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A new algorithm that generates the image of the attractor of a generalized iterated function systemMay 19 2019We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space and we compare it with the deterministic algorithm regarding generalized iterated ... More
A contact geometry framework for field theories with dissipationMay 17 2019We develop a new geometric framework suitable for the treatment of field theories with dissipation. To this end we define the notion of $k$-contact structure. With it, we introduce the so-called $k$-contact Hamiltonian systems, which are a generalization ... More
Counting and sampling gene family evolutionary histories in the duplication-loss and duplication-loss-transfer modelsMay 13 2019Given a set of species whose evolution is represented by a species tree, a gene family is a group of genes having evolved from a single ancestral gene. A gene family evolves along the branches of a species tree through various mechanisms, including - ... More
A little more on the zero-divisor graph and the annihilating-ideal graph of a reduced ringMay 11 2019We have tried to translate some graph properties of AG(R) and Gamma(R) to the topological properties of Zariski topology. We prove that Rad(Gamma(R)) and Rad(AG(R)) are equal and they are equal to 3, if and only if the zero ideal of R is an anti fixed-place ... More
Embeddings of Persistence Diagrams into Hilbert SpacesMay 11 2019Since persistence diagrams do not admit an inner product structure, a map into a Hilbert space is needed in order to use kernel methods. It is natural to ask if such maps necessarily distort the metric on persistence diagrams. We show that persistence ... More
Why scoring functions cannot assess tail propertiesMay 10 2019Motivated by the growing interest in sound forecast evaluation techniques with an emphasis on distribution tails rather than average behaviour, we investigate a fundamental question arising in this context: Can statistical features of distribution tails ... More
Asymptotics of multivariate sequences in the presence of a lacunaMay 10 2019We explain a discontinuous drop in the exponential growth rate for certain multivariate generating functions at a critical parameter value, in even dimensions $d \geq 4$. This result depends on computations in the homology of the algebraic variety where ... More
The asymptotic induced matching number of hypergraphs: balanced binary stringsMay 08 2019We compute the asymptotic induced matching number of the $k$-partite $k$-uniform hypergraphs whose edges are the $k$-bit strings of Hamming weight $k/2$, for any large enough even number $k$. Our lower bound relies on the higher-order extension of the ... More
Stable multivariate generalizations of matching polynomialsMay 06 2019May 08 2019The first part of this note concerns stable averages of multivariate matching polynomials. In proving the existence of infinite families of bipartite Ramanujan $d$-coverings, Hall, Puder and Sawin introduced the $d$-matching polynomial of a graph $G$, ... More
Stable multivariate generalizations of matching polynomialsMay 06 2019The first part of this note concerns stable averages of multivariate matching polynomials. In proving the existence of infinite families of bipartite Ramanujan $d$-coverings, Hall, Puder and Sawin introduced the $d$-matching polynomial of a graph $G$, ... More
Algorithms and Complexity for some Multivariate ProblemsMay 03 2019We study multivariate problems like function approximation, numerical integration, global optimization and dispersion. We obtain new results on the information complexity $n(\varepsilon,d)$ of these problems. The information complexity is the amount of ... More
The Total Variation Flow in Metric Random Walk SpacesMay 03 2019In this paper we study the Total Variation Flow (TVF) in metric random walk spaces which include as particular cases: the TVF on locally finite weighted connected graphs, the TVF determined by finite Markov chains and some nonlocal evolution problems. ... More
An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusionMay 01 2019May 20 2019We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law (this is so for ... More
An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusionMay 01 2019We propose and analyse the properties of a new class of models for the electromechanics of the cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law (this is so ... More
Tracelets and Tracelet Analysis Of Compositional Rewriting SystemsApr 29 2019Taking advantage of a recently discovered associativity property of rule compositions, we extend the classical concurrency theory for rewriting systems over adhesive categories. We introduce the notion of tracelets, which are defined as minimal derivation ... More
A Motion Planning Algorithm in a lollipop graphApr 29 2019May 01 2019This paper is concerned with problems relevant to motion planning in robotics. Configuration spaces are of practical relevance in designing safe control schemes for robots moving on a track. The topological complexity of a configuration space is an integer ... More
A Motion Planning Algorithm in a lollipop graphApr 29 2019This paper is concerned with problems relevant to motion planning in robotics. Configuration spaces are of practical relevance in designing safe control schemes for robots moving on a track. The topological complexity of a configuration space is an integer ... More
Computing A-Homotopy Groups Using Coverings and Lifting PropertiesApr 26 2019In classical homotopy theory, two spaces are homotopy equivalent if one space can be continuously deformed into the other. This theory, however, does not respect the discrete nature of graphs. For this reason, a discrete homotopy theory that recognizes ... More
Extremal set theory for the binomial normApr 23 2019Best possible bounds are established for families without s pairwise disjoint members and the more general problem for several families. The results are shown to apply several classical results.
Finding NHIM in 2 and 3 degrees-of-freedom with Hénon-Heiles type potentialApr 22 2019We present the capability of Lagrangian descriptors for revealing the high dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include normally hyperbolic invariant ... More
Compositionality of Rewriting Rules with ConditionsApr 19 2019We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the definition of rule ... More
Polynomial invariants and reciprocity theorems for the Hopf monoid of hypergraphs and its sub-monoidsApr 19 2019In arXiv:1709.07504 Aguiar and Ardila give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, we define in this paper a new polynomial invariant on hypergraphs. We give ... More
Polynomial invariants and reciprocity theorems for the Hopf monoid of hypergraphs and its sub-monoidsApr 19 2019May 03 2019In arXiv:1709.07504 Aguiar and Ardila give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, we define in this paper a new polynomial invariant on hypergraphs. We give ... More
Sesqui-Pushout Rewriting: Concurrency, Associativity and Rule Algebra FrameworkApr 17 2019Sesqui-pushout (SqPO) rewriting provides a variant of transformations of graph-like and other types of structures that fit into the framework of adhesive categories where deletion in unknown context may be implemented. We provide the first account of ... More
Inversion formula with hypergeometric polynomials and its application to an integral equationApr 16 2019For any complex parameters $x$ and $\nu$, we provide a new class of linear inversion formulas $T = A(x,\nu) \cdot S \Leftrightarrow S = B(x,\nu) \cdot T$ between sequences $S = (S_n)_{n \in \mathbb{N}^*}$ and $T = (T_n)_{n \in \mathbb{N}^*}$, where the ... More
Combinatorial Conversion and Moment Bisimulation for Stochastic Rewriting SystemsApr 15 2019We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship between the combinatorics ... More
All quasitrivial n-ary semigroups are reducible to semigroupsApr 11 2019We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary semigroups. We also ... More
Cartan Connections and Atiyah Lie AlgebroidsApr 09 2019This work extends previous developments carried out by some of the authors on Ehresmann connections on Atiyah Lie algebroids. In this paper, we study Cartan connections in a framework relying on two Atiyah Lie algebroids based on a $H$-principal fiber ... More
New bounds on even cycle creating Hamiltonian paths using expander graphsApr 09 2019We say that two graphs on the same vertex set are $G$-creating if their union (the union of their edges) contains $G$ as a subgraph. Let $H_n(G)$ be the maximum number of pairwise $G$-creating Hamiltonian paths of $K_n$. Cohen, Fachini and K\"orner proved ... More
New bounds on even cycle creating Hamiltonian paths using expander graphsApr 09 2019May 10 2019We say that two graphs on the same vertex set are $G$-creating if their union (the union of their edges) contains $G$ as a subgraph. Let $H_n(G)$ be the maximum number of pairwise $G$-creating Hamiltonian paths of $K_n$. Cohen, Fachini and K\"orner proved ... More
Elliptic problems and holomorphic functions in Banach spacesApr 05 2019In the first part we show that a vector-valued almost separably valued function $f$ is holomorphic (harmonic) if and only if it is dominated by an $L^1_\mathrm{loc}$ function and there exists a separating set $W\subset X'$ such that $\langle f,x'\rangle$ ... More
A Universal Algebraic Survey of $\mathcal{C}^{\infty}-$RingsApr 04 2019In this paper we present some basic results of the Universal Algebra of $\mathcal{C}^\infty$-rings which were nowhere to be found in the current literature. The outstanding book of I. Moerdijk and G. Reyes,[24], presents the basic (and advanced) facts ... More
Topics on Smooth Commutative AlgebraApr 04 2019We present, in the same vein as in [20] and [21], some results of the so-called "Smooth (or $\mathcal{C}^\infty$) Commutative Algebra", a version of Commutative Algebra of $\mathcal{C}^{\infty}-$rings instead of ordinary commutative unital rings, looking ... More
Large sparse networks of interacting diffusionsApr 04 2019We consider interacting particle systems on a large sparse, possibly random, interaction graph $G_n$, where each particle evolves infinitesimally like a d-dimensional diffusion whose drift coefficient depends on the histories of its own state and the ... More
Ecalle's averages, Rota-Baxter algebras and the construction of mouldsApr 04 2019Rota-Baxter algebras and Atkinson's method are powerful tools for the factorization of characters on Hopf algebras. The theory of real resummation discovered by J. Ecalle and known as \textit{well-behaved averages theory} can be reformulated in terms ... More
Existence of Regular Nut Graphs and the Fowler ExtensionApr 03 2019In this paper the problem of the existence of regular nut graphs is addressed. A generalization of Fowler's extension which is a local enlargement applied to a vertex in a graph is introduced to generate nut graphs of higher order. Let $N(\rho)$ denote ... More
A Theoretical Analysis of Deep Neural Networks and Parametric PDEsMar 31 2019We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent low-dimensionality of the solution ... More
Decomposition and Modeling in the Non-Manifold domainMar 30 2019The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the problem of ... More
Towards the undecidability of atomicity for permutation classes via the undecidability of joint embedding for hereditary graph classesMar 28 2019We work towards answering a question of Ru\v{s}kuc on the decidability of atomicity for permutation classes, which is equivalent to the decidability of the joint embedding property when permutations are viewed as structures in a language of two linear ... More
Error Analysis and Uncertainty Quantification for the Heterogeneous Transport Equation in Slab GeometryMar 28 2019We present an analysis of multilevel Monte Carlo techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients ({\em cross-sections}) are heterogenous random fields. To do this, we first give ... More
New Weak Error bounds and expansions for Optimal QuantizationMar 25 2019We propose new weak error bounds and expansion in dimension one for optimal quantization-based cubature formula for different classes of functions, such that piecewise affine functions, Lipschitz convex functions or differentiable function with piecewise-defined ... More
Network Horizon Dynamics I: Qualitative AspectsMar 25 2019Mostly acyclic directed networks, treated mathematically as directed graphs, arise in machine learning, biology, social science, physics, and other applications. Newman [1] has noted the mathematical challenges of such networks. In this series of papers, ... More
Finding NHIM: Identifying High Dimensional Phase Space Structures in Reaction Dynamics using Lagrangian DescriptorsMar 25 2019Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, their stable and unstable manifolds have been an integral part of computing quantitative results such as transition fraction, stability erosion in multi-stable ... More
Finsler spacetime geometry in PhysicsMar 25 2019Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general geometric clock ... More
Continued fractions associated with the topological index of the caterpillar-bond graphMar 24 2019In this paper, we give graphs whose topological index are exactly equal to the number $u_n$, satisfying the three term recurrence relation $$ u_n=a u_{n-1}+b u_{n-2}\quad(n\ge 2)\quad u_0=0\quad\hbox{and}\quad u_1=u\,, $$ where $a$, $b$ and $u$ are positive ... More
A Note on the Exponents of Primitive Companion MatricesMar 24 2019A nonnegative matrix $A$ is said to be {\it primitive} if for some positive integer $m$, entries in $A^m$ are positive, notationally represented as $A^m>0.$ The smallest such $m$ is called the {\it exponent} of $A$, denoted $exp(A).$ For the class of ... More
On extensions of partial isometriesMar 22 2019In this paper we define a notion of S-extension for a metric space and study minimality and coherence of S-extensions. We give a complete characterization of all finite minimal S-extensions of a given finite metric space. We also define a notion of ultraextensive ... More
Polynomial chaos expansions for dependent random variablesMar 22 2019Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast, the application ... More
Combining Model and Parameter Uncertainty in Bayesian Neural NetworksMar 18 2019Mar 20 2019Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: ... More
Combining Model and Parameter Uncertainty in Bayesian Neural NetworksMar 18 2019Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: ... More
Highly irregular separated netsMar 14 2019In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such ... More
Generalization of the cover pebbling number on treesMar 12 2019A pebbling move on a graph consists of taking two pebbles off from one vertex and add one pebble on an adjacent vertex, the $t$-pebbling number of a graph $G$ is the minimum number of pebbles so that we can move $t$ pebbles on any vertex on $G$ regardless ... 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
A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentationMar 08 2019We introduce a multi-agent meta-modeling game to generate data, knowledge, and models that make predictions on constitutive responses of elasto-plastic materials. We introduce a new concept from graph theory where a modeler agent is tasked with evaluating ... More
Lower semicontinuity of ADM mass under intrinsic flat convergenceMar 03 2019A natural question in mathematical general relativity is how the ADM mass behaves as a functional on the space of asymptotically flat 3-manifolds of nonnegative scalar curvature. In previous results, lower semicontinuity has been established by the first-named ... More
$t$-Pebbling in $k$-connected diameter two graphsMar 01 2019Graph pebbling models the transportation of consumable resources. As two pebbles move across an edge, one reaches its destination while the other is consumed. The $t$-pebbling number is the smallest integer $m$ so that any initially distributed supply ... More
Strict Superstablity and Decidability of Certain Generic GraphsMar 01 2019We show that the Hrushovski-\fraisse limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each $ \alpha\in\omega+1\backslash\{0\} $ we introduce a strictly superstable theory of U-rank $ \alpha. $ Furthermore, ... More
The Block-wise Circumcentered-Reflection MethodFeb 28 2019The elementary Euclidean concept of circumcenter has recently been employed to improve two aspects of the classical Douglas--Rachford method for projecting onto the intersection of affine subspaces. The so-called circumcentered-reflection method is able ... More
Formal structure of periodic system of elementsFeb 27 2019For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is. Herein, based ... More
Maximum Wiener index of unicyclic graphs with given bipartitionFeb 27 2019The Wiener index is a widely studied topological index of graphs. One of the main problems in the area is to determine which graphs of given properties attain the extremal values of Wiener index. In this paper we resolve an open problem posed by Du in ... More
(Lack of) Model Structures on the Category of GraphsFeb 25 2019In the present article, we study model structures on the category of graphs with $\times$-homotopy equivalences as the weak equivalences, namely, $(\mathcal{G},\times)$. We show that the analog of Strom-Hurewicz model structure in the category of graphs ... More
Integration with respect to deficient topological measures on locally compact spacesFeb 22 2019Topological measures and deficient topological measures generalize Borel measures and correspond to certain non-linear functionals. We study integration with respect to deficient topological measures on locally compact spaces. Such an integration over ... More
Manifold interpolation and model reductionFeb 18 2019One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric structure and thus ... More
Non-linear functionals, deficient topological measures, and representation theorems on locally compact spacesFeb 15 2019We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topological measures and topological measures on locally compact spaces. We prove ... More
Generalized semimodularity: order statisticsFeb 14 2019A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th Cartesian power ... More
On the Structure of Time-delay Embedding in Linear Models of Non-linear Dynamical SystemsFeb 14 2019It is known that for a non-linear dynamical system, periodic and quasi-periodic attractors can be reconstructed in a discrete sense using time-delay embedding. Following this argument, it has been shown that even chaotic non-linear systems can be represented ... More
Integral and differential structure on the free $C^{\infty}$-ring modalityFeb 12 2019This paper develops an example of an integral category whose integral transformation operates on smooth 1-forms. Further, we revisit the differential structure of this category, and we investigate derivations, coderelictions, and Rota-Baxter algebras ... More
The double point formula with isolated singularities and canonical embeddingsFeb 12 2019Motivated by the embedding problem of canonical models in small codimension, we extend Severi's double point formula to the case of surfaces with rational double points, and we give more general double point formulae for varieties with isolated singularities. ... More
The least H-eigenvalue of signless Laplacian of non-odd-bipartite hypergraphsFeb 12 2019Let $G$ be a connected non-odd-bipartite hypergraph with even uniformity. The least H-eigenvalue of the signless Laplacian tensor of $G$ is simply called the least eigenvalue of $G$ and the corresponding H-eigenvectors are called the first eigenvectors ... More
Direct and inverse limits of normed modulesFeb 11 2019The aim of this note is to study existence and main properties of direct and inverse limits in the category of normed $L^0$-modules (in the sense of Gigli) over a metric measure space.
Class of hypocomplex structures on the two dimensional torusFeb 11 2019We study the H\"{o}lder solvability of a class of complex vector fields on the torus $\mathbb{T}^2$. We make use of the Theta function to associate a Cauchy-Pompeiu type integral operator. A similarity principle for the solutions of the equation $Lu=au+b\bar{u}$ ... More
Majority categoriesFeb 08 2019We introduce the notion of a majority category --- the categorical counterpart of varieties of universal algebras admitting a majority term. This notion can be thought to capture properties of the category of lattices, in a way that parallels how Mal'tsev ... More
Cyclic Symmetry on Complex Tori and Bagnera-De Franchis ManifoldsFeb 05 2019We describe the possible linear actions of a cyclic group $G = \mathbb{Z} /n$ on a complex torus, using the cyclotomic exact sequence for the group algebra $\mathbb{Z} [G]$. The main application is devoted to a structure theorem for Bagnera-De Franchis ... More
The energy and spectrum of non commuting graphFeb 02 2019Let G be a non-abelian group and Z(G) be the center of G. The non-commuting graph {\Gamma}(G) of G is a graph with vertex set is non central elements of G and two vertices x, y are adjacent if and only if they are commute. In this paper we calculate the ... More
Some Enumeration Problems in the Duplication-Loss Model of Genome RearrangementFeb 01 2019Tandem-duplication-random-loss (TDRL) is an important genome rearrangement operation studied in evolutionary biology. This paper investigates some of the formal properties of TDRL operations on the symmetric group (the space of permutations over an $ ... More
An Optimization-Based Sum-of-Squares Approach to Vizing's ConjectureJan 29 2019Feb 04 2019Vizing's conjecture (open since 1968) relates the sizes of dominating sets in two graphs to the size of a dominating set in their Cartesian product graph. In this paper, we formulate Vizing's conjecture itself as a Positivstellensatz existence question. ... More
An Optimization-Based Sum-of-Squares Approach to Vizing's ConjectureJan 29 2019May 06 2019Vizing's conjecture (open since 1968) relates the sizes of dominating sets in two graphs to the size of a dominating set in their Cartesian product graph. In this paper, we formulate Vizing's conjecture itself as a Positivstellensatz existence question. ... More
Simple algorithms for optimization on Riemannian manifolds with constraintsJan 28 2019We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the Euclidean case to the ... More
Simple algorithms for optimization on Riemannian manifolds with constraintsJan 28 2019Apr 25 2019We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the Euclidean case to the ... More
Hereditary classes of ordered binary structuresJan 27 2019Balogh, Bollob\'{a}s and Morris (2006) have described a threshold phenomenon in the behavior of the profile of hereditary classes of ordered graphs. In this paper, we give an other look at their result based on the notion of monomorphic decomposition ... More
Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphsJan 24 2019Unlike an irreducible $Z$-matrices, a weakly irreducible $Z$-tensor $\mathcal{A}$ can have more than one eigenvector associated with the least H-eigenvalue. We show that there are finitely many eigenvectors of $\mathcal{A}$ associated with the least H-eigenvalue. ... More
Certain results on Euler-type integrals and their applicationsJan 22 2019This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite integrals. Further, ... More
A generalization of pde's from a Krylov point of viewJan 21 2019We introduce and investigate the notion of a `generalized equation' of the form $f(D^2 u)=0$, based on the notions of subequations and Dirichlet duality. Precisely, a subset ${{\mathbb H}}\subset {\rm Sym}^2({\mathbb R}^n)$ is a generalized equation if ... More
Four Deviations Suffice for Rank 1 MatricesJan 20 2019We prove a matrix discrepancy bound that strengthens the famous Kadison-Singer result of Marcus, Spielman, and Srivastava. Consider any independent scalar random variables $\xi_1, \ldots, \xi_n$ with finite support, e.g. $\{ \pm 1 \}$ or $\{ 0,1 \}$-valued ... More
Four Deviations Suffice for Rank 1 MatricesJan 20 2019Mar 28 2019We prove a matrix discrepancy bound that strengthens the famous Kadison-Singer result of Marcus, Spielman, and Srivastava. Consider any independent scalar random variables $\xi_1, \ldots, \xi_n$ with finite support, e.g. $\{ \pm 1 \}$ or $\{ 0,1 \}$-valued ... More
Sign Language Representation by TEO Humanoid Robot: End-User Interest, Comprehension and SatisfactionJan 17 2019In this paper, we illustrate our work on improving the accessibility of Cyber-Physical Systems (CPS), presenting a study on human-robot interaction where the end-users are either deaf or hearing-impaired people. Current trends in robotic designs include ... More
Double variational principle for mean dimension with potentialJan 17 2019This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of topological pressure. ... More
Double variational principle for mean dimensionJan 17 2019We develop a variational principle between mean dimension theory and rate distortion theory. We consider a minimax problem about the rate distortion dimension with respect to two variables (metrics and measures). We prove that the minimax value is equal ... More
Ramsey's CoheirsJan 14 2019We use the model theoretic notion of coheir to give short proofs of old and new theorems in Ramsey Theory. As an illustration we start from Ramsey's theorem itself. Then we prove Hindman's theorem and the Hales-Jewett theorem. Finally, we prove two Ramsey ... More
The shape of the reliability polynomial of a hammock networkJan 13 2019Motivated by the study of hammock (aka brick-wall) networks, we introduce in this paper the notion of X-path. Using the Jordan Curve Theorem for piecewise smooth curves, we prove duality properties for hammock networks. Consequences for reliability polynomials ... More
Recurrence equations and their classical orthogonal polynomial solutions on a quadratic or q-quadratic latticeJan 11 2019Every classical orthogonal polynomial system $p_n(x)$ satisfies a three-term recurrence relation of the type \[ p_{n+1}(x)=(A_nx+B_n)p_n(x)-C_np_{n-1}(x)~ (n=0,1,2,\ldots, p_{-1}\equiv 0), \] with $C_nA_nA_{n-1}>0$. Moreover, Favard's theorem states that ... More
On the Universality and Extremality of graphs with a distance constrained colouringJan 04 2019A lambda colouring (or $L(2,1)-$colouring) of a graph is an assignment of non-negative integers (with minimum assignment $0$) to its vertices such that the adjacent vertices must receive integers at least two apart and vertices at distance two must receive ... More
A mesh-free method for interface problems using the deep learning approachJan 03 2019In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the second one ... More
Lattice homomorphisms in harmonic analysisDec 31 2018Feb 12 2019Let $S$ be a non-empty, closed subspace of a locally compact group $G$ that is a subsemigroup of $G$. Suppose that $X, Y$, and $Z$ are Banach lattices that are vector sublattices of the order dual $\mathrm{C}_{\mathrm{c}}(S,\mathbb R)^\sim$ of the real-valued, ... More
Lattice homomorphisms in harmonic analysisDec 31 2018Let $S$ be a non-empty, closed subspace of a locally compact group $G$ that is a subsemigroup of $G$. Suppose that $X, Y$, and $Z$ are Banach lattices that are vector sublattices of the order dual $\mathrm{C}_{\mathrm{c}}(S,\mathbb R)^\sim$ of the real-valued, ... More
The smooth torus orbit closures in the GrassmanniansDec 30 2018It is known that for the natural algebraic torus actions on the Grassmannians, the closures of torus orbits are toric varieties, and that these toric varieties are smooth if and only if the corresponding matroid polytopes are simple. We prove that simple ... More
The Hitchhiker guide to: Secant Varieties and Tensor DecompositionDec 26 2018We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety $X$. The case we concentrate on is when $X$ is a Veronese variety, a Grassmannian or a Segre variety. Not only these ... More
A Scaling Limit for the Cover Time of the Binary TreeDec 25 2018Jan 21 2019We consider a continuous time random walk on the rooted binary tree of depth $n$ with all transition rates equal to one and study its cover time, namely the time until all vertices of the tree have been visited. We prove that, normalized by $2^{n+1} n$ ... More
Constraint algorithm for singular field theories in the $k$-cosymplectic frameworkDec 20 2018The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of $k$-cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of $k$-precosymplectic structure, ... More
Unitary invariants for commuting tuples of hypercontractionsDec 19 2018In this paper, we introduce the notion of characteristic functions for commuting tuples of $m$-hypercontractions on Hilbert spaces and investigate some properties. We prove that the characteristic function is a complete unitary invariant. We also offer ... More