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This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.
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.
A hands-on lab guide in the R programming language that enables students in the life sciences to reason quantitatively about living systems across scales This lab guide accompanies the textbook Quantitative Biosciences, providing students with the skills they need to translate biological principles and mathematical concepts into computational models of living systems. This hands-on guide uses a case study approach organized around central questions in the life sciences, introducing landmark advances in the field while teaching students—whether from the life sciences, physics, computational sciences, engineering, or mathematics—how to reason quantitatively in the face of uncertainty. Draws on real-world case studies in molecular and cellular biosciences, organismal behavior and physiology, and populations and ecological communities Encourages good coding practices, clear and understandable modeling, and accessible presentation of results Helps students to develop a diverse repertoire of simulation approaches, enabling them to model at the appropriate scale Builds practical expertise in a range of methods, including sampling from probability distributions, stochastic branching processes, continuous time modeling, Markov chains, bifurcation analysis, partial differential equations, and agent-based simulations Bridges the gap between the classroom and research discovery, helping students to think independently, troubleshoot and resolve problems, and embark on research of their own Stand-alone computational lab guides for Quantitative Biosciences also available in Python and MATLAB
A hands-on lab guide in the Python programming language that enables students in the life sciences to reason quantitatively about living systems across scales This lab guide accompanies the textbook Quantitative Biosciences, providing students with the skills they need to translate biological principles and mathematical concepts into computational models of living systems. This hands-on guide uses a case study approach organized around central questions in the life sciences, introducing landmark advances in the field while teaching students—whether from the life sciences, physics, computational sciences, engineering, or mathematics—how to reason quantitatively in the face of uncertainty. Draws on real-world case studies in molecular and cellular biosciences, organismal behavior and physiology, and populations and ecological communities Encourages good coding practices, clear and understandable modeling, and accessible presentation of results Helps students to develop a diverse repertoire of simulation approaches, enabling them to model at the appropriate scale Builds practical expertise in a range of methods, including sampling from probability distributions, stochastic branching processes, continuous time modeling, Markov chains, bifurcation analysis, partial differential equations, and agent-based simulations Bridges the gap between the classroom and research discovery, helping students to think independently, troubleshoot and resolve problems, and embark on research of their own Stand-alone computational lab guides for Quantitative Biosciences also available in R and MATLAB
This book covers Computational Models for Cell Processes, featuring enhanced contributions from the CompMod workshop (2009). Covers a wide range of topics in systems biology, addressing the dynamics and the computational principles of this emerging field.
A hands-on lab guide in the MATLAB programming language that enables students in the life sciences to reason quantitatively about living systems across scales This lab guide accompanies the textbook Quantitative Biosciences, providing students with the skills they need to translate biological principles and mathematical concepts into computational models of living systems. This hands-on guide uses a case study approach organized around central questions in the life sciences, introducing landmark advances in the field while teaching students—whether from the life sciences, physics, computational sciences, engineering, or mathematics—how to reason quantitatively in the face of uncertainty. Draws on real-world case studies in molecular and cellular biosciences, organismal behavior and physiology, and populations and ecological communities Encourages good coding practices, clear and understandable modeling, and accessible presentation of results Helps students to develop a diverse repertoire of simulation approaches, enabling them to model at the appropriate scale Builds practical expertise in a range of methods, including sampling from probability distributions, stochastic branching processes, continuous time modeling, Markov chains, bifurcation analysis, partial differential equations, and agent-based simulations Bridges the gap between the classroom and research discovery, helping students to think independently, troubleshoot and resolve problems, and embark on research of their own Stand-alone computational lab guides for Quantitative Biosciences also available in Python and R
This book constitutes the refereed conference proceedings of the 11th International Conference on Bio-Inspired Information and Communications Technologies, held in Pittsburgh, PA, USA, in March 2019. The 13 revised full papers and 2 short papers were selected from 29 submissions. Past iterations of the conference have attracted contributions in Direct Bioinspiration (physical biological materials and systems used within technology) as well as Indirect Bioinspiration (biological principles, processes and mechanisms used within the design and application of technology). This year, the scope has expanded to include a third thrust: Foundational Bioinspiration (bioinspired aspects of game theory, evolution, information theory, and philosophy of science).
A hands-on approach to quantitative reasoning in the life sciences Quantitative Biosciences establishes the quantitative principles of how living systems work across scales, drawing on classic and modern discoveries to present a case study approach that links mechanisms, models, and measurements. Each case study is organized around a central question in the life sciences: Are mutations dependent on selection? How do cells respond to fluctuating signals in the environment? How do organisms move in flocks given local sensing? How does the size of an epidemic depend on its initial speed of spread? Each question provides the basis for introducing landmark advances in the life sciences while teaching students—whether from the life sciences, physics, computational sciences, engineering, or mathematics—how to reason quantitatively about living systems given uncertainty. Draws on real-world case studies in molecular and cellular biosciences, organismal behavior and physiology, and populations and ecological communities Stand-alone lab guides available in Python, R, and MATLAB help students move from learning in the classroom to doing research in practice Homework exercises build on the lab guides, emphasizing computational model development and analysis rather than pencil-and-paper derivations Suitable for capstone undergraduate classes, foundational graduate classes, or as part of interdisciplinary courses for students from quantitative backgrounds Can be used as part of conventional, flipped, or hybrid instruction formats Additional materials available to instructors, including lesson plans and homework solutions
An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.