In this paper a procedure is presented for deriving parameters bounds in SISO Wiener models when the nonlinear block can be modeled by a polynomial and the output measurement errors are bounded. First, using steady-state input-output data, parameters of the nonlinear block are tightly bounded. Next in order to estimate the parameters of the linear block, the evaluation of the inner unmeasurable...

The probability of a stochastic process to first breach an upper and/or a lower level is an important quantity for optimal control and risk management. We present those probabilities for regime switching Brownian motion. In the 2and 3-state model, the Laplace transform of the (single and double barrier) first-passage times is – up to the roots of a polynomial of degree 4 (respectively 6) – deri...

The Wiener index of a connected graph G, denoted by W(G) , is defined as ∑ ( , ) , ∈ ( ) .Similarly, hyper-Wiener index of a connected graph G,denoted by WW(G), is defined as ( ) + ∑ ( , ) , ∈ ( ) .In this paper, we present the explicit formulae for the Wiener, hyper-Wiener and reverse Wiener indices of some graph operations. Using the results obtained here, the exact formulae for Wiener, hyper...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

motivated by the terminal wiener index‎, ‎we define the ashwini index $mathcal{a}$ of trees as‎ begin{eqnarray*}‎ % ‎nonumber to remove numbering (before each equation)‎ ‎mathcal{a}(t) &=& sumlimits_{1leq i‎&+& deg_{_{t}}(n(v_{j}))],‎ ‎end{eqnarray*}‎ ‎where $d_{t}(v_{i}‎, ‎v_{j})$ is the distance between the vertices $v_{i}‎, ‎v_{j} in v(t)$‎, ‎is equal to the length of the shortest path start...

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...

let $g$ be a simple connected graph. the edge-wiener index $w_e(g)$ is the sum of all distances between edges in $g$, whereas the hyper edge-wiener index $ww_e(g)$ is defined as {footnotesize $w{w_e}(g) = {frac{1}{2}}{w_e}(g) + {frac{1}{2}} {w_e^{2}}(g)$}, where {footnotesize $ {w_e^{2}}(g)=sumlimits_{left{ {f,g} right}subseteq e(g)} {d_e^2(f,g)}$}. in this paper, we present explicit formula fo...

The computation of classical higher-order statistics such as higher-order moments or spectra is difficult for images due to the huge number of terms to be estimated and interpreted. We propose an alternative approach in which multiplicative pixel interactions are described by a series of Wiener functionals. Since the functionals are estimated implicitly via polynomial kernels, the combinatorial...

‎let $g=(v(g),e(g))$ be a simple connected graph with vertex set $v(g)$ and edge‎ ‎set $e(g)$‎. ‎the (first) edge-hyper wiener index of the graph $g$ is defined as‎: ‎$$ww_{e}(g)=sum_{{f,g}subseteq e(g)}(d_{e}(f,g|g)+d_{e}^{2}(f,g|g))=frac{1}{2}sum_{fin e(g)}(d_{e}(f|g)+d^{2}_{e}(f|g)),$$‎ ‎where $d_{e}(f,g|g)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $e(g)$ and $d_{e}(f|g)=s...