# Mathematics

## New submissions

[ total of 243 entries: 1-243 ]
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### New submissions for Fri, 27 Mar 20

[1]
Title: On Banach algebras of band-dominated operators and their order structure
Subjects: Functional Analysis (math.FA); Operator Algebras (math.OA)

The goal of this paper is to study band-dominated operators on Banach spaces with Schauder basis with respect to uniformly locally finite metric spaces as well as the Banach algebras generated by them: the so called uniform Roe algebras. We investigate several kinds of isomorphisms between those Banach spaces (e.g., isomorphisms preserving norm, order, algebraic structure, etc) and prove several rigidity results on when a certain kind of isomorphism between the uniform Roe algebras implies that the base metric spaces are (bijectively) coarsely equivalent.

[2]
Title: Massive Access in Multi-cell Wireless Networks Using Reed-Muller Codes
Comments: 30 pages, 6 figures
Subjects: Information Theory (cs.IT)

Providing connectivity to a massive number of devices is a key challenge in 5G wireless systems. In particular, it is crucial to develop efficient methods for active device identification and message decoding in a multi-cell network with fading and path loss uncertainties. In this paper, we design such a scheme using second-order Reed-Muller (RM) sequences. For given positive integer $m$, a codebook is generated with up to $2^{m(m+3)/2}$ codewords of length $2^m$, where each codeword is a unique RM sequence determined by a matrix-vector pair with binary entries. This allows every device to send $m(m+3)/2$ bits of information where an arbitrary number of these bits can be used to represent the identity of a node, and the remaining bits represent a message. There can be up to $2^{m(m+3)/2}$ devices in total. Using an iterative algorithm, an access point can estimate the matrix-vector pairs of each nearby device, as long as not too many devices transmit simultaneously. To improve the performance, we also describe an enhanced RM coding scheme with slotting. We show that both the computational complexity and the error performance of the latter algorithm exceed another state-of-the-art algorithm. The device identification and message decoding scheme developed in this work can serve as the basis for grant-free massive access for billions of devices with hundreds of simultaneously active devices in each cell.

[3]
Title: A unified existence theorem for normal spanning trees
Authors: Max Pitz
Subjects: Combinatorics (math.CO)

We show that a graph $G$ has a normal spanning tree if and only if its vertex set is the union of countably many sets each separated from any subdivided infinite clique in $G$ by a finite set of vertices. This proves a conjecture by Brochet and Diestel from 1994, giving a common strengthening of two classical normal spanning tree criterions due to Jung and Halin.
Moreover, our method gives a new, algorithmic proof of Halin's theorem that every connected graph not containing a subdivision of a countable clique has a normal spanning tree.

[4]
Title: Large Parts of Random Plane Partitions: a Poisson Limit Theorem
Subjects: Combinatorics (math.CO)

We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the positive integer $n$, introduced by Stanley in 1973. We derive generating functions and determine the asymptotic behavior of counts of large parts using a general scheme based on the saddle point method. In this way, we are able to prove a Poisson limit theorem for the number of parts of a random and uniformly chosen plane partition of $n$, whose sizes are greater than a function $m=m(n)$ as $n\to\infty$. An explicit expression for $m(n)$ is also given.

[5]
Title: Hausdorff Dimension Regularity Properties and Games
Subjects: Logic (math.LO)

The Hausdorff $\delta$-dimension game was introduced by Das, Fishman, Simmons and {Urba{\'n}ski} and shown to characterize sets in $\mathbb{R}^d$ having Hausdorff dimension $\leq \delta$. We introduce a variation of this game which also characterizes Hausdorff dimension and for which we are able to prove an unfolding result similar to the basic unfolding property for the Banach-Mazur game for category. We use this to derive a number of consequences for Hausdorff dimension. We show that under $\mathsf{AD}$ any wellordered union of sets each of which has Hausdorff dimension $\leq \delta$ has dimension $\leq \delta$. We establish a continuous uniformization result for Hausdorff dimension. The unfolded game also provides a new proof that every $\boldsymbol{\Sigma}^1_1$ set of Hausdorff dimension $\geq \delta$ contains a compact subset of dimension $\geq \delta'$ for any $\delta'<\delta$, and this result generalizes to arbitrary sets under $\mathsf{AD}$.

[6]
Title: Sharp ultimate velocity bounds for the general solution of some linear second order evolution equation with damping and bounded forcing
Subjects: Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA)

We consider a class of linear second order differential equations with damping and external force. We investigate the link between a uniform bound on the forcing term and the corresponding ultimate bound on the velocity of solutions, and we study the dependence of that bound on the damping and on the "elastic force".
We prove three results. First of all, in a rather general setting we show that different notions of bound are actually equivalent. Then we compute the optimal constants in the scalar case. Finally, we extend the results of the scalar case to abstract dissipative wave-type equations in Hilbert spaces. In that setting we obtain rather sharp estimates that are quite different from the scalar case, in both finite and infinite dimensional frameworks.
The abstract theory applies, in particular, to dissipative wave, plate and beam equations.

[7]
Title: Topological torus fibrations on Calabi--Yau manifolds via Kato--Nakayama spaces
Authors: Hülya Argüz
Subjects: Algebraic Geometry (math.AG); Symplectic Geometry (math.SG)

This is an expository article on the Gross--Siebert approach to mirror symmetry and its interactions with the Strominger--Yau--Zaslow conjecture from a topological perspective.

[8]
Title: On the essential dimension of an algebraic group whose connected component is a torus
Subjects: Algebraic Geometry (math.AG)

Let $p$ be a prime integer, $k$ be a $p$-closed field of characteristic $\neq p$, $T$ be a torus defined over $k$, $F$ be a finite $p$-group, and $1\to T \to G \to F \to 1$ be an exact sequence of algebraic groups. Extending earlier work of N. Karpenko and A. Merkurjev, R. L\"otscher, M. MacDonald, A. Meyer, and the first author showed that $\min\dim(V) - \min\dim(G) \leqslant \text{ed}(G; p) \leqslant \min \dim(W) - \dim(G),$ where $V$ and $W$ range over the $p$-faithful and $p$-generically free $k$-representations of $G$, respectively. They conjectured that the upper bound is, in fact, sharp. This conjecture has remained open for some time. We prove it in the case, where $F$ is diagonalizable.

[9]
Title: Markov and Lagrange Spectra for Laurent series in 1/T with rational coefficients
Subjects: Number Theory (math.NT)

The field of formal Laurent series is a natural analogue of the real numbers, and mathematicians have been translating well-known results about rational approximations to that setting. In the framework of power series over the rational numbers, we define and study the Lagrange spectrum, related to Diophantine approximation of irrationals, and the Markov spectrum, related to representation by indefinite binary quadratic forms. We compute both spectra explicitly, and show that they coincide and exhibit no gaps, contrary to what happens over the reals.

[10]
Title: On the theory of kinetic equations for interacting particle systems with long range interactions
Subjects: Mathematical Physics (math-ph)

In this paper we review the formal derivation of different classes of kinetic equations for long range potentials. We consider suitable scaling limits for Lorentz and Rayleigh gases as well as interacting particle systems whose dynamics can be approximated by means of kinetic equations. The resulting kinetic equations are the Landau and the Balescu-Lenard equations. In the derivation of the kinetic equations particular emphasis is made in the fact that all the kinetic regimes can be obtained approximating the dynamics of the interacting particle systems by the evolution of a single particle in a random force field with a friction term which is due to the interaction with the surrounding particles. The case of particles interacting by means of Coulombian potentials as well as the cutoffs which yield the so-called Coulombian logarithm are discussed in detail.

[11]
Title: C-transfinite diameter
Comments: 18 pages, 1 figure
Subjects: Complex Variables (math.CV)

We give a general formula for the $C-$transfinite diameter $\delta_C(K)$ of a compact set $K\subset \mathbb{C}^2$ which is a product of univariate compacta where $C\subset (\mathbb{R}^+)^2$ is a convex body. Along the way we prove a Rumely type formula relating $\delta_C(K)$ and the $C-$Robin function $\rho_{V_{C,K}}$ of the $C-$extremal plurisubharmonic function $V_{C,K}$ for $C \subset (\mathbb{R}^+)^2$ a triangle $T_{a,b}$ with vertices $(0,0), (b,0), (0,a)$. Finally, we show how the definition of $\delta_C(K)$ can be extended to include many nonconvex bodies $C\subset \mathbb{R}^d$ for $d-$circled sets $K\subset \mathbb{C}^d$, and we prove an integral formula for $\delta_C(K)$ which we use to compute a formula for the $C-$transfinite diameter of the Euclidean unit ball $\mathbb{B}\subset \mathbb{C}^2$.

[12]
Title: Reflective prolate-spheroidal operators and the adelic Grassmannian
Subjects: Classical Analysis and ODEs (math.CA); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Spectral Theory (math.SP)

Beginning with the work of Landau, Pollak and Slepian in the 1960s on time-band limiting, commuting pairs of integral and differential operators have played a key role in signal processing, random matrix theory and integrable systems. Previously, such pairs were constructed by ad hoc methods, which worked because a commuting operator of low order could be found by a direct calculation. We describe a general approach to these problems that proves that every point $W$ of Wilson's infinite dimensional adelic Grassmannian $\mathrm Gr^ad$ gives rise to an integral operator $T_W$, acting on $L^2(\Gamma)$ for a contour $\Gamma\subset\mathbb C$, which reflects a differential operator $R(z,\partial_z)$ in the sense that $R(-z,-\partial_z)\circ T_W=T_W\circ R(w,\partial_w)$ on a dense subset of $L^2(\Gamma)$. By using analytic methods and methods from integrable systems, we show that the reflected differential operator can be constructed from the Fourier algebra of the associated bispectral function $\psi_W(x,z)$. The size of this algebra with respect to a bifiltration is in turn determined using algebro-geometric methods. Intrinsic properties of four involutions of the adelic Grassmannian naturally lead us to consider the reflecting property in place of plain commutativity. Furthermore, we prove that the time-band limited operators of the generalized Laplace transforms with kernels given by all rank one bispectral functions $\psi_W(x,-z)$ reflect a differential operator. A $90^\circ$ rotation argument is used to prove that the time-band limited operators of the generalized Fourier transforms with kernels $\psi_W(x,iz)$ admit a commuting differential operator. These methods produce vast collections of integral operators with prolate-spheroidal properties, associated to the wave functions of all rational solutions of the KP hierarchy vanishing at infinity, introduced by Krichever in the late 1970s.

[13]
Title: Equilibrium states for non-uniformly expanding maps with critical sets
Subjects: Dynamical Systems (math.DS)

In the context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding measures. The technique consists in using an inducing scheme in a finite Markov structure with infinitely many symbols to code the dynamics to obtain an equilibrium state for the associated symbolic dynamics and then projecting it to obtain an equilibrium state for the original map.

[14]
Title: The positive polynomial Schur property in Banach lattices
Subjects: Functional Analysis (math.FA)

We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary $L_p(\mu)$-spaces are shown to be positively polynomially Schur, lattice analogues of results on Banach spaces are obtained and relationships with the positive Schur and the weak Dunford-Pettis properties are established.

[15]
Title: On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case
Authors: Paolo Di Tella
Subjects: Probability (math.PR)

In this paper we investigate the propagation of the weak representation property (WRP) to an independently enlarged filtration. More precisely, we consider an $\mathbb{F}$-semimartingale $X$ possessing the WRP with respect to $\mathbb{F}$ and an $\mathbb{H}$-semimartingale $Y$ possessing the WRP with respect to $\mathbb{H}$. Assuming that $\mathbb{F}$ and $\mathbb{H}$ are independent, we show that the $\mathbb{G}$-semimartingale $Z=(X,Y)$ has the WRP with respect to $\mathbb{G}$, where $\mathbb{G}:=\mathbb{F}\vee\mathbb{H}$. In our setting, $X$ and $Y$ may have simultaneous jump-times. Furthermore, their jumps may charge predictable times. This generalizes all available results about the propagation of the WRP to independently enlarged filtrations.

[16]
Title: Wavelet Compressibility of Compound Poisson Processes
Subjects: Information Theory (cs.IT)

In this paper, we characterize the wavelet compressibility of compound Poisson processes. To that end, we expand a given compound Poisson process over the Haar wavelet basis and analyse its asymptotic approximation properties. By considering only the nonzero wavelet coefficients up to a given scale, what we call the sparse approximation, we exploit the extreme sparsity of the wavelet expansion that derives from the piecewise-constant nature of compound Poisson processes. More precisely, we provide nearly-tight lower and upper bounds for the mean $L_2$-sparse approximation error of compound Poisson processes. Using these bounds, we then prove that the sparse approximation error has a sub-exponential and super-polynomial asymptotic behavior. We illustrate these theoretical results with numerical simulations on compound Poisson processes. In particular, we highlight the remarkable ability of wavelet-based dictionaries in achieving highly compressible approximations of compound Poisson processes.

[17]
Title: Partial Trace Ideals And Berger's Conjecture
Authors: Sarasij Maitra
Subjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG)

Let $R$ be a commutative one-dimensional domain whose integral closure is a DVR. We assume further that $R$ is a complete $k$-algebra where $k$ is any perfect field. Under this hypothesis, there is a long standing conjecture of R.W. Berger which states that $R$ is regular if and only if the (universally finite) differential module $\Omega_{R/k}$ is torsionfree. We introduce an invariant of $\Omega_{R/k}$ based on a partial trace ideal, and discuss lower bounds on it which give new cases of this conjecture. In particular, we can generalize the quasihomogeneous case proved by Scheja. Finally, we explore some relations between this invariant and the colength of the conductor.

[18]
Title: Continued fraction expansions of Herglotz-Nevanlinna functions and generalized indefinite strings of Stieltjes type
Subjects: Spectral Theory (math.SP); Classical Analysis and ODEs (math.CA)

We employ some results about continued fraction expansions of Herglotz-Nevanlinna functions to characterize the spectral data of generalized indefinite strings of Stieltjes type. In particular, this solves the corresponding inverse spectral problem through explicit formulas.

[19]
Title: Diagrammatic categorification of the Chebyshev polynomials of the second kind
Subjects: Representation Theory (math.RT); Quantum Algebra (math.QA)

We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials. Diagrammatic algebras featured in these categorifications lead to the first topological interpretations of the Bernstein-Gelfand-Gelfand reciprocity property.

[20]
Title: Explicit expanders of every degree and size
Authors: Noga Alon
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)

An $(n,d,\lambda)$-graph is a $d$ regular graph on $n$ vertices in which the absolute value of any nontrivial eigenvalue is at most $\lambda$. For any constant $d \geq 3$, $\epsilon>0$ and all sufficiently large $n$ we show that there is a deterministic poly(n) time algorithm that outputs an $(n,d, \lambda)$-graph (on exactly $n$ vertices) with $\lambda \leq 2 \sqrt{d-1}+\epsilon$. For any $d=p+2$ with $p \equiv 1 \bmod 4$ prime and all sufficiently large $n$, we describe a strongly explicit construction of an $(n,d, \lambda)$-graph (on exactly $n$ vertices) with $\lambda \leq \sqrt {2(d-1)} + \sqrt{d-2} +o(1) (< (1+\sqrt 2) \sqrt {d-1}+o(1))$, with the $o(1)$ term tending to $0$ as $n$ tends to infinity. For every $\epsilon >0$, $d>d_0(\epsilon)$ and $n>n_0(d,\epsilon)$ we present a strongly explicit construction of an $(m,d,\lambda)$-graph with $\lambda < (2+\epsilon) \sqrt d$ and $m=n+o(n)$. All constructions are obtained by starting with known ones of Ramanujan or nearly Ramanujan graphs, modifying or packing them in an appropriate way. The spectral analysis relies on the delocalization of eigenvectors of regular graphs in cycle-free neighborhoods.

[21]
Title: Moduli Space of $Λ$-modules on Projective Deligne-Mumford Stacks
Authors: Hao Sun
Subjects: Algebraic Geometry (math.AG)

In this paper, we define the $\Lambda$-quotient functor on a Deligne-Mumford stack over an algebraic space. We prove that the $\Lambda$-quotient functor is representable by an algebraic space. We also define the moduli problem of $\Lambda$-modules on a projective Deligne-Mumford stack and construct its moduli space, which is a quasi-projective scheme.

[22]
Title: Mesh Refinement Method for Solving Optimal Control Problems with Nonsmooth Solutions Using Jump Function Approximations
Comments: 22 Pages, 8 Figures, 0 Tables
Subjects: Optimization and Control (math.OC)

A mesh refinement method is described for solving optimal control problems using Legendre-Gauss-Radau collocation. The method detects discontinuities in the control solution by employing an edge detection scheme based on jump function approximations. When discontinuities are identified, the mesh is refined with a targeted $h$-refinement approach whereby the discontinuity locations are bracketed with mesh points. The remaining smooth portions of the mesh are refined using previously developed techniques. The method is demonstrated on two examples, and results indicate that the method solves optimal control problems with discontinuous control solutions using fewer mesh refinement iterations and less computation time when compared with previously developed methods.

[23]
Title: The Hilbert series of Hodge ideals of hyperplane arrangements
Subjects: Algebraic Geometry (math.AG)

Given a reduced effective divisor D on a smooth variety X, we describe the generating function for the classes of the Hodge ideals of D in the Grothendieck group of coherent sheaves on X in terms of the motivic Chern class of the complement of the support of D. As an application, we compute the generating function for the Hilbert series of Hodge ideals of a hyperplane arrangement in terms of the Poincare polynomial of the arrangement.

[24]
Title: Latency Minimization for Task Offloading in Hierarchical Fog-Computing C-RAN Networks
Comments: accepted by ICC 2020
Subjects: Information Theory (cs.IT); Signal Processing (eess.SP)

[25]
Title: Cover 3-uniform hypergraphs by vertex-disjoint tight paths
Authors: Jie Han
Subjects: Combinatorics (math.CO)

Let $H$ be an $n$-vertex 3-graph such that every pair of vertices is in at least $n/3+o(n)$ edges. We show that $H$ contains two vertex-disjoint tight paths whose union covers the vertex set of $H$. The quantity two here is best possible and the degree condition is asymptotically best possible.

[26]
Title: Regular partitions of gentle graphs
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM); Logic in Computer Science (cs.LO); Logic (math.LO)

Szemeredi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the theory of (structural) sparsity, which leads to alternative proofs, refinements and solutions of open problems. It is interesting to note that many of these classes present challenging problems. Nevertheless, from the point of view of regularity lemma type statements, they appear as "gentle" classes.

[27]
Title: Information-Theoretic Foundations of Mismatched Decoding
Comments: Submitted to Foundations and Trends in Communications and Information Theory
Subjects: Information Theory (cs.IT)

Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical considerations such as channel uncertainty and implementation constraints rule out the use of an optimal decoder. The mismatched decoding problem addresses such scenarios by considering the case that the decoder cannot be optimized, but is instead fixed as part of the problem statement. This problem is not only of direct interest in its own right, but also has close connections with other long-standing theoretical problems in information theory.
In this monograph, we survey both classical literature and recent developments on the mismatched decoding problem, with an emphasis on achievable random-coding rates for memoryless channels. We present two widely-considered achievable rates known as the generalized mutual information (GMI) and the LM rate, and overview their derivations and properties. In addition, we survey several improved rates via multi-user coding techniques, as well as recent developments and challenges in establishing converse bounds, and an analogous mismatched encoding problem in rate-distortion theory. Throughout the monograph, we highlight a variety of applications and connections with other prominent information theory problems.

[28]
Title: Free coactions of a finite dimensional $C^*$-Hopf algebra and strong Morita equivalence
Subjects: Operator Algebras (math.OA)

We shall introduce a notion of free coactions of a finite dimensional $C^*$-Hopf algebra on a $C^*$-algebra modifying a notion of free actions of a discrete group on a $C^*$-algebra and we shall study several properties on coactions of a finite dimensional $C^*$-Hopf algebra on $C^*$-algebras, which are relating to strong Morita equivalence for inclusions of $C^*$-algebras.

[29]
Title: Variability of paths and differential equations with $BV$-coefficients
Subjects: Probability (math.PR); Analysis of PDEs (math.AP); Functional Analysis (math.FA)

We define compositions $\varphi(X)$ of H\"older paths $X$ in $\mathbb{R}^n$ and functions of bounded variation $\varphi$ under a relative condition involving the path and the gradient measure of $\varphi$. We show the existence and properties of generalized Lebesgue-Stieltjes integrals of compositions $\varphi(X)$ with respect to a given H\"older path $Y$. These results are then used, together with Doss' transform, to obtain existence and, in a certain sense, uniqueness results for differential equations in $\mathbb{R}^n$ driven by H\"older paths and involving coefficients of bounded variation. Examples include equations with discontinuous coefficients driven by paths of two-dimensional fractional Brownian motions.

[30]
Title: Gaussian Fluctuations and Free Energy Expansion for 2D and 3D Coulomb Gases at Any Temperature
Authors: Sylvia Serfaty
Subjects: Mathematical Physics (math-ph); Probability (math.PR)

We prove a Central Limit Theorem for the fluctuations of linear statistics of Coulomb gases in dimensions 2 and 3, which is valid down to microscales and for a broad temperature regime. This is the first such result in dimension 3. We show that the result can also be obtained in any dimension as soon as one can obtain a precise enough error rate for the expansion of the free energy -- such an expansion is obtained in any dimension, but the rate is good enough only in dimensions 2 and 3. In dimension 3 or larger, to obtain the CLT we need to make a "no phase transition" assumption. The CLT holds as soon as the test-function lives on a scale larger than the temperature-dependent minimal scale $\rho_\beta$ introduced in our previous work \cite{as}. It can be interpreted as a convergence to the Gaussian Free Field.

[31]
Title: Simple purely infinite $C^*$-algebras associated with normal subshifts
Authors: Kengo Matsumoto
Subjects: Operator Algebras (math.OA); Dynamical Systems (math.DS)

We will introduce a notion of normal subshifts. A subshift $(\Lambda,\sigma)$ is said to be normal if it satisfies a certain synchronizing property called $\lambda$-synchronizing and is infinite as a set. We have lots of purely infinite simple $C^*$-algebras from normal subshifts including irreducible infinite sofic shifts, Dyck shifts, $\beta$-shifts, and so on. Eventual conjugacy of one-sided normal subshifts and topological conjugacy of two-sided normal subshifts are characterized in terms of the associated $C^*$-algebras and the associated stabilized $C^*$-algebras with its diagonals and gauge actions, respectively.

[32]
Title: A note on multiplier ideal sheaves on complex spaces with singularities
Authors: Zhenqian Li
Subjects: Complex Variables (math.CV)

The goal of this note is to present some recent results of our research concerning multiplier ideal sheaves on complex spaces and singularities of plurisubharmonic functions. We firstly introduce multiplier ideal sheaves on complex spaces (\emph{not} necessarily normal) via Ohsawa's extension measure, as a special case of which, it turns out to be the so-called Mather-Jacobian multiplier ideals in the algebro-geometric setting. As applications, we obtain a reasonable generalization of (algebraic) adjoint ideal sheaves to the analytic setting and establish some extension theorems on K\"ahler manifolds from \emph{singular} hypersurfaces. Relying on our multiplier and adjoint ideals, we also give characterizations for several important classes of singularities of pairs associated to plurisubharmonic functions.
Moreover, we also investigate the local structure of singularities of log canonical locus of plurisubharmonic functions. Especially, in the three-dimensional case, we show that for any plurisubharmonic function with log canonical singularities, its associated multiplier ideal subscheme is weakly normal, by which we give a complete classification of multiplier ideal subschemes with log canonical singularities.

[33]
Title: Generalized Wireless-Powered Communications: When to Activate Wireless Power Transfer?
Subjects: Information Theory (cs.IT); Signal Processing (eess.SP)

Wireless-powered communication network (WPCN) is a key technology to power energy-limited massive devices, such as on-board wireless sensors in autonomous vehicles, for Internet-of-Things (IoT) applications. Conventional WPCNs rely only on dedicated downlink wireless power transfer (WPT), which is practically inefficient due to the significant energy loss in wireless signal propagation. Meanwhile, ambient energy harvesting is highly appealing as devices can scavenge energy from various existing energy sources (e.g., solar energy and cellular signals). Unfortunately, the randomness of the availability of these energy sources cannot guarantee stable communication services. Motivated by the above, we consider a generalized WPCN where the devices can not only harvest energy from a dedicated multiple-antenna power station (PS), but can also exploit stored energy stemming from ambient energy harvesting. Since the dedicated WPT consumes system resources, if the stored energy is sufficient, WPT may not be needed to maximize the weighted sum rate (WSR). To analytically characterize this phenomenon, we derive the condition for WPT activation and reveal how it is affected by the different system parameters. Subsequently, we further derive the optimal resource allocation policy for the cases that WPT is activated and deactivated, respectively. In particular, it is found that when WPT is activated, the optimal energy beamforming at the PS does not depend on the devices' stored energy, which is shown to lead to a new unfairness issue. Simulation results verify our theoretical findings and demonstrate the effectiveness of the proposed optimal resource allocation.

[34]
Title: Existence and Optimal Convergence Rates of Multi-dimensional Subsonic Potential Flows Through an Infinitely Long Nozzle with an Obstacle Inside
Authors: Lei Ma, Chunjing Xie
Comments: 32 pages, 2 figures
Subjects: Analysis of PDEs (math.AP)

In this paper, the well-posedness and optimal convergence rates of subsonic irrotational flows through a three dimensional infinitely long nozzle with a smooth obstacle inside are established. More precisely, the global existence and uniqueness of the uniformly subsonic flow are obtained via variational formulation as long as the incoming mass flux is less than a critical value. Furthermore, with the aid of delicate choice of weight functions, we prove the optimal convergence rates of the flow at far fields via weighted energy estimates and Nash-Moser iteration.

[35]
Title: Reduction Theorem for Secrecy over Linear Network Code for Active Attacks
Subjects: Information Theory (cs.IT)

We discuss the effect of sequential error injection on information leakage under a network code. We formulate a network code for the single transmission setting and the multiple transmission setting. Under this formulation, we show that the eavesdropper cannot improve the power of eavesdropping by sequential error injection when the operations in the network are linear operations. We demonstrate the usefulness of this reduction theorem by applying a concrete example of network.

[36]
Title: Low Mach Number Limit and Far Field Convergence Rates of Potential Flows in Muiti-Dimensional Nozzles With an Obstacle Inside
Comments: 37 pages, 1 figure
Subjects: Analysis of PDEs (math.AP)

This paper considers the low Mach number limit and far field convergence rates of steady Euler flows with external forces in three-dimensional infinitely long nozzles with an obstacle inside. First, the well-posedness theory for both incompressible and compressible subsonic flows with external forces in multidimensional nozzle with an obstacle inside are established by several uniform estimates. The uniformly subsonic compressible flows tend to the incompressible flows as quadratic order of Mach number as the compressibility parameter goes to zero. Furthermore, we also give the convergence rates of both incompressible flow and compressible flow at far fields as the boundary of nozzle goes to flat even when the forces do not admit convergence rate at far fields. The convergence rates obtained for the flows at far fields clearly describe the effects of the external force.

[37]
Title: $φ$-FEM, a finite element method on domains defined by level-sets: the Neumann boundary case
Subjects: Numerical Analysis (math.NA)

We extend a fictitious domain-type finite element method, called $\phi$-FEM and introduced in arXiv:1903.03703 [math.NA], to the case of Neumann boundary conditions. The method is based on a multiplication by the level-set function and does not require a boundary fitted mesh. Unlike other recent fictitious domain-type methods (XFEM, CutFEM), our approach does not need any non-standard numerical integration on cut mesh elements or on the actual boundary. We prove the optimal convergence of $\phi$-FEM and the fact that the discrete problem is well conditioned inependently of the mesh cuts. The numerical experiments confirm the theoretical results.

[38]
Title: Multiscale Substitution Tilings
Comments: 45 pages, 14 figures
Subjects: Dynamical Systems (math.DS); Metric Geometry (math.MG)

We introduce multiscale substitution tilings, which are a new family of tilings of Euclidean space. These tilings are generated by substitution schemes on a finite set of prototiles, in which multiple distinct scaling constants are allowed. This is in contrast to the standard case of the well-studied substitution tilings which includes examples such as the Penrose and the pinwheel tilings. Under an additional irrationality assumption on the scaling constants, our construction defines a new class of tilings and tiling spaces, which are intrinsically different from those that arise in the standard setup. We study various structural, geometric, statistical and dynamical aspects of these new objects and establish a wide variety of properties. Among our main results are explicit density formulas and the unique ergodicity of the associated tiling dynamical systems.

[39]
Title: Characterization of multilinear multipliers in terms of Sobolev space regularity
Subjects: Classical Analysis and ODEs (math.CA)

We provide necessary and sufficient conditions for multilinear multiplier operators with symbols in $L^r$-based product-type Sobolev spaces uniformly over all annuli to be bounded from products of Hardy spaces to a Lebesgue space. We consider the case $1<r\leq 2$ and we characterize boundedness in terms of inequalities relating the Lebesgue indices (or Hardy indices), the dimension, and the regularity and integrability indices of the Sobolev space. The case $r>2$ cannot be handled by known techniques and remains open. Our result not only extends but also establishes the sharpness of previous results of Miyachi, Nguyen, Tomita, and the first author, who only considered the case $r=2$.

[40]
Title: Reviews of Symbolic Moment Calculus
Comments: 32 pages, 2 figures, personal article
Subjects: Combinatorics (math.CO)

As a former engineering student, I have a great interest in a real world application of mathematics. Probability is something I can relate to. I am lucky enough that after I switched to Mathematics, this is one of many interests of my Ph.D. advisor, Doron Zeilberger, as well. In this article we create a program to apply the \textit{overlapping stage approach} to calculate the moments $E[X^r]$ and $E[(X-\mu)^r]$ of combinatorial objects. We also show the normality property of their distributions when these moments are easy enough to calculate.

[41]
Title: The Gray tensor product for 2-quasi-categories
Authors: Yuki Maehara
Subjects: Category Theory (math.CT); Algebraic Topology (math.AT)

We construct an $(\infty,2)$-version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an $n$-ary) functor on the category of $\Theta_2$-sets, and it is shown to be left Quillen with respect to Ara's model structure. Moreover we prove that this tensor product forms part of a "homotopical" monoidal (closed) structure, or more precisely a normal lax monoidal structure that is associative up to homotopy.

[42]
Title: Breaking the $O(1/ε)$ Optimal Rate for a Class of Minimax Problems
Comments: 23 pages, 6 figures
Subjects: Optimization and Control (math.OC)

It is known that for convex optimization $\min_{\mathbf{w}\in\mathcal{W}}f(\mathbf{w})$, the best possible rate of first order accelerated methods is $O(1/\sqrt{\epsilon})$. However, for the bilinear minimax problem: $\min_{\mathbf{w}\in\mathcal{W}}\max_{\mathbf{v}\in\mathcal{V}}$ $f(\mathbf{w})$ $+\langle\mathbf{w}, \boldsymbol{A}\mathbf{v}\rangle$ $-h(\mathbf{v})$ where both $f(\mathbf{w})$ and $h(\mathbf{v})$ are convex, the best known rate of first order methods slows down to $O(1/{\epsilon})$. It is not known whether one can achieve the accelerated rate $O(1/\sqrt{\epsilon})$ for the bilinear minimax problem without assuming $f(\mathbf{w})$ and $h(\mathbf{v})$ being strongly convex. In this paper, we fill this theoretical gap by proposing a bilinear accelerated extragradient (BAXG) method. We show that when $\mathcal{W}=\mathbb{R}^d$, $f(\mathbf{w})$ and $h(\mathbf{v})$ are convex and smooth, and $\boldsymbol{A}$ has full column rank, then the BAXG method achieves an accelerated rate $O(1/\sqrt{\epsilon}\log \frac{1}{\epsilon})$, within a logarithmic factor to the likely optimal rate $O(1/\sqrt{\epsilon})$. As result, a large class of bilinear convex concave minimax problems, including a few problems of practical importance, can be solved much faster than previously known methods.

[43]
Title: Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions
Subjects: Analysis of PDEs (math.AP)

We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.

[44]
Title: Symbol Detection for Massive MIMO AF Relays Using Approximate Bayesian Inference
Subjects: Information Theory (cs.IT)

For massive MIMO AF relays, symbol detection becomes a practical issue when the number of antennas is not large enough, since linear methods are non-optimal and optimal methods are exponentially complex. This paper proposes a new detection algorithm that offers Bayesian-optimal MSE at the cost of $O(n^3)$ complexity per iteration. The algorithm is in essence a hybrid of two methods recently developed for deep learning, with particular optimization for relay. As a hybrid, it inherits from the two a state evolution formulism, where the asymptotic MSE can be precisely predicted through a scalar equivalent model. The algorithm also degenerates easily to many results well-known when single-hop considered.

[45]
Title: Quantitative estimates for almost constant mean curvature hypersurfaces
Authors: Giulio Ciraolo
Comments: This note has been submitted for possible publication in the Proceedings of the XXI Congress of the Italian Mathematical Union
Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)

Alexandrov's soap bubble theorem asserts that spheres are the only connected closed embedded hypersurfaces in the Euclidean space with constant mean curvature. The theorem can be extended to space forms and it holds for more general functions of the principal curvatures.
In this short review, we discuss quantitative stability results regarding Alexandrov's theorem which have been obtained by the author in recent years. In particular, we consider hypersurfaces having mean curvature close to a constant and we quantitatively describe the proximity to a single sphere or to a collection of tangent spheres in terms of the oscillation of the mean curvature. Moreover, we also consider the problem in a non local setting, and we show that the non local effect gives a stronger rigidity to the problem and prevents the appearance of bubbling.

[46]
Title: Nonconvex sparse regularization for deep neural networks and its optimality
Subjects: Statistics Theory (math.ST); Machine Learning (cs.LG); Machine Learning (stat.ML)

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However, the sparsity constraint requires to know certain properties of the true model, which are not available in practice. Moreover, computation is difficult due to the discrete nature of the sparsity constraint. In this paper, we propose a novel penalized estimation method for sparse DNNs, which resolves the aforementioned problems existing in the sparsity constraint. We establish an oracle inequality for the excess risk of the proposed sparse-penalized DNN estimator and derive convergence rates for several learning tasks. In particular, we prove that the sparse-penalized estimator can adaptively attain minimax convergence rates for various nonparametric regression problems. For computation, we develop an efficient gradient-based optimization algorithm that guarantees the monotonic reduction of the objective function.

[47]
Title: Moderate deviation theorem for the Neyman-Pearson statistic in testing uniformity
Subjects: Statistics Theory (math.ST)

We show that for local alternatives to uniformity which are determined by a sequence of square integrable densities the moderate deviation (MD) theorem for the corresponding Neyman-Pearson statistic does not hold in the full range for all unbounded densities. We give a sufficient condition under which MD theorem holds. The proof is based on Mogulskii's inequality.

[48]
Title: Extending periodic automorphisms of surfaces to 3-manifolds
Comments: 17 pages, 5 figures
Subjects: Geometric Topology (math.GT)

Let $G$ be a finite group acting on a connected compact surface $\Sigma$, and $M$ be an integer homology 3-sphere. We show that if each element of $G$ is extendable over $M$ with respect to a fixed embedding $\Sigma\rightarrow M$, then $G$ is extendable over some $M'$ which is 1-dominated by $M$. From this result, in the orientable category we classify all periodic automorphisms of closed surfaces that are extendable over the 3-sphere. The corresponding embedded surface of such an automorphism can always be a Heegaard surface.

[49]
Title: A Counterexample to the $2$-jet determination Chern-Moser Theorem in higher codimension
Authors: Francine Meylan
Subjects: Complex Variables (math.CV)

One constructs an example of a generic quadratic submanifold of codimension $5$ in $\Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $3.$

[50]
Title: Uniform error bounds of an exponential wave integrator for the long-time dynamics of the nonlinear Klein-Gordon equation
Authors: Yue Feng, Wenfan Yi
Comments: 24 pages, 3 figures
Subjects: Numerical Analysis (math.NA)

We establish uniform error bounds of an exponential wave integrator Fourier pseudospectral (EWI-FP) method for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE) with a cubic nonlinearity whose strength is characterized by $\varepsilon^2$ with $\varepsilon \in (0, 1]$ a dimensionless parameter. When $0 < \varepsilon \ll 1$, the problem is equivalent to the long-time dynamics of the NKGE with small initial data (and $O(1)$ cubic nonlinearity), while the amplitude of the initial data (and the solution) is at $O(\varepsilon)$. For the long-time dynamics of the NKGE up to the time at $O(1/\varepsilon^{2})$, the resolution and error bounds of the classical numerical methods depend significantly on the small parameter $\varepsilon$, which causes severe numerical burdens as $\varepsilon \to 0^+$. The EWI-FP method is fully explicit, symmetric in time and has many superior properties in solving wave equations. By adapting the energy method combined with the method of mathematical induction, we rigorously carry out the uniform error bounds of the EWI-FP discretization at $O(h^{m_0} + \varepsilon^{2-\beta}\tau^2)$ up to the time at $O(1/\varepsilon^{\beta})$ with $0 \leq \beta \leq 2$, mesh size $h$, time step $\tau$ and $m_0$ an integer depending on the regularity of the solution. By a rescaling in time, our results are straightforwardly extended to the error bounds and $\varepsilon$-scalability (or meshing strategy requirement) of the EWI-FP method for an oscillatory NKGE, whose solution propagates waves with wavelength at $O(1)$ and $O(\varepsilon^{\beta})$ in space and time, respectively, and wave speed at $O(\varepsilon^{-\beta})$. Finally, extensive numerical results are reported to confirm our error estimates.

[51]
Title: A class of short-term models for the oil industry addressing speculative storage
Subjects: Analysis of PDEs (math.AP)

This is a work in progress. The aim is to propose a plausible mechanism for the short term dynamics of the oil market based on the interaction of economic agents. This is a theoretical research which by no means aim at describing all the aspects of the oil market. In particular, we use the tools and terminology of game theory, but we do not claim that this game actually exists in the real world. In parallel, we are currently studying and calibrating a long term model for the oil industry, which addresses the interactions of a monopolists with a competitive fringe of small producers. It is the object of another paper that will be available soon. The present premiminary version does not contain all the economic arguments and all the connections with our long term model. It mostly addresses the description of the model, the equations and numerical simulations focused on the oil industry short term dynamics. A more complete version will be available soon.

[52]
Title: The Essential Spectrum of the Discrete Laplacian on Klaus-sparse Graphs
Authors: Sylvain Golenia (IMB), Françoise Truc (IF)
Subjects: Functional Analysis (math.FA); Mathematical Physics (math-ph); Spectral Theory (math.SP)

In 1983, Klaus studied a class of potentials with bumps and computed the essential spectrum of the associated Schr{\"o}dinger operator with the help of some localisations at infinity. A key hypothesis is that the distance between two consecutive bumps tends to infinity at infinity. In this article, we introduce a new class of graphs (with patterns) that mimics this situation, in the sense that the distance between two patterns tends to infinity at infinity. These patterns tend, in some way, to asymptotic graphs. They are the localisations at infinity. Our result is that the essential spectrum of the Laplacian acting on our graph is given by the union of the spectra of the Laplacian acting on the asymptotic graphs. We also discuss the question of the stability of the essential spectrum in the appendix.

[53]
Title: Stability of optimal traffic plans in the irrigation problem
Authors: Maria Colombo (EPFL), Antonio de Rosa (CIMS), Andrea Marchese, Paul Pegon (CEREMADE, MOKAPLAN), Antoine Prouff (ENS Paris Saclay)
Subjects: Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA); Optimization and Control (math.OC)

We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This is the Lagrangian counterpart of the recent Eulerian version proved in [CDM19a].

[54]
Title: A Primal-Dual Weak Galerkin Method for Div-Curl Systems with low-regularity solutions
Subjects: Numerical Analysis (math.NA)

This article presents a new primal-dual weak Galerkin finite element method for the tangential boundary value problem of div-curl systems with low-regularity solutions. The numerical scheme is based on a weak formulation, called the primal equation, involving no partial derivatives for the exact solution supplemented by the its dual form in the context of weak Galerkin. Optimal order error estimates in $L^2$ are established for vector fields with $H^\alpha(\Omega)$-regularity, $\alpha>0$. The mathematical theory was derived for connected domains with general topological properties (namely, arbitrary Betti numbers). Numerical results are reported to not only verify the theoretical convergence but also demonstrate the performance of the new method.

[55]
Title: The method of super-solutions in Hardy and Rellich type inequalities in the $L^2$ setting: an overview of well-known results and short proofs
Authors: Cristian Cazacu
Subjects: Analysis of PDEs (math.AP)

In this survey we give a compact presentation of well-known functional inequalities of Hardy and Rellich type in the $L^2$ setting. In addition, we give some insights of their proofs by using standard and basic tools such as the method of super-solutions.

[56]
Title: Integral left-orderable surgeries on genus one fibered knots
Comments: 12 pages, 2 figures
Subjects: Geometric Topology (math.GT)

Following the classification of genus one fibered knots in lens spaces by Baker, we determine hyperbolic genus one fibered knots in lens spaces on whose all integral Dehn surgeries yield closed 3-manifolds with left-orderable fundamental groups.

[57]
Title: Stochastic optimal transport revisited
Authors: Toshio Mikami
Subjects: Probability (math.PR)

We prove the Duality Theorems for the stochastic optimal transportation problems with a convex cost function without a regularity assumption which is often supposed in the proof of the lower semicontinuity of an action integral. This is done by the so-called superposition principle and by an idea from the mother theory. The superposition principle is the construction of a local semimartingale from the Fokker-Planck equation. It is also considered as a class of the so-called marginal problems which construct stochastic processes from given marginal distributions. It was originally considered in stochastic mechanics by E. Nelson, called Nelson's problem and was first proved by E. Carlen. The semimartingale is called the Nelson process, provided it is Markovian. We also consider the Markov property of a minimizer of the stochastic optimal transportation problem with a nonconvex cost in one dimensional case by the superposition principle and by the minimizer of an optimal transportation problem with a concave cost function. It is done by the Duality Theorem in the case where a cost function is convex. Lastly, we prove the semiconcavity and the continuity of Schroedinger's problem which is a typical example of the stochastic optimal transportation problem.

[58]
Title: On $\underline{12}0$-avoiding inversion and ascent sequences
Subjects: Combinatorics (math.CO)

Recently, Yan and the first named author investigated systematically the enumeration of inversion or ascent sequences avoiding vincular patterns of length $3$, where two of the three letters are required to be adjacent. They established many connections with familiar combinatorial families and proposed several interesting conjectures. The objective of this paper is to address two of their conjectures concerning the enumeration of $\underline{12}0$-avoiding inversion or ascent sequences.

[59]
Title: Irreducibility of limits of Galois representations of Saito-Kurokawa type
Subjects: Number Theory (math.NT)

We prove (under certain assumptions) the irreducibility of the limit $\sigma_2$ of a sequence of irreducible essentially self-dual Galois representations $\sigma_k: G_{\mathbf{Q}} \to \mathrm{GL}_4(\overline{\mathbf{Q}}_p)$ (as $k$ approaches 2 in a $p$-adic sense) which mod $p$ reduce (after semi-simplifying) to $1 \oplus \rho \oplus \chi$ with $\rho$ irreducible, two-dimensional of determinant $\chi$, where $\chi$ is the mod $p$ cyclotomic character. More precisely, we assume that $\sigma_k$ are crystalline (with a particular choice of weights) and Siegel-ordinary at $p$. Such representations arise in the study of $p$-adic families of Siegel modular forms and properties of their limits as $k\to 2$ appear to be important in the context of the Paramodular Conjecture. The result is deduced from the finiteness of two Selmer groups whose order is controlled by $p$-adic $L$-values of an elliptic modular form (giving rise to $\rho$) which we assume are non-zero.

[60]
Title: Semidefinite programming bounds for the average kissing number
Subjects: Metric Geometry (math.MG); Optimization and Control (math.OC)

The average kissing number of $\mathbb{R}^n$ is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in $\mathbb{R}^n$. We provide an upper bound for the average kissing number based on semidefinite programming that improves previous bounds in dimensions $3, \ldots, 9$. A very simple upper bound for the average kissing number is twice the kissing number; in dimensions $6, \ldots, 9$ our new bound is the first to improve on this simple upper bound.

[61]
Title: Asymptotic behavior of scalar convection-diffusion equations
Authors: Enrique Zuazua
Subjects: Analysis of PDEs (math.AP)

In these lecture notes, we address the problem of large-time asymptotic behaviour of the solutions to scalar convection-diffusion equations set in ${R}^N$. The large-time asymptotic behaviour of the solutions to many convection-diffusion equations is strongly linked with the behavior of the initial data at infinity. In fact, when the initial datum is integrable and of mass $M$, the solutions to the equations under consideration oftentimes behave like the associated self-similar profile of mass $M$, thus emphasising the role of scaling variables in these scenarios. However, these equations can also manifest other asymptotic behaviors, including weakly non-linear, linear or strongly non-linear behavior depending on the form of the convective term. We give an exhaustive presentation of several results and techniques, where we clearly distinguish the role of the spatial dimension and the form of the nonlinear convective term.
Translation (English) by Borjan Geshovski

[62]
Title: Mathematical analysis of memory effects and thermal relaxation in nonlinear sound waves on unbounded domains
Subjects: Analysis of PDEs (math.AP)

Motivated by the propagation of nonlinear sound waves through relaxing hereditary media, we study a nonlocal third-order Jordan-Moore-Gibson-Thompson acoustic wave equation. Under the assumption that the relaxation kernel decays exponentially, we prove local well-posedness in unbounded two- and three-dimensional domains. In addition, we show that the solution of the three-dimensional model exists globally in time, while the energy of the system decays polynomially.

[63]
Title: Square Function Estimates for Dunkl Operators
Subjects: Probability (math.PR)

Dunkl operators may be regarded as differential-difference operators parameterized by finite reflection groups. In this paper, the Littlewood--Paley square function for Dunkl heat flows in $\mathbb{R}^d$ is introduced by employing the full "gradient" induced by the corresponding carr\'{e} du champ operator and then the $L^p$ boundedness is studied for all $p\in(1,\infty)$. For $p\in(1,2]$, we successfully adapt Stein's heat flows approach to overcome the difficult caused by the non-local difference part of the Dunkl operator and establish the $L^p$ boundedness, while for $p\in[2,\infty)$, we restrict to a particular case when the corresponding Coxeter group is isomorphic to $\mathbb{Z}_2^d$ and apply a probabilistic method to prove the $L^p$ boundedness. In the latter case, the curvature-dimension condition for Dunkl operators in the sense of Bakry--Emery, which may be of independent interest, plays a crucial role.

[64]
Title: Contractivity for Smoluchowski's coagulation equation with solvable kernels
Subjects: Analysis of PDEs (math.AP)

We show that the Smoluchowski coagulation equation with the solvable kernels $K(x,y)$ equal to $2$, $x+y$ or $xy$ is contractive in suitable Laplace norms. In particular, this proves exponential convergence to a self-similar profile in these norms. These results are parallel to similar properties of Maxwell models for Boltzmann-type equations, and extend already existing results on exponential convergence to self-similarity for Smoluchowski's coagulation equation.

[65]
Title: Complete cohomology for extriangulated categories
Subjects: Representation Theory (math.RT); Category Theory (math.CT)

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles. In this paper, we study complete cohomology of objects in $(\mathcal{C},\mathbb{E},\mathfrak{s})$ by applying $\xi$-projective resolutions and $\xi$-injective coresolutions constructed in $(\mathcal{C},\mathbb{E},\mathfrak{s})$. Vanishing of complete cohomology detects objects with finite $\xi$-projective dimension and finite $\xi$-injective dimension. As a consequence, we obtain some criteria for the validity of the Wakamatsu Tilting Conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein. Moreover, we give a general technique for computing complete cohomology of objects with finite $\xi$-$\mathcal{G}$projective dimension. As an application, the relationships between $\xi$-projective dimensions and $\xi$-$\mathcal{G}$projective dimensions for objects in $(\mathcal{C},\mathbb{E},\mathfrak{s})$ are given.

[66]
Title: Maximal non-compactness of Sobolev embeddings
Subjects: Functional Analysis (math.FA)

It has been known that sharp Sobolev embeddings into weak Lebesgue spaces are non-compact but the question of whether the measure of non-compactness of such an embedding equals to its operator norm constituted a well-known open problem. The existing theory suggested an argument that would possibly solve the problem should the target norms be disjointly superadditive, but the question of disjoint superadditivity of spaces $L^{p,\infty}$ has been open, too. In this paper we solve both these problems. We first show that weak Lebesgue spaces are never disjointly superadditive, so the suggested technique is ruled out. But then we show that, perhaps somewhat surprisingly, the measure of non-compactness of a sharp Sobolev embedding coincides with the embedding norm nevertheless, at least as long as $p<\infty$. Finally, we show that if the target space is $L^{\infty}$ (which formally is also a weak Lebesgue space with $p=\infty$), then the things are essentially different. To give a comprehensive answer including this case, too, we develop a new method based on a rather unexpected combinatorial argument and prove thereby a general principle, whose special case implies that the measure of non-compactness, in this case, is strictly less than its norm. We develop a technique that enables us to evaluate this measure of non-compactness exactly.

[67]
Title: Continuity of delta invariants and twisted Kähler--Einstein metrics
Authors: Kewei Zhang
Subjects: Differential Geometry (math.DG); Algebraic Geometry (math.AG)

We show that delta invariant is a continuous function on the big cone. We will also introduce an analytic delta invariant and show its continuity in the K\"ahler cone, from which we deduce the continuity of the greatest Ricci lower bound. Then building on the work Berman-Boucksom-Jonsson, we obtain a uniform Yau-Tian-Donaldson theorem for twisted K\"ahler-Einstein metrics in general K\"ahler classes.

[68]
Title: Multiplication operator and exceptional Jacobi polynomials
Authors: Á. P. Horváth
Subjects: Classical Analysis and ODEs (math.CA)

Below the normalized zero-counting measure based on the regular zeros of exceptional Jacobi polynomials, and the normalized weighted reciprocal of the Christoffel function with respect to exceptional Jacobi polynomials are investigated. It is proved that both measures tend to the equilibrium measure of the interval of orthogonality in weak-star sense. The main tool of this study is the multiplication operator and examination of the behavior of zeros of the corresponding average characteristic polynomial. Finally, as an application of multiplication operator, the zeros of certain self-inversive polynomials are examined.

[69]
Title: Existence of solution for a class of nonlocal problem via dynamical methods
Subjects: Analysis of PDEs (math.AP)

In this paper we use the dynamical methods to establish the existence of nontrivial solution for a class of nonlocal problem of the type $$\left\{\begin{array}{l} -a\left(x,\int_{\Omega}g(u)\,dx \right)\Delta u =f(u), \quad x \in \Omega \\ u=0, \hspace{2 cm} x \in \partial \Omega, \end{array}\right. \leqno{(P)}$$ where $\Omega \subset \mathbb{R}^N \, ( N \geq 2)$ is a smooth bounded domain and $a:\overline{\Omega} \times \mathbb{R} \to \mathbb{R}$ and $g,f: \mathbb{R} \to \mathbb{R}$ are $C^1$-functions that satisfy some technical conditions.

[70]
Title: Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models
Subjects: Probability (math.PR); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Dynamical Systems (math.DS)

Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transport. In this work we derive coarse-grained deterministic partial integro-differential equation (PIDE) models that provide a mean field approximation to the volume reactivity PBSRD model, a model commonly used for studying cellular processes. We formulate a weak measure-valued stochastic process (MVSP) representation for the volume reactivity PBSRD model, demonstrating for a simplified but representative system that it is consistent with the commonly used Doi Fock Space representation of the corresponding forward equation. We then prove the convergence of the general volume reactivity model MVSP to the mean field PIDEs in the large-population (i.e. thermodynamic) limit.

[71]
Title: A partial graphical model with a structural prior on the direct links between predictors and responses
Subjects: Statistics Theory (math.ST); Applications (stat.AP)

This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between potentially high-dimensional predictors and multiple responses, since it is known that Gaussian graphical models enable to exhibit direct links only, whereas coefficients in linear regressions contain both direct and indirect relations (due e.g. to strong correlations among the variables). A smooth penalty reflecting a generalized Gaussian Bayesian prior on the covariates is added, either enforcing patterns (like row structures) in the direct links or regulating the joint influence of predictors. We give a theoretical guarantee for our method, taking the form of an upper bound on the estimation error arising with high probability, provided that the model is suitably regularized. Empirical studies on synthetic data and real datasets are conducted to compare the efficiency of the model with well-known related procedures. Our work shows that the flexibility induced by the additional hyperparametrization may control the extent of structuring in the direct links and improve both predictions and statistical interpretations.

[72]
Title: Efficient Randomized Algorithms for Subspace System Identification
Subjects: Numerical Analysis (math.NA)

Eigensystem Realization Algorithm (ERA) is a data-driven approach for subspace system identification and is widely used in many areas of engineering. However, the computational cost of the ERA is dominated by a step that involves the singular value decomposition (SVD) of a large, dense matrix with block Hankel structure. This paper develops computationally efficient algorithms for reducing the computational cost of the SVD step by using randomized subspace iteration and exploiting the block Hankel structure of the matrix. We provide a detailed analysis of the error in the identified system matrices and the computational cost of the proposed algorithms. We demonstrate the accuracy and computational benefits of our algorithms on two test problems: the first involves a partial differential equation that models the cooling of steel rails, and the second is an application from power systems engineering.

[73]
Title: On Smoothness of the elements of some integrable Teichmüller spaces
Subjects: Complex Variables (math.CV)

In this paper we focus on the integrable Teichm\"uller spaces, subspaces of the universal Teichm\"uller space, and we prove that elements of some of them are continuously differentiable.

[74]
Title: Second order estimates for transition layers and a curvature estimate for the parabolic Allen-Cahn
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)

The parabolic Allen-Cahn equation is a semilinear partial differential equation linked to the mean curvature flow by a singular perturbation. We show an improved convergence property of the parabolic Allen-Cahn equation to the mean curvature flow, which is the parabolic analogue of the improved convergence property of the elliptic Allen-Cahn to minimal surfaces by Wang-Wei and Chodosh-Mantoulidis. More precisely, we show if the phase-transition level sets are converging in $C^2$, then they converge in $C^{2,\theta}$. As an application, we obtain a curvature estimate for parabolic Allen-Cahn equation, which can be viewed as a diffused version of Brakke's and White's regularity theorem for mean curvature flow

[75]
Title: On the geometry of discrete contact mechanics
Subjects: Mathematical Physics (math-ph); Numerical Analysis (math.NA)

In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a discrete Lagrangian in the contact setting. This allows us to develop convenient numerical integrators for contact Lagrangian systems that are conformally contact by construction. The existence of an exact Lagrangian function is also discussed.

[76]
Title: Properties of minimal charts and their applications VI: the graph $Γ_{m+1}$ in a chart $Γ$ of type $(m;2,3,2)$
Comments: 39 pages, 31 figures. arXiv admin note: text overlap with arXiv:1902.00007, arXiv:1603.04639, arXiv:1609.08257
Subjects: Geometric Topology (math.GT)

Let $\Gamma$ be a chart, and we denote by $\Gamma_m$ the union of all the edges of label $m$. A chart $\Gamma$ is of type $(m;2,3,2)$ if $w(\Gamma)=7$, $w(\Gamma_m\cap\Gamma_{m+1})=2$, $w(\Gamma_{m+1}\cap\Gamma_{m+2})=3$, and $w(\Gamma_{m+2}\cap\Gamma_{m+3})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we prove that if there is a minimal chart $\Gamma$ of type $(m;2,3,2)$, then each of $\Gamma_{m+1}$ and $\Gamma_{m+2}$ contains one of three kinds of graphs. In the next paper, we shall prove that there is no minimal chart of type $(m;2,3,2)$.

[77]
Title: Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold
Comments: 31 pages, 22 Figures
Subjects: Numerical Analysis (math.NA)

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. The first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity.

[78]
Title: A Bi-fidelity Ensemble Kalman Method for PDE-Constrained Inverse Problems
Comments: 33 pages. 9 figures
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Fluid Dynamics (physics.flu-dyn)

Mathematical modeling and simulation of complex physical systems based on partial differential equations (PDEs) have been widely used in engineering and industrial applications. To enable reliable predictions, it is crucial yet challenging to calibrate the model by inferring unknown parameters/fields (e.g., boundary conditions, mechanical properties, and operating parameters) from sparse and noisy measurements, which is known as a PDE-constrained inverse problem. In this work, we develop a novel bi-fidelity (BF) ensemble Kalman inversion method to tackle this challenge, leveraging the accuracy of high-fidelity models and the efficiency of low-fidelity models. The core concept is to build a BF model with a limited number of high-fidelity samples for efficient forward propagations in the iterative ensemble Kalman inversion. Compared to existing inversion techniques, salient features of the proposed methods can be summarized as follow: (1) achieving the accuracy of high-fidelity models but at the cost of low-fidelity models, (2) being robust and derivative-free, and (3) being code non-intrusive, enabling ease of deployment for different applications. The proposed method has been assessed by three inverse problems that are relevant to fluid dynamics, including both parameter estimation and field inversion. The numerical results demonstrate the excellent performance of the proposed BF ensemble Kalman inversion approach, which drastically outperforms the standard Kalman inversion in terms of efficiency and accuracy.

[79]
Title: Partially volume expanding diffeomorphisms
Subjects: Dynamical Systems (math.DS)

We call a partially hyperbolic diffeomorphism \emph{partially volume expanding} if the Jacobian restricted to any hyperplane that contains the unstable bundle $E^u$ is larger than $1$. This is a $C^1$ open property. We show that any $C^{1+}$ partially volume expanding diffeomorphisms admits finitely many physical measures, the union of whose basins has full volume.

[80]
Title: Twisting on pre-Lie algebras and quasi-pre-Lie bialgebras
Authors: Jiefeng Liu
Comments: 26 pages. arXiv admin note: text overlap with arXiv:1902.03033 by other authors
Subjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph)

We study (quasi-)twilled pre-Lie algebras and the associated $L_\infty$-algebras and differential graded Lie algebras. Then we show that certain twisting transformations on (quasi-)twilled pre-Lie algbras can be characterized by the solutions of Maurer-Cartan equations of the associated differential graded Lie algebras ($L_\infty$-algebras). Furthermore, we show that $\huaO$-operators and twisted $\huaO$-operators are solutions of the Maurer-Cartan equations. As applications, we study (quasi-)pre-Lie bialgebras using the associated differential graded Lie algebras ($L_\infty$-algebras) and the twisting theory of (quasi-)twilled pre-Lie algebras. In particular, we give a construction of quasi-pre-Lie bialgebras using symplectic Lie algebras, which is parallel to that a Cartan $3$-form on a semi-simple Lie algebra gives a quasi-Lie bialgebra.

[81]
Title: Peano continuum with regenerating fractal
Authors: Magdalena Nowak
Comments: 11 pages, 8 figures
Subjects: Dynamical Systems (math.DS); General Topology (math.GN)

We deal with the question of M. Hata: is every Peano continuum a topological fractal? A compact space $X$ is a topological fractal if there exists $\mathcal{F}$ a finite family of selmaps on $X$ such that $X=\bigcup_{f\in\mathcal{F}}f(X)$ and for every open cover $\mathcal{U}$ of $X$ there is $n\in\mathbb{N}$ such that for any maps $f_1,\dots,f_n\in\mathcal{F}$ the set $f_1\circ\dots\circ f_n(X)$ is contained in some set $U\in\mathcal{U}$.
In the paper we present some idea how to extend topological fractal and we use it to show that Peano continuum is a topological fractal if it contains so-called regenerating fractal with nonempty interior. A Hausdorff topological space $A$ is a regenerating fractal if for every non-empty open subset $U$, $A$ is topological fractal for some family of maps constant on $A\setminus U$.

[82]
Title: Averaging Principle on Infinite Intervals for Stochastic Ordinary Differential Equations
Comments: 25 pages, no figure. arXiv admin note: text overlap with arXiv:1702.02718
Subjects: Dynamical Systems (math.DS); Probability (math.PR)

In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations in Hilbert space with Poisson stable (in particular, periodic, quasi-periodic, almost periodic, almost automorphic etc) coefficients. Under some appropriate conditions we prove that there exists a unique recurrent solution to the original equation, which possesses the same recurrence property as the coefficients, in a small neighborhood of the stationary solution to the averaged equation, and this recurrent solution converges to the stationary solution of averaged equation uniformly on the whole real axis when the time scale approaches zero.

[83]
Title: From geometry to arithmeticity of compact hyperbolic Coxeter polytopes
Authors: Nikolay Bogachev
Comments: 21 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1903.08147
Subjects: Geometric Topology (math.GT); Group Theory (math.GR); Metric Geometry (math.MG); Number Theory (math.NT)

In this paper we prove that any compact hyperbolic Coxeter polyhedron in the three-dimensional Lobachevsky space contains an edge such that the distance between its framing faces is small enough. Also, we provide some applications of this theorem.

[84]
Title: Effective transmission conditions for reaction-diffusion processes in domains separated by thin channels
Subjects: Analysis of PDEs (math.AP)

We consider a reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $\epsilon$, and the equation inside the layer depends on the parameter $\epsilon$ and an additional parameter $\gamma \in [-1,1)$, which describes the size of the diffusion in the layer. We derive effective models for the limit $\epsilon \to 0$, when the channel-domain is replaced by an interface between the two bulk-domains.

[85]
Title: On the worst-case error of least squares algorithms for $L_2$-approximation with high probability
Authors: Mario Ullrich
Comments: 7 pages. arXiv admin note: substantial text overlap with arXiv:1905.02516
Subjects: Numerical Analysis (math.NA)

It was recently shown in [4] that, for $L_2$-approximation of functions from a Hilbert space, function values are almost as powerful as arbitrary linear information, if the approximation numbers are square-summable. That is, we showed that $e_n \,\lesssim\, \sqrt{\frac{1}{k_n} \sum_{j\geq k_n} a_j^2} \qquad \text{ with }\quad k_n \asymp \frac{n}{\ln(n)},$ where $e_n$ are the sampling numbers and $a_k$ are the approximation numbers. In particular, if $(a_k)\in\ell_2$, then $e_n$ and $a_n$ are of the same polynomial order. For this, we presented an explicit (weighted least squares) algorithm based on i.i.d. random points and proved that this works with positive probability. This implies the existence of a good deterministic sampling algorithm.
Here, we present a modification of the proof in [4] that shows that the same algorithm works with probability at least $1-{n^{-c}}$ for all $c>0$.

[86]
Title: Harder-Narasimhan theory
Subjects: Algebraic Geometry (math.AG); Category Theory (math.CT); Number Theory (math.NT)

An abstract formulation of Harder-Narasimhan theory is stated without proof by L. Fargues, and I found it helpful to write it all out.

[87]
Title: On the Complexity and Approximability of Optimal Sensor Selection and Attack for Kalman Filtering
Comments: arXiv admin note: text overlap with arXiv:1711.01920
Subjects: Optimization and Control (math.OC); Computational Complexity (cs.CC); Systems and Control (eess.SY)

Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design-time) to minimize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomial-time constant-factor approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity (or supermodularity) of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering. We then study the problem of attacking (i.e., removing) a set of installed sensors, under predefined attack budget constraints, to maximize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter. Again, we show that there is no polynomial-time constant-factor approximation algorithm for this problem, and show specifically that greedy algorithms can perform arbitrarily poorly.

[88]
Title: Revisiting T-Norms for Type-2 Fuzzy Sets
Comments: arXiv admin note: text overlap with arXiv:1908.10532, arXiv:1907.12394
Subjects: General Mathematics (math.GM)

Let $\mathbf{L}$ be the set of all normal and convex functions from ${[0, 1]}$ to ${[0, 1]}$. This paper proves that ${t}$-norm in the sense of Walker-and-Walker is strictly stronger that ${t_r}$-norm on $\mathbf{L}$, which is strictly stronger than ${t}$-norm on $\mathbf{L}$. Furthermore, let ${\curlywedge}$ and ${\curlyvee}$ be special convolution operations defined by $${(f\curlywedge g)(x)=\sup\left\{f(y)\star g(z): y\vartriangle z=x\right\},}$$ $${(f\curlyvee g)(x)=\sup\left\{f(y)\star g(z): y\ \triangledown\ z=x\right\},}$$ for ${f, g\in Map([0, 1], [0, 1])}$, where ${\vartriangle}$ and ${\triangledown}$ are respectively a ${t}$-norm and a ${t}$-conorm on ${[0, 1]}$ (not necessarily continuous), and ${\star}$ is a binary operation on ${[0, 1]}$. Then, it is proved that if the binary operation ${\curlywedge}$ is a ${t_r}$-norm (resp., ${\curlyvee}$ is a ${t_r}$-conorm), then ${\vartriangle}$ is a continuous ${t}$-norm (resp., ${\triangledown}$ is a continuous ${t}$-conorm) on ${[0, 1]}$, and ${\star}$ is a ${t}$-norm on ${[0, 1]}$.

[89]
Title: Local maximizers of adjoint Fourier restriction estimates for the cone, paraboloid and sphere
Comments: 34 pages, 2 figures
Subjects: Classical Analysis and ODEs (math.CA); Analysis of PDEs (math.AP)

We show that, possibly after a compactification of spacetime, constant functions are local maximizers of the Tomas-Stein adjoint Fourier restriction inequality for the cone and paraboloid in every dimension, and for the sphere in dimension up to 60. For the cone and paraboloid we work from the PDE framework, which enables the use of the Penrose and the Lens transformations, which map the conjectured optimal functions into constants.

[90]
Title: A micro-macro Markov chain Monte Carlo method for molecular dynamics using reaction coordinate proposals II: indirect reconstruction
Comments: 30 pages, 9 figures, 6 tables. arXiv admin note: text overlap with arXiv:2002.09324
Subjects: Numerical Analysis (math.NA)

We introduce a new micro-macro Markov chain Monte Carlo method (mM-MCMC) with indirect reconstruction to sample invariant distributions of molecular dynamics systems that exhibit a time-scale separation between the microscopic (fast) dynamics, and the macroscopic (slow) dynamics of some low-dimensional set of reaction coordinates. The algorithm enhances exploration of the state space in the presence of metastability by allowing larger proposal moves at the macroscopic level, on which a conditional accept-reject procedure is applied. Only when the macroscopic proposal is accepted, the full microscopic state is reconstructed from the newly sampled reaction coordinate value and is subjected to a second accept/reject procedure. The computational gain stems from the fact that most proposals are rejected at the macroscopic level, at low computational cost, while microscopic states, once reconstructed, are almost always accepted. This paper discusses an indirect method to reconstruct microscopic samples from macroscopic reaction coordinate values, that can also be applied in cases where direct reconstruction is cumbersome. The indirect reconstruction method generates a microscopic sample by performing a biased microscopic simulation, starting from the previous microscopic sample and driving the microscopic state towards the proposed reaction coordinate value. We show numerically that the mM-MCMC scheme with indirect reconstruction can significantly extend the range of applicability of the mM-MCMC method.

[91]
Title: Surface homogenization of an array of Helmholtz resonators for a viscoacoustic model using two-scale convergence
Comments: 33 pages, 10 figures, 1 table. arXiv admin note: text overlap with arXiv:1905.08566
Subjects: Analysis of PDEs (math.AP)

We derive the weak limit of a linear viscoacoustic model in an acoustic liner that is a chamber connected to a periodic repetition of elongated chambers -- the Helmholtz resonators. % As model we consider the time-harmonic and linearized compressible Navier-Stokes equations for the acoustic velocity and pressure. % Following the approach in Schmidt et al., J. Math. Ind 8:15, 2018 for the viscoacoustic transmission problem of multiperforated plates the viscosity is scaled as $\delta^{4}$ with the period $\delta$ of the array of chambers and the size of the necks as well as the wall thickness like $\delta^2$ such that the viscous boundary layers are of the order of the size of the necks. % Applying the method of two-scale convergence we obtain with a stability assumption in the limit $\delta \to 0$ that the acoustic pressure fulfills the Helmholz equation with impedance boundary conditions. % These boundary conditions depend on the frequency, the length of the resonators and through the effective Rayleigh conductivity -- that can be computed numerically -- on the shape of their necks. We compare the limit model to semi-analytical models in the literature.

[92]
Title: Completeness in affine and statistical geometry
Authors: Barbara Opozda
Subjects: Differential Geometry (math.DG)

We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.

[93]
Title: Georg Mohr's "Euclides Danicus" -- Preliminary Version
Authors: Ricardo Bianconi
Comments: 38 pages, 8 figures
Subjects: History and Overview (math.HO)

We present here a preliminary version of a translation with comments of Georg Mohr's book "Euclides Danicus", where the first proof of Mohr-Mascheroni Theorem appeared in 1672, 125 years before Mascheroni's book.

[94]
Title: Several extremal problems on graphs involving the circumference, girth, and hyperbolicity constant
Subjects: Combinatorics (math.CO)

To compute the hyperbolicity constant is an almost intractable problem, thus it is natural to try to bound it in terms of some parameters of the graph. Let $\mathcal{G}(g,c,n)$ be the set of graphs $G$ with girth $g(G)=g$, circumference $c(G)=c$, and $n$ vertices; and let $\mathcal{H}(g,c,m)$ be the set of graphs with girth $g$, circumference $c$, and $m$ edges. In this work, we study the four following extremal problems on graphs: $A(g,c,n)=\min\{\delta(G)\,|\; G \in \mathcal{G}(g,c,n) \}$, $B(g,c,n)=\max\{\delta(G)\,|\; G \in \mathcal{G}(g,c,n) \}$, $\alpha(g,c,m)=\min\{\delta(G)\,|\; \in \mathcal{H}(g,c,m) \}$ and $\beta(g,c,m)=\max\{\delta(G)\,|\; G \in \mathcal{H}(g,c,m) \}$. In particular, we obtain bounds for $A(g,c,n)$ and $\alpha(g,c,m)$, and we compute the precise value of $B(g,c,n)$ and $\beta(g,c,m)$ for all values of $g$, $c$, $n$ and $m$.

[95]
Title: Secure Groupcast with Shared Keys
Authors: Hua Sun
Subjects: Information Theory (cs.IT); Cryptography and Security (cs.CR)

We consider a transmitter and $K$ receivers, each of which shares a key variable with the transmitter. Through a noiseless broadcast channel, the transmitter wishes to send a common message $W$ securely to $N$ out of the $K$ receivers while the remaining $K-N$ receivers learn no information about $W$. We are interested in the maximum message rate, i.e., the maximum number of bits of $W$ that can be securely groupcast to the legitimate receivers per key block and the minimum broadcast bandwidth, i.e., the minimum number of bits of the broadcast information required to securely groupcast the message bits.
We focus on the setting of combinatorial keys, where every subset of the $K$ receivers share an independent key of arbitrary size. Under this combinatorial key setting, the maximum message rate is characterized for the following scenarios - 1) $N=1$ or $N=K-1$, i.e., secure unicast to 1 receiver with $K-1$ eavesdroppers or secure groupcast to $K-1$ receivers with $1$ eavesdropper, 2) $N=2, K=4$, i.e., secure groupcast to $2$ out of 4 receivers, and 3) the symmetric setting where the key size for any subset of the same cardinality is equal for any $N,K$. Further, for the latter two cases, the minimum broadcast bandwidth for the maximum message rate is characterized.

[96]
Title: Collared and non-collared manifold boundaries
Authors: Mathieu Baillif
Comments: 13 pages, 6 figures
Subjects: General Topology (math.GN)

We gather in this note results and examples about collared or non-collared boundaries of non-metrisable manifolds. Almost everything is well known but a bit scattered in the literature, and some of it is apparently not published at all.

[97]
Title: On the locus of genus $3$ curves that admit meromorphic differentials with a zero of order $6$ and a pole of order $2$
Subjects: Algebraic Geometry (math.AG)

The main goal of this article is to compute the class of the divisor of $\overline{\mathcal{M}}_3$ obtained by taking the closure of the image of $\Omega\mathcal{M}_3(6;-2)$ by the forgetful map. This is done using Porteous formula and the theory of test curves. For this purpose, we study the locus of meromorphic differentials of the second kind, computing the dimension of the map of these loci to $\mathcal{M}_g$ and solving some enumerative problems involving such differentials in low genus. A key tool of the proof is the compactification of strata recently introduced by Bainbridge-Chen-Gendron-Grushevsky-M\"oller.

[98]
Title: Character sums over products of prime polynomials
Authors: Samuel Porritt
Subjects: Number Theory (math.NT)

We study sums of Dirichlet characters over polynomials in $\mathbb{F}_q[t]$ with a prescribed number of irreducible factors. Our main results are explicit formulae for these sums in terms of zeros of Dirichlet L-functions. We also exhibit new phenomena concerning Chebyshev-type biases of such sums when the number of irreducible factors is very large.

[99]
Title: Homotopy theory of modules over a commutative $S$-algebra: some tools and examples
Authors: Andrew Baker
Subjects: Algebraic Topology (math.AT)

Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These have categories of modules which are generalisations of the classical categories of spectra that correspond to modules over the sphere spectrum; passing to their derived or homotopy categories leads to new contexts in which homotopy theory can be explored. In this paper we describe some of the tools available for studying these `brave new homotopy theories' and demonstrate them by considering modules over the $K$-theory spectrum, closely related to Mahowald's theory of $bo$-resolutions. In a planned sequel we will apply these techniques to the much less familiar context of modules over the $2$-local connective spectrum of topological modular forms.

[100]
Title: Robust Least Squares for Quantized Data
Comments: 11 pages, 5 figures, 2 tables
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)

In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error. Ordinary least squares fails to consider uncertainty in the data matrices, modeling all noise in the observed signal. Total least squares accounts for uncertainty in the data matrix, but necessarily increases the condition number of the system compared to ordinary least squares. Tikhonov regularization or ridge regression, is frequently employed to combat ill-conditioning, but requires heuristic parameter tuning which presents a host of challenges and places strong assumptions on parameter prior distributions. The proposed method also requires selection of a parameter, but it can be chosen in a natural way, e.g., a matrix rounded to the 4th digit uses an uncertainty bounding parameter of 0.5e-4. We show here that our robust method is theoretically appropriate, tractable, and performs favorably against ordinary and total least squares for both residual and absolute error reduction.

[101]
Title: Robust Recovery of Sparse Nonnegative Weights from Mixtures of Positive-Semidefinite Matrices
Comments: 13 pages; 3 figures
Subjects: Information Theory (cs.IT); Optimization and Control (math.OC)

We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and $s$-sparse weights from noisy observations is an important problem in various fields of signal processing and also a relevant pre-processing step in covariance estimation. We will present related recovery guarantees and focus on the case of nonnegative weights. The problem is formulated as a convex program and can be solved without further tuning. Such robust, non-Bayesian and parameter-free approaches are important for applications where prior distributions and further model parameters are unknown. Motivated by explicit applications in wireless communication, we will consider the particular rank-one case, where the known matrices are outer products of iid. zero-mean subgaussian $n$-dimensional complex vectors. We show that, for given $n$ and $N$, one can recover nonnegative $s$--sparse weights with a parameter-free convex program once $s\leq O(n^2 / \log^2(N/n^2)$. Our error estimate scales linearly in the instantaneous noise power whereby the convex algorithm does not need prior bounds on the noise. Such estimates are important if the magnitude of the additive distortion depends on the unknown itself.

[102]
Title: Linearly Self-Equivalent APN Permutations in Small Dimension
Subjects: Information Theory (cs.IT); Combinatorics (math.CO)

All almost perfect nonlinear (APN) permutations that we know to date admit a special kind of linear self-equivalence, i.e., there exists a permutation $G$ in their CCZ-class and two linear permutations $A$ and $B$, such that $G \circ A = B \circ G$. After providing a survey on the known APN functions with a focus on the existence of self equivalences, we explicitly search for APN permutations in dimension 6, 7, and 8 that admit such a linear self equivalence. In dimension six, we were able to conduct an exhaustive search and obtain that there is only one such APN permutation up to CCZ-equivalence. In dimensions 7 and 8, we exhaustively searched through parts of the space and conclude that the linear self equivalences of such APN permutations must be of a special form. As one interesting result in dimension 7, we obtain that all APN permutation polynomials with coefficients in $\mathbb{F}_2$ must be (up to CCZ-equivalence) monomial functions.

[103]
Title: Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws
Subjects: Numerical Analysis (math.NA)

In this work, we modify a continuous Galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures. Discrete entropy conditions are used to determine the minimal amount of entropy stabilization and constrain antidiffusive corrections of a property-preserving low-order scheme. The addition of a second-order entropy dissipative component to the antidiffusive part of a nearly entropy conservative numerical flux is generally insufficient to prevent violations of local bounds in shock regions. Our monolithic convex limiting technique adjusts a given target flux in a manner which guarantees preservation of invariant domains, validity of local maximum principles, and entropy stability. The new methodology combines the advantages of modern entropy stable/entropy conservative schemes and their local extremum diminishing counterparts. The process of algebraic flux correction is based on inequality constraints which provably provide the desired properties. No free parameters are involved. The proposed algebraic fixes are readily applicable to unstructured meshes, finite element methods, general time discretizations, and steady-state residuals. Numerical studies of explicit entropy-constrained schemes are performed for linear and nonlinear test problems.

[104]
Title: Coarse spaces, ultrafilters and dynamical systems
Authors: Igor Protasov
Comments: Keywords: Coarse spaces, balleans, ultrafilters, dynamical systems
Subjects: General Topology (math.GN)

For a coarse space $(X, \mathcal{E})$, $X^\sharp$ denotes the set of all unbounded ultrafilters on $X$ endowed with the parallelity relation: $p||q$ if there exists $E \in \mathcal{E}$ such that $E[P]\in q$ for each $P\in p$. If $(X, \mathcal{E})$ is finitary then there exists a group $G$ of permutations of $X$ such that the coarse structure $\mathcal{E}$ has the base $\{\{ (x,gx): x\in X$, $g\in F\}: F\in [G]^{<\omega}, \ id \in F \}.$ We survey and analyze interplays between $(X, \mathcal{E})$, $X^\sharp$ and the dynamical system $(G, X^\sharp)$.

[105]
Title: Commuting translations and multiplications by powers
Subjects: Number Theory (math.NT)

An open problem about finite geometric progressions in syndetic sets leads to a family of diophantine equations related to the commutativity of translation and multiplication by squares.

[106]
Title: The asymptotic distribution of cluster sizes for supercritical percolation on random split trees
Subjects: Probability (math.PR)

We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation on those trees and obtain a precise weak limit theorem for the sizes of the largest clusters. We also show that the approach developed in this work may be useful for studying percolation on other classes of trees with logarithmic height, for instance, we study also the case of $d$-regular trees.

[107]
Title: Linear Pullback components of the space of codimension one foliations
Comments: This is a pre-print of an article published in Bulletin of the Brazilian Mathematical Society, New Series (206). The final authenticated version is available online at:
Subjects: Algebraic Geometry (math.AG)

The space of holomorphic foliations of codimension one and degree $d\geq 2$ in $\mathbb{P}^n$ ($n\geq 3$) has an irreducible component whose general element can be written as a pullback $F^*\mathcal{F}$, where $\mathcal{F}$ is a general foliation of degree $d$ in $\mathbb{P}^2$ and $F:\mathbb{P}^n\dashrightarrow \mathbb{P}^2$ is a general rational linear map. We give a polynomial formula for the degrees of such components.

[108]
Title: The zeroth P^1-stable homotopy sheaf of a motivic space
Authors: Tom Bachmann
Subjects: K-Theory and Homology (math.KT); Algebraic Geometry (math.AG); Algebraic Topology (math.AT)

We establish a kind of "degree zero Freudenthal Gm-suspension theorem" in motivic homotopy theory. From this we deduce results about the conservativity of the P^1-stabilization functor.
In order to establish these results, we show how to compute certain pullbacks in the cohomology of a strictly homotopy invariant sheaf in terms of the Rost--Schmid complex. This establishes the main conjecture of [BY18], which easily implies the aforementioned results.

[109]
Title: On the conditional plurisubharmonic envelopes of bounded functions
Subjects: Complex Variables (math.CV)

In this paper, we extend some recent results of Guedj-Lu-Zeriahi about psh envelopes of bounded functions on bounded domains in $\mathbb{C}^n$. We also present a result on the regularity of psh envelopes.

[110]
Title: Schrödinger and polyharmonic operators on infinite graphs: Parabolic well-posedness and p-independence of spectra
Subjects: Spectral Theory (math.SP); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)

We analyze properties of semigroups generated by Schr\"odinger operators $-\Delta+V$ or polyharmonic operators $-(-\Delta)^m$, on metric graphs both on $L^p$-spaces and spaces of continuous functions. In the case of spatially constant potentials, we provide a semi-explicit formula for their kernel. Under an additional sub-exponential growth condition on the graph, we prove analyticity, ultracontractivity, and pointwise kernel estimates for these semigroups; we also show that their generators' spectra coincide on all relevant function spaces and present a Kre\u{\i}n-type dimension reduction, showing that their spectral values are determined by the spectra of generalized discrete Laplacians acting on various spaces of functions supported on combinatorial graphs.

[111]
Title: Hydrogen atom bound states whose spectral measures have positive upper fractal dimensions
Subjects: Mathematical Physics (math-ph); Spectral Theory (math.SP)

It is shown that, Baire generically, the bound states of the Hamiltonian of the Hydrogen atom have spectral measures with exact $0$-lower and $1/3$-upper generalized fractal dimensions; the relation to (a weak form of) dynamical delocalization along orthonormal bases is also discussed. Such result is a consequence of the distribution of the Hamiltonian eigenvalues.

[112]
Title: An Immersed Lagrangian-Eulerian Method for Fluid-Structure Interaction
Subjects: Numerical Analysis (math.NA)

This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving arbitrary rigid bodies immersed in viscous incompressible fluids. This approach, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid domains, as in a partitioned formulation, while also using non-conforming discretizations of the moving fluid and structure, as in an immersed formulation. A Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of fluid along that interface is constrained to match the solid velocity, so as to enforce the no-slip condition. We introduce a penalty approach that weakly imposes the no-slip condition along the fluid-solid interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure interaction scheme relies on a recently developed immersed interface method for discrete geometries, which enables the accurate determination of both velocities and stresses along the fluid-structure interface. The effectiveness of this straightforward FSI methodology is extensively tested against benchmark computational and experimental studies in two and three spatial dimensions, including for geometries with non-smooth features. Unlike commonly used partitioned methods, which can suffer from so-called added mass effect instabilities, our methodology avoids subiterations between fluid and solid solvers or complex handling of the fluid pressure, and it retains stability for models involving extremely low, nearly equal, equal, and high solid-fluid density ratios.

[113]
Title: A valley version of the Delta square conjecture
Comments: 20 pages, 16 figures
Subjects: Combinatorics (math.CO)

Inspired by [Qiu, Wilson 2019] and [D'Adderio, Iraci, Vanden Wyngaerd 2019 - Delta Square], we formulate a generalised Delta square conjecture (valley version). Furthermore, we use similar techniques as in [Haglund, Sergel 2019] to obtain a schedule formula for the combinatorics of our conjecture. We then use this formula to prove that the (generalised) valley version of the Delta conjecture implies our (generalised) valley version of the Delta square conjecture. This implication broadens the argument in [Sergel 2016], relying on the formulation of the touching version in terms of the $\Theta_f$ operators introduced in [D'Adderio, Iraci, Vanden Wyngaerd 2019 - Theta Operators].

[114]
Title: On the incomplete Srivastava's triple hypergeometric matrix functions
Authors: Ashish Verma
Comments: arXiv admin note: substantial text overlap with arXiv:2003.11419
Subjects: Classical Analysis and ODEs (math.CA)

The paper proposes to introduce incomplete Srivastava's triple hypergeometric matrix functions through application of the incomplete Pochhammer matrix symbols. We also derive certain properties such as matrix differential equation, integral formula, reduction formula, recursion formula, recurrence relation and differentiation formula of the incomplete Srivastava's triple hypergeometric matrix functions.

### Cross-lists for Fri, 27 Mar 20

[115]  arXiv:1912.09422 (cross-list from hep-th) [pdf, other]
Title: Planar Matrices and Arrays of Feynman Diagrams
Comments: 30 pages, v2 corrected typos and added (4,9) results
Subjects: High Energy Physics - Theory (hep-th); Combinatorics (math.CO)

Very recently planar collections of Feynman diagrams were proposed by Borges and one of the authors as the natural generalization of Feynman diagrams for the computation of $k=3$ biadjoint amplitudes. Planar collections are one-dimensional arrays of metric trees satisfying an induced planarity and compatibility condition. In this work we introduce planar matrices of Feynman diagrams as the objects that compute $k=4$ biadjoint amplitudes. These are symmetric matrices of metric trees satisfying compatibility conditions. We introduce two notions of combinatorial bootstrap techniques for finding collections from Feynman diagrams and matrices from collections. As applications of the first, we find all $693$, $13\,612$, and $346\,710$ collections for $(k,n)=(3,7), (3,8),$ and $(3,9)$ respectively. As applications of the second kind, we find all $90\, 608$ and $30\,659\,424$ planar matrices that compute $(k,n)=(4,8)$ and $(4,9)$ biadjoint amplitudes respectively. As an example of the evaluation of matrices of Feynman diagrams, we present the complete form of the $(4,8)$ and $(4,9)$ biadjoint amplitudes. We also start the study of higher dimensional arrays of Feynman diagrams, including the combinatorial version of the duality between $(k,n)$ and $(n-k,n)$ objects.

[116]  arXiv:2003.11553 (cross-list from cond-mat.str-el) [pdf, other]
Title: Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions
Comments: 39+18 pages, 20+13 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA); Quantum Physics (quant-ph)

Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this paper we demonstrate how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. We demonstrate how, given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group $G$, one can define a (3+1)D topologically invariant path integral in terms of a state sum for a $G$ symmetry-protected topological (SPT) state. We present an exactly solvable Hamiltonian for the system and demonstrate explicitly a (2+1)D $G$ symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. We present concrete algorithms that can be used to compute anomaly indicators in general. Our approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In addition to providing a general way to compute the anomaly, our result also shows, by explicit construction, that every symmetry fractionalization class for any UMTC can be realized at the surface of a (3+1)D SPT state. As a byproduct, this construction also provides a way of explicitly seeing how the algebraic data that defines symmetry fractionalization in general arises in the context of exactly solvable models. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the $\mathcal{H}^4(G, U(1))$ obstruction that arises in the theory of $G$-crossed braided tensor categories, for which no general method has been presented to date.

[117]  arXiv:2003.11663 (cross-list from cs.CR) [pdf, other]
Title: From Information Theory Puzzles in Deletion Channels to Deniability in Quantum Cryptography
Comments: PhD thesis, 152 pages, 5 figures
Subjects: Cryptography and Security (cs.CR); Discrete Mathematics (cs.DM); Information Theory (cs.IT); Quantum Physics (quant-ph)

From the output produced by a memoryless deletion channel with a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that of the uniform prior measures the amount of information about the channel input which is conveyed by the output of length $m$. We first conjecture on the basis of experimental data that the entropy of the posterior is minimized by the constant strings $\texttt{000}\ldots$, $\texttt{111}\ldots$ and maximized by the alternating strings $\texttt{0101}\ldots$, $\texttt{1010}\ldots$. We present related combinatorial theorems involving binary (sub/super)-sequences and prove the minimal entropy conjecture for single and double deletions using clustering techniques. We then prove the minimization conjecture in the asymptotic limit using results from hidden word statistics by showing how the analytic-combinatorial methods of Flajolet, Szpankowski and Vall\'ee, relying on generating functions, can be applied to resolve the case of fixed output length and $n\rightarrow\infty$.
Next, we revisit the notion of deniability in quantum key exchange (QKE). We introduce and formalize the notion of coercer-deniable QKE. We then establish a connection between covert communication and deniability to propose DC-QKE, a simple and provably secure construction for coercer-deniable QKE. We relate deniability to fundamental concepts in quantum information theory and suggest a generic approach based on entanglement distillation for achieving information-theoretic deniability, followed by an analysis of other closely related results such as the relation between the impossibility of unconditionally secure quantum bit commitment and deniability. Finally, we present an efficient coercion-resistant and quantum-secure voting scheme, based on fully homomorphic encryption.

[118]  arXiv:2003.11713 (cross-list from eess.SY) [pdf, other]
Title: Event-Driven Receding Horizon Control For On-line Distributed Persistent Monitoring on Graphs
Subjects: Systems and Control (eess.SY); Optimization and Control (math.OC)

This paper considers the optimal multi-agent persistent monitoring problem defined on a set of nodes (targets) interconnected according to a fixed graph topology (PMG). The objective is to minimize a measure of mean overall node state uncertainty evaluated over a finite time interval via controlling the motion of the team of agents. A class of threshold-based parametric controllers has been proposed in a prior work as a distributed on-line solution to this PMG problem. However, this approach involves a lengthy and computationally intensive parameter tuning process, which can still result in low performing solutions. Recent works have focused on appending a centralized off-line stage to the aforementioned parameter tuning process so as to improve its performance. However, this comes at the cost of sacrificing the on-line distributed nature of the original solution while also increasing the associated computational cost. Moreover, such parametric control approaches are slow to react to compensate for possible state perturbations. Motivated by these challenges, this paper proposes a computationally cheap novel event-driven receding horizon control (ED-RHC) approach as a distributed on-line solution to the PMG problem. In particular, the discrete-event nature of the PMG systems is exploited in this work to determine locally (i.e., both temporally and spatially) optimum trajectory decisions for each agent to make at different discrete event times on its trajectory. Numerical results obtained from this ED-RHC method show significant improvements compared to state of the art distributed on-line parametric control solutions.

[119]  arXiv:2003.11764 (cross-list from cs.CC) [pdf, ps, other]
Title: No-Rainbow Problem is NP-Hard
Authors: Dmitriy Zhuk
Subjects: Computational Complexity (cs.CC); Logic in Computer Science (cs.LO); Rings and Algebras (math.RA)

Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints. In this paper we show that one of the most popular variants of the SCSP, called No-Rainbow Problem, is NP-Hard.

[120]  arXiv:2003.11775 (cross-list from cs.DS) [pdf, other]
Title: On Structural Parameterizations of Node Kayles
Comments: a preliminary version was presented at JCDCG^3 2018
Subjects: Data Structures and Algorithms (cs.DS); Combinatorics (math.CO)

Node Kayles is a well-known two-player impartial game on graphs: Given an undirected graph, each player alternately chooses a vertex not adjacent to previously chosen vertices, and a player who cannot choose a new vertex loses the game. The problem of deciding if the first player has a winning strategy in this game is known to be PSPACE-complete. There are a few studies on algorithmic aspects of this problem. In this paper, we consider the problem from the viewpoint of fixed-parameter tractability. We show that the problem is fixed-parameter tractable parameterized by the size of a minimum vertex cover or the modular-width of a given graph. Moreover, we give a polynomial kernelization with respect to neighborhood diversity.

[121]  arXiv:2003.11810 (cross-list from quant-ph) [pdf, other]
Title: Searching for Coherent States, From Origins to Quantum Gravity
Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph); History and Philosophy of Physics (physics.hist-ph)

We discuss the notion of coherent states from three different perspectives: the seminal approach of Schroedinger, the experimental take of quantum optics, and the theoretical developments in quantum gravity. This comparative study tries to emphasise the connections between the approaches, and to offer a coherent short story of the field, so to speak. It may be useful for pedagogical purposes, as well as for specialists of quantum optics and quantum gravity willing to embed their perspective within a wider landscape.

[122]  arXiv:2003.11816 (cross-list from cs.CV) [pdf, other]
Title: Do Deep Minds Think Alike? Selective Adversarial Attacks for Fine-Grained Manipulation of Multiple Deep Neural Networks
Comments: 9 pages, submitted to ICML 2020
Subjects: Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG); Image and Video Processing (eess.IV); Optimization and Control (math.OC); Machine Learning (stat.ML)

Recent works have demonstrated the existence of {\it adversarial examples} targeting a single machine learning system. In this paper we ask a simple but fundamental question of "selective fooling": given {\it multiple} machine learning systems assigned to solve the same classification problem and taking the same input signal, is it possible to construct a perturbation to the input signal that manipulates the outputs of these {\it multiple} machine learning systems {\it simultaneously} in arbitrary pre-defined ways? For example, is it possible to selectively fool a set of "enemy" machine learning systems but does not fool the other "friend" machine learning systems? The answer to this question depends on the extent to which these different machine learning systems "think alike". We formulate the problem of "selective fooling" as a novel optimization problem, and report on a series of experiments on the MNIST dataset. Our preliminary findings from these experiments show that it is in fact very easy to selectively manipulate multiple MNIST classifiers simultaneously, even when the classifiers are identical in their architectures, training algorithms and training datasets except for random initialization during training. This suggests that two nominally equivalent machine learning systems do not in fact "think alike" at all, and opens the possibility for many novel applications and deeper understandings of the working principles of deep neural networks.

[123]  arXiv:2003.11830 (cross-list from cs.LG) [pdf, other]
Title: A lower bound for the ELBO of the Bernoulli Variational Autoencoder
Subjects: Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)

We consider a variational autoencoder (VAE) for binary data. Our main innovations are an interpretable lower bound for its training objective, a modified initialization and architecture of such a VAE that leads to faster training, and a decision support for finding the appropriate dimension of the latent space via using a PCA. Numerical examples illustrate our theoretical result and the performance of the new architecture.

[124]  arXiv:2003.11914 (cross-list from cs.CG) [pdf, ps, other]
Title: Geometric Sparsification of Closeness Relations: Eigenvalue Clustering for Computing Matrix Functions
Subjects: Computational Geometry (cs.CG); Mathematical Software (cs.MS); Numerical Analysis (math.NA)

We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and whose edges are pairs of eigenvalues that are at most \delta away from each other. Davies and Higham proposed solving this problem by enumerating the edges of the graph, which requires at least $\Omega(n^{2})$ work. We show that the problem can be solved by computing the Delaunay triangulation of the eigenvalues, removing from it long edges, and computing the connected components of the remaining edges in the triangulation. This leads to an $O(n\log n)$ algorithm. We have implemented both algorithms using CGAL, a mature and sophisticated computational-geometry software library, and we demonstrate that the new algorithm is much faster in practice than the naive algorithm. We also present a tight analysis of the naive algorithm, showing that it performs $\Theta(n^{2})$ work, and correct a misrepresentation in the original statement of the problem. To the best of our knowledge, this is the first application of computational geometry to solve a real-world problem in numerical linear algebra.

[125]  arXiv:2003.11920 (cross-list from q-bio.PE) [pdf, other]
Title: A simple Stochastic SIR model for COVID 19 Infection Dynamics for Karnataka: Learning from Europe
Subjects: Populations and Evolution (q-bio.PE); Dynamical Systems (math.DS)

In this short note we model the region-wise trends of the evolution to COVID-19 infections using a stochastic SIR model. The SIR dynamics are expressed using \textit{It\^o-stochastic differential equations}. We first derive the parameters of the model from the available daily data from European regions based on a 24-day history of infections, recoveries and deaths. The derived parameters have been aggregated to project future trends for the Indian subcontinent, which is currently at an early stage in the infection cycle. The projections are meant to serve as a guideline for strategizing the socio-political counter measures to mitigate COVID-19.

[126]  arXiv:2003.11936 (cross-list from cs.CR) [pdf, ps, other]
Title: Cryptography using generalized Fibonacci matrices with Affine-Hill cipher
Comments: Construction, development and efficiency
Subjects: Cryptography and Security (cs.CR); Combinatorics (math.CO); Number Theory (math.NT)

In this article, we have proposed a public key cryptography using Affine-Hill cipher with a generalized Fibonacci matrix(called multinacci matrix). Also proposed a key establishment(exchange of key matrix $K=Q_{\lambda}^{k}$ of order $\lambda\times\lambda$ for encryption-decryption) scheme with the help of multinacci sequences under prime modulo. In this scheme, instead of exchanging key matrix, we need to exchange the only pair of numbers $(\lambda, k)$, which reduces the time complexity as well as space complexity and comes with a large key-space.

[127]  arXiv:2003.11954 (cross-list from eess.SY) [pdf, other]
Title: Bounded state Estimation over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity
Comments: arXiv admin note: text overlap with arXiv:1902.00726
Subjects: Systems and Control (eess.SY); Information Theory (cs.IT)

We investigate bounded state estimation of linear systems over finite-state erasure and additive noise channels in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the topological entropy of the channel dynamics. Some examples are introduced and separate capacity bounds based on their specific features are derived and compared with bounds from topological entropy. Necessary and sufficient conditions for linear state estimation with bounded errors via such channels are then obtained, by extending previous results for nonstochastic memoryless channels to finite-state channels. These estimation conditions bring together the topological entropies of the linear system and the discrete channel.

[128]  arXiv:2003.11998 (cross-list from cs.DS) [pdf, other]
Title: A Blind Permutation Similarity Algorithm
Authors: Eric Barszcz
Subjects: Data Structures and Algorithms (cs.DS); Combinatorics (math.CO)

This paper introduces a polynomial blind algorithm that determines when two square matrices, $A$ and $B$, are permutation similar. The shifted and translated matrices $(A+\beta I+\gamma J)$ and $(B+\beta I+\gamma J)$ are used to color the vertices of two square, edge weighted, rook's graphs. Then the orbits are found by repeated symbolic squaring of the vertex colored and edge weighted adjacency matrices. Multisets of the diagonal symbols from non-permutation similar matrices are distinct within a few iterations, typically four or less.

[129]  arXiv:2003.12009 (cross-list from eess.SP) [pdf, other]
Title: Multi-Lead ECG Classification via an Information-Based Attention Convolutional Neural Network
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT); Machine Learning (cs.LG); Machine Learning (stat.ML)

Objective: A novel structure based on channel-wise attention mechanism is presented in this paper. Embedding with the proposed structure, an efficient classification model that accepts multi-lead electrocardiogram (ECG) as input is constructed. Methods: One-dimensional convolutional neural networks (CNN) have proven to be effective in pervasive classification tasks, enabling the automatic extraction of features while classifying targets. We implement the Residual connection and design a structure which can learn the weights from the information contained in different channels in the input feature map during the training process. An indicator named mean square deviation is introduced to monitor the performance of a particular model segment in the classification task on the two out of the five ECG classes. The data in the MIT-BIH arrhythmia database is used and a series of control experiments is conducted. Results: Utilizing both leads of the ECG signals as input to the neural network classifier can achieve better classification results than those from using single channel inputs in different application scenarios. Models embedded with the channel-wise attention structure always achieve better scores on sensitivity and precision than the plain Resnet models. The proposed model exceeds the performance of most of the state-of-the-art models in ventricular ectopic beats (VEB) classification, and achieves competitive scores for supraventricular ectopic beats (SVEB). Conclusion: Adopting more lead ECG signals as input can increase the dimensions of the input feature maps, helping to improve both the performance and generalization of the network model. Significance: Due to its end-to-end characteristics, and the extensible intrinsic for multi-lead heart diseases diagnosing, the proposed model can be used for the real-time ECG tracking of ECG waveforms for Holter or wearable devices.

[130]  arXiv:2003.12029 (cross-list from cs.MS) [pdf, other]
Title: FlexRiLoG -- A SageMath Package for Motions of Graphs
Subjects: Mathematical Software (cs.MS); Robotics (cs.RO); Combinatorics (math.CO)

In this paper we present the SageMath package FlexRiLoG (short for flexible and rigid labelings of graphs). Based on recent results the software generates motions of graphs using special edge colorings. The package computes and illustrates the colorings and the motions. We present the structure and usage of the package.

[131]  arXiv:2003.12034 (cross-list from cs.CR) [pdf, ps, other]
Title: Man-in-the-Middle and Denial of Service Attacks in Wireless Secret Key Generation
Subjects: Cryptography and Security (cs.CR); Information Theory (cs.IT)

Wireless secret key generation (W-SKG) from shared randomness (e.g., from the wireless channel fading realizations), is a well established scheme that can be used for session key agreement. W-SKG approaches can be of particular interest in delay constrained wireless networks and notably in the context of ultra reliable low latency communications (URLLC) in beyond fifth generation (B5G) systems. However, W-SKG schemes are known to be malleable over the so called "advantage distillation" phase, during which observations of the shared randomness are obtained at the legitimate parties. As an example, an active attacker can act as a man-in-the-middle (MiM) by injecting pilot signals and/or can mount denial of service attacks (DoS) in the form of jamming. This paper investigates the impact of injection and reactive jamming attacks in W-SKG. First, it is demonstrated that injection attacks can be reduced to - potentially less harmful - jamming attacks by pilot randomization; a novel system design with randomized QPSK pilots is presented. Subsequently, the optimal jamming strategy is identified in a block fading additive white Gaussian noise (BF-AWGN) channel in the presence of a reactive jammer, using a game theoretic formulation. It is shown that the impact of a reactive jammer is far more severe than that of a simple proactive jammer

[132]  arXiv:2003.12052 (cross-list from stat.ML) [pdf, other]
Title: Corella: A Private Multi Server Learning Approach based on Correlated Queries
Comments: 10 pages, 5 figures, 3 tables
Subjects: Machine Learning (stat.ML); Cryptography and Security (cs.CR); Information Theory (cs.IT); Machine Learning (cs.LG)

The emerging applications of machine learning algorithms on mobile devices motivate us to offload the computation tasks of training a model or deploying a trained one to the cloud. One of the major challenges in this setup is to guarantee the privacy of the client's data. Various methods have been proposed to protect privacy in the literature. Those include (i) adding noise to the client data, which reduces the accuracy of the result, (ii) using secure multiparty computation, which requires significant communication among the computing nodes or with the client, (iii) relying on homomorphic encryption methods, which significantly increases computation load. In this paper, we propose an alternative approach to protect the privacy of user data. The proposed scheme relies on a cluster of servers where at most $T$ of them for some integer $T$, may collude, that each running a deep neural network. Each server is fed with the client data, added with a $\textit{strong}$ noise. This makes the information leakage to each server information-theoretically negligible. On the other hand, the added noises for different servers are $\textit{correlated}$. This correlation among queries allows the system to be $\textit{trained}$ such that the client can recover the final result with high accuracy, by combining the outputs of the servers, with minor computation efforts. Simulation results for various datasets demonstrate the accuracy of the proposed approach.

### Replacements for Fri, 27 Mar 20

[133]  arXiv:1601.03207 (replaced) [pdf, other]
Title: On Generalizations of Cycles and Chordality to Hypergraphs from an Algebraic Viewpoint
Comments: A corrigendum is added in this version
Journal-ref: Algebra Colloquium 24:4 (2017) 611-624
Subjects: Combinatorics (math.CO); Commutative Algebra (math.AC)
[134]  arXiv:1609.02206 (replaced) [pdf, ps, other]
Title: A couple of real hyperbolic disc bundles over surfaces
Comments: 7 pages, to appear in "Groups, Geometry, and Dynamics"
Subjects: Geometric Topology (math.GT); Differential Geometry (math.DG)
[135]  arXiv:1611.05685 (replaced) [pdf, other]
Title: Teichmüller polynomials of fibered alternating links
Comments: 22 pages, 12 figures
Journal-ref: Osaka J. Math. 56 (2019), no. 4, 787-806
Subjects: Geometric Topology (math.GT)
[136]  arXiv:1705.08617 (replaced) [pdf, other]
Title: Which bridge estimator is optimal for variable selection?
Comments: 84 pages, 11 figures
Subjects: Statistics Theory (math.ST); Information Theory (cs.IT)
[137]  arXiv:1707.06593 (replaced) [pdf, ps, other]
Title: Lipschitz extensions to finitely many points
Authors: Giuliano Basso
Journal-ref: Anal. Geom. Metric Spaces, Volume 6, Issue 1 (2018), pp. 174-191
Subjects: Metric Geometry (math.MG)
[138]  arXiv:1708.00903 (replaced) [pdf, ps, other]
Title: Nef cones of nested Hilbert schemes of points on surfaces
Authors: Tim Ryan, Ruijie Yang
Subjects: Algebraic Geometry (math.AG)
[139]  arXiv:1708.03112 (replaced) [pdf, ps, other]
Title: Spectrum of signless 1-Laplacian on simplicial complexes
Authors: Xin Luo, Dong Zhang
Subjects: Spectral Theory (math.SP); Combinatorics (math.CO)
[140]  arXiv:1710.05136 (replaced) [pdf, ps, other]
Title: Probabilistic representation of weak solutions to a parabolic boundary value problem on a non-smooth domain
Subjects: Probability (math.PR); Analysis of PDEs (math.AP)
[141]  arXiv:1712.09035 (replaced) [pdf, other]
Title: Secure Network Code for Adaptive and Active Attacks with No-Randomness in Intermediate Nodes
Journal-ref: IEEE Transactions on Information Theory, Volume: 66, Issue: 3, 1428 -- 1448 (2020)
Subjects: Information Theory (cs.IT)
[142]  arXiv:1801.00465 (replaced) [pdf, ps, other]
Title: Hyperbolic 2-spheres with cone singularities
Journal-ref: Topology and its Applications, Volume 272, 1 March 2020, 107073
Subjects: Geometric Topology (math.GT)
[143]  arXiv:1801.03198 (replaced) [pdf, ps, other]
Title: Plane curves possessing two outer Galois points
Comments: 13 pages. The main theorem and its proof are revised
Subjects: Algebraic Geometry (math.AG)
[144]  arXiv:1802.04263 (replaced) [pdf]
Title: Generalized hypergeometric solutions of the Heun equation
Authors: A.M. Ishkhanyan
Journal-ref: Theor. Math. Phys. 202, 1-10 (2020)
Subjects: Classical Analysis and ODEs (math.CA)
[145]  arXiv:1805.05749 (replaced) [pdf, ps, other]
Title: On the genus defect of positive braid knots
Authors: Livio Liechti
Comments: 22 pages, 24 figures
Journal-ref: Algebr. Geom. Topol. 20 (2020), no. 1, 403-428
Subjects: Geometric Topology (math.GT)
[146]  arXiv:1805.05890 (replaced) [pdf, other]
Title: Differential-henselianity and maximality of asymptotic valued differential fields
Comments: 31 pages; v4: minor corrections and improvements made throughout, including those suggested by the reviewer
Subjects: Commutative Algebra (math.AC); Logic (math.LO)
[147]  arXiv:1805.08972 (replaced) [src]
Title: Almost Maximal Numerical Semigroups formed by Concatenation of Arithmetic Sequences
Comments: The contents of this paper has been merged with the paper arXiv:1802.02564 because of similarity of themes
Subjects: Commutative Algebra (math.AC)
[148]  arXiv:1805.11363 (replaced) [pdf, other]
Title: A transformed stochastic Euler scheme for multidimensional transmission PDE
Authors: Pierre Etore (IPS), Miguel Martinez (LAMA)
Subjects: Probability (math.PR)
[149]  arXiv:1806.00033 (replaced) [pdf, other]
Title: Minimal pseudo-Anosov stretch factors on nonoriented surfaces
Comments: 26 pages, 6 figures
Journal-ref: Algebr. Geom. Topol. 20 (2020), no. 1, 451-485
Subjects: Geometric Topology (math.GT)
[150]  arXiv:1806.06832 (replaced) [pdf, ps, other]
Title: Bounded and Divergent Trajectories And Expanding Curves on Homogeneous Spaces
Authors: Osama Khalil
Comments: 46 pages. Minor corrections based on referee comments. To appear in Transactions of the AMS
Subjects: Dynamical Systems (math.DS); Number Theory (math.NT)
[151]  arXiv:1807.05152 (replaced) [pdf, ps, other]
Title: Information theory with finite vector spaces
Comments: Presented in part at the Latin American Week on Coding and Information 2018 (Campinas, Brazil)
Journal-ref: IEEE Transactions on Information Theory, vol. 65, no. 9, pp. 5674-5687, Sept. 2019
Subjects: Mathematical Physics (math-ph); Information Theory (cs.IT); Probability (math.PR)
[152]  arXiv:1808.07890 (replaced) [pdf, ps, other]
Title: TAP free energy, spin glasses, and variational inference
Subjects: Probability (math.PR); Mathematical Physics (math-ph); Statistics Theory (math.ST)
[153]  arXiv:1809.06538 (replaced) [pdf, ps, other]
Title: A functional stable limit theorem for Gibbs-Markov maps
Comments: multidimensional version and applications added; 27 pages
Subjects: Dynamical Systems (math.DS)
[154]  arXiv:1809.09940 (replaced) [pdf, ps, other]
Title: Derived factorization categories of non-Thom--Sebastiani-type sums of potentials
Comments: Major improvements. The proof of the existence of a tilting object is added, and we compute the associated quiver with relations. 48 pages
Subjects: Algebraic Geometry (math.AG)
[155]  arXiv:1810.01106 (replaced) [pdf, other]
Title: Asymptotically optimal cubature formulas on manifolds for prefixed weights
Subjects: Numerical Analysis (math.NA)
[156]  arXiv:1810.06348 (replaced) [pdf, ps, other]
Title: Weak-Identification Robust Wild Bootstrap applied to a Consistent Model Specification Test
Authors: Jonathan B. Hill
Subjects: Statistics Theory (math.ST)
[157]  arXiv:1810.08028 (replaced) [pdf, ps, other]
Title: Rigidity in etale motivic stable homotopy theory
Authors: Tom Bachmann
Comments: v2: include results for schemes of finite p-etale dimension at one prime only
Subjects: K-Theory and Homology (math.KT); Algebraic Geometry (math.AG)
[158]  arXiv:1811.03996 (replaced) [pdf, ps, other]
Title: Uncertainty relations and sparse signal recovery
Comments: Chapter in Information-theoretic Methods in Data Science, M. Rodrigues and Y. Eldar, Eds., Cambridge University Press, 2020
Subjects: Information Theory (cs.IT)
[159]  arXiv:1811.04157 (replaced) [pdf, other]
Title: On the geometry, flows and visualization of singular complex analytic vector fields on Riemann surfaces
Comments: 25 figures, 65 pages
Journal-ref: Proceedings of the 2018 Workshop in Holomorphic Dynamics, C. Cabrera et al. Eds., Instituto de Matem\'aticas, UNAM, M\'exico, Serie Papirhos, Actas 1 (2019), 21--109
Subjects: Dynamical Systems (math.DS)
[160]  arXiv:1811.11502 (replaced) [pdf, other]
Title: Fully Discrete Positivity-Preserving and Energy-Dissipating Schemes for Aggregation-Diffusion Equations with a Gradient Flow Structure
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
[161]  arXiv:1812.04918 (replaced) [pdf, ps, other]
Title: On the arithmetic and the geometry of skew-reciprocal polynomials
Authors: Livio Liechti
Comments: 9 pages, 0 figures
Journal-ref: Proc. Amer. Math. Soc. 147 (2019), no. 12, 5131-5139
Subjects: Number Theory (math.NT); Geometric Topology (math.GT)
[162]  arXiv:1812.09373 (replaced) [pdf, ps, other]
Title: Another approach to volume of matroid polytopes
Subjects: Combinatorics (math.CO)
[163]  arXiv:1901.10326 (replaced) [pdf, ps, other]
Title: Some results concerning the $\mathsf{SRT}^2_2$ vs. $\mathsf{COH}$ problem
Subjects: Logic (math.LO)
[164]  arXiv:1902.02961 (replaced) [pdf, ps, other]
Title: Arithmetic subspaces of moduli spaces of rank one local systems
Comments: latex 20 pages
Subjects: Algebraic Geometry (math.AG)
[165]  arXiv:1902.04508 (replaced) [pdf, other]
Title: A hierarchy of dismantlings in Graphs
Comments: 17 pages, 9 figures
Subjects: Combinatorics (math.CO); Algebraic Topology (math.AT)
[166]  arXiv:1902.10930 (replaced) [pdf, other]
Title: Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds
Subjects: Optimization and Control (math.OC)
[167]  arXiv:1903.00911 (replaced) [pdf, ps, other]
Title: Randomized Discrete Empirical Interpolation Method for Nonlinear Model Reduction
Comments: 27 pages, 8 figures
Subjects: Numerical Analysis (math.NA)
[168]  arXiv:1903.03605 (replaced) [pdf, other]
Title: Understanding Sparse JL for Feature Hashing
Comments: Appeared at NeurIPS 2019; this is the full version
Subjects: Machine Learning (stat.ML); Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Probability (math.PR)
[169]  arXiv:1903.12123 (replaced) [pdf, ps, other]
Title: Around the nonlinear Ryll-Nardzewski theorem
Comments: 15 pages, to appear, Mathematische Annalen, Referee suggestions incorporated and some new references added, text has a few ideas in common with arXiv:1909.09723. Relations between the two papers await further exploration
Subjects: Dynamical Systems (math.DS); Functional Analysis (math.FA); Group Theory (math.GR)
[170]  arXiv:1904.08578 (replaced) [pdf, ps, other]
Title: Classification of simple weight modules for the $N=2$ superconformal algebra
Comments: 18 pages, Latex, in this version we delete the Section 7 for application to the $N=1$ superconformal algebra
Subjects: Representation Theory (math.RT); Mathematical Physics (math-ph); Quantum Algebra (math.QA); Rings and Algebras (math.RA)
[171]  arXiv:1904.12780 (replaced) [pdf, ps, other]
Title: A Simple Derivation of the Refined Sphere Packing Bound Under Certain Symmetry Hypotheses
Authors: Baris Nakiboglu
Subjects: Information Theory (cs.IT)
[172]  arXiv:1905.02173 (replaced) [pdf, other]
Title: Assisted concentration of Gaussian resources
Comments: 21 pages, 3 figures. In v2 we changed the title and added the new Figures 1 and 2, illustrating the one-way and two-way Gaussian collaboration protocols, respectively
Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph)
[173]  arXiv:1905.04250 (replaced) [pdf, ps, other]
Title: From path integrals to dynamical algebras: a macroscopic view of quantum physics
Comments: 9 pages, no figures; v2: exposition improved, reference added
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); History and Philosophy of Physics (physics.hist-ph)
[174]  arXiv:1905.09061 (replaced) [pdf, ps, other]
Title: Octahedral norms in duals and biduals of Lipschitz-free spaces
Subjects: Functional Analysis (math.FA)
[175]  arXiv:1905.09443 (replaced) [pdf, ps, other]
Title: Kochen-Specker sets in four-dimensional spaces
Comments: 10 pages. This version adds a new Proposition 2.5 about the vertex-transitivity of the orthogonality graph, and one of references was updated
Subjects: Combinatorics (math.CO); Quantum Physics (quant-ph)
[176]  arXiv:1906.03486 (replaced) [pdf, ps, other]
Title: On statistical Calderón problems
Subjects: Statistics Theory (math.ST); Analysis of PDEs (math.AP)
[177]  arXiv:1906.04607 (replaced) [pdf, ps, other]
Title: Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning
Comments: 38 pages, 11 figures, 10 tables. We are very thankful to the anonymous referees, whose comments were considered in this submission
Subjects: Statistics Theory (math.ST)
[178]  arXiv:1906.10345 (replaced) [pdf, other]
Title: Finite-Dimensional Controllers for Robust Regulation of Boundary Control Systems
Comments: 22 pages, 6 figures
Subjects: Optimization and Control (math.OC)
[179]  arXiv:1907.00862 (replaced) [pdf, ps, other]
Title: Independent sets in the hypercube revisited
Subjects: Combinatorics (math.CO); Probability (math.PR)
[180]  arXiv:1907.08047 (replaced) [pdf, other]
Title: Brownian bridge with random length and pinning point for modelling of financial information
Authors: Mohammed Louriki
Comments: 28 pages, 2 figures
Subjects: Probability (math.PR); Mathematical Finance (q-fin.MF)
[181]  arXiv:1907.08203 (replaced) [pdf, other]
Title: The closure-complement-frontier problem in saturated polytopological spaces
Subjects: General Topology (math.GN); Combinatorics (math.CO)
[182]  arXiv:1908.01448 (replaced) [pdf, ps, other]
Title: Characterizations of the Hardy space $\mathcal{H}_{FIO}^{1}(\mathbb{R}^{n})$ for Fourier Integral Operators
Comments: Revised and expanded version, 24 pages. Submitted
Subjects: Analysis of PDEs (math.AP)
[183]  arXiv:1908.05631 (replaced) [pdf, ps, other]
Title: Sharp polynomial decay rates for the damped wave equation with Hölder-like damping
Comments: 8 pages, minor revision, final changes before publication
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Spectral Theory (math.SP)
[184]  arXiv:1908.05865 (replaced) [pdf, other]
Title: A Unified Framework for Constructing Centralized Coded Caching Schemes
Subjects: Information Theory (cs.IT); Combinatorics (math.CO)
[185]  arXiv:1908.11271 (replaced) [pdf, other]
Title: Cubic bent functions outside the completed Maiorana-McFarland class
Subjects: Combinatorics (math.CO)
[186]  arXiv:1909.01611 (replaced) [pdf, ps, other]
Title: Derivation modules for Sum and Gluing
Subjects: Commutative Algebra (math.AC)
[187]  arXiv:1909.03145 (replaced) [pdf, ps, other]
Title: From differential equation solvers to accelerated first-order methods for convex optimization
Authors: Hao Luo, Long Chen
Subjects: Optimization and Control (math.OC)
[188]  arXiv:1909.08333 (replaced) [pdf, other]
Title: An Adaptive Parareal Algorithm
Authors: Y. Maday, O. Mula
Subjects: Numerical Analysis (math.NA)
[189]  arXiv:1909.10620 (replaced) [pdf, ps, other]
Title: The classification of ERP G2-structures on Lie groups
Comments: 16 pages. Final version to appear in Annali di Matematica Pura ed Applicata
Subjects: Differential Geometry (math.DG)
[190]  arXiv:1910.01134 (replaced) [pdf, ps, other]
Title: Unifying Lattice Models, Links and Quantum Geometric Langlands via Branes in String Theory
Comments: 31 pages. Typo corrected
Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Geometric Topology (math.GT); Quantum Algebra (math.QA); Representation Theory (math.RT)
[191]  arXiv:1910.04267 (replaced) [pdf, ps, other]
Title: Subspace Estimation from Unbalanced and Incomplete Data Matrices: $\ell_{2,\infty}$ Statistical Guarantees
Subjects: Statistics Theory (math.ST); Information Theory (cs.IT); Machine Learning (cs.LG); Machine Learning (stat.ML)
[192]  arXiv:1910.05948 (replaced) [pdf, other]
Title: Delay-Compensated Control of Sandwiched ODE-PDE-ODE Hyperbolic Systems for Oil Drilling and Disaster Relief
Comments: submitted to Automatica
Subjects: Optimization and Control (math.OC); Analysis of PDEs (math.AP)
[193]  arXiv:1910.11207 (replaced) [pdf, ps, other]
Title: On Higher regulators of Siegel varieties
Comments: 32 pages. Expanded and corrected version. Comments are more than welcome!
Subjects: Number Theory (math.NT)
[194]  arXiv:1910.11860 (replaced) [pdf, ps, other]
Title: Large deviations for conservative stochastic PDE and non-equilibrium fluctuations
Subjects: Probability (math.PR); Analysis of PDEs (math.AP)
[195]  arXiv:1911.02664 (replaced) [pdf, other]
Title: On fixed-point, Krylov, and $2\times 2$ block preconditioners for nonsymmetric problems
Comments: Accepted to SIMAX
Subjects: Numerical Analysis (math.NA)
[196]  arXiv:1911.04032 (replaced) [pdf, other]
Title: A Nonexistence Certificate for Projective Planes of Order Ten with Weight 15 Codewords
Comments: To appear in Applicable Algebra in Engineering, Communication and Computing
Subjects: Discrete Mathematics (cs.DM); Logic in Computer Science (cs.LO); Symbolic Computation (cs.SC); Combinatorics (math.CO)
[197]  arXiv:1911.08069 (replaced) [pdf, other]
Title: Scale Invariance of the Homentropic Inviscid Euler Equations with Application to the Noh Problem
Comments: 21 pages, 9 .png figures, For submission to Physical Review E, major revisions and format changes
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Fluid Dynamics (physics.flu-dyn)
[198]  arXiv:1911.09887 (replaced) [pdf, other]
Title: UAV-enabled Secure Communication with Finite Blocklength
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT)
[199]  arXiv:1911.10929 (replaced) [pdf, ps, other]
Title: Toric foliations with split tangent sheaf
Subjects: Algebraic Geometry (math.AG); Dynamical Systems (math.DS)
[200]  arXiv:1911.12074 (replaced) [pdf, other]
Title: Expected dispersion of uniformly distributed points
Subjects: Probability (math.PR); Computational Geometry (cs.CG)
[201]  arXiv:1912.00391 (replaced) [pdf, other]
Title: A higher order Faber spline basis for sampling discretization of functions
Subjects: Functional Analysis (math.FA); Numerical Analysis (math.NA)
[202]  arXiv:1912.07488 (replaced) [pdf, other]
Title: From a discrete model of chemotaxis with volume-filling to a generalised Patlak-Keller-Segel model
Subjects: Analysis of PDEs (math.AP)
[203]  arXiv:1912.08177 (replaced) [pdf, other]
Title: Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
Subjects: Numerical Analysis (math.NA); Machine Learning (cs.LG)
[204]  arXiv:1912.10031 (replaced) [pdf, ps, other]
Title: Spectral distribution of random matrices from Mutually Unbiased Bases
Comments: This is the updated version
Subjects: Probability (math.PR)
[205]  arXiv:1912.12917 (replaced) [pdf, other]
Title: Quandle colorings vs. biquandle colorings
Comments: 25 pages, 23 figures; Remark 6.1 is revised and there are other minor revisions
Subjects: Geometric Topology (math.GT); Quantum Algebra (math.QA)
[206]  arXiv:2001.06670 (replaced) [pdf, ps, other]
Title: Almost Hermitian Ricci flow
Subjects: Differential Geometry (math.DG)
[207]  arXiv:2001.10326 (replaced) [pdf, other]
Title: A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model
Subjects: Numerical Analysis (math.NA)
[208]  arXiv:2001.11974 (replaced) [pdf, other]
Title: Nonexistence Certificates for Ovals in a Projective Plane of Order Ten
Comments: To appear in Proceedings of the 31st International Workshop on Combinatorial Algorithms (IWOCA 2020)
Subjects: Discrete Mathematics (cs.DM); Logic in Computer Science (cs.LO); Symbolic Computation (cs.SC); Combinatorics (math.CO)
[209]  arXiv:2002.00451 (replaced) [pdf, other]
Title: Fair Allocation Based Soft Load Shedding
Comments: Accepted to Intelligent Systems Conference (IntelliSys) 2020
Subjects: Signal Processing (eess.SP); Optimization and Control (math.OC)
[210]  arXiv:2002.02564 (replaced) [pdf, other]
Title: Empirical Bayes for Large-scale Randomized Experiments: a Spectral Approach
Comments: Corrections and notational changes to Sec 4.4; added acknowledgments; some contents of Sec 2.3 are moved to the Appendix
Subjects: Methodology (stat.ME); Statistics Theory (math.ST)
[211]  arXiv:2002.03077 (replaced) [pdf, ps, other]
Title: Uniformly locally o-minimal open core
Authors: Masato Fujita
Subjects: Logic (math.LO)
[212]  arXiv:2002.05661 (replaced) [pdf, ps, other]
Title: Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
Subjects: Probability (math.PR)
[213]  arXiv:2002.10920 (replaced) [pdf, ps, other]
Title: Generalized Hamming weight of Projective Toric Code over Hypersimplices
Subjects: Commutative Algebra (math.AC); Information Theory (cs.IT)
[214]  arXiv:2002.10956 (replaced) [pdf, ps, other]
Title: Upper bounds on Kronecker coefficients with few rows
Comments: Long version of the paper "Bounds on Kronecker coefficients via contingency tables"
Subjects: Combinatorics (math.CO); Representation Theory (math.RT)
[215]  arXiv:2002.11814 (replaced) [pdf, ps, other]
Title: The period-index problem for elliptic curves and the essential dimension of Picard stacks
Authors: Anningzhe Gao
Comments: We add the proof for I(C)=i(C)
Subjects: Algebraic Geometry (math.AG)
[216]  arXiv:2002.11978 (replaced) [pdf, ps, other]
Title: Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian
Comments: 31pages, 11 tables, 4 figures. Updated: rewrite the Section 2 and correct some typos. Version3: udpated the reference information and submitted it to journal
Subjects: Numerical Analysis (math.NA)
[217]  arXiv:2003.00306 (replaced) [pdf, ps, other]
Title: Dimension-free convergence rates for gradient Langevin dynamics in RKHS
Subjects: Probability (math.PR); Machine Learning (cs.LG); Machine Learning (stat.ML)
[218]  arXiv:2003.00560 (replaced) [pdf, ps, other]
Title: Solid-On-Solid interfaces with disordered pinning
Authors: Hubert Lacoin
Comments: 43 pages 3 figures (minor changes)
Subjects: Probability (math.PR); Mathematical Physics (math-ph)
[219]  arXiv:2003.01951 (replaced) [pdf, other]
Title: Multiclass classification by sparse multinomial logistic regression
Subjects: Statistics Theory (math.ST); Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML)
[220]  arXiv:2003.02832 (replaced) [pdf, other]
Title: Ribbon knots, cabling, and handle decompositions
Comments: 11 pages, 8 figures, Version 2: Minor changes to abstract and introduction. Added a reference to Meier and Zupan's work
Subjects: Geometric Topology (math.GT)
[221]  arXiv:2003.04660 (replaced) [pdf, other]
Title: Impossible measurements require impossible apparatus
Comments: 5pp. v2: font issue fixed, minor textual changes, reference added
Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[222]  arXiv:2003.04773 (replaced) [pdf, ps, other]
Title: Interactive versus non-interactive locally differentially private estimation: Two elbows for the quadratic functional
Subjects: Statistics Theory (math.ST)
[223]  arXiv:2003.05962 (replaced) [pdf, other]
Title: Tube-based Robust Model Predictive Control for a Distributed Parameter System Modeled as a Polytopic LPV (extended version)
Comments: 8 Pages, American Control Conference, 2020
Journal-ref: American Control Conference, 2020
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
[224]  arXiv:2003.06953 (replaced) [pdf, other]
Title: Large deviations for backward stochastic differential equations driven by $G$-Brownian motion
Comments: 21 pages. This is a pre-print of an article published in Journal of Theoretical Probability. The final authenticated version is available online at:
Subjects: Probability (math.PR)
[225]  arXiv:2003.07001 (replaced) [pdf, ps, other]
Title: Resonances and viscosity limit for the Wigner-von Neumann type Hamiltonian
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
[226]  arXiv:2003.07273 (replaced) [pdf, other]
Title: Data Set Description: Identifying the Physics Behind an Electric Motor -- Data-Driven Learning of the Electrical Behavior (Part I)
Subjects: Systems and Control (eess.SY); Machine Learning (cs.LG); Signal Processing (eess.SP); Optimization and Control (math.OC)
[227]  arXiv:2003.07350 (replaced) [pdf, ps, other]
Title: A fractional Laplacian problem with mixed singular nonlinearities and nonregular data
Comments: We are grateful for any feedback or comments. arXiv admin note: text overlap with arXiv:1910.04716
Subjects: Analysis of PDEs (math.AP)
[228]  arXiv:2003.07937 (replaced) [pdf, ps, other]
Title: Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimator
Subjects: Statistics Theory (math.ST); Machine Learning (cs.LG); Systems and Control (eess.SY); Machine Learning (stat.ML)
[229]  arXiv:2003.08083 (replaced) [pdf, other]
Title: Additive Representations of Natural Numbers
Comments: 13 pages, feedback welcome, 2nd version
Subjects: Number Theory (math.NT)
[230]  arXiv:2003.08508 (replaced) [pdf, other]
Title: An Application of Gaussian Process Modeling for High-order Accurate Adaptive Mesh Refinement Prolongation
Subjects: Numerical Analysis (math.NA); Instrumentation and Methods for Astrophysics (astro-ph.IM); Fluid Dynamics (physics.flu-dyn)
[231]  arXiv:2003.09240 (replaced) [pdf, ps, other]
Title: On structured spaces and their properties
Authors: Manuel Norman
Comments: 30 pages; added new examples and references
Subjects: General Mathematics (math.GM)
[232]  arXiv:2003.09694 (replaced) [pdf, ps, other]
Title: Multivariate Hasse-Schmidt Derivation on Exterior Algebras
Subjects: Rings and Algebras (math.RA)
[233]  arXiv:2003.09907 (replaced) [pdf, ps, other]
Title: Log p-divisible groups associated to log 1-motives
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[234]  arXiv:2003.09927 (replaced) [pdf, ps, other]
Title: Abelian Splittings and JSJ-Decompositions of Bestvina--Brady Groups
Authors: Yu-Chan Chang
Comments: 7 pages, 4 figures. Comments are welcome
Subjects: Group Theory (math.GR)
[235]  arXiv:2003.10036 (replaced) [pdf, ps, other]
Title: Hypercyclic Sequences of weighted translations on hypergroups
Comments: 18 pages, Typos are corrected and one reference added
Subjects: Functional Analysis (math.FA)
[236]  arXiv:2003.10408 (replaced) [pdf, ps, other]
Title: Countable graphs are majority 3-choosable
Authors: John Haslegrave
Comments: 6 pages. Updated with discussion of a generalisation and related references
Subjects: Combinatorics (math.CO)
[237]  arXiv:2003.10470 (replaced) [pdf, ps, other]
Title: Taut foliations leafwise branch cover S^2
Authors: Danny Calegari
Comments: 12 pages; version 2: minor typos corrected; added remark on branched maps compatible with contact structures
Subjects: Geometric Topology (math.GT); Dynamical Systems (math.DS)
[238]  arXiv:2003.10755 (replaced) [pdf, ps, other]
Title: Contact interactions in Q.M. Gamma convergence and Bose-Einstein condensation
Subjects: Mathematical Physics (math-ph)
[239]  arXiv:2003.10988 (replaced) [pdf, ps, other]
Title: Points of bounded height on curves and the dimension growth conjecture over $\mathbb{F}_q[t]$
Authors: Floris Vermeulen
Comments: 20 pages, corrected typos
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[240]  arXiv:2003.11049 (replaced) [pdf, ps, other]
Title: A Note on the Disentanglement of Gaussian Quantum States by Symplectic Rotations
Comments: Submitted to CRAS, Paris, in French
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Operator Algebras (math.OA); Symplectic Geometry (math.SG)
[241]  arXiv:2003.11112 (replaced) [pdf, ps, other]
Title: Interior estimates and Convexity for Translating solitons of the $Q_k$-flows in $\mathbb{R}^{n+1}$
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)
[242]  arXiv:2003.11484 (replaced) [pdf, ps, other]
Title: An Approach to the Characterization of the Local Langlands Correspondence
Subjects: Number Theory (math.NT); Representation Theory (math.RT)
[243]  arXiv:2003.11490 (replaced) [pdf, other]
Title: Two almost-circles, and two real ones
Authors: Zoltán Kovács
Comments: 13 pages, 14 figures
Subjects: History and Overview (math.HO); Computational Geometry (cs.CG)
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