The arc costs are assumed to be online parameters of the network and decisions should be made while the costs of arcs are not known. The policies determine the permitted nodes and arcs to traverse and they are generally defined according to the departure nodes of the current policy nodes. In on-line created tours arc costs are not available for decision makers. The on-line traversed nodes are f...

We present theoretical and observational studies of strong gravitational lenses produced by clusters of galaxies. Our purpose is to test the Cold Dark Matter (CDM) model at small and highly nonlinear scales where it has been claimed that the CDM model may confront several difficulties. We concentrate our attention on the statistics of strong gravitational lenses because the strong lensing is se...

In 1969, Denniston gave a construction of maximal arcs of degree d in Desarguesian projective planes of even order q, for all d dividing q. In 2002 Mathon gave a construction method generalizing the one of Denniston. We will give a new geometric approach to these maximal arcs. This will allow us to count the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2, 2h), h 6= 7 and prime...

All the polygonalisation algorithms we can find in the literature proceed on 4-connected or 8-connected discrete arcs. In this article, we aim to polygonalise “thick arcs”. A first step consists in giving a definition of such arcs based on morphological properties. In a second step, we propose two methods in order to polygonalise such arcs. The first one is based on a squelettisation of the arc...

Cyclic arcs (defined by Storme and Van Maldghem, [1994]) and pseudocyclic MDS codes are equivalent objects. We survey known results on the existence of cyclic arcs. Some new results on cyclic arcs in PG(2, q) are also given.

OBJECTIVE This study investigated the ability of the Audio Recorded Cognitive Screen (ARCS) to detect cognitive deficit in individuals with schizophrenia, relative to the Mini Mental State Examination (MMSE) and the Repeatable Battery for the Assessment of Neuropsychological Status (RBANS), and explored the associations between the ARCS and functional outcomes. We hypothesised that the ARCS wou...

We study the gravitational lensing of high-redshift sources in a ΛCDM universe. We have performed a series of ray-tracing experiments, and selected a subsample of cases of strong lensing (multiple images, arcs, and Einstein rings). For each case, we identified a massive galaxy that is primarily responsible for lensing, and studied how the various density inhomogeneities along the line of sight ...

We study the gravitational lensing of high-redshift sources in a ΛCDM universe. We have performed a series of ray-tracing experiments, and selected a subsample of cases of strong lensing (multiple images, arcs, and Einstein rings). For each case, we identified a massive galaxy that is primarily responsible for lensing, and studied how the various density inhomogeneities along the line of sight ...

In a network, each arc is assigned a weight. The weight of a path or a cycle is defined as the minimum weight of its arcs. The maximum of weights of all paths between two nodes is defined as the strength of connectedness between the nodes. In network applications, the reduction in the strength of connectedness is more relevant than the total disconnection of the graph. A graph is totally weight...

Local 1-shock curve arcs and local reverse 2-shock curve arcs were constructed, in the geometric context of the wave manifold, in a previous paper. In that geometric context, sonic and sonic’ surfaces are the boundaries of admissible shock curve arcs; in order to introduce the concept of non-local 1-shock curve arcs and non-local reverse 2shock curve arcs it is necessary to understand how a hug...