arXiv subjects

C. Anteneodo

Publications and source records attributed to C. Anteneodo.

At least 37 records · Page 2Linked to original sources

arXiv2011

Non-parametric segmentation of non-stationary time series

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption of stationarity, it is important to detect in real time series intervals holding that property. With that aim, we introduce a segmentation algorithm based on a fully non-parametric approach. We illustrate its applicability through the analysis of real time series presenting diverse degrees of non-stationarity, thus showing that this segmentation procedure generalizes and allows to uncover features unresolved by previous proposals based on the discrepancy of low order statistical moments only.

cond-mat.stat-mech↗

arXiv2010

On low-sampling-rate Kramers-Moyal coefficients

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results aim at aiding the proper extraction of information in data-driven analysis.

cond-mat.stat-mech↗

arXiv2010

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, $λ$ and $λ^\star$ respectively. We discuss the numerical difficulties that arise in the numerical calculation of $λ^\star$ in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically $λ^\star$ by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.

cond-mat.stat-mech↗

arXiv2009

Exact results for the Barabasi queuing model

Previous works on the queuing model introduced by Barabási to account for the heavy tailed distributions of the temporal patterns found in many human activities mainly concentrate on the extremal dynamics case and on lists of only two items. Here we obtain exact results for the general case with arbitrary values of the list length $L$ and of the degree of randomness that interpolates between the deterministic and purely random limits. The statistically fundamental quantities are extracted from the solution of master equations. From this analysis, new scaling features of the model are uncovered.

cond-mat.stat-mech↗

arXiv2009

Poissonian bursts in e-mail correspondence

Recent work has shown that the distribution of inter-event times for e-mail communication exhibits a heavy tail which is statistically consistent with a cascading Poisson process. In this work we extend the analysis to higher-order statistics, using the Fano and Allan factors to quantify the extent to which the empirical data depart from the known correlations of Poissonian statistics. The analysis shows that the higher-order statistics from the empirical data is indistinguishable from that of randomly reordered time series, thus demonstrating that e-mail correspondence is no more bursty or correlated than a Poisson process. Furthermore synthetic data sets generated by a cascading Poisson process replicate the burstiness and correlations observed in the empirical data. Finally, a simple rescaling analysis using the best-estimate rate of activity, confirms that the empirically observed correlations arise from a non-homogeneus Poisson process.

physics.soc-ph↗

arXiv2009

Exact corrections for finite-time drift and diffusion coefficients

Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time approximations of the modeling diffusion processes are considered. On the other hand, there is a lack of simple estimating procedures based on higher order approximations. For standard diffusion models, that include additive and multiplicative noise components, we obtain the exact corrections to the empirical finite-time drift and diffusion coefficients, based on Itô-Taylor expansions. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments, that furnish extra theoretical checks for that class of diffusive models. The theoretical predictions are compared with the numerical outcomes of some representative artificial time-series.

physics.data-an↗

arXiv2009

Unraveling the fluctuations of animal motor activity

Human motor activities are known to exhibit scale-free long-term correlated fluctuations over a wide range of timescales, from few to thousands of seconds. The fundamental processes originating such fractal-like behavior are not yet understood. To untangle the most significant features of these fluctuations, in this work the problem is oversimplified by studying a much simpler system: the spontaneous motion of rodents, recorded during several days. The analysis of the animal motion reveals a robust scaling comparable with the results previously reported in humans. It is shown that the most relevant features of the experimental results can be replicated by the statistics of the activation-threshold model proposed in another context by Davidsen and Schuster.

physics.soc-ph↗

arXiv2008

Critical scaling in standard biased random walks

The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented with Monte Carlo simulations. We show that, for appropriate step sizes, the model displays a critical phenomenon, at $p=p_c$. Its scaling properties as well as the main features of the fragmented coverage occurring in the vicinity of the critical point are shown. In particular, in the limit $p\to p_c$, the distribution of fragment lengths is scale-free, with nontrivial exponents. Moreover, the spatial distribution of cracks (unvisited sites) defines a fractal set over the spanned interval. Thus, from the perspective of the covered territory, a very rich critical phenomenology is revealed in a simple one-dimensional standard model.

cond-mat.stat-mech↗

arXiv2008

From short to fat tails in financial markets: A unified description

In complex systems such as turbulent flows and financial markets, the dynamics in long and short time-lags, signaled by Gaussian and fat-tailed statistics, respectively, calls for a unified description. To address this issue we analyze a real dataset, namely, price fluctuations, in a wide range of temporal scales to embrace both regimes. By means of Kramers-Moyal (KM) coefficients evaluated from empirical time series, we obtain the evolution equation for the probability density function (PDF) of price returns. We also present consistent asymptotic solutions for the timescale dependent equation that emerges from the empirical analysis. From these solutions, new relationships connecting PDF characteristics, such as tail exponents, to parameters of KM coefficients arise. The results reveal a dynamical path that leads from Gaussian to fat-tailed statistics, furnishing insights on other complex systems where akin crossover is observed.

q-fin.ST↗

arXiv2007

Statistics of football dynamics

We investigate the dynamics of football matches. Our goal is to characterize statistically the temporal sequence of ball movements in this collective sport game, searching for traits of complex behavior. Data were collected over a variety of matches in South American, European and World championships throughout 2005 and 2006. We show that the statistics of ball touches presents power-law tails and can be described by $q$-gamma distributions. To explain such behavior we propose a model that provides information on the characteristics of football dynamics. Furthermore, we discuss the statistics of duration of out-of-play intervals, not directly related to the previous scenario.

physics.data-an↗

arXiv2005

Anomalous synchronization threshold in coupled logistic maps

We consider regular lattices of coupled chaotic maps. Depending on lattice size, there may exist a window in parameter space where complete synchronization is eventually attained after a transient regime. Close outside this window, an intermittent transition to synchronization occurs. While asymptotic transversal Lyapunov exponents allow to determine the synchronization threshold, the distribution of finite-time Lyapunov exponents, in the vicinity of the critical frontier, is expected to provide relevant information on phenomena such as intermittency. In this work we scrutinize the distribution of finite-time exponents when the local dynamics is ruled by the logistic map $x \mapsto 4x(1-x)$. We obtain a theoretical estimate for the distribution of finite-time exponents, that is markedly non-Gaussian. The existence of correlations, that spoil the central limit approximation, is shown to modify the typical intermittent bursting behavior. The present scenario could apply to a wider class of systems with different local dynamics and coupling schemes.

nlin.CD↗

arXiv2005

Additive-multiplicative stochastic models of financial mean-reverting processes

We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the system, the latter is purely exogenous. We focus on the stochastic dynamics of volatilities, but our model may also be suitable for other financial random variables exhibiting the mean reversion property. The generalized model contains, as particular cases, many early approaches in the literature of volatilities or, more generally, of mean-reverting financial processes. We analyze the long-time probability density function associated to the model defined through a Itô-Langevin equation. We obtain a rich spectrum of shapes for the probability function according to the model parameters. We show that additive-multiplicative processes provide realistic models to describe empirical distributions, for the whole range of data.

physics.soc-ph↗

arXiv2004

Non-extensive random walks

The stochastic properties of variables whose addition leads to $q$-Gaussian distributions $G_q(x)=[1+(q-1)x^2]_+^{1/(1-q)}$ (with $q\in\mathbb{R}$ and where $[f(x)]_+=max\{f(x),0\}$) as limit law for a large number of terms are investigated. These distributions have special relevance within the framework of non-extensive statistical mechanics, a generalization of the standard Boltzmann-Gibbs formalism, introduced by Tsallis over one decade ago. Therefore, the present findings may have important consequences for a deeper understanding of the domain of applicability of such generalization. Basically, it is shown that the random walk sequences, that are relevant to this problem, possess a simple additive-multiplicative structure commonly found in many contexts, thus justifying the ubiquity of those distributions. Furthermore, a connection is established between such sequences and the nonlinear diffusion equation $\partial_t ρ=\partial^2_{xx}ρ^ν$ ($ν\neq1$).

cond-mat.stat-mech↗

arXiv2004

Chaos synchronization in long-range coupled map lattices

We investigate the synchronization phenomenon in coupled chaotic map lattices where the couplings decay with distance following a power-law. Depending on the lattice size, the coupling strength and the range of the interactions, complete chaos synchronization may be attained. The synchronization domain in parameter space can be analytically delimited by means of the condition of negativity of the largest transversal Lyapunov exponent. Here we analyze in detail the role of all the system parameters in the ability of the lattice to achieve complete synchronization, testing analytical results with the outcomes of numerical experiments.

nlin.CD↗

arXiv2004

Analytical results for coupled map lattices with long-range interactions

We obtain exact analytical results for lattices of maps with couplings that decay with distance as $r^{-α}$. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements are piecewise linear maps, we get an algebraic expression for the Lyapunov spectrum. When the local dynamics is given by a nonlinear map, the Lyapunov spectrum for a completely synchronized state is analytically obtained. The critical lines characterizing the synchronization transition are determined from the expression for the largest transversal Lyapunov exponent. In particular, it is shown that in the thermodynamical limit, such transition is only possible for sufficiently long-range interactions, namely, for $α\le alpha_c<d$, where $d$ is the lattice dimension.

nlin.CD↗

arXiv2002

Risk aversion in economic transactions

Most people are risk-averse (risk-seeking) when they expect to gain (lose). Based on a generalization of ``expected utility theory'' which takes this into account, we introduce an automaton mimicking the dynamics of economic operations. Each operator is characterized by a parameter q which gauges people's attitude under risky choices; this index q is in fact the entropic one which plays a central role in nonextensive statistical mechanics. Different long term patterns of average asset redistribution are observed according to the distribution of parameter q (chosen once for ever for each operator) and the rules (e.g., the probabilities involved in the gamble and the indebtedness restrictions) governing the values that are exchanged in the transactions. Analytical and numerical results are discussed in terms of how the sensitivity to risk affects the dynamics of economic transactions.

cond-mat.stat-mech↗

arXiv2001

Escape time in anomalous diffusive media

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t ρ= \partial_x[\partial_x Uρ] + D\partial^2_x ρ^ν$, where the potential of the drift, $U(x)$, presents a double-well and $D, ν$ are real parameters. For systems close to the steady state we obtain an analytical expression of the mean first passage time, yielding a generalization of Arrhenius law. Analytical predictions are in very good agreement with numerical experiments performed through integration of the associated Ito-Langevin equation. For $ν\neq 1$ important anomalies are detected in comparison to the standard Brownian case. These results are compared to those obtained numerically for initial conditions far from the steady state.

cond-mat.stat-mech↗

arXiv2000

Comment on "Anomalous Spreading of Power-Law Quantum Wave Packets"

A family of wave packets with power law tails are employed to analyze the long time dependence of the corresponding probability density. The densities, associated to packets for free particles in the one-dimensional space, with sufficiently long tails decay asymptotically in time following a $t^{-β}$ law (with $β<1$), slower than the usual $t^{-1}$ one, including the particular case $(ln t)^2/t$ not correctly discussed in F. Lillo and R. N. Mantegna (Phys. Rev. Lett. 84, 1061 (2000)).

cond-mat.stat-mech↗