Expected Values of Some Molecular Descriptors in Random Cyclooctane Chains

Expected Number of Local Maxima of Some Gaussian Random Polnomials

expected number of local maxima of some gaussian random polnomials

Random molecular substructures as fragment-type descriptors

A novel approach for analysis of structure-activity relationships for sets of active compounds is reported. Molecular similarity relationships are analyzed among compounds with related biological activity based on the evaluation of randomly generated fragment populations. Fragments are randomly generated by iterative bond deletion in molecular graphs and hence depart from those obtained by well...

Hosoya polynomials of random benzenoid chains

Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...

On monotonicity of expected values of some run-related distributions

We prove that the expectation of the binomial distribution of order k with success probability p is monotonically increasing with respect to p for all n and k. The result is extended to the problems on exchangeable random sequences and expectations of distributions of mixtures of binomial distributions of order k are studied. If the mixing measure is stochastically increasing with respect to it...