Evolution Algebras and their Applications / Edition 1

by Jianjun Paul Tian

Overview

Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, shastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.

Product Details

ISBN-13:	9783540742838
Publisher:	Springer Berlin Heidelberg
Publication date:	11/08/2007
Series:	Lecture Notes in Mathematics , #1921
Edition description:	2008
Pages:	133
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

Motivations.- Evolution Algebras.- Evolution Algebras and Markov Chains.- Evolution Algebras and Non-Mendelian Genetics.- Further Results and Research Topics.

Editorial Reviews

From the reviews:

"The book introduces a new class of nonassociative algebras, called evolution algebras, and discusses in detail many applications of evolution algebras in shastic processes and genetics. … The book under review is suitable both for graduate students and researchers with interest in the theoretical biology, genetics, Markov process, graph theory, and nonassociative algebras and their applications. The text contains a clear, detailed and self-contained exposition of evolution algebras."(Fouad Zitan, Zentralblatt MATH, Vol. 1136 (14), 2008)

From the Publisher