The Wiener index is one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. A long standing conjecture on the Wiener index ([4], [5]) states that for any positive integer n (except numbers from a given 49 element set), one can find a tree with Wiener index n. In this paper, we prove that every i...

One of the essential components of a neuromotor prosthetic device is a neural decoder that translates the activity of a set of neurons into an estimate of the intended movement of the prosthetic limb. Wiener filter style approaches model this transformation as a linear function of the number of spikes observed from a set of neurons and over a range of distinct time bins. More recently, research...

We compute the Wiener-Poisson expansion of square-integrable functionals of a nite number of Poisson jump times in series of multiple Poisson stochastic integrals.

One of the most widely known topological index is the Wiener index. The Wiener Index Conjecture states that all positive integer numbers except a finite set are the Wiener indices of some trees. We explore the Wiener indices of the binary trees. We present efficient algorithms for generating the Wiener indices of the binary trees. Based on experiments we strengthen the conjecture for the class ...

This paper presents a detailed performance analysis of thirdorder nonlinear adaptive systems based on the Wiener model. In earlier work, we proposed the discrete Wiener model for adaptive filtering applications for any order. However, we had focused mainly on first and second-order nonlinear systems in our previous analysis. Now, we present new results on the analysis of third order systems. Al...

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...

This paper presents a two-dimensional Wiener model in spatial domain for a class of laser electrophotographic printers, and embeds it into a framework of model-based digital halftoning. The Wiener model comprises an FIR filter followed by a nonlinear static mapping. The nonlinear static mapping is synthesized using a fuzzy system to maximize its capability to approximate nonlinearity of high de...

The eccentric sequence of a connected graph \(G\) is the nondecreasing eccentricities its vertices. Wiener index sum distances between all unordered pairs vertices \(G\). unique trees that minimise among with given were recently determined by present authors. In this paper we show these results hold not only for index, but large class distance-based topological indices which term Wiener-type in...

It is a little over 75 years since two of the most important mathematicians of the 20th century collaborated on finding the exact solution of a particular equation with semi-infinite convolution type integral operator. The elegance and analytical sophistication of the method, now called the Wiener–Hopf technique, impress all who use it. Its applicability to almost all branches of engineering, m...