Evolution Algebras and their Applications

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Evolution Algebras and their Applications / Jianjun Paul Tian, F. Takens

資料種別:

電子ブック

出版情報:

SpringerLink Books - AutoHoldings
Springer Berlin Heidelberg, 2008

著者名:

ISBN:

9783540742838 [3540742832]
9783540742845 [3540742840]

書誌ID:

OB00493447

子書誌情報

フルテキスト

所蔵情報

書誌詳細

言語:

英語

目次情報:

Introduction / 1：

Motivations / 2：

Examples from Biology / 2.1：

Asexual propagation / 2.1.1：

Gametic algebras in asexual inheritance / 2.1.2：

The Wright-Fisher model / 2.1.3：

Examples from Physics / 2.2：

Particles moving in a discrete space / 2.2.1：

Flows in a discrete space (networks) / 2.2.2：

Feynman graphs / 2.2.3：

Examples from Topology / 2.3：

Motions of particles in a 3-manifold / 2.3.1：

Random walks on braids with negative probabilities / 2.3.2：

Examples from Probability Theory / 2.4：

Stochastic processes / 2.4.1：

Evolution Algebras / 3：

Definitions and Basic Properties / 3.1：

Departure point / 3.1.1：

Existence of unity elements / 3.1.2：

Basic definitions / 3.1.3：

Ideals of an evolution algebra / 3.1.4：

Quotients of an evolution algebra / 3.1.5：

Occurrence relations / 3.1.6：

Several interesting identities / 3.1.7：

Evolution Operators and Multiplication Algebras / 3.2：

Evolution operators / 3.2.1：

Changes of generator sets (Transformations of natural bases) / 3.2.2：

"Rigidness" of generator sets of an evolution algebra / 3.2.3：

The automorphism group of an evolution algebra / 3.2.4：

The multiplication algebra of an evolution algebra / 3.2.5：

The derived Lie algebra of an evolution algebra / 3.2.6：

The centroid of an evolution algebra / 3.2.7：

Nonassociative Banach Algebras / 3.3：

Definition of a norm over an evolution algebra / 3.3.1：

An evolution algebra as a Banach space / 3.3.2：

Periodicity and Algebraic Persistency / 3.4：

Periodicity of a generator in an evolution algebra / 3.4.1：

Algebraic persistency and algebraic transiency / 3.4.2：

Hierarchy of an Evolution Algebra / 3.5：

Periodicity of a simple evolution algebra / 3.5.1：

Semidirect-sum decomposition of an evolution algebra / 3.5.2：

Hierarchy of an evolution algebra / 3.5.3：

Reducibility of an evolution algebra / 3.5.4：

Evolution Algebras and Markov Chains / 4：

A Markov Chain and Its Evolution Algebra / 4.1：

Markov chains (discrete time) / 4.1.1：

The evolution algebra determined by a Markov chain / 4.1.2：

The Chapman-Kolmogorov equation / 4.1.3：

Concepts related to evolution operators / 4.1.4：

Basic algebraic properties of Markov chains / 4.1.5：

Algebraic Persistency and Probabilistic Persistency / 4.2：

Destination operator of evolution algebra M[subscript X] / 4.2.1：

On the loss of coefficients (probabilities) / 4.2.2：

On the conservation of coefficients (probabilities) / 4.2.3：

Certain interpretations / 4.2.4：

Algebraic periodicity and probabilistic periodicity / 4.2.5：

Spectrum Theory of Evolution Algebras / 4.3：

Invariance of a probability flow / 4.3.1：

Spectrum of a simple evolution algebra / 4.3.2：

Spectrum of an evolution algebra at zeroth level / 4.3.3：

Hierarchies of General Markov Chains and Beyond / 4.4：

Hierarchy of a general Markov chain / 4.4.1：

Structure at the 0th level in a hierarchy / 4.4.2：

1st structure of a hierarchy / 4.4.3：

kth structure of a hierarchy / 4.4.4：

Regular evolution algebras / 4.4.5：

Reduced structure of evolution algebra M[subscript X] / 4.4.6：

Examples and applications / 4.4.7：

Evolution Algebras and Non-Mendelian Genetics / 5：

History of General Genetic Algebras / 5.1：

Non-Mendelian Genetics and Its Algebraic Formulation / 5.2：

Some terms in population genetics / 5.2.1：

Mendelian vs. non-Mendelian genetics / 5.2.2：

Algebraic formulation of non-Mendelian genetics / 5.2.3：

Algebras of Organelle Population Genetics / 5.3：

Heteroplasmy and homoplasmy / 5.3.1：

Coexistence of triplasmy / 5.3.2：

Algebraic Structures of Asexual Progenies of Phytophthora infestans / 5.4：

Basic biology of Phytophthora infestans / 5.4.1：

Algebras of progenies of Phytophthora infestans / 5.4.2：

Further Results and Research Topics / 6：

Beginning of Evolution Algebras and Graph Theory / 6.1：

Further Research Topics / 6.2：

Evolution algebras and graph theory / 6.2.1：

Evolution algebras and group theory, knot theory / 6.2.2：

Evolution algebras and Ihara-Selberg zeta function / 6.2.3：

Continuous evolution algebras / 6.2.4：

Algebraic statistical physics models and applications / 6.2.5：

Evolution algebras and 3-manifolds / 6.2.6：

Evolution algebras and phylogenetic trees, coalescent theory / 6.2.7：

Background Literature / 6.3：

References

Index

Introduction / 1：

Motivations / 2：

Examples from Biology / 2.1：

Asexual propagation / 2.1.1：

Gametic algebras in asexual inheritance / 2.1.2：

The Wright-Fisher model / 2.1.3：

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