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The approach combines second and fourth order statistics to perform BSS of instantaneous mixtures. It applies for any number of receivers if they are as many as sources. It is a batch algorithm that uses non-Gaussianity and stationarity of source signals. It is linear algebra based direct method, reliable and robust, though large dimensions of sources may slow down the computation significantly. It is however limited to instantaneous mixtures.

In this paper, we study, in some new ways, the estimation of unimodal densities. Several methods for estimating unimodal densities are proposed: plug-in MLE, pregrouping techniques, linear spline MLE. Based on the maximum likelihood method, an automatic procedure for estimating a unimodal density as well as its mode is proposed. We also give asymptotic theory for the proposed estimators. An important consequence of this study is that having to estimate the location of a mode does not affect the limiting behavior of the proposed unimodal density estimate. Simulation studies illustrate the proposed methods.

We consider diffusivity of random walks with transition probabilities depending on the number of consecutive traversals of the last traversed edge, the so called senile reinforced random walk (SeRW). In one dimension, the walk is known to be sub-diffusive with identity reinforcement function. We perturb the model by introducing a small probability \delta of escaping the last traversed edge at each step. The perturbed SeRW model is diffusive for any \delta , with enhanced diffusivity (\delta ) in the small \delta regime. We further study stochastically perturbed SeRW models by having the last edge escape probability of the form \delta with \delta 's being independent random variables. Enhanced diffusivity in such models are logarithmically close to the so called residual diffusivity (positive in the zero \delta limit), with diffusivity between \delta and \delta . Finally, we generalize our results to higher dimensions where the unperturbed model is already diffusive. The enhanced diffusivity can be as much as \delta .

Motivated by the problem of colocalization analysis in fluorescence microscopic imaging, we study in this paper structured detection of correlated regions between two random processes observed on a common domain. We argue that although intuitive, direct use of the maximum log-likelihood statistic suffers from potential bias and substantially reduced power, and introduce a simple size-based normalization to overcome this problem. We show that scanning with the proposed size-corrected likelihood ratio statistics leads to optimal correlation detection over a large collection of structured correlation detection problems.