Title | Models of Neurons and Perceptrons: Selected Problems and Challenges [electronic resource] / by Andrzej Bielecki |
---|---|

Imprint | Cham : Springer International Publishing : Imprint: Springer, 2019 |

Connect to | https://doi.org/10.1007/978-3-319-90140-4 |

Descript | VI, 156 p. 30 illus. online resource |

SUMMARY

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

CONTENT

Introduction -- Part I: Preliminaries -- Foundations of artiﬁcial 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.

Engineering
Artificial intelligence
Neurobiology
Computational Intelligence. http://scigraph.springernature.com/things/product-market-codes/T11014
Artificial Intelligence. http://scigraph.springernature.com/things/product-market-codes/I21000
Mathematical Models of Cognitive Processes and Neural Networks. http://scigraph.springernature.com/things/product-market-codes/M13100
Complexity. http://scigraph.springernature.com/things/product-market-codes/T11022
Neurobiology. http://scigraph.springernature.com/things/product-market-codes/L25066