Untangling Complex Systems, page 111
nature, fractal-like structures in 386–8, 387
microeconomic systems 148
nature, Turing patterns in 255–6; ecology/sociology/
microemulsions 255
economy 263; geomorphology 263–4;
microfilaments of fiber 265
mechanochemical patterning 264–9
micro-mixing process 221
Navier-Stokes equation 335, 335n8, 342
microscopic techniques 34
nearest trajectory method 350
microstates 24–5
negative cooperativity 169–70
microtubule-organizing centers (MTOCs) 265
Némethy, G. 171
microtubules of fiber 265
networks, complex systems 420; clustering 422; degree
minimum entropy production theorem 67; many forces/
distribution 421, 422, 451; directed networks flow 68, 68–9; single force/flow 67–8
421; Internet 423n8; models 422; node 421, mixed economy 149
423; overall navigability 421; random network
modified Lotka-Volterra model 208–11, 209
423; scale-free network 423–4; undirected
modular networks 423, 445, 448, 452
networks 420, 421
modulator 169
Neural Information System (NIS) 437, 438, 462
molecular fuzzy sets 441, 441
neurofilaments 265
Index
565
neuron, waves in 275; action potential 276, 276–7, 277;
peripheral 187; pH 212–14, 213; predator-electric potential gradient 276; Hodgkin/
prey primary 208–11; primary see primary
Huxley model 278, 279; ionic current 278;
oscillators; ring 218, 219; synthetic 199
network 490; structure 275
out-of-equilibrium systems 41, 426, 426, 444; chemical neutralism relationship 129
reactions 44–7, 69–71; diffusion process 47, 47;
Newton, I. 8–9, 382
emergent properties 444; entropy change for
nicotinamide adenine dinucleotide phosphate (NADPH)
41–50; generalization 50; Glansdorff-Prigogine
435
stability criterion 71–2; heat conduction 43,
NIS (Neural Information System) 437, 438, 462
43–4; in macroscopic subsystems 42; migration
nodes of Ranvier 279n16
process 47–9, 48; in nonlinear regime 69–72;
noise 348n10
solar radiation/life on Earth 431–44; solar
Non-Deterministic Polynomial problems (NP-problems)
thermal radiation/climate change 430–1;
417–18
thermal radiation 426–30, 427; in three regimes
non-fractal geometries 386n6
99
nonhomogeneous second order linear difference equation
oxidation reactions 208n4
157
oxygenic photosynthesis 433
nonlinear equations 356, 360
nonlinear forecasting method 348
pacemaker point 273
nonlinearity and chaos: double pendulum 317–21;
Packard, N. 350
population growth/logistic map 321–6
parallax error 520, 520
nonlinear regime 98, 100–1; generic system from 100;
parasitism relationship 129, 143, 144
out-of-equilibrium systems in 69–72; in three
paroxysmal tachycardia 283
distinct regimes 99
partial adaptation 191
nonlinear systems 318, 340, 343
partial differential equations (PDE) 246, 307–8
NP-complete problem 418, 464
Particle Swarm Optimization (PSO) algorithm 479
nuclear reaction 426n10
Pascal, B. 485
nucleation/droplet growth 287
pattern recognition 419
null hypothesis 348
Pauling-KNF 171, 172
numerical problem, errors in 533–4
P-class problem 418
Nusselt number ( Nu) 332
PDE (partial differential equations) 246, 307–8
Péclet number ( Pe) 265
“objective” school 507
Peltier effect 54, 58, 59
Ockham’s razor 8–9
Peltier heat (Π) 58
ODEs (Ordinary Differential Equations) 477
pencil-and-paper algorithm 416, 416
Odysseus journey 101, 101
pendulum 318; see also double pendulum; single pendulum
The Odyssey (poem) 5
periodic precipitations 241, 242
Oeconomicus (book) 147
permutation entropy 347–8
Of clouds and clocks (essay) 14
Petri dish 255, 312
Ohm’s law 51, 51
PFK (phosphofructokinase) 174, 175
Ondatra zibethica (muskrat) 285
PGI (phosphoglucose isomerase) 477
one-electron redox system 205
phase space 343, 345–6, 346n9, 401; for chaotic Onsager, L. 56
Hamiltonian system 402; dimensions 401n18
Onsager reciprocal relations 56–7; for chemical reactions
phase waves 271, 272
73; through cross-diffusion 59
Philo-physicists 1, 3, 8
On the Elements according to Hippocrates (book) 7
Philosophiae Naturalis Principia Mathematica (book) 9
On the Generation of Animals (book) 260
A Philosophical Essay on Probabilities (book) 10
On the Origin of Species (book) 11n19
Philosophical Period 3, 3, 5–8
open systems, chemical reactions in 74–5; bi-dimensional
pH oscillators 212–14, 213; Al3+ 215; Ca2+/EDTA 215;
case 76–81; hosting 44; mono-dimensional
divalent cations (M2+) 216; fluoride anions/
case 75, 75–6; multi-dimensional case 81
aluminum ions 215
optical cavity 103, 104
phosphofructokinase (PFK) 174, 175
Orbán reaction 207
phosphoglucose isomerase (PGI) 477
Ordinary Differential Equations (ODEs) 477
phosphorylation reaction 174
Oregonator model 205–8, 208
photo-electrocyclization 340
organic semiconductors 490
photomorphogenesis 438–9
organized complexity 14, 491
photon absorption phenomena 103, 103
oscillations 197, 203; in chemical reactions 197–9;
photoreceptor cells/proteins 440
fluoride 216; in Orbán reaction 207; relaxation
phototropism and photoperiodism 439–40
203, 203
phyllotaxis 261
oscillators: chemical systematic design 199–202, 202;
physicochemical laws, computing by 482, 483; classical
delayed negative feedback 216, 216–19; flow
physics 484–6, 485; with subatomic particles/
control primary 212, 212–14; Hydrodynamic
atoms/molecules 486–90, 488, 489;
Photochemical Oscillator 340–2, 375;
thermodynamics 482–4, 483; ultimate laptop 491
566
Index
physics disciplines 21
random uncertainties 520–1
Phytochrome 438–9
Rapid Eye Movement (REM) sleep 282
pitchfork bifurcations 105, 106; chiral symmetry breaking
rate balance plot 177, 177, 179; with linear feedback 178,
105–10; subcritical 113, 113; supercritical
179, 195; with sigmoidal feedback 180; and
106, 113
stimulus-response curve 195
Planck, M. 426
Rayleigh number (Ra) 328–9, 329n6
Poincaré-Bendixson theorem 126, 126n8
RBQs (Really Big Questions) 6, 6n6, 19, 21
Poincaré, H. 12, 12n23, 352
RD see reaction-diffusion (RD) model
Poincaré map 379
reaction coordinate 266
Poincaré section 379, 380
reaction-diffusion (RD) model 241–6, 243, 251, pointillism, painting 290
256; applicability 256; in art 289–90;
Poiseuille’s law 52
equations 293; in technology 290; Turing
Poisson distribution 511
256, 258, 262
political economy 147
real business cycles theory 159–60
polymerase chain reaction (PCR) 466
Really Big Questions (RBQs) 6, 6n6, 19, 21
Pomacanthus (angelfish) 262, 262
reciprocal positive feedback action 1, 2, 156
Popper, K. 14, 256n6
reciprocal relations 56–9, 56n10, 59; see also Onsager
population growth 321–6
reciprocal relations
positional information 257, 260
recurrent networks 350
positive cooperativity 169
refractory period 203
positive/negative feedback 200–1, 204, 210
regular networks 422–3, 444–5
power laws 399–400; with exponent 401;
regulatory/sensory systems, amplification/adaptation
self-similarity 400
in 187; adaptation 190–1, 191; magnitude
power stroke mechanism 268
amplification 187–8, 188; sensitivity
Practical Period 2–5, 3
amplification 188–90, 189, 190
Prandtl number 329n6
relative uncertainty ( ε ) 518
rel
predator-prey relationships 117–21, 120, 123–8; functional relativistic physics 21–2
response 123; numerical response 123;
relaxation oscillations 203, 203
oscillators 208–11, 211
REM (Rapid Eye Movement) sleep 282
Prediction Company 350
repressilator 217, 217–18, 219
pressure gradient 52, 390
Resonance Energy Transfer (RET) 398–9
Prigogine, I. 198–9
reversibility/irreversibility 21–2; entropy, exhausting fight
primary oscillators 205, 220; chemical equilibrium
30–8; logical operations 484; thermodynamic
coupled to 214–16; delayed negative feedback
approach 22–9
oscillator 216, 216–19; with flow control
revert Liesegang patterning 287n20
212, 212–14; modified Lotka-Volterra model/
revolutionary intellectual events 2
predator-prey 208–11, 209; Oregonator model
Reynold’s number 266–7
205–8, 208
ring oscillator 218, 219
Prisoner’s Dilemma model 480, 481, 481
RNA computing 467
probability distributions 511, 511
RNA polymerase (RNAp) 182, 182
probability theory 507
robots device 476
producers and consumers 148–9, 151–2
root-mean-square distance 90
propagator-controller model 270, 270–1; chemical waves
Rosenstein’s method 345
shapes 273–5; phase waves 271, 272; trigger roundoff error 531–2; propagation 532–3
waves 271–3, 272
rule of thumb 218, 458
proteins 167, 257, 490; actin 265; allosteric 171; computing Runge, C. 504
476–7; protein Y, synthesis of 182, 183, 184, 185
Runge-Kutta method 504
protocell system 463
Proving Darwin. Making Biology Mathematical (book)
saddle-node bifurcations 101–2, 102, 113
257n8
saddle point 81
PSO (Particle Swarm Optimization) algorithm 479
Samuelson, P. A. 149n4, 156
P-system 463
Samuelson’s model 158
pumping, population inversion by 103, 104
sand dunes formation 263–4, 264
pyrimidine synthesis 170, 170
sandpile model 444
sandstone, Liesegang rings in 288
quadratic equations solution 79
satisfiability (SAT) problem 418
quantum bit (qubit) 486–8
scaffolded DNA origami 467
quantum logic 486
scalar force 55
quantum mechanics 12, 483
scale-free networks 423–4, 445
quantum physics 21, 477
Schnackenberg model 250; Jacobian 308; ODEs 307;
PDE 294; Turing patterns from 309
radius of gyration 392n14
Schrödinger equation 416, 416n1
RAND Corporation 480, 480n3
Science and Method (book) 12
random networks 423, 444–5
scientific knowledge mechanism 17, 17
Index
567
second law of thermodynamics 26, 30, 428; Feynman’s
states versus bits 27
device 32; local formulation 42
Static Random-Access Memory (SRAM) 460
secrets of nature 1–4, 9; Computational Period 3, 3, static self-assembly 100n3
15–16; Experimental Period 3, 3, 8–15;
statistical entropy 25, 25
Philosophical Period 3, 3, 5–8; Practical
stimulated emission process 103
Period 2–5, 3
stock solutions preparation 310, 310–12, 311, 312
Seebeck effect 54, 57–8, 59
stoichiometric coefficients 86
self-amplifying effect 390
Stokes–Einstein relation 54
self-organization 100, 100n3
straightforward transduction mechanism 176, 176
Self-Organized Criticality (SOC) 445
strange attractors 126n8, 337, 347, 355, 379, 381
self-similarity 380–1, 400
stretched exponential functions 398–401
sensitivity amplification 188–90, 189, 190
Strutt, J. W. (Lord Rayleigh) 327, 327n5
sensory system (SS) 471–2
Student’s t- distribution 525, 525–7, 526
serendipity 4–5, 4n3
subatomic particles/atoms/molecules 486–90, 488, 489
Seurat, G. 290
subcritical Hopf bifurcations 110, 111
Shakespeare, W. 21
“subjective” school 507
Shannon, C. 27, 29, 486
supercomputer 472; see also electronic computers
Shannon entropy 347
supercritical Hopf bifurcation 110, 111
Shapiro, E. 467
super-tertiary structure 172
short-term predictability 348–9, 349
supervised learning 351
Sierpinski gasket fractals 384, 384–5
supply and demand law 151, 151–2
sigmoidal feedback action 179, 179n6
surface tension (g) 331, 393
Signac, P. 290
surrogate data method 348
signal transduction pathway/system 176–7; with positive
swarm intelligence 445, 479
feedback 177, 177–81, 180
symbiotic relationships, mathematical modeling 130, 130;
silicone oils, types 357
antagonism 130–3, 133; mutualism 133–5, 135
simplicity, epistemological pillars 9–10
symmetry principle 55–6, 56
single pendulum 318; see also double pendulum;
synthetic biology 463
pendulum
systematic errors 517–20, 518, 522
single-photon counting technique 511
systems biology 463
single precision 531
systems chemistry 463
sinusoids shape/features 513, 514
system variables 266
SISs (Social Information Systems) 437n23, 462
Szent-Györgyi, A. 19
small-world network 423
Szilard, L. 32, 32n8
Smith, A. 147, 147n1, 444n28, 482
Szilard’s machine structure 33, 33
Smith, H. 381
Smoluchowski, M. 31, 31n5
Takens’ time-delay embedding theorem 343, 378
SOC (Self-Organized Criticality) 445
target pattern 269, 273
Social Information Systems (SISs) 437n23, 462
Theogony (poem) 5
sociology 263
Theory of Heat (book) 30
Socrates 147
theory of relativity 11–12
soft robot 476
thermal conductivity 50–1
solar radiation and life on Earth 431–3, 432; as
thermal diffusion 54, 61–3, 69
electrochemical energy 436; as energy source
thermal energy 426–7
433–7, 434; as information source 437–44;
thermal entropy 25
plants activities 438; as source of heat 436–7
thermal machine 23, 23
solar thermal radiation/climate change 430–1
thermal radiation, thermodynamics 426–30, 427
sol-coagulation process 287
thermocouple 57, 57–9
solidification process 393
thermodynamics approach 21–3, 23, 482–4, 483; classical somitogenesis 259
definition of entropy 23–4; logical definition of
Soret effect 54, 61, 63
entropy 27–9; statistical definition of entropy
spaceship earth 149–50
24–6
spacing law 286
Thomas’ model 250
spatial coordinates, profiles 303
Thomson, W. 23, 56
spherical/scroll waves 274, 274
three-dimensional waves 274
spindles, waves 282
The Three Princes of Serendip (book) 4n3
Spreading Depression event 282
Time-Correlated Single Photon Counting technique 511
spring-loaded trapdoor 31, 31
time delay (τ) 207–10, 343–4
SRAM (Static Random-Access Memory) 460
time law 286
SS (sensory system) 471–2
time-resolved measurement 508
stable node/spirals/star 79–80
time series prediction 349–51
starch ( St) molecules 254
tissues regeneration 260, 260
starvation 284
tit-for-tat strategy 481
state-space reconstruction 350
top-down approach 486
568
Index
transcription factors ( TFs) 181
undirected networks 420, 421, 447
transcription process 182
unicellular organisms 437, 440
trans-critical bifurcations 102, 103, 103–5
uniformitarianism 10
transformation functions 478
uniformity, epistemological pillars 10
