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Table of Contents


Subject Index

A

Absorbing barrier, 37
Acceptance function, 47
Acceptance ratio (initial), 56
Action, 4, 71
Action potential, 18, 21
Activation,

  (monotonic), 53
  instantaneous, 49, 52
  level, 23
  reference, 51
  rule, 59

Activation function, 130

  gaussian function 42
  ramp function 42
  sigmoidal function 42
  step function 42

Adaptive system, 9
Adiabatic hypothesis, 80
Algorithm, 30

  feedback, 42
  feed-forward, 42

All-or-none, 3, 22, 73
Annealing, 45, 46, 71, 202
Analyser, 191
Angular frequency, 131
Antiferromagnetic, 74
Artificial cooling temperature, 47
Artificial network, 1, 32
Associative array, 34
Associated memory, 13
Average energy, 54
Axon, 18
Axoplasm, 18

B

Backpropagation, 71
Basis function, 42
Baye’s (probability of) error, 183
Bernoulli function, 103, 104
Biochemical,

  activity, 13, 20
  effect, 26, 141

Biomime, 8
Blood vessels, 17
Bonds, 149, 201
Boltzmann

  distribution, 47
  energy, 44
  machine, 49, 61
  statistics, 46

Brain complex, 15, 17
Brown’s martingale

  central limit theorem, 161

Brownian movement, 136
Burst discharge (pattern), 87
Bursting (spontaneous), 87

C

Cauchy/Lorentzian distribution, 48
Cauchy machine, 48
Cerebellum, 17
Cerebrum, 17
Cerebral cortex, 20
Cerebrospinal fluid, 18
Central limit theorem, 112
Chapman-Kolmogorov equation, 114
Central nervous system, 17
Chemical potential, 65
Clamped mode, 63
Classifier, 191
Cognitive

  faculties, 11
  process, 13

Cognitive science, 12, 13
Colored noise (band-limited), 112
Collective activity, 15
Collective movement, 130, 144
Combinatoric (part), 121
Compacta, 163
Complex automata, 1
Connectionist (model), 47, 60
Conservation principle, 43
Consensus function, 48, 50
Continuum (model), 39
Controlling information, 167
Cooling

  polynomial time, 55
  rate, 55
  schedule, 47, 55,
  temperature, 47

Cooperative process, 72
Corpuscular motion, 132
Correlator, 191
Cost function, 46, 51
Cramer-Rao bound, 121
Criticality, 68

  precursor of, 68

Critical temperature, 49
Cross-entropy, 57, 165
Cross talk, 165
Curie point, 28, 78
(Curie temperature)
Current stimulus, 24
Cybernetics, 1, 6, 11, 48, 160
Cybernetic complex, 68
Cybernetic network, 86
C3I, 9, 15
Cyclic boundary conditions, 82

D

Dale’s law, 22
Decision procedure, 10
Declarative (message), 161
Degeneracy, 28, 76
(nondegenerate), 78
Degree of optimality, 59
Degree of organization, 169
Delocalized states, 150
Delta rule, 53
(Widrow-Hoff rule)
Dendrites, 18
Depolarization, 23
Descriptive (message), 161
Detailed balance, 150
Detailed balanced principle, 90
Deterministic decision, 52
Dichotomous potential, 8
Discrete time-step, 51
Disorganization, 7, 12, 160, 171
Disordered state, 79
Disturbance, 47
Distance

  parameter, 58
  function, 165

Duality principle, 36

E

Edward-Anderson parameter, 66
Effective model, 10
Effective procedure, 30
Effectors, 16
Electrical activity, 20, 142
Encoder, 191
End-bulb, 19
Energy function, 46, 54
Energy spread, 54
Energy state

  minimum, 45

Entropy, 4, 6, 72

  at equilibrium, 59
  thermodynamical, 65

Ergodicity, 54, 98
Exchange interaction, 74
Excitation function, 130
Excitatory, 22, 73
(postsynaptic potential)
Expected cost, 59
Extensive

  phenomenon, 27
  quantity, 70, 131
  regime, 112

Extrapolator, 191
(ECG, EEG, EMG), 25

F

Fast-simulated annealing (FSA), 48
Fault-tolerant, 17
Feature map, 40
Feedback

  control, 7
  negative, 9

Feed-forward, 13
Ferromagnetic, 74
Finite-automata, 10, 30
Firing activity, 36
(non-firing activity)
Fixed weight network, 41
Flow-of-activation, 44
Formal neuron, 25, 73
Frame language, 190
Free energy, 45, 134, 208

  thermodynamic, 64

Free-point

  dipoles, 5
  molecules, 97

Free-running mode, 63
Frustration, 203
Fokker-Planck

  relation, 111
  equation, 116

Function

  activation, 42
  gaussian, 42
  ramp, 42
  sigmoidal, 42
  step, 42

G

Gain factor, 59
Gaussian

  machine, 53
  statistics, 83

Generalization error, 68
Generating

  function, 46
  probability density, 47

Gibbs’

  ensemble, 64
  statement, 54
  free energy, 135

Glauber dynamics, 91, 211
(single spin-glass)
Glia, 17

  cell, 17, 26

Global minimum, 46
Goal pursuit problem, 163
Graded output, 53
Granule cell, 20
Group velocity, 132
Gupta’s transformation, 161

H

Hamilton’s first and second equations, 133
Hamiltonian, 4, 72
Hardware, 10
Hard spin, 202
Hartley-Shannon’s law, 162
Hebb’s rule, 32
Heisenberg model (isotropic), 105
Helmoltz free-energy, 135
Homeostatis, 6, 9
Hopfield

  machine, 53
  model/net/network, 28, 87, 154

Hyperbolic tangent function, 104
Hermitian, 149
Hyperpolarized, 75
Hypopolarized, 75

I

Information

  capacity, 162
  gain, 180
  processing, 2, 13
  theoretic, 121, 161

Informatics, 160

  knowledge-base, 7

Informational wave, 130
Inhibitory, 22, 73
(postsynaptic potential)
Interaction mechanism, 13
Interactive matrix, 33
Interacting neurons, 94-96
Interconnected units, 2
Ising spin, 27, 94-96, 204
Isotropic molecular arrangement, 98

J

Jensen-Shannon divergence, 182
J-divergence, 183
Jordon canonical form, 211

K

Kullback measure, 183
Kybernetic (principles), 8

L

Lagrangian, 4,72

  formalism, 89

Langevin

  equation, 110
  force equation, 136
  machine, 106
  modified function, 103, 104, 108

Latent summation (period), 22
Lattice gas, 149
Least squares error, 41
Learning

  behavior, 32
  Hebbian, 41, 84, 90
  naive, 68
  process, 162
  supervised, 40, 62
  through experience, 11
  unsupervised, 40, 62

Legendre transformation, 65
Linear least squares estimator, 122
Linear logorithmic weighting, 126
Liquid crystal, 5

  model, 94

Little’s model, 78, 91, 152, 210
Local minima, 46
Locally stable states, 46
Logical neuron, 25, 35, 73
Long-range (orientational) order, 5, 27, 78, 86
Lorentzian relation, 114
Low-pass action, 123
Lyapunov function, 54, 88

M

Machine, 47

  intelligence, 9

Machine-like, 10
Macrocosm, 9
Magnetism, 196
Magnetic material

  antiferro, 196-197
  ferro, 196-197
  ferri, 196-197
  para, 196-197

Magnetic spin, 4, 27, 74, 96
Markov chain, 50, 57
Markovian process, 36, 79-80, 90
Massively parallel, 2, 13
Master equation, 90
Mathematical neuron, 25, 28, 73
McCulloch-Pitts machine, 52
Mesomorphous state, 97
Mean firing rate, 22
Memory, 2, 7, 11, 13

  content addressable, 40, 63, 88
  distribution, 40
  function, 39
  intermediate, 79
  long term, 39, 79
  process, 162
  short term, 40, 79

Memoryless (model), 112
Metastability, 74
Metastable (state), 45
Metropolis criterion, 51, 52
Microscopic reversibility, 77
Mnemonic equation, 162
Moderate time-scale, 86
Module, 25
Modular net, 26, 29
Molecular free-point dipoles, 5
Momentum

  density, 134
  flow, 4, 131
  flux density, 134

Monodic part, 121
Mossy fibers, 161
Motoneurons, 18
Myelin, 18

N

Nemetic phase, 5, 97
Nerve cells, 17
Network

  fixed weight, 41
  feedback, 42
  feed-forward, 42
  Hopfield, 42

Neurobiology, 12, 13
Neurocybernetics, 5, 160
Neuroglia, 17
Neuromimetic, 1
Neurotransmitter, 2
Neuron, 17

  doctrine, 31
  input, 41
  output, 41

Neuronic equation, 162
Neutral

  activity, 7
  continuum, 39
  complex, 7, 11, 15
  dynamics, 130, 147
  environment, 16
  field theory, 130
  flow, 38
  net, 26

Neuronal “particle”, 132, 135
Normal state, 8
Nonlinear stochastical equation, 110
Null information, 161

O

Objective

  disorganization, 178
  function, 45, 161

Octant frame, 190
Optimum solution, 46
Order, 15

  function, 102
  general definition of, 85
  parameter, 68

Ordered state, 79
Organelles, 97
Organization of neuron, 74-75
Organizational deficiency, 167
Overlap parameter, 66, 220

P

Paraelectricity, 98
Parallel connections, 25
Parallel processing, 91
Paramagnetism, 98
Parametric space, 53
Parametric spread space, 161
Particle dynamics, 5
Partition function, 52, 80, 134, 200, 204
Perception, 33
Perceptron, 33, 62
Perceptive attribution, 11
Peretto model, 89, 152
Persistent (state), 4, 78
Phase transition, 81, 86
Presynaptic

  cell, 21
  membrane, 19

Planck’s constant, 131
Poissonian (process), 36, 83
Polarization, 23
Polarizability, 98
Postsynaptic membrane, 19
Potassium channel, 20
Potential

  barrier, 137
  bidirectional well, 132

Pragmatics, 169
Presynaptic cell, 21
Propagation vector (constant), 131
Pseudo -

  de Broglie wavelength, 139
  Fermi-level, 151
  inverse rule, 67
  mass (of neuronal “particle”), 136
  specific heat, 49
  temperature, 47, 51
  thermodynamics, 44

Purkinje cell, 20

Q

Quenching, 45, 202
Quenched random coupling, 91

R

Random

  noise, 7, 47
  walk (theory)/model, 3, 37

Reading phase, 41
Receptors, 16
Redundant

  information, 161
  system, 25

Refractory period, 73
Reinforcement (of learned information), 11
Replica symmetry ansatz, 67, 220
Response pattern, 40
Resting (intracellular)

  potential, 20, 37
  state, 20

Reticular doctrine, 31
Reverse cross-entropy (RCE), 57, 165
Reverberation, 87
(quasi)
Robust, 17

S

Scaling

  approximation, 117
  solution, 117

Sementics, 169
Semiotics, 169, 186
Semi-random telegraphic signal, 114
Self-consistent

  approximation, 150
  control, 7
  deficiency, 171
  organization, 1
  regulation, 7, 12

Sementic network, 189
Sensory array, 34
Serial processing, 90
Sharpening schedule, 56
Shannon’s (information capacity)

  concept, 162

Sigmoid (S-shaped), 29, 207
Signum function, 104
Simulated annealing, 47
Singularity (in the learning process), 68
Sites, 149, 201
Slow-time evolution process, 112
Smearing parameter, 83, 141
Sodium

  channel, 21
  pump, 20

Software, 10
Solver, 191
Specific heat, 49
Spike-generation, 3
Spinel-cord, 16, 17
Spin-flip (single), 91
(Glauber dynamics)
Spin-glass, 74, 78, 199
Squashing function, 59, 103
Stability dynamics, 110
Stable states, 164
Statistical mechanics, 1, 11-12

  non-equilibrium, 88
  nonlinear, 88

State

  normal, 6
  persistent, 40

Stationary distribution, 50
Stochastic(al)

  instability, 118
  process, 4, 7, 13

Stop criterion, 55
Storage

  mechanism, 40
  medium, 40

Structure order, 97
Subjective disorganization, 177
Supervised learning, 41, 62
Synapse, 19
Synaptic connections, 73
Syntagma, 190
Syntagmatic chain, 190
Syntax, 188
Symmetry constrains, 9
System parameter, 51

  first, 59
  second, 59

T

Teacher, 41
Temperature factor, 81
Thermodynamics, 44

  annealing, 45
  third law, 60

Thinking machine, 162
Thompson-Gibson model, 85
Thought process, 162
Threshold potential, 24
Time-reversibility, 63
Tonic firing, 87
Total energy, 72, 206
Total entropy, 4
Training, 41
Trapping (de-trapping), 46
Traveling

  salesman problem, 52
  wave, 8

Turing machine, 26

U

Uncertainity principle, 141
Universality, 93
Universal machine, 10
Unsupervised learning, 41, 62

V

Van der Pohl oscillator, 130
von Neumann random switch, 25, 44

W

Waiting time, 113
Wave function, 5, 131

  neuronal, 144

Wave-mechanics, 141, 147
Wave-packet, 131
Weight state, 46
Widrow-Hoff rule (Delta rule), 53
Writing phase, 41


Table of Contents

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