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Lagrangian pairs of pantsFeb 08 2018We construct a Lagrangian submanifold, inside the cotangent bundle of a real torus, which we call a Lagrangian pair of pants. It is given as the graph of the differential of a smooth function defined on the real blow up of a Lagrangian coamoeba. Lagrangian ... More

Singular values of large non-central random matricesFeb 08 2018We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It provides a decomposition ... More

Existence and uniqueness of solutions to singular Cahn-Hilliard equations with nonlinear viscosity terms and dynamic boundary conditionsFeb 08 2018We prove global existence and uniqueness of solutions to a Cahn-Hilliard system with nonlinear viscosity terms and nonlinear dynamic boundary conditions. The problem is highly singular, characterized by four nonlinearities and two separate diffusive terms, ... More

Compactly Generated Shape Index for Infinite-dimensional Local Dynamical Systems on Complete Metric SpacesFeb 08 2018In this paper, we establish a theory of compactly generated shape index for local semiflows on complete metric spaces via very ordinary shape index pairs. The main advantage is that the quotient space $N/E$ is not necessary to be metrizable for the shape ... More

Non-resonant tori in symplectic twist maps without conjugate pointsFeb 08 2018We study the dynamics of a symplectic twist map without conjugate points. We show that in a neighborhood of a totally periodic Lagrangian manifold, there exists a large family of invariant Lagrangian tori on which the twist map is conjugated to a translation ... More

On the Algebraic and Arithmetic structure of the monoid of Product-one sequences IIFeb 08 2018Let $G$ be a finite group. By a sequence over $G$, we mean a finite unordered sequence of terms from $G$, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals the identity ... More

Variance estimates for random disc-polygons in smooth convex discsFeb 08 2018In this paper we prove asymptotic upper bounds on the variance of the number of vertices and missed area of inscribed random disc-polygons in smooth convex discs whose boundary is $C^2_+$. We also consider a circumscribed variant of this probability model ... More

On a polynomial scalar perturbation of a Schrödinger system in $L^p$-spacesFeb 08 2018In the paper \cite{KLMR} the $L^p$-realization $L_p$ of the matrix Schr\"odinger operator $\mathcal{L}u=div(Q\nabla u)+Vu$ was studied. The generation of a semigroup in $L^p(\R^d,\C^m)$ and characterization of the domain $D(L_p)$ has been established. ... More

The topology of the set of non-escaping endpointsFeb 08 2018There are several classes of transcendental entire functions for which the Julia set consists of an uncountable union of disjoint curves each of which joins a finite endpoint to infinity. Many authors have studied the topological properties of this set ... More

The dynamics of disappearing pulses in a singularly perturbed reaction-diffusion system with parameters that vary in time and spaceFeb 08 2018We consider the evolution of multi-pulse patterns in an extended Klausmeier equation with parameters that change in time and/or space. We formally show that the full PDE dynamics of a $N$-pulse configuration can be reduced to a $N$-dimensional dynamical ... More

Nevanlinna theory and value distribution in the unicritical polynomials familyFeb 08 2018In the space $\mathbb{C}$ of the parameters $\lambda$ of the unicritical polynomials family $f(\lambda,z)=f_\lambda(z)=z^d+\lambda$ of degree $d>1$, we establish a quantitative equidistribution result towards the bifurcation current (indeed measure) $T_f$ ... More

Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class groupFeb 08 2018These notes are the English version of the paper "Hyperbolicit\'e du graphe des rayons et quasi-morphismes sur un gros groupe modulaire". The mapping class group Gamma of the complement of a Cantor set in the plane arises naturally in dynamics. We show ... More

Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functionsFeb 07 2018Three kinds of effective error bounds of the quadrature formulas with multiple nodes that are generalizations of the well known Micchelli-Rivlin quadrature formula, when the integrand is a function analytic in the regions bounded by confocal ellipses, ... More

Factors of generalised polynomials and automatic sequencesFeb 07 2018The aim of this short note is to generalise the result of Rampersad--Shallit saying that an automatic sequence and a Sturmian sequence cannot have arbitrarily long common factors. We show that the same result holds if a Sturmian sequence is replaced by ... More

Infinite series in cohomology: attractors and Conley indexFeb 07 2018In this paper we study the cohomological Conley index of arbitrary isolated invariant continua for continuous maps $f \colon U \subseteq \mathbb{R}^d \to \mathbb{R}^d$ by analyzing the topological structure of their unstable manifold. We provide a simple ... More

Samuel compactifications of automorphism groupsFeb 07 2018We study the Samuel compactification of the automorphism group of a countable first-order structure. A key motivating question is a problem of Ellis and a counter-conjecture by Pestov regarding the difference between $S(G)$, the Samuel compactification, ... More

Three Random Intercepts of a SegmentFeb 07 2018Feb 08 2018We construct random triangles via uniform sampling of certain families of lines in the plane. Two examples are given. The word "uniform" turns out to be vague; two competing models are examined. Everything we write is well-known to experts. Which model ... More

The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded FunctionsFeb 07 2018Consider the $3$-d primitive equations in a layer domain $\Omega=G \times (-h,0)$, $G=(0,1)^2$, subject to mixed Dirichlet and Neumann boundary conditions at $z=-h$ and $z=0$, respectively, and the periodic lateral boundary condition. It is shown that ... More

The $b$-branching problem in digraphsFeb 07 2018In this paper, we introduce the concept of $b$-branchings in digraphs, which is a generalization of branchings serving as a counterpart of $b$-matchings. Here $b$ is a positive integer vector on the vertex set of a digraph, and a $b$-branching is defined ... More

Delone sets and dynamical systemsFeb 07 2018In these expository notes we focus on selected topics around the themes: Delone sets as models for quasicrystals, inflation symmetries and expansion constants, substitution Delone sets and tilings, and associated dynamical systems.

Monodromy and Log GeometryFeb 06 2018A now classical construction due to Kato and Nakayama attaches a topological space (the "Betti realization") to a log scheme over $\mathbf{C}$. We show that in the case of a log smooth degeneration over the standard log disc, this construction allows ... More

Inequalities for integrals of the modified Struve function of the first kindFeb 06 2018Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality, involving the ... More

On the asymptotic of exit problems for controlled Markov diffusion processes with random jumps and vanishing diffusion termsFeb 06 2018In this paper, we study the asymptotic of exit problem for controlled Markov diffusion processes with random jumps and vanishing diffusion terms, where the random jumps are introduced in order to modify the evolution of the controlled diffusions by switching ... More

A new method for proving some inequalities related to several special functionsFeb 06 2018In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential inequalities.

Universal flows and automorphisms of $\mathcal P(ω)/\mathrm{fin}$Feb 06 2018We prove that for every countable discrete group $G$, there is a $G$-flow on $\omega^*$ that has every $G$-flow of weight $\leq\! \aleph_1$ as a quotient. It follows that, under the Continuum Hypothesis, there is a universal $G$-flow of weight $\leq\!\mathfrak{c}$. ... More

On some local cohomology spectral sequencesFeb 06 2018We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived functors of ... More

Crossed extensions and equivalences of topological 2-groupoidsFeb 06 2018We provide concrete models for generalized morphisms and Morita equivalences of topological 2-groupoids by introducing the notions of crossings and crossed extensions of groupoid crossed modules. A systematic study of these objects is elaborated and an ... More

Domination, almost additivity, and thermodynamical formalism for planar matrix cocyclesFeb 06 2018In topics such as the thermodynamic formalism of linear cocycles, the dimension theory of self-affine sets, and the theory of random matrix products, it has often been found useful to assume positivity of the matrix entries in order to simplify or make ... More

Cantor combinatorics and almost finitenessFeb 06 2018In this survey we give a concise introduction to a continuous version of Borel combinatorics. Our approach will have a certain algorithm-theoretic nature and we will give special emphasis to the notion of almost finiteness introduced by Matui as a continuous ... More

Induced Fuzzy Topological Spaces: A CharacterizationFeb 06 2018We introduce a simple property, affine invariance, which characterizes within the class of fuzzy topological spaces those which are induced from an underlying topology on the space. We illustrate it by considering the simple notions of compactness for ... More

Markov spectrum near Freiman's isolated points in $M\setminus L$Feb 06 2018Freiman proved in 1968 that the Lagrange and Markov spectra do not coincide by exhibiting a countable infinite collection $\mathcal{F}$ of isolated points of the Markov spectrum which do not belong the Lagrange spectrum. In this paper, we describe the ... More

Automorphism group of a moduli space of framed bundles over a curveFeb 06 2018Let $X$ be a smooth complex projective curve of genus $g > 2$, and let $x\in X$ be a point. We compute the automorphism group of the moduli space of framed vector bundles on $X$ with a framing over $x$. It is shown that this group is generated by pullbacks ... More

Topological symmetries of simply-connected four-manifolds and actions of automorphism groups of free groupsFeb 06 2018Let $M$ be a simply connected closed $4$-manifold. It is proved that any (possibly finite) compact Lie group acting effectively and homologically trivially on $M$ by homeomorphisms is an abelian group of rank at most two. As applications, let $\mathrm{Aut}(F_{n})$ ... More

Optimal consensus control of the Cucker-Smale modelFeb 05 2018We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive first-order necessary ... More

Vector Hamiltonians in Nambu mechanicsFeb 03 2018We give a generalization of the Nambu mechanics based on vector Hamiltonians theory. It is shown that any divergence-free phase flow in $\mathbb{R}^n$ can be represented as a generalized Nambu mechanics with $n-1$ integral invariants. For the case when ... More

Unitarity issues in higher derivative field theoriesFeb 03 2018We analyze the unitarity properties of higher derivative quantum field theories which are free of ghosts and ultraviolet singularities. We point out that in spite of the absence of ghosts most of these theories are not unitary. This result confirms the ... More

A strong averaging principle for Lévy diffusions in foliated spaces with unbounded leavesFeb 02 2018This article extends a strong averaging principle for L\'evy diffusions which live on the leaves of a foliated manifold subject to small transversal L\'evy type perturbation to the case of non-compact leaves. The main result states that the existence ... More

On computational issues for stability analysis of LPV systems using parameter dependent Lyapunov functions and LMIsFeb 02 2018This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some computational ... More

Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamicsFeb 02 2018In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cell density level, the spatial availability of the tumor density $n$ is governed ... More

Optimal interpolation formulas in $W_2^{(m,m-1)}$ spaceFeb 02 2018In the present paper optimal interpolation formulas are constructed in $W_2^{(m,m-1)}(0,1)$ space. Explicit formulas for coefficients of optimal interpolation formulas are obtained. Some numerical results are presented.

On the rattleback dynamicsFeb 01 2018In this paper we present some relevant dynamical properties of the rattleback, from the Poisson geometry point of view.

The Multiple Holomorphs of Finite $p$-Groups of Class TwoJan 31 2018$\DeclareMathOperator{\Hol}{Hol}$$\DeclareMathOperator{\Aut}{Aut}$$\newcommand{\Gp}[0]{\mathcal{G}(p)}$Let $G$ be a group, and $S(G)$ be the group of permutations on the set $G$. Define the holomorph of $G$ to be the normalizer of the image in $S(G)$ ... More

Nonautonomous gradient-like ODEs on the circle: classification, structural stability and autonomizationJan 31 2018We study a class of scalar differential equations on the circle $S^1$. This class is characterized mainly by the property that any solution of such an equation possesses exponential dichotomy both on the semi-axes $\R_+$ and $\R_+$. Also we impose some ... More

Dugundji systems and a retract characterization of effective zero-dimensionalityJan 31 2018In a previous paper, the author considered several conditions for effective zero-dimensionality of a computable metric space $X$; each of the (classically equivalent) properties of having vanishing small or large inductive dimension, or covering dimension, ... More

Compressed Anomaly Detection with Multiple Mixed ObservationsJan 31 2018We consider a collection of independent random variables that are identically distributed, except for a small subset which follows a different, anomalous distribution. We study the problem of detecting which random variables in the collection are governed ... More

On continued fraction expansions of quadratic irrationals in positive characteristicJan 30 2018Let $P$ be a prime polynomial in the variable $Y$ over a finite field and let $f$ be a quadratic irrational in the field of formal Laurant series in the variable $Y^{-1}$. We study the asymptotic properties of the degrees of the coefficients of the continued ... More

Analysis of the Continued Logarithm AlgorithmJan 30 2018Feb 01 2018The Continued Logarithm Algorithm - CL for short- introduced by Gosper in 1978 computes the gcd of two integers; it seems very efficient, as it only performs shifts and subtractions. Shallit has studied its worst-case complexity in 2016 and showed it ... More

Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operatorJan 30 2018We study the convergence of the graph Laplacian of a random geometric graph generated by an i.i.d. sample from a $m$-dimensional submanifold $M$ in $R^d$ as the sample size $n$ increases and the neighborhood size $h$ tends to zero. We show that eigenvalues ... More

Deformation Cohomology of Lie Algebroids and Morita EquivalenceJan 30 2018Let $A \Rightarrow M$ be a Lie algebroid. In this short note we prove that a pull-back of $A$ along a fibration with homologically $k$-connected fibers, shares the same deformation cohomology of $A$ up to degree $k$.

Analysis and optimal control of an intracellular delayed HIV model with CTL immune responseJan 30 2018A delayed model describing the dynamics of HIV (Human Immunodeficiency Virus) with CTL (Cytotoxic T Lymphocytes) immune response is investigated. The model includes four nonlinear differential equations describing the evolution of uninfected, infected, ... More

Weak functoriality of Cohen-Macaulay algebrasJan 30 2018We prove the weak functoriality of (big) Cohen-Macaulay algebras, which controls the whole skein of "homological conjectures" in commutative algebra [H1][HH2]. Namely, for any local homomorphism $ R\to R'$ of complete local domains, there exists a compatible ... More

A Class of Möbius Iterated Function SystemsJan 30 2018We give a procedure to produce M\"obius iterated function systems (MIFS) on the unit disc in the complex plane.

Almost cosymplectic statistical manifoldsJan 30 2018This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a corollary for the ... More

Quasiperiodic granular chains and Hofstadter butterfliesJan 30 2018We study quasiperiodicity-induced localization of waves in strongly precompressed granular chains. We propose three different setups, inspired by the Aubry--Andr\'e (AA) model, of quasiperiodic chains; and we use these models to compare the effects of ... More

Big polynomial rings and Stillman's conjectureJan 30 2018Feb 01 2018Ananyan-Hochster's recent proof of Stillman's conjecture reveals a key principle: if $f_1, \dots, f_r$ are elements of a polynomial ring such that no linear combination has small strength then $f_1, \dots, f_r$ behave approximately like independent variables. ... More

A consequence of the growth of rotation sets for families of diffeomorphisms of the torusJan 30 2018In this paper we consider $C^\infty $-generic families of area-preserving diffeomorphisms of the torus homotopic to the identity and their rotation sets. Let $f_t:\rm{T^2\rightarrow T^2}$ be such a family, $\widetilde{f}_t:\rm I\negthinspace R^2 \rightarrow ... More

Earthmover Resilience and Testing in Ordered StructuresJan 29 2018One of the main challenges in property testing is to characterize those properties that are testable with a constant number of queries. For unordered structures such as graphs and hypergraphs this task has been mostly settled. However, for ordered structures ... More

Kähler fibrations in quantum information theoryJan 29 2018We discuss the fibre bundle of co-adjoint orbits of compact Lie groups, and show how it admits a compatible K\"ahler structure. The case of the unitary group allows us to reformulate the geometric framework of quantum information theory. In particular, ... More

The Lyapunov dimension, convergency and entropy for a dynamical model of Chua memristor circuitJan 29 2018For the study of chaotic dynamics and dimension of attractors the concepts of the Lyapunov exponents was found useful and became widely spread. Such characteristics of chaotic behavior, as the Lyapunov dimension and the entropy rate, can be estimated ... More

Parameter Estimation, Sensitivity Analysis and Optimal Control of a Periodic Epidemic Model with Application to HRSV in FloridaJan 29 2018A state wide Human Respiratory Syncytial Virus (HRSV) surveillance system was implemented in Florida in 1999 to support clinical decision-making for prophylaxis of premature infants. The research presented in this paper addresses the problem of fitting ... More

Nonlinear Excitations in Magnetic Lattices with Long-Range InteractionsJan 29 2018We study - experimentally, theoretically, and numerically - nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with algebraically-decaying ... More

Brain-to-brain heteroclinic coordination: model of sequential episodic memory initiationJan 29 2018Retrieval of episodic memory is a dynamical process in the large scale brain networks. In social groups, the neural patterns, associated to specific events directly experienced by single members, are encoded, recalled and shared by all participants. Here ... More

On the validity of linear response theory in high-dimensional deterministic dynamical systemsJan 29 2018Feb 08 2018We provide a proof of concept for the validity of linear response theory in high-dimensional deterministic systems for large-scale observables. We consider observables of resolved degrees of freedom which are weakly coupled to a large number of unresolved ... More

Square Sierpiński carpets and Lattès mapsJan 29 2018Jan 30 2018We prove that every quasisymmetric homeomorphism of a standard square Sierpi\'nski carpet $S_p$, $p\ge 3$ odd, is an isometry. This strengthens and completes earlier work by the authors. We also show that a similar conclusion holds for quasisymmetries ... More

Smoothness of Topological Equivalence on the Half Line for Nonautonomous SystemsJan 26 2018We study the differentiabilty of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we construct a uniform homeomorphism inspired in ... More

On Uniform Admissibility of Unitary and Smooth RepresentationsJan 26 2018Let $G$ be a locally compact totally disconnected topological group. Under a necessary mild assumption, we show that the irreducible unitary representations of $G$ are uniformly admissible if and only if the irreducible smooth representations of $G$ are ... More

On a class of immersions of spheres into space forms of nonpositive curvatureJan 25 2018Let $ J $ be an interval and $ M^{n+1} $ be a simply-connected space form of curvature $ -\kappa $, where $ \kappa \geq 0$. If $ J \subset [-\kappa,\kappa] $, then no closed $ n $-manifold can be immersed in $ M $ subject to the restriction that the principal ... More

Generation of semigroup for symmetric matrix Schrödinger operators in $L^p$-spacesJan 25 2018In this paper we establish generation of analytic strongly continuous semigroup in $L^p$--spaces for the symmetric matrix Schr\"odinger operator $div(Q\nabla u)-Vu$, where, for every $x\in\mathbb{R}^d$, $V(x)=(v_{ij}(x))$ is a semi-definite positive and ... More

Maximal subgroups of ${}^2E_6(2)$ and its automorphism groupsJan 25 2018We give a new computer-assisted proof of the classification of maximal subgroups of the simple group ${}^2E_6(2)$ and its extensions by any subgroup of the outer automorphism group $S_3$. This is not a new result, but no earlier proof exists in the literature. ... More

Networks of piecewise linear neural mass modelsJan 25 2018Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ODEs with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlases they may be connected into ... More

Sets of values of equivalent almost periodic functionsJan 25 2018In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.

Modules of infinite regularity over commutative graded ringsJan 24 2018In this work, we prove that if a graded, commutative algebra $R$ over a field $k$ is not Koszul then, denoting by $\mathfrak{m}$ the maximal homogeneous ideal, the nonzero modules of the form $\mathfrak{m} M$ have infinite Castelnuovo-Mumford regularity. ... More

On the maximal graded shifts of ideals and modulesJan 24 2018We generalize a result of Eisenbud-Huneke-Ulrich on the maximal graded shifts of a module with prescribed annihilator and prove a linear regularity bound for ideals in a polynomial ring depending only on the first $p - c$ steps in the resolution, where ... More

On a new $q$-analogue of Appell polynomialsJan 24 2018A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their main representations ... More

Algebras with finitely many conjugacy classes of left ideals versus algebras of finite representation typeJan 24 2018Let A be a finite dimensional algebra over an algebraically closed field with the radical nilpotent of index 2. It is shown that A has finitely many conjugacy classes of left ideals if and only if A is of finite representation type provided that all simple ... More

Hartshorne's questions and weakly cofinitenessJan 23 2018Let $R$ be a commutative Noetherian ring, $\fa$ be an ideal of $R$ and $M$ be an $R$-module. The main purpose of this paper is to answer the Hartshorn's questions in the class of weakly Laskerian modules. It is shown that if $s\geq 1$ is a positive integer ... More

Torsion and Linking number for a surface diffeomorphismJan 23 2018For a $\mathcal{C}^1$ diffeomorphism $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ isotopic to the identity, we prove that for any value $l\in\mathbb{R}$ of the linking number at finite time of the orbits of two points there exists at least a point whose torsion ... More

Stable gonality is computableJan 23 2018Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with the minimum number ... More

Incidence bicomodules, Möbius inversion, and a Rota formula for infinity adjunctionsJan 23 2018In the same way decomposition spaces, also known as unital 2-Segal spaces, have incidence (co)algebras, and certain relative decomposition spaces have incidence (co)modules, we identify the structures that have incidence bi(co)modules: they are certain ... More

Almost Periodic Functions in terms of Bohr's Equivalence RelationJan 22 2018In this paper we introduce an equivalence relation on the classes of almost periodic functions of a real or complex variable which is used to refine Bochner's result that characterizes these spaces of functions. In fact, with respect to the topology of ... More

C-projective symmetries of submanifolds in quaternionic geometryJan 22 2018The generalized Feix--Kaledin construction shows that c-projective $2n$-manifolds with curvature of type $(1,1)$ are precisely the submanifolds of quaternionic $4n$-manifolds which are fixed points set of a special type of quaternionic $S^1$ action $v$. ... More

Uniform asymptotic stability of a fractional tuberculosis modelJan 22 2018We propose a Caputo type fractional-order mathematical model for the transmission dynamics of tuberculosis (TB). Uniform asymptotic stability of the unique endemic equilibrium of the fractional-order TB model is proved, for any $\alpha \in (0, 1)$. Numerical ... More

Interpolation of functional by integral continued C-fractionsJan 21 2018The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued fraction contains ... More

Global and Concrete Quantizations on General Type I GroupsJan 21 2018In recent papers and books, a global quantization has been developed for {\it unimodular} groups of type I\,. It involves operator-valued symbols defined on the product between the group $\G$ and its unitary dual $\wG$\,, composed of equivalence classes ... More

Infinite staircases in the symplectic embedding problem for four-dimensional ellipsoids into polydisksJan 21 2018We study the symplectic embedding capacity function $C_{\beta}$ for ellipsoids $E(1,\alpha)\subset R^4$ into dilates of polydisks $P(1,\beta)$ as both $\alpha$ and $\beta$ vary through $[1,\infty)$. For $\beta=1$ Frenkel and Mueller showed that $C_{\beta}$ ... More

An upper bound on the asymptotic translation lengths on the curve graph and fibered facesJan 20 2018We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold $M$ with $b_1(M) \geq 2$. For a sequence $(\Sigma_n, \psi_n)$ of fibers and ... More

A high-performance analog Max-SAT solver and its application to Ramsey numbersJan 20 2018Jan 28 2018We introduce a continuous-time analog solver for MaxSAT, a quintessential class of NP-hard discrete optimization problems, where the task is to find a truth assignment for a set of Boolean variables satisfying the maximum number of given logical constraints. ... More

On the asymptotic behavior of static perfect fluidsJan 20 2018Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite ... More

On certain multiples of Littlewood and Newman polynomialsJan 19 2018Polynomials with all the coefficients in $\{ 0,1\}$ and constant term 1 are called Newman polynomials, whereas polynomials with all the coefficients in $\{ -1,1\}$ are called Littlewood polynomials. By exploiting an algorithm developed earlier, we determine ... More

On connected preimages of simply-connected domains under entire functionsJan 19 2018Let $f$ be a transcendental entire function, and let $U,V\subset\mathbb{C}$ be disjoint simply-connected domains. Must one of $f^{-1}(U)$ and $f^{-1}(V)$ be disconnected? In 1970, Baker implicitly gave a positive answer to this question, in order to prove ... More

The Gromov width of generalized Bott manifoldsJan 19 2018By Delzant's theorem, closed symplectic toric manifolds are classified by the images of moment maps. In the case of a generalized Bott manifold, this image is a polytope $P$ combinatorially equivalent to the product of simplices. We compute the Gromov ... More

Groups whose elements are not conjugate to their powersJan 18 2018We call a finite group irrational if none of its elements is conjugate to a distinct power of itself. We prove that those groups are solvable and describe certain classes of these groups, where the above property is only required for $p$-elements, for ... More

Complexity of Combinations of Qualitative Constraint Satisfaction ProblemsJan 18 2018The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures. Nelson and Oppen ... More

Efficient Computation of the 8-point DCT via Summation by PartsJan 17 2018This paper introduces a new fast algorithm for the 8-point discrete cosine transform (DCT) based on the summation-by-parts formula. The proposed method converts the DCT matrix into an alternative transformation matrix that can be decomposed into sparse ... More

Einstein-Weyl structures on almost cosymplectic manifoldsJan 17 2018In this article, we study the Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(\kappa,\mu)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl ... More

Notes on Ricci solitons in $f$-cosymplectic manifoldsJan 17 2018The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class ... More

Rates in almost sure invariance principle for slowly mixing dynamical systemsJan 16 2018We prove the one-dimensional almost sure invariance principle with essentially optimal rates for slowly (polynomially) mixing deterministic dynamical systems, such as Pomeau-Manneville intermittent maps, with H\"older continuous observables. Our rates ... More

The Fermi-Pasta-Ulam problem and its underlying integrable dynamics: an approach through Lyapunov ExponentsJan 16 2018FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual $\beta$-model, perturbations of Toda include the usual $\alpha+\beta$ model. In this paper we explore ... More

Triviality properties of principal bundles on singular curves-IIJan 15 2018For $G$ a split semi-simple group scheme and $P$ a principal $G$-bundle on a relative curve $X\to S$, we study a natural obstruction for the triviality of $P$ on the complement of a relatively ample Cartier divisor $D \subset X$. We show, by constructing ... More

Graph Laplace and Markov operators on a measure spaceJan 13 2018The main goal of this paper is to build a measurable analogue to the theory of weighted networks on infinite graphs. Our basic setting is an infinite $\sigma$-finite measure space $(V, \mathcal B, \mu)$ and a symmetric measure $\rho$ on $(V\times V, \mathcal ... More