Search results for "Graph theory"
showing 10 items of 784 documents
The General Routing Problem polyhedron: Facets from the RPP and GTSP polyhedra
1998
[EN] In this paper we study the polyhedron associated with the General Routing Problem (GRP). This problem, first introduced by Orloff in 1974, is a generalization of both the Rural Postman Problem (RPP) and the Graphical Traveling Salesman Problem (GTSP) and, thus, is NP -hard. We describe a formulation of the problem such that from every non-trivial facet-inducing inequality for the RPP and GTSP polyhedra, we obtain facet-inducing inequalities for the GRP polyhedron, We describe a new family of facet-inducing inequalities for the GRP, the honeycomb constraints, which seem to be very useful for solving GRP and RPP instances. Finally, new classes of facets obtained by composition of facet-i…
An efficient algorithm for stopping on a sink in a directed graph
2013
Abstract Vertices of an unknown directed graph of order n are revealed one by one in some random permutation. At each point, we know the subgraph induced by the revealed vertices. Our goal is to stop on a sink, a vertex with no out-neighbors. We show that if a sink exists this can be achieved with probability Θ ( 1 / n ) , which is best possible.
Robust Conditional Independence maps of single-voxel Magnetic Resonance Spectra to elucidate associations between brain tumours and metabolites.
2020
The aim of the paper is two-fold. First, we show that structure finding with the PC algorithm can be inherently unstable and requires further operational constraints in order to consistently obtain models that are faithful to the data. We propose a methodology to stabilise the structure finding process, minimising both false positive and false negative error rates. This is demonstrated with synthetic data. Second, to apply the proposed structure finding methodology to a data set comprising single-voxel Magnetic Resonance Spectra of normal brain and three classes of brain tumours, to elucidate the associations between brain tumour types and a range of observed metabolites that are known to b…
A study on the degree of relationship between two individuals.
2000
The paper studies the likely degree of relationship between two individuals who could possibly be half sibs. The possible common ancestor was dead, which further complicated the problem. The model used was devised by Thompson [in Rao and Chakraborty (eds): Handbook of Statistics, North-Holland, Amsterdam, 1991] and establishes a correspondence between the possible degree of relationship and certain feasible probability distributions on the number of identical by descent genes. Two statistical approaches are considered: the classical one, in which the maximum likelihood estimation for the parameters of Thompson’s model are obtained, and the Bayesian one, in which the test of the hypothesis o…
Efficient and Long-Lived Field-Free Orientation of Molecules by a Single Hybrid Short Pulse
2005
We show that a combination of a half-cycle pulse and a short nonresonant laser pulse produces a strongly enhanced postpulse orientation. Robust transients that display both efficient and long-lived orientation are obtained. The mechanism is analyzed in terms of optimal oriented target states in finite Hilbert subspaces and shows that hybrid pulses can prove useful for other control issues.
On minimal non-PC-groups
2009
On dit qu'un groupe G est un PC-groupe, si pour tout x ∈ G, G/C G (x G ) est une extension d'un groupe polycyclique par un groupe fini. Un non-PC-groupe minimal est un groupe qui n'est pas un PC-groupe mais dont tous les sous-groupes propres sont des PC-groupes. Notre principal resultat est qu'un non-PC-groupe minimal ayant un groupe quotient fini non-trivial est une extension cyclique finie d'un groupe abelien divisible de rang fini.
Characterizing normal Sylow p-subgroups by character degrees
2012
Abstract Suppose that G is a finite group, let p be a prime and let P ∈ Syl p ( G ) . We prove that P is normal in G if and only if all the irreducible constituents of the permutation character ( 1 P ) G have degree not divisible by p.
Finite groups with real-valued irreducible characters of prime degree
2008
Abstract In this paper we describe the structure of finite groups whose real-valued nonlinear irreducible characters have all prime degree. The more general situation in which the real-valued irreducible characters of a finite group have all squarefree degree is also considered.
Linear Response Theory with finite-range interactions
2021
International audience; This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle–hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle–hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle–hole interactio…
A mixed geometric-systolic approach to parallel molecular dynamics simulations
1995
We have developed a flexible and efficient method of performing molecular dynamics simulations on distributed memory parallel computers. The novel feature is to use simultaneously spatial partitioning and systolic loop approaches according to a strategy which, for a given simulation, adapts itself to the multiprocessor system, allowing to approach optimal performance. The method assures high efficiencies even in situations in which, due to the exceeding large number of processors, the usage of a pure spatial decomposition would be impossible. The algorithm provides as particular cases both the pure spatial partitioning and the pure systolic parallelization schemes, so that its adoption assu…