Bonchev D., Rouvray D.H. (editors) Complexity in Chemistry, Biology, and Ecology
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336 Author Index
Terrones, M., 43
Testa, B., 256
Thakker, K. M., 116, 134
Thellier, M., 116
Thoma, J. U., 115
Thomas, R., 116
Thomas, S. R., 128, 133
Tildesley, D. J., 246
Tirado-Rives, J., 247
Tisza, L., 121
Toffoli, T., 257
Tong, A. H. Y., 185, 221
Townend, M. S., 239
Treacy, M. M. J., 43
Tribus, M., 319
Trinajsti´c, N., 192, 193, 203, 209, 210,
211
Trucco, E., 191
Truesdell, 121
Tuinenga, P. W., 128, 133
Turing, A., 72, 73, 90
Tyson, J. J., 53
Ulam, S. M., 257
Ulanowicz, R. E., 307, 308, 313, 316, 320,
322, 323, 324, 325, 326, 327
Van Obberghen-Schilling, E., 73
Varela, F. J., 112, 146, 311
V´azquez, A., 176, 178
Vichniac, G. Y., 257
Vogt, K., 27
von Dassow, G., 90
von Neumann, J., 257
Waddington, C. H., 83, 286
Wagensberg, J., 322
Wagner, A., 221
Wagner, G. P., 166
Waldrop. M. M., 254
Walz, D., 116
Watts, D., 163
Watts, D. J., 213
Weaver, W., 2, 191
Weber, B. H., 325
Welch, G. R., 284, 285
Wells, H. G., 256
Welz, G., 27
Weng, G., 221
White, J. C., 116, 134
Wiener, H., 1, 211
Wieschaus, E., 79
Winfree, A. T., 89
Witten, T. M., 239, 243, 245, 246, 252,
253
Wolfram, S., 257
Wolpert, L., 70
Wright, W. F., 192, 230
Wyatt, J. L., 115, 128, 134
Yamamoto, M., 76
Yomo, T., 60, 62, 64, 91
Yook, S. H., 226
Yost, H. J., 76
Zamfirescu, C. M., 27
Zeeman, E. C., 66, 90
Zengl, A. P., 221
Zhang, G., 43
Zhu, H., 37
Zhu, H. Y., 43
Zimmermann, H. J., 132
Zorach, A. C., 320, 322
Zuse, K., 257
SUBJECT INDEX
A/D index, 213–215, 217
Absolute gravity, 271
Accessible connectedness,
219–220
Activators, 55
Acyclic complexity, 5
Adjacency matrix, 195–196
leading eigenvalue of, 7–16
Adjacent vertices, 195
Adjusted average distance, 219
Admittance matrix, 129
Agents, 250–251
Algorithmic information, 191
Algorithms, 108
AMC (average mutual constraint),
320–321
Analog models of network
thermodynamics, 121
Arcs, 194
Armchair nanotubes, 39
Ascendency, 321
Assortativeness of networks, 172
Asynchronous cell movement,
264–266
Atom environments, local, 25–29
Atomic complexity index, 23
Augmented valence complexity index,
16–20, 30
Autocatalysis, 73
non–mechanical behavior and,
311–316
Autopoiesis, 146
Autopoietic unity, 112
Autoregulatory transcription factor
network model, Keller, 55–59
Average degree, 158
Average edge complexity, 206
Average graph distance, 198
Average mutual constraint (AMC),
320–321
Average path length, 159–161
Average vertex degree, 196
Axis formation
left–right symmetry and, 71–72
Meinhardt’s models for, 72–76
B index, 215–218
Basin of attraction, 54
Biochemical networks, modeling,
289–297
Biochemical state of cells, 52
Biochemical systems, complex, cellular
automata models of, 237–298
Biological development and evolution,
complex chemical systems in,
49–51
337
338 Subject Index
Biological networks, complexity
estimates of, 221–230
Biology, relational systems theory in,
141–144
Biosystems, complex, modeling emergence
in, 257–274
Blastulae, 51
Bond graphs, 118
Boolean network, random (RBN), 181–183
Boron, 36
Boundary conditions, zero–flux, 86
Brain, 101
Branching, 5
complexity and, 4–7
degree of, 6, 11
molecular, 5, 6–7
Breaking rules, 269
Canalizing selection, 83
Capacitance, electrical, 124–125
Capacitor, 122
Carbon, 36
Carbon nanotubes, see Nanotubes
Causality, 99, 316–317
Cayley–Hamilton theorem, 5
Cell differentiation, dependence
of, 59–64
Cell division cycle, 52
Cell movement, 262–267
Cell movement rules, 267–273
Cell rotation, 271, 273
Cell shape, 259
Cell theory, 146
Cell type diversification, multistability
in, 53–55
Cell types, 261–262
Cells, 155, 258–262
Cellular automata, 138, 257–262
Cellular automata models
collection of data in, 273–274
of complex biochemical systems,
237–298
examples of, 274–297
biochemical networks, 289–297
Cellular automata models (cont.)
chreode theory of diffusion in water,
283–289
diffusion in water, 280–283
molecular bond interactions,
277–280
water structure, 275–277
Chaotic systems, 115
Chemical dynamics, insect segmentation
and, 80–83
Chemical oscillations, somitogenesis and,
65–66
Chemical reaction networks, simulation of,
134
Chemistry
models in, 246–248
relational systems theory in, 141–144
Chreode theory of diffusion in water,
283–289
Chreodes, 280–281
Church–Turing thesis, 108
Circular reasoning, 3
Circularity of context dependence,
97–98
Clustering, hierarchical, in contact
maps, 166–169
Clustering coefficient, 161–162,
196–197
second, 197
Combinatorial complexity, 191
Community effect, 59–60
Comparability inequalities, Muirhead, 28
Compartmental systems, mass transport
in, 134
Complete graphs, 194
Complex chemical systems in biological
development and evolution, 49–51
Complex reality, 147
Complexity, 2, 90, 144
acyclic, 5
attempts to simplify, 97–148
branching and, 4–7
of carbon nanotubes, 36–43
combinatorial, 191
Subject Index 339
Complexity (cont.)
of complexity concept, 3–4
compositional, 191
defining, 248–257
of ecodynamics, 303–327
general principles of, 248–257
global, 24
molecular, 1
network, see Network complexity
of smaller fullerenes, 20–24
of smaller molecules, 7–16
Complexity concept, complexity of, 3–4
Complexity estimates of biological and
ecological networks, 221–230
Complexity index
atomic, 23
augmented valence, 16–20, 30
molecular, 23
Complexity index B, 215–218
Complexity measures, 1
combined, 213–218
desirable properties for, 2
Complexity theory, 114, 192
emergence in, 139–148
Complexity vectors, 35
Components, 4, 159
functional, 106
graph, 194
Compositional complexity, 191
Connected graph, 194
Connectedness, 196
accessible, 219–220
Connectivity, 4
extended, 17, 197
overall (OC), 210–211
Constitutive laws for physical systems,
122–123
Constraint(s)
incorporated, measuring effects of,
306–307
new, in ecosystems, 324–327
quantifying, in ecosystems, 318–324
Contact graphs, protein structure and,
164–169
Contact maps, hierarchical clustering in,
166–169
Context dependence
circularity of, 97–98
self reference and, 102–103
Contingency, ecosystems and, 307–311
Correlation profiles, 172–175
Crude symmetry (CS), 33, 34
CS (crude symmetry), 33, 34
Curie’s principle, 142–143
Cycle, 194
Cyclic graphs, 194
DDSs (distance degree sequences), 20–24,
198
Degree, 157
of branching, 6, 11
Degree distribution, 158
Dependency networks, 253
Determination, 51
Deterministic cell movement rules,
266–267
Developmental mechanisms, evolution of,
76–89
Developmental robustness, evolution of,
83–89
Differential gene expression, 49
Differentiation, 52
Diffusion in water, 280–283
Directed graphs, 127, 194, 253
Disconnected graph, 194
Distance, 198
Distance degree distribution, 198
Distance degree sequences (DDSs), 20–24,
198
Distance in–degrees, 200
Distance magnitude distribution, 198
Distance matrix, 198
Distance out–degrees, 200
Dynamics, 125
Newtonian, 112–114
Ecodynamics, 303
complexity of, 303–327
340 Subject Index
Ecological networks, complexity
estimates of, 221–230
Ecosystems
contingency and, 307–311
new constraints in, 324–327
quantifying constraints in, 318–324
Edges, 157, 193
Electric circuits, network
thermodynamics and, 119–120
Electrical capacitance, 124–125
Embryo pattern formation, reaction–
diffusion mechanisms and, 70–76
Embryogenesis, 49
Emergence, 256
in complexity theory, 139–148
modeling, in complex biosystems,
257–274
Entailment, 110
Entropy
of information, 202
Shannon, 204
Epigenetic inheritance, 54
Epigenetic multistability, 55–59
Epigenetic system, 84
Euler’s theorem, 194
Extended connectivity, 17, 197
External world, human mind and, 99–100
Fick’s law, 123
Food webs, 226–230
Formal description of networks, 126–128
Formal system, 99
Fragmentability, 108
Fullerenes
smaller, complexity of, 20–24
symmetry and, 29–34
Functional components, 106
Gene duplication, 175
Gene expression, differential, 49
Gene networks, 180–187
Genericity, 107
Giant component, 159
Global complexity, 24
Global edge complexity,
206
Gordon–Scantleburry index, 208
Graph center, 198, 200
Graph complexity, 2
Graph components, 194
Graph diameter, 198
Graph distances, 198–200
Graph theory, 193
basic notions in, 193–194
Graphitic cones, 43
Graphs, 157–158, 253
bond, 118
complete, 194
contact, protein structure and, 164–169
directed, 127
linear, 126
networks as, 193–201
random, 158
simple, 194
weighted, 201
Gravity, 113
Hasse diagrams, 10
Heaviside function, 86
Helicity, 39
of nanotubes, 38–43
Hierarchical clustering in contact maps,
166–169
Hierarchy, 251–254
Hill function, 85
Hopf instability, 79
Human mind, external world and,
99–100
Hydrophobic effect, 284–285
In–adjacency, 196
In–center, 200
In–component, 200
In–degree, 157, 196
Incidence matrix, 127
Incorporated constraints, measuring effects
of, 306–307
Induction, mesoderm, 70
Subject Index 341
Inductor, 122
Inferences, 100
Information, 104–105
algorithmic, 191
entropy of, 202
topological, 191
Information content, 2
Information indices, 192
Insect segmentation, 77–80
chemical dynamics and,
80–83
Interactions, 242–243
Isologous diversification, 60
Isologous diversification model,
Kaneko–Yomo, 59–64
Joining parameter, 267, 268
Kaneko–Yomo isologous diversification
model, 59–64
Keller autoregulatory transcription
factor network model,
55–59
Kirchhoff’s effort law, 128
Kirchhoff’s flow law, 127–128
Kirchhoff’s laws, 119
Knowledge, quest for, 101
Law of conservation of energy, 114
Law of inertia, 113
Leading eigenvalue of adjacency matrix,
7–16
Left–right symmetry, axis formation and,
71–72
Lewis–Monk model of somitogenesis
oscillator, 66–69
Linear graphs, 126
Linear multiports, 130–133
Linear resistive networks, 128–130
Link deletion, 178
Link–density, 322
Links, 157, 193
Local atom environments, 25–29
Loop, 193, 196
Machines, organisms versus,
108–112
MAPK cascade signaling pathway,
290–297
Mass transport in compartmental systems,
134
Mathematics of science, 117–118
Mechanisms, relational models of, 112
Mechanistic theories, 115
Meinhardt’s models for axis formation,
72–76
Memristor, 123
Mesoderm induction, 70
Metabolism–Repair [M, R] system, 104
Mind, human, external world and, 99–100
Model, 99
Modeling process, 238–244
Models, 238–239, 244–246
in chemistry and molecular biology,
246–248
simulations versus, 244–246
successful, 240–241
Molecular biology, models in, 246–248
Molecular bond interactions, 277–280
Molecular branching, 5, 6–7
Molecular complexity, 1
Molecular complexity index, 23, 192
Molecular dynamics approach, 246–248
Monocilia, 76
Monte Carlo calculations, 246–248
Moore neighborhood, 262, 263
Morgan algorithm, 17
Morphogens, 70
Movement probability, 267
[M, R] Metabolism–Repair system, 104
MRDH (mutual repression by dimer and
heterodimer) network, 56–58
Muirhead comparability inequalities, 28
Multigraph, 194
Multiports, 130
linear, 130–133
Multistability in cell type diversification,
53–55
epigenetic, 55–59
342 Subject Index
Mutations, 175
Mutual repression by dimer and
heterodimer (MRDH) network,
56–58
Nanotube diameter, 43
Nanotubes
complexity of, 36–43
helicity of, 38–43
Neighborhoods, 262–264
Network complexity
measuring, 202–213
quantitative measures of, 191–232
Network thermodynamics, 115–116, 135,
138, 144
analog models of, 121
electric circuits and, 119–120
structure of, 118–133
Networks, 103, 155, 221
assortativeness of, 172
biochemical, modeling, 289–297
characterizing, 120–121
chemical reaction, simulation of,
134
dependency, 253
formal description of, 126–128
gene, 180–187
as graphs, 193–201
linear resistive, 128–130
non–linear, simulation on SPICE,
133–138
of protein complexes, 222–226
protein interaction, 169–170
relational, 138–148
topology of, 120, 126
Newtonian dynamics, 112–114
Nieuwkoop center, 74
Nodes, 157, 193
Non–equilibrium thermodynamics, 141
Non–linear networks, simulation on
SPICE, 133–138
Non–mechanical behavior, autocatalysis
and, 311–316
Normalized edge complexity, 206
Objectivity, 100
science and, 100–102
Observables, 242
OC (overall connectivity), 210–211
Octane, isomers of, 8, 10, 12–14
Ohm’s law, 123
Onsager/Prigogine representation, 135
Onsager reciprocal relations (ORR), 131,
136–138
Organisms, machines versus, 108–112
ORR (Onsager reciprocal relations), 131,
136–138
Oscillatory mechanisms, 84
Out–adjacency, 196
Out–center, 200
Out–component, 200
Out–degree, 158, 195
Overall connectivity (OC), 210–211
Path, 194, 198
Path graph, 194
Path matrix, 8
Pattern, 4
Pattern formation, embryo, reaction–
diffusion mechanisms and,
70–76
Physical systems, constitutive laws for,
122–123
Physiology, 105
Platt index, 207
Poiseuille’s law, 124
Poisson distribution, 158
Probabilistic cell movement rules,
266–267
Propensity, 310
Protein complexes, networks of,
222–226
Protein folding maps, small–world
structure of, 165
Protein interaction networks, 169–170
Protein molecules, 155–156
Protein structure, 165
contact graphs and, 164–169
Proteins, 164
Subject Index 343
Proteome growth, rules of, 176
Proteome model, 175–180
Quasi power theorem, 137
Quest for knowledge, 101
Random Boolean network (RBN),
181–183
Random graphs, 158
RBM (random Boolean network),
181–183
Reaction–diffusion mechanisms, embryo
pattern formation and, 70–76
Reaction–diffusion systems, 71
Reductionism, 106, 117–118
relational systems theory versus,
107–108
Relational block diagrams, 103–104
Relational models of mechanisms, 112
Relational networks, 138–148
Relational systems theory, 103
in chemistry and biology, 141–144
reductionism versus, 107–108
Relative gravity, 269–271, 272
Repressors, 55
Resistive networks, linear, 128–130
Resistor, 122
Reversibility, 325
Riemann zeta function, 186
Robustness, developmental, evolution of,
83–89
SC (subgraph count), 207–209
SC (symmetry corrected), 31
Schlegel diagrams, 20
Science
mathematics of, 117–118
objectivity and, 100–102
Scientific model, 100–101
Second cluster coefficient, 197
Segmentation, 65
insect, see Insect segmentation
Self–organization, 254–256
Self reference, 106
Self reference (cont.)
context dependence and, 102–103
Sensory physiology, 99
Shannon entropy, 204
Shannon theory, 203
Silicon, 36
Simple graphs, 194
Simulations, models versus, 244–246
Small–world effect, 162–164
Small–world structure of protein folding
maps, 165
Somitogenesis, 65
chemical oscillations and, 65–66
Somitogenesis oscillator, Lewis–Monk
model of, 66–69
Spanning tree, 194
Spemann–Mangold organizer, 71–72, 74
SPICE, non–linear networks simulation on,
133–138
Star graph, 194
States of systems, 241–242
Strongly connected component, 200
Subgraph, 193
Subgraph count (SC), 207–209
Sulfur, 36
Symmetry
fullerenes and, 29–34
left–right, axis formation and, 71–72
Symmetry corrected (SC), 31
Symmetry factor, 31
Synchronous cell movement, 264–266
Synthesis, 109
System overhead, 322
Systems, 241
states of, 241–242
TC (topological complexity), 211
Tellegen’s theorem, 120, 137
Thermodynamics, 114
network, see Network thermodynamics
non–equilibrium, 141
Time lag, 90
TO (topological overlap), 166
Topological complexity (TC), 211
344 Subject Index
Topological indices, 35
Topological information, 191
Topological overlap (TO), 166
Topological reasoning, 116
Topology
of networks, 120, 126
vector calculus and, 118
Total adjacency, 195, 205–206
Total walk count (TWC), 211–213
Transcription factors, 55, 180–181
Trees, 194
Tube, 226
Turing instability, 71, 79
TWC (total walk count), 211–213
Undirected graph, 194
Unistors, 132
Vector calculus, topology and, 118
Vegetal pole organizer, 73
Vertex accessibility, 219
Vertex degree, 195
Vertex degree distribution, 195,
203
Vertex distance, 198
Vertex eccentricity, 198
Vertices, 157, 193
adjacent, 195
von Neumann neighborhood, 262, 263
extended, 264
Walk, 194
Walk count, 15
Walk length, 194
Water structure, 275–277
Weighted adjacency matrix, 201
Weighted graphs, 201
World, external, human mind and,
99–100
Zero–flux boundary conditions,
86
Zeta function, Riemann, 186
Zigzag nanotubes, 39, 40–42