Since the seminal work of Wiener (Am J Math 60:897–936, 1938), chaos expansion has evolved to a powerful methodology for studying broad range stochastic differential equations. Yet its complexity systems subject white noise remains significant. The issue appears due fact that random increments generated by Brownian motion result in growing set variables with respect which process could be measu...

The Wiener polarity indexWP (G) of a graph G is the number of unordered pairs of vertices {u, v} of G such that the distance of u and v is equal to 3. In this paper, we obtain the relation between Wiener polarity index and Zegreb indices, and the relation between Wiener polarity index and Wiener index (resp. hyper-Wiener index). Moreover, we determine the second smallest Wiener polarity index t...

This paper describes two novel Wiener-based approaches for frame-to-frame image registration. The first approach, Local Wiener Registration, incorporates the crosscorrelation between the two frames to determine the Wiener filter at each pixel location in order to predict the second frame from the first frame. The second approach, Block Wiener Registration, divides the image in nonoverlapping bl...

wiener index is a topological index based on distance between every pair of vertices in agraph g. it was introduced in 1947 by one of the pioneer of this area e.g, harold wiener. inthe present paper, by using a new method introduced by klavžar we compute the wiener andszeged indices of some nanostar dendrimers.

one of the generalizations of the wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. the reliability wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. closed expressions are derived for t...

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.

let g be a molecular graph. the wiener index of g is defined as the summation of alldistances between vertices of g. in this paper, an exact formula for the wiener index of a newtype of nanostar dendrimer is given.

A positive integer n is said to be Wiener graphical, if there exists a graph G with Wiener index n. In this paper, we prove that any positive integer n( 6= 2, 5) is Wiener graphical. For any positive integer p, an interval [a, b] is said to be a p-Wiener interval if for each positive integer n ∈ [a, b] there exists a graph G on p vertices such that W (G) = n. For any positive integer p, an inte...

We investigate a Wiener fusion method to optimally combine multiple estimates for the problem of image deblurring given a known blur and a corpus of sharper training images. Nearest-neighbor estimation of high frequency information from training images is fused with a standard Wiener deconvolution estimate. Results show an improvement in sharpness and decreased artifacts compared to either the ...