this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

Volterra and Wiener series are perhaps the best-understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series c...

In 1918 and 1919 Daniell's papers on what is now called the Daniell integral appeared. As an application he constructed the most general finite measure of Borel sets in Euclidean space of countable dimensionality. In 1933 Kolmogorov, in his formalization of probability as measure theory, rediscovered the Daniell result in constructing measures on Euclidean space of arbitrary dimensionality. Aft...

Compared to wired channels, time dispersive radio channels possess more frequent nulls in their spectral characteristics. Thus, the performance of linear filters to compensate intersymbol interference degrades dramatically. The well-known nonlinear Decision Feedback Equalizer (DFE) is one approach to improve this behavior. However, in systems with observations of high dimensionality, the optimu...

This paper addresses dereverberation of speech using an unsupervised approach utilizing speech prior and taking only weak assumptions on reverberation. Our approach uses a long time context representation of reverberated speech in spectral-temporal supervectors which are decorrelated by the PCA. In the decorrelated domain supervectors are mapped from reverberant speech distribution to clean spe...

Denoising and Dimensionality Reduction (DR) are key issue to improve the classifiers efficiency for Hyper spectral images (HSI). The multi-way Wiener filtering recently developed is used, Principal and independent component analysis (PCA; ICA) and projection pursuit (PP) approaches to DR have been investigated. These matrix algebra methods are applied on vectorized images. Thereof, the spatial ...

Gaussian process regression is a machine learning paradigm, where the regressor functions are modeled as realizations from an a priori Gaussian process model. We study abstract continuous-space Gaussian regression problems where the training set covers the whole input space instead of consisting of a finite number of distinct points. The model can be used for analyzing theoretical properties of...

whereas there is an exact linear relation between the wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal wiener indices exhibit a completely different behavior: correlation between terminal wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. in this article, we analyze the basic properties of terminal wiener indices...

the wiener polarity index wp(g) of a molecular graph g of order n is the number ofunordered pairs of vertices u, v of g such that the distance d(u,v) between u and v is 3. in anearlier paper, some extremal properties of this graph invariant in the class of catacondensedhexagonal systems and fullerene graphs were investigated. in this paper, some new bounds forthis graph invariant are presented....