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Bounds on Precipitate Hardening of Line and Surface Defects in SolidsMar 18 2019The yield behavior of crystalline solids is determined by the motion of defects like dislocations, twin boundaries and coherent phase boundaries. These solids are hardened by introducing precipitates -- small particles of a second phase. It is generally ... More

Existence and Regularity of Invariant Graphs for Cocycles in Bundles: partial hyperbolicity caseMar 18 2019We study the existence and regularity of the invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relatively partial hyperbolicity in non-trivial bundles without ... More

Rare events for Cantor target setsMar 17 2019We study the existence of limiting laws of rare events corresponding to the entrance of the orbits on certain target sets in the phase space. The limiting laws are obtained when the target sets shrink to a Cantor set of zero Lebesgue measure. We consider ... More

Generic-case complexity of Whitehead's algorithm, revisitedMar 17 2019In \cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that "generic" elements of $F_N$ are "strictly ... More

General selection models: Bernstein duality and minimal ancestral structuresMar 15 2019The $\Lambda$-Wright--Fisher process describes the type-frequency evolution of an infinite population. We model frequency-dependent selection pressure with a general polynomial drift vanishing at the boundary. An appropriate decomposition of the drift ... More

On the $\mathrm{L}^p$-theory for second-order elliptic operators in divergence form with complex coefficientsMar 15 2019Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly continuous semigroup ... More

Decorrelation of a class of Gibbs particle processes and asymptotic properties of U -statisticsMar 15 2019We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of a non-negative pair potential and an activity parameter. For small activity parameters, we prove a central limit theorem for certain ... More

Random Set Solutions to Stochastic Wave EquationsMar 15 2019This paper is devoted to three topics. First, proving a measurability theorem for multifunctions with values in non-metrizable spaces, which is required to show that solutions to stochastic wave equations with interval parameters are random sets; second, ... More

Dynamical systems with finite stopping times. Part 2: Dissipative Oscillations and their semigroupsMar 15 2019In this paper, we model, classify and investigate the solutions of (normalized) second order odes with \emph{nonconstant continuous coefficients}. We introduce a generalized \emph{frequency function} as the solution of a \emph{nonlinear integro-differential ... More

Dynamical systems with finite stopping times. Part 1: Relaxation, oscillation and their application to diffusion and wave dissipationMar 15 2019In this paper, we derive general theorems for controlling (vector-valued) first order ordinary differential equations such that its solutions stop at a finite time $T>0$ and apply them to relaxation and dissipative oscillation processes. We discuss several ... More

Method of discretizing of fractional-derivative linear systems of ordinary differential equations with constant coefficientsMar 15 2019An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in this case does ... More

On slightly degenerate fusion categoriesMar 15 2019In this paper, we first show for a slightly degenerate pre-modular fusion category $\mathcal{C}$ that squares of dimensions of simple objects divide half of the dimension of $\mathcal{C}$, and that slightly degenerate fusion categories of FP-dimensions ... More

On birational trivial families and Adjoint quadricsMar 15 2019Let $\pi\colon \mathcal{X}\to B$ be a family whose general fiber $X_b$ gives a $(d_1,...,d_a)$ polarisation of a general Abelian variety where $1\leq d_i\leq 2$, $i=1,...,a$ and $a\geq 4$. We show that the fibers are in the same birational class if all ... More

Variation of stable birational types in positive characteristicMar 14 2019We use results of Totaro and the author together with a decomposition of the diagonal argument and a moving lemma, to show that over any uncountable field (of arbitrary characteristic), two very general Fano hypersurfaces of the same dimension and the ... More

A Markov partition for Jeandel-Rao aperiodic Wang tilingsMar 14 2019We define a Markov partition for a $\mathbb{Z}^2$-rotation on the 2-dimensional torus whose associated symbolic dynamical system is a minimal and aperiodic Wang shift defined by 19 Wang tiles. We define another partition for another $\mathbb{Z}^2$-rotation ... More

Modified log-Sobolev inequalities for strongly log-concave distributionsMar 14 2019We show that the modified log-Sobolev constant for a natural Markov chain which converges to an r-homogeneous strongly log-concave distribution is at least 1/r. As a consequence, we obtain an asymptotically optimal mixing time bound for this chain. Applications ... More

On the Solution Calculation of Nonlinear Ordinary Differential Equations via Exact QuadratizationMar 14 2019We show a general method allowing the solution calculation, in the form of a power series, for a very large class of nonlinear Ordinary Differential Equations (ODEs), namely the real analytic $\sigma\pi$-ODEs (and, more in general, the real analytic $\sigma\pi$-{\it ... More

On polynomial-time solvable linear Diophantine problemsMar 14 2019We construct a polynomial-time algorithm that, given a primitive positive integer vector a = (a_1, ..., a_n) and an integer b that satisfies a certain bound b >= G(a) + a_n, finds a nonnegative integer solution to the linear Diophantine equation a_1 x_1 ... More

What could re-infection tell us about R0? a modeling case-study of syphilis transmissionMar 14 2019Many infectious diseases can lead to re-infection. We examined the relationship between the prevalence of repeat infection and the basic reproductive number (R0). First we solved a generic, deterministic compartmental model of re-infection to derive an ... More

Symmetries of vector fields: the diffeomorphism centralizerMar 14 2019In this paper we study the diffeomorphism centralizer of a vector field: given a vector field it is the set of diffeomorphisms that commutes with the flow. Our main theorem states that for a $C^1$-generic diffeomorphism having at most finitely many sinks ... More

Equivalents of the finitary non-deterministic inductive definitionsMar 14 2019We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology ... More

Syntactic approaches to opetopesMar 14 2019Opetopes are algebraic descriptions of shapes corresponding to compositions in higher dimensions. As such, they offer an approach to higher-dimensional algebraic structures, and in particular, to the definition of weak $\omega$-categories, which was the ... More

Qualitative Analysis of a Reaction-Diffusion System with cubic NonlinearityMar 13 2019The aim of this article is to provide some insights in the qualitative analysis of a two dimensional nonlinear reaction-diffusion system. This system can be seen, in some aspects, as a toy model of the FitzHugh-Nagumo model arising in Neuroscience context. ... More

Dynamic Structures of 2-adic Fibonacci PolynomialsMar 13 2019The dynamic structures of Fibonacci polynomials over the ring of 2-adic integers are described by investigating minimal decompositions which consist of minimal subsystems and attracting basins.

Borel subsystems and ergodic universality for compact $\mathbb Z^d$-systems via specification and beyondMar 13 2019A Borel system $(X,S)$ is `almost Borel universal' if any free Borel dynamical system $(Y,T)$ of strictly lower entropy is isomorphic to a Borel subsystem of $(X,S)$, after removing a null set. We obtain and exploit a new sufficient condition for a topological ... More

Counterexamples and supplements to chaos implied by fixed points for a class of differential inclusions that arise in economic modelsMar 13 2019In this paper, we deal with continuous multi-valued dynamical systems on $\mathbb{R}^2$ of the form $\dot x \in F(x)$ where $F(x)$ is a set-valued function and $F=\{f_1,f_2\}$. We focus on the results from B.R. Raines, D.R. Stockman, Fixed points imply ... More

Harmonic Stability of Standing Water WavesMar 13 2019A numerical method is developed to study the stability of standing water waves and other time-periodic solutions of the free-surface Euler equations using Floquet theory. A Fourier truncation of the monodromy operator is computed by solving the linearized ... More

Normal Vectors on Modified Hopf Manifolds of Delay Differential EquationsMar 13 2019This document states the normal vector system for modified Hopf boundaries of delay differential systems with state and parameter dependent delays. Specifically, it states the proof for Proposition 1 in the paper entitled "Robust optimization of delay ... More

A method for the optimization of nonlinear systems with delays that guarantees stability and robustnessMar 13 2019We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we ensure stability ... More

On interplay between the Frobenius functor and its dualMar 13 2019For a commutative Noetherian ring $R$ of prime characteristic, denote by $^{f}R$ the ring $R$ with the left structure given by the Frobenius map. We develop Thomas Marley's work on the property of the Frobenius functor $\F(-) = - \otimes_R {^f}R$ and ... More

On the location of roots of the independence polynomial of bounded degree graphsMar 13 2019In [1] Peters and Regts confirmed a conjecture by Sokal by showing that for every $\Delta \in \mathbb{Z}_{\geq 3}$ there exists a complex neighborhood of the interval $\left[0, \frac{\left(\Delta - 1\right)^{\Delta - 1}}{\left(\Delta-2\right)^\Delta}\right)$ ... More

Topological properties of Wazewski dendrite groupsMar 13 2019Homeomorphism groups of generalized Wa\.zewski dendrites act on the infinite countable set of branch points of the dendrite and thus have a nice Polish topology. In this paper, we study them in the light of this Polish topology. The group of the universal ... More

Regularity of Symbolic Powers of Edge IdealsMar 13 2019In this article, we prove that for several classes of graphs, the Castelnuovo-Mumford regularity of symbolic powers of their edge ideals coincide with that of their ordinary powers.

On the controllability and stabilization of the linearized Benjamin equation on a periodic domainMar 12 2019In this work we study the controllability and stabilization of the linearized Benjamin equation which models the unidirectional propagation of long waves in a two-fluid system where the lower fluid with greater density is infinitely deep and the interface ... More

Products of Luzin-type sets with combinatorial propertiesMar 12 2019We construct Luzin-type subsets of the real line in all finite powers Rothberger, with a non-Menger product. To this end, we use a purely combinatorial approach which allows to weaken assumptions used earlier to construct sets with analogous properties. ... More

Nonlocal gradient operators with a nonspherical interaction neighborhood and their applicationsMar 12 2019Nonlocal gradient operators are prototypical nonlocal differential operators thatare very important in the studies of nonlocal models. One of the simplest variational settings for such studies is the nonlocal Dirichlet energies wherein the energy densities ... More

The bifurcation set as a topological invariant for one-dimensional dynamicsMar 12 2019For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global perspective and focusing ... More

High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance lawsMar 12 2019We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. The phrase well-balancing is used in a wider sense, since the method can be applied to exactly follow any solution of any system ... More

Geometric properties of a certain class of functions related to the Fox-Wright functionsMar 12 2019The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disc. In particular, ... More

Measurable realizations of abstract systems of congruencesMar 12 2019An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congruences include paradoxical decompositions and $n$-divisibility of actions. ... More

The colored Jones polynomial and Kontsevich-Zagier series for double twist knots, IIMar 12 2019Let $K_{(m,p)}$ denote the family of double twist knots where $2m-1$ and $2p$ are non-zero integers denoting the number of half-twists in each region. Using a result of Takata, we prove a formula for the colored Jones polynomial of $K_{(-m,-p)}$ and $K_{(-m,p)}$. ... More

Linear system matrices of rational transfer functionsMar 12 2019In this paper we derive new sufficient conditions for a linear system matrix $$S(\lambda):=\left[\begin{array}{ccc} T(\lambda) & -U(\lambda) \\ V(\lambda) & W(\lambda) \end{array}\right],$$ where $T(\lambda)$ is assumed regular, to be strongly irreducible. ... More

Incidence strata of affine varieties with complex multiplicitiesMar 12 2019To each affine variety $X$ and $m_1,\ldots,m_k\in \mathbb{C}$ such that no subset of the $m_i$ add to zero, we construct a variety which for $m_1,\ldots,m_k \in \mathbb{N}$ specializes to the closed $(m_1,\ldots,m_k)$-incidence stratum of $Sym^{m_1+\ldots+m_k}X$. ... More

New Dependencies of Hierarchies in Polynomial OptimizationMar 12 2019We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove ... More

Gelfand-type theorems for dynamical Banach modulesMar 12 2019The representation theorems of Gelfand and Kakutani for commutative C*-algebras and AM- and AL-spaces are the basis for the Koopman linearization of topological and measure-preserving dynamical systems. In this article we prove versions of these results ... More

Hybrid Symplectic Integrators for Planetary DynamicsMar 12 2019Hybrid symplectic integrators such as MERCURY are widely used to simulate complex dynamical phenomena in planetary dynamics that could otherwise not be investigated. A hybrid integrator achieves high accuracy during close encounters by using a high order ... More

A quantitative Lovász criterion for Property BMar 12 2019A well known observation of Lov\'asz is that if a hypergraph is not $2$-colorable, then at least one pair of its edges intersect at a single vertex. %This very simple criterion turned out to be extremly useful . In this short paper we consider the quantitative ... More

Nonlinear expectations of random setsMar 12 2019Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions ... More

A rigidity result for normalized subfactorsMar 12 2019We show a rigidity result for subfactors that are normalized by a representation of a lattice $\Gamma$ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of $L\Gamma$ which is normalized by the ... More

On the Maximum Weight Independent Set Problem in graphs without induced cycles of length at least fiveMar 12 2019A hole in a graph is an induced cycle of length at least $4$, and an antihole is the complement of an induced cycle of length at least $4$. A hole or antihole is long if its length is at least $5$. For an integer $k$, the $k$-prism is the graph consisting ... More

Existence of Lyapunov function for the planar system with one arbitrary limit cycleMar 12 2019The existence of Lyapunov function for the planar system with an arbitrary limit cycle is proved. Firstly, the generalized definition of Lyapunov function for fixed point and limit cycle are given, respectively. And they are logically consistent with ... More

Functorial PBW theorems for post-Lie algebrasMar 11 2019Using the categorical approach to Poincar\'e-Birkhoff-Witt type theorems from our previous work with Tamaroff, we prove three such theorems: for universal enveloping Rota-Baxter algebras of tridendriform algebras, for universal enveloping Rota--Baxter ... More

Automorphisms of descending mod-p central seriesMar 11 2019Given a free group $\Gamma$ of finite rank $n$ and a prime number $p,$ denote by $\Gamma_k^\bullet$ the $k^\text{th}$ layer of the Stallings ($\bullet=S$) or Zassenhaus ($\bullet=Z$) $p$-central series, by $\mathcal{N}_{k}^\bullet$ the quotient $\Gamma/\Gamma_{k+1}^\bullet$ ... More

A Hybrid Controller for Obstacle Avoidance in an n-dimensional Euclidean SpaceMar 11 2019For a vehicle moving in an $n$-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded spherical region. ... More

Norm-variation of cubic ergodic averagesMar 11 2019In this paper we study cubic averages with respect to $d$ general commuting transformations and prove quantitative results on their convergence in the norm. The approach we are using is based on estimates for certain entangled multilinear singular integral ... More

Promoting circular-orderability to left-orderabilityMar 11 2019Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group $G$ is left-orderable if and only if $G \times \mathbb{Z}/n\mathbb{Z}$ ... More

The relationship between word complexity and computational complexity in subshiftsMar 11 2019We prove several results about the relationship between the word complexity function of a subshift and the set of Turing degrees of points of the subshift, which we call the Turing spectrum. Among other results, we show that a Turing spectrum can be realized ... More

Weighted inequalities for discrete iterated Hardy operatorsMar 11 2019We characterize a three-weight inequality for an iterated discrete Hardy-type operator. In the case when the domain space is a weighted space $\ell^p$ with $p\in(0,1]$, we develop characterizations which enable us to reduce the problem to another one ... More

Effective equidistribution of the horocycle flow on geometrically finite hyperbolic surfacesMar 11 2019We prove effective equidistribution of non-closed horocycles in the unit tangent bundle of infinite-volume geometrically finite hyperbolic surfaces.

Slope inequalities and a Miyaoka-Yau type inequalityMar 11 2019We prove several slope inequalities for a relative minimal surface fibration in positive characteristic. As an application, we prove a Miyaoka-Yau type ineqaulity $\chi(\sO_S)\ge\frac{p^2-4p-1}{4(3p+1)(p-3)}K_S^2$ for all minimal surface $S$ of general ... More

Application of spherical convex bodies to Wulff shapeMar 11 2019We present some relationships between the diameter, width and thickness of a reduced convex body on the $d$-dimensional sphere. We apply the obtained properties to recognize if a Wulff shape in the Euclidean $d$-space is self-dual.

On equality of inner and absolute central automorphismsMar 11 2019Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. We give necessary and sufficient conditions on G such that Aut_l(G) = Inn(G).

Dilogarithm identities for solutions to Pell's equation in terms of continued fraction convergentsMar 10 2019In this note, we derive a number of formulae for the dilogarithm using hyperbolic geometry. One such formula shows that solutions to the Pell equation $x^2-ny^2 =\pm 1$ satisfy an infinite dilogarithm formula in terms of their continued fraction expansion. ... More

A sequential RPF theorem and its applications to limit theorems for time dependent dynamical systems and inhomogeneous Markov chainsMar 10 2019In this paper we will prove various probabilistic limit theorems for some classes of sequential dynamical systems (SDS) and inhomogeneous Markov chains. Our proofs utilize a certain sequential Ruelle-Perron-Frobenius theorem for complex operators, which, ... More

Cup-product for Hom-Leibniz cohomologyMar 10 2019We define a cup-product for Hom-Leibniz cohomology and show that the cup-product satisfies a graded Hom-zinbiel type relation.

Representability theorems, up to homotopyMar 10 2019We prove two representability theorems, up to homotopy, for presheaves taking values in a closed symmetric combinatorial model category \cat V. The first theorem resembles the Freyd representability theorem, the second theorem is closer to the Brown representability ... More

Hyperchaos and Multistability in Nonlinear Dynamics of Two Interacting Microbubble Contrast AgentsMar 10 2019We study nonlinear dynamics of two coupled contrast agents that are micro-meter size gas bubbles encapsulated into a viscoelastic shell. Such bubbles are used for enhancing ultrasound visualization of blood flow and have other promising applications like ... More

A non-conservative Harris' ergodic theoremMar 10 2019We consider non-conservative positive semigroups and obtain necessary and sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements and provides quantitative estimates ... More

Quasi-multiplicativity of typical cocyclesMar 10 2019We show that typical (in the sense of Bonatti-Viana) H\"{o}lder and fiber-bunched $GL_d(\mathbb{R})$-valued cocycles over a subshift of finite type are uniformly quasi-multiplicative with respect to all singular value potentials. We prove the continuity ... More

Polynomials as spansMar 10 2019The paper defines polynomials in a bicategory $\mathscr{M}$. Polynomials in bicategories $\mathrm{Spn}\mathscr{C}$ of spans in a finitely complete category $\mathscr{C}$ agree with polynomials in $\mathscr{C}$ as defined by Nicola Gambino and Joachim ... More

Verlinde formulae on complex surfaces I: K-theoretic invariantsMar 09 2019We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between $K$-theoretic Donaldson ... More

Abelian Endoregular ModulesMar 09 2019In this paper, we introduce the notion of abelian endoregular modules as those modules whose endomorphism rings are abelian von Neumann regular. We characterize an abelian endoregular module $M$ in terms of its $M$-generated submodules. We prove that ... More

Stability and stabilization of linear positive systems on time scalesMar 09 2019It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then this fact is used ... More

Infinity Operads and Monoidal Categories with Group EquivarianceMar 09 2019This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action operad. A group operad is a planar operad with an action operad equivariant structure. In the ... More

Quantitative spectral gap estimate and Wasserstein contraction of simple slice samplingMar 09 2019We prove Wasserstein contraction of simple slice sampling for approximate sampling w.r.t. distributions with log-concave and rotational invariant Lebesgue densities. This yields, in particular, an explicit quantitative lower bound of the spectral gap ... More

The effect of Newtonian viscosity and relaxation on linear viscoelastic wave propagationMar 09 2019The effect of Newtonian viscosity superposed on relaxation on wave propagation in a linear viscoelastic medium is examined. It is shown that the Newtonian viscosity is a dominates over the features resulting from relaxation. Since a generic linear viscoelastic ... More

Boundedness of classical operators on rearrangement-invariant spacesMar 09 2019We study the behaviour on rearrangement-invariant spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fractional version), the Hilbert and Stieltjes transforms, and the Riesz potential. ... More

Infinitesimally Tight Lagrangian OrbitsMar 09 2019We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms and admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian orbits of complex flag ... More

Scalable and Congestion-aware Routing for Autonomous Mobility-on-Demand via Frank-Wolfe OptimizationMar 08 2019We consider the problem of vehicle routing for Autonomous Mobility-on-Demand (AMoD) systems, wherein a fleet of self-driving vehicles provides on-demand mobility in a given environment. Specifically, the task it to compute routes for the vehicles (both ... More

Toward Free Resolutions Over ScrollsMar 08 2019Let $R = k[x]/I$ where $I$ is the defining ideal of a rational normal $k$-scroll. We compute the Betti numbers of the ground field $\mathbb{k}$ as a module over $R$. For $k = 2$, we give the minimal free resolution of $\mathbb{k}$ over $R$.

Understanding Sparse JL for Feature HashingMar 08 2019Feature hashing and more general projection schemes are commonly used in machine learning to reduce the dimensionality of feature vectors. The goal is to efficiently project a high-dimensional feature vector living in $\mathbb{R}^n$ into a lower-dimensional ... More

On Lenagan's Theorem for finite length bimodulesMar 08 2019We offer a self-contained proof of Lenagan's Theorem which does not rely on Goldie's Theorem

Continuity and canceling operators of order $n$ on $\mathbb{R}^n$Mar 08 2019We prove that for elliptic and canceling linear differential operators $\mathbb{B}$ of order $n$ on $\mathbb{R}^n$, continuity of a map $u$ can be inferred from the fact that $\mathbb{B} u$ is a measure. We also prove strict continuity of the embedding ... More

Modeling fungal hypha tip growth via viscous sheet approximationMar 08 2019In this paper we present a new model for single-celled, non-branching hypha tip growth. The growth mechanism of hypha cells consists of transport of cell wall building material to the cell wall and subsequent incorporation of this material in the wall ... More

Generalized fractal dimensions of invariant measures of full-shift systems over uncountable alphabets: generic behaviorMar 08 2019In this paper we show that, for topological dynamical systems with a dense set (in the weak topology) of periodic measures, a typical (in Baire's sense) invariant measure has, for each $q>0$, zero lower $q$-generalized fractal dimension. This implies, ... More

A Constructive Proof of Beal's ConjectureMar 08 2019We prove that there is no non-trivial integral positive solution to the generalized Fermat equation.

Model order reduction of hyperbolic systems at the example of district heating networksMar 08 2019In this article a framework for the generation of a computationally fast surrogate model for district heating networks is presented. An appropriate model results in an index-1 hyperbolic, differential algebraic equation quadratic in state, exhibiting ... More

On the asymptotic normality of persistent Betti numbersMar 08 2019Persistent Betti numbers are a major tool in persistent homology, a subfield of topological data analysis. Many tools in persistent homology rely on the properties of persistent Betti numbers considered as a two-dimensional stochastic process $ (r,s) ... More

Triply periodic monopoles and difference modules on elliptic curvesMar 08 2019We explain the correspondences between monopoles with Dirac type singularity and polystable mini-holomorphic bundles with Dirac type singularity of degree $0$ on a $3$-dimensional torus. We also explain that they are equivalent to polystable parabolic ... More

Finite powers and products of Menger setsMar 07 2019We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two real sets that are Menger in all finite powers, with a non-Menger product. By a forcing-theoretic argument, we show that the same holds in the Blass--Shelah ... More

Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPIMar 07 2019Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that incorporates ... More

Permanence of Weakly Reversible Mass-Action Systems with a Single Linkage ClassMar 07 2019We give a new proof of the fact that each weakly reversible mass-action system with a single linkage class is permanent.

An algorithmic approach to the existence of ideal objects in commutative algebraMar 07 2019The existence of ideal objects, such as maximal ideals in nonzero rings, plays a crucial role in commutative algebra. These are typically justified using Zorn's lemma, and thus pose a challenge from a computational point of view. Giving a constructive ... More

A four dimensional Bernstein TheoremMar 07 2019We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result in terms of ... More

A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equationMar 07 2019We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674 2017) including: ... More

A Kruskal-Katona type result and applicationsMar 07 2019Inspired by the Kruskal-Katona theorem a minimization problem is studied, where the role of the shadow is replaced by the image of the action of the monoid of increasing functions. One of our main results shows that compressed sets are a solution to this ... More

Generic properties of invariant measures of full-shift systems over perfect separable metric spacesMar 07 2019In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is uncountable. %fixed dynamic system and with certain dimensional ... More

Lagrange Spectrum of Romik's Dynamical SystemMar 07 2019Let $\mathscr{L}(S^1)$ be the Lagrange spectrum arising from the intrinsic Diophantine approximation of the unit circle $S^1$ by its rational points. In this paper, we give a complete description of the structure of $\mathscr{L}(S^1)$ below its smallest ... More

Variational Graph Methods for Efficient Point Cloud SparsificationMar 07 2019Mar 08 2019In recent years new application areas have emerged in which one aims to capture the geometry of objects by means of three-dimensional point clouds. Often the obtained data consist of a dense sampling of the object's surface, containing many redundant ... More

Variational Graph Methods for Efficient Point Cloud SparsificationMar 07 2019In recent years new application areas have emerged in which one aims to capture the geometry of objects by means of three-dimensional point clouds. Often the obtained data consist of a dense sampling of the object's surface, containing many redundant ... More