| Description |
1 online resource |
| Contents |
Chapter 1. Introduction -- Logical Basis for Computation -- Logical Basis for Control -- Logical Basis of Communication -- Advanced Theory of Evolution -- Chapter 2. Multi/Infinite Dimensional Neural Networks, Multi/Infinite Dimensional Logic Theory -- 2.1 Introduction -- 2.2 Mathematical Model of Multidimensional Neural Networks -- 2.3 Convergence Theorem for Multidimensional Neural Networks -- 2.4 Multidimensional Logic Theory, Logic Synthesis -- 2.5 Infinite Dimensional Logic Theory : Infinite Dimensional Logic Synthesis -- 2.6 Neural Networks, Logic Theories, Constrained Static Optimization -- 2.7 Conclusions -- Chapter 3. Multi/Infinite Dimensional Coding Theory : Multi/Infinite Dimensional Neural Networks, Constrained Static Optimization -- 3.1 Introduction -- 3.2 Multidimensional Neural Networks : Minimum Cut computation in the Connection Structure -- 3.3 Multidimensional Error Correcting Codes : Associated Energy Functions, Generalized Neural Networks -- 3.4 Multidimensional Error Correcting Codes: Relationship to Stable States of Energy Functions -- 3.5 Non-Binary Linear Codes -- 3.6 Non-Linear Codes -- 3.7 Constrained Static Optimization -- 3.8 Conclusions -- Chapter 4. Tensor State Space Representation: Multidimensional Systems -- 4.1 Introduction -- 4.2 State of the Art in Multi/Infinite Dimensional Static/Dynamic System Theory : Representation by Tensor Linear Operator -- 4.3 State Space Representation of Certain Multi/Infinite Dimensional Dynamical Systems : Tensor Linear Operator -- 4.4 Multi/Infinite Dimensional System Theory : Linear Dynamical Systems State Space Representation by Tensor Linear Operators -- 4.5 Stochastic Dynamical Systems -- 4.6 Distributed Dynamical Systems -- 4.7 Conclusions -- Chapter 5. Unified Theory of Control, Communication and Computation : Multidimensional Neural Networks -- 5.1 Introduction -- 5.2 One-Dimensional Logic Functions, Codeword Vectors, Optimal Control Vectors : One-Dimensional Neural Networks -- 5.3 Optimal Control Tensors : Multidimensional Neural Networks -- 5.4 Multidimensional Systems : Optimal Control Tensors, Codeword Tensors And Switching Function Tensors -- 5.5 Conclusions -- Chapter 6. Complex Valued Neural Associative Memory on the Complex Hypercube -- 6.1 Introduction -- 6.2 Features of the Proposed Model -- 6.3 Convergence Theorems -- 6.4 Conclusions -- Chapter 7. Optimal Binary Filters : Neural Networks -- 7.1 Introduction -- 7.2 Optimal Signal Design Problem : Solution -- 7.3 Optimal Filter Design Problem : Solution (Dual of Signal design Problem) -- 7.4 Conclusions -- Chapter 8. Linear Filter Model of a Synapse : Associated Novel Real/Complex Valued Neural Networks -- 8.1 Introduction -- 8.2 Continuous Time Perceptron and Generalizations -- 8.3 Abstract Mathematical Structure of Neuronal Models -- 8.4 Finite Impulse Response Model of Synapses : Neural Networks -- 8.5 Novel Continuous Time Associative Memory -- 8.6 Multidimensional Generalizations -- 8.7 Generalization to Complex Valued Neural Networks (CVNNs) -- 8.8. Conclusions -- Chapter 9. Novel Complex Valued Neural Networks -- 9.1 Introduction -- 9.2 Discrete Fourier Transform : Some Complex Valued Neural Networks -- Chapter 10. Advanced Theory of Evolution of Living Systems |
| Summary |
About the Book: The book ''Multidimensional Neural Networks (MDNNs): Unified Theory'' has been conceived for serving 3 types of users: Senior undergraduate/graduate students, practising engineers, and advanced neural network researchers. This book is based on the following innovations: Multidimensional (M-D) logic theory i.e., conceiving logic gates/circuits operating on multidimensional arrays Tensor state space representation of certain M-D systems Relation M-D logic gates, M-D codeword tensors, M-D optimal control tensors to M-D neural networks unification Novel complex valued associative memory (CVNN) on the hypercube Novel models of biological neurons such as those with a linear filter model of synapse Neural network based signal processing The subject of M-D neural networks will have the applications in: Design of versatile associative memories, Optimal design of intelligent systems, Pattern recognition systems etc. Contents: Introduction Multi/Infinite Dimensional Neural Networks, Multi/Infinite Dimensional Logic Theory Multi/Infinite Dimensional Coding Theory: Multi/Infinite Dimensional Neural Networks?Constrained Static Optimization Tensor State Space Representation: Multi Dimensional Systems Unified Theory of Control, Communication and Computation: Multi Dimensional Neural Networks Complex Valued Neural Associative Memory on the Complex Hypercube Optimal Binary Filters: Neural Networks Linear Filter Model of a Synapse: Associated Novel Real/Complex Valued Neural Networks Novel Complex Valued Neural Networks Advanced Theory of Evolution of Living Systems |
| Notes |
Includes index |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
|
Print version record |
| Subject |
Neural networks (Computer science)
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COMPUTERS -- Neural Networks.
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Neural networks (Computer science)
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| Form |
Electronic book
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| ISBN |
9788122426298 |
|
8122426298 |
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1282074113 |
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9781282074118 |
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8122422284 |
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9788122422283 |
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