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Table of Content
NEURAL NETWORK NATURE
Fractal hierarchies of 'Perceptrons' fom Clusters of Galaxies to the World Wide Web
Introduction 5
Hierarchy Theory 8
What is a Hierarchy? Wikipedia 8
Hierarchy of Holons (1968 Koestler) 12
Living Systems (1978 Miller) 17
Compositional hierarchy vs. Subsumption hierarchy (2002 Salthe) 21
Operator hierarchy (1999 Jagers op Akkerhuis) 28
Network hierarchy (2002 Barabási) 29
Levels of evolutionary hierarchy (2008 Winiwarter) 32
A Summary of Principles of Hierarchy Theory 38
Power laws and the laws of Power 41
Common 3-level hierarchical structure 41
A short history of discovery across the disciplines 44
Pareto-Zipf-Mandelbrot (PZM) and parabolic fractal distributions 51
Illustrated
regularities of the Pareto-Zipf-Mandelbrot type
Data Source:
Google Images 55
Astrophysics, Nuclear networks 55
Geophysics (Gaia), Tectonic networks 62
Biophysics, Biochemistry : protein and metabolic networks 72
Biology Phylogeny: procariotes, eucariotes, genetic networks 75
Biology Ontogeny: trophic ecosystems, trophic networks 77
Social networks: the small world of scalefree networks 85
Technology networks: from stone tools to the internet 94
What do all these illustrated regularities have in common? 101
Self-similarity and the beauty of Fractals 104
fractals, Wikipedia 104
History 107
Generating fractals 109
Classification of fractals 109
Fractals in nature 110
Fractal dynamics and scale-free thinking 112
Networks everywhere 114
Networks, Wikipedia 114
The origins: the seven bridges of Königsberg 119
The random Networks of Erdős and Rényi 121
The small Worlds of Watts and Strogatz, the six degrees of separation 123
Barabási's scalefree networks from cells to the Internet 126
The mysteries of Artificial Neural Networks 134
Theoretical attempts to explain the PZM regularities: Birth and Death processors and Artificial Neural Networks 143
Self-organized critically, Wikipedia 143
West's MinMax priciple for scaling laws 145
Holistic Extremum principle (Mandelbrot, Winiwarter) 147
Pareto Pareto = Pareto , stability under addition ( Roehner, Winiwarter) 148
Birth and Death processor, the basic interaction unit 148
Artificial Neuron equivalent to birth and death processor 150
Networks of Birth and Death processors and Artificial Neural Networks 152
Trophic Web and Features of multilayer Perceptron (case study of lake Constance) 156
Future evolution: is the singularity near? 159
Increase in complexity, the first law of genesis (Winiwarter) 159
PZM power laws, the second law of genesis (Winiwarter) 159
Ritualization : the Self-Organization process of symbolic information 160
The singularity is near (Kurzweil) 164
Conclusions 170
Bibliography 174
> 10.000 citations : "The fractal revolution" 174
1.000 - 10.000 citations : "The network revolution" 174
500 - 1.000
citations "the EVOLUTION of Networks" 176
100 - 500 citations : "Evolving hierarchical systems" 178
15 - 100 citations : "The languages of Nature" 180
< 15 citations : "The Extended Mind" The Emergence of Language, the Human Mind, and Culture 182
List
of publications by Peter Winiwarter relevant to this book : 184
About the author, from Wikipedia, the free encyclopedia 186
Acknowledgments 188
Back cover Neural Network Nature 189
