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We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps,…
Properties of systems with majority voting rules have been exhaustingly studied. In this work we focus on the randomized case - where the system is initialized by randomized initial set of seeds. Our main aim is to give an asymptotic…
We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicability that allow, among others, to replace in a canonical way…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case…
This paper investigates the consensus problem in almost sure sense for uncertain multi-agent systems with noises and fixed topology. By combining the tools of stochastic analysis, algebraic graph theory, and matrix theory, we analyze the…
We propose monotone comparative statics results for maximizers of submodular functions, as opposed to maximizers of supermodular functions as in the classical theory put forth by Veinott, Topkis, Milgrom, and Shannon among others. We…
An n dimensional monomial dynamical system over a finite field K is a nonlinear deterministic time discrete dynamical system with the property that each of the n component functions is a monic nonzero monomial function in n variables. In…
Designing a multi-layer optical system with designated optical characteristics is an inverse design problem in which the resulting design is determined by several discrete and continuous parameters. In particular, we consider three design…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
Using monotonicity theory we investigate the continuous dependence on parameters for the discrete BVPs which can be written in a form of a nonlinear system.
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R^d and in some cases provide a full characterisation…
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…
In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. Firstly, a vector matroid is defined over F(z). Secondly, the full rank conditions of [sI-A|B] are derived in terms…
In this paper, we propose a distributed computing approach to solving large-scale robust stability problems on the simplex. Our approach is to formulate the robust stability problem as an optimization problem with polynomial variables and…
An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit…
In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the…
The aim of this paper is to discuss a combinatorial characterisation of stability for toric vector bundles (or equivariant reflexive sheaves) in the terms of their parliaments of polytopes, a generalization of moment polytopes for toric…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…