The Wiener polynomial of a graph G is a generating function for the distance distribution dd(G) = (D1,D2, . . . , Dt ), where Di is the number of unordered pairs of distinct vertices at distance i from one another and t is the diameter of G. We use the Wiener polynomial and several related generating functions to obtain generating functions for distance distributions of unweighted and weighted ...

During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predetermi...

A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Itô algebra has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular,...

In this paper a novel transversal split filter configuration is proposed and the split optimum Wiener filter is introduced, as well as the symmetric and antisymmetric linear phase Wiener filter. The approach consists of combining the idea of split filtering with a linearlyconstrained optimization scheme. Then, the continuously split procedure is introduced and the multi-split adaptive filter is...

A novel approach is proposed in order to reduce the number of sweeps (trials) required for the efficient extraction of the brain evoked potentials (EPs). This approach is developed by combining both the Wiener filtering and the subspace methods. First, the signal subspace is estimated by applying the singularvalue decomposition (SVD) to an enhanced version of the raw data obtained by Wiener fil...

This paper designs the recursive least-squares (RLS) Wiener finite impulse response (FIR) predictor and filter, based on the innovation approach, in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white noise and the signal process is uncorrelated with the observation noise process. This paper also presents the recursive algorithms for the estima...

Several methods of combining a number of time series into a single series are discussed. They are all individual filtering followed by summation and are somewhat like Wiener filtering in that a least squares criterion is used to define the filter coefficients. They differ from Wiener filtering in that signal information is given in the form of various linear constraints on the filter coefficien...

The problem of the identification of Hammerstein and Wiener models is considered in this paper. The suggested approach in this paper utilizes the spectral magnitude matching method that minimizes the sum squared error between the spectral magnitudes evaluated for a number of short-time frames of the measured output signal of the nonlinear system and the output signal of the nonlinear model. The...

Topological indices are numbers that applied to a graph and can be used describe specific properties through algebraic structures. Algebraic theory is helpful tool in range of chemistry domains. Because it helps explain how the different symmetries molecules crystals affect their structure dynamics, powerful theoretical approach for forecasting both common uncommon characteristics molecules. A ...