Stollenwerk, Nico
Population biology and criticality : from critical birth-death processes to self-organized criticality in mutation pathogen systems / Nico Stollenwerk, Vincent Jansen. -- London : Imperial College Press ; Singapore : Distributed by World Scientific, [2011]. -- ©2011. -- 1 online zdroj (xi, 224 stran) : ilustrace. -- Contents: 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. 1.6. The birth and death process, a non-linear stochastic system. 1.7. Solution of the birth-death ODE shows criticality -- 2. Spatial stochastic birth-death process or SIS-epidemics. 2.1. The spatial master equation. 2.2. Clusters and their dynamics. 2.3. Moment equations. 2.4. The SIS dynamics under pair approximation. 2.5. Conclusions and further reading -- 3. Criticality in equilibrium systems. 3.1. The Glauber model : Stochastic dynamics for the Ising model. 3.2. The Ising model, a paradigm for equilibrium phase transitions. 3.3. Equilibrium distribution around criticality. 3.4. Mean field theory and its exponents. 3.5. Critical exponents of the Ising model beyond mean field -- 4. Partial immunization models. 4.1. A model with partial immunization : SIRI. 4.2. Local quantities. 4.3. Dynamics equations for global pairs. 4.4. Mean field model : SIRI with reintroduced susceptibles. 4.5. Fruitful transfer between equilibrium and non-equilibrium systems -- 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. 5.4. Series expansions. 5.5. Generalization to the SIRI epidemic model -- 6. Criticality in measles under vaccination. 6.1. Measles around criticality. 6.2. The SIR model. 6.3. Stochastic simulations -- 7. Genetics and criticality. 7.1. Introduction. 7.2. Models in genetics. 7.3. Mean time until fixation -- 8. Evolution to criticality in meningococcal disease. 8.1. Accidental pathogens. 8.2. Modeling infection with accidental pathogens. 8.3. Evolution toward criticality. 8.4. Empirical data show fast epidemic response and long-lasting fluctuations. -- Summary: 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 findings, yet at same time allow him to actively follow the mathematical tools and scientific origins of critical phenomena. This book also seeks to pave the way to further fruitful applications of the mathematics of critical phenomena in other fields of the life sciences. -- ISBN : 9781848164024 (online ; pdf). -- 1848164025. -- 9781848164017. -- 1848164017. -- 9786613143341.
Jansen, Vincent
mutace (biologie). patogenní mikroorganismy. kritické jevy (fyzika). matematická fyzika. elektronické knihy
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