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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
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
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
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
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
A panorama of positivityDec 13 2018This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). ... More
An additive formula for multiplicities on reproducing kernel Hilbert spacesDec 13 2018In this paper, we compute the exact rank of a non-trivial co-doubly commuting submodule of analytic reproducing kernel Hilbert modules over $\mathbb{C}[z_1,\ldots,z_n]$. More precisely, let $\mathcal{H} = \mathcal{H}_{1} \otimes \ldots \otimes \mathcal{H}_{n}$ ... More
Winding number and Cutting number of Harmonic cycleDec 12 2018Dec 13 2018A harmonic cycle $\lambda$, also called a discrete harmonic form, is a solution of the Laplace's equation with the combinatorial Laplace operator obtained from the boundary operators of a chain complex. By the combinatorial Hodge theory, harmonic spaces ... More
An improved diameter bound for finite simple groups of Lie typeDec 11 2018For a finite group $G$, let $\mathrm{diam}(G)$ denote the maximum diameter of a connected Cayley graph of $G$. A well-known conjecture of Babai states that $\mathrm{diam}(G)$ is bounded by ${(\log_{2} |G|)}^{O(1)}$ in case $G$ is a non-abelian finite ... More
Multivariate Newton InterpolationDec 11 2018Jan 28 2019For $m,n \in \mathbb{N}$, $m\geq 1$ and a given function $f : \mathbb{R}^m\longrightarrow \mathbb{R}$, the polynomial interpolation problem (PIP) is to determine a unisolvent node set $P_{m,n} \subseteq \mathbb{R}^m$ of $N(m,n):=|P_{m,n}|=\binom{m+n}{n}$ ... More
A SQP Based Line Search Method for Multi-objective Optimization ProblemsDec 10 2018In this paper a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear approximation of all objective ... More
The $k$-conversion number of regular graphsDec 08 2018Given a graph $G=(V,E)$ and a set $S_0\subseteq V$, an irreversible $k$-threshold conversion process on $G$ is an iterative process wherein, for each $t=1,2,\dots$, $S_t$ is obtained from $S_{t-1}$ by adjoining all vertices that have at least $k$ neighbours ... More
A Conjectured Integer Sequence Arising From the Exponential IntegralDec 02 2018Dec 15 2018Let $f_0(z) = \exp(z/(1-z))$, $f_1(z) = \exp(1/(1-z))E_1(1/(1-z))$, where $E_1(x) = \int_x^\infty e^{-t}t^{-1}{\,d}t$. Let $a_n = [z^n]f_0(z)$ and $b_n = [z^n]f_1(z)$ be the corresponding Maclaurin series coefficients. We show that $a_n$ and $b_n$ may ... More
A systematic path to non-Markovian dynamics: New generalized FPK equations for dynamical systems under coloured noise excitation with arbitrary correlation functionNov 29 2018Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic dynamics, advanced ... More
Classifications of quasitrivial semigroupsNov 27 2018We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups, we address ... More
On Independent Cliques and Linear Complementarity ProblemsNov 24 2018In recent work (Pandit and Kulkarni [Discrete Applied Mathematics, 244 (2018), pp. 155--169]), the independence number of a graph was characterized as the maximum of the $\ell_1$ norm of solutions of a Linear Complementarity Problem (\LCP) defined suitably ... More
CGW-categoriesNov 19 2018We introduce a new perspective on the $K$-theory of exact categories via the notion of a CGW-category. CGW-categories are a generalization of exact categories that admit a Qullen $Q$-construction, but which also include examples such as finite sets and ... More
Quantifier free definable relations on finite dimensional subspace lattices with involutionNov 19 2018Jan 22 2019For finite dimensional hermitean inner product spaces $V$, over $*$-fields $F$, and in the presence of orthogonal bases providing form elements in the prime subfield of $F$, we show that quantifier free definable relations in the subspace lattice $L(V)$ ... More
Eigenvalues of symmetrized shuffling operatorsNov 17 2018This paper describes a combinatorial way of obtaining all the eigenvalues of the symmetrized shuffling operators introduced by Victor Reiner, Franco Saliola and Volkmar Welker. It allows us to prove their conjecture that these eigenvalues are integers. ... More
Extensions of the Novikov-Furutsu theorem, obtained by using Volterra functional calculusNov 15 2018Novikov-Furutsu (NF) theorem is a well-known mathematical tool, used in stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the product of a random functional with a Gaussian argument multiplied by the argument itself. ... More
The EdgeConflict Predicate in the 3D Apollonius DiagramNov 15 2018Nov 16 2018In this paper we study one of the fundamental predicates required for the construction of the 3D Apollonius diagram (also known as the 3D Additively Weighted Voronoi diagram), namely the EdgeConflict predicate: given five sites $S_i, S_j,S_k,S_l,S_m$ ... More
The Severi problem for abelian surfaces in the primitive caseNov 03 2018We prove that the irreducible components of primitive class Severi varieties of general abelian surfaces are completely determined by the maximal factorization through an isogeny of the maps from the normalized curves.
Quasi-random number generators for multivariate distributions based on generative neural networksNov 01 2018Generative moment matching networks are introduced as quasi-random number generators for multivariate distributions. So far, quasi-random number generators for non-uniform multivariate distributions require a careful design, often need to exploit specific ... More
The Affordable Care Act and the IRS Iterative Fixed Point ProcedureOct 31 2018We model the quantities appearing in Internal Revenue Service (IRS) tax guidance for calculating the health insurance premium tax credit created by the Patient Protection and Affordable Care Act, also called Obamacare. We ask the question of whether there ... More
Understanding Deep Neural Networks Using Topological Data AnalysisOct 31 2018Deep neural networks (DNN) are black box algorithms. They are trained using a gradient descent back propagation technique which trains weights in each layer for the sole goal of minimizing training error. Hence, the resulting weights cannot be directly ... More
On the linear static output feedback problem: the annihilating polynomial approachOct 27 2018Oct 30 2018One of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback. We are given a linear dynamical system defined through \begin{align*} \mydot{w} &= Aw + Bu ... More
Vertex connectivity of the power graph of a finite cyclic group IIOct 25 2018The power graph $\mathcal{P}(G)$ of a given finite group $G$ is the simple undirected graph whose vertices are the elements of $G$, in which two distinct vertices are adjacent if and only if one of them can be obtained as an integral power of the other. ... More
Fixing Match-FixingOct 23 2018Nov 13 2018In the soccer World Cup, at the group stage, before the knock-out stage, games whose outcome has no impact for qualification are played with little enthusiasm. If a team is already qualified when playing its last game, different factors come into play ... More
Reduced Basis Greedy Selection Using Random Training SetsOct 22 2018Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems has been theoretically confirmed in \cite{BCDDPW,DPW}, where it is shown ... More
Markov Operators, Transport Plans and TransfunctionsOct 19 2018A transfunction is a function which maps between sets of finite measures on measurable spaces. In this paper we characterize transfunctions that correspond to Markov operators and to transport plans. A single transfunction of this type will contain the ... More
Compatibility and attainability of matrices of correlation-based measures of concordanceOct 16 2018Necessary and sufficient conditions are derived under which concordance measures arise from correlations of transformed ranks of random variables. Compatibility and attainability of square matrices with entries given by such measures are studied, that ... More
Effective global generation on varieties with numerically trivial canonical classOct 16 2018Dec 16 2018We prove a Fujita-type theorem for varieties with numerically trivial canonical bundle. We deduce our result via a combination of algebraic and analytic methods, including the Kobayashi--Hitchin correspondence and positivity of direct image bundles. As ... More
Non-binary treebased unrooted phylogenetic networks and their relations to binary and rooted onesOct 16 2018Oct 17 2018Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of non-treelike evolutionary events such as hybridization. Typically, such networks have been analyzed based on their `level', i.e. based on the complexity ... More
Non vanishing of theta functions and sets of small multiplicative energyOct 12 2018Let $\chi$ range over the $(p-1)/2$ even Dirichlet characters modulo a prime $p$ and denote by $\theta (x,\chi)$ the associated theta series. The asymptotic behaviour of the second and fourth moments proved by Louboutin and the author implies that there ... More
On Isoclasses of Maximal Subalgebras Determined by AutomorphismsOct 01 2018Let $k$ be an algebraically-closed field, and let $B = kQ/I$ be a basic, finite-dimensional associative $k$-algebra with $n := \dim_kB < \infty$. Previous work shows that the collection of maximal subalgebras of $B$ carries the structure of a projective ... More
Convergence and perturbation theory for an infinite-dimensional Metropolis-Hastings algorithm with self-decomposable priorsSep 30 2018We study a Metropolis-Hastings algorithm for target measures that are absolutely continuous with respect to a large class of prior measures on Banach spaces. The algorithm is shown to have a spectral gap in a Wasserstein-like semimetric weighted by a ... More
Chip-Firing and Fractional BasesSep 25 2018We study a particular chip-firing process on an infinite path graph. At any time when there are at least $a+b$ chips at a vertex, $a$ chips fire to the left and $b$ chips fire to the right. We describe the final state of this process when we start with ... More
Christoffel function on planar domains with piecewise smooth boundarySep 24 2018Feb 18 2019We compute up to a constant factor the Christoffel function on planar domains with boundary consisting of finitely many $C^2$ curves such that each corner point of the boundary has interior angle strictly between $0$ and $\pi$. The resulting formula uses ... More
Machine Learning for semi linear PDEsSep 20 2018Dec 10 2018Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by using ... More
Percolation on Homology Generators in Codimension OneSep 20 2018This paper introduces a new percolation model motivated from polymer materials. The mathematical model is defined over a random cubical set in the $d$-dimensional space $\mathbb{R}^d$ and focuses on generations and percolations of $(d-1)$-dimensional ... More
The Liouville theorem for $p$-harmonic functions and quasiminimizers with finite energySep 19 2018We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite $p$th power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global $p$-Poincar\'e ... More
Factorisation of Greedoid Polynomials of Rooted DigraphsSep 09 2018Gordon and McMahon defined a two-variable greedoid polynomial $ f(G;t,z) $ for any greedoid $ G $. They studied greedoid polynomials for greedoids associated with rooted graphs and rooted digraphs. They proved that greedoid polynomials of rooted digraphs ... More
Heat Flow with Dirichlet Boundary Conditions via Optimal Transport and Gluing of Metric Measure SpacesSep 04 2018We introduce the transportation-annihilation distance $W_p^\sharp$ between subprobabilities and derive contraction estimates with respect to this distance for the heat flow with homogeneous Dirichlet boundary conditions on an open set in a metric measure ... More
The continuity of Darboux injections between manifoldsSep 02 2018Sep 12 2018We prove that an injective map $f:X\to Y$ between connected metrizable spaces $X,Y$ is continuous if for every connected subset $C\subset X$ the image $f(C)$ is connected and one of the following conditions is satisfied: (1) $Y$ is a 1-manifold and $X$ ... More
A construction of graphs with positive Ricci curvatureSep 01 2018Oct 28 2018Two complete graphs are connected by adding some edges. The obtained graph is called the gluing graph. The more we add edges, the larger the Ricci curvature on it becomes. We calculate the Ricci curvature of each edge on the gluing graph and obtain the ... More
Expected Number of Vertices of a Hypercube SliceAug 28 2018Given a random k-dimensional cross-section of a hypercube, what is its expected number of vertices? We show that, for a suitable distribution of random slices, the answer is $2^k$, independent of the dimension of the hypercube.
The structure of random automorphisms of the rational numbersAug 16 2018In order to understand the structure of the "typical" element of an automorphism group, one has to study how large the conjugacy classes of the group are. For the case when typical is meant in the sense of Baire category, Truss proved that there is a ... More
Discrete geometry for electoral geographyAug 15 2018We discuss the "compactness," or shape analysis, of electoral districts, focusing on some of the most popular definitions in the political science literature, which compare area to perimeter. We identify four problems that are present in these and all ... More
SINH-acceleration: efficient evaluation of probability distributions, option pricing, and Monte-Carlo simulationsAug 15 2018Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around $\mathbb{R}\subset \mathbb{C}$. The Fourier transform techniques reduces calculation of probability ... More
Differentiability of the argmin function and a minimum principle for semiconcave subsolutionsAug 13 2018Suppose $f(x,y) + \frac{\kappa}{2} \|x\|^2 - \frac{\sigma}{2}\|y\|^2$ is convex where $\sigma>0$, and the argmin function $\gamma(x) = \{ \gamma : \inf_y f(x,y) = f(x,\gamma)\}$ exists and is single valued. We will prove $\gamma$ is differentiable almost ... More
Convex Union Representability and Convex CodesAug 12 2018We introduce and investigate $d$-convex union representable complexes: the complexes that arise as the nerve of a finite collection of convex open sets in $\mathbb R^d$ whose union is also convex. Chen, Frick, and Shiu recently proved that such complexes ... More
On skew-symmetric algebroidsAug 09 2018Skew symmetric algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessary null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural extension ... More
A network theoretic study of potential movement and spread of Lantana camara in Rajaji Tiger Reserve, IndiaAug 08 2018Ecosystems are often under threat by invasive species which, through their invasion dynamics, create ecological networks to spread. We present preliminary results using a technique of GIS coupled with complex network analysis to model the movement and ... More
Theory of supports for linear codes endowed with the sum-rank metricAug 07 2018Jan 30 2019The sum-rank metric naturally extends both the Hamming and rank metrics in coding theory over fields. It measures the error-correcting capability of codes in multishot matrix-multiplicative channels (e.g. linear network coding or the discrete memoryless ... More
Idempotent Analysis, Tropical Convexity and Reduced DivisorsAug 06 2018Dec 01 2018We investigate a canonical extension of a conventional combinatorial notion of reduced divisors to a notion of tropical projections, which can be defined as the unique minimizers of the so-called $B$-pseudonorms with respect to compact tropical convex ... More
Displacement convexity of Boltzmann's entropy characterizes the strong energy condition from general relativityAug 04 2018Oct 06 2018On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation. These notions ... More
Large girth approximate Steiner triple systemsAug 03 2018In 1973 Erdos asked whether there are n-vertex partial Steiner triple systems with arbitrary high girth and quadratically many triples. (Here girth is defined as the smallest integer g \ge 4 for which some g-element vertex-set contains at least g-2 triples.) ... More
Affine geometric spaces in tangent categoriesJul 25 2018Jul 27 2018We continue the program of structural differential geometry that begins with the notion of a tangent category, an axiomatization of structural aspects of the tangent functor on the category of smooth manifolds. In classical geometry, having an affine ... More
The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg propertyJul 21 2018Prime end boundaries $\partial_P\Omega$ of domains $\Omega$ are studied in the setting of complete doubling metric measure spaces supporting a $p$-Poincar\'e inequality. Notions of rectifiably (in)accessible- and (in)finitely far away prime ends are introduced ... More
On graphs with 2 trivial distance idealsJul 20 2018Jul 24 2018Distance ideals generalize the Smith normal form of the distance matrix of a graph. The family of graphs with 2 trivial distance ideals contains the family of graphs whose distance matrix has at most 2 invariant factors equal to 1. Here we give an infinite ... More
On some special classes of contact $B_0$-VPG graphsJul 19 2018A graph $G$ is a $B_0$-VPG graph if one can associate a path on a rectangular grid with each vertex such that two vertices are adjacent if and only if the corresponding paths intersect at at least one grid-point. A graph $G$ is a contact $B_0$-VPG graph ... More
A Fixed-Parameter Linear-Time Algorithm to Compute Principal Typings of Planar Flow NetworksJul 18 2018We present an alternative and simpler method for computing principal typings of flow networks. When limited to planar flow networks, the method can be made to run in fixed-parameter linear-time -- where the parameter not to be exceeded is what is called ... More
Galoisian and Qualitative Approaches to Linear Polyanin-Zaitsev Vector FieldsJul 13 2018Sep 26 2018The analysis of dynamical systems has been a topic of great interest for researches mathematical sciences for a long times. The implementation of several devices and tools have been useful in the finding of solutions as well to describe common behaviors ... More
A Fixed-Parameter Linear-Time Algorithm for Maximum Flow in Planar Flow NetworksJul 11 2018We pull together previously established graph-theoretical results to produce the algorithm in the paper's title. The glue are three easy elementary lemmas.
Algebraic and qualitative remarks about the family $yy'= (α x^{m+k-1} + βx^{m-k-1})y + γx^{2m-2k-1}$Jul 10 2018Sep 26 2018The aim of this paper is the analysis, from algebraic and qualitative point of view, of the 5-parametric family of differential equations \begin{equation*}\label{folpz} yy'=(\alpha x^{m+k-1}+\beta x^{m-k-1})y+\gamma x^{2m-2k-1}, \quad y'=\frac{dy}{dx} ... More
Efficient Reassembling of Three-Regular Planar GraphsJul 10 2018A reassembling of a simple graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. There are several equivalent definitions of graph reassembling; in this report we use a definition which makes it closest to the ... More
Generic torus orbit closures in Schubert varietiesJul 09 2018Jul 30 2018The closure of a generic torus orbit in the flag variety $G/B$ of type $A_{n-1}$ is known to be a permutohedral variety and well studied. In this paper we introduce the notion of a generic torus orbit in the Schubert variety $X_w$ $(w\in \mathfrak{S}_n)$ ... More
Multi-kernel unmixing and super-resolution using the Modified Matrix Pencil methodJul 08 2018Oct 18 2018Consider $L$ groups of point sources or spike trains, with the $l^{\text{th}}$ group represented by $x_l(t)$. For a function $g:\mathbb{R} \rightarrow \mathbb{R}$, let $g_l(t) = g(t/\mu_l)$ denote a point spread function with scale $\mu_l > 0$, and with ... More
Characterization theorems for the spaces of derivations of evolution algebras associated to graphsJul 06 2018Nov 03 2018It is well-known that the space of derivations of $n$-dimensional evolution algebras with non-singular matrices is zero. On the other hand, the space of derivations of evolution algebras with matrices of rank $n-1$ has also been completely described in ... More
Cheeger inequalities for graph limitsJul 06 2018Nov 12 2018We introduce notions of Cheeger constants for graphons and graphings. We prove Cheeger and Buser inequalities for these. On the way we prove co-area formulae for graphons and graphings.
Rule Algebras for Adhesive CategoriesJul 02 2018Feb 04 2019We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative in a natural sense. Notably, our results ... More
Eigenvectors of Laplacian or signless Laplacian of Hypergraphs Associated with Zero EigenvalueJul 02 2018Jan 23 2019Let $G$ be a connected $m$-uniform hypergraph. In this paper we mainly consider the eigenvectors of the Laplacian or signless Laplacian tensor of $G$ associated with zero eigenvalue, called the first Laplacian or signless Laplacian eigenvectors of $G$. ... More
On the integrability of strongly regular graphsJun 29 2018Koolen et al. showed that if a connected graph with smallest eigenvalue at least $-3$ has large minimal valency, then it is $2$-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.