Untangling complex syste.., p.110
Untangling Complex Systems, page 110
cytoplasmic streaming 268
modeling 130–5
cytoskeleton 265
effective cooling system 459
effectors’ system (ES) 169–70, 471–2
Darwin, C. 11
eigenvalues 114, 155, 241–2
Das Capital (book) 153
Einstein, A. 11, 11n20, 17n29
Dd ( Dictyostelium discoideum) 284, 284–5
electric potential gradient 276
de Donder, T. 45, 45n2
electrocardiogram 282, 283
deduction, reasoning strategy 18, 18n30
electrochemical energy, solar radiation 435–6, 436
defuzzifier 474, 475
electrochemical waves 281, 282
delayed negative feedback oscillator 216, 216–19
electronic computers 12, 28, 457–61, 486; memory types dendritic fractals 392–3, 393
460; von Neumann 472
density correlation function 392
Elements (book) 7
deposition step 287
embedding dimension 344–5
De Revolutionibus orbium coelestium (book) 11
embryo development 256–60, 258, 259
determinism, epistemological pillars 10
emergent properties, complex systems 444; alignment
deterministic chaos 12–13, 345
rule 445; cohere rule 445; Complexity ( C) 444;
DFT (discrete Fourier transform) 514–15, 515
hierarchical networks 446; Integration ( Ig) 444;
Dictyostelium discoideum ( Dd) 284, 284–5
Interconnection ( Ic) 444; modular networks
dielectric breakdown 393
445; Multiplicity ( M) 444; phase transition 445;
difference machine 486
regular/random networks 444–5; scale-free
differential equations 503
networks 445; separate rule 445
diffusion-limited aggregation (DLA) model 393, 393
employment rate ( μ) 154–5, 163
9,10-dimethylanthracene (DMA) 340, 358; absorption
enantiomers 106, 106
spectra 372; structures 341; time evolutions 373
entropy 11n18, 23; AI involvement 32–4; classical Diminishing Information law 29
definition 23–4; exhausting fight against 30;
directed networks 420–1, 421
logical definition 27–9; Maxwell’s demon
direct measurements: errors in 517; total uncertainty in
30; mechanical attempt 30–2; production 36,
522–3, 523
36n16; see also entropy production; statistical
discrete Fourier transform (DFT) 514–15, 515
definition 24–6; Universe 97
disorganized complexity 14
The Entropy Law and the Economic Process (book) 148
dissipative chaos 346
entropy production 44, 47, 60, 62–3; in linear regime 67–9; dissipative force 329
in Lotka-Volterra model 121–3; in nonlinear
dissipative structures 100
regime 332–4
divergence theorem 243–4
enzyme 167, 167n1, 169; allosteric 170, 170–4; exonuclease DLA (diffusion-limited aggregation) model 393, 393
(exo) 210; interconvertible 189–90, 190;
DMA see 9,10-dimethylanthracene (DMA)
phosphorylation/dephosphorylation 189
DNA: computing 464–7, 490; polymerase 466; sequences epigenesis theory 260
466–7; strands 210, 464, 465, 466
epigenetic events 181–5
“Doctor in a cell,” computing device 467
epistemological pillars 9, 10; determinism 10; mechanism Douady, A. 386
10–11; simplicity 9–10; uniformity 10
double pendulum 317–21; see also pendulum; single
epithelial cells 268–9, 269
pendulum; angular displacements versus time
Equilibrium of planes (book) 7
562
Index
equilibrium reaction (ER) 214, 216
Fuzzy Inference Engine 474–5, 475
equilibrium self-assembly 100n3
fuzzy logic 472–6, 473, 489
ESMs (Earth system models) 431
Fuzzy Logic System (FLS) 474, 474
An Essay on the Principle of Population (book) 148,
fuzzy set 441, 443, 473, 474–5
322n1
euchromatin, genes in 398
GA (genetic algorithm) 468
Euclidean spaces 395
Gabor, D. 33, 33n10
Euler, L. 503
Galilean experimental method 517
Euler’s method 503–4, 504, 505
Galilei, G. 8–9
evolutionary computing 467–8, 468
Game of Life (game) 470–1, 471
Evolutionary Developmental Biology (Evo-Devo) theory
ganglion cells 442
260
gases, free mixing 25, 26
excitability system 202–3
gastrulation phase 257, 259
exonuclease (exo) enzyme 210
Gaussian distribution 521–2
Experimental Period 3, 3, 8–15
GDPs (Gross Domestic Products) 148–9; oscillations of
152; trend 159; for USA and China 162–3, 166
F-1,6-bP autocatalysis 174, 175
gel electrophoresis technique 466
Farmer, D. 350
Gell-Mann, M. 2, 2n2, 15
fast Fourier transform (FFT) 515
gel reactor 251, 254–5
FCMs (Fuzzy Cognitive Maps) 478
genetic algorithm (GA) 468
FC (Franck-Condon) state 434, 434n20, 435
genome 432, 467
feedback networks 350
geomorphology 263–4
feed-forward networks 350
germ cells layers 258, 258n9
Feigenbaum, M. 326
Gibbs free energy 97, 97n1, 98
Feigenbaum’s constant 327
Gierer, A. 255
Fertile Crescent 5, 5n5
Gierer and Meinhardt model 250, 255
FET (Field-Effect-Transistor) 457
Glansdorff-Prigogine stability criterion 71–2
Feynman, R. P. 31, 31n6, 486
global warming 431
FFT (fast Fourier transform) 515
glycolysis process 174–5, 176
fibrillation 283
Goodwin’s predator-prey model 153–5, 155
Fick, A. 53
graphene transistors 459
Fick’s law 53, 53–4, 66
Grashof number (Gr) 329n6
Field-Effect-Transistor (FET) 457
Grassberger-Procaccia algorithm 347
Field, Körös, and Noyes (FKN) mechanism 199, 206
Gutenberg-Richter law 399
Filmer, D. 171
gypsy moth ( Lymantria dispar) 285
FinFET transistor 459, 459
Fisher-Kolmogorov equation 279–81, 280n18, 281
Haeckel, E. 147, 147n1
Fisher, R. 280
Hamiltonian Path Problem 464; by Adleman 465;
FKN (Field, Körös, and Noyes) mechanism 199, 206
algorithm instructions 464; by DNA strands/
flow control primary oscillator 212, 212–14
DNA-hybridization reaction 465; solution 465
FLS (Fuzzy Logic System) 474, 474
Hamiltonian system 320, 346
fluctuation theorem 35–7, 98
heart, waves in 282–3, 283
fluoride oscillations 216
heat: conduction 328, 328–9; engine 23; radiation 426
forced convection 327n4
Hegel, G. W. F. 8n13
Fourier, J. 50
Hegel’s dialectic 8
Fourier’s law 50–1
Hele-Shaw cell 389–90, 390
Fourier spectrum 515
Hele-Shaw, H. S. 389n9
Fourier transforms 375, 376, 513–15
hemoglobin (Hb) 171–2, 257
fractal-like croissant 401, 402
Hénon attractor 380
fractal-like structures: in lab 389–92, 391; in nature Hénon, M. 379
386–8, 387
heterochromatin 398
fractals 381–3, 383; chaos and entropy 402–3; chaos heterotropic interactions 170
generating 401–2; dendritic 392–3; diffusion in hierarchical networks 423, 446, 448
395–6; dimension 383–5, 384; kinetics in cells, Hilbert, D. 13
chemical reactions on 396–9; multifractals
Hilbert space 487
394–5; non self-similar 385–6, 388, 388–9;
Hill kinetics 169–70
Sierpinski gasket 384, 384–5
HNS (human nervous system) 471, 471n1
Franck-Condon (FC) state 434, 434n20, 435
H-nullcline curve 119
free market economy 149
HOBr (hypobromous acid) 205–6
fruit-fly ( Drosophila) 258, 258
Hodgkin, A. 278
functional responses types 123, 124; Type I 123; Type II Holling, C. S. 123n5
123–6, 126; Type III 126–8, 128
Hopf bifurcations 110–11, 111
fuzzifier 474, 475
human intelligence 471–2
Fuzzy Cognitive Maps (FCMs) 478
human nervous system (HNS) 471, 471n1
Index
563
Hutton, J. 289
K.U. Leuven Competition 350
Hutton’s Law 289
Kutta, M. 504
Huxley, A. 278
hybrid learning 351
laboratory, fractal-like structures in 389–92, 391
hydra, regeneration 260, 260
laminar flow 52, 52
Hydrodynamic Photochemical Oscillator 340–2, 375
Landauer, R. 34, 34n13
hypobromous acid (HOBr) concentration 205–6
Landauer’s principle 484
hysteresis 181
landscape shapes 241, 242
Langton, C. 462
IAAFT (Iterative Amplitude Adjusted Fourier
Laplace, P.-S. 10, 10n17, 352
Transformed) 348
Laplace transform inversion 173
Ibn al-Haytham 7, 7n10
LASER see light amplification by stimulated emission of
IF-THEN statement 474
radiation (LASER)
The Iliad (poem) 5
The Last Question (book) 30
Immune Information System (IIS) 437, 438, 462
last universal common ancestor (LUCA) 11, 463
immune network algorithms 469
lateral inhibition 250, 298–9
immune system 425
learning rule 351
incompatibility principle 472, 473
least-squares fitting 527–30
incompleteness theorem 13
Leibniz, G. W. 382, 485
indirect reciprocity behavior 481
Leibniz wheel device 485
induction, reasoning strategy 6, 18n30
Leonardo da Vinci 8, 517
information entropy 484, 484n4, 509
Libchaber, A. 329
information source, solar radiation/life on Earth
Liesegang patterns 285–7; in biology 289; in geology
437; animals 440–4; photomorphogenesis
288–9; rings in 315; within test tube 313; in two
438–9; phototropism/photoperiodism 439–40; dimensions 316; wavelengths 313, 315, 315
unicellular organisms 440
Liesegang, R. E. 285
information storage 457
ligands 169–71
infradian rhythms processes 186
light amplification by stimulated emission of radiation
Instrumental Response Function (IRF) 507, 508
(LASER) 103; beam 37, 39; radiation
integration by parts method 332, 332n7
production 103
intermediate filaments, fiber 265
light-driven phase 433
Internet 423n8, 461
linear differential equations 79
inverse discrete Fourier transform 514–15
linear economy 149–50, 150
inverted microscope 37, 37n17
linear equations 356, 360
An Investigation of the Laws of Thought (book) 486
linear regime 317; chemical reactions, Onsager’s
ion-product, supersaturation 287
reciprocal relations 73; and chemical
IRF (Instrumental Response Function) 507, 508
transformations 72–4; diffusion case
Ising, E. 418
65, 65–7; generic system from 100; heat
isotropic aggregation process 392
conduction case 64, 64–5; minimum entropy
Iterative Amplitude Adjusted Fourier Transformed
production theorem in 67–9; non-equilibrium
(IAAFT) 348
thermodynamics in 50–63; out-of-equilibrium
systems in 63–7; particular case 73–4; in three Jablczynski law 286
regimes 99
Jaynes, E. T. 173n5
linear stability analysis 75
Juglar, C. 165
linear time series model 350
Julia, G. M. 385, 385n4
Liouville’s theorem 346, 402–3
Julia set 386, 386, 386n5, 410
local equilibrium condition 121
junk DNA 260
local self-activation 250, 298–9
logic gates 458
kangaroo problem 509–10
logistic function 322, 322
Kantz’s method 345
logistic map 321–6; bifurcation diagram 325, 326;
kinematic waves 271n12
iterations using MATLAB 365; population
kinetic laws, average rates for 298, 298
evolution 325, 363–4, 364; profile 323; KNF (Koshland, Némethy and Filmer) model 171
unimodal map 365
Known Nature Island 17–18
long-term unpredictability 348–9, 349
Koch curve 381–2, 382, 384; dimension 383
Lorenz attractor 379, 381
Koch snowflake 382, 382
Lorenz, E. 13, 335, 337–8
Kolmogorov, A. 280
Lorenz’s model 335–6; projection 338; in strange attractor Kolmogorov-Sinai entropy 346–7, 346n9, 354
337–8; time evolution for volume/variables
Koshland, D. E. 171
336, 336–7, 337
Koshland, Némethy and Filmer (KNF) model 171
Lotka, A. J. 117n1
Kosko, B. 478
Lotka-Volterra model 117–21, 197; entropy production
Krebs cycle 198, 198n1
in 121–3, 122; modified 138, 208–11, 209; in Kühne, W. 167n1
phase plane 120; trajectories for 121
564
Index
LUCA (last universal common ancestor) 11, 463
molecular motors 266–8
Lyapunov exponents 345–7, 377
mono- and bi-dimensional waves 273, 273–4
Lymantria dispar (gypsy moth) 285
mono-dimensional case 75, 75–6
Monod, Wyman and Changeux (MWC) model 171
macroeconomic systems 148, 152
Moore, G. 458
macro-mixing process 221
Moore’s law 459
macroscopic motor 266–7
Morgan, T. H. 258
macroscopic systems 24, 35
MOS (Metal Oxide Semiconductor) 458
magnitude amplification 187–8, 188
MOSFET 458, 458
malonic acid, oxidation 209
motor proteins 265–8
Malthus, T. 148, 322n1
MTOCs (microtubule-organizing centers) 265
Mandelbrot, B. 385–6
multi-core CPU 459
Mandelbrot set 385, 385
multi-dimensional case 81
Marangoni-Bénard convection 330–1
multifractals 394; see also fractals; complex images
Marangoni number 331
analysis 394–5; complex time series analysis
marginal propensity to consume ( c) 156, 156n8, 161
395; spectrum 394
Marx, K. 153
multiplier and accelerator model 156–8, 165
Matalon-Packter law 286
muscle contraction 265
A Mathematical Theory of Communication (book) 27
muskrat ( Ondatra zibethica) 285
MATLAB software: bifurcation diagram 365; file
mutualism 129, 133–5, 135
299–302, 308–9; logistic map, iterations using myelin sheath 279n16
365; ODEs45 solver 368
Maximum Entropy Method (MEM) 172–3, 507–12, 508,
NADPH (nicotinamide adenine dinucleotide phosphate)
510
435
Maximum Entropy Production principle (MaxEP) 333–4
nanoscale robots 467
maximum likelihood principle 521–2
Napier, J. 485
maximum priori absolute error 525
nasal cycle 186
Maxwell, J. 30
Natural Complexity Challenges 3, 415
Maxwell’s demon 30, 34–5
natural complex systems, computational complexity
MC (merocyanine) 340–1
415–19
McNames, J. 350
natural computing 461, 461–2; levels 461–2; by natural measurement protagonists 517, 518
information systems 462, 462–82; by
mechanism, epistemological pillars 10–11, 15
physicochemical laws 482–91, 483
mechanochemical patterning 264–9
natural convection 327n4
Meinhardt, H. 255
natural information systems, computing by 462, 462;
melanin/melanocytes 262
agent-based modeling 479–82, 480, 481, 482;
MEM see Maximum Entropy Method (MEM)
AI 471–2; amorphous computing 477; artificial
membrane computing 463, 463
immune systems 468–9; artificial life 462–3;
memristors 460
Boolean networks 477–8; cellular automata
meristematic cells 261n10
469–71, 470; DNA and RNA computing
merocyanine (MC) 340–1
464–7; evolutionary computing 467–8, 468; Messor Sancta ant colonies 263
FCMs 478; fuzzy logic 472–6, 473; membrane metabolic events 167–8; allosteric enzymes, nonlinearity
computing 463, 463; ODEs 477; protein
170–4, 172; glycolysis 174–5, 176; Hill kinetics computing 476–7; robots 476; synthetic
169–70; Michaelis-Menten kinetics 168
biology 463; systems biology 463; systems
metabolism 167
chemistry 463
Metal Oxide Semiconductor (MOS) 458
natural wonders 1, 2
Michaelis-Menten kinetics 168
