resulting in a stochastic p.d.e. driven by a noise that is white in time but coloured in space.
We discuss the (rather limited) situations under which there is a duality with a system of branching and annihilating particles. We also write down a system of equations that captures the frequency of descendants of particular subsets of the population and use this same idea of 'tracers', which we learned from Hallatschek and Nelson (2008) and Durrett and Fan (2016), in numerical experiments with a closely related model based on the classical Moran model.

[115]
Title: Large-scale limit of interface fluctuation models
Comments: 64 pages
Subjects: Probability (math.PR); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)

We extend the weak universality of KPZ in [Hairer-Quastel] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of Gaussians in terms of their polynomial counterparts. This enables us to reduce the problem of a general nonlinearity with sufficient regularity to that of a polynomial.

[116]
Title: Localization theory for derivators
Authors: Fosco Loregian
Comments: 40 pages
Subjects: Category Theory (math.CT)

We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions, reflective factorization systems, and categories of algebras for idempotent monads. This is a further development of the theory of monads and factorization systems for derivators.

[117]
Title: Grothendieck-Lefschetz for vector bundles
Comments: 7 pages
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)

According to the Grothendieck-Lefschetz theorem from SGA 2, there are no nontrivial line bundles on the punctured spectrum $U_R$ of a local ring $R$ that is a complete intersection of dimension $\ge 4$. Dao conjectured a generalization for vector bundles $\mathscr{V}$ of arbitrary rank on $U_R$: such a $\mathscr{V}$ is free if and only if $\mathrm{depth}_R(\mathrm{End}_R(\Gamma(U_R, \mathscr{V}))) \ge 4$. We use deformation theoretic techniques to settle Dao's conjecture. We also present examples showing that its assumptions are sharp.

[118]
Title: P-adic Asai L-functions of Bianchi modular forms
Comments: 27 pages
Subjects: Number Theory (math.NT)

The Asai (or twisted tensor) $L$-function of a Bianchi modular form $\Psi$ is the $L$-function attached to the tensor induction to $\mathbb{Q}$ of its associated Galois representation. In this paper, when $\Psi$ is ordinary at $p$ we construct a $p$-adic analogue of this $L$-function: that is, a $p$-adic measure on $\mathbb{Z}_p^\times$ that interpolates the critical values of the Asai $L$-function twisted by Dirichlet characters of $p$-power conductor. The construction uses techniques analogous to those used by Lei, Zerbes and the first author in order to construct an Euler system attached to the Asai representation of a quadratic Hilbert modular form.

[119]
Title: Half-space Macdonald processes
Comments: 106 pages, 17 figures
Subjects: Probability (math.PR); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Combinatorics (math.CO)

Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the integrability of many probabilistic systems, including the Kardar-Parisi-Zhang (KPZ) equation and a number of other models in its universality class. In this paper we develop the structural theory behind half-space variants of these models and the corresponding half-space Macdonald processes. These processes are built using a Littlewood summation identity instead of the Cauchy identity, and their analysis is considerably harder than their full-space counterparts.
We compute moments and Laplace transforms of observables for general half-space Macdonald measures. Introducing new dynamics preserving this class of measures, we relate them to various stochastic processes, in particular the log-gamma polymer in a half-quadrant (they are also related to the stochastic six-vertex model in a half-quadrant and the half-space ASEP). For the polymer model, we provide explicit integral formulas for the Laplace transform of the partition function. Non-rigorous saddle point asymptotics yield convergence of the directed polymer free energy to either the Tracy-Widom GOE, GSE or the Gaussian distribution depending on the average size of weights on the boundary.

[120]
Title: Achievable Rate of Private Function Retrieval from MDS Coded Databases
Comments: 5 pages, 1 table, submitted for publication
Subjects: Information Theory (cs.IT); Information Retrieval (cs.IR)

We study the problem of private function retrieval (PFR) in a distributed storage system. In PFR the user wishes to retrieve a linear combination of $M$ messages stored in non-colluding $(N,K)$ MDS coded databases while revealing no information about the coefficients of the intended linear combination to any of the individual databases. We present an achievable scheme for MDS coded PFR with a rate that matches the capacity for coded private information retrieval derived recently, $R=(1+R_c+R_c^2+\dots+R_c^{M-1})^{-1}=\frac{1-R_c}{1-R_c^M}$, where $R_c=\frac{K}{N}$ is the rate of the MDS code. This achievable rate is tight in some special cases.

[121]
Title: Thresholds for vanishing of Isolated' faces in random Čech and Vietoris-Rips complexes
Comments: 29 pages, 1 figure
Subjects: Probability (math.PR); Combinatorics (math.CO)

We study combinatorial connectivity for two models of random geometric complexes. These two models - \v{C}ech and Vietoris-Rips complexes - are built on a homogeneous Poisson point process of intensity $n$ on a $d$-dimensional torus using balls of radius $r_n$. In the former, the $k$-simplices/faces are formed by subsets of $(k+1)$ Poisson points such that the balls of radius $r_n$ centred at these points have a mutual interesection and in the latter, we require only a pairwise intersection of the balls. Given a (simplicial) complex (i.e., a collection of $k$-simplices for all $k \geq 1$), we can connect $k$-simplices via $(k+1)$-simplices (up-connectivity') or via $(k-1)$-simplices (down-connectivity). Our interest is to understand these two combinatorial notions of connectivity for the random \v{C}ech and Vietoris-Rips complexes asymptically as $n \to \infty$. In particular, we analyse in detail the threshold radius for vanishing of isolated $k$-faces for up and down connectivity of both types of random geometric complexes. Though it is expected that the threshold radius $r_n = \Theta((\frac{\log n}{n})^{1/d})$ in coarse scale, our results give tighter bounds on the constants in the logarithmic scale as well as shed light on the possible second-order correction factors. Further, they also reveal interesting differences between the phase transition in the \v{C}ech and Vietoris-Rips cases. The analysis is interesting due to the non-monotonicity of the number of isolated $k$-faces (as a function of the radius) and leads one to consider `monotonic' vanishing of isolated $k$-faces. The latter coincides with the vanishing threshold mentioned above at a coarse scale (i.e., $\log n$ scale) but differs in the $\log \log n$ scale for the \v{C}ech complex with $k = 1$ in the up-connected case.

[122]
Title: Proper holomorphic mappings onto symmetric products of a Riemann surface
Comments: 16 pages
Subjects: Complex Variables (math.CV); Algebraic Geometry (math.AG)

We show that the structure of proper holomorphic maps between the $n$-fold symmetric products, $n\geq 2$, of a pair of non-compact Riemann surfaces $X$ and $Y$, provided these are reasonably nice, is very rigid. Specifically, any such map is determined by a proper holomorphic map of $X$ onto $Y$. This extends existing results concerning bounded planar domains, and is a non-compact analogue of a phenomenon observed in symmetric products of compact Riemann surfaces. Along the way, we also provide a condition for the complete hyperbolicity of all $n$-fold symmetric products of a non-compact Riemann surface.

[123]
Title: Bounds on mean energy in the Kuramoto-Sivashinsky equation computed using semidefinite programming
Comments: 32 pages, 6 figures
Subjects: Dynamical Systems (math.DS); Numerical Analysis (math.NA); Fluid Dynamics (physics.flu-dyn)

We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov functionals but satisfy different inequalities. The inequalities are enforced by requiring certain expressions to be sums of squares of polynomials, and the optimal choice of auxiliary functional is posed as a semidefinite program (SDP) that can be solved computationally. To formulate these SDPs we approximate the PDE by truncated systems of ODEs and proceed in one of two ways. The first approach is to compute bounds for the ODE systems, increasing the truncation order until bounds converge numerically. The second approach incorporates the ODE systems with analytical estimates on their deviation from the PDE, thereby using finite truncations to produce bounds for the full PDE. We apply both methods to the Kuramoto-Sivashinsky equation. In particular, we compute upper bounds on the spatiotemporal average of energy by employing polynomial auxiliary functionals up to degree six. The first approach is used for most computations, but a subset of results are checked using the second approach, and the results agree to high precision. These bounds apply to all odd solutions of period $2\pi L$, where $L$ is varied. Sharp bounds are obtained for $L\le10$, and trends suggest that more expensive computations would yield sharp bounds at larger $L$ also. The bounds are known to be sharp (to within 0.1% numerical error) because they are saturated by the simplest nonzero steady states, which apparently have the largest mean energy among all odd solutions. Prior authors have conjectured that mean energy remains $O(1)$ for $L\gg1$ since no particular solutions with larger energy have been found. Our bounds constitute the first positive evidence for this conjecture, albeit up to finite $L$, and offer guidance for analytical proofs.

### Cross-lists for Fri, 23 Feb 18

[124]  arXiv:1606.07678 (cross-list from nlin.PS) [pdf, other]
Title: On solutions of a Boussinesq-type equation with amplitude-dependent nonlinearities: the case of biomembranes
Subjects: Pattern Formation and Solitons (nlin.PS); Mathematical Physics (math-ph)

Boussinesq-type wave equations involve nonlinearities and dispersion. In this paper a Boussinesq-type equation with amplitude-dependent nonlinearities is presented. Such a model was proposed by Heimburg and Jackson (2005) for describing longitudinal waves in biomembranes and later improved by Engelbrecht et al. (2015) taking into account the microinertia of a biomembrane. The steady solution in the form of a solitary wave is derived and the influence of nonlinear and dispersive terms over a large range of possible sets of coefficients demonstrated. The solutions emerging from arbitrary initial inputs are found using the numerical simulation. The properties of emerging trains of solitary waves waves are analysed. Finally, the interaction of solitary waves which satisfy the governing equation is studied. The interaction process is not fully elastic and after several interactions radiation effects may be significant. This means that for the present case the solitary waves are not solitons in the strict mathematical sense. However, like in other cases known in solid mechanics, such solutions may be conditionally called solitons.

[125]  arXiv:1706.06499 (cross-list from cond-mat.str-el) [pdf, other]
Title: The splitting of electrons
Authors: Eoin Quinn
Comments: Focus switched to the purely electronic model. Derivation of an expansion in the strength of correlated hopping included. Notations and conventions improved. Discussion of large-S limit postponed, previous versions implicitly suppress spin correlations which drive ordering
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

We obtain a controlled description of a strongly correlated regime of electronic behaviour. We begin by arguing that there are two ways to characterise the electronic degree of freedom, either by the canonical fermion algebra or the graded Lie algebra su(2|2). The first underlies the Fermi liquid description of correlated matter, and we identify a novel regime governed by the latter. We exploit an exceptional central extension of su(2|2) to employ a perturbative scheme recently developed by Shastry, and obtain a series of successive approximations for the electronic Green's function. We then focus on the leading approximation, which reveals a splitting in two of the electronic dispersion. The Luttinger sum rule is violated, and a Mott metal-insulator transition is exhibited. We offer a perspective.

[126]  arXiv:1707.05371 (cross-list from math-ph) [pdf, ps, other]
Title: Comparing Classical and Relativistic Kinematics in First-Order Logic
Comments: 58 pages, 10 figures
Subjects: Mathematical Physics (math-ph); Logic (math.LO)

The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics. We show that the axioms of special relativity can be interpreted in the language of classical kinematics. This means that there is a logical translation function from the language of special relativity to the language of classical kinematics which translates the axioms of special relativity into consequences of classical kinematics. We will also show that if we distinguish a class of observers (representing observers stationary with respect to the "Ether") in special relativity and exclude the non-slower-than light observers from classical kinematics by an extra axiom, then the two theories become definitionally equivalent (i.e., they become equivalent theories in the sense as the theory of lattices as algebraic structures is the same as the theory of lattices as partially ordered sets). Furthermore, we show that classical kinematics is definitionally equivalent to classical kinematics with only slower-than-light inertial observers, and hence by transitivity of definitional equivalence that special relativity theory extended with "Ether" is definitionally equivalent to classical kinematics. So within an axiomatic framework of mathematical logic, we explicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no "Ether", accompanied by a redefinition of the concepts of time and space.

[127]  arXiv:1802.00813 (cross-list from hep-th) [pdf, other]
Title: Geometric engineering on flops of length two
Comments: 41 pages, 6 figures, 1 appendix
Subjects: High Energy Physics - Theory (hep-th); Algebraic Geometry (math.AG)

Type IIA on the conifold is a prototype example for engineering QED with one charged hypermultiplet. The geometry admits a flop of length one. In this paper, we study the next generation of geometric engineering on singular geometries, namely flops of length two such as Laufer's example, which we affectionately think of as the conifold 2.0. Type IIA on the latter geometry gives QED with higher-charge states. In type IIB, even a single D3-probe gives rise to a nonabelian quiver gauge theory. We study this class of geometries explicitly by leveraging their quiver description, showing how to parametrize the exceptional curve, how to see the flop transition, and how to find the noncompact divisors intersecting the curve. With a view towards F-theory applications, we show how these divisors contribute to the enhancement of the Mordell--Weil group of the local elliptic fibration defined by Laufer's example.

[128]  arXiv:1802.05427 (cross-list from eess.SP) [pdf, other]
Title: Implementation of Massive MIMO Uplink Receiver on RaPro Prototyping Platform
Comments: 14 pages, 10 figures
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT)

The updated physical layer standard of the fifth generation wireless communication suggests the necessity of a rapid prototyping platform. To this end, we develop RaPro, a multi-core general purpose processor-based massive multiple-input-multiple-output (MIMO) prototyping platform. To enhance RaPro, high performance detection and beamforming are needed, whereas both of them request for accurate channel state information (CSI). In this paper, linear minimum mean square error (LMMSE)-based channel estimator is adopted and encapsulated inside RaPro to gain more accurate CSI. Considering the high comlexity and unknown of channel statistics, we design low-complexity LMMSE channel estimator to alleviate the rising complexity along with increasing antenna number and set more computational resource aside for massive MIMO uplink detection and downlink beamforming. Simulation results indicate the high mean square error performance and robustness of designed low-complexity method. Indoor and corridor scenario tests show prominent improvement in bit error rate performance. Time cost analysis proves the practical use and real-time transmission ability of the implemented uplink receiver on RaPro.

[129]  arXiv:1802.07601 (cross-list from cs.CE) [pdf, other]
Title: Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space
Subjects: Computational Engineering, Finance, and Science (cs.CE); Numerical Analysis (math.NA)

This work focuses on the development of a non-conforming domain decomposition method for the approximation of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a discrete number of Lagrange multipliers defined over the interfaces of adjacent subdomains. The method falls into the class of primal hybrid methods, which also include the well-known mortar method. Differently from the mortar method, we discretize the space of basis functions on the interface by spectral approximation independently of the discretization of the two adjacent domains; one of the possible choices is to approximate the interface variational space by Fourier basis functions. As we show in the numerical simulations, our approach is well-suited for the solution of problems with non-conforming meshes or with finite element basis functions with different polynomial degrees in each subdomain. Another application of the method that still needs to be investigated is the coupling of solutions obtained from otherwise incompatible methods, such as the finite element method, the spectral element method or isogeometric analysis.

[130]  arXiv:1802.07809 (cross-list from physics.soc-ph) [pdf, other]
Title: Communication Melting in Graphs and Complex Networks
Comments: 39 pages, 11 figures
Subjects: Physics and Society (physics.soc-ph); Combinatorics (math.CO); Pattern Formation and Solitons (nlin.PS)

Complex networks are the representative graphs of interactions in many complex systems. Usually, these interactions are abstractions of the communication/diffusion channels between the units of the system. Real complex networks, e.g. traffic networks, reveal different operation phases governed by the dynamical stress of the system. Here we show how, communicability, a topological descriptor that reveals the efficiency of the network functionality in terms of these diffusive paths, could be used to reveal the transitions mentioned. By considering a vibrational model of nodes and edges in a graph/network at a given temperature (stress), we show that the communicability function plays the role of the thermal Green's function of a network of harmonic oscillators. After, we prove analytically the existence of a universal phase transition in the communicability structure of every simple graph. This transition resembles the melting process occurring in solids. For instance, regular-like graphs resembling crystals, melts at lower temperatures and display a sharper transition between connected to disconnected structures than the random spatial graphs, which resemble amorphous solids. Finally, we study computationally this graph melting process in some real-world networks and observe that the rate of melting of graphs changes either as an exponential or as a power-law with the inverse temperature. At the local level we discover that the main driver for node melting is the eigenvector centrality of the corresponding node, particularly when the critical value of the inverse temperature approaches zero. These universal results sheds light on many dynamical diffusive-like processes on networks that present transitions as traffic jams, communication lost or failure cascades.

[131]  arXiv:1802.07883 (cross-list from physics.optics) [pdf, other]
Title: Non-invasive imaging through random media
Subjects: Optics (physics.optics); Probability (math.PR)

When waves propagate through a strongly scattering medium the energy is transferred to the incoherent wave part by scattering. The wave intensity then forms a random speckle pattern seemingly without much useful information. However, a number of recent physical experiments show how one can extract useful information from this speckle pattern. Here we present the mathematical analysis that explains the quite stunning performance of such a scheme for speckle imaging. Our analysis identifies a scaling regime where the scheme works well. This regime is the white-noise paraxial regime, which leads to the Ito-Schrodinger model for the wave amplitude. The results presented in this paper conform with the sophisticated physical intuition that has motivated these schemes, but give a more detailed characterization of the performance.
The analysis gives a description of (i) the information that can be extracted and with what resolution (ii) the statistical stability or signal-to-noise ratio with which the information can be extracted.

[132]  arXiv:1802.07889 (cross-list from cs.LG) [pdf, ps, other]
Title: Entropy Rate Estimation for Markov Chains with Large State Space
Subjects: Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)

Estimating the entropy based on data is one of the prototypical problems in distribution property testing and estimation. For estimating the Shannon entropy of a distribution on $S$ elements with independent samples, [Paninski2004] showed that the sample complexity is sublinear in $S$, and [Valiant--Valiant2011] showed that consistent estimation of Shannon entropy is possible if and only if the sample size $n$ far exceeds $\frac{S}{\log S}$. In this paper we consider the problem of estimating the entropy rate of a stationary reversible Markov chain with $S$ states from a sample path of $n$ observations. We show that:
(1) As long as the Markov chain mixes not too slowly, i.e., the relaxation time is at most $O(\frac{S}{\ln^3 S})$, consistent estimation is achievable when $n \gg \frac{S^2}{\log S}$.
(2) As long as the Markov chain has some slight dependency, i.e., the relaxation time is at least $1+\Omega(\frac{\ln^2 S}{\sqrt{S}})$, consistent estimation is impossible when $n \lesssim \frac{S^2}{\log S}$.
Under both assumptions, the optimal estimation accuracy is shown to be $\Theta(\frac{S^2}{n \log S})$. In comparison, the empirical entropy rate requires at least $\Omega(S^2)$ samples to be consistent, even when the Markov chain is memoryless. In addition to synthetic experiments, we also apply the estimators that achieve the optimal sample complexity to estimate the entropy rate of the English language in the Penn Treebank and the Google One Billion Words corpora, which provides a natural benchmark for language modeling and relates it directly to the widely used perplexity measure.

[133]  arXiv:1802.07932 (cross-list from cs.SC) [pdf, ps, other]
Title: Faster integer multiplication using short lattice vectors
Comments: 16 pages
Subjects: Symbolic Computation (cs.SC); Data Structures and Algorithms (cs.DS); Number Theory (math.NT)

We prove that $n$-bit integers may be multiplied in $O(n \log n \, 4^{\log^* n})$ bit operations. This complexity bound had been achieved previously by several authors, assuming various unproved number-theoretic hypotheses. Our proof is unconditional, and depends in an essential way on Minkowski's theorem concerning lattice vectors in symmetric convex sets.

[134]  arXiv:1802.08011 (cross-list from hep-th) [pdf, ps, other]
Title: Ruijsenaars-Schneider models with extended supersymmetry
Authors: Anton Galajinsky
Comments: 9 pages
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N=2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism.

[135]  arXiv:1802.08050 (cross-list from hep-th) [pdf, other]
Title: Renormalization Group Flow of the Aharonov-Bohm Scattering Amplitude
Comments: 23 pages; 6 figures
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

The Aharonov-Bohm elastic scattering with incident particles described by plane waves is revisited by using the phase-shifts method. The formal equivalence between the cylindrical Schr\"odinger equation and the one-dimensional Calogero problem allows us to show that up to two scattering phase-shifts modes in the cylindrical waves expansion must be renormalized. The renormalization procedure introduces new length scales giving rise to spontaneous breaking of the conformal symmetry. The new renormalized cross-section has an amazing property of being non-vanishing even for a quantized magnetic flux, coinciding with the case of Dirac delta function potential. The knowledge of the exact beta function permits us to describe the renormalization group flows within the two-parametric family of renormalized Aharonov-Bohm scattering amplitudes. Our analysis demonstrates that for quantized magnetic fluxes a BKT-like phase transition at the coupling space occurs.

[136]  arXiv:1802.08054 (cross-list from cs.LG) [pdf, other]
Title: VBALD - Variational Bayesian Approximation of Log Determinants
Subjects: Learning (cs.LG); Information Theory (cs.IT)

Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discrete graphical models. In order to avoid the canonical, yet prohibitive, Cholesky $\mathcal{O}(n^{3})$ computational cost, we propose a novel approach, with complexity $\mathcal{O}(n^{2})$, based on a constrained variational Bayes algorithm. We compare our method to Taylor, Chebyshev and Lanczos approaches and show state of the art performance on both synthetic and real-world datasets.

[137]  arXiv:1802.08135 (cross-list from q-fin.TR) [pdf, other]
Title: Optimal inventory management and order book modeling
Authors: Nicolas Baradel (CEREMADE, ENSAE), Bruno Bouchard (CEREMADE, PSL), David Evangelista (KAUST), Othmane Mounjid (CMAP)
Subjects: Trading and Market Microstructure (q-fin.TR); Probability (math.PR)

We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [14, 20, 21], the MM and the HFT define their trading strategy by optimizing the expected utility of terminal wealth, while the IB has a prescheduled task to sell or buy many shares of the considered asset. We derive the variational partial differential equations that characterize the value functions of the MM and HFT and explain how almost optimal control can be deduced from them. We then provide a first illustration of the interactions that can take place between these different market participants by simulating the dynamic of an order book in which each of them plays his own (optimal) strategy.

[138]  arXiv:1802.08154 (cross-list from eess.SP) [pdf, other]
Title: Sliding Bidirectional Recurrent Neural Networks for Sequence Detection in Communication Systems
Comments: accepted for publication in the proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2018. arXiv admin note: text overlap with arXiv:1802.02046 and arXiv:1705.08044
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT); Learning (cs.LG)

The design and analysis of communication systems typically rely on the development of mathematical models that describe the underlying communication channel. However, in some systems, such as molecular communication systems where chemical signals are used for transfer of information, the underlying channel models are unknown. In these scenarios, a completely new approach to design and analysis is required. In this work, we focus on one important aspect of communication systems, the detection algorithms, and demonstrate that by using tools from deep learning, it is possible to train detectors that perform well without any knowledge of the underlying channel models. We propose a technique we call sliding bidirectional recurrent neural network (SBRNN) for real-time sequence detection. We evaluate this algorithm using experimental data that is collected by a chemical communication platform, where the channel model is unknown and difficult to model analytically. We show that deep learning algorithms perform significantly better than a detector proposed in previous works, and the SBRNN outperforms other techniques considered in this work.

[139]  arXiv:1802.08227 (cross-list from quant-ph) [pdf, other]
Title: Quantum linear systems algorithms: a primer
Comments: 55 pages, 5 figures, comments welcome
Subjects: Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS); Numerical Analysis (math.NA)

The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of applications, and thus HHL constitutes an important algorithmic primitive. In these notes, we present the HHL algorithm and its improved versions in detail, including explanations of the constituent sub- routines. More specifically, we discuss various quantum subroutines such as quantum phase estimation and amplitude amplification, as well as the important question of loading data into a quantum computer, via quantum RAM. The improvements to the original algorithm exploit variable-time amplitude amplification as well as a method for implementing linear combinations of unitary operations (LCUs) based on a decomposition of the operators using Fourier and Chebyshev series. Finally, we discuss a linear solver based on the quantum singular value estimation (QSVE) subroutine.

[140]  arXiv:1802.08242 (cross-list from stat.ME) [pdf, other]
Title: Structured low-rank matrix completion for forecasting in time series analysis
Comments: 25 pages, 12 figures
Subjects: Methodology (stat.ME); Systems and Control (cs.SY); Numerical Analysis (math.NA); Machine Learning (stat.ML)

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices and a convex relaxation based on the nuclear norm. Based on new theoretical results and a number of numerical and real examples, we investigate the cases when the proposed approach can work. Our results highlight the importance of choosing a proper weighting scheme for the known observations.

### Replacements for Fri, 23 Feb 18

[141]  arXiv:1111.2174 (replaced) [pdf, ps, other]
Title: Small Covers, infra-solvmanifolds and curvature
Comments: 22 pages, no figure
Journal-ref: Forum Mathematicum 27 (2015), no. 5, 2981-3004
Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT); Combinatorics (math.CO)
[142]  arXiv:1303.3575 (replaced) [pdf, ps, other]
Title: Lie algebras responsible for zero-curvature representations of scalar evolution equations
Comments: 39 pages; v3: new examples and results added, a coauthor added, exposition improved
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Rings and Algebras (math.RA)
[143]  arXiv:1312.7449 (replaced) [pdf, other]
Title: Extinction times in the subcritical stochastic SIS logistic epidemic
Comments: Revised; 34 pages; 6 figures
Journal-ref: Journal of Mathematical Biology, 2018
Subjects: Probability (math.PR)
[144]  arXiv:1410.2906 (replaced) [pdf, ps, other]
Title: The emergence of torsion in the continuum limit of distributed edge-dislocations
Comments: See an erratum regarding Definition 4.1 and Lemma 4.8 in arxiv:1701.08903 (v3 is the same as v2 but for this comment)
Subjects: Differential Geometry (math.DG)
[145]  arXiv:1411.5308 (replaced) [pdf, ps, other]
Title: Koszulity of directed categories in representation stability theory
Comments: Published version
Subjects: Representation Theory (math.RT); Algebraic Topology (math.AT); Rings and Algebras (math.RA)
[146]  arXiv:1503.05436 (replaced) [pdf, other]
Title: Inference in Additively Separable Models With a High-Dimensional Set of Conditioning Variables
Authors: Damian Kozbur
Subjects: Statistics Theory (math.ST)
[147]  arXiv:1505.06371 (replaced) [pdf, ps, other]
Title: Unique equilibrium states for Bonatti-Viana diffeomorphisms
Comments: 46 pages, 2 figures. In response to referee reports, we added an appendix on the regularity of the geometric potential, and made other suggested minor changes. Accepted for publication in Nonlinearity
Subjects: Dynamical Systems (math.DS)
[148]  arXiv:1508.00268 (replaced) [pdf, ps, other]
Title: New and old results on spherical varieties via moduli theory
Comments: v3: 45 pages, minor improvements, final version
Journal-ref: Advances in Mathematics, vol. 328 (2018), 1299-1352
Subjects: Algebraic Geometry (math.AG); Representation Theory (math.RT)
[149]  arXiv:1511.01163 (replaced) [pdf, ps, other]
Title: Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses
Comments: Corrected more typos
Journal-ref: Journal of Statistical Physics 167 (2017), 383-415
Subjects: Probability (math.PR); Mathematical Physics (math-ph); Combinatorics (math.CO)
[150]  arXiv:1512.00495 (replaced) [pdf, ps, other]
Title: Strongly étale difference algebras and Babbitt's decomposition
Comments: 22 pages, minor changes, several examples added
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
[151]  arXiv:1512.09028 (replaced) [pdf, other]
Title: The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2
Comments: 31 pages, 5 figures, 1 table, improvements in the algorithms
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
[152]  arXiv:1601.04726 (replaced) [pdf, ps, other]
Title: Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial Gauge
Authors: Timothy Nguyen
Comments: 28 pages. Results of paper are deprecated and now subsumed by arxiv:1508.06305. However, the perspectives and different techniques here are still noteworthy
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Differential Geometry (math.DG)
[153]  arXiv:1604.00424 (replaced) [pdf, other]
Title: Local sparsity and recovery of fusion frames structured signals
Comments: 7 figures, 24 pages
Subjects: Information Theory (cs.IT)
[154]  arXiv:1604.00437 (replaced) [pdf, ps, other]
Title: A priori estimates for rough PDEs with application to rough conservation laws
Comments: 55 pages, substantially revised version
Subjects: Analysis of PDEs (math.AP); Probability (math.PR)
[155]  arXiv:1604.01616 (replaced) [pdf, ps, other]
Title: A local characterization of Kazhdan projections and applications
Comments: 31 pages. v2: small changes to the introduction. Added a discussion on the speed of convergence, and on a notion of positivity for Kazhdan constants (p 14). This version was submitted to a journal v3: small changes to the presentation, background details added on Banach space geometry. Accepted for publication to Commentarii Mathematici Helvetici
Subjects: Functional Analysis (math.FA); Group Theory (math.GR); Operator Algebras (math.OA)
[156]  arXiv:1606.00249 (replaced) [pdf, ps, other]
Title: Strong Klee-Andô Theorems through an Open Mapping Theorem for cone-valued multi-functions
Comments: Major rewrite. Large parts were removed which a referee pointed out can be proven through much easier methods
Subjects: Functional Analysis (math.FA)
[157]  arXiv:1606.01294 (replaced) [pdf, ps, other]
Title: Congruence primes for automorphic forms on unitary groups and applications to the arithmetic of Ikeda lifts
Comments: 37 pages; slightly strengthened Theorem 3.5, added Remarks 3.6 and 8.1. Added section 9 with examples and made a few minor modifications throughout. To appear in Kyoto J. Math
Subjects: Number Theory (math.NT)
[158]  arXiv:1606.05140 (replaced) [src]
Title: Characterizing Relative Frame Definability in Team Semantics via the Universal Modality
Comments: Preprint of a WoLLIC 2016 paper. This preprint has been merged with and superseded by a preprint arXiv:1502.07884
Subjects: Logic (math.LO)
[159]  arXiv:1608.05835 (replaced) [pdf, ps, other]
Title: On the separability of the underlying space of a scheme
Comments: 13 pages
Subjects: Commutative Algebra (math.AC)
[160]  arXiv:1608.07016 (replaced) [pdf, ps, other]
Title: Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals
Authors: Konrad Aguilar
Comments: 42 pages. Sections 3 and 4 condensed into one section as stronger results were found that shortened many proofs. The article arXiv:1608.07016v1 was split into this current version and the new article arXiv:1612.02404 due to length
Subjects: Operator Algebras (math.OA); Functional Analysis (math.FA)
[161]  arXiv:1609.00027 (replaced) [pdf, ps, other]
Title: The Riemann zeta function and Gaussian multiplicative chaos: statistics on the critical line
Comments: Supersedes arXiv:1604.08378. Version 2 contains a limit theorem describing the mesoscopic behavior of the characteristic polynomial of random unitary matrices
Subjects: Probability (math.PR); Number Theory (math.NT)
[162]  arXiv:1609.00947 (replaced) [pdf, ps, other]
Title: On the finiteness of minimal and maximal spectra
Comments: 4 pages
Subjects: Commutative Algebra (math.AC)
[163]  arXiv:1609.04558 (replaced) [pdf, ps, other]
Title: Statistical Inference in a Directed Network Model with Covariates
Comments: 31 pages. Revised
Subjects: Methodology (stat.ME); Statistics Theory (math.ST)
[164]  arXiv:1611.00439 (replaced) [pdf]
Title: Paradox with just self-reference
Authors: T. Parent
Subjects: Logic (math.LO)
[165]  arXiv:1701.03279 (replaced) [pdf, ps, other]
Title: Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces
Comments: 34 pages. v2: Corrected an error in Definition 2.1 that caused Theorem 2.2 to be false. Numerous other minor corrections and clarifications
Subjects: Algebraic Geometry (math.AG)
[166]  arXiv:1701.05661 (replaced) [pdf, other]
Title: Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media
Authors: Shane Cooper
Subjects: Analysis of PDEs (math.AP); Spectral Theory (math.SP)
[167]  arXiv:1701.07522 (replaced) [pdf, other]
Title: Joint Uplink-Downlink Cell Associations for Interference Networks with Local Connectivity
Comments: 10 pages, Part of this work was in proc. 55th Annual Allerton Conference on Communication, Control, and Computing, Oct. 2017. Also, part of this work is submitted to International Symposium of Information Theory (ISIT 2018)
Subjects: Information Theory (cs.IT)
[168]  arXiv:1701.07990 (replaced) [pdf, ps, other]
Title: Minimal free resolutions of lattice ideals of digraphs
Comments: 40 pages
Subjects: Commutative Algebra (math.AC); Combinatorics (math.CO)
[169]  arXiv:1701.08903 (replaced) [pdf, ps, other]
Title: The emergence of torsion in the continuum limit of distributed edge-dislocations - erratum
Comments: v2: includes references to the numbering (of lemmas) in the arXiv version of the article (arXiv:1410.2906), which differs from the published version; otherwise v2 is the same as v1
Subjects: Differential Geometry (math.DG)
[170]  arXiv:1702.03873 (replaced) [pdf, ps, other]
Title: Measure-geometric Laplacians for discrete distributions
Comments: 8 pages, 4 figures
Subjects: Dynamical Systems (math.DS); Functional Analysis (math.FA); Spectral Theory (math.SP)
[171]  arXiv:1702.05636 (replaced) [pdf, ps, other]
Title: $(\varphi, Γ)$-modules de de Rham et fonctions $L$ $p$-adiques
Comments: 39 pages, submitted. In french. Minor modifications following the referees comments
Subjects: Number Theory (math.NT)
[172]  arXiv:1702.05702 (replaced) [pdf, ps, other]
Title: Dynamic Data-Driven Estimation of Non-Parametric Choice Models
Subjects: Optimization and Control (math.OC)
[173]  arXiv:1702.08281 (replaced) [pdf, ps, other]
Title: Abstract elementary classes stable in $\aleph_0$
Comments: 27 pages
Subjects: Logic (math.LO)
[174]  arXiv:1704.00650 (replaced) [pdf, ps, other]
Title: A Central Limit Theorem for Vincular Permutation Patterns
Authors: Lisa Hofer
Comments: 22 pages, v3: minor modifications including a new section about Stein's method, according to the referee's comments
Subjects: Combinatorics (math.CO); Probability (math.PR)
[175]  arXiv:1704.04841 (replaced) [pdf, ps, other]
Title: Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches
Comments: 16 pages, Contribution for the proceedings of QMath13: Mathematical Results in Quantum Physics, Atlanta, 2016
Subjects: Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[176]  arXiv:1704.07479 (replaced) [pdf, other]
Title: A direct method for reconstructing inclusions and boundary conditions from electrostatic data
Subjects: Analysis of PDEs (math.AP)
[177]  arXiv:1705.00882 (replaced) [pdf, ps, other]
Title: Asymptotic behaviors of representations of graded categories with inductive functors
Comments: Minor revisions
Subjects: Representation Theory (math.RT); Commutative Algebra (math.AC); K-Theory and Homology (math.KT); Rings and Algebras (math.RA)
[178]  arXiv:1705.01188 (replaced) [pdf, other]
Title: Dynamics of Virus and Immune Response in Multi-Epitope Network
Comments: Revised preprint, to appear in Journal of Mathematical Biology
Subjects: Populations and Evolution (q-bio.PE); Dynamical Systems (math.DS)
[179]  arXiv:1705.01755 (replaced) [pdf, ps, other]
Title: Quantum Klein Space and Superspace
Comments: 1+22 pages, 1 Table. v2 : discussion improved, ref. added
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Algebra (math.QA)
[180]  arXiv:1705.04296 (replaced) [pdf, other]
Title: Displayed Categories
Comments: v2: Slightly revised and expanded. Theorem numbering unchanged up to Prop. 45
Subjects: Category Theory (math.CT); Logic (math.LO)
[181]  arXiv:1706.00364 (replaced) [pdf, other]
Title: A new stochastic STDP Rule in a neural Network Model
Authors: Pascal Helson
Subjects: Probability (math.PR)
[182]  arXiv:1706.01713 (replaced) [pdf, other]
Title: A Birational Anabelian Reconstruction Theorem for Curves over Algebraically Closed Fields in Arbitrary Characteristic
Authors: Martin Lüdtke
Comments: 15 pages, final version accepted by the journal
Subjects: Algebraic Geometry (math.AG)
[183]  arXiv:1706.02612 (replaced) [pdf, other]
Title: Strong Forms of Stability from Flag Algebra Calculations
Comments: 44 pages; incorporates reviewers' suggestions
Subjects: Combinatorics (math.CO)
[184]  arXiv:1706.04839 (replaced) [pdf, ps, other]
Title: Asymptotic normality of high level-large time crossings of a Gaussian process
Comments: 18 pages, corrected version
Subjects: Probability (math.PR)
[185]  arXiv:1707.07293 (replaced) [pdf, ps, other]
Title: On the number of cyclic subgroups of a finite group
Subjects: Group Theory (math.GR)
[186]  arXiv:1707.07350 (replaced) [pdf, ps, other]
Title: Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries
Comments: 29 pages; minor changes, and a lemma added on convergence of Laplace transforms and weak convergence
Subjects: Probability (math.PR)
[187]  arXiv:1708.01403 (replaced) [pdf, ps, other]
Title: Optimal Throughput Fairness Trade-offs for Downlink Non-Orthogonal Multiple Access over Fading Channels
Comments: 35 pages, 10 figures, 3 tables, the longer version of the paper with the same title
Subjects: Information Theory (cs.IT); Networking and Internet Architecture (cs.NI)
[188]  arXiv:1708.02658 (replaced) [pdf, ps, other]
Title: The universal connection for principal bundles over homogeneous spaces and twistor space of coadjoint orbits
Comments: 31 pages
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG)
[189]  arXiv:1708.03199 (replaced) [pdf, ps, other]
Title: On the Zariski compactness of minimal spectrum and flat compactness of maximal spectrum
Comments: 9 pages
Subjects: Commutative Algebra (math.AC)
[190]  arXiv:1708.05503 (replaced) [pdf, ps, other]
Title: Equidistribution of signs for Hilbert modular forms of half-integral weight
Comments: To appear in Research in Number Theory
Subjects: Number Theory (math.NT)
[191]  arXiv:1708.06264 (replaced) [pdf, ps, other]
Title: Remarks on the Gaudin model modulo $p$
Comments: Latex, v2 and v3: misprints corrected, v4: misprints corrected, a reference added
Subjects: Algebraic Geometry (math.AG); Mathematical Physics (math-ph); Number Theory (math.NT); Quantum Algebra (math.QA)
[192]  arXiv:1708.06279 (replaced) [pdf, other]
Title: Asymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equation
Subjects: Numerical Analysis (math.NA)
[193]  arXiv:1708.08287 (replaced) [pdf, other]
Title: Robust Viability Analysis of a Controlled Epidemiological Model
Comments: arXiv admin note: text overlap with arXiv:1510.01055
Subjects: Optimization and Control (math.OC)
[194]  arXiv:1709.00175 (replaced) [pdf, ps, other]
Title: Homological dimension of isogeny categories of commutative algebraic groups
Authors: Michel Brion
Comments: Proof of Lemma 3.8 corrected; further minor changes
Subjects: Algebraic Geometry (math.AG)
[195]  arXiv:1709.01426 (replaced) [pdf, ps, other]
Title: A fresh look into monoid rings and formal power series rings
Comments: 15 pages
Subjects: Commutative Algebra (math.AC)
[196]  arXiv:1709.03331 (replaced) [pdf, ps, other]
Title: Twin subgraphs and core-semiperiphery-periphery structures
Authors: Ricardo Riaza
Subjects: Combinatorics (math.CO)
[197]  arXiv:1709.06046 (replaced) [pdf, ps, other]
Title: Is the Multiset of $n$ Integers Uniquely Determined by the Multiset of Its $s$-sums?
Authors: Dmitri Fomin
Subjects: Number Theory (math.NT); History and Overview (math.HO)
[198]  arXiv:1709.09792 (replaced) [pdf, other]
Title: Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: Nonspherical Schwarzschild waves and singularities at null infinity
Comments: 20 pages, 5 figures
Journal-ref: Class. Quantum Grav. 35, 065015 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
[199]  arXiv:1710.00533 (replaced) [pdf, other]
Title: First explicit constrained Willmore minimizers of non-rectangular conformal class
Comments: 65 pages, comments welcome!
Subjects: Differential Geometry (math.DG)
[200]  arXiv:1710.00646 (replaced) [pdf, other]
Title: Optimal heat transfer and optimal exit times
Comments: 16 pages, 5 figures. SIAM LaTeX style with custom margins. Fixed a few typos
Journal-ref: SIAM Journal on Applied Mathematics 78, 591-608 (2018)
Subjects: Fluid Dynamics (physics.flu-dyn); Analysis of PDEs (math.AP)
[201]  arXiv:1710.01067 (replaced) [pdf, other]
Title: Radial symmetry of p-harmonic minimizers
Comments: 18 pages, 2 figures
Subjects: Complex Variables (math.CV)
[202]  arXiv:1710.04640 (replaced) [pdf, other]
Title: Hard and Easy Instances of L-Tromino Tilings
Comments: 15 pages, 17 figures. In v2 all theorems were generalized to aztec rectangles and the exposition of most proofs were improved. Also added Manjil P. Saikia as a new coauthor
Subjects: Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS); Combinatorics (math.CO)
[203]  arXiv:1710.05180 (replaced) [pdf, ps, other]
Title: Space-time $L^2$ estimates, regularity and almost global existence for elastic waves
Subjects: Analysis of PDEs (math.AP)
[204]  arXiv:1710.09251 (replaced) [pdf, ps, other]
Title: Symmetric, separable equivalence of rings
Authors: Lars Kadison
Comments: 9 pages, an addendum to Hokkaido Mathematical Journal 24 (1995), 527-549, additional theorems and improvements
Subjects: Rings and Algebras (math.RA)
[205]  arXiv:1710.10009 (replaced) [pdf, ps, other]
Title: Homotopical Stable Ranks for Certain C*-algebras
Comments: Revised. Submitted
Subjects: Operator Algebras (math.OA)
[206]  arXiv:1710.10704 (replaced) [pdf, other]
Title: Training Probabilistic Spiking Neural Networks with First-to-spike Decoding
Comments: A shorter version will be published on Proc. IEEE ICASSP 2018
Subjects: Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Information Theory (cs.IT); Learning (cs.LG); Neural and Evolutionary Computing (cs.NE)
[207]  arXiv:1711.03291 (replaced) [pdf, other]
Title: Portfolio Optimization and Model Predictive Control: A Kinetic Approach
Subjects: Portfolio Management (q-fin.PM); Analysis of PDEs (math.AP); Optimization and Control (math.OC); Trading and Market Microstructure (q-fin.TR)
[208]  arXiv:1711.03477 (replaced) [pdf, other]
Title: Achievable Rates and Training Overheads for a Measured LOS Massive MIMO Channel
Comments: 4 pages, 5 figures
Journal-ref: IEEE Wireless Communications Letters 2018
Subjects: Information Theory (cs.IT)
[209]  arXiv:1711.08824 (replaced) [pdf, ps, other]
Title: The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal
Subjects: Machine Learning (stat.ML); Information Theory (cs.IT)
[210]  arXiv:1711.09995 (replaced) [pdf, ps, other]
Title: Quiver mutations and Boolean reflection monoids
Comments: 35 pages
Subjects: Rings and Algebras (math.RA); Combinatorics (math.CO); Group Theory (math.GR)
[211]  arXiv:1711.10616 (replaced) [pdf, other]
Title: Bulk diffusion in a kinetically constrained lattice gas
Comments: 29 pages, 12 figures. v2: minor changes
Journal-ref: J. Phys. A: Math. Theor. 51, 125002 (2018)
Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Probability (math.PR); Cellular Automata and Lattice Gases (nlin.CG)
[212]  arXiv:1712.01723 (replaced) [pdf, ps, other]
Title: Lattice homomorphisms between weak orders
Authors: Nathan Reading
Comments: 44 pages, about 5 of which are taken up by figures. Version 2: Minor expository changes, in the abstract and introduction only. Version 3: Added uniform Lie-theoretic proof of root system containment result for Kac-Moody root systems
Subjects: Combinatorics (math.CO)
[213]  arXiv:1712.02082 (replaced) [pdf, ps, other]
Title: Elliptic curves induced by Diophantine triples
Comments: minor corrections, to appear in RACSAM, 15 pages
Subjects: Number Theory (math.NT)
[214]  arXiv:1712.03597 (replaced) [pdf, ps, other]
Title: Exact relations for Green's functions in linear PDE and boundary field equalities: a generalization of conservation laws
Comments: 34 Pages, no figures
Subjects: Analysis of PDEs (math.AP)
[215]  arXiv:1712.05069 (replaced) [pdf, other]
Title: Majorana Fermions and Orthogonal Complex Structures
Comments: 15 pages, 6 figures, typos corrected
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[216]  arXiv:1712.06356 (replaced) [pdf, other]
Title: On convergence of infinite matrix products with alternating factors from two sets of matrices
Authors: Victor Kozyakin
Comments: 6 pages, 12 bibliography references, expanded Section 4 "Remarks and Open Questions"
Subjects: Optimization and Control (math.OC); Rings and Algebras (math.RA)
[217]  arXiv:1712.06575 (replaced) [pdf, other]
Title: Combinatorics of chemical reaction systems
Comments: 33+12 pages, 4 figures
Subjects: Mathematical Physics (math-ph); Combinatorics (math.CO); Probability (math.PR); Applications (stat.AP)
[218]  arXiv:1712.07606 (replaced) [pdf, ps, other]
Title: Bestvina complex for group actions with a strict fundamental domain
Comments: 24 pages, 6 figures. In Theorem 1.2 the assumption that the action on the building is minimal is removed as it always holds. This is shown in Lemma 5.1
Subjects: Group Theory (math.GR); Algebraic Topology (math.AT)
[219]  arXiv:1801.00170 (replaced) [pdf, ps, other]
Title: Robust Optimization under Regime Switching
Comments: 34 pages, 2 figures
Subjects: Optimization and Control (math.OC)
[220]  arXiv:1801.03017 (replaced) [pdf, other]
Title: Stochastic Optimization of Braking Energy Storage and Ventilation in a Subway Station
Subjects: Optimization and Control (math.OC)
[221]  arXiv:1801.04003 (replaced) [pdf, ps, other]
Title: Some techniques in density estimation
Comments: 18 pages; new version includes tight results on mixtures of general Gaussians
Subjects: Statistics Theory (math.ST); Learning (cs.LG)
[222]  arXiv:1801.04504 (replaced) [pdf, other]
Title: Non-Orthogonal Multiple Access for mmWave Drone Networks with Limited Feedback
Subjects: Information Theory (cs.IT)
[223]  arXiv:1801.04695 (replaced) [pdf, other]
Title: Sparsity-based Defense against Adversarial Attacks on Linear Classifiers
Comments: Submitted to IEEE International Symposium on Information Theory (ISIT) 2018. ZM and SG are joint first authors
Subjects: Machine Learning (stat.ML); Information Theory (cs.IT); Learning (cs.LG)
[224]  arXiv:1801.06064 (replaced) [pdf, ps, other]
Title: Boundedness and compactness of commutators associated with Lipschitz functions
Comments: arXiv admin note: text overlap with arXiv:1712.08292
Subjects: Classical Analysis and ODEs (math.CA)
[225]  arXiv:1801.06095 (replaced) [pdf, ps, other]
Title: A Gauss-Jacobi Kernel Compression Scheme for Fractional Differential Equations
Authors: Daniel Baffet
Subjects: Numerical Analysis (math.NA)
[226]  arXiv:1801.06348 (replaced) [pdf, ps, other]
Title: Higher order concentration for functions of weakly dependent random variables
Comments: Added concentration results for some polynomials in Ising models with external fields; streamlined a few proofs
Subjects: Probability (math.PR)
[227]  arXiv:1801.06684 (replaced) [pdf, ps, other]
Title: Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equation
Subjects: Probability (math.PR)
[228]  arXiv:1801.06921 (replaced) [pdf, other]
Title: String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
Authors: Dmitry Tonkonog
Comments: 46 pages, 5 figures; v2: added a proof comparing two versions of descendants, minor intro revision
Subjects: Symplectic Geometry (math.SG); Algebraic Geometry (math.AG); Algebraic Topology (math.AT)
[229]  arXiv:1801.08071 (replaced) [pdf, ps, other]
Title: The $A_{\infty}$-coalgebra Structure on a Closed Compact Surface
Comments: 12 pages, 6 figures. Comments welcome
Subjects: Algebraic Topology (math.AT)
[230]  arXiv:1801.08425 (replaced) [pdf, ps, other]
Title: On Sidorenko's conjecture for determinants and Gaussian Markov random fields
Comments: Significant text overlap with arXiv:1701.03632. In fact, this paper is a significantly expanded version of arXiv:1701.03632 with one new author
Subjects: Combinatorics (math.CO)
[231]  arXiv:1801.10088 (replaced) [pdf, other]
Title: An SPDE Model for Systemic Risk with Endogenous Contagion
Comments: 53 pages, 2 figures
Subjects: Probability (math.PR); Mathematical Finance (q-fin.MF)
[232]  arXiv:1801.10147 (replaced) [pdf, ps, other]
Title: Weak adiabatic limit in quantum field theories with massless particles
Authors: Paweł Duch
Comments: Based on author's PhD thesis arXiv:1709.09907, 64 pages, matches published version
Subjects: Mathematical Physics (math-ph)
[233]  arXiv:1802.01503 (replaced) [pdf, other]
Title: Motivic Chern classes and K-theoretic stable envelopes
Subjects: Algebraic Geometry (math.AG)
[234]  arXiv:1802.01734 (replaced) [pdf, ps, other]
Title: Stochastic parabolic Anderson model with time-homogeneous generalized potential: Mild formulation of solution
Authors: Hyun-Jung Kim
Comments: 17 pages
Subjects: Analysis of PDEs (math.AP)
[235]  arXiv:1802.02447 (replaced) [pdf, ps, other]
Title: Field extensions, Derivations, and Matroids over Skew Hyperfields
Authors: Rudi Pendavingh
Subjects: Combinatorics (math.CO); Algebraic Geometry (math.AG)
[236]  arXiv:1802.02726 (replaced) [pdf, ps, other]
Title: Some counterexamples on recent algorithms constructed by the inverse strongly monotone and the relaxed $(u, v)$-cocoercive mappings
Authors: Ebrahim Soori
Comments: 8 pages
Subjects: Functional Analysis (math.FA)
[237]  arXiv:1802.03569 (replaced) [pdf, other]
Title: Riemannian Manifold Kernel for Persistence Diagrams
Authors: Tam Le, Makoto Yamada
Comments: fixed a misleading typo (p.6)
Subjects: Machine Learning (stat.ML); Learning (cs.LG); Algebraic Topology (math.AT)
[238]  arXiv:1802.04852 (replaced) [pdf, other]
Title: Persistence Codebooks for Topological Data Analysis
Subjects: Machine Learning (stat.ML); Learning (cs.LG); Algebraic Topology (math.AT)
[239]  arXiv:1802.05184 (replaced) [pdf, other]
Title: Enhancing Compressed Sensing Photoacoustic Tomography by Simultaneous Motion Estimation
Subjects: Numerical Analysis (math.NA)
[240]  arXiv:1802.05339 (replaced) [pdf, other]
Title: Two- and Multi-dimensional Curve Fitting using Bayesian Inference
Subjects: Data Analysis, Statistics and Probability (physics.data-an); Instrumentation and Methods for Astrophysics (astro-ph.IM); Statistics Theory (math.ST)
[241]  arXiv:1802.05544 (replaced) [pdf, ps, other]
Title: Integration in terms of exponential integrals and incomplete gamma functions I
Authors: Waldemar Hebisch
Subjects: Number Theory (math.NT); Symbolic Computation (cs.SC)
[242]  arXiv:1802.05557 (replaced) [pdf, other]
Title: The Gauss-Bonnet Theorem for coherent tangent bundles over surfaces with boundary and its applications
Comments: 28 pages, 8 figures
Subjects: Differential Geometry (math.DG)
[243]  arXiv:1802.06726 (replaced) [pdf, other]
Title: On quasi-invariant curves
Comments: 13 pages, 3 figures. Technical construction of quasi-invariant curves from arXiv:1802.03630
Subjects: Dynamical Systems (math.DS); Complex Variables (math.CV)
[244]  arXiv:1802.06978 (replaced) [pdf, ps, other]
Title: Inner cohomology of $GL_n$
Authors: Krishna Kishore
Comments: 26 pages, 1 table
Subjects: Number Theory (math.NT)
[245]  arXiv:1802.07123 (replaced) [pdf, other]
Title: Building Large Free Subshifts Using the Local Lemma
Authors: Anton Bernshteyn
Comments: 13 pages
Subjects: Dynamical Systems (math.DS); Combinatorics (math.CO)
[246]  arXiv:1802.07291 (replaced) [pdf, ps, other]
Title: On spin distributions for generic p-spin models
Comments: 15 pages, an early version of these results appeared in Sections 1.2 and 7 of arXiv:1612.06359v1
Subjects: Probability (math.PR); Mathematical Physics (math-ph)
[247]  arXiv:1802.07445 (replaced) [pdf, ps, other]
Title: A compactness result for non-local unregularized gradient flow lines
Comments: 27 pages
Subjects: Functional Analysis (math.FA); Symplectic Geometry (math.SG)
[248]  arXiv:1802.07449 (replaced) [pdf, ps, other]
Title: An iterated graph construction and periodic orbits of Hamiltonian delay equations
Comments: 25 pages, 3 figures
Subjects: Dynamical Systems (math.DS); Symplectic Geometry (math.SG)
[249]  arXiv:1802.07453 (replaced) [pdf, ps, other]
Title: What might a Hamiltonian delay equation be?
Comments: 9 pages
Subjects: Dynamical Systems (math.DS); Symplectic Geometry (math.SG)
[ total of 249 entries: 1-249 ]
[ showing up to 2000 entries per page: fewer | more ]

Disable MathJax (What is MathJax?)