Cumulant (higher-order statistics) based inverse filter criteria maximizing J,,, = / C,l’/IC,I”, where m # r and C, (C,) denotes the mth-order (rth-order) cumulant of the inverse filter output, have been proposed for blind deconvolution and equalization with only non-Gaussian output measurements of an unknown linear time-invariant (LTI) system. This paper shows that the maximum of J,,,, associa...

In modern communication technology design of inverse filter i.e. channel equalizer on receiver side is important in order to combat the effects of channel distortion. In this paper we address different approaches of inverse filter design. The different approaches used are based on second order statistics methods such as Shank’s algorithm, WienerHopf equations (both FIR and IIR), LMS algorithm. ...

One-dimensional (1D) model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green’s function (hole propagator) at any rational interaction coupling constant λ = p/q a...

SUMMARY Consider a regression problem in which there are many more explanatory variables than data points, i.e., p >> n. Essentially, without reducing the number of variables inference is impossible. So, we group the p explanatory variables into blocks by clustering, evaluate statistics on the blocks and then regress the response on these statistics under a penalized error criterion to obtain e...

The generalized inverse has many important applications in aspects of the theoretical research matrices and statistics. One core problems is finding necessary sufficient conditions reverse order laws for operator product. In this paper, we study law g-inverse an product T1T2T3 using technique matrix form bounded linear operators. particular, some inclusion T3{1}T2{1}T1{1} ⊆ (T1T2T3){1} presente...

High-resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussian behavior of velocity differences statistics are quantitatively investigated. The level of statistical convergence is pushed enough to permit reliable measurement of the asymmetries in the probability distribution functions of longitudinal increments an...