Mathematical Models of Chemical Reactions
| Author | : Péter Érdi |
| Publisher | : Manchester University Press |
| Total Pages | : 296 |
| Release | : 1989 |
| Genre | : Chemical reactions |
| ISBN | : 9780719022081 |
Mathematical Models Of Chemical Reactions Theory Applications Of Deterministic Stochastic Models
Download Mathematical Models Of Chemical Reactions Theory Applications Of Deterministic Stochastic Models full books in PDF, epub, and Kindle. Read online free Mathematical Models Of Chemical Reactions Theory Applications Of Deterministic Stochastic Models ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Mathematical Models of Chemical Reactions - Theory & Applications of Deterministic & Stochastic Models
| Author | : P. Erdi |
| Publisher | : Wiley |
| Total Pages | : 284 |
| Release | : 1992-09-14 |
| Genre | : Mathematics |
| ISBN | : 9780471935155 |
Stochastic Chemical Kinetics
| Author | : Péter Érdi |
| Publisher | : Springer |
| Total Pages | : 174 |
| Release | : 2014-05-06 |
| Genre | : Science |
| ISBN | : 149390387X |
This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.
Stochastic Chemical Reaction Systems in Biology
| Author | : Hong Qian |
| Publisher | : Springer Nature |
| Total Pages | : 364 |
| Release | : 2021-10-18 |
| Genre | : Mathematics |
| ISBN | : 3030862526 |
This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.
Stochastic Dynamics in Computational Biology
| Author | : Stefanie Winkelmann |
| Publisher | : Springer Nature |
| Total Pages | : 284 |
| Release | : 2021-01-04 |
| Genre | : Mathematics |
| ISBN | : 3030623874 |
The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.
Mathematical Modeling in Systems Biology
| Author | : Brian P. Ingalls |
| Publisher | : MIT Press |
| Total Pages | : 423 |
| Release | : 2022-06-07 |
| Genre | : Science |
| ISBN | : 0262545829 |
An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.
Foundations of Chemical Reaction Network Theory
| Author | : Martin Feinberg |
| Publisher | : Springer |
| Total Pages | : 475 |
| Release | : 2019-01-31 |
| Genre | : Mathematics |
| ISBN | : 3030038580 |
This book provides an authoritative introduction to the rapidly growing field of chemical reaction network theory. In particular, the book presents deep and surprising theorems that relate the graphical and algebraic structure of a reaction network to qualitative properties of the intricate system of nonlinear differential equations that the network induces. Over the course of three main parts, Feinberg provides a gradual transition from a tutorial on the basics of reaction network theory, to a survey of some of its principal theorems, and, finally, to a discussion of the theory’s more technical aspects. Written with great clarity, this book will be of value to mathematicians and to mathematically-inclined biologists, chemists, physicists, and engineers who want to contribute to chemical reaction network theory or make use of its powerful results.
Deterministic Versus Stochastic Modelling in Biochemistry and Systems Biology
| Author | : Paola Lecca |
| Publisher | : Elsevier |
| Total Pages | : 411 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 1908818212 |
Stochastic kinetic methods are currently considered to be the most realistic and elegant means of representing and simulating the dynamics of biochemical and biological networks. Deterministic versus stochastic modelling in biochemistry and systems biology introduces and critically reviews the deterministic and stochastic foundations of biochemical kinetics, covering applied stochastic process theory for application in the field of modelling and simulation of biological processes at the molecular scale. Following an overview of deterministic chemical kinetics and the stochastic approach to biochemical kinetics, the book goes onto discuss the specifics of stochastic simulation algorithms, modelling in systems biology and the structure of biochemical models. Later chapters cover reaction-diffusion systems, and provide an analysis of the Kinfer and BlenX software systems. The final chapter looks at simulation of ecodynamics and food web dynamics. Introduces mathematical concepts and formalisms of deterministic and stochastic modelling through clear and simple examples Presents recently developed discrete stochastic formalisms for modelling biological systems and processes Describes and applies stochastic simulation algorithms to implement a stochastic formulation of biochemical and biological kinetics
Reaction Kinetics: Exercises, Programs and Theorems
| Author | : János Tóth |
| Publisher | : Springer |
| Total Pages | : 476 |
| Release | : 2018-09-18 |
| Genre | : Science |
| ISBN | : 1493986430 |
Fifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.
Mathematical Modelling
| Author | : Simon Serovajsky |
| Publisher | : CRC Press |
| Total Pages | : 589 |
| Release | : 2021-11-24 |
| Genre | : Mathematics |
| ISBN | : 1000503984 |
Mathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens. The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented. Features Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc.
