For the numerical solution of the hypersingular integral equation of a notched half-plane problem we propose collocation methods which look for an approximation of the derivative of the solution of the original equation. This derivative is the solution of a Cauchy singular integral equation with additional fixed singularities. We also give a solvability analysis of the original equation which motivates the suggested numerical methods.

We have developed a rat brain organotypic culture model, in which tissue slices contain cortex-subventricular zone-striatum regions, to model neuroblast activity in response to in vitro ischemia. Neuroblast activation has been described in terms of two main parameters, proliferation and migration from the subventricular zone into the injured cortex. We observed distinct phases of neuroblast activation as is known to occur after in vivo ischemia. Thus, immediately after oxygen/glucose deprivation (6–24 hours), neuroblasts reduce their proliferative and migratory activity, whereas, at longer time points after the insult (2 to 5 days), they start to proliferate and migrate into the damaged cortex. Antagonism of ionotropic receptors for extracellular ATP during and after the insult unmasks an early activation of neuroblasts in the subventricular zone, which responded with a rapid and intense migration of neuroblasts into the damaged cortex (within 24 hours). The process is further enhanced by elevating the production of the chemoattractant SDf-1α and may also be boosted by blocking the activation of microglia. This organotypic model which we have developed is an excellent in vitro system to study neurogenesis after ischemia and other neurodegenerative diseases. Its application has revealed a SOS response to oxygen/glucose deprivation, which is inhibited by unfavorable conditions due to the ischemic environment. Finally, experimental quantifications have allowed us to elaborate a mathematical model to describe neuroblast activation and to develop a computer simulation which should have promising applications for the screening of drug candidates for novel therapies of ischemia-related pathologies.

The Push-Tree Problem is a recently addressed optimization problem, with the aim to minimize the total amount of traffic generated on information broadcasting networks by a compromise between the use of "push" and "pull" mechanisms. That is, the push-tree problem can be seen as a mixture of building multicast trees with respect to nodes receiving pieces of information while further nodes may obtain information from the closest node within the tree by means of shortest paths. In this sense we are accounting for tradeoffs of push and pull mechanisms in information distribution. The objective of this paper is to extend the literature on the problem by presenting four mathematical formulations and by defining and applying some metaheuristics for its resolution. © Springer Science+Business Media, LLC 2009.

We provide a polynomial algorithm that determines for any given undirected graph G = (V, E), positive integer k, and convex functions fv : N -> R (v ? V ) a subgraph H = (V, F ) of k edges that minimizes ?v?V fv (dH (v)), where dH (v) is the degree of v in H. The motivation and at the same time the main application of the results is the problem of finding a subset of k vertices in a line graph that covers as many edges as possible. The latter problem generalizes the vertex cover problem for line graphs, which is in turn equivalent to the maximum matching problem in graphs. Improving paths or walks for factorization problems have to be completed by pairs of such walks for this problem. We provide several solutions leading to different variants of the problem and also show the limits of the methods by proving the NP-completeness of some direct extensions, in particular to all convex functions.

Edge-Path-Tree (EPT) graphs are intersection graphs of EPT matrices that is matrices whose columns are incidence vectors of edge-sets of paths in a given tree. EPT graphs have polynomially many cliques [M.C. Golumbic, R.E. Jamison, The edge intersection graphs of paths in a tree, Journal of Combinational Theory Series B 38 (1985) 8-22; C.L. Monma, V.K. Wey, Intersection graphs of paths in a tree, Journal of Combinational Theory Series B 41 (1986) 141-181]. Therefore, the problem of finding a clique of maximum weight in these graphs is solvable in strongly polynomial time. We extend this result to a proper superclass of EPT graphs.

An Edge Path Tree (EPT) family is a family whose members are edge sets of paths in a tree. Relying on the notion of Pie introduced in [M.C. Golumbic, R.E. Jamison, The edge intersection graphs of paths in a tree, Journal of Combinatorial Theory, Series B 38 (1985) 8-22], we characterize Ideal and Mengerian EPT families. In particular, we show that an EPT family is Ideal if and only if it is Mengerian. If, in addition, the EPT family is uniform, then it is Ideal if and only if it is Unimodular. The latter equivalence generalizes the well-known fact that the edge set of a graph is an Ideal clutter if and only if the graph is bipartite

A Directed Path Family is a family of subsets of some finite ground set whose members can be realized as arc sets of simple directed paths in some directed graph. In this paper we show that recognizing whether a given family is a Directed Path family is an NP-Complete problem, even when all members in the family have at most two elements. If instead of a family of subsets, we are given a collection of words from some finite alphabet, then deciding whether there exists a directed graph G such that each word in the language is the set of arcs of some path in G, is a polynomial-time solvable problem.

It is proposed the use of a mobile device based on a NMR single-sided sensor for in situ non-invasive determination of the moisture content (MC) of wood items, especially items of Cultural Heritage interest. The MC is obtained through the moisture volume fraction, which is an appropriate quantity for the sensor and corresponds to the fraction of its measurements sensitive volume occupied by water. The device has been used here to track changes in MC of wood specimens caused by changes over time of the environmental relative humidity. The kinetics of water adsorption has been related to results obtained with the gravimetric method. Measurements on an old painting, the Pietà (1516-1517), oil on a poplar wood panel by Sebastiano del Piombo (1485 Venice, 1547 Rome), Civic Museum, Viterbo, Italy, have shown, conclusively, the good sensitivity of the sensor and its capability to behave as a non-invasive and in situ utilizable device. Results of in situ painting measurements show that the NMR sensor can track moisture fluctuations that are outside the sensitivity range and precision of electro-hygrometric approach. © 2008 Springer-Verlag.

Relative dispersion of tracers - i.e. very small, neutrally buoyant particles-, is particularly efficient in incompressible turbulent flows. Due to the non smooth behaviour of velocity differences in the inertial range, the separation distance between two trajectories, R(t)=X1(t)-X2(t) , grows as a power of time superdiffusively, R2(t)t3 , as first observed by L.F. Richardson [1]. This now well established result has no counterpart in the theory of heavy particle suspensions, namely finite-size particles with a mass density much larger that of the carrier fluid. The complete knowledge of particle properties of mixing in turbulent flows -yet an open problem-, is of great importance in cloud physics, or in estimating pollutant dispersion for hazardous safety purposes.