A ladder is a 2 × k grid graph. When does graph class $${\cal C}$$ exclude some as minor? We show that this the case if and only all graphs G in admit proper vertex coloring with bounded number of colors such for every 2-connected subgraph H G, there color appears exactly once H. This type relaxation notion centered coloring, where connected must be The minimum treedepth it known classes are th...

The usual chain ladder metlwd is a deterministic claims reserving method. In the last years. o stochastic loglineor approximation to the chain ladder method hav been u~rl by several authors especially in order to quantify the variability of the estimated claims reserves. Although the reserves estimated by both merAo& are clenrly diflerent. rk logknenrapproxi-mation has been called " chain ladde...

Let T be an edge weighted tree, let dT (u, v) be the sum of the weights of the edges on the path from u to v in T , and let dmin and dmax be two non-negative real numbers such that dmin ≤ dmax. Then a pairwise compatibility graph of T for dmin and dmax is a graph G = (V, E), where each vertex u ∈ V corresponds to a leaf u of T and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (u, v) ≤ dm...

This work regards the order polytopes arising from class of generalized snake posets and their meet-irreducible elements. Among same rank, we characterize those whose have minimal maximal volume. We give a combinatorial characterization circuits in related then conclude that all triangulations are unimodular. For word, count number flips for canonical triangulation these polytopes. determine fl...

Under some relaxed conditions, in this paper we obtain some equivalent conditions on the asymptotics of the density of the supremum of a random walk with heavy-tailed increments. To do this, we investigate the asymptotics of the first ascending ladder height of a randomwalk with heavy-tailed increments. The results obtained improve and extend the corresponding classical results.

Injuries from slips, falls and overexertion during ladder cfimbing activities are common in both occupational and non-occupational environments. Little is known, however, about the task, equipment, and user parameters which may cause these injuries. In order to evaluate the hazards assocmted with ladder climbing, ten male subjects were tested under combinations of ladder rung separation, ladder...

A link between matroid theory and p-branes is discussed. The Schild type action for p-branes and matroid bundle notion provide the two central structures for such a link. We use such a connection to bring the duality concept in matroid theory to p-branes physics. Our analysis may be of particular interest in M-theory and in matroid bundle theory.