Lecture 23

Lectures: 1 | 2 | 3 | 4-5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 15 | 16 | 17 | 19 | 20 | 21 | 22 | 23 | 26

Networks

1. Introduction to Networks:
   • Random (Erdös-Rényi) Networks Page 1 (GIF) of Lecture Notes)
   • Percolation (Page 2 (GIF) of Lecture Notes)
   • Distance, Diameter, and Degree Distribution (page 3 (GIF) of Lecture Notes)
2. Scale Free Networks:
   • Examples from the Colloquium by A.-L. Barabasi:
     • The World Wide Web - Description (GIF) and Results (GIF)
     • Food Web (GIF)
     • Yeast Protein Network (GIF)
     • Metabolic Network (GIF)
   • The Degree Distribution of the BA Model (Page 4 (GIF) of Lecture Notes)
3. Dynamics on Networks: (Page 5 (GIF) of Lecture Notes)
   • Node Variables Evolving According to Inputs from Connected Nodes
   • Examples - Chemical Flux Balance Equations, Neural Networks
   • Possible Collective Outcomes: Fixed Points, Temporal Oscillations, Spatial Patterns, ...
4. Some Conditions for Existence of Fixed Point Solutions: (Page 6 (GIF) of Lecture Notes)
   • One Dimensional Systems - Stability, Noise
   • Gradient Descent in Higher Dimensional Systems
   • Hopfield, J. J. "Neurons with Graded Response Have Collective Computational Properties like Those of Two-State Neurons." Proceedings of the National Academy of Sciences of the United States of America 81, no. 10 (May 15, 1984): 3088-3092. (Part 1: Biological Sciences.) (Page 7 (GIF) of Lecture Notes)

Some Related Links

• Biological Networks at Harvard CGR
• A Course (U. Wisconsin) on Learning and Modeling Biological Networks
• Networks group at Notre Dame
• Albert, R., and A. -L. Barabasi. "Statistical mechanics of complex networks." RMP 74, no. 47 (2002).

Metabolic Networks

• Principles of Metabolic Flux Analysis

Neural Networks

• Computation in the Brain
• Associative Memories in the Hopfield Model
• An Applet for Demonstrating Associative Memory in the Hopfield Model