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Ricci-flat cubic graphs with girth fiveFeb 08 2018We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We use the definition of Ricci curvature on graphs given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Anal., 2009. A graph ... More
Real zeros of random analytic functions associated with geometries of constant curvatureFeb 07 2018Feb 08 2018Let $\xi_0, \xi_1, \dots$ be i.i.d. random variables with zero mean and unit variance. We study the following four families of random analytic functions: $\sum_{k=0}^n \sqrt{\binom nk} \xi_k z^k$ (spherical polynomials), $\sum_{k=0}^\infty \sqrt{\frac{n^k}{k!}} ... More
Total perfect codes in zero-divisor graphsFeb 01 2018Let R be a commutative ring with unity not equal to zero and let G = (V, E) be a simple, undirected graph. A total perfect code denoted by C(G), in G is a subset C(G) of V (G) such that cardinality of the set {N (v) \cap C(G)} is 1, for all v \in V (G), ... 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
Remarks on GraphonsJan 14 2018The notion of the graphon (a symmetric measurable fuzzy set of $[0, 1]^2$) was introduced by L. Lov\'asz and B. Szegedy in 2006 to describe limit objects of convergent sequences of dense graphs. In their investigation the integral \[t(F,W)=\int _{[0, ... More
Frobenius Theorem in Banach SpaceJan 04 2018Let $\Lambda$ be an open set in Banach space $E$, $M(x)$ for $x\in \Lambda$ a subspace in $E$, and $\mathcal F=\{M(x)\}_{x\in\Lambda}$. In this paper, we introduce the concept of the co-final set $J(x_0,E_*)$ for $\mathcal F$ at $x_0\in \Lambda$, then ... More
Lie algebra representations and rigged Hilbert spaces: the SO(2) caseNov 10 2017It is well known that related with the irreducible representations of the Lie group $SO(2)$ we find a discrete basis as well a continuous one. In this paper we revisited this situation under the light of Rigged Hilbert spaces, which are the suitable framework ... More
Critical ideals, minimum rank and zero forcing numberOct 10 2017There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is defined as the largest $i$ such that the $i$-th critical ideal is trivial. ... More
Hamilton decompositions of one-ended Cayley graphsSep 27 2017We prove that any one-ended, locally finite Cayley graph with non-torsion generators admits a decomposition into edge-disjoint Hamiltonian (i.e. spanning) double-rays. In particular, the $n$-dimensional grid $\mathbb{Z}^n$ admits a decomposition into ... More
A novel algorithmic approach to Bayesian Logic RegressionMay 22 2017Logic regression was developed more than a decade ago as a tool to construct predictors from Boolean combinations of binary covariates. It has been mainly used to model epistatic effects in genetic association studies, which is very appealing due to the ... More
A Remark on the Localization formulas about two Killing vector fieldsApr 28 2017In this article, we will discuss a localization formulas of equivariant cohomology about two Killing vector fields on the set of zero points ${\rm{Zero}}(X_{M}-\sqrt{-1}Y_{M})=\{x\in M \mid |Y_{M}(x)|=|X_{M}(x)|=0 \}.$ As application, we use it to get ... More
Some remarks on protolocalizations and protoadditive reflectionsFeb 28 2017Oct 29 2017We investigate additional properties of protolocalizations, introduced and studied by F. Borceux, M. M. Clementino, M. Gran, and L. Sousa, and of protoadditive reflections, introduced and studied by T. Everaert and M. Gran. Among other things we show ... More
Full diversity sets of unitary matrices from orthogonal sets of idempotentsDec 07 2016Orthogonal sets of idempotents are used to design sets of unitary matrices, known as constellations, such that the modulus of the determinant of the difference of any two distinct elements is greater than $0$. It is shown that unitary matrices in general ... More
Relative generalized matrix weights of matrix codes for universal security on wire-tap networksDec 06 2016Universal security over a network with linear network coding has been intensively studied. However, previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network. In this work, we introduce new ... More
Cospan construction of the graph category of Borisov and ManinNov 30 2016It is shown how the graph category of Borisov and Manin can be constructed from (a variant of) the graph category of Joyal and Kock, essentially by reversing the generic morphisms. More precisely, the morphisms in the Borisov-Manin category are exhibited ... More
Nonlinear WavesNov 30 2016A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary flow of a compressible ... More
Comparing entropy rates on finite and infinite rooted trees with length functionsNov 22 2016We consider stochastic processes with (or without) memory whose evolution is encoded by a finite or infinite rooted tree. The main goal is to compare the entropy rates of a given base process and a second one, to be considered as a perturbation of the ... More
Actions of trees on semigroups, and an infinitary Gowers--Hales--Jewett Ramsey theoremNov 19 2016We introduce the notion of (Ramsey) action of a tree on a (filtered) semigroup. We then prove in this setting a general result providing a common generalization of the infinitary Gowers Ramsey theorem for multiple tetris operations, the infinitary Hales--Jewett ... More
Some elementary observations on Narayana polynomials and related topics II: q-Narayana polynomialsNov 16 2016Nov 30 2016We show that q-Catalan numbers, q- central binomial coefficients and q- Narayana polynomials are moments of q-analogues of Fibonacci and Lucas polynomials and related polynomials.
Some elementary observations on Narayana polynomials and related topics II: q-Narayana polynomialsNov 16 2016We show that q-Catalan numbers, q- central binomial coefficients and q- Narayana polynomials are moments of q-analogues of Fibonacci and Lucas polynomials and related polynomials.
Some elementary observations on Narayana polynomials and related topics II: q-Narayana polynomialsNov 16 2016Nov 25 2016We show that q-Catalan numbers, q- central binomial coefficients and q- Narayana polynomials are moments of q-analogues of Fibonacci and Lucas polynomials and related polynomials.
Multinomial VaR Backtests: A simple implicit approach to backtesting expected shortfallNov 15 2016Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that backtesting of expected ... More
Combinatorics of cyclic shifts in sylvester monoidsNov 13 2016The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. In the cyclic shift graph of the sylvester monoid (the monoid of binary search trees) of rank $n$, connected ... More
Extracting information from random data. Applications of laws of large numbers in technical sciences and statisticsNov 10 2016We formulate conditions for convergence of Laws of Large Numbers and show its links with of parts mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of Law of Large Numbers such as Stochastic ... More
Algèbre commutative Meéthodes constructivesNov 08 2016This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the constructive point ... More
Sharp isoperimetric inequalities for small volumes in complete noncompact Riemannian manifolds of bounded geometry involving the scalar curvatureNov 05 2016We provide an isoperimetric comparison theorem for small volumes in an $n$-dimensional Riemannian manifold $(M^n,g)$ with strong bounded geometry, as in Definition $2.3$, involving the scalar curvature function. Namely in strong bounded geometry, if the ... More
Sharp isoperimetric inequalities for small volumes in complete noncompact Riemannian manifolds of bounded geometry involving the scalar curvatureNov 05 2016Nov 11 2016We provide an isoperimetric comparison theorem for small volumes in an $n$-dimensional Riemannian manifold $(M^n,g)$ with strong bounded geometry, as in Definition $2.3$, involving the scalar curvature function. Namely in strong bounded geometry, if the ... More
Classifying unavoidable Tverberg partitionsNov 03 2016Dec 01 2016Let $T(d,r) = (r-1)(d+1)+1$ be the parameter in Tverberg's theorem. We say that a partition $\mathcal I$ of $\{1,2,\ldots,T(d,r)\}$ into $r$ parts "occurs" in an ordered point sequence $P$ if $P$ contains a subsequence $P'$ of $T(d,r)$ points such that ... More
Classifying unavoidable Tverberg partitionsNov 03 2016Let $T(d,r) = (r-1)(d+1)+1$ be the parameter in Tverberg's theorem. We say that a partition $\mathcal I$ of $\{1,2,\ldots,T(d,r)\}$ into $r$ parts "occurs" in an ordered point sequence $P$ if $P$ contains a subsequence $P'$ of $T(d,r)$ points such that ... More
Plabic graphs and zonotopal tilingsNov 02 2016We say that two sets $S,T\subset\{1,2,\dots,n\}$ are chord separated if there does not exist a cyclically ordered quadruple $a,b,c,d$ of integers satisfying $a,c\in S-T$ and $b,d\in T-S$. This is a weaker version of Leclerc and Zelevinsky's weak separation. ... More
Two statements on path systems related to quantum minorsNov 01 2016In ArXiv:1604.00338[math.QA] we gave a complete combinatorial characterization of homogeneous quadratic identities for minors of quantum matrices. It was obtained as a consequence of results on minors of matrices of a special sort, the so-called path ... More
Kernel Bandwidth Selection for SVDD: Peak Criterion Approach for Large DataOct 31 2016Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD formulation allows ... More
Truncation In Unions of Hahn Fields with a DerivationOct 31 2016Truncation in Generalized Series fields is a robust notion, in the sense that it is preserved under various algebraic and some transcendental extensions. In this paper, we study conditions that ensure that a truncation closed set extends naturally to ... More
Forward sensitivity analysis for contracting stochastic systemsOct 29 2016In this work we investigate gradient estimation for a class of contracting stochastic systems on a continuous state space. We find conditions on the one-step transitions, namely differentiability and contraction in a Wasserstein distance, that guarantee ... More
Defining the q-analogue of a matroidOct 28 2016This paper defines the q-analogue of a matroid and establishes several properties like duality, restriction and contraction. We discuss possible ways to define a q-matroid, and why they are (not) cryptomorphic. Also, we explain the motivation for studying ... More
Data-driven time parallelism via forecastingOct 28 2016This work proposes a data-driven method for enabling the efficient, stable time-parallel numerical solution of systems of ordinary differential equations (ODEs). The method assumes that low-dimensional bases that accurately capture the time evolution ... More
Minimal unsatisfiability and deficiency: recent developmentsOct 26 2016Starting with Aharoni and Linial in 1986, the deficiency delta(F) = c(F) - n(F) >= 1 for minimally unsatisfiable clause-sets F, the difference of the number of clauses and the number of variables, is playing an important role in investigations into the ... More
Hopf Monoids in semi-additive VarietiesOct 26 2016We study Hopf monoids in entropic semi-additive varieties (equivalently, entropic J\'onsson-Tarski varieties and categories of semimodules over a commutative semiring, respectively) with an emphasis on adjunctions related to the enveloping monoid functor ... More
Two-phase flow with surfactants: Diffuse interface models and their analysisOct 26 2016New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a particular diffuse ... More
Counting Zeros of Cosine Polynomials: On a Problem of LittlewoodOct 24 2016We show that if $A$ is a finite set of non-negative integers then the number of zeros of the function \[ f_A(\theta) = \sum_{a \in A } \cos(a\theta) , \] in $[0,2\pi]$, is at least $(\log \log \log |A|)^{1/2-\varepsilon}$. This gives the first unconditional ... More
The first Cheeger constant of a simplexOct 23 2016The coboundary expansion generalizes the classical graph expansion to the case of the general simplicial complexes, and allows the definition of the higher-dimensional Cheeger constants $h_k(X)$ for an arbitrary simplicial complex $X$, and any $k\geq ... More
Error estimates with explicit constants for the Sinc approximation over infinite intervalsOct 21 2016The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation still works accurately when combined with a ... More
Parameter spaces for algebraic equivalenceOct 20 2016A cycle is algebraically trivial if it can be exhibited as the difference of two fibers in a family of cycles parameterized by a smooth scheme. Over an algebraically closed field, it is a result of Weil that it suffices to consider families of cycles ... More
Lexicographically optimal integer points: structural properties and complexityOct 20 2016We study lexicographically maximal and minimal, under different permutations, integer points in a compact convex set $X$. First, we give a necessary and sufficient condition for a knapsack polytope to be equivalent to a lex-ordered set. Then we show that ... More
Lexicographically optimal integer points: structural properties and complexityOct 20 2016Nov 04 2016We study lexicographically maximal and minimal, under different permutations, integer points in a compact convex set $X$. First, we give a necessary and sufficient condition for a knapsack polytope to be equivalent to a lex-ordered set. Then we show that ... More
High codegree subgraphs in weakly quasirandom 3-graphsOct 20 2016We show that we can extract large subgraphs with high minimum codegree from sequences of weakly quasirandom $3$-graphs, for a particular notion of weakly quasirandom studied by Reiher, R\"odl and Schacht. In particular for any family of nonempty $3$-graphs ... More
Universality of the nodal length of bivariate random trigonometric polynomialsOct 17 2016We consider random trigonometric polynomials of the form \[ f_n(x,y)=\sum_{1\le k,l \le n} a_{k,l} \cos(kx) \cos(ly), \] where the entries $(a_{k,l})_{k,l\ge 1}$ are i.i.d. random variables that are centered with unit variance. We investigate the length ... More
An ideal-based cozero-divisor graph of a commutative ringOct 17 2016Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we introduce the cozero-divisor graph $\acute{\Gamma}_I(R)$ of $R$ and obtain some related results.
Constraint Control of Nonholonomic Mechanical SystemsOct 08 2016Nov 30 2016We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body ... More
Constraint Control of Nonholonomic Mechanical SystemsOct 08 2016Dec 07 2016We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body ... More
Incidences with curves and surfaces in three dimensions, with applications to distinct and repeated distancesOct 05 2016We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a variety of tools ... More
Sidon Sets of Fixed Cardinality and Lattice-Packings of SimplicesOct 05 2016Oct 08 2016A $ B_h $ set (or Sidon set of order $ h $) in an Abelian group $ G $ is any subset $ \{b_0, b_1, \ldots,b_{n}\} \subset G $ with the property that all the sums $ b_{i_1} + \cdots + b_{i_h} $ are different up to the order of the summands. Let $ \phi(h,n) ... More
Improved Bounds on Sidon Sets via Lattice Packings of SimplicesOct 05 2016Nov 17 2016A $ B_h $ set (or Sidon set of order $ h $) in an Abelian group $ G $ is any subset $ \{b_0, b_1, \ldots,b_{n}\} \subset G $ with the property that all the sums $ b_{i_1} + \cdots + b_{i_h} $ are different up to the order of the summands. Let $ \phi(h,n) ... More
Optimal line packings from association schemesSep 30 2016We provide a general recipe that leverages association schemes to construct optimal packings of lines through the origin. We apply this recipe to association schemes corresponding to general Gelfand pairs before focusing on the special case of group schemes. ... More
Polish spaces of causal curvesSep 29 2016We propose and study a new approach to the topologization of spaces of (possibly not all) future-directed causal curves in a stably causal spacetime. It relies on parametrizing the curves "in accordance" with a chosen time function. Thus obtained topological ... More
Singular elliptic equation involving the GJMS operator on the standard unit sphereSep 27 2016Given a Riemannian compact manifold (M,g) of dimension n>4, we have proven in [1] under some conditions that the equation : Pg(u) = Bu +Au2+Cu (1) where Pg is the GJMS-operator, n = dim(M) > 2k, A, B and C are smooth positive functions on M, p > 1 and ... More
Inductive limits of finite dimensional hermitian symmetric spaces and K-theorySep 22 2016K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite dimensional hermitian ... More
Pre-adjunctions and the Ramsey propertySep 22 2016Oct 17 2016Showing that the Ramsey property holds for a class of finite structures can be an extremely challenging task and a slew of sophisticated methods have been proposed in literature. In this paper we propose a new strategy to show that a class of structures ... More
Pre-adjunctions and the Ramsey propertySep 22 2016Showing that the Ramsey property holds for a class of finite structures can be an extremely challenging task and a slew of sophisticated methods have been proposed in literature. In this paper we propose a new strategy to show that a class of structures ... More
Hankel-type determinants for some combinatorial sequencesSep 22 2016Sep 26 2016In this paper we confirm several conjectures of Z.-W. Sun on Hankel-type determinants for some combinatorial sequences including Franel numbers, Domb numbers and Ap\'ery numbers. For any nonnegative integer $n$, define \begin{gather*}f_n:=\sum_{k=0}^n\binom ... More
Rare event simulation via importance sampling for linear SPDE'sSep 14 2016The goal of this paper is to develop provably efficient importance sampling Monte Carlo methods for the estimation of rare events within the class of linear stochastic partial differential equations (SPDEs). We find that if a spectral gap of appropriate ... More
Newton flows for elliptic functions II Structural stability: Classification & RepresentationSep 05 2016In our previous paper we associated to each non-constant elliptic function $f$ on a torus $T$ a dynamical system, the elliptic Newton flow corresponding to $f$. We characterized the functions for which these flows are structurally stable and showed a ... More
Newton flows for elliptic functions I Structural stability: Characterization & GenericitySep 05 2016Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy between the rational ... More
The mechanical modes of a $2$-periodic triangulated surfaceSep 04 2016A recent "hidden symmetry" conjecture of B. Gin-ge Chen et al is resolved, concerning the dimension of the mechanical modes of a generic $2$-periodic triangulated surface $O$ in $R^3$ whose structure graph corresponds to a triangular tiling of $R^2$. ... More
The large sum graph related to comultiplication modulesSep 04 2016Let R be a commutative ring and M be an R-module. We define the large sum graph, denoted by \acute{G}(M), as a graph with the vertex set of non-large submodules of M and two distinct vertices are adjacent if and only if N + K is a non-large submodule ... More
Enumerating independent vertex sets in grid graphsSep 02 2016A set of vertices in a graph is called independent if no two vertices of the set are connected by an edge. In this paper we use the state matrix recursion algorithm, developed by Oh, to enumerate independent vertex sets in a grid graph and even further ... More
Sparse approximation of multilinear problems with applications to kernel-based methods in UQSep 01 2016We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations ... More
Sparse approximation of multilinear problems with applications to kernel-based methods in UQSep 01 2016Dec 02 2016We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations ... More
Extremal theory of locally sparse multigraphsAug 31 2016An $(n,s,q)$-graph is an $n$-vertex multigraph where every set of $s$ vertices spans at most $q$ edges. In this paper, we determine the maximum product of the edge multiplicities in $(n,s,q)$-graphs if the congruence class of $q$ modulo ${s\choose 2}$ ... More
(Co)associative $3$-ary (co)algebras and infinitesimal bialgebras: construction and main propertiesAug 29 2016Oct 04 2016The (co)associative, partially (co)associative and totally (co)associative $3$-ary (co) algebras and infinitesimal bialgebras are constructed and discussed. Their trimodules and matched pairs are defined and completely characterized. The main structural ... More
A multisymplectic manifold not covered by Darboux chartsAug 26 2016The Darboux theorem in symplectic geometry implies that any two points in a connected symplectic manifold have neighbourhoods symplectomorphic to each other. The impossibility of such a theorem in the more general multisymplectic framework appears to ... More
Homological combinatorics and extensions of the cd-indexAug 22 2016Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to comprehensible ... More
On Primes, Graphs and CohomologyAug 22 2016The counting function on the natural numbers defines a discrete Morse-Smale complex with a cohomology for which topological quantities like Morse indices, Betti numbers or counting functions for critical points of Morse index are explicitly given in number ... More
The configuration space of a robotic arm in a tunnelAug 16 2016We study the motion of a robotic arm inside a rectangular tunnel. We prove that the configuration space of all possible positions of the robot is a CAT(0) cubical complex. This allows us to use techniques from geometric group theory to find the optimal ... More
A Dynamic Uncertainty Principle for Jacobi OperatorsAug 15 2016We prove that a solution of the Schr\"odinger-type equation $\mathrm{i}\partial_t u= Hu$, where $H$ is a Jacobi operator with asymptotically constant coefficients, cannot decay too fast at two different times unless it is trivial.
Closeness Centralization Measure for Two-mode Data of Prescribed SizesAug 14 2016We confirm a conjecture by Everett, Sinclair, and Dankelmann~[Some Centrality results new and old, J. Math. Sociology 28 (2004), 215--227] regarding the problem of maximizing closeness centralization in two-mode data, where the number of data of each ... More
Tight framelets and fast framelet transforms on manifoldsAug 13 2016Tight framelets on a smooth and compact Riemannian manifold $\mathcal{M}$ provide a tool of multiresolution analysis for data from geosciences, astrophysics, medical sciences, etc. This work investigates the construction, characterizations, and applications ... More
On super integral groupsAug 09 2016A finite non-abelian group $G$ is called super integral if the spectrum, Laplacian spectrum and signless Laplacian spectrum of its commuting graph contain only integers. In this paper, we first compute various spectra of several families of finite non-abelian ... More
Mogami manifolds, nuclei, and 3D simplicial gravityAug 06 2016Mogami introduced in 1995 a large class of triangulated 3-dimensional pseudomanifolds, henceforth called "Mogami pseudomanifolds". He proved an exponential bound for the size of this class in terms of the number of tetrahedra. The question of whether ... More
Graphons and cut metric on sigma-finite measure spacesAug 05 2016Aug 16 2016Borgs, Chayes, Cohn and Holden (2016+) recently extended the definition of graphons from probability spaces to arbitrary $\sigma$-finite measure spaces, in order to study limits of sparse graphs. They also extended the definition of the cut metric, and ... More
A spectral theory for simply periodic solutions of the sinh-Gordon equationJul 29 2016In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral data is described ... More
On the roots of the node reliability polynomialJul 28 2016Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational nodes can all communicate ... More
Linear representations of convolutional codes over ringsJul 28 2016In this paper we extend the relation between convolutional codes and linear systems over finite fields to certain commutative rings through first order representations . We introduce the definition of rings with representations as those for which these ... More
An extremal graph problem with a transcendental solutionJul 26 2016Aug 04 2016We prove that the number of multigraphs with vertex set $\{1, \ldots, n\}$ such that every four vertices span at most nine edges is $a^{n^2 + o(n^2)}$ where $a$ is transcendental (assuming Schanuel's conjecture from number theory). This is an easy consequence ... More
Classifying Poincaré Inequalities and the local geometry of RNP-Differentiability SpacesJul 25 2016We give a classification of doubling metric measure spaces admitting a $(1,p)$-Poincar\'e inequality for some $p$ in terms of connectivity and without reference to modulus estimates. Further we give a classification of spaces that are rectifiable with ... More
Classifying Poincaré Inequalities and the local geometry of RNP-Differentiability SpacesJul 25 2016Nov 02 2016We give a new condition on a metric measure space guaranteeing a $(1,p)$-Poincar\'e inequality for some $p$. This condition doesn't use a modulus of a curve family, is technically more flexible and allows for several applications. We also introduce an ... More
Powers of sums and their homological invariantsJul 25 2016Jul 27 2016Let $R$ and $S$ be standard graded algebras over a field $k$, and $I \subseteq R$ and $J \subseteq S$ homogeneous ideals. Denote by $P$ the sum of the extensions of $I$ and $J$ to $R\otimes_k S$. We investigate several important homological invariants ... More
Low growth equational complexityJul 25 2016The equational complexity function $\beta_\mathscr{V}:\mathbb{N}\to\mathbb{N}$ of an equational class of algebras $\mathscr{V}$ bounds the size of equation required to determine membership of $n$-element algebras in $\mathscr{V}$. Known examples of finitely ... More
Structure and enumeration theorems for hereditary properties in finite relational languagesJul 17 2016Jul 19 2016Given a finite relational language $\calL$, a hereditary $\calL$-property is a class of finite $\calL$-structures which is closed under isomorphism and model theoretic substructure. This notion encompasses many objects of study in extremal combinatorics, ... More
Finding binomials in polynomial idealsJul 07 2016We describe an algorithm which finds binomials in a given ideal $I\subset\mathbb{Q}[x_1,\dots,x_n]$ and in particular decides whether binomials exist in $I$ at all. We demonstrate with several examples that binomials in polynomial ideals can be well hidden. ... More
Unifying notions of generalized weights for universal security on wire-tap networksJul 05 2016Universal security over a network with linear network coding has been intensively studied. However, previous linear codes used for this purpose were linear over a larger field than that used on the network. In this work, we introduce new parameters (relative ... More
A Macroscopic Mathematical Model For Cell Migration Assays Using A Real-Time Cell AnalysisJul 05 2016Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This technology ... More
Maximal operators of exotic and non-exotic Laguerre and other semigroups associated with classical orthogonal expansionsJul 04 2016Classical settings of discrete and continuous orthogonal expansions, like Laguerre, Bessel and Jacobi, are associated with second order differential operators playing the role of the Laplacian. These depend on certain parameters of type that are usually ... More
Unique Measure for Time-Dependent Random Dynamical SystemsJun 29 2016Jun 30 2016This paper proves the uniqueness of measure for the two-dimensional Navier-Stokes equations under a random kick-force and a time-dependent deterministic force. By extending a result for uniqueness of measure for time-homogeneous Markov processes to the ... More
Canonical idempotents of multiplicity-free families of algebrasJun 28 2016Any multiplicity-free family of finite dimensional algebras has a canonical complete set of of pairwise orthogonal primitive idempotents in each level. We give various methods to compute these idempotents. In the case of symmetric group algebras over ... More
A criterion for Leavitt path algebras having invariant basis numberJun 15 2016In this paper, we give a matrix-theoretic criterion for the Leavitt path algebra of a finite graph has Invariant Basis Number. Consequently, we show that the Cohn path algebra of a finite graph has Invariant Basis Number, as well as provide some certain ... More
A new characterisation of groups amongst monoidsJun 08 2016We prove that a monoid $M$ is a group if and only if, in the category of monoids, all points over $M$ are strong. This sharpens and greatly simplifies a result of Montoli, Rodelo and Van der Linden which characterises groups amongst monoids as the protomodular ... More
On implementation of the minimal perimeter triangle enclosing a convex polygon algorithmJun 07 2016A high-level description of an algorithm which computes the minimum perimeter triangle enclosing a convex polygon in linear time exists in the literature. Besides that an implementation of the algorithm is given in the subsequent work. However, that implementation ... More
Tessellations derived from random geometric graphsJun 06 2016In this paper we consider a random partition of the plane into cells, the partition being based on the nodes and links of a {\it random planar geometric graph}. The resulting structure generalises the \emph{random \tes}\ hitherto studied in the literature. ... More
Bounds for approximating lower envelopes with polynomials of degree at most $d$Jun 04 2016Given a lower envelope in the form of an arbitrary sequence $u$, let $LSP(u, d)$ denote the maximum length of any subsequence of $u$ that can be realized as the lower envelope of a set of polynomials of degree at most $d$. Let $sp(m, d)$ denote the minimum ... More