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Books of the Lab

Books published in the lab.

IV- D. Holcman, Polymer models and simulations to understand nuclear organization, Springer 2021----finalized.

III- D. Holcman, Z. Schuss, Asymptotics of Elliptic and Parabolic PDEs : And Their Applications in Statistical Physics, Computational Neuroscience, and Biophysics, Springer 2018
“This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory.”

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II- D. Holcman ,Ed Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, Springer 2017.
“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.”

I-D. Holcman, Z. Schuss, Stochastic Narrow Escape, Springer 2015
“This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology.The first part of the book concentrates on mathematical methods, including advanced asymptotic methods in partial equations, and is aimed primarily at applied mathematicians and theoretical physicists who are interested in biological applications. The second part of the book is intended for computational biologists, theoretical chemists, biochemists, biophysicists, and physiologists. It includes a summary of output formulas from the mathematical portion of the book and concentrates on their applications in modeling specific problems in theoretical molecular and cellular biology.”

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