Models of Neurons and Perceptrons: Selected Problems and Challenges

Description

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. Front Matter ....Pages i-vi Introduction (Andrzej Bielecki)....Pages 1-3 Front Matter ....Pages 5-5 Biological Foundations (Andrzej Bielecki)....Pages 7-13 Foundations of Artificial Neural Networks (Andrzej Bielecki)....Pages 15-28 Front Matter ....Pages 29-29 General Foundations (Andrzej Bielecki)....Pages 31-33 Foundations of Dynamical Systems Theory (Andrzej Bielecki)....Pages 35-55 Front Matter ....Pages 57-57 Models of the Whole Neuron (Andrzej Bielecki)....Pages 59-65 Models of Parts of the Neuron (Andrzej Bielecki)....Pages 67-96 Front Matter ....Pages 97-97 General Model of the Perceptron (Andrzej Bielecki)....Pages 99-110 Linear Perceptrons (Andrzej Bielecki)....Pages 111-119 Weakly Nonlinear Perceptrons (Andrzej Bielecki)....Pages 121-124 Nonlinear Perceptrons (Andrzej Bielecki)....Pages 125-132 Concluding Remarks and Comments (Andrzej Bielecki)....Pages 133-134 Front Matter ....Pages 135-135 Approximation Properties of Perceptrons (Andrzej Bielecki)....Pages 137-139 Proofs (Andrzej Bielecki)....Pages 141-147 Back Matter ....Pages 149-156