Models of Neurons and Perceptrons: Selected Problems and Challenges

Softcover Nachdruck of the original 1. Auflage 2019
ISBN: 978-3-030-07942-0
Verlag: Springer International Publishing

Buch, Englisch, Band 770, 156 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 260 g

Reihe: Studies in Computational Intelligence

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.

Zielgruppe

Research

Autoren/Hrsg.

Bielecki, Andrzej

Fachgebiete

• Naturwissenschaften Biowissenschaften Biowissenschaften Neurobiologie, Verhaltensbiologie
• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Neuronale Netzwerke

Inhaltsverzeichnis

Introduction.- Part I: Preliminaries.- Foundations of arti?cial neural networks.- Part II: Mathematical foundations.- General foundations.- Foundations of dynamical systems theory.- Part III: Mathematical models of the neuron.- Models of the whole neuron.- Models of parts of the neuron.- Part IV: Mathematical models of the perceptron.- General model of the perceptron.- Linear perceptrons.- Weakly nonlinear perceptrons.- Nonlinear perceptrons.- Concluding remarks and comments.