We investigate numerically the inverse participation ratio, P(2), of the 3D Anderson model and of the power-law random banded matrix (PRBM) model at criticality. We found that the variance of lnP(2) scales with system size L as sigma(2)(L) = sigma(2)(infinity)-AL(-D(2)/2d), with D(2) being the correlation dimension and d the system dimension. Therefore the concept of a correlation dimension is ...

We present the correlation dimension of resolved young stars in four actively star-forming dwarf galaxies that are sufficiently resolved and transparent to be modeled as projections of three-dimensional point distributions. We use data in the Hubble Space Telescope archive; photometry for one of them, UGCA 292, is presented here for the first time. We find that there are statistically distingui...

We focus on an anomalous scaling region in correlation integral [C(epsilon)] analysis of electrocorticogram in epilepsy patients. We find that epileptic seizures typically are accompanied by wide fluctuations in the slope of this scaling region. An explanation, based on analyzing the interplay between the autocorrelation and C(epsilon), is provided for these fluctuations. This anomalous slope a...

AMS subject classifications: primary 62G10 secondary 62H20 Keywords: dCor dCov Multivariate independence Distance covariance Distance correlation High dimension a b s t r a c t Distance correlation is extended to the problem of testing the independence of random vectors in high dimension. Distance correlation characterizes independence and determines a test of multivariate independence for rand...

Recurrent sigmoidal neural networks with asymmetric weight matrices and recurrent neural networks with nonmonotone transfer functions can exhibit ongoing uctuations rather than settling into point attractors. It is, however, an open question if these uctuations are the sign of low dimensional chaos or if they can be considered as close to stochastic. We report on the calculation of the correlat...

Plateau Onset for Correlation Dimension: When Does it Occur? Mingzhou Ding, ' Celso Grebogi, ' Edward Ott, ) Tim Sauer, and James A. Yorket ) 'iCenter for Complex Systems and Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431 t iLaboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 t iDepartment of Mathematics and Institute for Physi...

Reports in the literature have indicated potential value of the correlation integral and dimension for prediction of epileptic seizures up to several minutes before electrographic onset. We apply these measures to over 2000 total hours of continuous electrocortiogram, taken from 20 patients with epilepsy, examine their sensitivity to quantifiable properties such as the signal amplitude and auto...

Abstract: We analyze the dimension of a financial correlation-based network and apply our analysis to characterize the complexity of the network. First, we generalize the volume-based dimension and find that it is well defined by the correlation-based network. Second, we establish the relationship between the Rényi index and the volume-based dimension. Third, we analyze the meaning of the dimen...

Surface electromyography (sEMG) has been widely applied to disease diagnosis, pathologic analysis and rehabilitation evaluation. It is the nonlinear summation of the electrical activity of the motor units in a muscle and can reflect the state of neuromuscular function. Traditional linear and statistical analysis methods have some significant limitations due to the short-term stationary and lowe...

The technique of surrogate data analysis may be employed to test the hypothesis that an observed data set was generated by one of several specific classes of dynamical system. Current algorithms for surrogate data analysis enable one, in a generic way, to test for membership of the following three classes of dynamical system: (0) independent and identically distributed noise, (1) linearly filte...