Neural Fields

Neural Fields
Author: Stephen Coombes
Publisher: Springer
Total Pages: 488
Release: 2014-06-17
Genre: Mathematics
ISBN: 3642545939

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Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.

Neural Modeling Fields

Neural Modeling Fields
Author: Fouad Sabry
Publisher: One Billion Knowledgeable
Total Pages: 189
Release: 2023-07-04
Genre: Computers
ISBN:

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What Is Neural Modeling Fields Neural modeling field (NMF) is a mathematical framework for machine learning that integrates ideas from neural networks, fuzzy logic, and model based recognition. Its acronym stands for "Neural Modeling Field." Modeling fields, modeling fields theory (MFT), and Maximum likelihood artificial neural networks (MLANS) are some of the other names that have been used to refer to this concept.At the AFRL, Leonid Perlovsky is the one responsible for developing this framework. The NMF can be understood as a mathematical description of the machinery that make up the mind. These mechanisms include ideas, feelings, instincts, imagination, reasoning, and comprehension. The NMF is organized in a hetero-hierarchical structure that contains many levels. There are concept-models that encapsulate the knowledge at each level of the NMF. These concept-models generate so-called top-down signals, which interact with input signals that come from lower levels. These interactions are governed by dynamic equations, which are responsible for driving concept-model learning, adaptation, and the development of new concept-models for better correspondence to the input, bottom-up signals. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Neural modeling fields Chapter 2: Machine learning Chapter 3: Supervised learning Chapter 4: Unsupervised learning Chapter 5: Weak supervision Chapter 6: Reinforcement learning Chapter 7: Neural network Chapter 8: Artificial neural network Chapter 9: Fuzzy logic Chapter 10: Adaptive neuro fuzzy inference system (II) Answering the public top questions about neural modeling fields. (III) Real world examples for the usage of neural modeling fields in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of neural modeling fields' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of neural modeling fields.

Neuronal Dynamics

Neuronal Dynamics
Author: Wulfram Gerstner
Publisher: Cambridge University Press
Total Pages: 591
Release: 2014-07-24
Genre: Computers
ISBN: 1107060834

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

Statistical Field Theory for Neural Networks

Statistical Field Theory for Neural Networks
Author: Moritz Helias
Publisher: Springer Nature
Total Pages: 203
Release: 2020-08-20
Genre: Science
ISBN: 303046444X

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This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.

Artificial Higher Order Neural Networks for Modeling and Simulation

Artificial Higher Order Neural Networks for Modeling and Simulation
Author: Zhang, Ming
Publisher: IGI Global
Total Pages: 455
Release: 2012-10-31
Genre: Computers
ISBN: 1466621761

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"This book introduces Higher Order Neural Networks (HONNs) to computer scientists and computer engineers as an open box neural networks tool when compared to traditional artificial neural networks"--Provided by publisher.

Dynamic Thinking

Dynamic Thinking
Author: Gregor Schöner
Publisher: Oxford University Press
Total Pages: 421
Release: 2016
Genre: Psychology
ISBN: 0199300569

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"This book describes a new theoretical approach--Dynamic Field Theory (DFT)--that explains how people think and act"--

Neural Modeling

Neural Modeling
Author: Ronald MacGregor
Publisher: Springer Science & Business Media
Total Pages: 413
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1468421905

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The purpose of this book is to introduce and survey the various quantitative methods which have been proposed for describing, simulating, embodying, or characterizing the processing of electrical signals in nervous systems. We believe that electrical signal processing is a vital determinant of the functional organization of the brain, and that in unraveling the inherent complexities of this processing it will be essential to utilize the methods of quantification and modeling which have led to crowning successes in the physical and engineering sciences. In comprehensive terms, we conceive neural modeling to be the attempt to relate, in nervous systems, function to structure on the basis of operation. Sufficient knowledge and appropriate tools are at hand to maintain a serious and thorough study in the area. However, work in the area has yet to be satisfactorily integrated within contemporary brain research. Moreover, there exists a good deal of inefficiency within the area resulting from an overall lack of direction, critical self-evaluation, and cohesion. Such theoretical and modeling studies as have appeared exist largely as fragmented islands in the literature or as sparsely attended sessions at neuroscience conferences. In writing this book, we were guided by three main immediate objectives. Our first objective is to introduce the area to the upcoming generation of students of both the hard sciences and psychological and biological sciences in the hope that they might eventually help bring about the contributions it promises.

Introduction to Neural and Cognitive Modeling

Introduction to Neural and Cognitive Modeling
Author: Daniel S. Levine
Publisher: Psychology Press
Total Pages: 573
Release: 2000-02-01
Genre: Psychology
ISBN: 1135692246

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This thoroughly, thoughtfully revised edition of a very successful textbook makes the principles and the details of neural network modeling accessible to cognitive scientists of all varieties as well as to others interested in these models. Research since the publication of the first edition has been systematically incorporated into a framework of proven pedagogical value. Features of the second edition include: * A new section on spatiotemporal pattern processing * Coverage of ARTMAP networks (the supervised version of adaptive resonance networks) and recurrent back-propagation networks * A vastly expanded section on models of specific brain areas, such as the cerebellum, hippocampus, basal ganglia, and visual and motor cortex * Up-to-date coverage of applications of neural networks in areas such as combinatorial optimization and knowledge representation As in the first edition, the text includes extensive introductions to neuroscience and to differential and difference equations as appendices for students without the requisite background in these areas. As graphically revealed in the flowchart in the front of the book, the text begins with simpler processes and builds up to more complex multilevel functional systems. For more information visit the author's personal Web site at www.uta.edu/psychology/faculty/levine/

Neural Masses and Fields: Modelling the Dynamics of Brain Activity

Neural Masses and Fields: Modelling the Dynamics of Brain Activity
Author: Karl Friston
Publisher: Frontiers Media SA
Total Pages: 238
Release: 2015-05-25
Genre: Differential equations
ISBN: 2889194272

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Biophysical modelling of brain activity has a long and illustrious history and has recently profited from technological advances that furnish neuroimaging data at an unprecedented spatiotemporal resolution. Neuronal modelling is a very active area of research, with applications ranging from the characterization of neurobiological and cognitive processes, to constructing artificial brains in silico and building brain-machine interface and neuroprosthetic devices. Biophysical modelling has always benefited from interdisciplinary interactions between different and seemingly distant fields; ranging from mathematics and engineering to linguistics and psychology. This Research Topic aims to promote such interactions by promoting papers that contribute to a deeper understanding of neural activity as measured by fMRI or electrophysiology. In general, mean field models of neural activity can be divided into two classes: neural mass and neural field models. The main difference between these classes is that field models prescribe how a quantity characterizing neural activity (such as average depolarization of a neural population) evolves over both space and time as opposed to mass models, which characterize activity over time only; by assuming that all neurons in a population are located at (approximately) the same point. This Research Topic focuses on both classes of models and considers several aspects and their relative merits that: span from synapses to the whole brain; comparisons of their predictions with EEG and MEG spectra of spontaneous brain activity; evoked responses, seizures, and fitting data - to infer brain states and map physiological parameters.

Neural Networks and Neural Fields

Neural Networks and Neural Fields
Author: Roderick Edwards
Publisher:
Total Pages: 0
Release: 1994
Genre: Neural circuitry
ISBN:

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