Random Fragmentation and Coagulation Processes PDF Download

Author: Jean Bertoin
Publisher: Cambridge University Press
ISBN: 1139459155
Category : Mathematics
Languages : en
Pages : 259

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Book Description
Fragmentation and coagulation are two natural phenomena that can be observed in many sciences and at a great variety of scales - from, for example, DNA fragmentation to formation of planets by accretion. This book, by the author of the acclaimed Lévy Processes, is the first comprehensive theoretical account of mathematical models for situations where either phenomenon occurs randomly and repeatedly as time passes. This self-contained treatment develops the models in a way that makes recent developments in the field accessible. Each chapter ends with a comments section in which important aspects not discussed in the main part of the text (often because the discussion would have been too technical and/or lengthy) are addressed and precise references are given. Written for readers with a solid background in probability, its careful exposition allows graduate students, as well as working mathematicians, to approach the material with confidence.

Author: David Holcman
Publisher: Springer
ISBN: 3319626272
Category : Mathematics
Languages : en
Pages : 377

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Book Description
This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.

Author: Emma Horton
Publisher: Springer Nature
ISBN: 3031395468
Category : Mathematics
Languages : en
Pages : 278

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Book Description
This monograph highlights the connection between the theory of neutron transport and the theory of non-local branching processes. By detailing this frequently overlooked relationship, the authors provide readers an entry point into several active areas, particularly applications related to general radiation transport. Cutting-edge research published in recent years is collected here for convenient reference. Organized into two parts, the first offers a modern perspective on the relationship between the neutron branching process (NBP) and the neutron transport equation (NTE), as well as some of the core results concerning the growth and spread of mass of the NBP. The second part generalizes some of the theory put forward in the first, offering proofs in a broader context in order to show why NBPs are as malleable as they appear to be. Stochastic Neutron Transport will be a valuable resource for probabilists, and may also be of interest to numerical analysts and engineers in the field of nuclear research.

Author: Weizhu Bao
Publisher: World Scientific
ISBN: 9811266158
Category : Mathematics
Languages : en
Pages : 243

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Book Description
The thematic program Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications was held at the Institute for Mathematical Sciences at the National University of Singapore, from September 2019 to March 2020. Leading experts presented tutorials and special lectures geared towards the participating graduate students and junior researchers.Readers will find in this significant volume four expanded lecture notes with self-contained tutorials on modeling and simulation for collective dynamics including individual and population approaches for population dynamics in mathematical biology, collective behaviors for Lohe type aggregation models, mean-field particle swarm optimization, and consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints.This volume serves to inspire graduate students and researchers who will embark into original research work in kinetic models for collective dynamics and their applications.

Author: Vassili N. Kolokoltsov
Publisher: Cambridge University Press
ISBN: 1139489739
Category : Mathematics
Languages : en
Pages : 394

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Book Description
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.

Author: N. H. Bingham
Publisher: Cambridge University Press
ISBN: 1139487922
Category : Mathematics
Languages : en
Pages : 547

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Book Description
No leading university department of mathematics or statistics, or library, can afford to be without this unique text. Leading authorities give a unique insight into a wide range of currently topical problems, from the mathematics of road networks to the genomics of cancer.

Author: Robert Sims
Publisher: American Mathematical Soc.
ISBN: 0821868985
Category : Mathematics
Languages : en
Pages : 234

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Book Description
The goal of the Entropy and the Quantum schools has been to introduce young researchers to some of the exciting current topics in mathematical physics. These topics often involve analytic techniques that can easily be understood with a dose of physical intuition. In March of 2010, four beautiful lectures were delivered on the campus of the University of Arizona. They included Isoperimetric Inequalities for Eigenvalues of the Laplacian by Rafael Benguria, Universality of Wigner Random Matrices by Laszlo Erdos, Kinetic Theory and the Kac Master Equation by Michael Loss, and Localization in Disordered Media by Gunter Stolz. Additionally, there were talks by other senior scientists and a number of interesting presentations by junior participants. The range of the subjects and the enthusiasm of the young speakers are testimony to the great vitality of this field, and the lecture notes in this volume reflect well the diversity of this school.

Author: Remco van der Hofstad
Publisher: Cambridge University Press
ISBN: 110717287X
Category : Computers
Languages : en
Pages : 341

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Book Description
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Author: Catherine Donati-Martin
Publisher: Springer Science & Business Media
ISBN: 3642017622
Category : Mathematics
Languages : en
Pages : 457

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Book Description
The tradition of specialized courses in the Séminaires de Probabilités is continued with A. Lejay's Another introduction to rough paths. Other topics from this 42nd volume range from the interface between analysis and probability to special processes, Lévy processes and Lévy systems, branching, penalization, representation of Gaussian processes, filtrations and quantum probability.

Author: Giacomo Albi
Publisher: Springer Nature
ISBN: 3030671046
Category : Science
Languages : en
Pages : 251

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Book Description
In recent decades, kinetic theory - originally developed as a field of mathematical physics - has emerged as one of the most prominent fields of modern mathematics. In recent years, there has been an explosion of applications of kinetic theory to other areas of research, such as biology and social sciences. This book collects lecture notes and recent advances in the field of kinetic theory of lecturers and speakers of the School “Trails in Kinetic Theory: Foundational Aspects and Numerical Methods”, hosted at Hausdorff Institute for Mathematics (HIM) of Bonn, Germany, 2019, during the Junior Trimester Program “Kinetic Theory”. Focusing on fundamental questions in both theoretical and numerical aspects, it also presents a broad view of related problems in socioeconomic sciences, pedestrian dynamics and traffic flow management.