When are cellular automata random?

Of the 256 elementary cellular automata, 28 of them exhibit random behavior over time, but spatio-temporal currents still lurk underneath.

EPL 84, 50005 (2011)

J. Coe, S. Ahnert, T. Fink

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A random cellular automaton is one in which a cell's behaviour is independent of its previous states. We derive analytical conditions which must be satisfied by random cellular automata and find deterministic and probabilistic cellular automata that satisfy these conditions. Many random cellular automata are seen to have a flow as they are updated through time. We define a correlation current that describes this flow and develop an analytical expression for its size. We compare results from this analytical expression with those from simulation. The randomness in a cell comes from randomness in adjacent cells or from the stochastic nature of update rules. We give an expression for how much randomness comes from each of these two sources.

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The space of functions computed by deep layered machines

A. Mozeika, B. Li, D. Saad

Sub. to Physical Review Letters

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Replica analysis of overfitting in generalized linear models

T. Coolen, M. Sheikh, A. Mozeika, F. Aguirre-Lopez, F. Antenucci

Sub. to Journal of Physics A

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Taming complexity

M. Reeves, S. Levin, T. Fink, A. Levina

Harvard Business Review

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Replica analysis of Bayesian data clustering

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Journal of Physics A

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Degree-correlations in a bursting dynamic network model

F. Vanni, P. Barucca

Journal of Economic Interaction and Coordination

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Scale of non-locality for a system of n particles

S. Talaganis, I. Teimouri

Sub. to Physical Review D

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