Regensburg 2004 – scientific programme

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DY: Dynamik und Statistische Physik

DY 34: Nonlinear Dynamics and Chaos I

DY 34.8: Talk

Wednesday, March 10, 2004, 16:15–16:30, H2

Synchronization of Random Walks with Reflecting Boundaries — •Andreas Ruttor, Georg Reents, and Wolfgang Kinzel — Institut für Theoretische Physik, Universität Würzburg, Am Hubland, 97074 Würzburg

Neural networks can synchronize by mutual learning. If the learning algorithm changes the values of the weights only in discrete steps of equal size, the dynamics of each weight can be described as a random walk. In this case it is possible to calculate statistical properties of the synchronization process by replacing neural networks with ensembles of random walks.

We consider two random walks with reflecting boundaries. In each step both random walkers are moved in the same, randomly chosen direction. If one hits the boundary, the distance between both is decreased. This leads to synchronization after some steps. We calculate the mean and the variance of the synchronization time analytically. By using the probability distribution of this quantity, we can also determine the average number of steps, after which two ensembles of random walks reach a synchronized state.
For publications and preprints see:
http://theorie.physik.uni-wuerzburg/TP3/publi.html