The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact form...

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...

The Wiener filter is analyzed for stationary complex Gaussian signals from an information-theoretic point of view. A dual-port analysis of the Wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the Wiener filter using a nested chain of scalar Wiener filters. This new representation of the Wiener filter provides the capa...

Wiener filter is widely used for image denoising and restoration. It is alternatively known as the minimum mean square error filter or the least square error filter, since the objective function used in Wiener filter is an age-old benchmark called the Mean Square Error (MSE). Wiener filter tries to approximate the degraded image so that its objective function is optimized. Although MSE is consi...

According to classical results by M. G. Krein and L. de Branges, for every positive measure μ on the real line R such that ∫ R dμ(t) 1+t2 <∞ there exists a Hamiltonian H such that μ is the spectral measure for the corresponding canonical Hamiltonian system JX ′ = zHX. In the case where μ is an even measure from Steklov class on R, we show that the Hamiltonian H normalized by detH = 1 belongs to...

By using multiple Wiener-Itô stochastic integrals, we study the cubic variation of a class of selfsimilar stochastic processes with stationary increments (the Rosenblatt process with selfsimilarity order H ∈ ( 12 , 1)). This study is motivated by statistical purposes. We prove that this renormalized cubic variation satis es a non-central limit theorem and its limit is (in the L(Ω) sense) still ...

published by sshresth on Mon, 08/19/2013 12:58pm Title Functional FCGR2B gene variants influence intravenous immunoglobulin response in patients with Kawasaki disease. Publication Type Journal Article Year of Publication 2011 Authors Shrestha, S, Wiener, HW, Olson, AK, Edberg, JC, Bowles, NE, Patel, H, Portman, MA Journal J Allergy Clin Immunol Volume 128 Issue 3 Pagination 677-80 Date Publishe...

It is well known that the vertices of any graph can be put in a linear preorder so that for random walk on the graph vertices appearing earlier in the preorder are “easier to reach but more difficult to get out of”. We exhibit further such preorders corresponding to various functions related to random walk and study their relationships. These preorders coincide when the graph is a tree, but not...

In this paper, we give solutions for the two conjectures on the inverse problem of the Wiener index of peptoids proposed by Goldman et al. We give the first conjecture a positive proof and the second conjecture a negative answer.