About the Algebraic Solutions of Smallest Enclosing Cylinders Problems

Given n points in Euclidean space E^d, we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication (previous version is a copy of the original one of 2010

Improved Implementation of Point Location in General Two-Dimensional Subdivisions

We present a major revamp of the point-location data structure for general two-dimensional subdivisions via randomized incremental construction, implemented in CGAL, the Computational Geometry Algorithms Library. We can now guarantee that the constructed directed acyclic graph G is of linear size and provides logarithmic query time. Via the construction of the Voronoi diagram for a given point set S of size n, this also enables nearest-neighbor queries in guaranteed O(log n) time. Another major innovation is the support of general unbounded subdivisions as well as subdivisions of two-dimensional parametric surfaces such as spheres, tori, cylinders. The implementation is exact, complete, and general, i.e., it can also handle non-linear subdivisions. Like the previous version, the data structure supports modifications of the subdivision, such as insertions and deletions of edges, after the initial preprocessing. A major challenge is to retain the expected O(n log n) preprocessing time while providing the above (deterministic) space and query-time guarantees. We describe an efficient preprocessing algorithm, which explicitly verifies the length L of the longest query path in O(n log n) time. However, instead of using L, our implementation is based on the depth D of G. Although we prove that the worst case ratio of D and L is Theta(n/log n), we conjecture, based on our experimental results, that this solution achieves expected O(n log n) preprocessing time.Comment: 21 page

Structural and paramagnetic properties of dilute Ga1-xMnxN

Systematic investigations of the structural and magnetic properties of single crystal (Ga,Mn)N films grown by metal organic vapor phase epitaxy are presented. High resolution transmission electron microscopy, synchrotron x-ray diffraction, and extended x-ray absorption fine structure studies do not reveal any crystallographic phase separation and indicate that Mn occupies Ga-substitutional sites in the Mn concentration range up to 1%. The magnetic properties as a function of temperature, magnetic field and its orientation with respect to the c-axis of the wurtzite structure can be quantitatively described by the paramagnetic theory of an ensemble of non-interacting Mn$^{3+}$ ions in the relevant crystal field, a conclusion consistent with the x-ray absorption near edge structure analysis. A negligible contribution of Mn in the 2+ charge state points to a low concentration of residual donors in the studied films. Studies on modulation doped p-type (Ga,Mn)N/(Ga,Al)N:Mg heterostructures do not reproduce the high temperature robust ferromagnetism reported recently for this system.Comment: 15 pages, 14 figure

Simultaneous Petri Net Synthesis

Petri net synthesis deals with the problem whether, given a labelled transition system TS, one can find a Petri net N with an initial marking M0 such that the reachability graph of (N. M0) is isomorphic to TS. This may be preceded by a pre-synthesis phase that will quickly reject ill-formed transition systems (and give structural reasons for the failure) and otherwise build data structures needed by the proper synthesis. The last phase proceeds by solving systems of linear inequalities, and may still fail but for less transparent reasons. In this paper, we consider an extended problem. A finite set of transition systems {TS1, ...,TSm} shall be called simultaneously Petri net solvable if there is a single Petri net N with several initial markings {M01,...,M0m}, such that for every i = 1,...,m, the reachability graph of (N, M0i) is isomorphic to TSi. The focus will be on choice-free nets, that is, nets without structural choices, and we explore how previously published efficient algorithms for the pre-synthesis and proper synthesis of bounded and choice-free Petri nets can be generalised for the simultaneous pre-synthesis and synthesis of such multi-marked nets. At the same time, the choice-free pre-synthesis of a single transition system shall be strengthened by introducing new structural checks

Etude télécrânienne des mouvements cervicaux et palatins au cours de la croissance

The sagittal and anterior position of the hyoid bone is at the origin of the changes in orientation of the palatine laminae. A posterior-anterior movement of this bone allows the tongue to liberate the posterior part of the oral cavity; the palatine laminae rotate forwards and downwards. The opposite case is verified in the same way; the naso-palatine canal is a very malleable area, allowing a lowering of the anterior part of the palatine laminae. The vertical variations of the hyoid bone have little effect on the palate.La position sagittale de l’os hyoïde est à l’origine des modifications d’orientation des lames palatines. Ceci a été montré à partir de télécrânes sagittaux. Un mouvement postéro-antérieur de cet os permet à la langue de libérer la partie postérieure de la cavité buccale: les lames palatines font une rotation vers le bas et l’avant. Le contraire se vérifie de la même façon. Le canal naso-palatin est une zone très plastique; il permet un abaissement de la partie antérieure de la lame palatine. Les variations verticales hyoïdiennes influencent peu le palais

Influence du développement vertical du massif facial supérieur sur les différents composants palatins

We put the vertical rotations of the premaxilla and of the hard palate in relation with the vertical development of the maxillary fied. The latter has been evaluated by the changes of length of the right segment that was defined by the prof. Delaire point and its MH1 projection of the hard palate.The vertical variations of the maxillary fields, evaluated from the M-MH1, have an influence on the orientation of the hard palate and the premaxilla in relation to the angle of the pterygoclivian compass.This action is very perceptible at the level of the premaxilla-palatinal junction. It is lower at the level of the hard palate and of the premaxilla when these are separately studied.We got the impression that the front and the back nasal thorns are relatively steady zones during the growth compared to the premaxillo-palatinal junction.Nous avons mis en relation les rotations dans le sens vertical du prémaxillaire et des lames palatines avec le développement vertical du champ maxillaire. Celui-ci a été évalué par les changements de longueur du segment de droite défini par le point M. de DELAIRE et sa projection MH1 sur les lames palatines.Les variations verticales du champ maxillaire, évaluées à partir de MMH1 influencent l'orientation des lames palatines et du prémaxillaire par rapport au compas ptérygo-clivien. Cette action est fort sensible au niveau de la jonction prémaxillo-palatine. Elle est moindre au niveau des lames palatines et du prémaxillaire lorsque ceux-ci sont étudiés séparément.Nous avons tiré l'impression que les épines nasales antérieure et postérieure sont des zones relativement fixes par rapport à la jointure prémaxillopalatine

Shortest Path Problems on a Polyhedral Surface

We develop algorithms to compute shortest path edge sequences, Voronoi diagrams, the Fréchet distance, and the diameter for a polyhedral surface

High-throughput screening of tick-borne pathogens in Europe

Due to increased travel, climatic, and environmental changes, the incidence of tick-borne disease in both humans and animals is increasing throughout Europe. Therefore, extended surveillance tools are desirable. To accurately screen tick-borne pathogens (TBPs), a large scale epidemiological study was conducted on 7050 Ixodes ricinus nymphs collected from France, Denmark, and the Netherlands using a powerful new high-throughput approach. This advanced methodology permitted the simultaneous detection of 25 bacterial, and 12 parasitic species (including; Borrelia, Anaplasma, Ehrlichia, Rickettsia, Bartonella, Candidatus Neoehrlichia, Coxiella, Francisella, Babesia, and Theileria genus) across 94 samples. We successfully determined the prevalence of expected (Borrelia burgdorferi sensu lato, Anaplasma phagocytophilum, Rickettsia helvetica, Candidatus Neoehrlichia mikurensis, Babesia divergens, Babesia venatorum), unexpected (Borrelia miyamotoi), and rare (Bartonella henselae) pathogens in the three European countries. Moreover we detected Borrelia spielmanii, Borrelia miyamotoi, Babesia divergens, and Babesia venatorum for the first time in Danish ticks. This surveillance method represents a major improvement in epidemiological studies, able to facilitate comprehensive testing of TBPs, and which can also be customized to monitor emerging diseases

The Fe-Mg interplay and the effect of deposition mode in (Ga,Fe)N doped with Mg

The effect of Mg codoping and its deposition mode on the Fe distribution in (Ga,Fe)N layers grown by metalorganic vapor phase epitaxy is investigated. Both homogeneously- and digitally-Mg codoped samples are considered and contrasted to the case of (Ga,Fe)N layers obtained without any codoping by shallow impurities. The structural analysis of the layers by high-resolution transmission electron microscopy and by high-resolution- and synchrotron x-ray diffraction gives evidence of the fact that in the case of homogenous-Mg doping, Mg and Fe competitively occupy the Ga-substitutional cation sites, reducing the efficiency of Fe incorporation. Accordingly, the character of the magnetization is modified from ferromagnetic-like in the non-codoped films to paramagnetic in the case of homogeneous Mg codoping. The findings are discussed vis-`a-vis theoretical results obtained by ab initio computations, showing only a weak effect of codoping on the pairing energy of two Fe cations in bulk GaN. However, according to these computations, codoping reverses the sign of the paring energy of Fe cations at the Ga-rich surface, substantiating the view that the Fe aggregation occurs at the growth surface. In contrast to the homogenous deposition mode, the digital one is found to remarkably promote the aggregation of the magnetic ions. The Fe-rich nanocrystals formed in this way are distributed non-uniformly, giving reason for the observed deviation from a standard superparamagnetic behavior.Comment: 13 pages, 14 figure