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Unconstrained optimization in a stochastic cellular automata system. (English) Zbl 1413.68070

Summary: This paper considers a stochastic cellular automata system which models a random dynamical system, and introduces a simple unconstrained optimization problem on such a system to capture hidden characteristics over time. To achieve this goal, we create a random metric which is applied to nearby and far-away locations of automata in order to find hidden characteristics in the automata system over time. Solving the random metric based unconstrained optimization problem, we found that solutions show high and low level fluctuations, depending on the choice of the perturbation parameter \(\lambda\) and the corresponding locations. The application of our method to cell concentration data reveals its consistency and adaptability. This work is an expanded version of our previous work [H. C. Jimbo and M. Craven, in: Proceedings of neural, parallel, and scientific computations. Vol. 4. Proceedings of the 4th international conference, Atlanta, GA, USA, August 11–14, 2010. Atlanta, GA: Dynamic Publishers. 187–192 (2010; Zbl 1222.68116)].

MSC:

68Q80 Cellular automata (computational aspects)
37B15 Dynamical aspects of cellular automata
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
90C26 Nonconvex programming, global optimization

Citations:

Zbl 1222.68116
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