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Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the…
We obtain new parameterized algorithms for the classical problem of determining whether a directed acyclic graph admits an upward planar drawing. Our results include a new fixed-parameter algorithm parameterized by the number of sources, an…
In this paper we show how we can transform quadratic systems into new quadratic systems after some kind of birational transformations, the quadratic plane Cremona maps. We afterwards apply these transformations to the families of quadratic…
This paper presents an algorithm to geometrically characterize inertial parameter identifiability for an articulated robot. The geometric approach tests identifiability across the infinite space of configurations using only a finite set of…
I describe a mathematical framework for the efficient processing of the very large sets of Feynman diagrams contributing to the scattering of many particles. I reexpress the established numerical methods for the recursive construction of…
We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree growth of these birational maps. We find the all the maps in…
In this paper, we consider a one-parameter family of degree $d\ge 2$ rational maps with an automorphism group containing the cyclic group of order $d$. We construct a polynomial whose roots correspond to parameter values for which the…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
This note will discuss the dynamics of iterated cubic maps from the real or complex line to itself, and will describe the geography of the parameter space for such maps. It is a rough survey with few precise statements or proofs, and…
Phase diagrams are an invaluable tool for material synthesis and provide information on the phases of the material at any given thermodynamic condition. Conventional phase diagram generation involves experimentation to provide an initial…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
We use methods from algebra and discrete geometry to study the irreducibility of the dispersion polynomial of a discrete periodic operator associated to a periodic graph after changing the period lattice. We provide numerous applications of…
We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
In order to illustrate the adaptation of traditional continuum numerical techniques to the study of complex network systems, we use the equation-free framework to analyze a dynamically evolving multigraph. This approach is based on coupling…