Related papers: Some large polyominoe's perimeter: a stochastic an…
We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a non-equilibrium…
Recent work of Brlek \textit{et al.} gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to analyze…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
Although Poisson-Voronoi diagrams have interesting mathematical properties, there is still much to discover about the geometrical properties of its grains. Through simulations, many authors were able to obtain numerical approximations of…
We obtain explicit formulas for the enumeration of labelled parallelogram polyominoes. These are the polyominoes that are bounded, above and below, by north-east lattice paths going from the origin to a point (k,n). The numbers from 1 and n…
For the perimeter length and the area of the convex hull of the first $n$ steps of a planar random walk, we study $n \to \infty$ mean and variance asymptotics and establish non-Gaussian distributional limits. Our results apply to random…
Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with…
In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
Polynomials commute under composition are referred to as commuting polynomials. In this paper, we study division properties for commuting polynomials with rational (and integer) coefficients. As a consequence, we show an algebraic…
The recently found hypergeometric multiple orthogonal polynomials on the step-line by Lima and Loureiro are shown to be random walk polynomials. It is proven that the corresponding Jacobi matrix and its transpose, which are nonnegative…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented…
The properties of semiflexible polymers tethered by one end to an impenetrable wall and exposed to oscillatory shear flow are investigated by mesoscale simulations. A polymer, confined in two dimensions, is described by a linear bead-spring…
A permutomino of size n is a polyomino determined by a pair of permutations of size n+1, such that they differ in each position. In this paper, after recalling some enumerative results about permutominoes, we give a first algorithm for the…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends…