数据分析、统计与概率

The fundamentals of the Maximum Entropy principle as a rule for assigning and updating probabilities are revisited. The Shannon-Jaynes relative entropy is vindicated as the optimal criterion for use with an updating rule. A constructive…

The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…

Continuous time random walks have been developed as a straightforward generalisation of classical random walk processes. Some 10 years ago, Fogedby introduced a continuous representation of these processes by means of a set of Langevin…

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…

Avalanches, or Avalanche-like, events are often observed in the dynamical behaviour of many complex systems which span from solar flaring to the Earth's crust dynamics and from traffic flows to financial markets. Self-organized criticality…

When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…

Recently, several powerful tools for the reconstruction of stochastic differential equations from measured data sets have been proposed [e.g. Siegert et al., Physics Letters A 243, 275 (1998); Hurn et al., Journal of Time Series Analysis…

We show that it can be considered some of Bach pitches series as a stochastic process with scaling behavior. Using multifractal deterend fluctuation analysis (MF-DFA) method, frequency series of Bach pitches have been analyzed. In this view…

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…

We propose a new approach to the problem of the first passage time. Our method is applicable not only to the Wiener process but also to the non--Gaussian L$\acute{\rm e}$vy flights or to more complicated stochastic processes whose…

Formulas are derived to compute the mean number of times a site has been visited during symmetric Levy flights. Unrestricted Levy flights are considered first, for lattices of any dimension: conditions for the existence of finite asymptotic…

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that occurrence of major earthquakes in California correlates with time intervals when fluctuations in…

We investigate precursors and predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially interested in understanding how the quality of…

Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess…

Traffic flows are studied in terms of their noise of sound, which is an easily accessible experimental quantity. The sound noise data is studied making use of scaling properties of wavelet transforms and Hurst exponents are extracted. The…

A theory of additive Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such…

We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the Normalized Total Wavelet Entropy (NTWS) family [Phys. Rev. E 57 (1998) 932; J. Neuroscience Method 105 (2001) 65; Physica A…

Detrended fluctuation analysis (DFA) [1] of the volatility series has been found to be useful in dentifying possible nonlinear/multifractal dynamics in the empirical sample [2-4]. Long-range volatile correlation can be an outcome of static…

Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed…

With the advancement in the information age, people are using electronic media more frequently for communications, and social relationships are also increasingly resorting to online channels. While extensive studies on traditional social…