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Quantum Neural Computation

Quantum Neural ComputationTitoloQuantum Neural Computation
AutoreIvancevic, Vladimir G. ; Ivancevic, Tijana T.
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€ 244,90   Spedizioni gratuite in Italia
(Prezzo € 252,47)
CategoriaComputers: Intelligence (AI) & Semantics
Medical: Neuroscience
Science: Physics - Quantum Theory
RilegaturaHardcover
Dati929 p.; ill.
Anno2009
EditoreSpringer
CollanaIntelligent Systems, Control, and Automation: Science and Engineering
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Descrizione

This book presents an introduction, both non-technical and technical, to modern quantum neural computation. It combines quantum computation with neural computation and provides a blueprint for the future quantum brain.

Indice e argomenti trattati
Introduction
1
Neurodynamics
2
Quantum Computation
3
Discrete Quantum Computers
4
Topological Quantum Computers
14
Computation at the Edge of Chaos and Quantum Neural Networks
18
Adaptive Path Integral: An ∞-Dimensional QNN
22
Computational Partition Function
22
From Thermodynamics to Quantum Field Theory
24
∞-Dimensional QNNs
24
Brain Topology vs. Small-World Topology
26
Quantum Brain and Mind
30
Connectionism, Control Theory and Brain Theory
30
Neocortical Biophysics
31
Quantum Neurodynamics
35
Bi-Stable Perception and Consciousness
37
Notational Conventions
40
Brain and Classical Neural Networks
43
Human Brain
43
Basics of Brain Physiology
50
Modern 3D Brain Imaging
70
Biological versus Artificial Neural Networks
78
Common Discrete ANNs
80
Common Continuous ANNs
98
Synchronization in Neurodynamics
106
Phase Synchronization in Coupled Chaotic Oscillators
106
Oscillatory Phase Neurodynamics
109
Kuramoto Synchronization Model
112
Lyapunov Chaotic Synchronization
113
Spike Neural Networks and Wavelet Resonance
114
Ensemble Neuron Model
117
Wavelet Neurodynamics
119
Wavelets of Epileptic Spikes
129
Human Motor Control and Learning
133
Motor Control
134
Human Memory
138
Human Learning
140
Spinal Musculo-Skeletal Control
142
Cerebellum and Muscular Synergy
145
Quantum Theory Basics
151
Basics of Non-Relativistic Quantum Mechanics
151
Soft Introduction to Quantum Mechanics
152
Quantum States and Operators
157
The Tree Standard Quantum Pictures
163
Dirac's Probability Amplitude and Perturbation
165
State-Space for n Non-Relativistic Quantum Particles
168
Quantum Fourier Transform
170
Introduction to Quantum Fields
171
Amplitude, Relativistic Invariance and Causality
171
Gauge Theories
173
Free and Interacting Field Theories
176
Dirac's Quantum Electrodynamics (QED)
177
Abelian Higgs Model
179
Topological Quantum Computation
181
The Feynman Path Integral
188
The Action-Amplitude Formalism
188
Correlation Functions and Generating Functional
191
Quantization of the Electromagnetic Field
193
Wavelet-Based QFT
194
The Path-Integral TQFT
199
Schwarz-Type and Witten-Type Theories
199
Hodge Decomposition Theorem
201
Hodge Decomposition and Chern--Simons Theory
204
Non-Abelian Gauge Theories
207
Introduction to Non-Abelian Theories
207
Yang--Mills Theory
207
Quantization of Yang--Mills Theory
212
Basics of Conformal Field Theory (CFT)
214
Spatio-Temporal Chaos, Solitons and NLS
219
Reaction--Diffusion Processes and Ricci Flow
219
Bio-Reaction--Diffusion Systems
223
Reactive Neurodynamics
236
Dissipative Evolution Under the Ricci Flow
246
Turbulence and Chaos in PDEs
258
Quantum Chaos and Its Control
266
Quantum Chaos vs. Classical Chaos
271
Optimal Control of Quantum Chaos
280
Solitons
288
Short History of Solitons
288
Lie--Poisson Bracket
309
Solitons and Muscular Contraction
310
Dispersive Wave Equations and Stability of Solitons
312
KdV Solitons
321
The Inverse Scattering Approach
323
Nonlinear Schrodinger Equation (NLS)
327
Cubic NLS
327
Nonlinear Wave and Schrodinger Equations
331
Physical NLS-Derivation
335
A Compact Attractor for High-Dimensional NLS
337
Finite-Difference Scheme for NLS
345
Method of Lines for NLS
345
Quantum Brain and Cognition
349
Biochemistry of Microtubules
349
Kink Soliton Model of MT-Dynamics
351
Fractal Neurodynamics
353
Open Liouville Equation
355
Dissipative Quantum Brain Model
360
QED Brain Model
366
Stochastic NLS-Filtering and Robotic Eye Tracking
373
QNN-Based Neural Motor Control
376
Spinal Reflex Control of Biodynamics
378
Local Muscle-Joint Mechanics
379
Cerebellum: Adaptive Path-Integral Comparator
383
Quantum Cognition in the Life Space Foam
388
Classical versus Quantum Probability
390
The Life Space Foam
395
Geometric Chaos and Topological Phase Transitions
402
Joint Action of Several Agents
408
Chaos and Bernstein--Brooks Adaptation
411
Quantum Cognition in Crowd Dynamics
413
Cognition and Crowd Behavior
414
Generic Three-Step Crowd Behavioral Dynamics
416
Formal Individual, Aggregate and Crowd dynamics
417
Crowd Entropy, Chaos and Phase Transitions
430
Crowd Ricci Flow and Perelman Entropy
430
Chaotic Inter-Phase in Crowd Dynamics
433
Crowd Phase Transitions
434
Quantum Information, Games and Computation
437
Quantum Information and Computing
437
Entanglement, Teleportation and Information
437
The Circuit Model for Quantum Computers
440
Elementary Quantum Algorithms
441
Quantum Games
442
Quantum Strategies
444
Quantum Games
447
Two-Qubit Quantum Games
449
Quantum Cryptography and Quantum Gambling
460
Formal Quantum Games
467
Hardware for Quantum Computers
478
Josephson Effect and Pendulum Analog
482
Dissipative Josephson Junction
484
Josephson Junction Ladder (JJL)
489
Synchronization in Arrays of Josephson Junctions
498
Topological Machinery for Quantum Computation
511
Non-Abelian Anyons
512
Emergent Anyons
519
Option Price Modeling Using Quantum Neural Computation
551
Bidirectional, Spatio-Temporal, Complex-Valued Associative Memory Machine
554
Appendix: Mathematical and Computational Tools
559
Meta-Language of Categories and Functors
559
Maps
559
Categories
567
Functors
570
Natural Transformations
573
Limits and Colimits
575
Adjunction
576
n-Categories and n-Functors
578
Topological Structure of n-Categories
583
Frequently Used Mathematical Concepts
586
Groups and Related Algebraic Structures
586
Manifolds, Bundles and Lie Groups
590
Unitary Matrix and Group
594
Differential Forms and Stokes Theorem
600
Symmetry Breaking and Partition Function
604
Basics of Kalman Filtering
607
Basics of Wavelet Transforms
619
Basic of Nonlinear Dynamics and Chaos Theory
639
Basics of Nash's Game Theory
713
Frequently Used Computational Tools
729
Basic Numerical Algorithms
729
Numerical Integration of Functions
734
Numerical Integration of ODEs
738
Vector-Field and Lyapunov Function
755
Basics of Qualitative Dynamics
759
Kuramoto's Neural Model
761
Boundary Value Problems and PDEs
767
Evolution PDEs in Mathematica(TM)
788
Fourier Transforms
791
Sophisticated Random Algorithms
800
Sophisticated Integration Algorithms
810
References841
Index913

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