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Metastability and Markov State Models in Molecular Dynamics: Modeling, Analysis, Algorithmic Approaches [Mīkstie vāki]

  • Formāts: Paperback / softback, 133 pages, weight: 266 g
  • Sērija : Courant Lecture Notes
  • Izdošanas datums: 30-Jan-2014
  • Izdevniecība: American Mathematical Society
  • ISBN-10: 0821843591
  • ISBN-13: 9780821843598
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  • Mīkstie vāki
  • Cena: 44,31 €
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  • Formāts: Paperback / softback, 133 pages, weight: 266 g
  • Sērija : Courant Lecture Notes
  • Izdošanas datums: 30-Jan-2014
  • Izdevniecība: American Mathematical Society
  • ISBN-10: 0821843591
  • ISBN-13: 9780821843598
Citas grāmatas par šo tēmu:
Applications in modern biotechnology and molecular medicine often require simulation of biomolecular systems in atomic representation with immense length and timescales that are far beyond the capacity of computer power currently available. As a consequence, there is an increasing need for reduced models that describe the relevant dynamical properties while at the same time being less complex. In this book the authors exploit the existence of metastable sets for constructing such a reduced molecular dynamics model, the so-called Markov State Model (MSM), with good approximation properties on the long timescales.

With its many examples and illustrations, this book is addressed to graduate students, mathematicians, and practical computational scientists wanting an overview of the mathematical background for the ever increasing research activity on how to construct MSMs for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecular sensors to molecular aggregation. This book bridges the gap between mathematical research on molecular dynamics and its practical use for realistic molecular systems by providing readers with tools for performing in-depth analysis of simulation and data-analysis methods.
Introduction vii
Chapter 1 Transfer Operator Approach to Conformation Dynamics
1(4)
Chapter 2 Dynamics
5(10)
2.1 Markov Processes and Transition Functions
5(2)
2.2 Markov Processes in Molecular Dynamics
7(8)
Chapter 3 Metastability
15(10)
3.1 Hitting Times and Committors
15(6)
3.2 Exit Times and Exit Rates
21(2)
3.3 Metastable Full Partitions and Almost Invariance
23(1)
3.4 Definitions of Metastability
24(1)
Chapter 4 Transfer Operators and Generators
25(36)
4.1 Transfer Operators in Molecular Dynamics
28(2)
4.2 Mean Hitting Times and Committors
30(3)
4.3 Dominant Eigenvalues
33(23)
4.4 Spectral Approach to Metastability
56(1)
4.5 Numerical Experiments
57(4)
Chapter 5 Projected Transfer Operators
61(38)
5.1 Galerkin Projection
61(7)
5.2 Density Propagation Error
68(10)
5.3 Eigenvalue Error
78(4)
5.4 Committor Projection and Core Sets
82(9)
5.5 Numerical Experiments
91(8)
Chapter 6 Transition Path Theory
99(16)
6.1 Reactive Trajectories
100(9)
6.2 Illustrative Examples
109(6)
Chapter 7 Concluding Remarks
115(2)
Appendix A Some Mathematical Aspects of Transfer Operators 117(4)
Appendix B Definition of Exit Rates 121(2)
Bibliography 123
Christof Schutte, Freie Universitat Berlin, Germany, and Zuse Institut Berlin, Germany

Marco Sarich, Freie Universitat Berlin, Germany