473 research outputs found
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 dynamics of norm change in the cultural evolution of language
What happens when a new social convention replaces an old one? While the possible forces favoring norm change - such as institutions or committed activists - have been identified since a long time, little is known about how a population adopts a new convention, due to the diffculties of finding representative data. Here we address this issue by looking at changes occurred to 2,541 orthographic and lexical norms in English and Spanish through the analysis of a large corpora of books published between the years 1800 and 2008. We detect three markedly distinct patterns in the data, depending on whether the behavioral change results from the action of a formal institution, an informal authority or a spontaneous process of unregulated evolution. We propose a simple evolutionary model able to capture all the observed behaviors and we show that it reproduces quantitatively the empirical data. This work identifies general mechanisms of norm change and we anticipate that it will be of interest to researchers investigating the cultural evolution of language and, more broadly, human collective behavior
Arrow of time across five centuries of classical music
The concept of time series irreversibility—the degree by which the statistics of signals are not invariant under time reversal—naturally appears in nonequilibrium physics in stationary systems which operate away from equilibrium and produce entropy. This concept has not been explored to date in the realm of musical scores as these are typically short sequences whose time reversibility estimation could suffer from strong finite size effects which preclude interpretability. Here we show that the so-called horizontal visibility graph method—which recently was shown to quantify such statistical property even in nonstationary signals—is a method that can estimate time reversibility of short symbolic sequences, thus unlocking the possibility of exploring such properties in the context of musical compositions. Accordingly, we analyze over 8000 musical pieces ranging from the Renaissance to the early Modern period and show that, indeed, most of them display clear signatures of time irreversibility. Since by construction stochastic processes with a linear correlation structure (such as
1
/
f
noise) are time reversible, we conclude that musical compositions have a considerably richer structure, that goes beyond the traditional properties retrieved by the power spectrum or similar approaches. We also show that musical compositions display strong signs of nonlinear correlations, that nonlinearity is correlated to irreversibility, and that these are also related to asymmetries in the abundance of musical intervals, which we associate to the narrative underpinning a musical composition. These findings provide tools for the study of musical periods and composers, as well as criteria related to music appreciation and cognition
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
Nuevo género de ave fósil del yacimiento neocomiense del Montsec (provincia de Lérida, España)
It is described in this paper for the frrst time the fossil bird skeleton found at the famous quarry of Iimestones of Montsec mountain dated from Early Cretaceous. Unfortunately it is only preserved a few part of this skeleton concerning to the fore arms mainly. The few characters preserved do not allow to assign any taxonomic position but they show some mixed signs between the Sauriurae and Ornithurae.Se describe el primer esqueleto fósil perteneciente a un ave hallada en la célebre cantera de calizas litográficas del Montsec de edad Neocomiense. Desafortunadamente solamente se ha preservado una pequeña parte de dicho esqueleto relativa a los miembros anteriores principalmente. Los pocos caracteres conservados no permiten adscripción taxonómica aunque presentan rasgos mixtos entre la Saururas y Omithuras
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
A combinatorial framework to quantify peak/pit asymmetries in complex dynamics
LL’s acknowledges funding from an EPSRC Early Career Fellowship EP/P01660X/1
Phase transition in a stochastic prime number generator
We introduce a stochastic algorithm that acts as a prime number generator.
The dynamics of such algorithm gives rise to a continuous phase transition
which separates a phase where the algorithm is able to reduce a whole set of
integers into primes and a phase where the system reaches a frozen state with
low prime density. We present both numerical simulations and an analytical
approach in terms of an annealed approximation, by means of which the data are
collapsed. A critical slowing down phenomenon is also outlined.Comment: accepted in PRE (Rapid Comm.
Number theoretic example of scale-free topology inducing self-organized criticality
In this work we present a general mechanism by which simple dynamics running
on networks become self-organized critical for scale free topologies. We
illustrate this mechanism with a simple arithmetic model of division between
integers, the division model. This is the simplest self-organized critical
model advanced so far, and in this sense it may help to elucidate the mechanism
of self-organization to criticality. Its simplicity allows analytical
tractability, characterizing several scaling relations. Furthermore, its
mathematical nature brings about interesting connections between statistical
physics and number theoretical concepts. We show how this model can be
understood as a self-organized stochastic process embedded on a network, where
the onset of criticality is induced by the topology.Comment: 4 pages, 3 figures. Physical Review Letters, in pres
- …