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On the complexity function for sequences which are not uniformly recurrentJul 15 2019We prove that every non-minimal transitive subshift $X$ satisfying a mild aperiodicity condition satisfies $\limsup c_n(X) - 1.5n = \infty$, and give a class of examples which shows that the threshold of $1.5n$ cannot be increased. As a corollary, we ... More

On The Entropy of Continuous Flows With Uniformly Expansive PointsJul 15 2019We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a sufficient condition to the existence of a suspension of a subshift. This complements a result due to Moriyasu. To do this we exploit ... More

Discretized Fast-Slow Systems with Canard Points in Two DimensionsJul 15 2019We study the behaviour of slow manifolds for two different discretization schemes of fast-slow systems with canard fold points. The analysis uses the blow-up method to deal with the loss of normal hyperbolicity at the canard point. While the Euler method ... More

Legendrian Hopf linksJul 15 2019We completely classify Legendrian realisations of the Hopf link, up to coarse equivalence, in the 3-sphere with any contact structure.

Optimal Control of a Hot PlasmaJul 15 2019The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma is located ... More

Linked partition ideals, directed graphs and $q$-multi-summationsJul 15 2019Finding an Andrews--Gordon type generating function identity for a linked partition ideal is difficult in most cases. In this paper, we will handle this problem in the setting of graph theory. With the generating function of directed graphs with an ``empty'' ... More

Subsystems of transitive subshifts with linear complexityJul 15 2019We bound the number of distinct minimal subsystems of a given transitive subshift of linear complexity, continuing work of Ormes and Pavlov [7]. We also bound the number of generic measures such a subshift can support based on its complexity function. ... More

Regularity of weak solutions to a certain class of parabolic systemJul 15 2019We study the regularity of weak solutions to a certain class of second order parabolic system under the only assumption of continuous coefficients. By using the $A-$caloric approximation argument, we claim that the weak solution $u$ to such system is ... More

$C^1$-smooth dependence on initial conditions and delay: spaces of initial histories of Sobolev type, and differentiability of translation in $L^p$Jul 14 2019The objective of this paper is to clarify the relationship between the $C^1$-smooth dependence of solutions to delay differential equations (DDEs) on initial histories (i.e., initial conditions) and delay parameters. For this purpose, we consider a class ... More

Square-integrability of the Mirzakhani function and statistics of simple closed geodesics on hyperbolic surfacesJul 14 2019Given integers $g,n \geq 0$ satisfying $2-2g-n < 0$, let $\mathcal{M}_{g,n}$ be the moduli space of connected, oriented, complete, finite area hyperbolic surfaces of genus $g$ with $n$ cusps. We study the global behavior of the Mirzakhani function $B ... More

Trees, length spectra for rational maps via barycentric extensions and Berkovich spacesJul 14 2019In this paper, we study the dynamics of degenerating sequences of rational maps on Riemann sphere $\hat{\mathbb{C}}$ using $\mathbb{R}$-trees. Given a sequence of degenerating rational maps, we give two constructions for limiting dynamics on $\mathbb{R}$-trees: ... More

New integrable two-centre problem on sphere in Dirac magnetic fieldJul 14 2019We present a new integrable version of the two-centre problem on two-dimensional sphere in the presence of the Dirac magnetic monopole. The new system can be written on the dual space of Lie algebra $e(3)$ and is integrable both in classical and quantum ... More

On Rado conditions for nonlinear Diophantine equationsJul 14 2019Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These conditions are inspired by Rado's characterization of partition regular linear homogeneous equations. ... More

Large and Small Data Blow-Up Solutions in the Trojan Y Chromosome ModelJul 13 2019The Trojan Y Chromosome Strategy (TYC) is an extremely well investigated biological control method for controlling invasive populations with an XX-XY sex determinism. In \cite{GP12, WP14} various dynamical properties of the system are analyzed, including ... More

Combinatorics in the exterior algebra and the Bollobás Two Families TheoremJul 13 2019We investigate the combinatorial structure of subspaces of the exterior algebra of a finite-dimensional real vector space, working in parallel with the extremal combinatorics of hypergraphs. As an application, we prove a new extension of the Two Families ... More

Efficient average-case population recovery in the presence of insertions and deletionsJul 12 2019Several recent works have considered the \emph{trace reconstruction problem}, in which an unknown source string $x\in\{0,1\}^n$ is transmitted through a probabilistic channel which may randomly delete coordinates or insert random bits, resulting in a ... More

Planar Disjoint Paths in Linear TimeJul 12 2019The Disjoint Paths problem asks whether a fixed number of pairs of terminals in a graph $G$ can be linked by pairwise disjoint paths. In the context of this problem, Robertson and Seymour introduced the celebrated irrelevant vertex technique that has ... More

On a Generalization of the Marriage ProblemJul 12 2019We present a generalization of the marriage problem underlying Hall's famous Marriage Theorem to what we call the Symmetric Marriage Problem, a problem that can be thought of as a special case of Maximal Weighted Bipartite Matching. We show that there ... More

Linear instability for periodic orbits of non-autonomous Lagrangian systemsJul 12 2019Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic solutions of a ... More

Patterns in sets of positive density in trees and affine buildingsJul 12 2019We prove an analogue for homogeneous trees and certain affine buildings of a result of Bourgain on pinned distances in sets of positive density in Euclidean spaces. Furthermore, we construct an example of a non-homogeneous tree with positive Hausdorff ... More

Asymmetric unimodal maps with non-universal period-doubling scaling lawsJul 12 2019We consider a family of strongly-asymmetric unimodal maps $\{f_t\}_{t\in [0,1]}$ of the form $f_t=t\cdot f$ where $f\colon [0,1]\to [0,1]$ is unimodal, $f(0)=f(1)=0$, $f(c)=1$ is of the form and $$f(x)=\left\{ \begin{array}{ll} 1-K_-|x-c|+o(|x-c|)& \mbox{ ... More

Cotilting with balanced big Cohen-Macaualay modulesJul 12 2019Over a Cohen-Macaulay local ring admitting a canonical module the definable closure of the class of balanced big Cohen-Macaulay modules is cotilting and is the smallest such class containing the maximal Cohen-Macaulay modules. We describe its cotilting ... More

Non-Existence of Periodic Orbits for Forced-Damped Potential Systems in Bounded DomainsJul 12 2019We prove Lr-estimates on periodic solutions of periodically-forced, linearly-damped mechanical systems with polynomially-bounded potentials. The estimates are applied to obtain a non-existence result of periodic solutions in bounded domains, depending ... More

Structured inversion of the Bernstein mass matrixJul 12 2019Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to interesting linear ... More

Herglotz' variational principle and Lax-Oleinik evolutionJul 12 2019We develop an elementary method to give a Lipschitz estimate for the minimizers in the problem of Herglotz' variational principle proposed in \cite{CCWY2018} in the time-dependent case. We deduce Erdmann's condition and the Euler-Lagrange equation separately ... More

Dynamics and stability of sessile drops with contact pointsJul 12 2019In an effort to study the stability of contact lines in fluids, we consider the dynamics of a drop of incompressible viscous Stokes fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary problem: the ... More

Partial stabilization of stochastic systems with application to rotating rigid bodiesJul 12 2019This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets and has important ... More

On exponential stabilization of nonholonomic systems with time-varying driftJul 12 2019A class of nonlinear control-affine systems with bounded time-varying drift is considered. It is assumed that the control vector fields together with their iterated Lie brackets satisfy Hormander's condition in a neighborhood of the origin. Then the problem ... More

Pointwise dynamics under Orbital ConvergenceJul 12 2019We obtain sufficient conditions under which the limit of a sequence of functions exhibits a particular dynamical behaviour at a point like expansivity, shadowing, mixing, sensitivity and transitivity. We provide examples to show that the set of all expansive, ... More

The boundary of the $p$-rank $0$ stratum of the moduli space of cyclic covers of the projective lineJul 12 2019We study the $p$-rank stratification of the moduli space of cyclic degree $\ell$ covers of the projective line in characteristic $p$ for distinct primes $p$ and $\ell$. The main result is about the intersection of the $p$-rank $0$ stratum with the boundary ... More

Local rigidity for periodic generalised interval exchange transformationsJul 12 2019We prove that the local $\mathcal{C}^1$-conjugacy class of a periodic interval exchange transformation, with d intervals, whose associated surface has genus g and whose Lyapounoff exponents are all non zero is a codimension $g - 1 + d - 1$ topological ... More

Well-posedness and Critical Index Set of the Cauchy Problem for the Coupled KdV-KdV Systems on $\mathbb{T}$Jul 12 2019Studied in this paper is the well-posedness of the Cauchy problem for the coupled KdV-KdV systems \[ u_t+a_1u_{xxx} = c_{11}uu_x+c_{12}vv_x+d_{11}u_{x}v+d_{12}uv_{x}, \quad u(x,0)= u_0(x) \] \[ v_t+a_2v_{xxx}= c_{21}uu_x+c_{22}vv_x +d_{21}u_{x}v+d_{22}uv_{x}, ... More

Quadratic Algebras arising from Hopf operads generated by a single elementJul 12 2019The operads of Poisson and Gerstenhaber algebras are generated by a single binary element if we consider them as Hopf operads (i.e. as operads in the category of cocommutative coalgebras). In this note we discuss in details the Hopf operads generated ... More

$\mathcal{U}$-Frequent hypercyclicity notions and related weighted densitiesJul 11 2019We study dynamical notions lying between $\mathcal{U}$-frequent hypercyclicity and reiterative hypercyclicity by investigating weighted upper densities between the unweighted upper density and the upper Banach density. While chaos implies reiterative ... More

Nearly Frobenius AlgebrasJul 11 2019In this introductory paper we study nearly Frobenius algebras which are generalizations of the concept of a Frobenius algebra which appear naturally in topology: nearly Frobenius algebras have no traces (co-units). We survey the most basic foundational ... More

Eccentricity function in distance-hereditary graphsJul 11 2019A graph $G = (V,E)$ is distance hereditary if every induced path of $G$ is a shortest path. In this paper, we show that the eccentricity function $e(v) = \max\{d(v, u) : u \in V \}$ in any distance-hereditary graph $G$ is almost unimodal, that is, every ... More

Quantum and Classical Algorithms for Approximate Submodular Function MinimizationJul 11 2019Submodular functions are set functions mapping every subset of some ground set of size $n$ into the real numbers and satisfying the diminishing returns property. Submodular minimization is an important field in discrete optimization theory due to its ... More

Upper bounds for the regularity of symbolic powers of certain classes of edge idealsJul 11 2019Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal in a polynomial ring over a field $\mathbb{K}$. In this paper, we obtain upper bounds for the Castelnuovo-Mumford regularity of symbolic powers of certain classes of edge ... More

Partial coherent state transforms, $G \times T$-invariant Kähler structures and geometric quantization of cotangent bundles of compact Lie groupsJul 11 2019In this paper, we study the analytic continuation to complex time of the Hamiltonian flow of certain $G\times T$-invariant functions on the cotangent bundle of a compact connected Lie group $G$ with maximal torus $T$. Namely, we will take the Hamiltonian ... More

Homotopy invariance of convolution productsJul 11 2019The purpose of this paper is to show that various convolution products are fully homotopical, meaning that they preserve weak equivalences in both variables without any cofibrancy hypothesis. We establish this property for diagrams of simplicial sets ... More

Rank-1 sheaves and stable pairs on del Pezzo surfacesJul 11 2019We study rank 1 sheaves and stable pairs on a del Pezzo surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which agrees with the usual deformation-obstruction ... More

Stochastic mortality models: An infinite dimensional approachJul 11 2019Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener process and a compensated ... More

A survey on the classical theory for Kolmogorov equationJul 11 2019We present a survey on the regularity theory for classic solutions to subelliptic degenerate Kolmogorov equations. In the last part of this note we present a detailed proof of a Harnack inequality and a strong maximum principle.

Global Stabilization of 2D Forced Viscous Burgers' Equation Around Nonconstant Steady State Solution by Nonlinear Neumann Boundary Feedback Control:Theory and Finite Element AnalysisJul 11 2019Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers' equation around a ... More

Further remarks on rigidity of Hénon mapsJul 11 2019For a H\'{e}non map $H$ in $\mathbb{C}^2$, we characterize the polynomial automorphisms of $\mathbb{C}^2$ which keep any fixed level set of the Green function of $H$ completely invariant. The interior of any non-zero sublevel set of the Green function ... More

Artin glueings of frames as semidirect productsJul 11 2019Artin glueings provide a way to reconstruct a frame from a closed sublocale and its open complement. We show that Artin glueings can be described as split extensions satisfying a Schreier-type condition in the category frames with finite-meet preserving ... More

A prey-predator model with three interacting speciesJul 11 2019In this paper we consider a class of discrete time prey-predator models with three interacting species defined on the two-dimensional simplex. For some choices of parameters of the operator describing the evolution of the relative frequencies, we show ... More

Hom-Poisson-Nijenhuis structures on Hom-Lie algebroids and Hom-Dirac structures on Hom-Courant algebroidsJul 11 2019In this paper, we develop the theory of Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids introduced by Cai, Liu and Sheng. Specifically, we introduce the notions of Hom-Poisson, Hom-Nijenhuis and Hom-Poisson-Nijenhuis structures on ... More

On the behavior of $π$-submaximal subgroups under homomorphismsJul 11 2019We construct examples that show the difference in behavior or $\pi$-maximal and $\pi$-submaximal subgroups under group homomorphisms.

Collective dynamics of opposing groups with stochastic communicationJul 11 2019We propose models describing the collective dynamics of two opposing groups of individuals with stochastic communication. Individuals from the same group are assumed to align in a stochastic manner, while individuals from different groups are assumed ... More

Mathematical Analysis of Dynamic Risk Default in MicrofinanceJul 10 2019In this work we will develop a new approach to solve the non repayment problem in microfinance due to the problem of asymmetric information. This approach is based on modeling and simulation of ordinary differential systems where time remains a primordial ... More

A non commutative Kähler structure on the Poincaré disk of a C*-algebraJul 10 2019We study the Poincar\'e disk $\d=\{z\in\a: \|z\|<1\}$ of a C$^*$-algebra $\a$ as a homogeneous space under the action of an appropriate Banach-Lie group $\u(\theta)$ of $2\times 2$ matrices with entries in $\a$. We define on $\d$ a homogeneous K\"ahler ... More

Fixed point branes, singular loci and mirror symmetryJul 10 2019This is the extended abstract of the talk given at the workshop "Geometry and physics of Higgs bundles", held at the Mathematisches Forschungsinstitut Oberwolfach in May 2019.

Vertex-Fault Tolerant Complete Matching in Bipartite graphs: the Biregular CaseJul 10 2019Given a family $\mathcal{H}$ of graphs and a positive integer $k$, a graph $G$ is called vertex $k$-fault-tolerant with respect to $\mathcal{H}$, denoted by $k$-FT$(\mathcal{H})$, if $G-S$ contains some $H\in\mathcal{H}$ as a subgraph, for every $S\subset ... More

Higher-order ergodicity coefficientsJul 10 2019Ergodicity coefficients for stochastic matrices provide valuable upper bounds for the magnitude of subdominant eigenvalues, allow to bound the convergence rate of methods for computing the stationary distribution and can be used to estimate the sensitivity ... More

Superdiffusive limits for deterministic fast-slow dynamical systemsJul 10 2019We consider deterministic fast-slow dynamical systems on $\mathbb{R}^m\times Y$ of the form \[ \begin{cases} x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a(x_k^{(n)}) + n^{-1/\alpha} b(x_k^{(n)}) v(y_k)\;,\quad y_{k+1} = f(y_k)\;, \end{cases} \] where $\alpha\in(1,2)$. ... More

New fifth and seventh order mock theta function identitiesJul 10 2019We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan fifth order mock theta functions $\chi_0(q)$ and $\chi_1(q)$ and all three of Ramanujan's seventh order mock theta functions. We find that the coefficients ... More

Ultracontractive Properties for Directed Graph Semigroups with Applications to Coupled OscillatorsJul 10 2019It is now well known that ultracontractive properties of semigroups with infinitesimal generator given by an undirected graph Laplacian operator can be obtained through an understanding of the geometry of the underlying infinite weighted graph. The aim ... More

Ergodicity and partial hyperbolicity on Seifert manifoldsJul 10 2019We show that conservative partially hyperbolic diffeomorphism isotopic to the identity on Seifert 3-manifolds are ergodic.

Endpoint estimates for the maximal function over prime numbersJul 10 2019Given an ergodic dynamical system $(X, \mathcal{B}, \mu, T)$, we prove that for each function $f$ belonging to the Orlicz space $L(\log L)^2(\log \log L)(X, \mu)$, the ergodic averages \[ \frac{1}{\pi(N)} \sum_{p \in \mathbb{P}_N} f\big(T^p x\big), \] ... More

Matroid Bases with Cardinality Constraints on the IntersectionJul 10 2019Given two matroids $\mathcal{M}_{1} = (E, \mathcal{B}_{1})$ and $\mathcal{M}_{2} = (E, \mathcal{B}_{2})$ on a common ground set $E$ with base sets $\mathcal{B}_{1}$ and $\mathcal{B}_{2}$, some integer $k \in \mathbb{N}$, and two cost functions $c_{1}, ... More

Constructing a quasiregular analogue of $z \exp(z)$ in dimension 3Jul 10 2019We construct a quasiregular analogue of the function $z\exp(z)$ in dimension 3, which gives the first explicit example of a quasiregular mapping of transcendental type that has exactly one zero. We then modify the construction to create a family of such ... More

Minimal semi-flat-cotorsion replacements and cosupportJul 10 2019Over a commutative noetherian ring $R$ of finite Krull dimension, we show that every complex of flat cotorsion $R$-modules decomposes as a direct sum of a minimal complex and a contractible complex. Moreover, we define the notion of a semi-flat-cotorsion ... More

The Ruelle operator for symmetric $β$-shiftsJul 10 2019Consider $m \in \mathbb{N}$ and $\beta \in (1, m + 1]$. Assume that $a\in \mathbb{R}$ can be represented in base $\beta$ using a development in series $a = \sum^{\infty}_{n = 1}x(n)\beta^{-n}$ where the sequence $x = (x(n))_{n \in \mathbb{N}}$ take values ... More

Smoothed Analysis of Order TypesJul 10 2019Consider an ordered point set $P = (p_1,\ldots,p_n)$, its order type (denoted by $\chi_P$) is a map which assigns to every triple of points a value in $\{+,-,0\}$ based on whether the points are collinear(0), oriented clockwise(-) or counter-clockwise(+). ... More

Connections between vector-valued and highest weight Jack and Macdonald polynomialsJul 10 2019We analyze conditions under which a projection from the vector-valued Jack or Macdonald polynomials to scalar polynomials has useful properties, especially commuting with the actions of the symmetric group or Hecke algebra, respectively, and with the ... More

Stabilization on periodic impulse control systemsJul 10 2019This paper studies the stabilization for a kind of linear and impulse control systems in finite-dimensional spaces, where impulse instants appear periodically. We present several characterizations on the stabilization; show how to design feedback laws; ... More

On optimal cover and its possible shape for fractals embedded into 2D Euclidian spaceJul 10 2019In this article a definition of optimal cover for fractal structures is proposed. Expression for Minkowsky dimension is rewritten in terms of functional equation on areas of covers that constructed for different scales.Given the definition, the functional ... More

The maximum length of $K_r$-Bootstrap PercolationJul 10 2019Graph-bootstrap percolation, also known as weak saturation, was introduced by Bollob\'as in 1968. In this process, we start with initial "infected" set of edges $E_0$, and we infect new edges according to a predetermined rule. Given a graph $H$ and a ... More

Two species nonlocal diffusion systems with free boundariesJul 10 2019We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the species, but here ... More

The complexity of the first-order theory of pure equalityJul 10 2019We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to equality (or equational-nontrivial), namely, each of these theories is consistent with the formula, whose sense is that there exist two various elements ... More

An affine model of a Riemann surface associated to a Schwarz-Christoffel mappingJul 09 2019In this paper we construct an affine model of a Riemann surface with a flat Riemannian metric associated to a Schwarz-Christoffel mapping of the upper half plane onto a rational triangle. We explain the relation between the geodesics on this Riemann surface ... More

On the construction of large Algebra not contained in the image of the Borel mapJul 09 2019The Borel map $j^{\infty}$ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. It is well known that the restriction of $j^{\infty}$ to the germs of quasianalytic ultradifferentiable classes which are strictly containing ... More

A complexity dichotomy for hitting connected minors on bounded treewidth graphs: the chair and the banner draw the boundaryJul 09 2019For a fixed connected graph $H$, the $\{H\}$-M-DELETION problem asks, given a graph $G$, for the minimum number of vertices that intersect all minor models of $H$ in $G.$ It is known that this problem can be solved in time $f(tw)\cdot n^{O(1)}$, where ... More

Finite Regret and Cycles with Fixed Step-Size via Alternating Gradient Descent-AscentJul 09 2019Gradient descent is arguably one of the most popular online optimization methods with a wide array of applications. However, the standard implementation where agents simultaneously update their strategies yields several undesirable properties; strategies ... More

Betti numbers of symmetric shifted idealsJul 09 2019We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be considered as ... More

Singular limits of the quasi-linear Kolmogorov-type equation with a source termJul 09 2019Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem for the Kolmogorov-type genuinely nonlinear ultra-parabolic equation with a smooth source term is established. After this, we consider the case when the ... More

Non-homogeneous extensions of Cantor minimal systemsJul 09 2019Floyd gave an example of a minimal dynamical system which was an extension of an odometer and the fibres of the associated factor map were either singletons or intervals. Gjerde and Johansen showed that the odometer could be replaced by any Cantor minimal ... More

Wandering domains arising from Lavaurs maps with Siegel disksJul 09 2019The classification of Fatou components for rational functions was concluded with Sullivan's proof of the No Wandering Domains Theorem in 1985. In 2016 it was shown, in joint work of the first and last author with Buff, Dujardin and Raissy, that wandering ... More

Shock Capturing by Bernstein Polynomials for Scalar Conservation LawsJul 09 2019A main disadvantage of many high-order methods for hyperbolic conservation laws lies in the famous Gibbs-Wilbraham phenomenon, once discontinuities appear in the solution. Due to the Gibbs-Wilbraham phenomenon, the numerical approximation will be polluted ... More

A note on uniform exponential stability of linear periodic time-varying systemsJul 09 2019In this paper we derive new criterion for uniform stability assessment of the linear periodic time-varying systems $\dot x=A(t)x,$ $A(t+T)=A(t).$ As a corollary, the lower and upper bounds for the Floquet characteristic exponents are established. The ... More

Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg EquationJul 09 2019We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg equation $$u_t+\Delta^2u+2\Delta u+au+b|\nabla u|^2+u^3=g(t,x).$$ We employ Conley index theory to show that, if the forcing $g:\mathbb{R}\rightarrow L^2(\Omega)$ is a recurrent ... More

Word operads and admissible orderingsJul 09 2019We use Giraudo's construction of combinatorial operads from monoids to offer a conceptual explanation of the origins of Hoffbeck's path sequences of shuffle trees, and use it to define new monomial orders of shuffle trees. One such order is utilised to ... More

$H^\infty$-functional calculus for commuting families of Ritt operators and sectorial operatorsJul 09 2019We introduce and investigate $H^\infty$-functional calculus for commuting finite families of Ritt operators on Banach space $X$. We show that if either $X$ is a Banach lattice or $X$ or $X^*$ has property $(\alpha)$, then a commuting $d$-tuple $(T_1,\ldots, ... More

Vertex-weighted Online Stochastic Matching with Patience ConstraintsJul 09 2019Online Bipartite Matching is a classic problem introduced by Karp, Vazirani, and Vazirani (Proc. ACM STOC, 1990) and motivated by applications such as e-commerce, online advertising, and ride-sharing. We wish to match a set of online vertices (e.g., webpage ... More

Irreducibility criterion for certain trinomialsJul 09 2019In this article we study the irreducibility of polynomials of the form $x^n+\epsilon_1 x^m+p^k\epsilon_2$, $p$ being a prime number. We will show that they are irreducible for $m=1$. We have also provided the cyclotomic factors and reducibility criterion ... More

Near-optimal Repair of Reed-Solomon Codes with Low Sub-packetizationJul 09 2019Minimum storage regenerating (MSR) codes are MDS codes which allow for recovery of any single erased symbol with optimal repair bandwidth, based on the smallest possible fraction of the contents downloaded from each of the other symbols. Recently, certain ... More

Approximating integrals with respect to stationary probability measures of iterated function systemsJul 08 2019Jul 10 2019We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the iterated function ... More

Large fronts in nonlocally coupled systems using Conley-Floer homologyJul 08 2019In this paper we study travelling front solutions for nonlocal equations of the type \begin{equation} \partial_t u = N * S(u) + \nabla F(u), \qquad u(t,x) \in \mathbf{R}^d. \end{equation} Here $N *$ denotes a convolution-type operator in the spatial variable ... More

Constructions in minimal amenable dynamics and applications to the classification of $\mathrm{C}^*$-algebrasJul 08 2019We study the existence of minimal dynamical systems, their orbit and minimal orbit-breaking equivalence relations, and their applications to C*-algebras and K-theory. We show that given any finite CW-complex there exists a space with the same K-theory ... More

Constructions in minimal amenable dynamics and applications to the classification of $\mathrm{C}^*$-algebrasJul 08 2019Jul 10 2019We study the existence of minimal dynamical systems, their orbit and minimal orbit-breaking equivalence relations, and their applications to C*-algebras and K-theory. We show that given any finite CW-complex there exists a space with the same K-theory ... More

Optimal Control and Analysis of a Modified Trojan Y-Chromosome StrategyJul 08 2019The Trojan Y Chromosome (TYC) Strategy is a promising eradication method that attempts to manipulate the female to male ratio to promote the reduction of the population of an invasive species. The manipulation stems from an introduction of sex-reversed ... More

The Realization Problem for Finitely Generated Refinement MonoidsJul 08 2019We show that every finitely generated conical refinement monoid can be represented as the monoid $\mathcal V(R)$ of isomorphism classes of finitely generated projective modules over a von Neumann regular ring $R$. To this end, we use the representation ... More

When does a Steady-State Response Exist in a Periodically Forced Multi-Degree-of-Freedom Mechanical System?Jul 08 2019While steady-state responses of periodically forced dissipative nonlinear mechanical systems are commonly observed in experiments and numerics, their existence can rarely be concluded in rigorous mathematical terms. This lack of a priori existence criteria ... More

Degrees of bi-embeddable categoricityJul 08 2019We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure $\mathcal A$ as the family of Turing degrees that compute embeddings between ... More

Some discontinuous functional differential equation and its connection to smoothness of composition operators in $L^p$Jul 08 2019The objective of this paper is to deepen the understanding of the connection between the continuous and smooth dependence of solutions on initial conditions and the regularity of the history functionals for retarded functional differential equations. ... More

Lagrangian coherent sets in turbulent Rayleigh-Bénard convectionJul 08 2019Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh--B\'{e}nard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number ${\rm Ra}=10^6$ and at a Prandtl ... More

There are no deviations for the ergodic averages of the Giulietti-Liverani horocycle flows on the two-torusJul 08 2019We show that the ergodic averages for the horocycle flow on the two-torus associated by Giulietti and Liverani to an Anosov diffeomorphism either grow linearly or are bounded, in other words there are no deviations. For this, we use topological invariance ... More

How many groups? A statistical methodology for data-driven partitioning of infectious disease incidence into age-groupsJul 08 2019Understanding age-group dynamics of infectious diseases is a fundamental issue for both scientific study and policymaking. Age-structure epidemic models were developed in order to study and improve our understanding of these dynamics. By fitting the models ... More

Sharp Logarithmic Sobolev and related inequalities with monomial weightsJul 08 2019We derive a sharp Logarithmic Sobolev inequality with monomial weights starting from a sharp Sobolev inequality with monomial weights. Several related inequalities such as Shannon type and Heisenberg's uncertain type are also derived. A characterization ... More