Download or read book Mathematical Neurobiology written by John Stanley Griffith and published by . This book was released on 1971 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Mathematics for Neuroscientists written by Fabrizio Gabbiani and published by Academic Press. This book was released on 2017-02-04 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory. - Fully revised material and corrected text - Additional chapters on extracellular potentials, motion detection and neurovascular coupling - Revised selection of exercises with solutions - More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts

Download or read book Mathematical Foundations of Neuroscience written by G. Bard Ermentrout and published by Springer Science & Business Media. This book was released on 2010-07-01 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.

Download or read book Neuroscience written by Alwyn Scott and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will be of interest to anyone who wishes to know what role mathematics can play in attempting to comprehend the dynamics of the human brain. It also aims to serve as a general introduction to neuromathematics. The book gives the reader a qualitative understanding and working knowledge of useful mathematical applications to the field of neuroscience. The book is readable by those who have little knowledge of mathematics for neuroscience but are committed to begin acquiring such knowledge.

Download or read book Mathematical Foundations of Neuroscience written by G. Bard Ermentrout and published by Springer Science & Business Media. This book was released on 2010-07-08 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising from several courses taught by the authors, this book provides a needed overview illustrating how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience.

Download or read book Dynamical Systems in Neuroscience written by Eugene M. Izhikevich and published by MIT Press. This book was released on 2010-01-22 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

Download or read book Mathematical Neuroscience written by Stanislaw Brzychczy and published by Academic Press. This book was released on 2013-08-16 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. - The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience - Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain - Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling

Download or read book Some Mathematical Questions in Biology Neurobiology written by Robert M. Miura and published by American Mathematical Soc.. This book was released on 1982-12-31 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures presented at the 15th annual meeting on mathematical biology, organized by a joint AMS-SIAM committee, as part of the mathematical activities at the annual AAAS meeting, held January 7, 1982, in Washington, D.C. The meeting was devoted to neurobiology, and was very ably organized by Robert M. Miura. Neurobiology is a very large field, and there are many applications of mathematics that could have been selected. Miura and the committee wisely chose to concentrate on one or two topics concerned mainly with the properties of individual neurons and their processes. In summary, this is an excellent collection of articles on some of the more interesting and timely problems of cellular neurobiology. The articles, especially those by Plant, Rinzel, and Nicholson and Phillips, are all excellent expositions of important problems. I recommend this volume to anyone interested in mathematical neurobiology.

Download or read book Tutorials in Mathematical Biosciences I written by Alla Borisyuk and published by Springer. This book was released on 2005-01-28 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.

Download or read book Introduction to Theoretical Neurobiology Volume 2 Nonlinear and Stochastic Theories written by Henry C. Tuckwell and published by Cambridge University Press. This book was released on 1988-04-29 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and nonspaceclamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.

Download or read book Models of the Mind written by Grace Lindsay and published by Bloomsbury Publishing. This book was released on 2021-03-04 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate – and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it. In Models of the Mind, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain's processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. Each chapter of Models of the Mind focuses on mathematical tools that have been applied in a particular area of neuroscience, progressing from the simplest building block of the brain – the individual neuron – through to circuits of interacting neurons, whole brain areas and even the behaviours that brains command. In addition, Grace examines the history of the field, starting with experiments done on frog legs in the late eighteenth century and building to the large models of artificial neural networks that form the basis of modern artificial intelligence. Throughout, she reveals the value of using the elegant language of mathematics to describe the machinery of neuroscience.

Download or read book Neuroscience of Mathematical Cognitive Development written by Rhonda Douglas Brown and published by Springer. This book was released on 2018-04-13 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​This book examines the neuroscience of mathematical cognitive development from infancy into emerging adulthood, addressing both biological and environmental influences on brain development and plasticity. It begins by presenting major theoretical frameworks for designing and interpreting neuroscience studies of mathematical cognitive development, including developmental evolutionary theory, developmental systems approaches, and the triple-code model of numerical processing. The book includes chapters that discuss findings from studies using neuroscience research methods to examine numerical and visuospatial cognition, calculation, and mathematical difficulties and exceptionalities. It concludes with a review of mathematical intervention programs and recommendations for future neuroscience research on mathematical cognitive development. Featured neuroscience research methods include: Functional Magnetic Resonance Imaging (fMRI). Diffusion Tensor Imaging (DTI). Event Related Potentials (ERP). Transcranial Magnetic Stimulation (TMS). Neuroscience of Mathematical Cognitive Development is an essential resource for researchers, clinicians and related professionals, and graduate students in child and school psychology, neuroscience, educational psychology, neuropsychology, and mathematics education.

Download or read book Mathematics for Neuroscientists written by Fabrizio Gabbiani and published by Academic Press. This book was released on 2010-09-16 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Virtually all scientific problems in neuroscience require mathematical analysis, and all neuroscientists are increasingly required to have a significant understanding of mathematical methods. There is currently no comprehensive, integrated introductory book on the use of mathematics in neuroscience; existing books either concentrate solely on theoretical modeling or discuss mathematical concepts for the treatment of very specific problems. This book fills this need by systematically introducing mathematical and computational tools in precisely the contexts that first established their importance for neuroscience. All mathematical concepts will be introduced from the simple to complex using the most widely used computing environment, Matlab. This book will provide a grounded introduction to the fundamental concepts of mathematics, neuroscience and their combined use, thus providing the reader with a springboard to cutting-edge research topics and fostering a tighter integration of mathematics and neuroscience for future generations of students. - A very didactic and systematic introduction to mathematical concepts of importance for the analysis of data and the formulation of concepts based on experimental data in neuroscience - Provides introductions to linear algebra, ordinary and partial differential equations, Fourier transforms, probabilities and stochastic processes - Introduces numerical methods used to implement algorithms related to each mathematical concept - Illustrates numerical methods by applying them to specific topics in neuroscience, including Hodgkin-Huxley equations, probabilities to describe stochastic release, stochastic processes to describe noise in neurons, Fourier transforms to describe the receptive fields of visual neurons - Allows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework

Download or read book The Computational Neurobiology of Reaching and Pointing written by Reza Shadmehr and published by MIT Press. This book was released on 2004-10-28 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the computational biology of reaching and pointing, with an emphasis on motor learning. Neuroscience involves the study of the nervous system, and its topics range from genetics to inferential reasoning. At its heart, however, lies a search for understanding how the environment affects the nervous system and how the nervous system, in turn, empowers us to interact with and alter our environment. This empowerment requires motor learning. The Computational Neurobiology of Reaching and Pointing addresses the neural mechanisms of one important form of motor learning. The authors integrate material from the computational, behavioral, and neural sciences of motor control that is not available in any other single source. The result is a unified, comprehensive model of reaching and pointing. The book is intended to be used as a text by graduate students in both neuroscience and bioengineering and as a reference source by experts in neuroscience, robotics, and other disciplines. The book begins with an overview of the evolution, anatomy, and physiology of the motor system, including the mechanisms for generating force and maintaining limb stability. The sections that follow, "Computing Locations and Displacements", "Skills, Adaptations, and Trajectories", and "Predictions, Decisions, and Flexibility", present a theory of sensorially guided reaching and pointing that evolves organically based on computational principles rather than a traditional structure-by-structure approach. The book also includes five appendixes that provide brief refreshers on fundamentals of biology, mathematics, physics, and neurophysiology, as well as a glossary of relevant terms. The authors have also made supplemental materials available on the Internet. These web documents provide source code for simulations, step-by-step derivations of certain mathematical formulations, and expanded explanations of some concepts.

Download or read book Mathematical Modeling and Simulation in Enteric Neurobiology written by Roustem Miftahof and published by World Scientific. This book was released on 2009 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lack of scientists equally trained and prepared to understand both mathematics and biology/medicine hampers the development and application of computer simulation methods in biology and neurogastrobiology. Currently, there are no texts for navigating the extensive and intricate field of mathematical and computational modeling in neurogastrobiology. This book bridges the gap between mathematicians, computer scientists and biologists, and thus assists in the study and analysis of complex biological phenomena that cannot be done through traditional in vivo and in vitro experimental approaches. The book recognizes the complexity of biological phenomena under investigation and treats the subject matter with a degree of mathematical rigor. Special attention is given to computer simulations for interpolation and extrapolation of electromechanical and chemoelectrical phenomena, nonlinear self-sustained electromechanical wave activity, pharmacological effects including co-localization and co-transmission by multiple neurotransmitters, receptor polymodality, and drug interactions. Mathematical Modeling and Simulation in Enteric Neurobiology is an interdisciplinary book and is an essential source of information for biologists and doctors who are interested in knowing about the role and advantages of numerical experimentation in their subjects, as well as for mathematicians who are interested in exploring new areas of applications.

Download or read book Foundations and Methods from Mathematics to Neuroscience written by Colleen Crangle and published by Center for the Study of Language and Information Publica Tion. This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: During his long and continuing scholarly career, Patrick Suppes contributed significantly both to the sciences and to their philosophies. The volume consists of papers by an international group of Suppes colleagues, collaborators, and students in many of the areas of his expertise, building on or adding to his insights. Michael Friedman offers an overview of Suppes accomplishments and of his unique perspective on the relation between science and philosophy. Paul Humphreys, Stephen Hartmann, and Tom Ryckman present essays in the philosophy of physics. Jens-Erik Fenstad, Harvey Friedman, and Jaako Hintikka consider problems in the foundations of mathematics, while the late Duncan Luce, Jean-Claude Falmagne, Brian Skyrms, and Hannes Leitgeb have contributed essays in theory of measurement, decision theory and probability. Foundations of economics and political theory are addressed by Adolfo Garcia de la Sienra, Russell Hardin, and Kenneth Arrow. Psychology, language, and philosophy of language are addressed by Elizabeth Loftus, Anne Fagot-Largeault, Willem Levelt, Dagfinn Follesdal, and Marcos Perreau-Guimares and some of Suppes most recent research in neurobiology is addressed in essays by Colleen Crangle, Acadio de Barros and Claudio Carvalhes. Finally Nancy Cartwright and Alexandre Marcelles consider the alignment (or misalignment) of method and policy. Each of the essays is accompanied by a response from Suppes."