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Full-Text Articles in Dynamical Systems
The Game Of Life On The Hyperbolic Plane, Yuncong Gu
The Game Of Life On The Hyperbolic Plane, Yuncong Gu
Mathematical Sciences Technical Reports (MSTR)
In this paper, we work on the Game of Life on the hyperbolic plane. We are interested in different tessellations on the hyperbolic plane and different Game of Life rules. First, we show the exponential growth of polygons on the pentagon tessellation. Moreover, we find that the Group of 3 can keep the boundary of a set not getting smaller. We generalize the existence of still lifes by computer simulations. Also, we will prove some propositions of still lifes and cycles. There exists a still life under rules B1, B2, and S3.
Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang
Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang
Mathematical Sciences Technical Reports (MSTR)
A cellular automaton is a type of mathematical system that models the behavior of a set of cells with discrete values in progressing time steps. The often complicated behaviors of cellular automata are studied in computer science, mathematics, biology, and other science related fields. Lattice gas cellular automata are used to simulate the movements of particles. This thesis aims to discuss the properties of lattice gas models, including periodicity and invertibility, and to examine their accuracy in reflecting the physics of particles in real life. Analysis of elementary cellular automata is presented to introduce the concept of cellular automata and …
Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez
Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez
Mathematical Sciences Technical Reports (MSTR)
In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic …