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Index

ability to think abstractly, 2

absorption and emission operators, 484

abstract intelligent agent, 71

abstraction, 23

access control, 125

action, 504

action estimates, 136

action functional, 504

action of the flow, 287

action value function, 133

action–amplitude picture, 592

activation derivative, 209

activation dynamics, 210

Adaline, 189

adaptation, 111, 176

adaptive filter, 210

adaptive Lie–derivative controller, 448

adaptive motor control, 456

adaptive path integral, 506, 592, 594,595

adaptive resonance theory, 213

adaptive sensory–motor control, 215

adaptive system, 186

additive fuzzy system, 228

affine Hamiltonian function, 446

agent theory, 167

Airy functions, 364

algorithm theory, 237

algorithmic learning theory, 128

alife, 254

all possible routes, 501

all the routes, 504

alpha, 447

ambivert, 110amplitude, 500, 502

analytic philosophy, 103analytical philosophy, 101analytical psychology, 106

and, 358Andronov–Hopf bifurcation, 294anima, 108

animus, 108ant colony optimization, 251antecedent, 216

anti–control of chaos, 281antibody, 256antibody hypermutation, 256

antigen, 256archetypal psychology, 109archetype, 107

archetypes, 109area–preserving map, 323array of N Josephson Junctions, 611

arrow of time, 559artificial evolution, 240artificial immune system, 255

artificial immune systems , 237artificial intelligence, 111artificial life, 237, 254

artificial neural network, 186atmospheric convection, 315attack function, 215

attracting equilibrium points, 302attracting fixed points, 302attracting focus, 289

attracting Jordan node, 289

676 Index

attracting line, 289attracting node, 289attracting spiral, 289attractor, 302, 314attractor associative memory ANNs,

206attractor of the Poincare map, 293attractors, 313autogenetic motor servo, 447Avida, 255axiom schemata, 141axiomatic system, 102axioms, 141

backpropagation, 194backpropagation algorithm, 115backtracking, 142Backus–Naur form, 143backward evolution, 396Baker map, 325barrier to scientific prediction, 314base variable, 220basin of attraction, 302, 314basins of attraction, 323Baum–Welch algorithm, 158Bayes’ theorem, 161, 162Bayesian inference, 128Bayesian probability, 128Bayesian statistics, 121behaviorism, 8, 102belief–desire–intention agents, 167bell curve, 47Bell test experiments, 522Bell’s theorem, 524Bellman equation, 155Belouzov–Zhabotinski reaction, 378best known future action, 136Betti numbers, 449Bhagavad Gita, 160bifurcation, 280, 293bifurcation diagram, 321bifurcation point, 278bifurcations, 313bijective, 26binary signals, 209binary system, 99Binet IQ test, 45bio–diversity, 321bioinformatics, 158

biological complexity, 440biological control laws, 440biomorph, 327biomorphic systems, 327bipolar signals, 209block entropy, 330Bloom’s Taxonomy, 11blue–sky bifurcation, 295body motion manifold, 456Boolean functions, 426bootstraping, 134Born–Dirac rule, 538Bose–Einstein condensate, 502Bose–Einstein statistics, 484Bourbaki, 25box–counting dimension, 314, 335, 360bra–covectors, 502bra–ket, 502Brahman, 100brain, 455brain dynamics, 274, 281brain motion manifold, 456brainstorming, 29brute force, 155Buddha, 39Burgers dynamical system, 374butterfly effect, 279, 314, 316

calculus, 99candidate solutions, 237canonical quantization, 465Cantor set, 259capacity dimension, 325, 381capture time, 367carrying capacity, 320Cartesian coordinate system, 95case–based reasoning, 7cat map matrix, 351catastrophe theory, 294catastrophes, 280, 295categorial abstraction, 105Cauchy–Schwarz inequality, 49causal Bayesian network, 159causal relations, 159cellular automata, 114, 251cellular automaton, 251center, 289cerebellar robotics, 438ch’i, 110

Index 677

chaos, 285chaos control, 274, 295, 379chaotic attractor, 274chaotic behavior, 94chaotic saddle, 336Chapman–Kolmogorov equation, 153Chapman–Kolmogorov integro–

differential equation, 154character, 2character structure, 36characteristic equation, 472characteristic Lyapunov exponents, 380charging energy, 626Chebyshev polynomial fitting problem,

254Chomsky hierarchy, 21chromosome, 246Chua–Matsumoto circuit, 378Church’s theorem, 138Church’s thesis, 138Church—Turing thesis, 138circle map, 324classification, 123, 163classify, 59Clifford algebras, 38clonal selection algorithms, 256closure property, 474co–active neuro–fuzzy inference system,

204code, 558coefficient of determination, 46cognitive agent, 71cognitive architecture, 70cognitive information processing, 213cognitive linguistics, 19cognitive science, 1cognitive test scores, 45Cohen–Grossberg activation equations,

214Cohen–Grossberg theorem, 215coherent quantum oscillations, 608collective unconscious, 107, 109collision–avoidance problem, 268combinatorial optimization, 237combinatorial route, 504common factor analysis, 54communalities, 54communication studies, 18commutation relations, 486

competitive learning, 254

complement, 220

complete set of all possible states, 503

complete synchronization, 402

complex adaptive systems, 242

complex number, 500, 502

complex–valued ANNs, 207

complex–valued generalization, 500

complexity, 424

composite Hilbert space, 476

computational complexity, 124

computational complexity theory, 237

Computational Intelligence, 112

computational learning theory, 124

computational linguistics, 141

computational rules, 440

computer science, 1

conation, 67

concentration, 578

concept of causality, 159

concept space, 122

condensed, 558

conditional dependencies, 155

confirmatory factor analysis, 57

conformal z−map, 325

Confucius, 39

conjugate gradient method, 197

conjunction, 216

conjunctive normal form, 142

connectionism, 16

connectionist, 190

connectionist approach, 186

connectionist learning, 122

consciousness, 89

consequent, 216

conservation law, 318

conservative–reversible systems, 295

Consistent Histories, 522

constant relative degree, 447

constrained SE(3)−group, 441

constraint satisfaction problems, 142

context–free grammar, 21, 143

continental philosophy, 103

continuous, 499

continuous eigenvalue, 473

continuous projectors, 474

continuous spectral form, 474

continuous spectrum, 473

678 Index

continuous–time Markov stochasticprocess, 500

contravariant velocity equation, 444

control, 179

control law, 447

control on SE(3)−group, 441

control parameters, 297

control parameters are iterativelyadjusted, 456

control systems, 116

convective Benard fluid flow, 315

Conventional AI, 112

conversation analysis, 18

convex optimization problem, 164

convexity, 238

Cooper pair box, 608

Cooper pairs, 607

Copenhagen interpretation, 522

Corinna Cortes, 167

corpus callosum, 68

corrective feedback, 116

correlation, 46

correlation coefficient, 46

correlation flow, 65

correlation function, 48

correspondence principle, 501

cortical motion control, 456

cost function, 167

coupling, 451

covariance matrix, 150

covariant force equation, 444

covariant force functor, 606

covariant force law, 606

craniometry, 67

creative agent, 27

creativity, 2

crisp, 219

criterion of falsifiability, 97

critical bifurcation value, 313

critical current, 610

critical rationalism, 96

critical value, 327

crossing, 246

crossover, 239

cryptography, 125

cube, 448

cumulative distribution function, 47,499

current–phase relation, 612curse of dimensionality, 155curve, 219cybernetics, 115cycle, 292, 332cyclic forms of human motion, 457

damped pendulum, 283, 303Darwinian evolution, 255data and goals, 122data mining, 121data–processing neurons, 308De Rham theorem, 449debugging, 179decision ladder, 184decision–maker, 174decision–support systems, 266decoherence, 467deductive reasoning agents, 169Deep Blue, 112Defuzzification, 451defuzzification, 227, 232degrees of truth, 216Delaunay triangulation, 254deliberation reasoning, 181delta–rule, 193DENFIS system, 236depth psychology, 109design, 179deterministic chaos, 275, 315deterministic drift, 154diagnosis, 179dialectics, 104diffeomorphism, 456difference equation, 320differential evolution, 237, 254differential Hebbian law, 215diffusion, 296diffusion fluctuations, 154digital organism, 255Dijkstra’s algorithms, 156dimension formula, 348dimensionality reduction, 52Dirac, 462Dirac interaction picture, 470Dirac rules for quantization, 465Dirac’s electrodynamic action principle,

479Dirac’s formalism, 462

Index 679

Direct oblimin rotation, 58directed acyclic graph, 158discontinuous jumps, 154discourse analysis, 19discrete, 499discrete characteristic projector, 472discrete eigenvalues, 472discrete Laplacian, 624discrete sine–Gordon equation, 622discrete spectral form, 473discrete spectrum, 472discrete–time models, 320discriminant functions, 186disjunction, 216dissipation, 564dissipative structures, 296distribution function, 498dot product, 166dream analysis, 107dreams, 109driven pendulum, 304dual Hilbert space, 502dualism, 95Duffing map, 325Duffing oscillator, 309Duffing–Van der Pol equation, 309dynamic Bayesian network, 154dynamic link matching, 146, 151dynamic optimization task, 268dynamic programming, 130, 133, 155dynamic ray, 327dynamical system, 275dynamics, 282dynamics on SE(3)−group, 441

EGreedy policy, 136eigenfaces, 146, 150eigenfrequency, 150eigenfunction, 150eigenspace, 150eigenvalue, 150eigenvectors, 150Einstein’s laws of radiation, 462Either–Or, 218electricity and magnetism, 116electroencephalogram, 271electroencephalography, 271electronic communication systems, 116elementary amplitude, 504

elitism strategy, 248embedding methods, 198emergent behaviors, 254emergent properties, 252emotion, 89emotional intelligence, 69empirical mean, 53empty set, 26encoding scheme, 123energy flow, 110entangled state, 563entropy, 299environment, 174, 455environmental decoherence, 536epistemological paradigm shift, 10EPR paradox, 520, 524equilibrium points, 284error bound, 166error function, 448escape rate, 335Euclidean distance , 256Euclidean geometry, 49Euclidean space, 49, 238, 291Euler characteristic, 605Euler–Poincare characteristic, 449evidence node, 158evolution laws, 297evolution strategy, 250evolution window, 250evolutionary algorithms, 237evolutionary computation, 205, 237, 252evolutionary programming, 249existence & uniqueness theorems for

ordinary differential equations(ODEs), 275

existence–uniqueness theorem, 301existential quantifier, 216existentialism, 104expansion principle, 503expectation–maximization algorithm,

161experience, 39expert systems, 179, 266exploiting, 136exploration/exploitation problem, 136exploratory, 61exploratory factor analysis, 56exploring, 136extended Kalman filter, 197

680 Index

external rays, 327extinction, 17extroversion, 33extrovert, 109extrovert/introvert model, 108

factor analysis, 33, 43, 45, 150factor Hilbert spaces, 476factor loadings, 57factor matrix, 57factor rotation, 54factor scores, 57factor–correlation flow, 65factors, 50family of Markov stochastic histories,

501feasible region, 237feasible solutions, 237, 238feature extraction, 52feature selection, 52feedback control, 449feedback fuzzy systems, 235feedforward neural network, 188feeling, 108Feigenbaum cascade, 317Feigenbaum constant, 317Feigenbaum number, 321Feigenbaum phenomenon, 295Feynman diagram, 373, 496Feynman path integral, 503, 592Feynman–Vernon formalism, 560Fibonacci sequence, 155Fick equation, 296field, 282fifth generation computer systems, 141filter, 52final state, 501, 502finite–dimensional Hilbert space, 472first quantization, 467first–order resolution, 141first–order–search methods, 196fitness, 247fitness function, 243, 256fitness landscape, 238, 243fitness value, 250FitzHugh–Nagumo neuron, 419fixed points, 274, 284, 300, 314Floquet exponents, 635Floquet multiplicator, 387

Floquet stability analysis, 387

flow, 275

flux, 300

flux–flow regime, 626

Flynn effect, 44

focal objects, 86

Fock state, 502

focus, 285

Fokker’s action integral, 491

Fokker–Planck diffusion equation, 153

Fokker–Planck equation, 500, 554

fold bifurcation, 295

force, 300

force HBE servo–controller, 446

force–field psychodynamics, 592

forced Duffing oscillator, 370

forced Rossler oscillator, 397

forced Van der Pol oscillator, 306

formal language, 22

formal logic, 113, 216

formation rules, 105, 141

forward algorithm, 155

Fourier analysis, 93

Fourier equation, 296

Fourier transform, 464

fractal attractor, 316

fractal dimension, 258, 295, 314

fractal pattern, 322

fractals, 325

fractional dimension, 325

freethinkers, 38

freethinking, 38

freethought, 38

Frege–Russell definition, 101

frequency–to–voltage converter, 610

Freudian psychoanalysis, 109

frustrated XY models, 617

fully recurrent networks, 206

function, 463

function collapse, 526

functional approximators, 186

functional causal relation, 46

functional programming language, 138,156

functional view, 91

Fuzzification, 225, 445, 450

Index 681

fuzzy associative memory, 229

fuzzy diffusion parameter, 224

fuzzy IF–THEN rules, 230

fuzzy inference engine, 225

fuzzy inference system, 450

fuzzy logic, 215

fuzzy logic controller, 235

fuzzy membership function, 218

fuzzy mutual entropy, 222, 224

fuzzy parameter space, 224

fuzzy patches, 224

fuzzy set theory, 215

fuzzy sets, 179

fuzzy variable, 220

fuzzy wave equation, 224

fuzzy–stochastic HBE system, 445

Godel’s incompleteness theorem, 102,540

game theory, 114

gamma, 447

gamma–EEG waves, 535

gauge condition, 520

gauge–invariant phase difference, 629

Gauss–Bolyai–Lobachevsky space, 24

Gaussian distribution, 47

Gaussian function, 47

Gaussian saddlepoint approximation,373

gene regulatory networks, 160

general cognitive ability, 66

general human/humanoid behavior, 458

general intelligence, 66

general kinematics, 441

general sense, 378

general systems theory, 117

generalized feedforward network, 201

generalized Gaussian, 210

generalized Henon map, 323

generalized policy iteration, 134

generalized solution, 378

generalized synchronization, 402

genetic algorithm, 84, 130, 196, 205, 242

genetic control, 205

genetic programming, 248

genetic recombination, 239

genotype, 244, 246

genotype–phenotype distinction, 242

geometric algebra, 38

geometrodynamical functor, 594

Giaever tunnelling junction, 609

Gibbs ensemble, 302, 488

Ginzburg–Landau equation, 374

Giti, 4

global factors., 31

globally–coupled Kuramoto model, 627

globular cluster, 322

Goldstone theorem, 558

Golgi tendon organs, 447

grade of membership, 218, 219

gradient, 238

gradient descent method, 195

gradient information, 190

gradient of the performance surface, 190

Gram–Schmidt procedure, 395

Gray code, 245

greedy action, 136

greedy algorithms, 155

Green’s function, 327

group, 287

growing neural gas , 253

grows exponentially, 279

grows linearly, 279

growth inhibition effects, 259

growth rate, 319

Henon map, 322, 394

Henon strange attractor, 323

Hamilton–Jacobi equation, 464

Hamilton–Jacobi–Bellman equation,155

Hamiltonian energy function, 296

Hamiltonian system, 323

Hamming distance, 256

Hamming weight, 256

heat conduction, 296

Hecht–Nielsen counterpropagationnetwork, 212

Heisenberg, 461

Heisenberg picture, 470, 515

Heisenberg uncertainty principle, 522,525, 527

Heisenberg’s method, 462

682 Index

Heisenberg’s Principle of indeterminacy,464

Heisenberg’s uncertainty relation, 469

Hermitian (self–adjoint) linear operator,464

Hermitian inner product, 502

Hessian matrix, 238

heuristic IF–THEN rules, 172

heuristic search, 122

hidden Markov model, 146, 153

hidden variable, 154, 155

hidden variable theory, 527

high–level cognitive model, 158

Hilbert space, 164, 166, 466, 502, 572

Hindley–Milner type inference systems,138

Hindmarsh–Rose thalamic neuron, 419

Hindu scriptures, 39

history, 500

Hodgkin–Huxley model, 306

Hodgkin–Huxley neuron, 420

Hodgkin–Huxley–type functions, 422

holists, 39

holographic hypothesis, 557

holonomic brain model, 93

homeomorphism, 290

homeostatic balance, 110

homoclinic bifurcation, 295

homomorphism of vector spaces, 52

homotopy methods, 197

Horn clause, 141

Hotelling transform, 52

Hotelling’s law, 53

Hotelling’s lemma, 53

Hotelling’s rule, 53

Hotelling’s T–square distribution, 53

Huffman trees, 156

human heart beat and respiration, 402

human mind, 1

human–like design, 428

humanoid robot, 438

hybrid dynamical system of variablestructure, 376

hybrid systems, 378

hyperbolic geometry, 24

hyperbolic system, 278

hyperbolic tangent threshold activationfunctions, 189

hyperplane, 164hysteresis loops, 295

imaginary part, 500imaginary unit, 500imagination, 89imitation, 11, 39impossible to integrate, 451in the sense of Filippov, 378incompatible observables, 525incompleteness of description, 463incompleteness of quantum mechanics,

522independent component analysis

networks, 204indeterminacy principle, 534, 536individual transition probability, 500inductive inference, 128inference, 227infinite set, 218infinite–dimensional Hilbert space, 473infinite–dimensional neural network,

592infinity, 456information, 117, 380information confidentiality, 125information dimension, 335, 355initial conditions, 302initial state, 501, 502injective, 26instanton vacua, 373integrate–and–fire neuron, 416integrate–and–fire–or–burst neuron, 418integration, 275intellect, 89intellegentia, 1intelligence, 1, 95intelligence quotient, 44intelligent behavior, 111intelligent information systems, 266intelligent systems, 268intelligible world, 4intention, 181interactionism, 96interactive genetic algorithms, 243interpretation, 179intersection, 220introspection, 8, 42introvert, 109

Index 683

intuition, 39, 108intuitionistic logic, 105inversion, 247irregular and unpredictable, 275irreversible processes, 296Ising–spin, 259Ising–spin Hopfield network, 212iteration of conditioned reflexes, 456iterated map, 302iteration, 143

Jacobian matrix, 285jnana, 39Jordan and Elman networks, 202Jordan canonical form, 289Josephson constant, 610Josephson current, 607Josephson current–phase relation, 610Josephson effect, 607Josephson interferometer, 607Josephson junction, 606Josephson junction ladder , 617Josephson tunnelling, 607, 610Josephson voltage–phase relation, 610Josephson–junction quantum computer,

608Jungian psychology, 106

Kaplan–Yorke conjecture, 336Kaplan–Yorke dimension, 382Kaplan–Yorke formula, 338Kaplan–Yorke map, 325Karhunen–Loeve transform, 52Karhunen–Loeve covariance matrix, 210karma, 39kernel, 166Kernel Language, 141kernel trick, 163, 166ket–vectors, 502kinetic theory of gases, 116kink–phason resonance, 624Klein–Gordon Lagrangian, 519Klein–Gordon wave equation, 480knapsack problem, 243knowledge base, 169knowledge representation, 122knowledge–based systems, 266Kohonen continuous self organizing

map, 213

Kohonen self–organizing map, 202Kolmogorov–Sinai, 382Kolmogorov–Sinai entropy, 330, 380,

382Kruskal’s algorithm, 156Kuramoto order parameter, 635Kuramoto–Sivashinsky equation, 374

ladder, 627lag synchronization, 402Lagrange multipliers, 167, 238Lagrangian density, 519, 597lambda calculus, 138, 139Landau gauge, 623landing point, 327language, 1largest Lyapunov exponent, 380lateral thinking, 29law of contradiction, 104law of the excluded middle, 104laws of probability, 503learn by trial and error, 130learnable evolution model, 237, 256learning, 2, 111learning algorithm, 123learning classifier systems, 250learning dynamics, 210, 211learning operations, 122learning rate, 191learning rate scheduling, 191learning to learn, 122least means square algorithm, 191Lebesgue integral, 473Lebesgue measure, 313Levenberg–Marquardt algorithm, 197Lewinian force–field theory, 593libido, 110Lie bracket, 448Lie derivative, 376, 447limit cycle, 291, 292, 305, 314, 422limit set, 292linear, 46linear classification, 163linear classifier, 166linear dynamical systems, 286linear flow, 287linear homotopy ODE, 377linear homotopy segment, 377linear map, 52

684 Index

linear operator, 52linear representation, 465linear transformation, 52linearization, 285linearly equivalent, 288linguistic variable, 220linguistics, 19, 20Liouville equation, 153Lisp, 137locality, 526locally–coupled Kuramoto model, 627,

636locally–optimal solution, 567logic programming, 140logicism, 102logistic equation, 319logistic growth, 319logistic map, 320, 322, 384long–range connections, 636long–range correlation, 558long–range order, 607long–term memory, 210Lorentz equation of motion, 493Lorentz transformations, 480Lorenz attractor, 376Lorenz mask, 316Lorenz system, 316, 322lower limit of complexity, 440Lyapunov dimension, 381Lyapunov exponent, 277, 295, 314, 329,

336, 395Lyapunov function, 212Lyapunov stability, 278Lyapunov time, 277

M, 432, 433machine learning, 121, 160machine translation, 158macroscopic entanglement, 456magneto–encephalography, 272Malthus model, 319Malthusian parameter, 319, 321Mamdani fuzzy controller, 232Mamdani inference, 229, 450management information systems, 266management–support systems, 266Mandelbrot and Julia sets, 325Manhattan distance, 256manifest variables, 48

map, 320, 395

map sink, 314

margin, 164

Markov assumption, 153

Markov blanket, 159

Markov chain, 331

Markov decision process, 132

Markov network, 159

Markov process, 153, 331

Markov property, 153

Markov–chain Monte–Carlo, 161, 506

mass communication, 18

Master equation, 153

match–based learning, 214

material metric tensor, 444

matrix cost function, 196

matrix–symplectic explicit integrator,451

matroids, 156

maximum likelihood estimate, 158

maximum likelihood estimator, 48

maximum–entropy, 208

maximum–margin hyperplane, 164

McCulloch–Pitts neurons, 189

mean, 7, 47

mean square error, 190

means–ends reasoning, 181

mechanical–control structure, 428

meditation, 578

meiosis, 239

Meissner–states, 620

membership function, 219

memory, 89

memory recall, 123

mental abilities, 1

mental force law, 606

meta–GP, 249

metaheuristic optimization algorithm,251

metaheuristic optimization algorithms,237

metamorphoses, 313

Metaphysics, 38

method of least squares, 7

microtubules, 532, 547

mind, 89

mind maps, 39

Index 685

mind–body problem, 94minimizing the error, 190minimum–time reward functions, 132Minu, 4model fit, 56modified Duffing equation, 311modular feedforward networks, 201modulus, 500momentum learning, 195momentum phase–space, 449monism, 100monitoring, 179Monte–Carlo, 47Monte–Carlo method, 133, 322Moore’s law, 120morphism, 52Morris–Lecar neuron, 419motor conditioned reflexes, 451multi–agent systems, 168multilayer perceptron, 188, 199multiple–intelligence theories, 68multivariate correlation statistical

method, 45mutation, 240, 247, 249mutually alternative processes, 503Myers–Briggs Type Indicator, 107

natural measure, 406natural selection, 240natural transient measure, 336Navier–Stokes equations, 262, 315negative feedback loop, 117Neimark–Sacker bifurcation, 295network topology, 123neural adaptation, 14neural gas, 253neurobiology, 105neurology of creativity, 29neuroticism, 33neutral line, 289Newton–Raphson method, 197Newtonian deterministic system, 274Newtonian dynamics, 440Newtonian mechanics, 274Newtonian method, 195next chosen action, 136node, 285noise filtering, 123non–autonomuous system, 283

non–periodic orbit, 65, 288

nonfuzzy, 219

nonlinear classification, 163

nonlinear function approximation, 224

nonlinearity, 297

nonlocal behavior, 524

nonlocal process, 523

nonrelativistic quantum mechanics , 63

nonrigid, 61

normal distribution, 47

normalization condition, 466

normalized, 219

normally distributed random variables,47

number of mechanical degrees–of–freedom, 440

number of physical degrees–of–freedom,443

object relations theory, 111

object–oriented programming, 168

objective function, 238, 243, 268

oblique factor model, 61

observation, 42

observational resolution, 443, 457

observed variable, 154, 155

Oja–Hebb learning rule, 210

one–way functions, 125

Onsager relations, 300

operations research, 237

optimal hyperplane, 164

optimal solution, 238

optimal value function, 133

optimism, 99

optimization, 123, 165

orbit, 275, 287, 332

orbit Hilbert space, 478

orchestration, 441

order parameter, 406

ordering chaos, 281

organizational communication, 18

orthogonal sum, 474

oscillatory cortical–control, 457

oscillatory dynamics, 457

Ott–Grebogi–Yorke map, 325

output–space dimension, 456

overdamped junction, 628

686 Index

overdamped ladder, 637, 638overdamped limit, 611

P–complete problem, 141paradigm shift, 10parameter ray, 327parent node, 158parsimony principle, 61particle swarm optimization , 252path–integral, 373, 496, 504path–integral expression, 518path–integral formalism, 515path–integral formulation, 515path–integral quantization, 514pattern matching process, 214pattern recognition, 123pattern–recognition machine, 191Penrose paradox, 533perception, 89, 586perceptron, 191perceptual world, 4perfect environment model, 133performance surface, 190period, 290period doubling, 295period–doubling bifurcation, 295, 317,

321, 384periodic orbit, 65, 288, 292periodic orbit theory, 334periodic phase synchronization, 402periodic solution, 290personality, 2, 30personality psychology, 109personality tests, 68phase, 500, 502phase change, 239phase coherence, 607phase difference, 403, 610, 624phase plane, 284phase space, 275, 302phase synchronization, 402phase trajectory, 296phase transition, 280phase–flow, 275, 283phase–locking, 457phase–space, 296phase–space path integral, 511phenomenology, 104phenotype, 244, 246

physical Hamiltonian function, 444physically–controllable systems

of nonlinear oscillators, 627Piaget theory, 71Pickover’s biomorphs, 328pinball game, 276plan, 1Planck’s constant, 464planning, 179playground swing, 279Poincare map, 293Poincare section, 309, 386Poincare–Bendixson theorem, 285Poincare map, 323Poincare section, 322, 333Poincare–Bendixson theorem, 280point orbit, 65, 288Poisson bracket, 494Poisson detection statistics, 502polar form, 500policy, 131political philosophy, 91population models, 318position of equilibrium, 296positional stiffness, 447positive leading Lyapunov exponent,

381positive Lyapunov exponent, 273posterior–mode estimate, 158potential function, 294, 327practical reasoning, 180pragmatics, 19Prakrti, 95Prandtl number, 316predicate calculus, 141predicate logic, 216predictability time, 381prediction/forecasting, 123, 179predictive validity, 69premises, 216Prigogine, 296Prim’s algorithm, 156primary factors, 31primary term, 220principal axis factoring, 54principal component analysis networks,

204principal components analysis, 52principal factor analysis, 54

Index 687

principal factors, 60

principal intelligence factor, 45

principle of locality, 522

Principle of relativity, 479

Principle of superposition of states, 464

pristine, 636

probabilistic description, 498

probability, 6, 463

probability amplitude, 466, 514

probability conservation law, 464

probability density function, 47, 500

probability distribution, 150

probability distribution function, 631

probably approximately correctlearning, 127, 129

problem solving, 8

product–moment, 46

product–topology theorem, 449

production rule, 143

production–rule agents, 169

products, 296

Prolog atom, 143

Prolog term, 143

Promax rotation, 58

proof by contradiction, 142

propositional logic, 142, 216

protozoan morphology, 327

pruning, 332

psyche, 107

psychic energy, 110

psychoanalysis, 109

psychological continuum, 219

psychological tests, 68

psychology, 1

psychometric function, 79

psychometric testing, 41

psychometrics, 42

psychophysics, 76

psychoticism, 33

pull–back, 447

pulse, 585

punishment, 17

pure continuous spectral form, 476

pure delayed reward functions, 132

pure discrete spectral form, 475

Purusha, 95

Pyragas control, 387

Qlearning, 135quadratic I&F neuron, 419quadratic programming, 165qualitative changes, 313quantization, 465quantum brain, 592quantum coherent state, 501quantum computation, 534quantum computers, 607quantum consciousness, 583quantum decoherence, 527quantum entanglement, 455, 467, 524,

526quantum Hamilton’s equations, 470quantum observables, 526quantum pictures, 470quantum superposition, 466quantum teleportation, 455quantum tunneling, 110quantum–mechanical wave function,

607quaternions, 38qubits, 607

radial basis function, 166radial basis function network, 203random variable, 498ransition–emission pair, 158rate of error growth, 380Raven’s Progressive Matrices, 44Rayleigh–Benard convection, 378reactants, 296real part, 500reason, 1reasoning ability, 44recognize–act cycle, 180recombination, 240rectified–and–discretized, 450recursive behaviour, 143recursive homotopy dynamics, 603reduce, 59reflectance pattern, 212reflection, 39regression, 163regular points, 301reinforcement, 17reinforcement learning, 84, 122, 130,

456relative degree, 376

688 Index

relativistic Hamiltonian form, 479relaxation oscillator, 305reliable predictor, 319repeller, 334repelling focus, 289repelling Jordan node, 289repelling line, 289repelling node, 289repelling spiral, 289representative point, 296reproduction, 240resistive loading, 611resistively & capacitively–shunted

junction, 628resistively–shunted Josephson junctions,

623resistively–shunted junction, 628resolution rule, 142resonance, 608resonate–and–fire neuron, 418rest points, 284return map, 333reward–signal, 130Ricatti ODE, 364Riemann curvature tensor, 605rigged Hilbert space, 473Rosenblatt, 191Rossler, 310Rossler system, 310roulette, 248roulette wheel algorithm, 241route to chaos, 280, 295rules fire, 231Russell Paradox, 102

saddle, 285, 289saddle–node bifurcation, 295saddle–node bifurcation theorem, 359samadhi, 578sample, 48Sankaracharya, 160Sankhya school, 95Sarsa, 135satisfiability, 142Scholastic tradition, 99Schrodinger, 462Schrodinger equation, 501, 510Schrodinger evolution, 538Schrodinger picture, 470, 515

Schrodinger’s Cat, 525Schrodinger’s method, 462Schrodinger’s wave , 463Scientific Community Metaphor, 140scientific method, 84scientific revolution, 10scope, 137score, 59scoring function, 161search, 190search algorithm, 142search for truth, 97search space, 238search strategy, 161second quantization, 484selection method, 248Self, 108, 111self–limiting process, 319self–organization, 117, 252, 456self–organizing maps, 252semantic theory of truth, 97semi–parametric classifiers, 186semi–supervised learning, 122semiotics, 19sensation, 108, 174sensitive dependence on initial

conditions, 279sensitivity to initial conditions, 279sensitivity to parameters, 279sensory adaptation, 14sensory analysis, 80sensory threshold, 79servo–controllers, 447servoregulatory loops, 447set, 218set of high mountains, 218set of probability coefficients, 462set operation, 220shadow, 108short–term memory, 210short–term predictability, 280signal detection theory, 80signal velocity, 210simulated annealing, 84, 196, 252single deterministic trajectory, 501singleton, 219singular value decomposition, 53situation, 174situation awareness, 174

Index 689

slope parameter, 189slow–wave bursting, 422Smale’s horseshoe, 279small world, 629small–world networks, 627SMO algorithm, 166social and emergent learning, 130Social Darwinism, 239social organization analysis, 184sociolinguistics, 19soft margin method, 167SoftMax action selection, 136solution, 378solution curve, 288space, 166spatiotemporal networks, 215spectral theorem, 53spectral theory, 462speech recognition, 158speech–to–text translation, 157spin–wave modes, 622spindle receptors, 447split–brain, 68stable manifold, 302, 323, 336Standard Additive Model, 228standard deviation, 47standard map, 324standard normal distribution, 47standard problem–solving techniques,

84standard saddle, 290standard sink, 290standard source, 290standardised likelihood, 162Stanford–Binet, 44state, 174, 282state space, 275state value function, 133static backpropagation, 188statistical learning theory, 127steepest descent method, 191step size, 191stochastic diffusion search, 252Stochastic forces, 445stochastic processes, 116stochastic system, 283strange attractor, 118, 260, 281, 309,

314–316stretch–and–fold, 309

strong AI, 112strong alife, 254structural equation modelling, 55structural stability, 278structure–finding algorithm, 161substantial view, 90subsumption architecture, 171sum, 503sum–over–histories, 500, 503superconducting–normal transition, 617superconductivity, 576, 606superfluidity, 576superposition principle, 286supervised, 456supervised learning, 122, 163supervised network, 188support, 219support vector machine, 128, 129, 163support vector regression, 167support vectors, 164supra–personal archetypes, 107surjective, 26survival of the fittest, 240survival probability, 334survivor selection, 249swarm intelligence, 237, 251syllogism, 4symbol–based learning, 122symbolic dynamics, 332symmetric–key cryptography, 125synchronicity, 107synchronization, 394, 457synchronization in chaotic oscillators,

402synchronization of coupled nonlinear

oscillators, 626synergetics, 406system input–output relation, 224

tail recursion, 142Tao, 100targeting, 379taste, 219tautology, 142taxicab geometry, 256teleological mechanisms, 116temperature value, 136temporal dynamical systems, 211

690 Index

temporary phase–locking, 402tensor–field, 275term set, 220the angle between the two vectors, 49theoretical ecology, 321theory of cognitive development, 71thermodynamic equilibrium, 298thermodynamics, 262theta–neuron, 419thinking, 108thought, 89thought experiment, 520three–point iterative dynamics equation,

66Tierra, 255time–dependent Schrodinger equation,

465, 500time–difference method, 133time–independent, 363time–lagged recurrent networks, 205time–ordering operator, 616TOGA meta–theory paradigms, 70top–down object–based goal–oriented

approach, 70topological entropy, 277topologically equivalent, 290torus, 448total Hilbert state–space, 474total spectral form, 474total spectral measure, 475total transition amplitude, 500total transition probability, 500tournament method, 241tournament selection, 248training data, 164trajectory, 275, 284, 332transcritical bifurcation, 411transducer neurons, 308transduction, 122transformation rules, 105, 141transition, 462, 501transition amplitude, 502, 509transition probability, 501, 502trapdoor one–way function, 127trapped attractor, 311traveling salesman problem, 155Triarchic theory of intelligence, 41true beliefs, 13truth as correspondence, 97

truth–in–itself, 105turbulence, 278Turing test, 119turiya state, 577, 580two forms of quantum electrodynamics,

486

uncertainty, 179uncertainty dimension method, 349uncertainty exponent, 313unconscious complex, 107undamped pendulum, 303underdamped junction, 628underdamped ladder array, 636unification, 142union, 220universal approximation theorem, 198universal quantifier, 216universe of discourse, 218, 219unstable manifold, 323, 336unstable periodic orbits, 335unsupervised/self–organized learning,

122utility theory, 128uzzy expert systems, 215

vacuum distribution, 482vacuum state, 502, 562value function, 132Van der Pol oscillator, 375Vapnik–Chervo-nenkis SVM theory, 166Varimax rotation, 57Vashishta, 160vector–field, 275, 284velocity and jerk, 447very–large–scale integration, 111Viterbi algorithm, 157Viterbi path, 157Vivekananda, 160voltage–to–frequency converter, 610Voronoi tessellation, 254

Wada basins, 360wave equation, 464wave psi–function, 466wave–particle duality, 110, 502weak AI, 112weak alife, 255weakly–connected neural network, 94

Index 691

Weber–Fechner law, 76Wechsler Adult Intelligence Scale, 44Wechsler–Bellevue I, 45whirling modes, 622whirling regime, 625Wigner function, 559, 560Wigner’s friend paradox, 526will, 89Winfree–type phase models, 626wisdom, 2, 37work domain analysis, 184

work organization analysis, 184working coexistence, 428wrapper, 52

yang, 110Yang–Mills relation, 373Yerkes–Dodson Law, 35yin, 110young people, 218

Zero–Moment Point, 431