Abstract

Table of Contents

Introduction (.pdf), (.pdfscreen)

Emergence

The Many are Unpredictable
Self-organization
The Bottom-Up Approach and Emergence
Modeling Tools

Networks
Cellular Automata
Random Graphs
Science of Networks

Physics and Networks
Networks in a Social Context
Brain as a Network
Neuropercolation Ideas
Similarities of Systems

Neural and Social Systems
Decisions
Not So Homogeneous Due to Learning

Biological Inspiration - Neurodynamics (.pdf), (.pdfscreen)

Neurons Make Up the Brain

Introduction
Conceptual Description of Neuron
Neural Connections
Activity of Neuron

Single Neuron States
Microscopic vs. Mesoscopic
Building Blocks of Neurodynamics

Short Description of Building Block of Neurodynamics
Figures of Couple Building Blocks of Neurodynamics
State Space of a Cortex

Itinerancy of Brain States
Intentionality and Meaning Created by Brain

Tools to Study the Brain
Intentionality and Meaning
Brains and Societies

Brains are Small Worlds
Relationship between Neural and Social Networks
Changes Due to Learning
Questions

Percolation (.pdf), (.pdfscreen)

Classical Percolation

Introduction
Cluster Numbers
Exact Solution in One Dimension
2-dimensional Complications
Bootstrap Percolation

Introduction
Random Cellular Automata as Generalized Bootstrap Percolation
Simple Model of Bootstrap Percolation with a Solution
Neuropercolation

Description
Neuropercolation Directions

System Description (.pdf, .pdfscreen)

General Model Description

Introduction
A Decision Rule
Neighborhood Characteristics
Global Behavior Description

Activation Density
Activation Clustering
Overlap
Jump Description
Synchrony Description
General Behaviors

Criticality Description (.pdf, .pdfscreen)

State Transition and Criticality

Criticality
Density of Systems with Homogeneous Components

Statistical Physics and Scaling Theory

Critical Exponents and Their Measurement
Real-space Renormalization
Finite Size Scaling Method
Calculation of Critical Exponents
An Example: Toom Cellular Automata

Criticality in a Local Random Cellular Automata (.pdf, .pdfscreen)

Introduction

Models of Neurons
Model Description
Simulation of RCA and Results Analysis

Phase Transition
Critical Exponent and Finite Size Scaling
Quality of Estimation

State Transitions in the Probabilistic Cellular Networks (.pdf, .pdfscreen)

Oscillations in the Probabilistic Cellular Networks (.pdf, .pdfscreen)

Synchrony in the Probabilistic Cellular Networks (.pdf, .pdfscreen)

Activation Clustering in Neural and Social Networks (.pdf, .pdfscreen)

Effects of Hebbian-like Adjustments (.pdf, .pdfscreen)

Epilogue