The Simplicial Characterisation of TS networks: Theory and applications

We use the visibility algorithm to construct the time series networks obtained from the time series of different dynamical regimes of the logistic map. We define the simplicial characterisers of networks which can analyse the simplicial structure at both the global and local levels. These characterisers are used to analyse the TS networks obtained in different dynamical regimes of the logisitic map. It is seen that the simplicial characterisers are able to distinguish between distinct dynamical regimes. We also apply the simplicial characterisers to time series networks constructed from fMRI data, where the preliminary results indicate that the characterisers are able to differentiate between distinct TS networks.Comment: 11 pages, 2 figures, 4 tables. Accepted for publication in Proceedings of the 4th International Conference on Applications in Nonlinear Dynamics (ICAND 2016

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

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

Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011

Description of stochastic and chaotic series using visibility graphs

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In the last years, some methods mapping time series to network representations have been proposed. The purpose is to investigate on the properties of the series through graph theoretical tools recently developed in the core of the celebrated complex network theory. Among some other methods, the so-called visibility algorithm has received much attention, since it has been shown that series correlations are captured by the algorithm and translated in the associated graph, opening the possibility of building fruitful connections between time series analysis, nonlinear dynamics, and graph theory. Here we use the horizontal visibility algorithm to characterize and distinguish between correlated stochastic, uncorrelated and chaotic processes. We show that in every case the series maps into a graph with exponential degree distribution P (k) ~ exp(-{\lambda}k), where the value of {\lambda} characterizes the specific process. The frontier between chaotic and correlated stochastic processes, {\lambda} = ln(3/2), can be calculated exactly, and some other analytical developments confirm the results provided by extensive numerical simulations and (short) experimental time series

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

Effect of genetic background on resistance to Meloidogyne incognita in pepper

[SPA] En pimiento (Capsicum annuum L.) los genes mayores Me1, Me3 y N confieren resistencia cualitativa frente a M. incognita (principal nematodo patógeno de solanáceas). Sin embargo se han encontrado poblaciones del nematodo virulentas a algunos de estos genes que comprometen la eficacia de estas resistencias. No obstante se ha constatado una mayor durabilidad de estos genes mayores cuando se introgresan en fondos genéticos parcialmente resistentes. El objetivo fue explorar la influencia del fondo genético del pimiento controlando la resistencia parcial cuando se combina con los genes Me1 y Me3, su estabilidad y su modo de herencia. Se utilizaron líneas puras de pimiento susceptibles, parcialmente resistentes y portadoras de Me1 o Me3, y se construyeron diversos híbridos F1. Este material vegetal se testó frente a 3 aislados de M. incognita (dos de éstos virulentos a Me3), y se comparó su nivel de resistencia. Los resultados mostraron diferencias de tipo cuantitativo en la resistencia a M. incognita debidas al efecto del fondo genético, que se expresaron tanto en ausencia como en presencia de genes mayores de resistencia. Esta resistencia cuantitativa se mostró estable frente a los distintos aislados del patógeno y presentó un modo de herencia intermedio. [ENG] In pepper, three major genes –Me1, Me3 and N–confer qualitative resistance against Meloidogyne incognita (main pathogen nematode of Solanaceae). However, nematode virulent populations to some of these genes have been found, threatening the effectiveness of these resistances. Nevertheless higher durability of these major genes has been found when these are introgressed in partially resistant genetic background. The aim was to explore the influence of pepper genetic background controlling partial resistance when combined with Me1 and Me3 genes, its stability and its mode of inheritance. Some pepper inbred lines susceptible, partially resistant or resistant (that carriers Me1 or Me3) were used, and several hybrids F1 were built. This plant material was tested against 3 M. incognita isolates (two virulent to Me3), and their level of resistance was compared. The results showed quantitative differences in resistance to M. incognita due to the effect of genetic background, which was expressed both in presence and absence of qualitative resistance genes. This quantitative resistance was stable against different isolates of the pathogen and presented an intermediate inheritance mode.El equipo de Horticultura (IMIDA) y el Dr. A. Palloix (INRA) proporcionaron el material vegetal. Estudio financiado a través del Proyecto INIA RTA2009-0058 participado con Fondos FEDER. F. Sánchez ha disfrutado de una beca FPI-INIA

Development of a tomato spotted wilt virus (TSWV) risk evaluation methology for a processing tomato region

A risk map for the Tomato spotted wilt virus (TSWV) was elaborated for the main Portuguese processing tomato producing region, the “Ribatejo e Península de Setúbal” region, where periodically this virus causes severe losses. Forty nine tomato fields were monitored. Risk factors for TSWV infection were identified and quantified according to their relative importance in TSWV incidence. The risk factors considered for each field were: (1) presence of TSWV in tomato plants; (2) presence of TSWV in weeds which are hosts of TSWV vectors; (3) presence of TSWV vector thrips; (4) presence of TSWV host crops previously (in the two years before), namely, tomato, potato and sweet pepper; and (5) presence of greenhouses, urban areas or TSWV host crops next to the field (up to about 100m from its borders). A risk estimator was calculated for each field. Among the thrips (Thysanoptera) identified, belonging to 11 genera, four vector thrips species were detected: Frankliniella occidentalis (Pergande) and Thrips tabaci Lindman, the two most abundant ones, and F. intonsa (Trybom) and F. schultzei (Trybom). Blue sticky traps placed up to about 75 cm above the crop canopy caught F. occidentalis and T. tabaci more efficiently than the beating technique. The weeds Datura stramonium L., Arctotheca calendula (L.), and Conyza bonariensis (L.) were identified as TSWV winter repositories. This study proposes a methodology to be used by field technicians for the annual evaluation of TSWV risk at a regional level, for an improved planning of processing tomato crop in the following season

Symbolic dynamics techniques for complex systems: Application to share price dynamics

The symbolic dynamics technique is well known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Our main example is the investigation of share price returns in a coarse-grained way. A nontrivial spectrum of Rényi entropies is found. We study how the spectrum depends on the time scale of returns, the sector of stocks considered, as well as the number of symbols used for the symbolic description. Overall our analysis confirms that in the symbol space transition probabilities of observed share price returns depend on the entire history of previous symbols, thus emphasizing the need for a modelling based on non-Markovian stochastic processes. Our method allows for quantitative comparisons of entirely different complex systems, for example the statistics of symbol sequences generated by share price returns using 4 symbols can be compared with that of genomic sequences