Quasiperiodic graphs: structural design, scaling and entropic properties

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy

Macroporous materials: microfluidic fabrication, functionalization and applications

This article provides an up-to-date highly comprehensive overview (594 references) on the state of the art of the synthesis and design of macroporous materials using microfluidics and their applications in different fields

Highest weight Macdonald and Jack Polynomials

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio

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

Determination of Arsenic, Mercury and Barium in herbarium mount paper using dynamic ultrasound-assisted extraction prior to atomic fluorescence and absorption spectrometry

A dynamic ultrasound-assisted extraction method using Atomic Absorption and Atomic Flourescence spectrometers as detectors was developed to analyse mercury, arsenic and barium from herbarium mount paper originating from the herbarium collection of the National Museum of Wales. The variables influencing extraction were optimised by a multivariate approach. The optimal conditions were found to be 1% HNO3 extractant solution used at a flow rate of 1 mL min-1. The duty cycle and amplitude of the ultrasonic probe was found to be 50% in both cases with an ultrasound power of 400 W. The optimal distance between the probe and the top face of the extraction chamber was found to be 0 cm. Under these conditions the time required for complete extraction of the three analytes was 25 min. Cold vapour and hydride generation coupled to atomic fluorescence spectrometry was utilized to determine mercury and arsenic, respectively. The chemical and instrumental conditions were optimized to provide detection limits of 0.01ng g-1 and 1.25 ng g-1 for mercury and arsenic, respectively. Barium was determined by graphite-furnace atomic absorption spectrometry, with a detection limit of 25 ng g-1. By using 0.5 g of sample, the concentrations of the target analytes varied for the different types of paper and ranged between 0.4–2.55 µg g-1 for Ba, 0.035–10.47 µg g-1 for As and 0.0046–2.37 µg g-1 for Hg

Morfología polínica de las especies de cítricos cultivadas en Andalucía occidental (España)

. Morfología polínica de las especies de cítricos cultivadas en Andalucía occidental (España). Se estudia la morfología polínica de seis especies de cítricos de los géneros Citrus (C. aurantium, C. deliciosa, C. grandis, C. limon y C. sinensis) y Fortunella (F. margarita), con los microscopios óptico y electrónico de barrido. Por los caracteres estudiados (polaridad, simetría, contorno (en visión ecuatorial y corte óptico meridiano y visión polar y corte ecuatorial), tamaño, número, tipo y dimensiones de las aberturas, grosor de la exina y ornamentación) se describe la morfología del polen y se discuten los resultados obtenidos.No es posible la separación de los dos géneros, pero se pueden diferenciar parte de las especies del género Citrus

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

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