98 research outputs found
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
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 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 spin system BaTiMnO
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
BaTiMnO. Our structural analysis by neutron diffraction
supports the existence of structural trimers with chemically disordered
occupancy of Mn and Ti ions, with the valence of the Mn ions
confirmed by the XAS measurements. The magnetic properties are explored by
combining dc-susceptibility and -band ( GHz) electron spin resonance,
both in the temperature interval of K. A scenario is
presented under which the magnetism is explained by considering magnetic dimers
and trimers, with exchange constants K and
K, and orphan spins. Thus, BaTiMnO
is proposed as a rare case of an intrinsically disordered 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 BaTiMnO
Magnetic frustration and disorder are key ingredients to prevent the onset of
magnetic order. In the disordered hexagonal double perovskite
BaTiMnO, Mn cations, with spins, can
either form highly correlated states of magnetic trimers or dimers or remain as
weakly interacting orphan spins. At low temperature (), 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- magnetic properties of the remaining magnetic degrees
of freedom of BaTiMnO 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
SR experiments. The zero field relaxation rate data show no
static magnetism down to mK and longitudinal field experiments support
as well that dynamic magnetism persists at low . 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 BaTiMnO,
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 TbRhIn intermetallic system
We report measurements of the temperature dependence specific heat, magnetic
susceptibility in single crystals of the series of intermetallic compounds
TbYRhIn (nominal concentrations and
). A mean field approximation to simulate the macroscopic properties
along the series has been used. Neutron diffraction data in powdered sample of
nominal concentration TbYRhIn reveal AFM propagation vector
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 cuboctahedra distortion,
are responsible for changes in the Tb crystalline potential and the possible
reorientation of Tb magnetic moments for 0.4. This reflects non negligible
variations of the crystal field parameters and the energy levels
splitting with \textit{x}
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