N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

中枢神経系疾患の治療は正常細胞（ニューロン）の機能維持を目的とするが，脳血管障害のように機能障害の原因が細胞の死滅に基づくことは多い．一方，脳腫瘍の治療においては薬物療法や放射線療法といった腫瘍細胞の死滅を目標とするものが大きな位置を占める．いずれの場合にも，細胞死の機序を理解することは各種病態や治療法の理解のうえで重要である．現在のところ最も研究の進んでいる細胞死の型はアポトーシスである．そのなかで重要な位置を占めるミトコンドリアにおける反応および抗アポトーシス因子について概要を紹介する．

Neuroscience 細胞死：最近の知見

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

This ebook is the first authorized digital version of Kernighan and Ritchie's 1988 classic, The C Programming Language (2nd Ed.). One of the best-selling programming books published in the last fifty years, "K&R" has been called everything from the "bible" to "a landmark in computer science" and it has influenced generations of programmers. Available now for all leading ebook platforms, this concise and beautifully written text is a "must-have" reference for every serious programmers digital library.

As modestly described by the authors in the Preface to the First Edition, this "is not an introductory programming manual; it assumes some familiarity with basic programming concepts like variables, assignment statements, loops, and functions. Nonetheless, a novice programmer should be able to read along and pick up the language, although access to a more knowledgeable colleague will help."

The C programming language

The journal of neuroscience : the official journal of the Society for Neuroscience.

Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses U nstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the R eaction-D iffusion M aster E quation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at an early stage of development. In this paper we demonstrate, in a series of examples with high relevance to the molecular systems biology community, that the proposed software framework is a useful tool for both practitioners and developers of spatial stochastic simulation algorithms. Through the combined efforts of algorithm development and improved modeling accuracy, increasingly complex biological models become feasible to study through computational methods. URDME is freely available at http://www.urdme.org
 .

/pdf/urdme-a-modular-framework-for-stochastic-simulation-of-1ct0c3keg4.pdf

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries

We model stochastic chemical systems with diffusion by a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with a discretized Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered in our method by an unstructured mesh, and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology.

https://www.it.uu.se/research/publications/reports/2008-012/2008-012-nc.pdf

Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes

https://www.it.uu.se/research/publications/reports/2005-020/2005-020-nc.pdf

Computing the moments of high dimensional solutions of the master equation

Spectral approximation of solutions to the chemical master equation

A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in ...

https://www.it.uu.se/research/publications/reports/2008-020/2008-020-nc.pdf

Stefan Engblom

Papers

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries

Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes

Computing the moments of high dimensional solutions of the master equation

Spectral approximation of solutions to the chemical master equation

Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics