Advertisement

Models of Neurons and Perceptrons: Selected Problems and Challenges

  • Andrzej¬†Bielecki

Part of the Studies in Computational Intelligence book series (SCI, volume 770)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Andrzej Bielecki
    Pages 1-3
  3. Preliminaries

    1. Front Matter
      Pages 5-5
    2. Andrzej Bielecki
      Pages 7-13
    3. Andrzej Bielecki
      Pages 15-28
  4. Mathematical Foundations

    1. Front Matter
      Pages 29-29
    2. Andrzej Bielecki
      Pages 31-33
    3. Andrzej Bielecki
      Pages 35-55
  5. Mathematical Models of the Neuron

    1. Front Matter
      Pages 57-57
    2. Andrzej Bielecki
      Pages 59-65
    3. Andrzej Bielecki
      Pages 67-96
  6. Mathematical Models of the Perceptron

    1. Front Matter
      Pages 97-97
    2. Andrzej Bielecki
      Pages 99-110
    3. Andrzej Bielecki
      Pages 111-119
    4. Andrzej Bielecki
      Pages 121-124
    5. Andrzej Bielecki
      Pages 125-132
    6. Andrzej Bielecki
      Pages 133-134
  7. Appendix

    1. Front Matter
      Pages 135-135
    2. Andrzej Bielecki
      Pages 137-139
    3. Andrzej Bielecki
      Pages 141-147
  8. Back Matter
    Pages 149-156

About this book

Introduction

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.

Keywords

Computational Intelligence Neurons Perceptron Dynamical Systems Artificial Neural Networks

Authors and affiliations

  • Andrzej¬†Bielecki
    • 1
  1. 1.Faculty of Electrical Engineering, Automation, Computer Science and Biomedical EngineeringAGH University of Science and TechnologyCracowPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-90140-4
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2019
  • Publisher Name Springer, Cham
  • eBook Packages Intelligent Technologies and Robotics
  • Print ISBN 978-3-319-90139-8
  • Online ISBN 978-3-319-90140-4
  • Series Print ISSN 1860-949X
  • Series Online ISSN 1860-9503
  • Buy this book on publisher's site