# Mathematics

## New submissions

[ total of 205 entries: 1-205 ]
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### New submissions for Thu, 22 Aug 19

[1]
Title: Basel problem: a physicist's solution
Comments: 11 pages, to be published in The Mathematical Intelligencer
Subjects: History and Overview (math.HO); Mathematical Physics (math-ph)

Some time ago Wastlund reformulated the Basel problem in terms of a physical system using the proportionality of the apparent brightness of a star to the inverse square of its distance. Inspired by this approach, we give another physical interpretation which, in our opinion, is simpler, natural enough, and very Eulerian in its spirit.

[2]
Title: Reducing the Sarnak Conjecture to Toeplitz systems
Subjects: Dynamical Systems (math.DS)

In this paper, we show that for any sequence ${\bf a}=(a_n)_{n\in \Z}\in \{1,\ldots,k\}^\mathbb{Z}$ and any $\epsilon>0$, there exists a Toeplitz sequence ${\bf b}=(b_n)_{n\in \Z}\in \{1,\ldots,k\}^\mathbb{Z}$ such that the entropy $h({\bf b})\leq 2 h({\bf a})$ and $\lim_{N\to\infty}\frac{1}{2N+1}\sum_{n=-N}^N|a_n-b_n|<\epsilon$. As an application of this result, we reduce Sarnak Conjecture to Toeplitz systems, that is, if the M\"{o}bius function is disjoint from any Toeplitz sequence with zero entropy, then the Sarnak conjecture holds.

[3]
Title: $Λ$-linked coupling for drifting Brownian motions
Authors: Motoya Machida
Subjects: Probability (math.PR)

We raise a question on whether a dynamical system driven by Markov process is Markovian, for which we are able to propose a criterion and examples of positive case. This investigation leads us to develop (i) a general construction of intertwining dual via Liggett duality, and (ii) a realization of $\Lambda$-linked coupling in a form of dynamical system. We show this construction of intertwining dual and $\Lambda$-linked coupling for an $n$-dimensional drifting Brownian motion when it is a characteristic diffusion. In particular, it includes an extension of Pitman's $2M-W$ theorem by Rogers and Pitman as a special case.

[4]
Title: The doubling metric and doubling measures
Subjects: General Topology (math.GN); Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG)

We introduce the so--called doubling metric on the collection of non--empty bounded open subsets of a metric space. Given a subset $U$ of a metric space $X$, the predecessor $U_{*}$ of $U$ is defined by doubling the radii of all open balls contained inside $U$, and taking their union. If $U$ is open, the predecessor of $U$ is an open set containing $U$. The directed doubling distance between $U$ and another subset $V$ is the number of times that the predecessor operation needs to be applied to $U$ to obtain a set that contains $V$. Finally, the doubling distance between $U$ and $V$ is the maximum of the directed distance between $U$ and $V$ and the directed distance between $V$ and $U$.

[5]
Title: Algebraic integer totally in a compact
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG); Complex Variables (math.CV)

An algebraic integer is a complex number that is a root of some monic polynomial with integer coefficients. An algebraic integer is said to be totally in a compact of the complex plan if all its conjugates are in the same compact as well. Given a compact, how to tell if there exists a finite or infinite number of algebraic integers totally in it ? Though this problem might seem like an algebra problem, it is actually linked to a problem of energy minimisation stemming from the electrostatic field of study: given a very large number of electrical charges in a given domain, what is the distribution at the equilibrium ? Rigorously solving this problem requires the potential theory framework and introduces a central concept: the capacity of a set, akin to the "capacity of a capacitor". In this report, we will present the theory of capacity and some theorems derived from it (Fekete-Szeg\"o, Robinson) that partially answer the question: in the case of a union of real segments, when the capacity is smaller (resp. larger) than 1, it contains a finite (resp. infinite) number of algebraic integers totally in it. As an example, for real segments, the limit length is 4.
This report is redacted following a collective project conducted in \'Ecole Polytechnique (France). It is aimed towards an undergraduate audience in mathematics, with basic knowledge in algebra, topology, analysis, and dwells into a modern topic of research.

[6]
Title: Expansion properties for finite subdivision rules II
Subjects: Dynamical Systems (math.DS)

We prove that every sufficiently large iterate of a Thurston map which is not doubly covered by a torus endomorphism and which does not have a Levy cycle is isotopic to the subdivision map of a finite subdivision rule. We determine which Thurston maps doubly covered by a torus endomorphism have iterates that are isotopic to subdivision maps of finite subdivision rules. We give conditions under which no iterate of a given Thurston map is isotopic to the subdivision map of a finite subdivision rule.

[7]
Title: Chance-Constrained Yield Optimization of Photonic IC with Non-Gaussian Correlated Process Variations
Subjects: Optimization and Control (math.OC)

Uncertainty quantification has become an efficient tool for yield prediction, but its power in yield-aware optimization has not been well explored from either theoretical or application perspectives. Yield optimization is a much more challenging task. On one side, optimizing the generally non-convex probability measure of performance metrics is difficult. On the other side, evaluating the probability measure in each optimization iteration requires massive simulation data, especially when the process variations are non-Gaussian correlated. This paper proposes a data-efficient framework for the yield-aware optimization of the photonic IC. This framework optimizes design performance with a yield guarantee, and it consists of two modules: a modeling module that builds stochastic surrogate models for design objectives and chance constraints with a few simulation samples, and a novel yield optimization module that handles probabilistic objectives and chance constraints in an efficient deterministic way. This deterministic treatment avoids repeatedly evaluating probability measures at each iteration, thus it only requires a few simulations in the whole optimization flow. We validate the accuracy and efficiency of the whole framework by a synthetic example and two photonic ICs. Our optimization method can achieve more than $30\times$ reduction of simulation cost and better design performance on the test cases compared with a recent Bayesian yield optimization approach.

[8]
Title: Entropy in Themodynamics: from Foliation to Categorization
Comments: 19 pages, 1 figure, a survey paper by no means an original research;
Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech)

We overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on set that is induced by adiabatic processes will be outlined. Finally, the viewpoint of category theory is provided, which reinterprets the ordering structure as a category of pre-ordered sets.

[9]
Title: Bounds On $(t,r)$ Broadcast Domination of $n$-Dimensional Grids
Authors: Tom Shlomi
Subjects: Combinatorics (math.CO)

In this paper, we look at a variant of graph domination known as $(t, r)$ broadcast domination, first defined in \cite{BleInsJohMau15}, and we describe some upper and lower bounds on the density of a $(t, r)$ dominating pattern of an infinite grid, as well as methods of computing them. When $r \ge 2$, we describe a family of counterexamples to a generalization of Vizing's Conjecture to $(t,r)$ broadcast domination.

[10]
Title: Classic dynamic fracture recovered as the limit of a nonlocal peridynamic model: The single edge notch in tension
Subjects: Analysis of PDEs (math.AP)

A simple nonlocal field theory of peridynamic type is applied to model brittle fracture. The fracture evolution is shown to converge in the limit of vanishing nonlocality to classic plane elastodynamics with a running crack. The kinetic relation for the crack is recovered directly from the nonlocal model in the limit of vanishing nonlocality. We carry out our analysis for a single crack in a plate subject to mode one loading. The convergence is corroborated by numerical experiments.

[11]
Title: Covert Millimeter-Wave Communication via a Dual-Beam Transmitter
Subjects: Information Theory (cs.IT)

In this paper, we investigate covert communication over millimeter-wave (mmWave) frequencies. In particular, a dual-beam mmWave transmitter, comprised of two independent antenna arrays, attempts to reliably communicate to a receiver Bob when hiding the existence of transmission from a warden Willie. In this regard, operating over mmWave bands not only increases the covertness thanks to directional beams, but also increases the transmission data rates given much more available bandwidths and enables ultra-low form factor transceivers due to the lower wavelengths used compared to the conventional radio frequency (RF) counterpart. We assume that the transmitter Alice employs one of its antenna arrays to form a directive beam for transmission to Bob. The other antenna array is used by Alice to generate another beam toward Willie as a jamming signal with its transmit power changing independently from a transmission block to another block. We characterize Willie's detection performance with the optimal detector and the closed-form of its expected value from Alice's perspective. We further derive the closed-form expression for the outage probability of the Alice-Bob link, which enables characterizing the optimal covert rate that can be achieved using the proposed setup. Our results demonstrate the superiority of mmWave covert communication, in terms of covertness and rate, compared to the RF counterpart.

[12]
Title: Connection probabilities in the double-dimer model -- the case of two connectivity patterns
Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech)

We apply the Grassmannian representation of the dimer model, an equivalent approach to Kasteleyn's solution to the close-packed dimer problem, to calculate the connection probabilities for the double-dimer model with wired/free/wired/free boundary conditions, on a rectangular subdomain of the square lattice with four marked boundary points at the corners. Using some series identities related to Schwarz-Christoffel transformations, we show that the continuum of the result is consistent with the corresponding one in the upper half-plane (previously obtained by Kenyon-Wilson), which is in turn identical to the connection probabilities for 4SLE$_4$ emanating from the boundary, or equivalently, to a conditioned version of CLE$_4$ with wired/free/wired/free boundary conditions in the context of conformal loop ensembles.

[13]
Title: Piecewise Visual, Linearly Connected Metrics on Boundaries of Relatively Hyperbolic Groups
Subjects: Group Theory (math.GR); Geometric Topology (math.GT)

Suppose a finitely generated group $G$ is hyperbolic relative to $\mathcal P$ a set of proper finitely generated subgroups of $G$. Established results in the literature imply that a "visual" metric on $\partial (G,\mathcal P)$ is "linearly connected" if and only if the boundary $\partial (G,\mathcal P)$ has no cut point. Our goal is to produce linearly connected metrics on $\partial (G,\mathcal P)$ that are "piecewise" visual when $\partial (G,\mathcal P)$ contains cut points. %Visual metrics for $\partial (G,\mathcal P)$ are tightly linked to inner products of geodesic rays in "cusped" spaces for $(G,\mathcal P)$. The identity vertex $\ast$ is usually our base point in these cusped spaces and visual metrics depend on this base point. %We say the visual metric $d_p$ on $\partial(G,\mathcal P)$, with base point $p$, is {\it $G$-equivariant} if for points $x_1,x_2\in \partial(G,\mathcal P)$, we have $d_p(x_1,x_2)=d_{gp}(gx_1,gx_2)$ for all $g\in G$.
Our main theorem is about graph of groups decompositions of relatively hyperbolic groups $(G,\mathcal P)$, and piecewise visual metrics on their boundaries. We assume that each vertex group of our decomposition has a boundary with linearly connected visual metric or the vertex group is in $\mathcal P$. If a vertex group is not in $\mathcal P$, then it is hyperbolic relative to its adjacent edge groups. Our linearly connected metric on $\partial (G,\mathcal P)$ agrees with the visual metric on limit sets of vertex groups and is in this sense piecewise visual.

[14]
Title: Iterative Linearized Control: Stable Algorithms and Complexity Guarantees
Comments: Short version appeared in International Conference on Machine Learning (ICML) 2019
Subjects: Optimization and Control (math.OC)

We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals that the complexity bounds can be clearly stated in terms of calls to a computational oracle related to dynamic programming and implementable by gradient back-propagation using machine learning software libraries such as PyTorch or TensorFlow. Finally, we propose a regularized Gauss-Newton algorithm enjoying worst-case complexity bounds and improved convergence behavior in practice. The software library based on PyTorch is publicly available.

[15]
Title: Tree Builder Random Walk: recurrence, transience and ballisticity
Subjects: Probability (math.PR)

The Tree Builder Random Walk is a special random walk that evolves on trees whose size increases with time, randomly and depending upon the walker. After every s steps of the walker, a random number of vertices are added to the tree and attached to the current position of the walker. These processes share similarities with other important classes of markovian and non-markovian random walks presenting a large variety of behaviors according to parameters specifications. We show that for a large and most significant class of tree builder random walks, the process is either null recurrent or transient. If s is odd, the walker is ballistic and thus transient. If s is even, the walker's behavior can be explained from local properties of the growing tree and it can be either null recurrent or it gets trapped on some limited part of the growing tree.

[16]
Title: On Cores in Yetter-Drinfel'd Hopf Algebras
Subjects: Rings and Algebras (math.RA); Quantum Algebra (math.QA); Representation Theory (math.RT)

By constructing explicit examples, we show that the core of a group-like element in a cocommutative cosemisimple Yetter-Drinfel'd Hopf algebra over the group ring of a finite abelian group is not always completely trivial.

[17]
Title: Algebraic relations between moments of plane polygons
Subjects: Complex Variables (math.CV); Classical Analysis and ODEs (math.CA)

We describe the algebraic relations satisfied by the harmonic and anti-harmonic moments of simply connected, but not necessarily convex planar polygons with a given number of vertices.

[18]
Title: A $C^m$ Lusin Approximation Theorem for Horizontal Curves in the Heisenberg Group
Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA)

We prove a $C^m$ Lusin approximation theorem for horizontal curves in the Heisenberg group. This states that every absolutely continuous horizontal curve whose horizontal velocity is $m-1$ times $L^1$ differentiable almost everywhere coincides with a $C^m$ horizontal curve except on a set of small measure. Conversely, we show that the result no longer holds if $L^1$ differentiability is replaced by approximate differentiability. This shows our result is optimal and highlights differences between the Heisenberg and Euclidean settings.

[19]
Title: Over-rotation intervals of bimodal interval maps
Comments: 33 pages and 13 figures
Subjects: Dynamical Systems (math.DS)

We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal interval maps called well behaved, and generalize the above results onto well behaved maps.

[20]
Title: Quadratic residues in $\mathbb{F}_{p^2}$ and related permutations involving primitive roots
Authors: Hai-Liang Wu
Comments: This is a preliminary version
Subjects: Number Theory (math.NT)

Let $p=2n+1$ be an odd prime, and let $\zeta_{p^2-1}$ be a primitive $(p^2-1)$-th root of unity in the algebraic closure $\overline{\mathbb{Q}_p}$ of $\mathbb{Q}_p$. We let $g\in\mathbb{Z}_p[\zeta_{p^2-1}]$ be a primitive root modulo $p\mathbb{Z}_p[\zeta_{p^2-1}]$ with $g\equiv \zeta_{p^2-1}\pmod {p\mathbb{Z}_p[\zeta_{p^2-1}]}$. Let $\Delta\equiv3\pmod4$ be an arbitrary quadratic non-residue modulo $p$ in $\mathbb{Z}$. By the Local Existence Theorem we know that $\mathbb{Q}_p(\sqrt{\Delta})=\mathbb{Q}_p(\zeta_{p^2-1})$. For all $x\in\mathbb{Z}[\sqrt{\Delta}]$ and $y\in\mathbb{Z}_p[\zeta_{p^2-1}]$ we use $\bar{x}$ and $\bar{y}$ to denote the elements $x\mod p\mathbb{Z}[\sqrt{\Delta}]$ and $y\mod p\mathbb{Z}_p[\zeta_{p^2-1}]$ respectively. If we set $a_k=k+\sqrt{\Delta}$ for $0\le k\le p-1$, then we can view the sequence $$S := \overline{a_0^2}, \cdots, \overline{a_0^2n^2}, \cdots,\overline{a_{p-1}^2}, \cdots, \overline{a_{p-1}^2n^2}\cdots, \overline{1^2}, \cdots,\overline{n^2}$$ as a permutation $\sigma$ of the sequence $$S^* := \overline{g^2}, \overline{g^4}, \cdots,\overline{g^{p^2-1}}.$$ We determine the sign of $\sigma$ completely in this paper.

[21]
Title: K-Nearest Neighbor Approximation Via the Friend-of-a-Friend Principle
Subjects: Combinatorics (math.CO); Statistics Theory (math.ST)

Suppose $V$ is an $n$-element set where for each $x \in V$, the elements of $V \setminus \{x\}$ are ranked by their similarity to $x$. The $K$-nearest neighbor graph %$G:=(V, E)$ is a directed graph including an arc from each $x$ to the $K$ points of $V \setminus \{x\}$ most similar to $x$. Constructive approximation to this graph using far fewer than $n^2$ comparisons is important for the analysis of large high-dimensional data sets. \emph{$K$-Nearest Neighbor Descent} is a parameter-free heuristic where a sequence of graph approximations is constructed, in which second neighbors in one approximation are proposed as neighbors in the next. We provide a rigorous justification for $O( n \log{n} )$ complexity of a similar algorithm, using range queries, when applied to a homogeneous Poisson process in suitable dimension, but show that the basic algorithm fails to achieve subquadratic complexity on sets whose similarity rankings arise from a "generic" linear order on the $\binom{n}{2}$ inter-point distances in a metric space.

[22]
Title: Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms
Subjects: Probability (math.PR); Analysis of PDEs (math.AP)

In this paper, we consider the following symmetric Dirichlet forms on a metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g) = \mathcal{E}(^{(c)}(f,g)+\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $\mathcal{E}(^{(c)}$ is a strongly local symmetric bilinear form and $J(dx,dy)$ is a symmetric Random measure on $M\times M$. Under general volume doubling condition on $(M,d,\mu)$ and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp.\ two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp.\ the Poincar\'e inequalities). We also obtain characterizations of parabolic Harnack inequalities. Our results apply to symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than $2$.

[23]
Title: Heat kernel estimates for general symmetric pure jump Dirichlet forms
Subjects: Probability (math.PR)

In this paper, we consider the following symmetric non-local Dirichlet forms of pure jump type on metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g)=\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $J(dx,dy)$ is a symmetric Radon measure on $M\times M\setminus {\rm diag}$ that may have different scalings for small jumps and large jumps. Under general volume doubling condition on $(M,d,\mu)$ and some mild quantitative assumptions on $J(dx, dy)$ that are allowed to have light tails of polynomial decay at infinity, we establish stability results for two-sided heat kernel estimates as well as heat kernel upper bound estimates in terms of jumping kernel bounds, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp.\ the Poincar\'e inequalities). We also give stable characterizations of the corresponding parabolic Harnack inequalities.

[24]
Title: On the trend to global equilibrium for Kuramoto Oscillators
Subjects: Analysis of PDEs (math.AP)

In this paper, we study the convergence to the stable equilibrium for Kuramoto oscillators. Specifically, we derive estimates on the rate of convergence to the global equilibrium for solutions of the Kuramoto-Sakaguchi equation in a large coupling strength regime from generic initial data. As a by-product, using the stability of the equation in the Wasserstein distance, we quantify the rate at which discrete Kuramoto oscillators concentrate around the global equilibrium. In doing this, we achieve a quantitative estimate in which the probability that the oscillators will concentrate at the given rate tends to one as the number of oscillators increases. Among the essential steps in our proof are: 1) An entropy production estimate inspired by the formal Riemannian structure of the space of probability measures, first introduced by F. Otto in [35]; 2) A new quantitative estimate on the instability of equilibria with antipodal oscillators based on the dynamics of norms of the solution in sets evolving by the continuity equation; 3) The use of generalized local logarithmic Sobolev and Talagrand type inequalities, similar to the ones derived by F. Otto and C. Villani in [36]; 4) The study of a system of coupled differential inequalities, by a treatment inspired by the work of L. Desvillettes and C. Villani [13]. Since the Kuramoto-Sakaguchi equation is not a gradient flow with respect to the Wasserstein distance, we derive such inequalities under a suitable fibered transportation distance.

[25]
Title: A Generalization of Parking Functions Allowing Backward Movement
Subjects: Combinatorics (math.CO)

Classical parking functions are defined as the parking preferences for $n$ cars driving (from west to east) down a one-way street containing parking spaces labeled from $1$ to $n$ (from west to east). Cars drive down the street toward their preferred spot and park there if the spot is available. Otherwise, the car continues driving down the street and takes the first available parking space, if such a space exists. If all cars can park using this parking rule, we call the $n$-tuple containing the cars' parking preferences a parking function.
In this paper, we introduce a generalization of the parking rule allowing cars whose preferred space is taken to first proceed up to $k$ spaces west of their preferred spot to park before proceeding east if all of those $k$ spaces are occupied. We call parking preferences which allow all cars to park under this new parking rule $k$-Naples parking functions of length $n$. This generalization gives a natural interpolation between classical parking functions, the case when $k=0$, and all $n$-tuples of positive integers $1$ to $n$, the case when $k\geq n-1$. Our main result provides a recursive formula for counting $k$-Naples parking functions of length $n$. We also give a characterization for the $k=1$ case by introducing a new function that maps $1$-Naples parking functions to classical parking functions, i.e. $0$-Naples parking functions. Lastly, we present a bijection between $k$-Naples parking functions of length $n$ whose entries are in weakly decreasing order and a family of signature Dyck paths.

[26]
Title: On graphic arrangement groups
Subjects: Geometric Topology (math.GT); Combinatorics (math.CO)

A finite simple graph $\Gamma$ determines a quotient $P_\Gamma$ of the pure braid group, called a graphic arrangement group. We analyze homomorphisms of these groups defined by deletion of sets of vertices, using methods developed in prior joint work with R. Randell. We show that, for a $K_4$-free graph $\Gamma$, a product of deletion maps is injective, embedding $P_\Gamma$ in a product of free groups. Then $P_\Gamma$ is residually free, torsion-free, residually torsion-free nilpotent, and acts properly on a CAT(0) cube complex. We also show $P_\Gamma$ is of homological finiteness type $F_{m-1}$, but not $F_m$, where $m$ is the number of copies of $K_3$ in $\Gamma$, except in trivial cases. The embedding result is extended to graphs whose 4-cliques share at most one edge, giving an injection of $P_\Gamma$ into the product of pure braid groups corresponding to maximal cliques of $\Gamma$. We give examples showing that this map may inject in more general circumstances. We define the graphic braid group $B_\Gamma$ as a natural extension of $P_\Gamma$ by the automorphism group of $\Gamma$, and extend our homological finiteness result to these groups.

[27]
Title: Liouvillian solutions for second order linear differential equations with polynomial coefficients
Subjects: Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA)

In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymptotic iteration method we find a degree independent algebraic description of the spectral set: the subset, in the parameter space, of Liouiville integrable differential equations. For each fixed degree, we prove that the spectral set is a countable union of non accumulating algebraic varieties. This algebraic description of the spectral set allow us to bound the number of eigenvalues for algebraically quasi-solvable potentials in the Schr\"odinger equation.

[28]
Title: Non-negativity of CR Paneitz operator for embeddable CR manifolds
Authors: Yuya Takeuchi
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP); Complex Variables (math.CV)

The non-negativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this non-negativity for embeddable CR manifolds. This result and previous works give an affirmative solution of the CR Yamabe problem for embeddable CR manifolds. We also show the existence of a contact form with zero CR $Q$-curvature, and generalize the total $Q$-prime curvature to embeddable CR manifolds with no pseudo-Einstein contact forms. Furthermore, we discuss the logarithmic singularity of the Szeg\H{o} kernel.

[29]
Title: Topological dynamics of continuous maps induced on the space of probability measures
Subjects: Dynamical Systems (math.DS)

Let $f$ be a continuous self-map on a compact interval $I$ and $\hat f$ be the induced map on the space $\mathcal{M}(I)$ of probability measures. We obtain a sharp condition to guarantee that $(I,f)$ is transitive if and only if $(\mathcal{M}(I),\hat f)$ is transitive. We also show that the sensitivity of $(I,f)$ is equivalent to that of $(\mathcal{M}(I),\hat f)$. We prove that $(\mathcal{M}(I),\hat f)$ must have infinite topological entropy for any transitive system $(I,f)$, while there exists a transitive non-autonomous system $(I,f_{0,\infty})$ such that $(\mathcal{M}(I),\hat f_{0,\infty})$ has zero topological entropy, where $f_{0,\infty}=\{f_n\}_{n=0}^\infty$ is a sequence of continuous self-maps on $I$. For a continuous self-map $f$ on a general compact metric space $X$, we show that chain transitivity of $(X, f)$ implies chain mixing of $(\mathcal{M}(X),\hat f)$, and we provide two counterexamples to demonstrate that the converse is not true. We confirm that shadowing of $(X,f)$ is not inherited by $(\mathcal{M}(X),\hat f)$ in general. For a non-autonomous system $(X,f_{0,\infty})$, we prove that Li-Yorke chaos (resp., distributional chaos) of $(X,f_{0,\infty})$ carries over to $(\mathcal{M}(X),\hat f_{0,\infty})$, and give an example to show that the converse may not be true. We prove that if $f_n$ is surjective for all $n\geq 0$, then chain mixing of $(\mathcal{M}(X),\hat f_{0,\infty})$ always holds true, and shadowing of $(\mathcal{M}(X),\hat f_{0,\infty})$ implies topological mixing of $(X, f_{0,\infty})$. In addition, we prove that topological mixing (resp., mild mixing and topological exactness) of $(X, f_{0,\infty})$ is equivalent to that of $(\mathcal{M}(X),\hat f_{0,\infty})$, and that $(X, f_{0,\infty})$ is cofinitely sensitive if and only if $(\mathcal{M}(X),\hat f_{0,\infty})$ is cofinitely sensitive.

[30]
Title: Stabilization Control for ItO Stochastic System with Indefinite State and Control Weight Costs
Comments: 8 pages, 3 figures, This paper has been submitted to Automatica and the current publication decision is Accept provisionally as Brief Paper
Subjects: Optimization and Control (math.OC)

In standard linear quadratic (LQ) control, the first step in investigating infinite-horizon optimal control is to derive the stabilization condition with the optimal LQ controller. This paper focuses on the stabilization of an Ito stochastic system with indefinite control and state weighting matrices in the cost functional. A generalized algebraic Riccati equation (GARE) is obtained via the convergence of the generalized differential Riccati equation (GDRE) in the finite-horizon case. More importantly, the necessary and sufficient stabilization conditions for indefinite stochastic control are obtained. One of the key techniques is that the solution of the GARE is decomposed into a positive semi-definite matrix that satisfies the singular algebraic Riccati equation (SARE) and a constant matrix that is an element of the set satisfying certain linear matrix inequality conditions. Using the equivalence between the GARE and SARE, we reduce the stabilization of the general indefinite case to that of the definite case, in which the stabilization is studied using a Lyapunov functional defined by the optimal cost functional subject to the SARE.

[31]
Title: Isoperimetric Inequality for Disconnected Regions
Subjects: Geometric Topology (math.GT)

The isoperimetric inequality in the Euclidean geometry (for polygons) states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon. One can generalise this result to simple closed curves; in this case, the curve with the maximum area is the circle. The statement is true in hyperbolic geometry as well (see Bezdek \cite{Bez}).
In this paper, we generalize the isoperimetric inequality to disconnected regions, i.e. we allow the area to be split between regions. We give necessary and sufficient conditions for the isoperimetric inequality (in Euclidean and hyperbolic geometry) to hold for multiple $n$-gons whose perimeters add up to $p$.

[32]
Title: Tensor Methods for Generating Compact Uncertainty Quantification and Deep Learning Models
Subjects: Optimization and Control (math.OC); Signal Processing (eess.SP)

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate decision making or machine learning. In this paper, we summarize the recent applications of tensor computation in obtaining compact models for uncertainty quantification and deep learning. In uncertainty analysis where obtaining data samples is expensive, we show how tensor methods can significantly reduce the simulation or measurement cost. To enable the deployment of deep learning on resource-constrained hardware platforms, tensor methods can be used to significantly compress an over-parameterized neural network model or directly train a small-size model from scratch via optimization or statistical techniques. Recent Bayesian tensorized neural networks can automatically determine their tensor ranks in the training process.

[33]
Title: An iterative method for Kirchhoff type equations and its applications
Authors: Qiuyi Dai
Subjects: Analysis of PDEs (math.AP)

In this short note, we propose an iterative method for finding nonnegative solutions of Kirchhoff type equations.

[34]
Title: Lyapunov exponents of polynomials with respect to certain weighted Lyubich's measures
Subjects: Dynamical Systems (math.DS)

In this paper, we consider a monic, centred, hyperbolic polynomial of degree $d \ge 2$, restricted on its Julia set and compute its Lyapunov exponents with respect to certain weighted Lyubich's measures. In particular, we show a certain well-behavedness of some coefficients of the Lyapunov exponents, that quantifies the non-well-behavedness in a system.

[35]
Title: New Method of Smooth Extension of Local Maps on Linear Topological Spaces. Applications and Examples
Subjects: Dynamical Systems (math.DS)

The question of extension of locally defined maps to the entire space arises in many problems of analysis (e.g., local linearization of functional equations). A known classical method of extension of smooth local maps on Banach spaces uses smooth bump functions. However, such functions are absent in the majority of infinite-dimensional spaces. We suggest a new approach to localization of Banach spaces with the help of locally identical maps, which we call blid maps. In addition to smooth spaces, blid maps also allow to extend local maps on non-smooth spaces (e.g., $C^q [0, 1]$, $q=0, 1, 2,...$).
For the spaces possessing blid maps, we show how to reconstruct a map from its derivatives at a point (see the Borel Lemma). We also demonstrate how blid maps assist in finding global solutions of cohomological equations having linear transformation of the argument. We present application of blid maps to local differentiable linearization of maps on Banach spaces.
We discuss differentiable localization for metric spaces (e.g., $C^{\infty}(\R)$), prove an extension result for locally defined maps and present examples of such extensions for the specific metric spaces. In conclusion, we formulate open problems.

[36]
Title: Existence of Large deviations rate function for any $S$-unimodal map
Subjects: Dynamical Systems (math.DS)

For any unimodal map with negative Schwarzian derivative and with non-flat critical point, we establish the level-2 Large Deviation Principle for empirical distributions.

[37]
Title: Asymptotic analysis of card guessing with feedback
Authors: Pengda Liu
Subjects: Probability (math.PR)

This paper studies the game of guessing shuffled cards with feedback. A deck of $n$ cards labelled 1 to $n$ is shuffled in some fashion and placed on a table. A player tries to guess the cards from top and is given certain feedback after each guess. The goal is to find the guessing strategy with maximum reward (expected number of correct guesses). This paper first provides an exposition of the previous work and introduces some general framework for studying this problem. We then review and correct one mistake in the work done by Ciucu in the setting of {riffle shuffle, no feedback}. We also generalize one of his results by proving that the optimal strategy in that scenario has expected reward $2/\sqrt{\pi}\cdot\sqrt{n}+O(1)$. Finally, with our framework, we partially solve an open problem of Bayer and Diaconis by providing the optimal strategy for {riffle shuffle, complete feedback} and proving that the maximum expected reward is $n/2+\sqrt{2/\pi}\cdot\sqrt{n}+O(1)$.

[38]
Title: Tensor Product $L$-Functions On Metaplectic Covering Groups of $GL_r$
Authors: David Ginzburg
Subjects: Representation Theory (math.RT); Number Theory (math.NT)

In this note we compute some local unramified integrals defined on metaplectic covering groups of $GL$. These local integrals which were introduced by Suzuki, represent the standard tensor product $L$ function $L(\pi^{(n)}\times \tau^{(n)},s)$ and extend the well known local integrals which represent $L(\pi\times \tau,s)$. The computation is done using a certain "generating function" which extends a similar function introduced by the author in a previous paper. In the last section we discuss the Conjectures of Suzuki and introduce a global integral which unfolds to the above local integrals. This last part is mainly conjectural and relies heavily on the existence of Suzuki representations defined on covering groups. In the last subsection we introduce a new global doubling integral which represents the partial tensor product $L$ function $L^S(\pi\times \tau,s)$.

[39]
Title: Data-driven model reduction, Wiener projections, and the Mori-Zwanzig formalism
Authors: Kevin K. Lin, Fei Lu
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Machine Learning (stat.ML)

First-principles models of complex dynamic phenomena often have many degrees of freedom, only a small fraction of which may be scientifically relevant or observable. Reduced models distill such phenomena to their essence by modeling only relevant variables, thus decreasing computational cost and clarifying dynamical mechanisms. Here, we consider data-driven model reduction for nonlinear dynamical systems without sharp scale separation. Motivated by a discrete-time version of the Mori-Zwanzig projection operator formalism and the Wiener filter, we propose a simple and flexible mathematical formulation based on Wiener projection, which decomposes a nonlinear dynamical system into a component predictable by past values of relevant variables and its orthogonal complement. Wiener projection is equally applicable to deterministic chaotic dynamics and randomly-forced systems, and provides a natural starting point for systematic approximations. In particular, we use it to derive NARMAX models from an underlying dynamical system, thereby clarifying the scope of these widely-used tools in time series analysis. We illustrate its versatility on the Kuramoto-Sivashinsky model of spatiotemporal chaos and a stochastic Burgers equation.

[40]
Title: Eliminating Impulsive Noise in Pilot-Aided OFDM Channels via Dual of Penalized Atomic Norm
Subjects: Information Theory (cs.IT); Signal Processing (eess.SP)

In this paper, we propose a novel estimator for pilot-aided orthogonal frequency division multiplexing (OFDM) channels in an additive Gaussian and impulsive perturbation environment. Due to sensor failure which might happen because of man-made noise, a number of measurements in high rate communication systems is often corrupted by impulsive noise. High power impulsive noise is generally an obstacle for OFDM systems as valuable information will be completely lost. To overcome this concern, an objective function based on a penalized atomic norm minimization (PANM) is provided in order to promote the sparsity of time dispersive channels and impulsive noise. The corresponding dual problem of the PANM is then converted to tractable semidefinite programming. It has shown that one can simultaneously estimate the time dispersive channels in a continuous dictionary and the location of impulsive noise using the dual problem. Several numerical experiments are carried out to evaluate the performance of the proposed estimator.

[41]
Title: Some results on vanishing coefficients in infinite product expansions
Journal-ref: The Ramanujan Journal, 2019
Subjects: Number Theory (math.NT)

Recently, M. D. Hirschhorn proved that, if $\sum_{n=0}^\infty a_nq^n := (-q,-q^4;q^5)_\infty(q,q^9;q^{10})_\infty^3$ and $\sum_{n=0}^\infty b_nq^n:=(-q^2,-q^3;q^5)_\infty(q^3,q^7;q^{10})_\infty^3$, then $a_{5n+2}=a_{5n+4}=0$ and $b_{5n+1}=b_{5n+4}=0$. Motivated by the work of Hirschhorn, D. Tang proved some comparable results including the following: If $\sum_{n=0}^\infty c_nq^n := (-q,-q^4;q^5)_\infty^3(q^3,q^7;q^{10})_\infty$ and $\sum_{n=0}^\infty d_nq^n := (-q^2,-q^3;q^5)_\infty^3(q,q^9;q^{10})_\infty$, then $c_{5n+3}=c_{5n+4}=0$ and $d_{5n+3}=d_{5n+4}=0$.
In this paper, we prove that $a_{5n}=b_{5n+2}$, $a_{5n+1}=b_{5n+3}$, $a_{5n+2}=b_{5n+4}$, $a_{5n-1}=b_{5n+1}$, $c_{5n+3}=d_{5n+3}$, $c_{5n+4}=d_{5n+4}$, $c_{5n}=d_{5n}$, $c_{5n+2}=d_{5n+2}$, and $c_{5n+1}>d_{5n+1}$. We also record some other comparable results not listed by Tang.

[42]
Title: Dynamics of quadratic operators generated by China's Five elements philosophy
Subjects: Dynamical Systems (math.DS)

Motivating by the China's five element philosophy (CFEP) we construct a permuted Volterra quadratic stochastic operator acting on the four dimensional simplex. This operator (depending on 10 parameters) is considered as an evolution operator for CFEP. We study the discrete time dynamical system generated by this operator. Mainly our results related to a symmetric operator (depending on one parameter). We show that this operator has a unique fixed point, which is repeller. Moreover, in the case of non-zero parameter, it has two 5-periodic orbits. We divide the simplex to four subsets: the first set consists a single point (the fixed point); the second (resp. third) set is the set of initial points trajectories of which converge to the first (resp. second) 5-periodic orbit; the fourth subset is the set of initial points trajectories of which do not converge and their sets of limit points are infinite and lie on the boundary of the simplex. We give interpretations of our results to CFEP.

[43]
Title: Generating Functions and Congruences for Some Partition Functions Related to Mock Theta Functions
Subjects: Number Theory (math.NT)

Recently, Andrews, Dixit and Yee introduced partition functions associated with Ramanujan/Watson third order mock theta functions $\omega(q)$ and $\nu(q)$. In this paper, we find several new exact generating functions for those partition functions as well as the associated smallest parts functions and deduce several new congruences modulo powers of 5.

[44]
Title: Algebra of convolution type operators with continuous data on Banach function spaces
Comments: To appear in the "Proceedings of Function Spaces XII"
Subjects: Functional Analysis (math.FA)

We show that if the Hardy-Littlewood maximal operator is bounded on a reflexive Banach function space $X(\mathbb{R})$ and on its associate space $X'(\mathbb{R})$, then the space $X(\mathbb{R})$ has an unconditional wavelet basis. As a consequence of the existence of a Schauder basis in $X(\mathbb{R})$, we prove that the ideal of compact operators $\mathcal{K}(X(\mathbb{R}))$ on the space $X(\mathbb{R})$ is contained in the Banach algebra generated by all operators of multiplication $aI$ by functions $a\in C(\dot{\mathbb{R}})$, where $\dot{\mathbb{R}}=\mathbb{R}\cup\{\infty\}$, and by all Fourier convolution operators $W^0(b)$ with symbols $b\in C_X(\dot{\mathbb{R}})$, the Fourier multiplier analogue of $C(\dot{\mathbb{R}})$.

[45]
Title: Delete Nim
Subjects: Combinatorics (math.CO)

In this paper, we study an impartial game called Delete Nim. In this game, there are two heaps of stones. The player chooses one of the heaps and delete the other heap. Next, she takes away one stone from the chosen heap and optionally splits it into two heaps. We show the way to calculate the G-value of this game by using the OR operation and 2-adic valuation.

[46]
Title: Mobility in the Sky: Performance and Mobility Analysis for Cellular-Connected UAVs
Subjects: Information Theory (cs.IT); Signal Processing (eess.SP)

Providing connectivity to unmanned aerial vehicle-user equipments such as drones or flying taxis is a major challenge for tomorrow cellular systems. In this paper, the use of coordinated multi-point transmission for providing seamless connectivity to UAV user equipments is investigated. In particular, a network of clustered ground base stations that cooperatively serve a number of UAVUEs is considered. Two scenarios are studied: scenarios with static, hovering UAV user equipments and scenarios with mobile UAV-UEs. Under a maximum ratio transmission, a novel framework is developed and leveraged to derive upper and lower bounds on the UAV-UE coverage probability for both scenarios. Using the derived results, the effects of various system parameters such as collaboration distance, UAVUE altitude, and UAV-UE velocity on the achievable performance are studied. Results reveal that, for both static and mobile UAV user equipments, when the BS antennas are tilted downwards, the coverage probability of a high-altitude UAV-UE is upper bounded by that of ground users regardless of the transmission scheme. Moreover, for low signal-to-interference-ratio thresholds, it is shown that CoMP transmission can improve the coverage probability of UAV user equipments, e.g., from 28% under the nearest association scheme to 60% for a collaboration distance of 200m.

[47]
Title: Quantum Euclidean Spaces with Noncommutative Derivatives
Subjects: Operator Algebras (math.OA)

Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical commutation relation (CCR). This gives an example of semi-finite spectral triple with non-flat geometric structure. We develop an abstract symbol calculus for the pseudo-differential operators with noncommuting derivatives. We also obtain a simplified local index formula (even case) that is similar to the commutative setting.

[48]
Title: Analysis of Impulsive $\varphi$--Hilfer Fractional Differential Equations
Subjects: Dynamical Systems (math.DS); Analysis of PDEs (math.AP)

This paper is concerned with the existence and uniqueness, and Ulam--Hyers stabilities of solutions of nonlinear impulsive $\varphi$--Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the initial conditions, order of derivative and the functions involved in the equations. The outcomes are acquired in the space of weighted piecewise continuous functions by means of fixed point theorems and the generalized version of Gronwall inequality.

[49]
Title: On the Banach lattice c_0
Subjects: Functional Analysis (math.FA)

We show that $c_0$ is not a projective Banach lattice, answering a question of B. de Pagter and A. Wickstead. On the other hand, we show that $c_0$ is complemented in the free Banach lattice generated by itself (seen as a Banach space). As a consequence, the free Banach lattice generated by $c_0$ is not projective.

[50]
Title: Torsion groups of Mordell curves over cubic and sextic fields
Subjects: Number Theory (math.NT)

In this paper, we classify torsion groups of rational Mordell curves explicitly over cubic fields as well as over sextic fields. Also, we classify torsion groups of Mordell curves over cubic fields and for Mordell curves over sextic fields, we produce all possible torsion groups.

[51]
Title: On the Impulsive Implicit $Ψ$--Hilfer Fractional Differential Equations with Delay
Subjects: Dynamical Systems (math.DS); Analysis of PDEs (math.AP)

In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit $\Psi$--Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam--Hyers and generalized Ulam--Hyers stability are the specific cases of Ulam--Hyers--Mittag--Leffler stability. Extended version of Gronwall inequality, abstract Gronwall lemma and Picard operator theory are the primary devices in our investigation. We give an example to illustrate the obtained results.

[52]
Title: Existence of solutions for a nonlocal type problem in fractional Orlicz Sobolev spaces
Subjects: Analysis of PDEs (math.AP)

In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend the fractional Sobolev spaces $W^{s,p}$ to include the general case $W^sL_A$, where $A$ is an N-function and $s\in (0,1)$. We are concerned with some qualitative properties of the space $W^sL_A$ (completeness, reflexivity and separability). Moreover, we prove a continuous and compact embedding theorem of these spaces into Lebesgue spaces.

[53]
Title: Groups of extended affine Lie type
Comments: 19 pages, Lemma 3.4 is revisited
Journal-ref: Publ. RIMS Kyoto Univ. 55 (2019)
Subjects: Quantum Algebra (math.QA)

We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie algebra. Afterwards, we show that the extended affine Weyl group of the ground Lie algebra can be recovered as a quotient group of two subgroups of the group associated to the underlying algebra similar to Kac-Moody groups.

[54]
Title: Stationary characters on lattices of semisimple Lie groups
Subjects: Group Theory (math.GR); Dynamical Systems (math.DS); Operator Algebras (math.OA); Representation Theory (math.RT)

We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications in representation theory, operator algebras, ergodic theory and topological dynamics. In particular, we show that for any such irreducible lattice $\Gamma < G$, the left regular representation $\lambda_\Gamma$ is weakly contained in any weakly mixing representation $\pi$. We prove that for any such irreducible lattice $\Gamma < G$, any uniformly recurrent subgroup (URS) of $\Gamma$ is finite, answering a question of Glasner-Weiss. We also obtain a new proof of Peterson's character rigidity result for irreducible lattices $\Gamma < G$. The main novelty of our paper is a structure theorem for stationary actions of lattices on von Neumann algebras.

[55]
Title: Quasi-local Algebras and Asymptotic Expanders
Subjects: Operator Algebras (math.OA); Combinatorics (math.CO); Functional Analysis (math.FA)

In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a discrete metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being asymptotic expanders is a coarse property, and it implies non-uniformly local amenability. Moreover, we also analyse some $C^*$-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underlying metric space has Property A.

[56]
Title: On conditioning a self-similar growth-fragmentation by its intrinsic area
Subjects: Probability (math.PR)

The genealogical structure of self-similar growth-fragmentations can be described in terms of a branching random walk. The so-called intrinsic area $\mathrm{A}$ arises in this setting as the terminal value of a remarkable additive martingale. Motivated by connections with some models of random planar geometry, the purpose of this work is to investigate the effect of conditioning a self-similar growth-fragmentation on its intrinsic area. The distribution of $\mathrm{A}$ satisfies a useful smoothing transform which enables us to establish the existence of a regular density $a$ and to determine the asymptotic behavior of $a(r)$ as $r\to \infty$ (this can be seen as a local version of Kesten-Grincevicius-Goldie theorem's for random affine fixed point equations in a particular setting). In turn, this yields a family of martingales from which the formal conditioning on $\mathrm{A}=r$ can be realized by probability tilting. We point at a limit theorem for the conditional distribution given $\mathrm{A}=r$ as $r\to \infty$, and also observe that such conditioning still makes sense under the so-called canonical measure for which the growth-fragmentation starts from $0$

[57]
Title: The classification of the trivial source modules in blocks with cyclic defect groups
Subjects: Representation Theory (math.RT); Group Theory (math.GR)

Relying on the classification of the indecomposable liftable modules in arbitrary blocks with non-trivial cyclic defect groups we give a complete classification of the trivial source modules lying in such blocks, describing in particular their associated path on the Brauer tree of the block in the sense of Janusz (1969). The appendix contains a description of the minimal distance from an arbitrary non-projective indecomposable liftable module to the boundary of the stable Auslander-Reiten quiver of the block.

[58]
Title: Deep neural networks, generic universal interpolation, and controlled ODEs
Subjects: Optimization and Control (math.OC); Dynamical Systems (math.DS)

A recent paradigm views deep neural networks as discretizations of certain controlled ordinary differential equations. We make use of this perspective to link expressiveness of deep networks to the notion of controllability of dynamical systems. Using this connection, we study an expressiveness property that we call universal interpolation, and show that it is generic in a certain sense. The universal interpolation property is slightly weaker than universal approximation, and disentangles supervised learning on finite training sets from generalization properties. We also show that universal interpolation holds for certain deep neural networks even if large numbers of parameters are left untrained, and instead chosen randomly. This lends theoretical support to the observation that training with random initialization can be successful even when most parameters are largely unchanged through the training.

[59]
Title: Essential singularities of fractal zeta functions
Authors: Michel L. Lapidus (1), Goran Radunović (2), Darko Žubrinić (2) ((1) University of California, Riverside, (2) University of Zagreb)
Subjects: Mathematical Physics (math-ph)

We study the essential singularities of geometric zeta functions $\zeta_{\mathcal L}$, associated with bounded fractal strings $\mathcal L$. For any three prescribed real numbers $D_{\infty}$, $D_1$ and $D$ in $[0,1]$, such that $D_{\infty}<D_1\le D$, we construct a bounded fractal string $\mathcal L$ such that $D_{\rm par}(\zeta_{\mathcal L})=D_{\infty}$, $D_{\rm mer}(\zeta_{\mathcal L})=D_1$ and $D(\zeta_{\mathcal L})=D$. Here, $D(\zeta_{\mathcal L})$ is the abscissa of absolute convergence of $\zeta_{\mathcal L}$, $D_{\rm mer}(\zeta_{\mathcal L})$ is the abscissa of meromorphic continuation of $\zeta_{\mathcal L}$, while $D_{\rm par}(\zeta_{\mathcal L})$ is the infimum of all positive real numbers $\alpha$ such that $\zeta_{\mathcal L}$ is holomorphic in the open right half-plane $\{{\rm Re}\, s>\alpha\}$, except for possible isolated singularities in this half-plane. Defining $\mathcal L$ as the disjoint union of a sequence of suitable generalized Cantor strings, we show that the set of accumulation points of the set $S_{\infty}$ of essential singularities of $\zeta_{\mathcal L}$, contained in the open right half-plane $\{{\rm Re}\, s>D_{\infty}\}$, coincides with the vertical line $\{{\rm Re}\, s=D_{\infty}\}$. We extend this construction to the case of distance zeta functions $\zeta_A$ of compact sets $A$ in $\mathbb{R}^N$, for any positive integer $N$.

[60]
Title: On the Simple Quasi Crossing Number of $K_{11}$
Subjects: Combinatorics (math.CO)

We show that the simple quasi crossing number of $K_{11}$ is $4$.

[61]
Title: New Classes of Multicone Graphs Determinable by Their Spectra
Authors: Ali Zafari
Subjects: Combinatorics (math.CO)

A multicone graph is defined to be the join of a complete graph and a regular graph. A graph $\Gamma$ is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. It seems hard to prove a graph to be determined by its spectrum. In this paper, we investigate some new classes of multicone graphs determinable by their spectra.

[62]
Title: Optimal Portfolio of Distinct Frequency-Response Services in Low-Inertia Systems
Subjects: Optimization and Control (math.OC)

A reduced level of system inertia due to renewable integration increases the need for cost-effective provision of ancillary services, such as Frequency Response (FR). In this paper we propose a closed-form solution to the differential equation describing frequency dynamics, which allows to obtain frequency-security algebraic constraints to be implemented in optimisation routines. This is done while considering any finite number of FR services with distinguished characteristics, such as different delivery times and activation delays. The problem defined by these frequency-security constraints can be formulated as a Mixed-Integer Second-Order Cone Program (MISOCP), which can be efficiently handled by off-the-shelf conic optimisation solvers. This paper also takes into account the uncertainty in inertia contribution from the demand side by formulating the frequency-security conditions as chance constraints, for which an exact convex reformulation is provided. Finally, case studies highlighting the effectiveness of this frequency-secured formulation are presented.

[63]
Title: Curvature properties of Melvin magnetic metric
Subjects: Differential Geometry (math.DG)

This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with $1$-dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in general, is generalized Roter type, $Ein(3)$ and has pseudosymmetric Weyl conformal tensor satisfying the pseudosymmetric type condition $R\cdot R-Q(S,R)=\mathcal L' Q(g,C)$. The condition for which it satisfies the Roter type condition has been obtained. It is interesting to note that Melvin magnetic metric is pseudosymmetric and pseudosymmetric due to conformal tensor. Moreover such metric is $2$-quasi-Einstien, its Ricci tensor is Reimann compatible and Weyl conformal $2$-forms are recurrent. The Maxwell tensor is also pseudosymmetric type.

[64]
Title: A Lyapunov analysis for accelerated gradient methods: From deterministic to stochastic case
Subjects: Optimization and Control (math.OC)

The article [SBC14] made a connection between Nesterov's accelerated gradient descent method and an ordinary differential equation (ODE). We show that this connection can be extended to the case of stochastic gradients, and develop Lyapunov function based convergence rates proof for Nesterov's accelerated stochastic gradient descent. In the gradient case, we show if a Hessian damping term is added to the ODE from [SBC14], then Nesterov's method arises as a straightforward discretization of the modified ODE. Established Lyapunov analysis is used to recover the accelerated rates of convergence in both continuous and discrete time. Moreover, the Lyapunov analysis can be extended to the case of stochastic gradients which allows the full gradient case to be considered as a special case of the stochastic case. The result is a unified approach to convex acceleration in both continuous and discrete time and in both the stochastic and full gradient cases.

[65]
Title: Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes
Subjects: Probability (math.PR); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such fields have been studied in systems with a single species, the multi-species setting is much less understood. Among other results, we show that, when the system starts from stationary states, with a particular property, the scaling limits of the multi-species fluctuation fields, seen in a characteristic traveling frame, solve a coupled Burgers SPDE, which is a formal spatial gradient of a coupled KPZ equation.

[66]
Title: On Differential Invariants of Parabolic Surfaces
Comments: 92 Pages, 11 figures, explicit expressions and algorithms
Subjects: Differential Geometry (math.DG)

The algebra of differential invariants under $SA_3(\mathbb{R})$ of generic parabolic surfaces $S^2 \subset \mathbb{R}^3$ with nonvanishing Pocchiola $4^{\text{th}}$ invariant $W$ is shown to be generated, through invariant differentiations, by only one other invariant, $M$, of order $5$, having $57$ differential monomials. The proof is based on Fels-Olver's recurrence formulas, pulled back to the parabolic jet bundles.

[67]
Title: Functional CLT for the range of stable random walks
Subjects: Probability (math.PR)

In this note, we establish a functional central limit theorem for the capacity of the range for a class of $\alpha$-stable random walks on the integer lattice $\mathbb{Z}^d$ with $d \ge 3\alpha$. Using similar methods, we also prove an analogous result for the cardinality of the range when $d > 3\alpha / 2$.

[68]
Title: On an optimal potential of Schrödinger operator with prescribed $m$ eigenvalue
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Spectral Theory (math.SP)

The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a priori given potential $V_0$ find the closest function $\hat{V}$ such that $m$ eigenvalues of one-dimensional space Schrodinger operator with potential $\hat{V}$ would coincide with the given values $E_1$, $\ldots$, $E_m \in \mathbb {R}$. In our main result, we prove the existence of a solution to this problem, and more importantly, we show that such a solution can be directly found by solving a system of nonlinear differential equations.

[69]
Title: Configurations related to combinatorial Veronesians representing a skew perspective
Subjects: Combinatorics (math.CO)

A combinatorial object representing schemas of, possibly skew, perspectives, called {\em a configuration of skew perspective} has been defined in \cite{klik:binom}, \cite{maszko}. Here we develop the theory of configurations generalizing perspectives defined in combinatorial Veronesians. The complete classification of thus obtained $({15}_4 {20}_3)$-configurations is presented.

[70]
Title: Complete boundedness of multiple operator integrals
Authors: Clément Coine
Subjects: Functional Analysis (math.FA)

In this paper, we characterize the multiple operator integrals mappings which are bounded on the Haagerup tensor product of spaces of compact operators. We show that such maps are automatically completely bounded and prove that this is equivalent to a certain factorization property of the symbol associated to the operator integral mapping. This generalizes a result by Juschenko-Todorov-Turowska on the boundedness of continuous multilinear Schur multipliers.

[71]
Title: Free self-decomposability and unimodality of the Fuss-Catalan distributions
Subjects: Probability (math.PR); Combinatorics (math.CO)

We study properties of the Fuss-Catalan distributions $\mu(p,r)$, $p\geq1$, $0<r\leq p$: free infinite divisibility, free self-decomposability, free regularity and unimodality. We show that the Fuss-Catalan distribution $\mu(p,r)$ is freely self-decomposable if and only if $1 \leq p=r \leq 2$.

[72]
Title: Capacity & Perimeter from $α$-Hermite Bounded Variation
Subjects: Classical Analysis and ODEs (math.CA)

Let $\mathcal{H}_{\alpha}=\Delta-(\alpha-1)|x|^{\alpha}$ be an $[1,\infty)\ni\alpha$-Hermite operator for the hydrogen atom located at the origin in $\mathbb R^d$. In this paper, we are motivated by the classical case $\alpha=1$ to investigate the space of functions with $\alpha$-{\it Hermite Bounded Variation} and its functional capacity and geometrical perimeter.

[73]
Title: Flexibility of Lyapunov exponents
Subjects: Dynamical Systems (math.DS)

We outline the flexibility program in smooth dynamics, focusing on flexibility of Lyapunov exponents for volume-preserving diffeomorphisms. We prove flexibility results for Anosov diffeomorphisms admitting dominated splittings into one-dimensional bundles.

[74]
Title: Tropical Ehrhart Theory and Tropical Volume
Subjects: Metric Geometry (math.MG); Combinatorics (math.CO)

We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.

[75]
Title: Fractional heat semigroups on metric measure spaces with finite densities and applications to fractional dissipative equations
Subjects: Analysis of PDEs (math.AP)

Let $(\mathbb M, d,\mu)$ be a metric measure space with upper and lower
densities: $$\begin{cases} |||\mu|||_{\beta}:=\sup_{(x,r)\in \mathbb M\times(0,\infty)} \mu(B(x,r))r^{-\beta}<\infty;\\ |||\mu|||_{\beta^{\star}}:=\inf_{(x,r)\in \mathbb M\times(0,\infty)} \mu(B(x,r))r^{-\beta^{\star}}>0, \end{cases}$$ where $\beta, \beta^{\star}$ are two positive constants which are less than or equal to the Hausdorff dimension of $\mathbb M$. Assume that $p_t(\cdot,\cdot)$ is a heat kernel on $\mathbb M$ satisfying Gaussian upper estimates and $\mathcal L$ is the generator of the semigroup associated with $p_t(\cdot,\cdot)$. In this paper, via a method independent of Fourier transform, we establish the decay estimates for the kernels of the fractional heat
semigroup $\{e^{-t \mathcal{L}^{\alpha}}\}_{t>0}$ and the operators $\{{\mathcal{L}}^{\theta/2} e^{-t \mathcal{L}^{\alpha}}\}_{t>0}$, respectively. By these estimates, we obtain the regularity for the Cauchy problem of the fractional dissipative
equation associated with $\mathcal L$ on $(\mathbb M, d,\mu)$. Moreover, based on the geometric-measure-theoretic analysis of a new $L^p$-type capacity defined in $\mathbb{M}\times(0,\infty)$, we also characterize a nonnegative Randon measure $\nu$ on $\mathbb M\times(0,\infty)$ such that $R_\alpha L^p(\mathbb M)\subseteq L^q(\mathbb M\times(0,\infty),\nu)$ under $(\alpha,p,q)\in (0,1)\times(1,\infty)\times(1,\infty)$, where $u=R_\alpha f$ is the weak solution of the fractional diffusion equation $(\partial_t+ \mathcal{L}^\alpha)u(t,x)=0$
in $\mathbb M\times(0,\infty)$ subject to $u(0,x)=f(x)$ in $\mathbb M$.

[76]
Title: Constrained convex bodies with extremal affine surface areas
Subjects: Functional Analysis (math.FA)

Given a convex body K in R^n and p in R, we introduce and study the extremal inner and outer affine surface areas
IS_p(K) = sup_{K'\subseteq K} (as_p(K') ) and os_p(K)=inf_{K'\supseteq K} (as_p(K') ), where as_p(K') denotes the L_p-affine surface area of K', and the supremum is taken over all convex subsets of K and the infimum over all convex compact subsets containing K.
The convex body that realizes IS_1(K) in dimension 2 was determined by Barany. He also showed that this body is the limit shape of lattice polytopes in K. In higher dimensions no results are known about the extremal bodies.
We use a thin shell estimate of Guedon and Milman and the L\"owner ellipsoid to give asymptotic estimates on the size of IS_p(K) and os_p(K). Surprisingly, both quantities are proportional to a power of volume.

[77]
Title: No two Jellyfish graphs are L-cospectral and Q-cospectral
Subjects: Combinatorics (math.CO)

In this paper, it is proved that the jellyfish graphs, a natural generalization of sun graphs, are both DLS and DQS.

[78]
Title: Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse Problems
Subjects: Numerical Analysis (math.NA)

An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element computations. The analysis of the functional is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere manifold. It is found to agree with the discrete total mean curvature known in discrete differential geometry. A split Bregman iteration is proposed for the solution of discretized shape optimization problems, in which the total variation of the normal appears as a regularizer. Unlike most other priors, such as surface area, the new functional allows for piecewise flat shapes. As two applications, a mesh denoising and a geometric inverse problem of inclusion detection type involving a partial differential equation are considered. Numerical experiments confirm that polyhedral shapes can be identified quite accurately.

[79]
Title: On cyclic Schur-positive sets of permutation
Subjects: Combinatorics (math.CO)

We introduce a notion of {\em cyclic Schur-positivity} for sets of permutations, which naturally extends the classical notion of Schur-positivity, and it involves the existence of a bijection from permutations to standard Young tableaux that preserves the cyclic descent set. Cyclic Schur-positive sets of permutations are always Schur-positive, but the converse does not hold, as exemplified by inverse descent classes, Knuth classes and conjugacy classes.
In this paper we show that certain classes of permutations invariant under either horizontal or vertical rotation are cyclic Schur-positive. The proof unveils a new equidistribution phenomenon of descent sets on permutations, provides affirmative solutions to conjectures from [9] and [2], and yields new examples of Schur-positive sets.

[80]
Title: The mean square of real character sums
Authors: Peng Gao
Comments: 11 pages. arXiv admin note: text overlap with arXiv:0907.4747 by other authors
Subjects: Number Theory (math.NT)

In this paper, we evaluate a smoothed sum of the form $\displaystyle \sideset{}{^*}\sum_{d \leq X}\left(\sum_{n \leq Y} \left(\frac{8d}{n} \right ) \right)^2$, where $\left ( \frac{8d}{\cdot} \right )$ is the Kronecker symbol and $\sideset{}{^*}\sum$ denotes a sum over positive odd square-free integers.

[81]
Title: Stability of the linear complementarity problem properties under interval uncertainty
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)

We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite number of solutions etc.) are reflected by the properties of the constraint matrix. In order that the problem has desired properties even in the uncertain environment, we have to be able to check them for all possible realizations of interval data. This leads us to the robust properties of interval matrices. In particular, we will discuss $S$-matrix, $Z$-matrix, copositivity, semimonotonicity, column sufficiency, principal nondegeneracy, $R_0$-matrix and $R$-matrix. We characterize the robust properties and also suggest efficiently recognizable subclasses.

[82]
Title: On automorphisms and the cone conjecture for Enriques surfaces in odd characteristic
Authors: Long Wang
Comments: Master's thesis, 20 pages, comments welcome. arXiv admin note: substantial text overlap with arXiv:1904.04451 by other authors
Subjects: Algebraic Geometry (math.AG)

We prove that, for an Enriques surface in odd characteristic, the automorphism group is finitely generated and it acts on the effective nef cone with a rational polyhedral fundamental domain. We also construct a smooth projective surface in odd characteristic which is birational to an Enriques surface and whose automorphism group is discrete but not finitely generated.

[83]
Title: Lifting $G$-irreducible but $\mathrm{GL}_n$-reducible Galois representations
Subjects: Number Theory (math.NT)

In recent work, the authors proved a general result on lifting $G$-irreducible odd Galois representations $\mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_{\ell})$, with $F$ a totally real number field and $G$ a reductive group, to geometric $\ell$-adic representations. In this note we take $G$ to be a classical group and construct many examples of $G$-irreducible representations to which these new lifting methods apply, but to which the lifting methods provided by potential automorphy theorems do not.

[84]
Title: Real polynomials with constrained real divisors. I. Fundamental groups
Subjects: Algebraic Topology (math.AT); Combinatorics (math.CO)

In the late 80s, V.~Arnold and V.~Vassiliev initiated the study of the topology of the space of real univariate polynomials of a given degree d and with no real roots of multiplicity exceeding a given positive integer. Expanding their studies, we consider the spaces of real monic univariate polynomials of degree d whose real divisors avoid sequences of root multiplicities taken from a given poset \Theta of compositions, closed under certain natural combinatorial operations. In this paper, we calculate the fundamental group of these spaces and of some related topological spaces. The mechanism that generates the fundamental groups is similar to the one that produces the braid groups as the fundamental groups of spaces of complex degree d polynomials with no multiple roots. The fundamental groups admit an interpretation as special bordisms of immersions of 1-manifolds into the cylinder S^1 \times \R, immersions whose images avoid the tangency patterns from \Theta with respect to the generators of the cylinder.

[85]
Title: Subgroups, hyperbolicity and cohomological dimension for totally disconnected locally compact groups
Subjects: Group Theory (math.GR)

This article is part of the program of studying large-scale geometric properties of totally disconnected locally compact groups, TDLC-groups, by analogy with the theory for discrete groups. We provide a characterization of hyperbolic TDLC-groups, in terms of homological isoperimetric inequalities. This characterization is used to prove that, for hyperbolic TDLC-groups with rational discrete cohomological dimension $\leq 2$, hyperbolicity is inherited by compactly presented open subgroups. As a consequence, every open compactly presented subgroup of the automorphism group $aut(X)$ of a negatively curved locally finite $2$-dimensional building $X$ is a hyperbolic TDLC-group, whenever $aut(X)$ acts with finitely many orbits on $X$. Examples where this result applies include hyperbolic Bourdon's buildings.

[86]
Title: Monogenic trinomials with non-squarefree discriminant
Subjects: Number Theory (math.NT)

For each integer $n\ge 2$, we identify new infinite families of monogenic trinomials $f(x)=x^n+Ax^m+B$ with non-squarefree discriminant, many of which have small Galois group. These families are thus different from many previous examinations of specific trinomial forms in the literature. Moreover, in certain situations when $A=B\ge 2$ with fixed $n$ and $m$, we produce asymptotics on the number of such trinomials with $A\le X$.

[87]
Title: Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation
Subjects: Numerical Analysis (math.NA); Dynamical Systems (math.DS)

We consider the large-sparse symmetric linear systems of equations that arise in the solution of weak constraint four-dimensional variational data assimilation. These systems can be written as saddle point systems with a 3x3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2x2 block structure, or further to symmetric positive definite systems. In this paper, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.

[88]
Title: A central limit theorem for the two-sided descent statistic on Coxeter groups
Subjects: Combinatorics (math.CO); Group Theory (math.GR); Probability (math.PR)

We study the asymptotic behaviour of the statistic (des+ides) which assigns to an element w of a finite Coxeter group W the number of descents of w plus the number of descents of its inverse. Our main result is a central limit theorem for the probability distributions associated to this statistic. This answers a question of Kahle-Stump and generalises work of Chatterjee-Diaconis, \"Ozdemir and R\"ottger.

[89]
Title: Deterministic epidemic models for ebola infection with time-dependent controls
Subjects: Dynamical Systems (math.DS); Optimization and Control (math.OC); Populations and Evolution (q-bio.PE)

In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola virus infection using vaccination, treatment and educational campaign as time-dependent controls functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and the Pontryagin maximum principle to construct adjoint equations and optimality systems. The forward-backward sweep numerical scheme with fourth-order Runge-Kutta method is used to solve the optimality system for the various optimal control strategies. From our simulation results, we observed that, SIR model with optimal control strategies shows a significant decrease in the proportions of infected and susceptible individuals and a rapid increase in the recovered individuals compared to SIR model without optimal control. A similar effect was observed in the SEIR model with control strategies. Following the numerical solutions, we can conclude that, effective educational campaigns and vaccination of susceptible individuals as were as effective treatments of infected individuals can help reduce the disease transmission.

[90]
Title: Bloch wave approach to almost periodic homogenization and approximations of effective coefficients
Subjects: Analysis of PDEs (math.AP)

Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of periodic operators, which is not available in a suitable form for almost periodic operators. In particular, the notion of Bloch eigenvalues and eigenvectors does not exist for almost periodic operators. However, we are able to recover the homogenization result in this case, by employing a sequence of periodic approximations to almost periodic operators. We also establish a rate of convergence for Dirichlet approximations of homogenized tensors for a class of almost periodic media. The results are supported by a numerical study.

[91]
Title: A tree-based radial basis function method for noisy parallel surrogate optimization
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG); Machine Learning (stat.ML)

Parallel surrogate optimization algorithms have proven to be efficient methods for solving expensive noisy optimization problems. In this work we develop a new parallel surrogate optimization algorithm (ProSRS), using a novel tree-based "zoom strategy" to improve the efficiency of the algorithm. We prove that if ProSRS is run for sufficiently long, with probability converging to one there will be at least one point among all the evaluations that will be arbitrarily close to the global minimum. We compare our algorithm to several state-of-the-art Bayesian optimization algorithms on a suite of standard benchmark functions and two real machine learning hyperparameter-tuning problems. We find that our algorithm not only achieves significantly faster optimization convergence, but is also 1-4 orders of magnitude cheaper in computational cost.

[92]
Title: Minimal residual multistep methods for large stiff non-autonomous linear problems
Authors: Boris Faleichik
Subjects: Numerical Analysis (math.NA)

The purpose of this work is to introduce a new idea of how to avoid the factorization of large matrices during the solution of stiff systems of ODEs. Starting from the general form of an explicit linear multistep method we suggest to adaptively choose its coefficients on each integration step in order to minimize the norm of the residual of an implicit BDF formula. Thereby we reduce the number of unknowns on each step from $n$ to $O(1)$, where $n$ is the dimension of the ODE system. We call this type of methods Minimal Residual Multistep (MRMS) methods. In the case of linear non-autonomous problem, besides the evaluations of the right-hand side of ODE, the resulting numerical scheme additionally requires one solution of a linear least-squares problem with a thin matrix per step. We show that the order of the method and its zero-stability properties coincide with those of the used underlying BDF formula. For the simplest analog of the implicit Euler method the properties of linear stability are investigated. Though the classical absolute stability analysis is not fully relevant to the MRMS methods, it is shown that this one-step method is applicable in stiff case. In the numerical experiment section we consider the fixed-step integration of a two-dimensional non-autonomous heat equation using the MRMS methods and their classical BDF counterparts. The starting values are taken from a preset slowly-varying exact solution. The comparison showed that both methods give similar numerical solutions, but in the case of large systems the MRMS methods are faster, and their advantage considerably increases with the growth of dimension. Python code with the experimantal code can be downloaded from the GitHub repository https://github.com/bfaleichik/mrms.

[93]
Title: Dynamics and Topology of Conformally Anosov Contact 3-Manifolds
Authors: Surena Hozoori
Subjects: Geometric Topology (math.GT); Dynamical Systems (math.DS); Symplectic Geometry (math.SG)

We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show $\mathbb{S}^3$ does not admit conformally Anosov Reeb flows. We also give a Riemannian geometric condition on a metric compatible with a contact structure implying that a Reeb field is Anosov. From this we can give curvature conditions on a metric compatible with a contact structure that implies universal tightness of the contact structure among other things.

[94]
Title: Time Delay in the Swing Equation: A Variety of Bifurcations
Comments: 12 pages, 6 figures, "The following article has been submitted to 'Chaos: An Interdisciplinary Journal of Nonlinear Science'. After it is published, it will be found at this https URL"
Subjects: Dynamical Systems (math.DS); Systems and Control (eess.SY)

The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased. To this end, a general formula for the first Lyapunov coefficient in second order systems with additional delayed damping and delay-free nonlinearity is given. In so far the paper extends results about stability switching of equilibria in linear time delay systems from Cooke and Grossmann and complements an analysis of Campbell et al., who consider time delay in the restoring force. In addition to the analytical results, periodic solutions are numerically dealt with. The numerical results demonstrate how a variety of qualitative behaviors is generated in the simple swing equation by only introducing time delay in a damping term.
keywords: retarded functional differential equation (RFDE); delay differential equation (DDE); bifurcation analysis; Hopf bifurcation; first Lyapunov coefficient; limit cycle; period doubling cascade; invariant torus; driven pendulum equation; power system stability

[95]
Title: Adaptive Morley FEM for the von Kármán equations with optimal convergence rates
Subjects: Numerical Analysis (math.NA)

The adaptive nonconforming Morley finite element method (FEM) approximates a regular solution to the von K\'{a}rm\'{a}n equations with optimal convergence rates for sufficiently fine triangulations and small bulk parameter in the D\"orfler marking. This follows from the general axiomatic framework with the key arguments of stability, reduction, discrete reliability, and quasiorthogonality of an explicit residual-based error estimator. Particular attention is on the nonlinearity and the piecewise Sobolev embeddings required in the resulting trilinear form in the weak formulation of the nonconforming discretisation. The discrete reliability follows with a conforming companion for the discrete Morley functions from the medius analysis. The quasiorthogonality also relies on a novel piecewise $H^1$ a~priori error estimate and a careful analysis of the nonlinearity.

[96]
Title: Analog for the Wiener Lemma for Wolff-Denjoy Series
Subjects: Functional Analysis (math.FA)

Let a function f with real poles be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the note states that if we subtract its linear part from the function 1/f, then the remaining fractional part of this function will also expand into Wolff-Denjoy series (its poles are also real, and the coefficients of the series are negative). In other words, for Wolff-Denjoy series of the indicated form, an analogue of the well-known Wiener lemma in the theory of Fourier series is true up to a linear term. Applications of the result to operator theory are given.

[97]
Title: Good Fibrations through the Modal Prism
Authors: David Jaz Myers
Subjects: Category Theory (math.CT); Algebraic Topology (math.AT); Logic (math.LO)

Homotopy type theory is a formal language for doing abstract homotopy theory -- the study of identifications. But in unmodified homotopy type theory, there is no way to say that these identifications come from identifying the path-connected points of a space. In other words, we can do abstract homotopy theory, but not algebraic topology. Shulman's Real Cohesive HoTT remedies this issue by introducing a system of modalities that relate the spatial structure of types to their homotopical structure. In this paper, we develop a theory of modal fibrations for a general modality, and apply it in particular to the shape modality of Real Cohesion. To demonstrate the use of these modal fibrations, we calculate the homotopy type of the topological circle without using the higher inductive circle as an intermediary, and classify the $n$-fold covers of the circle.

### Cross-lists for Thu, 22 Aug 19

[98]  arXiv:1908.07521 (cross-list from stat.OT) [pdf, other]
Title: Distributed Hypothesis Testing over a Noisy Channel: Error-exponents Trade-off
Subjects: Other Statistics (stat.OT); Information Theory (cs.IT)

A distributed hypothesis testing problem with two parties, one referred to as the observer and the other as the detector, is considered. The observer observes a discrete memoryless source and communicates its observations to the detector over a discrete memoryless noisy channel. The detector observes a side-information correlated with the observer's observations, and performs a binary hypothesis test on the joint probability distribution of its own observations with that of the observer. With the objective of characterizing the performance of the hypothesis test, we obtain two inner bounds on the trade-off between the exponents of the type I and type II error probabilities. The first inner bound is obtained using a combination of a type-based quantize-bin scheme and Borade et al.'s unequal error protection scheme, while the second inner bound is established using a type-based hybrid coding scheme. These bounds extend the achievability result of Han and Kobayashi obtained for the special case of a rate-limited noiseless channel to a noisy channel. For the special case of testing for the marginal distribution of the observer's observations with no side-information at the detector, we establish a single-letter characterization of the optimal trade-off between the type I and type II error-exponents. Our results imply that a separation holds in this case, in the sense that the optimal trade-off between the error-exponents is achieved by a scheme that performs independent hypothesis testing and channel coding.

[99]  arXiv:1908.07568 (cross-list from eess.SP) [pdf]
Title: Power-Efficient Resource Allocation in Massive MIMO Aided Cloud RANs
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT)

This paper considers the power-efficient resource allocation problem in a cloud radio access network (C-RAN). The C-RAN architecture consists of a set of base-band units (BBUs) which are connected to a set of radio remote heads (RRHs) equipped with massive multiple input multiple output (MIMO), via fronthaul links with limited capacity. We formulate the power-efficient optimization problem in C-RANs as a joint resource allocation problem in order to jointly allocate the RRH and transmit power to each user, and fronthaul links and BBUs assign to active RRHs while satisfying the minimum required rate of each user. To solve this non-convex optimization problem we suggest iterative algorithm with two-step based on the complementary geometric programming (CGP) and the successive convex approximation (SCA). The simulation results indicate that our proposed scheme can significantly reduce the total transmission power by switching off the under-utilized RRHs.

[100]  arXiv:1908.07585 (cross-list from cs.LG) [pdf, ps, other]
Title: Fast-rate PAC-Bayes Generalization Bounds via Shifted Rademacher Processes
Subjects: Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)

The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by viewing Gibbs classifiers as linear operators. The goal of this paper is to extend this bridge between Rademacher complexity and state-of-the-art PAC-Bayesian theory. We first demonstrate that one can match the fast rate of Catoni's PAC-Bayes bounds (Catoni, 2007) using shifted Rademacher processes (Wegkamp, 2003; Lecu\'{e} and Mitchell, 2012; Zhivotovskiy and Hanneke, 2018). We then derive a new fast-rate PAC-Bayes bound in terms of the "flatness" of the empirical risk surface on which the posterior concentrates. Our analysis establishes a new framework for deriving fast-rate PAC-Bayes bounds and yields new insights on PAC-Bayesian theory.

[101]  arXiv:1908.07626 (cross-list from q-fin.MF) [pdf, other]
Title: Optimal Investment with Correlated Stochastic Volatility Factors
Subjects: Mathematical Finance (q-fin.MF); Probability (math.PR)

The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to a classical distortion transformation. In the present paper, we address the problem with several factors using a perturbation technique around the case where these factors are perfectly correlated reducing the problem to the case with a single factor. We illustrate our result with a particular model for which we have explicit formulas. A rigorous accuracy result is also derived using sub- and super-solutions of the HJB equation involved. In order to keep the notations as explicit as possible, we treat the case with one stock and two factors and we describe an extension to the case with two stocks and two factors.

[102]  arXiv:1908.07636 (cross-list from stat.ML) [pdf, other]
Title: How to gamble with non-stationary $\mathcal{X}$-armed bandits and have no regrets
Authors: Vakeriy Avanesov
Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST)

In $\mathcal{X}$-armed bandit problem an agent sequentially interacts with environment which yields a reward based on the vector input the agent provides. The agent's goal is to maximise the sum of these rewards across some number of time steps. The problem and its variations have been a subject of numerous studies, suggesting sub-linear and some times optimal strategies. The given paper introduces a novel variation of the problem. We consider an environment, which can abruptly change its behaviour an unknown number of times. To that end we propose a novel strategy and prove it attains sub-linear cumulative regret. Moreover, in case of highly smooth relation between an action and the corresponding reward, the method is nearly optimal. The theoretical result are supported by experimental study.

[103]  arXiv:1908.07668 (cross-list from cs.CG) [pdf, other]
Title: Existence and hardness of conveyor belts
Subjects: Computational Geometry (cs.CG); Combinatorics (math.CO)

An open problem of Manuel Abellanas asks whether every set of disjoint closed unit disks in the plane can be connected by a conveyor belt, which means a tight simple closed curve that touches the boundary of each disk, possibly multiple times. We prove three main results. First, for unit disks whose centers are both $x$-monotone and $y$-monotone, or whose centers have $x$-coordinates that differ by at least two units, a conveyor belt always exists and can be found efficiently. Second, it is NP-complete to determine whether disks of varying radii have a conveyor belt, and it remains NP-complete when we constrain the belt to touch disks exactly once. Third, any disjoint set of $n$ disks of arbitrary radii can be augmented by $O(n)$ "guide" disks so that the augmented system has a conveyor belt touching each disk exactly once, answering a conjecture of Demaine, Demaine, and Palop.

[104]  arXiv:1908.07691 (cross-list from eess.SY) [pdf, other]
Title: Detection-averse optimal and receding-horizon control for Markov decision processes
Subjects: Systems and Control (eess.SY); Optimization and Control (math.OC)

In this paper, we consider a Markov decision process (MDP), where the ego agent has a nominal objective to pursue while needs to hide its state from detection by an adversary. After formulating the problem, we first propose a value iteration (VI) approach to solve it. To overcome the "curse of dimensionality" and thus gain scalability to larger-sized problems, we then propose a receding-horizon optimization (RHO) approach to obtain approximate solutions. We use examples to illustrate and compare the VI and RHO approaches, and to show the potential of our problem formulation for practical applications.

[105]  arXiv:1908.07694 (cross-list from quant-ph) [pdf, other]
Title: The Complementary Information Principle of Quantum Mechanics
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)

The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in quantum technologies. However, neither the uncertainty principle nor uncertainty relations can fully describe the complementarity between quantum measurements. As an attempt to advance the efforts of complementarity in quantum theories, we formally propose a complementary information principle, significantly extending the one introduced by Heisenberg. First, we build a framework of black box testing consisting of pre- and post-testing with two incompatible measurements, introducing a rigorous mathematical expression of complementarity with definite information causality. Second, we provide majorization lower and upper bounds for the complementary information by utilizing the tool of semidefinite programming. In particular, we prove that our bounds are optimal under majorization due to the completeness of the majorization lattice. Finally, as applications to our framework, we present a general method to outer-approximating all uncertainty regions and also establish fundamental limits for all qualified joint uncertainties.

[106]  arXiv:1908.07950 (cross-list from cond-mat.dis-nn) [pdf, other]
Title: On the multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classes
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Mathematical Physics (math-ph)

We introduce a power-law banded random matrix model for the third of the three classical Wigner-Dyson ensembles, i.e., the symplectic ensemble. A detailed analysis of the statistical properties of its eigenvectors and eigenvalues, at criticality, is presented. This ensemble is relevant for time-reversal symmetric systems with strong spin-orbit interaction. For the sake of completeness, we also review the statistical properties of eigenvectors and eigenvalues of the power-law random banded matrix model for the corresponding systems in the presence and absence of time reversal invariance, previously considered in the literature. Our results show a good agreement with heuristic relations for the eigenstate and eigenenergy statistics at criticality, proposed in previous studies. With this, we provide a full picture of the power-law random banded matrix model corresponding to the three classical Wigner-Dyson ensembles.

[107]  arXiv:1908.07967 (cross-list from eess.SP) [pdf, other]
Title: Multi-Antenna Relaying and Reconfigurable Intelligent Surfaces: End-to-End SNR and Achievable Rate
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT)

In this report, we summarize the end-to-end signal-to-noise ratio and the rate of half-duplex, full-duplex, amplify-and-forward, and decode-and-forward relay-aided communications, and well as the signal-to-noise ratio and the rate of the emerging technology known as reconfigurable intelligent surfaces.

[108]  arXiv:1908.08002 (cross-list from cond-mat.dis-nn) [pdf, other]
Title: Virtual clusters model on branching random graphs for confined fluid thermodynamics in heterogeneous solid geometry
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

Fluid properties near rough surfaces are crucial in both a description of fundamental surface phenomena and modern industrial material design implementations. One of the most powerful approach to model real rough materials is based on the surface representation in terms of random geometry. Understanding the influence of random solid geometry on the low temperature fluid thermodynamics is a cutting edge problem. Therefor this work extends recent studies bypassing high temperature expansion and small heterogeneity scale. We introduce random branching trees whose topology reflects the hierarchical properties of random solid geometry. This mathematical representation allows to obtain averaged free energy using novel statistical model of virtual clusters interacting through random ultrametric pairwise potentials. Excellent agreement with direct Monte Carlo calculations is obtained. Moreover, we find that this model leads to interesting features of fluid-solid interactions that have not been discussed in the literature. Our results demonstrate that at low temperature a significant impact to fluid-solid interface energy is induced by hierarchical structure of random geometry. Due to the interdisciplinary nature of the study, our approach can be generalized and applied to a wide range of quenched disorder systems on random graphs. Cooperative phenomena in biological populations and social networks seem most attractive.

[109]  arXiv:1908.08022 (cross-list from cs.NE) [pdf]
Title: Genetic Algorithm for the 0/1 Multidimensional Knapsack Problem
Authors: Shalin Shah
Subjects: Neural and Evolutionary Computing (cs.NE); Optimization and Control (math.OC)

The 0/1 multidimensional knapsack problem is the 0/1 knapsack problem with m constraints which makes it difficult to solve using traditional methods like dynamic programming or branch and bound algorithms. We present a genetic algorithm for the multidimensional knapsack problem with Java code that is able to solve publicly available instances in a very short computational duration. Our algorithm uses iteratively computed Lagrangian multipliers as constraint weights to augment the greedy algorithm for the multidimensional knapsack problem and uses that information in a greedy crossover in a genetic algorithm. The algorithm uses several other hyperparameters which can be set in the code to control convergence. Our algorithm improves upon the algorithm by Chu and Beasley in that it converges to optimum or near optimum solutions much faster.

[110]  arXiv:1908.08030 (cross-list from hep-th) [pdf, ps, other]
Title: Integrability and cycles of deformed ${\cal N}=2$ gauge theory
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)

To analyse pure ${\cal N}=2$ $SU(2)$ gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken) discrete symmetry in its extended version with {\it two} singular irregular points. Actually, this symmetry appears to be 'manifestation' of the spontaneously broken $\mathbb{Z}_2$ R-symmetry of the original gauge problem and the two deformed SW cycles are simply connected to the Baxter's $T$ and $Q$ functions, respectively, of the Liouville conformal field theory at the self-dual point. The liaison is realised via a second order differential operator which is essentially the 'quantum' version of the square of the SW differential. Moreover, the constraints imposed by the broken $\mathbb{Z}_2$ R-symmetry acting on the moduli space (Bilal-Ferrari equations) seem to have their quantum counterpart in the $TQ$ and the $T$ periodicity relations, and integrability yields also a useful Thermodynamic Bethe Ansatz (TBA) for the cycles ($Y(\theta,\pm u)$ or their square roots, $Q(\theta,\pm u)$). A latere, two efficient asymptotic expansion techniques are presented. Clearly, the whole construction is extendable to gauge theories with matter and/or higher rank groups.

### Replacements for Thu, 22 Aug 19

[111]  arXiv:1408.2903 (replaced) [pdf, other]
Title: Poincaré--Birkhoff--Witt isomorphisms and Kapranov dg-manifolds
Subjects: Differential Geometry (math.DG); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Quantum Algebra (math.QA)
[112]  arXiv:1411.2522 (replaced) [pdf, ps, other]
Title: Characteristic polyhedra of singularities without completion -- Part II
Comments: 46 pages; reworked the article and extended the result to more general cases
Subjects: Algebraic Geometry (math.AG)
[113]  arXiv:1607.02330 (replaced) [pdf, other]
Title: Two Measures of Dependence
Comments: 40 pages; 1 figure; published in Entropy
Journal-ref: Entropy 2019, 21(8), 778
Subjects: Information Theory (cs.IT)
[114]  arXiv:1703.04811 (replaced) [pdf, other]
Title: Equilibrium configurations for generalized Frenkel-Kontorova models on quasicrystals
Authors: Rodrigo Treviño
Subjects: Mathematical Physics (math-ph); Dynamical Systems (math.DS)
[115]  arXiv:1703.07021 (replaced) [pdf, ps, other]
Title: Regularity of Schroedinger's functional equation and mean field PDEs for h-path processes
Authors: Toshio Mikami
Subjects: Probability (math.PR); Mathematical Physics (math-ph); Optimization and Control (math.OC)
[116]  arXiv:1704.05745 (replaced) [pdf, ps, other]
Title: Conditional measure on the Brownian path and other random sets
Authors: Ábel Farkas
Subjects: Probability (math.PR)
[117]  arXiv:1704.06510 (replaced) [pdf, ps, other]
Title: Criteria for generalized translation-invariant frames
Comments: To appear in Studia Mathematica
Subjects: Functional Analysis (math.FA)
[118]  arXiv:1707.00091 (replaced) [pdf, ps, other]
Title: Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields
Subjects: Number Theory (math.NT)
[119]  arXiv:1707.03324 (replaced) [pdf, ps, other]
Title: Dynamic Stochastic Approximation for Multi-stage Stochastic Optimization
Subjects: Optimization and Control (math.OC); Computational Complexity (cs.CC); Machine Learning (cs.LG); Machine Learning (stat.ML)
[120]  arXiv:1710.00348 (replaced) [pdf, ps, other]
Title: Large deviations for level sets of branching Brownian motion and Gaussian free fields
Comments: Dedicated to the memory of Professor V.N. Sudakov. The project was partly supported by ANR MALIN; E.A. also acknowledges supports from ANR GRAAL and ANR Liouville. This version corrects a mistake in the original version
Subjects: Probability (math.PR)
[121]  arXiv:1710.04909 (replaced) [src]
Title: Moments and One level density of quadratic Hecke $L$-functions of $\mathbb{Q}(ω)$
Comments: 16 pages. Result combined with those in arXiv:1711.10557 and arXiv:1707.00091
Subjects: Number Theory (math.NT)
[122]  arXiv:1712.09066 (replaced) [pdf, other]
Title: Existence of closed geodesics through a regular point on translation surfaces
Comments: 30 pages. Revised and expanded according to referee's report
Subjects: Geometric Topology (math.GT); Complex Variables (math.CV); Differential Geometry (math.DG); Dynamical Systems (math.DS)
[123]  arXiv:1801.07595 (replaced) [pdf, other]
Title: Gaussian Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims
Comments: 21 pages,3 figures. arXiv admin note: text overlap with arXiv:1607.06624, arXiv:1702.05852, arXiv:1309.7621 by other authors
Journal-ref: Methodology and Computing in Applied Probability 2019
Subjects: Risk Management (q-fin.RM); Probability (math.PR)
[124]  arXiv:1803.01664 (replaced) [pdf, ps, other]
Title: Adjoint functor theorems for $\infty$-categories
Comments: v1: 21 pages; v2: updated the references, minor changes; v3: 22 pages, changed the terminology from "final" to "coinitial" functors, added three further Corollaries 4.1.5, 5.1.4 and 5.1.5, additional minor changes, accepted for publication in the Journal of the London Mathematical Society
Subjects: Category Theory (math.CT); Algebraic Topology (math.AT)
[125]  arXiv:1803.05408 (replaced) [pdf, other]
Title: Maximum likelihood drift estimation for a threshold diffusion
Authors: Antoine Lejay (TOSCA, IECL), Paolo Pigato (WIAS)
Subjects: Probability (math.PR); Statistics Theory (math.ST)
[126]  arXiv:1803.08750 (replaced) [pdf, ps, other]
Title: Homogeneous symplectic 4-manifolds and finite dimensional Lie algebras of symplectic vector fields on the symplectic 4-space
Comments: 37 pages, 2 tables; v4: minor comments, few typos corrected and one reference added. To appear on Mosc. Math. J
Subjects: Differential Geometry (math.DG); High Energy Physics - Theory (hep-th); Symplectic Geometry (math.SG)
[127]  arXiv:1804.09312 (replaced) [pdf, ps, other]
Title: Calibrated zero-norm regularized LS estimator for high-dimensional error-in-variables regression
Subjects: Optimization and Control (math.OC)
[128]  arXiv:1805.04625 (replaced) [pdf, ps, other]
Title: Strong Converse using Change of Measure Arguments
Comments: 35 pages, no figure; v2 updated references
Subjects: Information Theory (cs.IT)
[129]  arXiv:1805.07451 (replaced) [pdf, ps, other]
Title: Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks
Subjects: Numerical Analysis (math.NA); Machine Learning (cs.LG); Machine Learning (stat.ML)
[130]  arXiv:1805.11736 (replaced) [pdf, ps, other]
Title: Quantum function algebras from finite-dimensional Nichols algebras
Comments: 25 pages. Some remarks added after referee's suggestion, particularly, on the existence of localization (with or without Ore condition) and on the type of examples. Some references added
Subjects: Quantum Algebra (math.QA); Rings and Algebras (math.RA)
[131]  arXiv:1806.09811 (replaced) [pdf, other]
Title: The multifaceted behavior of integrated supOU processes: The infinite variance case
Subjects: Probability (math.PR)
[132]  arXiv:1807.01359 (replaced) [pdf, other]
Title: Revisiting the Jones eigenproblem in fluid-structure interaction
Subjects: Numerical Analysis (math.NA)
[133]  arXiv:1807.07198 (replaced) [pdf, other]
Title: Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type
Comments: Preliminary version; any comment welcome
Subjects: Group Theory (math.GR)
[134]  arXiv:1807.10832 (replaced) [pdf, ps, other]
Title: ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration
Subjects: Optimization and Control (math.OC)
[135]  arXiv:1808.01999 (replaced) [pdf, ps, other]
Title: Mass-spring-damper Networks for Distributed Optimization in Non-Euclidean Spaces
Subjects: Optimization and Control (math.OC)
[136]  arXiv:1808.08080 (replaced) [pdf, ps, other]
Title: On the Finite Horizon Optimal Switching Problem with Random Lag
Authors: Magnus Perninge
Subjects: Optimization and Control (math.OC)
[137]  arXiv:1808.09604 (replaced) [pdf, other]
Title: Conjugator lengths in hierarchically hyperbolic groups
Comments: Streamlined proof of Theorem A
Subjects: Group Theory (math.GR); Geometric Topology (math.GT)
[138]  arXiv:1808.10593 (replaced) [pdf, other]
Title: Asymptotic Seed Bias in Respondent-driven Sampling
Subjects: Statistics Theory (math.ST); Social and Information Networks (cs.SI); Probability (math.PR); Methodology (stat.ME)
[139]  arXiv:1809.04618 (replaced) [pdf, other]
Title: Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Acceleration
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG)
[140]  arXiv:1809.05083 (replaced) [pdf, ps, other]
Title: Quotients of the magmatic operad: lattice structures and convergent rewrite systems
Journal-ref: Experimental Mathematics, 2019
Subjects: Combinatorics (math.CO); Quantum Algebra (math.QA)
[141]  arXiv:1809.08806 (replaced) [pdf, ps, other]
Title: The theory of N-Mixed-Spin-P fields
Subjects: Algebraic Geometry (math.AG); Mathematical Physics (math-ph)
[142]  arXiv:1810.03299 (replaced) [pdf, ps, other]
Title: Spanning trees in random graphs
Comments: 71 pages, 31 figures, version accepted for publication in Advances in Mathematics
Subjects: Combinatorics (math.CO)
[143]  arXiv:1810.05548 (replaced) [pdf, ps, other]
Title: A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent
Subjects: Differential Geometry (math.DG)
[144]  arXiv:1810.06505 (replaced) [pdf, ps, other]
Title: An Axiomatic Characterization of Steenrod's cup-$i$ Products
Subjects: Algebraic Topology (math.AT)
[145]  arXiv:1810.07830 (replaced) [pdf, ps, other]
Title: (Bi)Hom-Leibniz algebras
Comments: arXiv admin note: text overlap with arXiv:0811.3076, arXiv:1301.4047 by other authors
Subjects: Rings and Algebras (math.RA)
[146]  arXiv:1810.12599 (replaced) [pdf, other]
Title: The Hausdorff dimension function of the family of conformal iterated function systems of generalized complex continued fractions
Comments: To appear in Discrete and Continuous Dynamical Systems Ser. A
Subjects: Dynamical Systems (math.DS); Complex Variables (math.CV); Probability (math.PR)
[147]  arXiv:1811.11608 (replaced) [pdf, ps, other]
Title: The Strauss conjecture on negatively curved backgrounds
Comments: In this revision we also include an alternate proof of a dispersive estimate for hyperbolic space of Tataru
Subjects: Analysis of PDEs (math.AP)
[148]  arXiv:1811.12010 (replaced) [pdf, other]
Title: On the inducibility of small trees
Subjects: Combinatorics (math.CO)
[149]  arXiv:1812.07687 (replaced) [pdf, ps, other]
Title: Symplectic resolutions for multiplicative quiver varieties and character varieties for punctured surfaces
Comments: 44 pages, several corrections in v2
Subjects: Algebraic Geometry (math.AG); Rings and Algebras (math.RA); Representation Theory (math.RT); Symplectic Geometry (math.SG)
[150]  arXiv:1901.01398 (replaced) [pdf, ps, other]
Title: A note on the singularities of residue currents of integrally closed ideals
Authors: Elizabeth Wulcan
Subjects: Complex Variables (math.CV)
[151]  arXiv:1901.02746 (replaced) [pdf, other]
Title: Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization
Subjects: Optimization and Control (math.OC)
[152]  arXiv:1902.00424 (replaced) [pdf, other]
Title: A low-rank projector-splitting integrator for the Vlasov--Maxwell equations with divergence correction
Subjects: Numerical Analysis (math.NA)
[153]  arXiv:1902.05972 (replaced) [pdf, ps, other]
Title: Fedoryuk values and stability of global Hölderian error bounds for polynomial functions
Subjects: Algebraic Geometry (math.AG); Optimization and Control (math.OC)
[154]  arXiv:1902.06863 (replaced) [pdf, ps, other]
Title: Rosser provability and the second incompleteness theorem
Authors: Taishi Kurahashi
Subjects: Logic (math.LO)
[155]  arXiv:1903.00561 (replaced) [pdf, other]
Title: A mean field approach to model flows of agents with path preferences over a network
Comments: 6 pages, Accepted in 58th IEEE Conference on Decision and Control 2019. arXiv admin note: text overlap with arXiv:1808.00537
Subjects: Optimization and Control (math.OC)
[156]  arXiv:1903.00597 (replaced) [pdf, ps, other]
Title: Block-Coordinate Minimization for Large SDPs with Block-Diagonal Constraints
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG)
[157]  arXiv:1903.01098 (replaced) [pdf, ps, other]
Title: Quadratic residues and related permutations concerning cyclotomic fields
Authors: Hai-Liang Wu
Subjects: Number Theory (math.NT)
[158]  arXiv:1903.03262 (replaced) [pdf, ps, other]
Title: Capitulation kernels of class groups over Z_p^d-extensions
Subjects: Number Theory (math.NT)
[159]  arXiv:1903.03792 (replaced) [pdf, ps, other]
Title: A Characterization of the Finiteness of Perpetual Integrals of Levy Processes
Subjects: Probability (math.PR)
[160]  arXiv:1903.04922 (replaced) [pdf, ps, other]
Title: Some weighted isoperimetric problems on $\mathbb{R}^N _+$ with stable half balls have no solutions
Subjects: Analysis of PDEs (math.AP)
[161]  arXiv:1903.05070 (replaced) [pdf, other]
Title: A generalized Noether theorem for scaling symmetry
Comments: Extended version. 18 pages, 3 figures. Details and relations to the Bargmann framework clarified and illustrated with further examples. v4: earlier results summarized
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th)
[162]  arXiv:1903.09376 (replaced) [pdf, other]
Title: Deep Fictitious Play for Stochastic Differential Games
Authors: Ruimeng Hu
Subjects: Optimization and Control (math.OC); Computer Science and Game Theory (cs.GT); Machine Learning (stat.ML)
[163]  arXiv:1903.11211 (replaced) [pdf, ps, other]
Authors: John R. Klauder
Comments: 14 pages, a novel approach to quantizing general relativity, minor corrections; NEW RESULTS, SHARPER EXAMPLES; Important correction
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[164]  arXiv:1904.01211 (replaced) [pdf, ps, other]
Title: The Loewner function of a log-concave function
Subjects: Functional Analysis (math.FA)
[165]  arXiv:1904.02034 (replaced) [pdf, other]
Title: Internal versus external balancing in the evaluation of graph-based number types
Subjects: Computational Geometry (cs.CG); Data Structures and Algorithms (cs.DS); Numerical Analysis (math.NA)
[166]  arXiv:1904.03755 (replaced) [pdf, other]
Title: Load Balancing in Mobility-on-Demand Systems: Reallocation Via Parametric Control Using Concurrent Estimation
Subjects: Optimization and Control (math.OC)
[167]  arXiv:1904.11657 (replaced) [pdf, ps, other]
Title: Retractability of solutions to the Yang-Baxter equation and $p$-nilpotency of skew braces
Comments: 23 pages, 3 tables. Final version, accepted for publication in International Journal of Algebra and Computation
Subjects: Rings and Algebras (math.RA); Group Theory (math.GR); Quantum Algebra (math.QA)
[168]  arXiv:1904.12825 (replaced) [pdf, ps, other]
Title: Using Uncertainty Data in Chance-Constrained Trajectory Planning
Journal-ref: 2019 18th European Control Conference (ECC)
Subjects: Systems and Control (eess.SY); Optimization and Control (math.OC)
[169]  arXiv:1904.12954 (replaced) [pdf, ps, other]
Title: Convergence of point processes associated with coupon collector's and Dixie cup problems
Authors: Andrii Ilienko
Subjects: Probability (math.PR)
[170]  arXiv:1905.00604 (replaced) [pdf, other]
Title: IRS-Enhanced OFDM: Power Allocation and Passive Array Optimization
Comments: to appear in IEEE GLOBECOM 2019. arXiv admin note: substantial text overlap with arXiv:1906.09956
Subjects: Signal Processing (eess.SP); Information Theory (cs.IT)
[171]  arXiv:1905.00659 (replaced) [pdf, ps, other]
Title: Lie Algebroid Gauging of Non-linear Sigma Models
Authors: Kyle Wright
Comments: 32 pages. V2: fixed small typos to match published version
Journal-ref: J. Geom. Phys. 146 (2019) 103490
Subjects: Differential Geometry (math.DG); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[172]  arXiv:1905.00802 (replaced) [pdf, ps, other]
Title: Concentration inequalities for random tensors
Authors: Roman Vershynin
Comments: Typos and minor inaccuracies corrected
Subjects: Probability (math.PR)
[173]  arXiv:1905.00864 (replaced) [pdf, other]
Title: Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[174]  arXiv:1905.01282 (replaced) [pdf, other]
Title: Learning Some Popular Gaussian Graphical Models without Condition Number Bounds
Comments: V2: Updated version with some new results
Subjects: Machine Learning (cs.LG); Data Structures and Algorithms (cs.DS); Statistics Theory (math.ST); Machine Learning (stat.ML)
[175]  arXiv:1905.02641 (replaced) [pdf, ps, other]
Title: The contact process with dynamic edges on $\mathbb{Z}$
Comments: 14 pages, 4 figures. New results were added about the extinction time of the process and about extensions to general vertex-transitive graphs
Subjects: Probability (math.PR)
[176]  arXiv:1905.08903 (replaced) [pdf, other]
Title: Topology optimization on two-dimensional manifolds
Subjects: Computational Physics (physics.comp-ph); Computational Engineering, Finance, and Science (cs.CE); Optimization and Control (math.OC)
[177]  arXiv:1906.00466 (replaced) [pdf, other]
Title: Tilings, traces and triangles
Authors: Rodrigo Treviño
Subjects: Dynamical Systems (math.DS); Operator Algebras (math.OA)
[178]  arXiv:1906.01172 (replaced) [pdf, ps, other]
Title: Spectral average of central values of automorphic L-functions for holomorphic cusp forms on SO_0(m,2) II
Authors: Masao Tsuzuki
Subjects: Number Theory (math.NT)
[179]  arXiv:1906.01229 (replaced) [pdf, ps, other]
Title: An optimization problem for finite point interaction families
Authors: Pavel Exner
Comments: typos corrected, to appear in J. Phys. A: Math. Theor
Subjects: Spectral Theory (math.SP); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[180]  arXiv:1906.02619 (replaced) [pdf, other]
Title: Hyperbolic spin Ruijsenaars-Schneider model from Poisson reduction
Comments: 16 pages. The statement about coincidence of the Poisson structure of spin variables at generic $N$ and $\ell$ with that of 1811.08727 was corrected
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
[181]  arXiv:1906.04448 (replaced) [pdf, other]
Title: Reinforcement Learning for Channel Coding: Learned Bit-Flipping Decoding
Subjects: Information Theory (cs.IT); Machine Learning (cs.LG)
[182]  arXiv:1906.07238 (replaced) [pdf, ps, other]
Title: Heterotic/$F$-theory Duality and Narasimhan-Seshadri Equivalence
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[183]  arXiv:1906.08234 (replaced) [pdf, ps, other]
Title: On edge-ordered Ramsey numbers
Authors: Jacob Fox, Ray Li
Subjects: Combinatorics (math.CO)
[184]  arXiv:1906.09503 (replaced) [pdf, ps, other]
Title: LNL-FPC: The Linear/Non-linear Fixpoint Calculus
Comments: Extended version of the ICFP paper "Mixed linear and non-linear recursive types" available at this https URL
Subjects: Programming Languages (cs.PL); Logic in Computer Science (cs.LO); Category Theory (math.CT)
[185]  arXiv:1906.11150 (replaced) [pdf, other]
Title: Bi-parameter Carleson embeddings with product weights
Comments: v3: 24 pages, incorporates arXiv:1906.11145
Subjects: Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA)
[186]  arXiv:1907.06357 (replaced) [pdf, other]
Title: Entanglement-assisted Quantum Codes from Algebraic Geometry Codes
Comments: Some results in this paper were presented at the 2019 IEEE International Symposium on Information Theory
Subjects: Information Theory (cs.IT); Quantum Physics (quant-ph)
[187]  arXiv:1907.07096 (replaced) [pdf, other]
Title: A conjecture on the lengths of filling pairs
Subjects: Geometric Topology (math.GT); General Topology (math.GN)
[188]  arXiv:1907.08204 (replaced) [pdf, other]
Title: Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
Comments: 27 pages + 12 pages of appendices. v2 updated references
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
[189]  arXiv:1907.08318 (replaced) [pdf, ps, other]
Title: A study of convex convex-composite functions via infimal convolution with applications
Subjects: Optimization and Control (math.OC)
[190]  arXiv:1907.10318 (replaced) [pdf, ps, other]
Title: Universality of the Langevin diffusion as scaling limit of a family of Metropolis-Hastings processes I: fixed dimension
Subjects: Probability (math.PR); Statistics Theory (math.ST)
[191]  arXiv:1908.00301 (replaced) [pdf, other]
Title: General Information Theory: Time and Information
Authors: Yilun Liu, Lidong Zhu
Comments: This work has been submitted to the IEEE T-IT for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible
Subjects: Information Theory (cs.IT)
[192]  arXiv:1908.02185 (replaced) [pdf, ps, other]
Title: On the initial geometry of a vacuum cosmological spacetime
Authors: John Lott
Subjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)
[193]  arXiv:1908.04340 (replaced) [pdf, ps, other]
Title: On Reeb graphs induced from smooth functions on closed or open surfaces
Authors: Naoki Kitazawa
Comments: 11 pages, 6 figures, new stuffs including two theorems have be added and this version is submitted to a refereed journal, mistakes are due to carelessness of the author
Subjects: Geometric Topology (math.GT); General Topology (math.GN)
[194]  arXiv:1908.04365 (replaced) [pdf, ps, other]
Title: On $q$-deformed real numbers
Subjects: Quantum Algebra (math.QA)
[195]  arXiv:1908.05532 (replaced) [pdf, ps, other]
Title: Bubbling solutions for a planar exponential nonlinear elliptic equation with a singular source
Authors: Yibin Zhang
Subjects: Analysis of PDEs (math.AP)
[196]  arXiv:1908.05587 (replaced) [pdf, ps, other]
Title: A New Class of Irreducible Polynomials
Subjects: Number Theory (math.NT); Commutative Algebra (math.AC)
[197]  arXiv:1908.06315 (replaced) [pdf, other]
Title: Implicit Deep Learning
Subjects: Machine Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML)
[198]  arXiv:1908.06417 (replaced) [pdf, other]
Title: On a progressive and iterative approximation method with memory for least square fitting
Subjects: Numerical Analysis (math.NA)
[199]  arXiv:1908.06667 (replaced) [pdf, ps, other]
Title: Irrationality and monodromy for cubic threefolds
Authors: Ivan Smith
Comments: 21 pages, 6 figures; v2, minor typographic and bibliographic corrections
Subjects: Algebraic Geometry (math.AG); Group Theory (math.GR); Symplectic Geometry (math.SG)
[200]  arXiv:1908.06891 (replaced) [pdf, ps, other]
Title: Weil descent and cryptographic trilinear maps
Subjects: Cryptography and Security (cs.CR); Number Theory (math.NT)
[201]  arXiv:1908.07029 (replaced) [pdf, ps, other]
Title: Operators which are polynomially isometric to a normal operator
Subjects: Functional Analysis (math.FA)
[202]  arXiv:1908.07065 (replaced) [pdf, other]
Title: Non-perturbative approaches to the quantum Seiberg-Witten curve
Comments: 46 pages, 4 figures, 12 tables; new references added, typos corrected
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[203]  arXiv:1908.07248 (replaced) [pdf, ps, other]
Title: On the geometry of asymptotically flat manifolds
Authors: Xiuxiong Chen, Yu Li
Comments: 101 pages, Table 1 is corrected
Subjects: Differential Geometry (math.DG)
[204]  arXiv:1908.07301 (replaced) [pdf, ps, other]
Title: Causality from the Point of View of Classical Statistics