Many Roads to Synchrony: Natural Time Scales and Their Algorithms

Details Many Roads to Synchrony: Natural Time Scales and Their Algorithms Many Roads to Synchrony: Natural Time Scales and Their Algorithms

2010-10-27

arxiv.org/abs/1010.5545v1

Nonlinear Sciences

Chaotic Dynamics

8 pages, 3 figures, 1 table: http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm

Scientific paper

We survey the variety of ways in which one synchronizes to a stochastic process. We define associated length scales, providing characterization theorems and efficient algorithms for their calculation. We demonstrate that many of the length scales are minimized by using the epsilon-machine, compared to all of a process's alternative models. We also show that the concept of Markov order, familiar in stochastic process theory, is a topological property of the epsilon-machine presentation. Moreover, we find that it can only be computed when using the epsilon-machine, not any alternative. We illustrate the results by presenting evidence that infinite Markov order and infinite crypticity are dominant properties in the space of finite-memory processes.

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