Computational capabilities at the edge of chaos for one dimensional systems undergoing continuous transitions.

While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular automata, there is an enhancement of computation capabilities as the system moves towards cellular automata with chaotic spatiotemporal behavior. The computation capabilities are followed by looking into the Shannon entropy rate and the excess entropy, which allow identifying the balance between unpredictability and complexity. Enhanced computation power shows an increase of excess entropy, while the system entropy density has a sudden jump to values near one. The analysis is extended to a system of non-linear locally coupled oscillators that have been reported to exhibit spatiotemporal diagrams similar to cellular automata.

Lempel-Ziv complexity analysis of one dimensional cellular automata.

Lempel-Ziv complexity measure has been used to estimate the entropy density of a string. It is defined as the number of factors in a production factorization of a string. In this contribution, we show that its use can be extended, by using the normalized information distance, to study the spatiotemporal evolution of random initial configurations under cellular automata rules. In particular, the transfer information from time consecutive configurations is studied, as well as the sensitivity to perturbed initial conditions. The behavior of the cellular automata rules can be grouped in different classes, but no single grouping captures the whole nature of the involved rules. The analysis carried out is particularly appropriate for studying the computational processing capabilities of cellular automata rules.

On the non-randomness of maximum Lempel Ziv complexity sequences of finite size.

Random sequences attain the highest entropy rate. The estimation of entropy rate for an ergodic source can be done using the Lempel Ziv complexity measure yet, the exact entropy rate value is only reached in the infinite limit. We prove that typical random sequences of finite length fall short of the maximum Lempel-Ziv complexity, contrary to common belief. We discuss that, for a finite length, maximum Lempel-Ziv sequences can be built from a well defined generating algorithm, which makes them of low Kolmogorov-Chaitin complexity, quite the opposite to randomness. It will be discussed that Lempel-Ziv measure is, in this sense, less general than Kolmogorov-Chaitin complexity, as it can be fooled by an intelligent enough agent. The latter will be shown to be the case for the binary expansion of certain irrational numbers. Maximum Lempel-Ziv sequences induce a normalization that gives good estimates of entropy rate for several sources, while keeping bounded values for all sequence length, making it an alternative to other normalization schemes in use.

Tuning the pressure-induced superconducting phase in doped CeRhIn5.

Pressure- and temperature-dependent heat capacity and electrical resistivity experiments on Sn- and La-doped CeRhIn5 are reported for two samples with specific concentrations, Ce(0.90)La(0.10)RhIn5 and CeRhIn(4.84)Sn(0.16), which present the same TN=2.8 K. The obtained P-T phase diagrams for doped CeRhIn5 compared to that for the pure compound show that Sn doping shifts the diagram to lower pressures while La doping does exactly the opposite, indicating that the important energy scale to define the pressure range for superconductivity in CeRhIn5 is the strength of the on-site Kondo coupling.