Code Recognition and Set Selection with Neural Networks

0-The Neural Network Approach to Problem Solving.- 0.1 Defining a Neural Network.- 0.2 Neural Networks as Dynamical Systems.- 0.3 Additive and High Order Models.- 0.4 Examples.- 0.5 The Link with Neuroscience.- 1-Neural Networks as Dynamical Systems.- 1.1 General Neural Network Models.- 1.2 General Features of Neural Network Dynamics.- 1.3 Set Selection Problems.- 1.4 Infeasible Constant Trajectories.- 1.5 Another Set Selection Problem.- 1.6 Set Selection Neural Networks with Perturbations.- 1.7 Learning.- Problems and Answers.- 2-Hypergraphs and Neural Networks.- 2.1 Multiproducts in Neural Network Models.- 2.2 Paths, Cycles, and Volterra Multipliers.- 2.3 The Cohen-Grossberg Function.- 2.4 The Foundation Function ?.- 2.5 The Image Product Formulation of High Order Neural Networks.- Problems and Answers.- 3-The Memory Model.- 3.1 Dense Memory with High Order Neural Networks.- 3.2 High Order Neural Network Models.- 3.3 The Memory Model.- 3.4 Dynamics of the Memory Model.- 3.5 Modified Memory Models Using the Foundation Function.- 3.6 Comparison of the Memory Model and the Hopfield Model.- Problems and Answers.- 4-Code Recognition, Digital Communications, and General Recognition.- 4.1 Error Correction for Binary Codes.- 4.2 Additional Tests of the Memory Model as a Decoder.- 4.3 General Recognition.- 4.4 Scanning in Image Recognition.- 4.5 Commercial Neural Network Decoding.- Problems and Answers.- 5-Neural Networks as Dynamical Systems.- 5.1 A Two-Dimensional Limit Cycle.- 5.2 Wiring.- 5.3 Neural Networks with a Mixture of Limit Cycles and Constant Trajectories.- Problems and Answers.- 6-Solving Operations Research Problems with Neural Networks.- 6.1 Selecting Permutation Matrices with Neural Networks.- 6.2 Optimization in a Modified Permutation Matrix Selection Model.- 6.3 The Quadratic Assignment Problem.- Appendix A-An Introduction to Dynamical Systems.- A.1 Elements of Two-Dimensional Dynamical Systems.- A.2 Elements of n-Dimensional Dynamical Systems.- A.3 The Relation Between Difference and Differential Equations.- A.4 The Concept of Stability.- A.5 Limit Cycles.- A.6 Lyapunov Theory.- A.7 The Linearization Theorem.- A.8 The Stability of Linear Systems.- Appendix B-Simulation of Dynamical Systems with Spreadsheets.- References.- Index of Key Words.- Epilog.