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E-raamat: Stochasticity in Processes: Fundamentals and Applications to Chemistry and Biology

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  • Formaat: PDF+DRM
  • Sari: Springer Series in Synergetics
  • Ilmumisaeg: 14-Oct-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319395029
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Stochasticity in Processes: Fundamentals and Applications to Chemistry and BiologySuurem pilt
  • Formaat: PDF+DRM
  • Sari: Springer Series in Synergetics
  • Ilmumisaeg: 14-Oct-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319395029
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This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic collection of the mathematical background material needed to understand probability, statistics, and stochastic processes as a prerequisite for the increasingly challenging practical applications in chemistry and the life sciences examined in the second part.Recent advances in the development of new techniques and in the resolution of conventional experiments at nano-scales have been tremendous: today molecular spectroscopy can provide insights into processes down to scales at which current theories at the interface of physics, chemistry and the life sciences cannot be successful without a firm grasp of randomness and its sources. Routinely measured data is now sufficiently accurate to allow the direct recording of fluctuations. As a result, the sampling of data and the modeling of r

elevant processes are doomed to produce artifacts in interpretation unless the observer has a solid background in the mathematics of limited reproducibility.The material covered is presented in a modular approach, allowing more advanced sections to be skipped if the reader is primarily interested in applications. At the same time, most derivations of analytical solutions for the selected examples are provided in full length to guide more advanced readers in their attempts to derive solutions on their own. The book employs uniform notation throughout, and a glossary has been added to define the most important notions discussed.

Probability.- Distributions, Moments and Statistics.- Stochastic Processes.- Applications in Chemistry.- Applications in Biology.- Perspectives.- References.- Glossary.- Notation.

Arvustused

This book is a much needed contribution to the foundations of chemistry and biology. Its focus is timely, and it provides its readers with a well-rounded and well-written summary of stochasticity with a view toward chemistry and biology. The mathematical prerequisites are kept at the undergraduate level and the book is designed to be as self-contained as possible. Key equestions are derived unless too much mathematical effort would be required. (Clemens F. Heitzinger, Mathematical Reviews, April, 2018)

There are 585 references, a notation index, an author index and a subject index. The book is extremely well produced. Without any reservation, I do not hesitate to say this is an exceptional piece of work. (Marius Iosifescu, zbMATH 1359.60006, 2017)

1 Probability
1(82)
1.1 Fluctuations and Precision Limits
2(4)
1.2 A History of Probabilistic Thinking
6(5)
1.3 Interpretations of Probability
11(5)
1.4 Sets and Sample Spaces
16(4)
1.5 Probability Measure on Countable Sample Spaces
20(7)
1.5.1 Probability Measure
21(3)
1.5.2 Probability Weights
24(3)
1.6 Discrete Random Variables and Distributions
27(17)
1.6.1 Distributions and Expectation Values
27(2)
1.6.2 Random Variables and Continuity
29(5)
1.6.3 Discrete Probability Distributions
34(4)
1.6.4 Conditional Probabilities and Independence
38(6)
1.7 * Probability Measure on Uncountable Sample Spaces
44(11)
1.7.1 * Existence of Non-measurable Sets
46(3)
1.7.2 * Borel σ-Algebra and Lebesgue Measure
49(6)
1.8 Limits and Integrals
55(15)
1.8.1 Limits of Series of Random Variables
55(4)
1.8.2 Riemann and Stieltjes Integration
59(4)
1.8.3 Lebesgue Integration
63(7)
1.9 Continuous Random Variables and Distributions
70(13)
1.9.1 Densities and Distributions
71(5)
1.9.2 Expectation Values and Variances
76(1)
1.9.3 Continuous Variables and Independence
77(1)
1.9.4 Probabilities of Discrete and Continuous Variables
78(5)
2 Distributions, Moments, and Statistics
83(116)
2.1 Expectation Values and Higher Moments
83(18)
2.1.1 First and Second Moments
84(7)
2.1.2 Higher Moments
91(4)
2.1.3 * Information Entropy
95(6)
2.2 Generating Functions
101(6)
2.2.1 Probability Generating Functions
101(2)
2.2.2 Moment Generating Functions
103(2)
2.2.3 Characteristic Functions
105(2)
2.3 Common Probability Distributions
107(17)
2.3.1 The Poisson Distribution
109(2)
2.3.2 The Binomial Distribution
111(4)
2.3.3 The Normal Distribution
115(5)
2.3.4 Multivariate Normal Distributions
120(4)
2.4 Regularities for Large Numbers
124(13)
2.4.1 Binomial and Normal Distributions
125(5)
2.4.2 Central Limit Theorem
130(3)
2.4.3 Law of Large Numbers
133(2)
2.4.4 Law of the Iterated Logarithm
135(2)
2.5 Further Probability Distributions
137(31)
2.5.1 The Log-Normal Distribution
137(3)
2.5.2 The χ2-Distribution
140(3)
2.5.3 Student's t-Distribution
143(4)
2.5.4 The Exponential and the Geometric Distribution
147(4)
2.5.5 The Pareto Distribution
151(3)
2.5.6 The Logistic Distribution
154(2)
2.5.7 The Cauchy--Lorentz Distribution
156(3)
2.5.8 The Levy Distribution
159(2)
2.5.9 The Stable Distribution
161(5)
2.5.10 Bimodal Distributions
166(2)
2.6 Mathematical Statistics
168(31)
2.6.1 Sample Moments
169(4)
2.6.2 Pearson's Chi-Squared Test
173(7)
2.6.3 Fisher's Exact Test
180(2)
2.6.4 The Maximum Likelihood Method
182(8)
2.6.5 Bayesian Inference
190(9)
3 Stochastic Processes
199(148)
3.1 Modeling Stochastic Processes
203(21)
3.1.1 Trajectories and Processes
203(5)
3.1.2 Notation for Probabilistic Processes
208(1)
3.1.3 Memory in Stochastic Processes
209(5)
3.1.4 Stationarity
214(2)
3.1.5 Continuity in Stochastic Processes
216(4)
3.1.6 Autocorrelation Functions and Spectra
220(4)
3.2 Chapman--Kolmogorov Forward Equations
224(79)
3.2.1 Differential Chapman--Kolmogorov Forward Equation
225(10)
3.2.2 Examples of Stochastic Processes
235(25)
3.2.3 Master Equations
260(13)
3.2.4 Continuous Time Random Walks
273(11)
3.2.5 Levy Processes and Anomalous Diffusion
284(19)
3.3 Chapman--Kolmogorov Backward Equations
303(16)
3.3.1 Differential Chapman--Kolmogorov Backward Equation
305(2)
3.3.2 Backward Master Equations
307(3)
3.3.3 Backward Poisson Process
310(3)
3.3.4 Boundaries and Mean First Passage Times
313(6)
3.4 Stochastic Differential Equations
319(28)
3.4.1 Mathematics of Stochastic Differential Equations
321(2)
3.4.2 Stochastic Integrals
323(14)
3.4.3 Integration of Stochastic Differential Equations
337(10)
4 Applications in Chemistry
347(222)
4.1 A Glance at Chemical Reaction Kinetics
350(65)
4.1.1 Elementary Steps of Chemical Reactions
351(7)
4.1.2 Michaelis--Menten Kinetics
358(14)
4.1.3 Reaction Network Theory
372(16)
4.1.4 Theory of Reaction Rate Parameters
388(19)
4.1.5 Empirical Rate Parameters
407(8)
4.2 Stochasticity in Chemical Reactions
415(20)
4.2.1 Sampling of Trajectories
416(2)
4.2.2 The Chemical Master Equation
418(7)
4.2.3 Stochastic Chemical Reaction Networks
425(7)
4.2.4 The Chemical Langevin Equation
432(3)
4.3 Examples of Chemical Reactions
435(55)
4.3.1 The Flow Reactor
436(5)
4.3.2 Monomolecular Chemical Reactions
441(9)
4.3.3 Bimolecular Chemical Reactions
450(9)
4.3.4 Laplace Transform of Master Equations
459(18)
4.3.5 Autocatalytic Reaction
477(8)
4.3.6 Stochastic Enzyme Kinetics
485(5)
4.4 Fluctuations and Single Molecule Investigations
490(19)
4.4.1 Single Molecule Enzymology
491(9)
4.4.2 Fluorescence Correlation Spectroscopy
500(9)
4.5 Scaling and Size Expansions
509(17)
4.5.1 Kramers--Moyal Expansion
509(3)
4.5.2 Small Noise Expansion
512(2)
4.5.3 Size Expansion of the Master Equation
514(7)
4.5.4 From Master to Fokker--Planck Equations
521(5)
4.6 Numerical Simulation of Chemical Master Equations
526(43)
4.6.1 Basic Assumptions
527(4)
4.6.2 Tau-Leaping and Higher-Level Approaches
531(2)
4.6.3 The Simulation Algorithm
533(9)
4.6.4 Examples of Simulations
542(27)
5 Applications in Biology
569(110)
5.1 Autocatalysis and Growth
572(13)
5.1.1 Autocatalysis in Closed Systems
572(3)
5.1.2 Autocatalysis in Open Systems
575(5)
5.1.3 Unlimited Growth
580(3)
5.1.4 Logistic Equation and Selection
583(2)
5.2 Stochastic Models in Biology
585(64)
5.2.1 Master Equations and Growth Processes
585(4)
5.2.2 Birth-and-Death Processes
589(16)
5.2.3 Fokker--Planck Equation and Neutral Evolution
605(6)
5.2.4 Logistic Birth-and-Death and Epidemiology
611(20)
5.2.5 Branching Processes
631(18)
5.3 Stochastic Models of Evolution
649(24)
5.3.1 The Wright--Fisher and the Moran Process
651(7)
5.3.2 Master Equation of the Moran Process
658(7)
5.3.3 Models of Mutation
665(8)
5.4 Coalescent Theory and Phylogenetic Reconstruction
673(6)
Notation 679(4)
References 683(24)
Author Index 707(4)
Index 711
Peter Schuster, born 07.03.1941, received his Ph.D. (sub auspiciis praesidentis) in Chemistry and Physics from the University of Vienna in 1967. His professional career includes:





Postdoctoral assistant with Prof. Manfred Eigen at the Max Planck Institute of Physical Chemistry in Göttingen, Germany, 1968-1969,





Habilitation in Theoretical Chemistry at the "Universität Wien", 1971,





Full professor of Theoretical Chemistry at the "Universität Wien", 1973-2009,





Head of the Institute of Theoretical Chemistry at the Universität Wien, 1973-1992 and 1996-2010,





External Faculty member of the Santa Fe Institute, Santa Fe, USA, 1991-2003 and 2004-2013, and External Professor emeritus of this institute, since 2013,







Founding director of the Institute of Molecular Biotechnology in Jena, Germany, 1992-1995,





Member of the Austrian Academy of Sciences, since 1984. He was Vice-President of this academy in the years 2000 2003 and President 2006-2009,





Member of the Deutsche Akademie der Naturforscher Leopoldina, Nationale Akademie der Wissenschaften, since 1993. He was member of the Presiding Committee of this academy in the years 2001-2006,





Foreign Associate of the National Academy of Sciences USA, since 2009





Member of the Academia Europaea, London, since 2009





Member of the European Molecular Biology Organization (EMBO), since 2014





Professor emeritus of the Universität Wien, since 2009.





Peter Schuster is a member of the Springer Complexity and Synergetics editorial boards and has been Editor-in-Chief of the journal "Complexity", 2001-2016. 
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