A design method is presented that extends least mean squared (LMS) adaptation of time-varying parameters by including general linear time-invariant filters that operate on the instantaneous gradient vector. The aim is to track time-varying parameters of linear regression models in situations where the regressors are stationary or have slowly time-varying properties. The adaptation law is optimi...

The Wiener index is one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. A long standing conjecture on the Wiener index ([4], [5]) states that for any positive integer n (except numbers from a given 49 element set), one can find a tree with Wiener index n. In this paper, we prove that every i...

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The para...

In this work, we consider the adaptive Wiener filtering of noisy images and image sequences. We begin by using an adaptive weighted averaging (AWA) approach to estimate the second-order statistics required by the Wiener filter. Experimentally, the resulting Wiener filter is improved by about 1dB in the sense of peak-to-peak SNR (PSNR). Also, the subjective improvement is significant in that the...

Graphical matrices are presented. Their construction via selected sets of subgraphs and the replacement of subgraphs by numbers representing graph invariants are discussed. The last step of the procedure is to apply the method of choice for obtaining the desired double invariant from the graphical matrix in the numerical form. It is also pointed out that many so-called special graph-theoretical...

A novel unsymmetric square matrix, WPU , is proposed for calculating both Wiener, W , and hyper-Wiener, WW, numbers. This matrix is constructed by using single endpoint characterization of paths. Its relations with Wiener-type numbers are discussed.

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

the edge versions of reverse wiener indices were introduced by mahmiani et al. veryrecently. in this paper, we find their relation with ordinary (vertex) wiener index in somegraphs. also, we compute them for trees and tuc4c8(s) naotubes.

The diffraction by impenetrable wedges having arbitrary aperture angle is studied by means of the Wiener-Hopf (W-H) technique. A system of functional equations called generalized Wiener-Hopf equations (GWHE) is obtained. Only for certain values of the aperture angle these equations are recognizable as standard or classical Wiener-Hopf equations (CWHE). However, in all cases, a mapping to a suit...