With the availability of high speed computers and advances in computational techniques, the application of mathematical modeling to biological systems is expanding. This comprehensive and richly illustrated volume pro...
ISBN:
(数字)9783642273674
ISBN:
(纸本)9783642273667
With the availability of high speed computers and advances in computational techniques, the application of mathematical modeling to biological systems is expanding. This comprehensive and richly illustrated volume provides up-to-date, wide-ranging material on the mathematical modeling of kidney physiology, including clinical data analysis and practice exercises. Basic concepts and modeling techniques introduced in this volume can be applied to other areas (or organs) of *** models presented describe the main homeostatic functions performed by the kidney, including blood filtration, excretion of water and salt, maintenance of electrolyte balance and regulation of blood pressure. Each chapter includes an introduction to the basic relevant physiology, a derivation of the essential conservation equations and then a discussion of a series of mathematical models, with increasing level of *** volume will be of interest to biological and mathematical scientists, as well as physiologists and nephrologists, who would like an introduction to mathematical techniques that can be applied to renal transport and function. The material is written for students who have had college-level calculus, but can be used in modeling courses in applied mathematics at all levels through early graduate courses.
This book provides a self-contained introduction to a new class of stochastic models for systems of spiking neurons. These systems have a large number of interacting components, each one evolving as a stochastic proce...
详细信息
ISBN:
(数字)9783031684098
ISBN:
(纸本)9783031684081
This book provides a self-contained introduction to a new class of stochastic models for systems of spiking neurons. These systems have a large number of interacting components, each one evolving as a stochastic process with a memory of variable length. Several mathematical tools are put to use, such as Markov chains, stochastic chains having memory of variable length, point processes having stochastic intensity, Hawkes processes, random graphs, mean field limits, perfect sampling algorithms, the Context algorithm, and statistical model selection.
mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology an...
详细信息
ISBN:
(数字)9781461441786
ISBN:
(纸本)9781461441779
mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.
This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions.;Through the rigorous development of the linea...
详细信息
ISBN:
(数字)9789402411461
ISBN:
(纸本)9789402411454
This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions.;Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics.;will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.
This book provides an overview of recent mathematical models for dynamics in cellular systems and offers a unique vision of the field by prominent experts.It covers, among others, the regulatory basis of oscillations ...
详细信息
ISBN:
(数字)9783031823961
ISBN:
(纸本)9783031823954
This book provides an overview of recent mathematical models for dynamics in cellular systems and offers a unique vision of the field by prominent experts.
It covers, among others, the regulatory basis of oscillations in biological systems; ergodic and chaotic properties in biological models with the example of maturity distribution of precursors of blood cells; time-delayed feedbacks; mathematical models of cell division and heterogeneous stem cell regeneration; quantitative mathematical modeling of glucose regulation; data-driven models of chemotherapy-induced neutropenia; and effects of irradiation and antioxidants in Alzheimer’s disease.
This book is directed towards mathematicians interested in learning about modeling in cellular systems and is accessible also to theoreticians in biology and medicine.
暂无评论