[Dept. of Computer Science]

Experimentation Project ACS


Title Fixed and Volatile connections in self-clustering networks
Student Mark Jeronimus
Supervisor Ad Feelders, Daan van den Berg (external)
ECTS 7.5
Related Course(s) Algorithms and Networks
Description

Introduction

A high Clustering Coefficient (CC) in combination with a low Characteristic Path Length (CPL) are the defining characteristics of the category of graphs called small-world networks [1].
Numerical results have shown that small-world networks are highly efficient and robust in terms of information spreading [2].
In this sense, small-world networks are optimal functional architectures for information processing.
These architectures are predominant in networks like the Internet, social communication networks, and other networks that communicate through sparse connections [3,4].
Recently, the functional architecture of the brain was shown to have small-world connectivity [5].

In [6] it was shown that an algorithm coupled chaotic activation functions consistently evolve to small-world structures.
Chaotic activation has been observed in various real-life neural systems.
We may, therefore, propose the chaotic-adaptive rewiring algorithm as an extremely simplified model for the evolution of small-world connectivity in the brain.

Recent studies have shown that the human visual cortex consists of various densely connected cluster with relatively few connections between them [7].
The suspicion is that the previously presented algorithm produces very similar networks. The goal of this study is to investigate these properties.

Assignment

Part 1 - Survey

In the Survey, connections should be labeled by an integer value which replaces the boolean value.
As such, the connections 'movement' can be traced throughout the network's evolution.
A network of 400 units with 5000 connections should be used. It should be iterated 4 000 000 times and during this cycle, a record of all changes in connections should be kept.
In an initial phase, it could be taken every 1000 iterations to gain a global perspective.

Goal of this survey is to verify or falsify the hypothesis that when this network reaches its global dynamical attractor,
a small percentage of connections keeps changing whereas a large part becomes fixed within the clusters.

Part 2 - Analysis

This part will only be commenced in succession to succesful completement of part 1. After analysing which connections stay fixed,
it might be possible to determine which units and connections form fixed clusters and what their size is. In an extended case, other networks could be probed.

Links:

References:

  1. Watts, D.J. & Strogatz, S.H., Nature, 393 (1998) 440-442.
  2. Strogatz, S.H., Nature, 410 (2001) 268-276
  3. Broder, A. et al., Comput. Netw. 33 (2000) 309-320
  4. Watts, D.J., in Small Worlds. (Princeton University Press) 1999.
  5. Stephan, K.E., Hilgetag, C.-C, Burns, G.A.P.C., O'Neill, M.A., Young, M.P. & Koetter, R. Philosophical Transactions of the Royal Society of London, B., 355 (2000) 111-126.
  6. Van den Berg, D. & Van Leeuwen, C., Europhysics Letters, 65 (2004), 459-464
  7. Kaiser, M & Hilgetag, C.C., Neuroinformatics, 2-3 (2004), 353-360
Special Note