CNN: A Paradigm for Complexity

The following sections are included:

• PREFACE

• CONTENTS

Please refer to full text.

The following sections are included:

• Isolated Cell

• Sphere of influence

• Local couplings

• The standard CNN equation

• General CNN equations

The following sections are included:

• Standard CNNs are uniquely specified by CNN genes

• Oscillations and chaos from standard CNNs

• Complete stability criteria for standard CNNs

• Bistable criterion

• Coding the CNN gene
  • Edge detection CNN
  • Corner detection CNN

• A gallery of basic CNN genes
  • Threshold CNN
  • Horizontal Translation CNN
  • Vertical Translation CNN
  • Diagonal Translation CNN
  • Point Extraction CNN
  • Point Removal CNN
  • Logic NOT Operation CNN
  • Logic AND Operation CNN
  • Logic OR Operation CNN
  • Edge Detection CNN
  • Corner Detection CNN
  • Right Edge Detection CNN
  • Erosion CNN
  • Dilation CNN
  • Shadow Projection CNN
  • Horizontal Hole Detection CNN
  • Vertical Hole Detection CNN
  • Diagonal Hole Detection CNN
  • Diagonal Line Detection CNN
  • Selected Objects Extraction CNN
  • Filled Contour Extraction CNN
  • Global Connectivity Detection CNN
  • Hole-Filling CNN
  • Face-Vase Illusion CNN
  • Half-Toning CNN
  • Inverse Half-Toning CNN
  • Texture Discrimination CNN
  • Histogram Generation CNN
  • Pixel-Wise Parity Detection CNN
  • Row-Wise Parity Detection CNN
  • Contour Extraction CNN
  • Gradient Detection CNN
  • Motion Detection CNN
  • Image Difference Computation CNN
  • Speed Detection CNN
  • Herring-Grid Illusion CNN
  • De-blurring CNN
  • Muller-Lyer Illusion CNN

• Does there exist a CNN gene for solving Minsky's global connectivity problem?

• Decoding the CNN gene
  • Examples of input–output CNN operators
  • Uncoupled CNN genes
  • Boolean CNN genes and truth tables

• What task can an uncoupled Boolean CNN gene perform?

• Bifurcation of CNN genes

• The game-of-life CNN gene

• The CNN universal machine

• Generalized cellular automata

• A glimpse at some real-world CNN applications

The following sections are included:

• Pattern formation in standard CNNs
  • Characterization of stable equilibria
  • The dynamics of pattern formation
  • CNN pattern formation in biology and physics

• Pattern formation in reaction-diffusion CNNs

• Nonlinear waves in reaction-diffusion CNNs

• Simulating nonlinear PDEs via autonomous CNNs

The following sections are included:

• Transistors and local activity: What do they have in common?

• Nonlinear circuit models for reaction-diffusion CNNs

• What is local activity?
  • Cell equilibrium points
  • Local state equations and local power flows
  • Local activity in reaction-diffusion CNN cells

• Testing for local activity
  • Testing one-port CNN cells for local activity
  • Testing two-port CNN cells for local activity

• Why is local activity necessary for pattern formation?

• How to choose locally-active CNN parameters?

• Local activity and stability are different concepts

• The local activity dogma

The following sections are included:

• REFERENCES

• INDEX