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

Properties of maximum Lempel-Ziv complexity strings

The properties of maximum Lempel-Ziv complexity strings are studied for the binary case. A comparison between MLZs and random strings is carried out. The length profile of both type of sequences show different distribution functions. The non-stationary character of the MLZs are discussed. The issue of sensitiveness to noise is also addressed. An empirical ansatz is found that fits well to the Lempel-Ziv complexity of the MLZs for all lengths up to $10^6$ symbols

Lempel-Ziv complexity analysis of one dimensional cellular automata

Cellular automata (CA) have long attracted attention as dynamical systems with local updating rules and yet can exhibit, for certain rules, complex, long space and time correlated patterns. This contrast with other rules which results in trivial patterns being homogeneous or periodic. In this article we approach CA from two related angles: we analyze the information transfer in the time evolution of CA driven sequences and; we revisit the sensibility of the initial configuration on sequence evolution. In order to do so, we borrow a recently reported information distance based on Kolmogorov algorithmic complexity. The normalized information distance has been used previously to find a hierarchical clustering of CA rules. What is different in our approach, is the temporal analysis of the sequence evolutions by correlating different calculated distances with entropy density. Entropy rate, is a length invariant measure of the amount of irreducible randomness in a dynamical process. In order to perform our analysis, we incorporate to the practical calculation of the entropy rate and the distance measure, the use of Lempel-Ziv complexity. Lempel-Ziv complexity carries a number of practical advantages while avoiding the uncomputable nature of Kolmogorov randomness. The reduction of entropy density during time evolution can be related to energy dissipation through Landauer principle. Related to the last fact, is the computational capabilities of CA as information processing rules, were the performed analysis could be used to select CA rules amiable for simulating different physical process. The tools developed in this article for the analysis of the CA are easily extendible to the study of other one dimensional dynamical systems.Comment: Accepted at Chao

La-dilution effects in TbRhIn5 antiferromagnet

We report measurements of temperature dependent magnetic susceptibility, resonant x-ray magnetic scattering (XRMS) and heat capacity on single crystals of Tb1-xLaxRhIn5 for nominal concentrations in the range 0.0 < x < 1.0. TbRhIn5 is an antiferromagnetic (AFM) compound with TN ~ 46 K, which is the highest TN values along the RRhIn5 series. We explore the suppression of the antiferromagnetic (AFM) state as a function of La-doping considering the effects of La-induced dilution and perturbations to the tetragonal crystalline electrical field (CEF) on the long range magnetic interaction between the Tb$^{3+}$ ions. Additionally, we also discuss the role of disorder. Our results and analysis are compared to the properties of the undoped compound and of other members of the RRhIn5 family and structurally related compounds (R2RhIn8 and RIn3). The XRMS measurements reveal that the commensurate magnetic structure with the magnetic wave-vector (0,1/2,1/2) observed for the undoped compound is robust against doping perturbations in Tb0.6La0.4RhIn5 compound.Comment: 8 pages, 8 figures, Submitted to Phys. Rev.

Computational capabilities at the edge of chaos for one dimensional system 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 allows identifying the balance between unpredictability and complexity. Enhanced computation power shows as 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.Comment: Accepted in CHAO

Magnetic structure of Sm2IrIn8

The magnetic structure of the intermetallic antiferromagnet Sm2IrIn8 was determined using x-ray resonant magnetic scattering (XRMS). Below TN = 14.2, Sm2IrIn8 has a commensurate antiferromagnetic structure with a propagation vector (1/2,0,0). The Sm magnetic moments lie in the ab plane and are rotated roughly 18 degrees away from the a axis. The magnetic structure of this compound was obtained by measuring the strong dipolar resonant peak whose enhancement was of over two orders of magnitude at the L2 edge. At the L3 edge both quadrupolar and dipolar features were observed in the energy line shape. The magnetic structure and properties of Sm2IrIn8 are found to be consistent with the general trend already seen for the Nd-, Tb- and the Ce-based compounds from the RmMnIn3m+2n family (R = rare earth; M=Rh or Ir, m = 1, 2; n = 0, 1), where the crystalline electrical field (CEF) effects determine the direction of magnetic moments and the TN evolution in the series. The measured Neel temperature for Sm2IrIn8 is slightly suppressed when compared to the TN of the parent cubic compound SmIn3.Comment: 09 pages, 06 figures, Submitted to Phys. Rev.

Physical properties and magnetic structure of TbRhIn5 intermetallic compound

In this work we report the physical properties of the new intermetallic compound TbRhIn5 investigated by means of temperature dependent magnetic susceptibility, electrical resistivity, heat-capacity and resonant x-ray magnetic diffraction experiments. TbRhIn5 is an intermetallic compound that orders antiferromagnetically at TN = 45.5 K, the highest ordering temperature among the existing RRhIn5 (1-1-5, R = rare earth) materials. This result is in contrast to what is expected from a de Gennes scaling along the RRhIn5 series. The X-ray resonant diffraction data below TN reveal a commensurate antiferromagnetic (AFM) structure with a propagation vector (1/2 0 1/2) and the Tb moments oriented along the c-axis. Strong (over two order of magnitude) dipolar enhancements of the magnetic Bragg peaks were observed at both Tb absorption edges LII and LIII, indicating a fairly high polarization of the Tb 5d levels. Using a mean field model including an isotropic first-neighbors exchange interaction J(R-R) and the tetragonal crystalline electrical field (CEF), we were able to fit our experimental data and to explain the direction of the ordered Tb-moments and the enhanced TN of this compound. The evolution of the magnetic properties along the RRhIn5 series and its relation to CEF effects for a given rare-earth is discussed.Comment: 8 pages, 8 figures, 1 table. Submitted to Physical Review

Magnetic dimers and trimers in the disordered S=3/2S=3/2 spin system BaTi1/2_{1/2}Mn1/2_{1/2}O3_{3}

We report a structural/magnetic investigation by X-ray absorption spectroscopy (XAS), neutron diffraction, dc-susceptibility (\chi_{\mbox{dc}}) and electron spin resonance (ESR) of the 12R-type perovskite BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$. Our structural analysis by neutron diffraction supports the existence of structural trimers with chemically disordered occupancy of Mn$^{4+}$ and Ti$^{4+}$ ions, with the valence of the Mn ions confirmed by the XAS measurements. The magnetic properties are explored by combining dc-susceptibility and $X$-band ($9.4$ GHz) electron spin resonance, both in the temperature interval of $2\leq T\leq1000$ K. A scenario is presented under which the magnetism is explained by considering magnetic dimers and trimers, with exchange constants $J_{a}/k_{B}=200(2)$ K and $J_{b}/k_{B}=130(10)$ K, and orphan spins. Thus, BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$ is proposed as a rare case of an intrinsically disordered $S=3/2$ spin gap system with a frustrated ground state.Comment: 8 pages, 7 figures, final version to appear in Phys Rev

Dynamic magnetism in the disordered hexagonal double perovskite BaTi1/2_{1/2}Mn1/2_{1/2}O3_{3}

Magnetic frustration and disorder are key ingredients to prevent the onset of magnetic order. In the disordered hexagonal double perovskite BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$, Mn$^{4+}$ cations, with $S=3/2$ spins, can either form highly correlated states of magnetic trimers or dimers or remain as weakly interacting orphan spins. At low temperature ($T$), the dimer response is negligible, and magnetism is dominated by the trimers and orphans. To explore the role of magnetic frustration, disorder and possibly of quantum fluctuations, the low-$T$ magnetic properties of the remaining magnetic degrees of freedom of BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$ are investigated. Heat-capacity data and magnetic susceptibility display no evidence for a phase transition to a magnetically ordered phase but indicate the formation of a correlated spin state. The low-temperature spin dynamics of this state is then explored by $\mu$SR experiments. The zero field $\mu^{+}$ relaxation rate data show no static magnetism down to $T=19$ mK and longitudinal field experiments support as well that dynamic magnetism persists at low $T$. Our results are interpreted in terms of a spin glass state which stems from a disordered lattice of orphans spins and trimers. A spin liquid state in BaTi$_{1/2}$Mn$_{1/2}$O$_{3}$, however, is not excluded and is also discussed.Comment: Main Text: 6 pages, 4 figures; Supplemental: 11 pages, 7 figure

Antiferromagnetism weakening with Y-substitution in the TbRhIn5_5 intermetallic system

We report measurements of the temperature dependence specific heat, magnetic susceptibility in single crystals of the series of intermetallic compounds Tb$_{1-x}$Y$_x$RhIn$_5$ (nominal concentrations $x= 0.15, 0.30, 0.40, 0.50$ and $0.70$). A mean field approximation to simulate the macroscopic properties along the series has been used. Neutron diffraction data in powdered sample of nominal concentration Tb$_{0.6}$Y$_{0.4}$RhIn$_5$ reveal AFM propagation vector $k=[\frac{1}{2}~0~\frac{1}{2}]$ with the magnetic moments oriented close to the tetragonal \textit{c} axis. We discuss the role of combined effects of crystalline electric field (CEF) perturbations and dilution in the magnetic properties evolution with Y content. In particular, we suggest that changes in the Tb-In first neighbors distances, i.e. the TbIn$_3$ cuboctahedra distortion, are responsible for changes in the Tb crystalline potential and the possible reorientation of Tb magnetic moments for $x>$0.4. This reflects non negligible variations of the $B^{m}_{n}$ crystal field parameters and the energy levels splitting with \textit{x}