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

Using network science to analyze football passing networks: dynamics, space, time and the multilayer nature of the game

From the diversity of applications of Network Science, in this Opinion Paper we are concerned about its potential to analyze one of the most extended group sports: Football (soccer in U.S. terminology). As we will see, Network Science allows addressing different aspects of the team organization and performance not captured by classical analyses based on the performance of individual players. The reason behind relies on the complex nature of the game, which, paraphrasing the foundational paradigm of complexity sciences "can not be analyzed by looking at its components (i.e., players) individually but, on the contrary, considering the system as a whole" or, in the classical words of after-match interviews "it's not just me, it's the team".Comment: 7 pages, 1 figur

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

New invariants for entangled states

We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature.Comment: published versio

Phase transition in the Countdown problem

Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We then derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.Comment: 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