Pattern formation in biology, vision and dynamics:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 423 S. Ill., graph. Darst. |
| ISBN: | 9810237928 |
Internformat
MARC
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| 245 | 1 | 0 | |a Pattern formation in biology, vision and dynamics |c Alessandra Carbone ... |
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Datensatz im Suchindex
| _version_ | 1804138987664703488 |
|---|---|
| adam_text | Pattern Formation
in Biology, Vision
and Dynamics
Alessandra Carbone
Department of Mathematics and Computer Sciences,
University of Paris XII
Misha Gromov
Institut d Hautes Etudes Scientiftques and
Courant Institute of Mathematical Sciences
Przemyslaw Prusinkiewicz
Department of Computer Science,
University of Calgary
Vfe World Scientific
Singapore • New Jersey • London • Hong Kong
CONTENTS
Preface vii
GROWTH AND FORM 1
Paradigms of Pattern Formation: Towards a Computational
Theory of Morphogenesis 3
Przemyslaw Prusinkiewicz 3
1 Introduction 3
2 Single blind agent with finite memory 6
3 Single blind agent with infinite memory 7
4 Single sighted agent receiving cues from the environment (one-way
exogenous control) 8
5 Single sighted agent receiving cues from the structure (two-way
exogenous control) 10
6 Single self-controlled agent (endogenous control) 11
7 Multiple blind agents with finite memory 12
8 Multiple blind agents with infinite memory 14
9 Multiple sighted agents 14
10 Multiple endogenously-controlled agents 16
11 Combined effect of multiple mechanisms 18
12 Conclusions 19
Growth and Form of Sponges and Corals in a Moving Fluid 24
Jaap A Kaandorp and Peter M A Sloot 24
1 Introduction 24
1 1 Biological background 24
1 2 Simulation of growth in a mono directional flow 26
1 3 Simulation of growth in a bidirectional (alternating) flow 28
2 Methods 29
2 1 Modelling the nutrient distribution 29
2 2 Modelling the growth process in an alternating flow 31
3 Results - 32
4 Discussion 37
From Pseudo-Random Numbers to Stochastic Growth Models
and Texture Images 42
Leonid P Yaroslavsky 42
1 Introduction 42
2 Pseudo-random number generators 43
3 Growth models 45
3 1 Eden s type growth models 45
3 2 Conway s Game of Life and its modifications 48
4 Algorithmic models of texture images 54
4 1 The algorithmic approach to synthesis and analysis of
texture images 55
xiii
xiv Contents
Crystal Growth, Biological Cell Growth, and Geometry 65
James W Cannon, William J Floyd and Walter R Parry 65
1 Introduction 65
2 A growing tree trunk whose shape oscillates wildly in time 66
2 1 Cell growth versus crystal growth 66
2 2 The groundrules 66
2 3 The plan 67
2 4 The coordination problem 68
2 5 The signal problem 68
2 6 The delay problem 69
2 7 The signal cascade 70
2 8 Using boundaries 70
2 9 Measuring shape 70
2 10 The example 71
3 The geometry of rat tissue 72
3 1 Discrete geometry 72
3 2 Euclidean geometry, the lens of the eye, and muscle fibers 73
3 3 Spherical geometry and the bladder 73
3 4 Negatively curved geometry and the lung, brain, digestive,
and endocrine systems 73
3 5 Conflicting geometries 74
4 Crystals 75
4 1 Examples of crystals 75
4 2 Ways of viewing crystals 76
5 Negatively curved crystals are asymptotically fractal 78
5 1 The Cayley crystal 78
5 2 Thin triangles 79
5 3 Asymptotic shape 79
5 4 Fractal Theorem 80
5 5 Proof 80
Recent Results on Aperiodic Wang Tilings 83
Jarkko Kari - __ 83
1 Introduction ~ 83
2 Algebraic construction of aperiodic tile sets 87
3 Forced tiles and determinism 89
4 Beyond aperiodicity 93
5 Conclusions and open problems 94
REACTION-DIFFUSION AND BEYOND 97
Biological Pattern Formation as a Complex Dynamic
Phenomenon 99
Hans Meinhardt 99
1 The problem of pattern formation 99
1 1 The egg cannot contain the final pattern 100
Contents xv
1 2 Organizing regions 100
1 3 The concept of positional information 101
2 Generation of a primary pattern by autocatalysis and lateral inhibition 101
2 1 The Activator-Inhibitor concept 102
2 2 Comparison with Taring s mechanism 105
3 The wave length problem — stabilization of a monotonic gradient
by a feedback on the source density 106
3 1 How to generate structures close to each other, how at a
distance: head, foot and tentacle formation in Hydra 108
4 Activation of genes under the influence of morphogenetic signalling 110
5 Formation of filament-like branching structures 113
6 Segmentation by mutual activation of cell states that locally exclude
each other 115
7 Pattern formation in secondary embryonic fields: differentiation
borders obtain organizing properties 116
8 Pigmentation pattern of shells of mollusk — a natural picture book
to study dynamic systems 117
8 1 Traces of a stable pattern, oscillations and travelling waves:
lines parallel, perpendicular or oblique to the direction of growth 118
9 Travelling waves with unusual properties 119
9 1 -Formation of branches: the sudden formation of
backwards-running waves 119
9 2 Penetration of waves without annihilation 121
9 3 Not all together now 123
9 4 Travelling waves without pace-maker 124
10 Complex patterns result from the superposition of two patterns 124
10 1 Superposition of two time-dependent patterns 126
10 2 Open problems in shell patterning 127
Andronov Bifurcations and Sea Shell Patterns 133
M Argentina and P Coullet 133
1 Andronov bifurcations in extended systems 136
2 Sea shell patterns 139
2 1 Cavitation like patterns 141
2 2 Patterns of excitable waves 141
Rational and Irrational Angles in Phyllotaxis 145
Y Couder and S Douady 145
1 Introduction 145
1 1 The geometry of phyllotaxis 145
1 2 The dynamics of phyllotaxis 146
2 The self organisation in model iterative systems 147
2 1 Hofmeister s rules: the spiral modes 147
2 2 The dynamical selection of the Fibonacci modes 148
2 3 The generalised model: Snow and Snow s rules 153
2 4 The selection of the actually observed patterns 155
xvi Contents
3 The selection during the plant growth 156
4 Conclusions 156
CELLULAR PATTERNS 161
Organogenetic Cellular Patterning in Plants 163
P W Barlow, H B Luck and J Luck 163
1 Introduction 163
2 Cell patterning from the perspective of the cell body 164
3 What lies behind analyses of cell patterning? 167
4 A simple autoregenerating cell pattern related to organogenesis 169
5 Simulation of cell patterns and the uncovery of division rules 172
5 1 The Simulation System for the Psilotum Apex 172
5 2 Identification of cell types 177
5 3 Merophyte formation by apical divisions 178
5 4 Wall-offsetting leads to refinement of the wall production system 179
5 5 The distribution of apical triangular cells and the problem
of dichotomous axis branching 181
6 Possible regulatory factors underlying cell patterning and its
simulation at the psilotum apex 182
61A System s View of Division Wall Site Selection 182
6 2 Cytological View of Division Wall Site Selection 186
7 Was there a precursor of the psilotum pattern? 189
8 Prospects 193
A Classification of Plant Meristems based on Cellworks
(3D L-systems) The Maintainance and Complexity of Their
Cellular Patterns 199
Jacqueline Luck and Hermann B Luck 199
1 Introduction 199
2 Cellworks 201
3 A classification of plant forms 203
4 Specification of a cellwork system_with double labelled walls 208
5 How to find a Cellwork system with an autoreproductive initial cell 209
6 Extended classification of plant forms 210
7 Passage from one generating system to another 212
8 Limits of the classification tables 212
9 From topology to geometry 212
10 Conclusion 214
Plant Meristems and Their Patterns 217
Beata Zagorska-Marek 217
1 Introduction 217
2 Patterns of the shoot apical meristem 218
2 1 Developmental variation of cellular patterns 218
2 2 The geometry of a growing apex 222
Contents xvii
2 3 Phyllotaxis 224
3 Cellular patterns of vascular cambium 228
3 1 Storied pattern 229
3 2 The pattern of growth activity 231
3 3 Structural wavy patterns 232
4 Conclusions 235
Mechanical Stress Patterns in Plant Cell Walls and Their
Morphogenetical Importance 240
Zygmunt Hejnowicz 240
1 Introduction 240
2 Stress anisotropy 240
3 Stress distribution ~ 245
4 Conclusions 248
Tensorial Model for Growth and Cell Division in the
Shoot Apex 252
Jerzy Nakielski 252
1 Symplastic Growth and the Growth Tensor 252
2 Model for Growth and Cell Division in the Shoot Apex
(2-dimensional) 254
3 The Example of Application of the Model 259
4 Discussion 263
DNA AND GENETIC CONTROL 269
DNA Nanotechnology: From Topological Control to Structural
Control 271
Nadrian C Seeman 271
1 DNA Nanotechnology 271
2 Double Helical DNA 272
3 Genetic Recombination and the Holliday Junction 274
4 Immobile BranchedMunctions _ 275
5 Characterization of Unusual DNA Motifs and Structures 277
6 DNA Ligation and Cohesion 278
7 Branched DNA and Sticky Ends 280
8 Connectivity 281
9 Topological Features of DNA Constructs 281
10 Construction of DNA Polyhedra 282
11 DNA Catenanes and Knots 286
12 Construction of DNA Knots 288
13 DNA Borromean Rings 289
14 Rigid Components 292
15 1-D and 2-D Periodic Arrays 294
16 Nanomechanical Devices 297
17 Prospects 300
i
xviii Contents
3D DNA Patterns and Computation 310
Natasa Jonoska 310
1 Introduction 310
2 Constructing Graphs with fc-Armed Branched Molecules 312
2 1 The Hamiltonian cycle problem 312
3 The Three Vertex Colorability Problem (3VC) 315
4 Recognition of Graph Structures 318
4 1 Covering graphs and complexity 318
4 2 Graphs made of one single stranded DNA molecule 319
5 Final Remarks 321
Circular Suggestions for DNA Computing 325
Tom Head ~ 325
1 Introduction 325
2 Naturally Occurring Plasmids 326
3 The Delphic Plasmid, DEL 327
4 Independent Subsets and Vertex Covers for Undirected Graphs 329
5 Partitions into Hamiltonian Subgraphs 331
6 Satisfiability of Boolean Formulas 332
DNA Computing by Matching: Sticker Systems and
Watson-Crick Automata 336
Gheorghe Pawn 336
1 Introduction 336
2 DNA: Structure and Annealing Operation 339
3 Formal Language Theory Prerequisites 341
4 The Twin-shuffle Language and its Relation with DNA 342
5 The Operation of Sticking 344
6 Sticker Systems 346
7 The Power of Sticker Systems 349
8 Watson-Crick Finite Automata 352
9 The Power of Watson-Crick Finite Automata 353
10 Variants of Watson-Crick Automata 356
11 Conclusions - 359
IMAGES AND PERCEPTION 363
Aspects of Human Shape Perception 365
Jacques Ninio 365
1 Shape from motion 365
2 From moving to static shapes 367
3 Static shapes: the gestalt approach 367
4 Static shapes: the importance of orientations 370
5 2D perceptual geometry 373
6 From 2D to 3D 374
7 Shape synthesis 378
Contents xix
Pattern Recognition in The Visual System and The Nature
of Neural Coding 382
Simon Thorpe 382
1 Introduction 382
2 The efficiency of pattern recognition by the human visual system 382
3 The Coding Problem 385
4 An alternative — Using patterns of spikes 386
5 Rank Order Coding 387
6 Rank Order Decoding 388
7 Conclusions and Perspectives 390
How can Singularity Theory Help in Image Processing? 392
M Briskin, Y Elichai and Y Yomdin 392
1 Introduction 392
2 Digital images 395
3 Compression problem 396
4 An example of data representation, based on normal forms of
singularities 400
5 Singularities of digital images and their normal forms 402
6 Detection of singularities and their approximation by normal forms 408
7 Vectorized images 415
8 Creation of virtual worlds 418
9 Possible implications for human visual perception 423
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