While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models. © EDP Sciences, 2009.

Following some general ideas on the discrete kinetic and stochastic game theory proposed by one of the authors in a previous work, this paper develops a discrete velocity mathematical model for vehicular traffic along a one-way road. The kinetic scale is chosen because, unlike the macroscopic one, it allows to capture the probabilistic essence of the interactions among the vehicles, and offers at the same time, unlike the microscopic one, the opportunity of a pro. table analytical investigation of the relevant global features of the system.

Multidimensional extensions of the Bernoulli and Appell polynomials are defined generalizing the corresponding generating functions, and using the Hermite-Kampe de Feriet (or Gould-Hopper) polynomials. Furthermore the differential equations satisfied by the corresponding 2D polynomials are derived exploiting the factorization method, introduced in [15].

General classes of two variables Appell polynomials are introduced by exploiting properties of an iterated isomorphism, related to the so-called Laguerre-type exponentials. Further extensions to the multi-index and multivariable cases are mentioned. (C) 2004 Elsevier Ltd. All rights reserved.

The realization of innovative transport services requires greater flexibility and inexpensive service. In many cases the solution is to realize demand responsive transportation system. A Demand Responsive Transport System (DRTS) requires the planning of travel paths (routing) and customer pick-up and drop-off times (scheduling) according to received requests. In particular, the problem has to deal with multiple vehicles, limited capacity of the fleet vehicles and temporal constraints (time windows). A DRTS may operate according to static or dynamic mode.

The formation of vascular networks in vitro develops along two rather distinct stages: during the early migration-dominated stage the main features of the pattern emerge, later the mechanical interaction of the cells with the substratum stretches the network. Mathematical models in the relevant literature have been focusing just on either of the aspects of this complex system. In this paper, a unified view of the morphogenetic process is provided in terms of physical mechanisms and mathematical modeling.

The role of protein Z (PZ) in the etiology of human disorders is unclear. A number of PZ gene variants, sporadic or polymorphic and found exclusively in the serine protease domain, have been observed. Crystal structures of PZ in complex with the PZ-dependent inhibitor (PZI) have been recently obtained. The aim of this study was a structural investigation of the serine protease PZ domain, aiming at finding common traits across disease-linked mutations. We performed 10-20 ns molecular dynamics for each of the observed PZ mutants to investigate their structure in aqueous solution.