In this paper we prove a Faber-Krahn-type inequality for regular trees and give a complete characterization of extremal trees. The main tools are rearrangements and perturbation of regular trees.

The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles and W and shorter cycles. It is shown that each minimum cycle basis contains the same number of...

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the t-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the...

It is well known that for highly skewed distributions the standard method of using the t statistic for the confidence interval of the mean does not give robust results. This is an important problem for importance sampling (IS) as its final distribution is often skewed due to a heavy tailed...

The inversion method for generating non-uniformly distributed random variates is a crucial part in many applications of Monte Carlo techniques, e.g., when low discrepancy sequences or copula based models are used. Unfortunately, closed form expressions of quantile functions of important...

There exists a vast literature on nonuniform random variate generators. Most of these generators are especially designed for a particular distribution. However, in pratice only a few of these are available to practioners. Moreover, for problems as (e.g.) sampling from the truncated normal...

The cycle space of a strongly connected graph has a basis consisting of directed circuits. The concept of relevant circuits is introduced as a generalization of the relevant cycles in undirected graphs. A polynomial time algorithm for the computation of a minimum weight directed circuit basis is...

Two-connected outerplanar graphs have a unique minimal cycle basis with length $2|E|-|V|$. They are the only Hamiltonian graphs with a cycle basis of this length.