Complexity Measures from Interaction Structures

We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between $k-1$ units. We demonstrate that these measures are able to identify complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Asynchronism Induces Second Order Phase Transitions in Elementary Cellular Automata

Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For some particular rules, varying the synchrony rate continuously produces a qualitative change in the behaviour of the cellular automaton. We investigate the nature of this change of behaviour using Monte-Carlo simulations. We show that this phenomenon is a second-order phase transition, which we characterise more specifically as belonging to the directed percolation or to the parity conservation universality classes studied in statistical physics

Measuring Shared Information and Coordinated Activity in Neuronal Networks

Most nervous systems encode information about stimuli in the responding activity of large neuronal networks. This activity often manifests itself as dynamically coordinated sequences of action potentials. Since multiple electrode recordings are now a standard tool in neuroscience research, it is important to have a measure of such network-wide behavioral coordination and information sharing, applicable to multiple neural spike train data. We propose a new statistic, informational coherence, which measures how much better one unit can be predicted by knowing the dynamical state of another. We argue informational coherence is a measure of association and shared information which is superior to traditional pairwise measures of synchronization and correlation. To find the dynamical states, we use a recently-introduced algorithm which reconstructs effective state spaces from stochastic time series. We then extend the pairwise measure to a multivariate analysis of the network by estimating the network multi-information. We illustrate our method by testing it on a detailed model of the transition from gamma to beta rhythms.Comment: 8 pages, 6 figure

On the relativistic viability of multi-automaton systems: essential concepts, challenges and prospects

Our understanding of the Universe breaks down for very small spacetime intervals, corresponding to an extremely high level of granularity (and energy), commonly referred to as the ``Planck scale''. At this fundamental level, there are attempts of describing physics in terms of interacting automata that perform classical, deterministic computation. On one hand, various mathematical arguments have already illustrated how quantum laws (which describe elementary particles and interactions) could in principle arise as low-granularity approximations of automata-based systems. On the other hand, understanding how such systems might give rise to relativistic laws (which describe spacetime and gravity) remains a major problem. I explain here a few ideas that seem crucial for overcoming this problem, along with related algorithmic challenges that need to be addressed. Giving emphasis to meaningful computational counterparts of locality and general covariance, I outline basic ingredients of a distributed communication-rewiring protocol that would allow us to construct multi-automaton models that are viable from a relativistic perspective. I also explain how viable models can be evaluated using a variety of criteria, and discuss related aspects pertaining to the falsifiability and plausibility of the automata paradigm.Comment: 7 pages, 1 figur