Machine learning applied to pattern characterization in spatially extended dynamical systems

Cellular automata (CA) are important as prototypical, spatially extended, discrete dynamical systems. Because the problem of forecasting dynamic behavior of CA is undecidable, various parameter-based approximations have been developed to address the problem. Out of the analysis of the most important parameters available to this end we proposed some guidelines that should be followed when defining a parameter of that kind. Based upon the guidelines, new parameters were proposed and a set of five parameters was selected; two of them were drawn from the literature and three are new ones, defined here. This article presents all of them and makes their qualities evident. Then, two results are described, related to the use of the parameter set in the Elementary Rule Space: a phase transition diagram, and some general heuristics for forecasting the dynamics of one-dimensional CA. Finally, as an example of the application of the selected parameters in high cardinality spaces, results are presented from experiments involving the evolution of radius-3 CA in the Density Classification Task, and radius-2 CA in the Synchronization Task.

Download Full-text

Study of spatially extended dynamical systems using probabilistic cellular automata

Physics-Uspekhi ◽

10.1070/pu1999v042n05abeh000558 ◽

1999 ◽

Vol 42 (5) ◽

pp. 413-434 ◽

Cited By ~ 14

Author(s):

Vladimir K Vanag

Keyword(s):

Dynamical Systems ◽

Cellular Automata ◽

Probabilistic Cellular Automata ◽

Spatially Extended

Download Full-text

Expanding perspectives on cognition in humans, animals, and machines

10.1101/037192 ◽

2016 ◽

Author(s):

Alex Gomez-Marin ◽

Zachary F Mainen

Keyword(s):

Machine Learning ◽

Dynamical Systems ◽

Molecular Biology ◽

Future Research ◽

Learning Behavior ◽

The Past ◽

The Mind ◽

The Brain

Over the past decade neuroscience has been attacking the problem of cognition with increasing vigor. Yet, what exactly is cognition, beyond a general signifier of anything seemingly complex the brain does? Here, we briefly review attempts to define, describe, explain, build, enhance and experience cognition. We highlight perspectives including psychology, molecular biology, computation, dynamical systems, machine learning, behavior and phenomenology. This survey of the landscape reveals not a clear target for explanation but a pluralistic and evolving scene with diverse opportunities for grounding future research. We argue that rather than getting to the bottom of it, over the next century, by deconstructing and redefining cognition, neuroscience will and should expand rather than merely reduce our concept of the mind.

Download Full-text