Random walk can be used as a centrality measure of a directed graph. However, if the graph is reducible the random walk will be absorbed in some subset of nodes and will never visit the rest of the graph. In Google PageRank the problem was solved by introduction of uniform random jumps with some probability. Up to the present, there is no clear criterion for the choice this parameter. We propos...

We consider the sub-Riemannian metric g h on S 3 provided by the restriction of the Riemannian metric of curvature 1 to the plane distribution orthogonal to the Hopf vector field. We compute the geodesics associated to the Carnot-Carathéodory distance and we show that, depending on their curvature, they are closed or dense subsets of a Clifford torus. We study area-stationary surfaces with or w...

Time series of financial asset values exhibit well known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from Extreme Value Theory to fit the time varying volatility in situations where the stationarity assumption may be violated by erratic changes of regime, say. As a result, we provide a meth...

We consider two independent and stationary measures over χN, where χ finite or countable alphabet. For each pair of n-strings in the product space we define T (2) n as the length of the shortest path connecting one string to the other where the paths are generated by the underlying dynamics of the measure. For ergodic measures with positive entropy we prove that, for almost every pair of realiz...

For a large class of stationary probability measures on AN, where A is a finite alphabet, we compute the specific Rényi entropy of order α and the specific guesswork moments of order β > −1. We show that the specific guesswork moment of order β equals the specific Rényi entropy of order α = 1/(1+ β) multiplied by β. The method is based on energy–entropy estimates suggested by statistical physic...

We describe new techniques to detect and analyze periodic motion as seen from both a static and moving camera. By tracking objects of interest, we compute an object’s self-similarity as it evolves in time. For periodic motion, the self-similarity measure is also periodic, and we apply Time-Frequency analysis to detect and characterize the periodic motion. The periodicity is also analyzed robust...

A new similarity measure, called SimilB, for time series analysis, based on the cross-ΨB-energy operator (2004), is introduced. ΨB is a nonlinear measure which quantifies the interaction between two time series. Compared to Euclidean distance (ED) or the Pearson correlation coefficient (CC), SimilB includes the temporal information and relative changes of the time series using the first and sec...

We propose a new statistical model of musical timbre that handles the different segments of the temporal envelope (attack, sustain and release) separately in order to account for their different spectral and temporal behaviors. The model is based on a reduced-dimensionality representation of the spectro-temporal envelope. Temporal coefficients corresponding to the attack and release segments ar...

It is shown that for every stationary sequence of random riie permutations there is a natural associated dynamical system consisting of random orbits in the space of sequences from a nite alphabet. For many interesting models of card-shuuing, the associated dynamical systems have simple descriptions in terms of random or deterministic measure-preserving maps of the unit interval. It is shown th...

We consider the behaviour of the distribution for stationary solutions of the complex Ginzburg–Landau equation perturbed by a random force. It was proved in [KS04] that if the random force is proportional to the square root of the viscosity ν > 0, then the family of stationary measures possesses an accumulation point as ν → 0. We show that if μ is such point, then the distributions of the L nor...