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Stochastic Chemical Kinetics: Theory and (Mostly) Systems Biological Applications 2014 ed. [Kietas viršelis]

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  • Formatas: Hardback, 162 pages, aukštis x plotis: 235x155 mm, weight: 4227 g, 2 Illustrations, color; 20 Illustrations, black and white; XIV, 162 p. 22 illus., 2 illus. in color., 1 Hardback
  • Serija: Springer Series in Synergetics
  • Išleidimo metai: 07-May-2014
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1493903861
  • ISBN-13: 9781493903863
Kitos knygos pagal šią temą:
Stochastic Chemical Kinetics: Theory and (Mostly) Systems Biological Applications 2014 ed.Didesnis paveikslėlis
  • Formatas: Hardback, 162 pages, aukštis x plotis: 235x155 mm, weight: 4227 g, 2 Illustrations, color; 20 Illustrations, black and white; XIV, 162 p. 22 illus., 2 illus. in color., 1 Hardback
  • Serija: Springer Series in Synergetics
  • Išleidimo metai: 07-May-2014
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1493903861
  • ISBN-13: 9781493903863
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781493903863.html
Raktažodžiai:
This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.

Recenzijos

This is the first book in a new, highly exciting, growing area of applied mathematics, with applications to modern cell biology. The level is very accessible to a wide range of readers from the physical sciences to biology and the life sciences. The book is lucidly written and has an extensive, scholarly researched bibliography which will certainly be useful to anyone who wants to go deeper into the subject. (Hong Qian, SIAM Review, Vol. 57 (3), September, 2015)

1 Stochastic Kinetics: Why and How?
1(24)
1.1 Chemical Kinetics: A Prototype of Nonlinear Science
1(10)
1.1.1 The Power Law and Mass Action Type Deterministic Model of Homogeneous Reaction Kinetics
3(8)
1.1.2 Stationary States and Their Stability
11(1)
1.2 Applicability of the Deterministic Model
11(2)
1.3 Fluctuation Phenomena
13(4)
1.3.1 Brownian Motion
13(1)
1.3.1.1 Diffusion
14(2)
1.3.1.2 Fluctuation-Dissipation Theorem
16(1)
1.3.1.3 Towards the Theory of Stochastic Processes
17(1)
1.3.1.4 Experimental Determination of the Avogadro Constant
17(1)
1.4 Stochastic Chemical Kinetics
17(8)
1.4.1 Model Framework: Preliminary Remarks
17(1)
1.4.2 Historical Remarks
18(1)
1.4.3 On the Solutions of the Stochastic Kinetic Models: Analytical Calculations Versus Simulations
19(1)
1.4.4 The Renaissance of Stochastic Kinetics: Systems Biology
19(1)
References
20(5)
2 Continuous Time Discrete State Stochastic Models
25(46)
2.1 Model Frameworks
25(1)
2.2 Stochastic Processes
26(9)
2.2.1 Definition
26(1)
2.2.2 Time and State Space
27(1)
2.2.3 Important Types of Stochastic Processes
27(1)
2.2.4 Markov Chains
28(3)
2.2.5 Continuous Time Discrete State Markov Process
31(3)
2.2.6 Semi-Markov Processes
34(1)
2.3 The Standard Stochastic Model of Homogeneous Reaction Kinetics
35(10)
2.3.1 State Space: Size and Enumeration
36(2)
2.3.2 Master Equation
38(3)
2.3.3 Connection Between Deterministic and Stochastic Kinetics: Similarities and Differences
41(3)
2.3.4 Stochastic Maps
44(1)
2.4 Solutions of the Master Equation
45(9)
2.4.1 What Do We Mean by Exact Analytical Solutions?
45(1)
2.4.2 Direct Matrix Operations
45(2)
2.4.3 Time-Independent g-Functions
47(1)
2.4.4 Laplace Transformation
48(1)
2.4.5 Generating Functions
49(1)
2.4.6 Poisson Representation
50(3)
2.4.7 Mathematical Induction
53(1)
2.4.8 Initial Conditions Given with a Probability Distribution
53(1)
2.4.9 Time Scales
54(1)
2.5 Stationary and Transient Distributions
54(4)
2.5.1 Stationary Distributions
54(2)
2.5.2 Transient Distributions
56(1)
2.5.3 Properties of Stationary and Transient Distributions: Unimodality Versus Multimodality
56(2)
2.6 Simulation Methods
58(4)
2.7 Deterministic Continuation
62(1)
2.8 Continuous State Approximations
63(3)
2.9 Non-Markovian Approaches
66(5)
References
67(4)
3 Applications
71(78)
3.1 Introductory Remarks
71(1)
3.2 Fluctuations Near Instabilities
72(6)
3.2.1 Stochastic Chemical Reaction: A Simple Example
72(1)
3.2.1.1 Keizer's Paradox
73(1)
3.2.2 Stochastic Theory of Bistable Reactions
74(1)
3.2.2.1 Schlogl Reaction of the First-Order Phase Transition
74(1)
3.2.2.2 Time Spent in Each Steady State, and Time Scale of Transitions
75(3)
3.2.2.3 The lac Operon Genetic Network
78(1)
3.3 Compartmental Systems
78(59)
3.3.1 Model Frameworks
78(2)
3.3.2 Master Equation and State Space
80(1)
3.3.3 Solutions
81(54)
3.10.2 Stochastic Resonance in One- and Multi-parameter System
135(2)
3.10.3 Stochastic Resonance of Aperiodic Signals
137(1)
3.11 Computation with Small Stochastic Kinetic Systems
137(12)
References
139(10)
4 The Book in Retrospect and Prospect
149(10)
References
156(3)
Index 159