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Population Biology and Criticality : From Critical Birth-Death Processes to Self-Organized Criticality in Mutation Pathogen Systems.
The present book describes novel theories of mutation pathogen systems showing critical fluctuations, as a paradigmatic example of an application of the mathematics of critical phenomena to the life sciences. It will enable the reader to understand the implications and future impact of these finding...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific,
2010.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Contents; Chapter 1 From Deterministic to Stochastic Dynamics; 1.1 Basic Probability Theory: The Tool Box; 1.2 Stochastic Description of a Deterministic System: The Ulam Map; 1.3 A Fully Stochastic Dynamic System: The AR(1)-Process; 1.4 From Perron-Frobenius to Master Equation; 1.5 A First Example of a Master Equation: The Linear Infection Model; 1.5.1 Solving the first example of a master equation; 1.5.2 Solution of the linear infection model; 1.5.3 Mean value and its dynamics; 1.5.4 Mean dynamics; 1.6 The Birth and Death Process, a Non-Linear Stochastic System.
- 1.7 Solution of the Birth-Death ODE Shows Criticality1.7.1 Numerical integration shows power law at criticality; 1.7.2 Temporal correlation length diverges at criticality; Chapter 2 Spatial Stochastic Birth-Death Process or SIS-Epidemics; 2.1 The Spatial Master Equation; 2.1.1 A first inspection of the spatial birth-death process; 2.2 Clusters and their Dynamics; 2.2.1 Time evolution of marginals and local expectations; 2.3 Moment Equations; 2.3.1 Mean field behavior; 2.3.2 Pair approximation; 2.4 The SIS Dynamics under Pair Approximation; 2.5 Conclusions and Further Reading.
- Chapter 3 Criticality in Equilibrium Systems3.1 The Glauber Model: Stochastic Dynamics for the Ising Model; 3.1.1 A first glance at the dynamic Ising model; 3.2 The Ising Model, a Paradigm for Equilibrium Phase Transitions; 3.2.1 Distribution of magnetization and Gibbs free energy; 3.3 Equilibrium Distribution around Criticality; 3.3.1 Distribution of magnetization; 3.3.2 External magnetic field; 3.3.3 The maximum of the total magnetization distribution; 3.3.3.1 Approximation with Lagrange polynomials; 3.3.3.2 The maximum magnetization with changing parameters.
- 4.1 A Model with Partial Immunization: SIRI4.2 Local Quantities; 4.3 Dynamics Equations for Global Pairs; 4.3.1 The SIRI dynamics under pair approximation; 4.3.2 Balance equations for means and pairs; 4.4 Mean Field Model: SIRI with Reintroduced Susceptibles; 4.4.1 Pair dynamics for the SIRI model; 4.5 Fruitful Transfer between Equilibrium and Non-Equilibrium Systems; Chapter 5 Renormalization and Series Expansion: Techniques to Study Criticality; 5.1 Introduction; 5.2 Real Space Renormalization in One-Dimensional Lattice Gas; 5.3 Directed Percolation and Path Integrals.