The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion

Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst parameter H requires sophisticated techniques that often yield ambiguous results. In this work we show that fBm series map into a scale free visibility graph whose degree distribution is a function of H. Concretely, it is shown that the exponent of the power law degree distribution depends linearly on H. This also applies to fractional Gaussian noises (fGn) and generic f^(-b) noises. Taking advantage of these facts, we propose a brand new methodology to quantify long range dependence in these series. Its reliability is confirmed with extensive numerical simulations and analytical developments. Finally, we illustrate this method quantifying the persistent behavior of human gait dynamics.Comment: 5 pages, submitted for publicatio

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

The Partition Function of Multicomponent Log-Gases

We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field) in terms of the Berezin integral of an associated non- homogeneous alternating tensor. This is the analog of the de Bruijn integral identities [3] (for {\beta} = 1 and {\beta} = 4) ensembles extended to multicomponent ensembles.Comment: 14 page

Probing background ionization: Positive streamers with varying pulse repetition rate and with a radioactive admixture

Positive streamers need a source of free electrons ahead of them to propagate. A streamer can supply these electrons by itself through photo-ionization, or the electrons can be present due to external background ionization. Here we investigate the effects of background ionization on streamer propagation and morphology by changing the gas composition and the repetition rate of the voltage pulses, and by adding a small amount of radioactive Krypton 85. We find that the general morphology of a positive streamer discharge in high purity nitrogen depends on background ionization: at lower background ionization levels the streamers branch more and have a more feather-like appearance. This is observed both when varying the repetition rate and when adding Krypton 85, though side branches are longer with the radioactive admixture. But velocities and minimal diameters of streamers are virtually independent of the background ionization level. In air, the inception cloud breaks up into streamers at a smaller radius when the repetition rate and therefore the background ionization level is higher. When measuring the effects of the pulse repetition rate and of the radioactive admixture on the discharge morphology, we found that our estimates of background ionization levels are consistent with these observations; this gives confidence in the estimates. Streamer channels generally do not follow the paths of previous discharge channels for repetition rates of up to 10 Hz. We estimate the effect of recombination and diffusion of ions and free electrons from the previous discharge and conclude that the old trail has largely disappeared at the moment of the next voltage pulse; therefore the next streamers indeed cannot follow the old trail.Comment: 30 pages, 13 figure

Classification of qubit entanglement: SL(2,C) versus SU(2) invariance

The role of SU(2) invariants for the classification of multiparty entanglement is discussed and exemplified for the Kempe invariant I_5 of pure three-qubit states. It is found to being an independent invariant only in presence of both W-type entanglement and threetangle. In this case, constant I_5 admits for a wide range of both threetangle and concurrences. Furthermore, the present analysis indicates that an SL^3 orbit of states with equal tangles but continuously varying I_5 must exist. This means that I_5 provides no information on the entanglement in the system in addition to that contained in the tangles (concurrences and threetangle) themselves. Together with the numerical evidence that I_5 is an entanglement monotone this implies that SU(2) invariance or the monotone property are too weak requirements for the characterization and quantification of entanglement for systems of three qubits, and that SL(2,C) invariance is required. This conclusion can be extended to general multipartite systems (including higher local dimension) because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex

Probing photo-ionization: simulations of positive streamers in varying N2:O2 mixtures

Photo-ionization is the accepted mechanism for the propagation of positive streamers in air though the parameters are not very well known; the efficiency of this mechanism largely depends on the presence of both nitrogen and oxygen. But experiments show that streamer propagation is amazingly robust against changes of the gas composition; even for pure nitrogen with impurity levels below 1 ppm streamers propagate essentially with the same velocity as in air, but their minimal diameter is smaller, and they branch more frequently. Additionally, they move more in a zigzag fashion and sometimes exhibit a feathery structure. In our simulations, we test the relative importance of photo-ionization and of the background ionization from pulsed repetitive discharges, in air as well as in nitrogen with 1 ppm O2 . We also test reasonable parameter changes of the photo-ionization model. We find that photo- ionization dominates streamer propagation in air for repetition frequencies of at least 1 kHz, while in nitrogen with 1 ppm O2 the effect of the repetition frequency has to be included above 1 Hz. Finally, we explain the feather-like structures around streamer channels that are observed in experiments in nitrogen with high purity, but not in air.Comment: 12 figure

Biobased supramolecular ionic networks with optimized crystallinity and mechanical properties as promising dynamic materials for eutectogels design

Ionic supramolecular networks are attractive materials for technological applications with unique properties such as ionic conductivity, stimuli-responsiveness, recyclability, and self-healing. Herein, new semicrystalline supramolecular ionic networks are designed from fully biobased building blocks such as tartaric acid, phytic acid, sebacic acid, and a fatty dimer diamine (Priamine™ 1071). The combination of tartaric acid with Priamine™ 1071 results in a crystalline and brittle polymer, but its molecular regularity can be controlled by incorporating sebacic acid or phytic acid, affording tough materials with appropriate mechanical properties (elastic moduli ranging 19–42 MPa). Furthermore, the ionic polymers show network-to-liquid phase transitions between 75 and 127 °C, and in the liquid state, they were found to be miscible with a lithium-based deep eutectic solvent, yielding flexible and conductive eutectogels. Altogether, these dynamic networks could open new prospects for developing fully green soft ionic materials from their combination with other innovative and low-cost eutectic mixtures.Open Access funding provided by the University of Basque Country. The financial support received from CONICET and ANPCyT (PICT 2018-01032) (Argentina) is gratefully acknowledged

HE 0557-4840 - Ultra-Metal-Poor and Carbon-Rich

We report the discovery and high-resolution, high S/N, spectroscopic analysis of the ultra-metal-poor red giant HE 0557-4840, which is the third most heavy-element deficient star currently known. Its atmospheric parameters are T_eff = 4900 K, log g = 2.2, and [Fe/H]= -4.75. This brings the number of stars with [Fe/H] < -4.0 to three, and the discovery of HE 0557-4840 suggests that the metallicity distribution function of the Galactic halo does not have a "gap" between [Fe/H] = -4.0, where several stars are known, and the two most metal-poor stars, at [Fe/H] ~ -5.3. HE 0557-4840 is carbon rich - [C/Fe] = +1.6 - a property shared by all three objects with [Fe/H] < -4.0, suggesting that the well-known increase of carbon relative to iron with decreasing [Fe/H] reaches its logical conclusion - ubiquitous carbon richness - at lowest abundance. We also present abundances (nine) and limits (nine) for a further 18 elements. For species having well-measured abundances or strong upper limits, HE 0557-4840 is "normal" in comparison with the bulk of the stellar population at [Fe/H] ~ -4.0 - with the possible exception of Co. We discuss the implications of these results for chemical enrichment at the earliest times, in the context of single ("mixing and fallback") and two-component enrichment models. While neither offers a clear solution, the latter appears closer to the mark. Further data are required to determine the oxygen abundance and improve that of Co, and hence more strongly constrain the origin of this object.Comment: Submitted to Astrophysical Journal. 52 pages (41 text, 11 figures

Rescaling multipartite entanglement measures for mixed states

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant 1 local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.Comment: Published version plus one important reference (Ref. [39]

Multiplicity and oscillations in a model for catalyzed oxidation of carbon monoxide

We extend a model proposed for explaining multiplicity and oscillations of concentrations and temperature in catalyzed oxidation of carbon monoxide; the importance of the dimension of the system and the closure approximation applied to the results, and, especially to the oscillatory behavior, is analyzed. Kinetic phase transitions, namely, single state multiplicity, single state oscillations, and multiplicity oscillations are found, depending on the reaction heat and the temperature relaxation parameter. Also, the role played by desorption of reactants is considered. When there is no desorption, temperature oscillations take place around room temperature, but if desorption is operative, oscillations occur about a higher temperature. For the one-dimensional case a spurious kinetic phase transition is obtained when the singlet closure approximation is appliedDirección General de Investigación Científica y Técnica PB91-060