Weakly Connected Neural Networks

Author: Frank C. Hoppensteadt
Publisher: Springer Science & Business Media
ISBN: 1461218284
Format: PDF, ePub, Mobi
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Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.

Weakly Connected Neural Networks

Author: Frank C. Hoppensteadt
Publisher: Springer Science & Business Media
ISBN: 1461218284
Format: PDF
Download Now
Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.

Quasi static State Analysis of Differential Difference Integral and Gradient Systems

Author: F. C. Hoppensteadt
Publisher: American Mathematical Soc.
ISBN: 0821852698
Format: PDF, ePub, Docs
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This book is based on a course on advanced topics in differential equations given in Spring 2010 at the Courant Institute of Mathematical Sciences. It describes aspects of mathematical modeling, analysis, computer simulation, and visualization in the mathematical sciences and engineering that involve singular perturbations. There is a large literature devoted to singular perturbation methods for ordinary and partial differential equations, but there are not many studies that deal with difference equations, Volterra integral equations, and purely nonlinear gradient systems where there is no dominant linear part. Designed for a one-semester course for students in applied mathematics, it is the purpose of this book to present sufficient rigorous methods and examples to position the reader to investigate singular perturbation problems in such equations. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.|This book is based on a course on advanced topics in differential equations given in Spring 2010 at the Courant Institute of Mathematical Sciences. It describes aspects of mathematical modeling, analysis, computer simulation, and visualization in the mathematical sciences and engineering that involve singular perturbations. There is a large literature devoted to singular perturbation methods for ordinary and partial differential equations, but there are not many studies that deal with difference equations, Volterra integral equations, and purely nonlinear gradient systems where there is no dominant linear part. Designed for a one-semester course for students in applied mathematics, it is the purpose of this book to present sufficient rigorous methods and examples to position the reader to investigate singular perturbation problems in such equations. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Informative Psychometric Filters

Author: Robert A. M. Gregson
Publisher: ANU E Press
ISBN: 1920942661
Format: PDF, Kindle
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This book is a series of case studies with a common theme. Some refer closely to previous work by the author, but contrast with how they have been treated before, and some are new. Comparisons are drawn using various sorts of psychological and psychophysiological data that characteristically are particularly nonlinear, non-stationary, far from equilibrium and even chaotic, exhibiting abrupt transitions that are both reversible and irreversible, and failing to meet metric properties. A core idea is that both the human organism and the data analysis procedures used are filters, that may variously preserve, transform, distort or even destroy information of significance.

Nonnegative Matrices in the Mathematical Sciences

Author: Abraham Berman
Publisher: Academic Press
ISBN: 1483260860
Format: PDF, ePub
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Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.

Controlling Chaos and Bifurcations in Engineering Systems

Author: Guanrong Chen
Publisher: CRC Press
ISBN: 9780849305795
Format: PDF, ePub
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Over the last two decades, chaos in engineering systems has moved from being simply a curious phenomenon to one with real, practical significance and utility. Engineers, scientists, and mathematicians have similarly advanced from the passive role of analyzing chaos to their present, active role of controlling chaos-control directed not only at suppression, but also at exploiting its enormous potential. We now stand at the threshold of major advances in the control and synchronization of chaos for new applications across the range of engineering disciplines. Controlling Chaos and Bifurcations in Engineering Systems provides a state-of-the-art survey of the control-and anti-control-of chaos in dynamical systems. Internationally known experts in the field join forces in this volume to form this tutorial-style combination of overview and technical report on the latest advances in the theory and applications of chaos control. They detail various approaches to control and show how designers can use chaos to create a wider variety of properties and greater flexibility in the design process. Chaos control promises to have a major impact on novel time- and energy-critical engineering applications. Within this volume, readers will find many challenging problems-yet unsolved-regarding both the fundamental theory and potential applications of chaos control and anti-control. Controlling Chaos and Bifurcations in Engineering Systems will bring readers up-to-date on recent development in the field and help open the door to new advances.

Vorticity and Turbulence

Author: Alexandre J. Chorin
Publisher: Springer Science & Business Media
ISBN: 1441987282
Format: PDF, ePub
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This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial. The first three chapters of the book contain a reasonably standard intro duction to homogeneous turbulence (the simplest case); a quick review of fluid mechanics is followed by a summary of the appropriate Fourier theory (more detailed than is customary in fluid mechanics) and by a summary of Kolmogorov's theory of the inertial range, slanted so as to dovetail with later vortex-based arguments. The possibility that the inertial spectrum is an equilibrium spectrum is raised.

Networks

Author: Mark Newman
Publisher: OUP Oxford
ISBN: 0191500704
Format: PDF, ePub, Docs
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The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks. The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.