We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations suject to uncertain inputs. In particular, we focus on the solution of the Poisson equation with random diffusivity, forcing and boundary conditions. The stochastic input and solution are represented spectrally by employing the orthogonal polynomial functionals from the Ask...

The Wiener filter is the well-known solution for linear minimum mean square error (LMMSE) signal estimation. This filter assumes the mean to be known and usually constant. On the other hand, the Kriging filter is an incremental theory, developed within the Geostatistical community, with respect to that of Wiener filters. The extension relies on adopting a parametric model for the mean (usually ...

We present a simple criterion, only based on second moment assumptions, for the convergence of polynomial or Wiener chaos to Gaussian limit. exploit this criterion obtain new asymptotics partition functions two-dimensional directed polymers in sub-critical regime, including singular product between function and disorder. These results can also be applied KPZ Stochastic Heat Equation. As tool in...

Methods are described for extracting the trend from an economic data sequence and for isolating the cycles that surround it. The latter often consist of a business cycle of variable duration and a perennial seasonal cycle. There is no evident point in the frequency spectrum where the trend ends and the business cycle begins. Therefore, unless it can be represented by a simple analytic function,...

Drugs and other chemical compounds are often modeled as polygonal shapes, where each vertex represents an atom of the molecule, and covalent bonds between atoms are represented by edges between the corresponding vertices. This polygonal shape derived from a chemical compound is often called its molecular graph, and can be a path, a tree, or in general a graph. An indicator defined over this mol...

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....

Let G be a non–linear function of a Gaussian process {Xt}t∈Z with long–range dependence. The resulting process {G(Xt)}t∈Z is not Gaussian when G is not linear. We consider random wavelet coefficients associated with {G(Xt)}t∈Z and the corresponding wavelet scalogram which is the average of squares of wavelet coefficients over locations. We obtain the asymptotic behavior of the scalogram as the ...

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...