Download or read book Stochastic Processes in the Neurosciences written by Henry C. Tuckwell and published by SIAM. This book was released on 1989-01-01 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is centered on quantitative analysis of nerve-cell behavior. The work is foundational, with many higher order problems still remaining, especially in connection with neural networks. Thoroughly addressed topics include stochastic problems in neurobiology, and the treatment of the theory of related Markov processes.
Download or read book Stochastic Processes in the Neurosciences written by Henry C. Tuckwell and published by SIAM. This book was released on 1989-01-01 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is centered on quantitative analysis of nerve-cell behavior. The work is foundational, with many higher order problems still remaining, especially in connection with neural networks. Thoroughly addressed topics include stochastic problems in neurobiology, and the treatment of the theory of related Markov processes.
Download or read book Stochastic Methods in Neuroscience written by Carlo Laing and published by Oxford University Press. This book was released on 2010 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Great interest is now being shown in computational and mathematical neuroscience, fuelled in part by the rise in computing power, the ability to record large amounts of neurophysiological data, and advances in stochastic analysis. These techniques are leading to biophysically more realistic models. It has also become clear that both neuroscientists and mathematicians profit from collaborations in this exciting research area.Graduates and researchers in computational neuroscience and stochastic systems, and neuroscientists seeking to learn more about recent advances in the modelling and analysis of noisy neural systems, will benefit from this comprehensive overview. The series of self-contained chapters, each written by experts in their field, covers key topics such as: Markov chain models for ion channel release; stochastically forced single neurons and populations of neurons; statistical methods for parameterestimation; and the numerical approximation of these stochastic models.Each chapter gives an overview of a particular topic, including its history, important results in the area, and future challenges, and the text comes complete with a jargon-busting index of acronyms to allow readers to familiarize themselves with the language used.
Download or read book Stochastic Processes and their Applications written by M.J. Beckmann and published by Springer Science & Business Media. This book was released on 1991-12-11 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with Stochastic tools with special reference to applications in the areas of Physics, Biology and Operations Research. Quitea few of the papers deal with the applications of the rich theory of point processes in Physics and Operations Research. A few of the papers deal with the problems of Inference and Stochastic theory. In addition papers of some leading specialists are included. These papers reflect the latest trends in these areas and will, therefore, be of value and interest to researchers in these fields.
Download or read book Analysis and Data Based Reconstruction of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and published by Springer. This book was released on 2019-07-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.
Download or read book An Introduction to Continuous Time Stochastic Processes written by Vincenzo Capasso and published by Springer Nature. This book was released on 2021-06-18 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book.
Download or read book Elementary Applications of Probability Theory written by Henry C. Tuckwell and published by CRC Press. This book was released on 2018-02-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.
Download or read book Mathematical Methods in Biology and Neurobiology written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2014-02-13 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for the emerging field of systems biology. Mathematical Methods in Biology and Neurobiology introduces and develops these mathematical structures and methods in a systematic manner. It studies: • discrete structures and graph theory • stochastic processes • dynamical systems and partial differential equations • optimization and the calculus of variations. The biological applications range from molecular to evolutionary and ecological levels, for example: • cellular reaction kinetics and gene regulation • biological pattern formation and chemotaxis • the biophysics and dynamics of neurons • the coding of information in neuronal systems • phylogenetic tree reconstruction • branching processes and population genetics • optimal resource allocation • sexual recombination • the interaction of species. Written by one of the most experienced and successful authors of advanced mathematical textbooks, this book stands apart for the wide range of mathematical tools that are featured. It will be useful for graduate students and researchers in mathematics and physics that want a comprehensive overview and a working knowledge of the mathematical tools that can be applied in biology. It will also be useful for biologists with some mathematical background that want to learn more about the mathematical methods available to deal with biological structures and data.
Download or read book Statistics for the 21st Century written by Gabor Szekely and published by CRC Press. This book was released on 2000-01-25 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: A selection of articles presented at the Eighth Lukacs Symposium held at the Bowling Green State University, Ohio. They discuss consistency and accuracy of the sequential bootstrap, hypothesis testing, geometry in multivariate analysis, the classical extreme value model, the analysis of cross-classified data, diffusion models for neural activity, estimation with quadratic loss, econometrics, higher order asymptotics, pre- and post-limit theorems, and more.
Download or read book Origins written by Karl H. Pribram and published by Routledge. This book was released on 2018-10-24 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: The result of the second Appalachian conference on neurodynamics, this volume focuses on the problem of "order," its origins, evolution, and future. Central to this concern lies our understanding of time. Both classical and quantum physics have developed their conceptions within a framework of time symmetry. Divided into four major sections, this book: * provides refreshingly new approaches to the problem of the evolution of order, indicating the directions that need to be taken in subsequent conferences which will address learning and memory more directly; * addresses the issue of how information becomes transmitted in the nervous system; * shows how patterns are constructed at the synaptodendritic level of processing and how such pattern construction relates to image processing; and * deals with the control operations which operate on image processing to construct entities such as visual and auditory objects such as phonemes. The aim of the conference was to bring together professionals to exchange ideas -- some were fairly worked out; others were in their infancy. As a result, one of the most valuable aspects of the conference is that it fostered lasting interactive relationships among these leading researchers.
Download or read book Disorder Versus Order in Brain Function written by Peter rhem and published by World Scientific. This book was released on 2000 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a collection of diverse essays by such authors as Diana Smetters, Hermann Haken, and Scott Kelso.
Download or read book Cybernetics And Systems 94 Proceedings Of The 12th European Meeting On Cybernetics And Systems Research In 2 Volumes written by Robert Trappl and published by World Scientific. This book was released on 1994-03-15 with total page 1964 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume reflect the most recent research findings in cybernetics and systems research. They were selected from 298 draft final papers which were submitted to the conference by authors from more than 30 different countries from five continents.
Download or read book Applied Stochastic Processes and Control for Jump Diffusions written by Floyd B. Hanson and published by SIAM. This book was released on 2007-11-22 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical, entry-level text integrating the basic principles of applied mathematics and probability, and computational science.
Download or read book Phylogeny written by Mike Steel and published by SIAM. This book was released on 2016-09-29 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phylogenetics is a topical and growing area of research. Phylogenies (phylogenetic trees and networks) allow biologists to study and graph evolutionary relationships between different species. These are also used to investigate other evolutionary processes?for example, how languages developed or how different strains of a virus (such as HIV or influenza) are related to each other. This self-contained book addresses the underlying mathematical theory behind the reconstruction and analysis of phylogenies. The theory is grounded in classical concepts from discrete mathematics and probability theory as well as techniques from other branches of mathematics (algebra, topology, differential equations). The biological relevance of the results is highlighted throughout. The author supplies proofs of key classical theorems and includes results not covered in existing books, emphasizes relevant mathematical results derived over the past 20 years, and provides numerous exercises, examples, and figures.
Download or read book Neuronal Dynamics written by Wulfram Gerstner and published by Cambridge University Press. This book was released on 2014-07-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: What happens in our brain when we make a decision? What triggers a neuron to send out a signal? What is the neural code? This textbook for advanced undergraduate and beginning graduate students provides a thorough and up-to-date introduction to the fields of computational and theoretical neuroscience. It covers classical topics, including the Hodgkin–Huxley equations and Hopfield model, as well as modern developments in the field such as generalized linear models and decision theory. Concepts are introduced using clear step-by-step explanations suitable for readers with only a basic knowledge of differential equations and probabilities, and are richly illustrated by figures and worked-out examples. End-of-chapter summaries and classroom-tested exercises make the book ideal for courses or for self-study. The authors also give pointers to the literature and an extensive bibliography, which will prove invaluable to readers interested in further study.
Download or read book Advances on Methodological and Applied Aspects of Probability and Statistics written by N. Balakrishnan and published by CRC Press. This book was released on 2004-03-01 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of two volumes that sets forth invited papers presented at the International Indian Statistical Association Conference. This volume emphasizes advancements in methodology and applications of probability and statistics. The chapters, representing the ideas of vanguard researchers on the topic, present several different subspecialties, including applied probability, models and applications, estimation and testing, robust inference, regression and design and sample size methodology. The text also fully describes the applications of these new ideas to industry, ecology, biology, health, economics and management. Researchers and graduate students in mathematical analysis, as well as probability and statistics professionals in industry, will learn much from this volume.
Download or read book Stochastic Models In The Life Sciences And Their Methods Of Analysis written by Frederic Y M Wan and published by World Scientific. This book was released on 2019-08-29 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: '… the volume is impressively accessible. The result is a book that is valuable and approachable for biologists at all levels, including those interested in deepening their skills in mathematical modeling and those who seek an overview to aid them in communicating with collaborators in mathematics and statistics. The former group of readers may especially appreciate the first chapter, an introduction to key concepts in probability, and the set of ten assignments provided as an appendix.'CHOICEBiological processes are evolutionary in nature and often evolve in a noisy environment or in the presence of uncertainty. Such evolving phenomena are necessarily modeled mathematically by stochastic differential/difference equations (SDE), which have been recognized as essential for a true understanding of many biological phenomena. Yet, there is a dearth of teaching material in this area for interested students and researchers, notwithstanding the addition of some recent texts on stochastic modelling in the life sciences. The reason may well be the demanding mathematical pre-requisites needed to 'solve' SDE.A principal goal of this volume is to provide a working knowledge of SDE based on the premise that familiarity with the basic elements of a stochastic calculus for random processes is unavoidable. Through some SDE models of familiar biological phenomena, we show how stochastic methods developed for other areas of science and engineering are also useful in the life sciences. In the process, the volume introduces to biologists a collection of analytical and computational methods for research and applications in this emerging area of life science. The additions broaden the available tools for SDE models for biologists that have been limited by and large to stochastic simulations.
