Overview
- Presents the modeling of neural systems, as well as hardware and software implementations of these models and their analysis using mathematical tools
- Discusses models of neural networks in the context of their modeling
- Unifies the studies on mathematical modeling of the biological neural structures and artificial neural networks
Part of the book series: Studies in Computational Intelligence (SCI, volume 770)
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About this book
This book describes models of the neuron and multilayer neural structures, with a particular focus on mathematical models. It also discusses electronic circuits used as models of the neuron and the synapse, and analyses the relations between the circuits and mathematical models in detail.
The first part describes the biological foundations and provides a comprehensive overview of the artificial neural networks. The second part then presents mathematical foundations, reviewing elementary topics, as well as lesser-known problems such as topological conjugacy of dynamical systems and the shadowing property. The final two parts describe the models of the neuron, and the mathematical analysis of the properties of artificial multilayer neural networks.
Combining biological, mathematical and electronic approaches, this multidisciplinary book it useful for the mathematicians interested in artificial neural networks and models of the neuron,for computer scientists interested in formal foundations of artificial neural networks, and for the biologists interested in mathematical and electronic models of neural structures and processes.
The first part describes the biological foundations and provides a comprehensive overview of the artificial neural networks. The second part then presents mathematical foundations, reviewing elementary topics, as well as lesser-known problems such as topological conjugacy of dynamical systems and the shadowing property. The final two parts describe the models of the neuron, and the mathematical analysis of the properties of artificial multilayer neural networks.
Combining biological, mathematical and electronic approaches, this multidisciplinary book it useful for the mathematicians interested in artificial neural networks and models of the neuron,for computer scientists interested in formal foundations of artificial neural networks, and for the biologists interested in mathematical and electronic models of neural structures and processes.
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Table of contents (14 chapters)
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Front Matter
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Preliminaries
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Front Matter
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Mathematical Foundations
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Front Matter
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Mathematical Models of the Neuron
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Front Matter
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Mathematical Models of the Perceptron
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Front Matter
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Appendix
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Front Matter
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Authors and Affiliations
Bibliographic Information
Book Title: Models of Neurons and Perceptrons: Selected Problems and Challenges
Authors: Andrzej Bielecki
Series Title: Studies in Computational Intelligence
DOI: https://doi.org/10.1007/978-3-319-90140-4
Publisher: Springer Cham
eBook Packages: Intelligent Technologies and Robotics, Intelligent Technologies and Robotics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2019
Hardcover ISBN: 978-3-319-90139-8Published: 28 May 2018
Softcover ISBN: 978-3-030-07942-0Published: 08 February 2019
eBook ISBN: 978-3-319-90140-4Published: 17 May 2018
Series ISSN: 1860-949X
Series E-ISSN: 1860-9503
Edition Number: 1
Number of Pages: VI, 156
Number of Illustrations: 30 b/w illustrations
Topics: Computational Intelligence, Artificial Intelligence, Mathematical Models of Cognitive Processes and Neural Networks, Complexity, Neurobiology