Spikes, Decisions, and Actions


Book Description

The nervous system of higher animals is both very complex and very nonlinear. Nervous systems are constantly making decisions between alternative actions, and switching gears among dynamical modes. There are several neural phenomena that can be modelled to great effect through the applicationof nonlinear dynamics, including: * ionic currents * action potentials * short-term memory * motor activity. This book is an exploration of the mathematical principles by which brains generate neural spikes, make decisions, store memories, and control actions. Assuming only a basic knowledge ofmathematics, and including problem sets and simulations on disk, Spikes, Decisions, and Actions is an ideal text for courses in neuronal modelling in particular, and mathematical modelling in biology generally.




Spikes, Decisions, and Actions


Book Description

The nervous system of higher animals is very complex and highly nonlinear. among its many capabilities are making decisions and carrying out complex motor actions such as swimming. Nonlinear dynamical modelling can be used to understand and explain neural phenomena at many different levels, including - ion-currents and action potentials; short - and long - term memory; visual hallucinations; neural synchronization; motor control This book explores the mathematical principles by which brains generate spikes, make decisions, store memories, and control actions. It assumes a basic knowledge of calculus and develops the dynamical foundations of neuroscience using problem sets and computer simulations on the accompanying PC and Mac compatible MatLab disk.




Spikes


Book Description

Intended for neurobiologists with an interest in mathematical analysis of neural data as well as the growing number of physicists and mathematicians interested in information processing by "real" nervous systems, Spikes provides a self-contained review of relevant concepts in information theory and statistical decision theory.




Brain Dynamics


Book Description

This is an excellent introduction for graduate students and nonspecialists to the field of mathematical and computational neurosciences. The book approaches the subject via pulsed-coupled neural networks, which have at their core the lighthouse and integrate-and-fire models. These allow for highly flexible modeling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. The more advanced pulse-averaged equations are discussed.




Brain Dynamics


Book Description

This book addresses a large variety of models in mathematical and computational neuroscience. It is written for the experts as well as for graduate students wishing to enter this fascinating field of research. The author studies the behaviour of large neural networks composed of many neurons coupled by spike trains. He devotes the main part to the synchronization problem. He presents neural net models more realistic than the conventional ones by taking into account the detailed dynamics of axons, synapses and dendrites, allowing rather arbitrary couplings between neurons. He gives a complete stabile analysis that goes significantly beyond what has been known so far. He also derives pulse-averaged equations including those of the Wilson--Cowan and the Jirsa-Haken-Nunez types and discusses the formation of spatio-temporal neuronal activity pattems. An analysis of phase locking via sinusoidal couplings leading to various kinds of movement coordination is included.




Neuronal Dynamics


Book Description

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.




Neuroscience


Book Description

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.




Fechner's Legacy in Psychology


Book Description

A compendium of modern psychophysics, in the spirit of the discipline's inventor, Gustav Fechner.




Cerebral Cortex


Book Description

The aim of this book is to provide insight into the principles of operation of the cerebral cortex. These principles are key to understanding how we, as humans, function. There have been few previous attempts to set out some of the important principles of operation of the cortex, and this book is pioneering. The book goes beyond separate connectional neuroanatomical, neurophysiological, neuroimaging, neuropsychiatric, and computational neuroscience approaches, by combining evidence from all these areas to formulate hypotheses about how and what the cerebral cortex computes. As clear hypotheses are needed in this most important area of 21st century science, how our brains work, I have formulated a set of hypotheses about the principles of cortical operation to guide thinking and future research. The book focusses on the principles of operation of the cerebral cortex, because at this time it is possible to propose and describe many principles, and many are likely to stand the test of time, and provide a foundation for further developments, even if some need to be changed. In this context, I have not attempted to produce an overall theory of operation of the cerebral cortex, because at this stage of our understanding, such a theory would be incorrect or incomplete. However, many of the principles described will provide the foundations for more complete theories of the operation of the cerebral cortex. This book is intended to provide a foundation for future understanding, and it is hoped that future work will develop and add to these principles of operation of the cerebral cortex. The book includes Appendices on the operation of many of the neuronal networks described in the book, together with simulation software written in Matlab.




Synergetics


Book Description

This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.