Gravitating superconducting strings with timelike or spacelike currents

We construct gravitating superconducting string solutions of the U(1)_{local} x U(1)_{global} model solving the coupled system of Einstein and matter field equations numerically. We study the properties of these solutions in dependence on the ratio between the symmetry breaking scale and the Planck mass. Using the macroscopic stability conditions formulated by Carter, we observe that the coupling to gravity allows for a new stable region that is not present in the flat space-time limit. We match the asymptotic metric to the Kasner metric and show that the relations between the Kasner coefficients and the energy per unit length and tension suggested previously are well fulfilled for symmetry breaking scale much smaller than the Planck mass. We also study the solutions to the geodesic equation in this space-time. While geodesics in the exterior space-time of standard cosmic strings are just straight lines, test particles experience a force in a general Kasner space-time and as such bound orbits are possible.Comment: 16 pages including 14 figure

Sur la forme de la boule unit\'{e} de la norme stable unidimensionnelle

For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are completely described by combinatorial properties of the graph. We study then the realizable forms as stable ball of Riemannan manifolds of dimension larger than three. For a Riemannian manifold $(M, g)$ fixed, we show that a broad class of polytopes can appear as stable ball of metrics in the conformal class of $g$. We use for that a polyhedral technique.Comment: 13 pages, in Frenc

Double tungstate lasers: From bulk toward on-chip integrated waveguide devices

It has been recognized that the monoclinic double tungstates $KY{(WO_4)}_2$, $KGd{(WO_4)}_2$, and $KLu{(WO_4)}_2$ possess a high potential as rare-earth-ion-doped solid-state laser materials, partly due to the high absorption and emission cross sections of rare-earth ions when doped into these materials. Besides, their high refractive indexes make these materials potentially suitable for applications that require optical gain and high power in integrated optics, with rather high integration density. We review the recent advances in the field of bulk lasers in these materials and present our work toward the demonstration of waveguide lasers and their integration with other optical structures on a chip

Detecting seasonal variations in seismic velocities within Los Angeles basin from correlations of ambient seismic noise.

International audienceWe analyze 3 years of continuous seismic records from broadband stations of the Caltech Regional Seismic Network (CI) in vicinity of the Los Angeles basin. Using correlations of ambient seismic noise, relative velocity variations in the order of 0.1 % can be measured between all inter-station pairs. It is the first time that such an extensive study between 861 inter-station pairs over such a large area has been carried out. We perform these measurements using the 'stretching' technique, assuming that one of the two waveforms is merely a stretched version of the other. Obviously this assumption is always violated and the two waveforms are generally decorrelated due to temporal changes in the Earth crust, due to different sources or simply because the cross-correlations are not fully converged. We investigate the stability of these measurements by repeating each measurement over various time-windows of equal length. On average between all inter-station pairs in the Los Angeles basin a seasonal signal in the relative velocity variation is observed, with peaks and troughs during winter and summer time respectively. Generally the observed signal decreases with increasing inter-station distance and relative travel-time perturbations can only be measured up to an inter-station distance of 60 km. Furthermore the travel-time perturbations do not depend on azimuth of station pairs, suggesting that they are not related to seasonal variations of the noise sources. Performing a simple regionalization by laterally averaging measurements over a subset of stations we found the sedimentary basin showing the most consistent signal and conclude that the observed seasonality might be induced either by changes in the ground-water aquifer or thermo-elastic strain variations that persist down to a depth of 15-22 km

Monitoring edge-geodetic sets in graphs

We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in order to detect and prevent failures. Inspired by two notions studied in the literature (edge-geodetic sets and distance-edge-monitoring sets), we define the notion of a monitoring edge-geodetic set (MEG-set for short) of a graph $G$ as an edge-geodetic set $S\subseteq V(G)$ of $G$ (that is, every edge of $G$ lies on some shortest path between two vertices of $S$) with the additional property that for every edge $e$ of $G$, there is a vertex pair $x, y$ of $S$ such that $e$ lies on \emph{all} shortest paths between $x$ and $y$. The motivation is that, if some edge $e$ is removed from the network (for example if it ceases to function), the monitoring probes $x$ and $y$ will detect the failure since the distance between them will increase. We explore the notion of MEG-sets by deriving the minimum size of a MEG-set for some basic graph classes (trees, cycles, unicyclic graphs, complete graphs, grids, hypercubes,...) and we prove an upper bound using the feedback edge set of the graph

Valeurs de références photogrammétriques faciales angulaires et esthétiques du jeune adulte bantu congolais de Kinshasa en normocclusion dentaire: Angular and esthetic facial photogrammetric peculiarities in young Bantu Congolese adults with dental normocclusion in Kinshasa

Context and objective. The relevance of facial morphometric reference values is pivotal in the diagnosis and therapeutic approach in orthodontic practice. Ethnic disparities are not yet established in our country. This pilot study aimed to describe the facial morphological angular peculiarities and those related to the aesthetic analyzes of the cutaneous profile of the young adult congolese Bantu with dental normocclusion. Methods. A cross-sectional study enrolled 156 young Congolese adults (males, 54.4%), with a mean age of 24.6 (range 18-30 years), randomly selected among Dental medicine students having complete permanent dentition and molar Class I dental occlusion. Collected data included the angles of the face and aesthetic analyzes. Standardized lateral photographic images were were considered for photogrammetric measurements. Student t test allowed statistical analysis. Results. Sexual dimorphism was observed in 10; out of 17 assessed variables. A relatively important method error was observed for the nasolabial and labio-mental angles. Two areas of fluctuation of mean values related to the sex were established in the form of polygons, providing orthodontic practitioners with an opportunity allowing quantification and localization of dysmorphoses. Conclusion. The current study relaying on photogrammetric data of the face highlights morphological facial angular and aesthetic peculiarities in young adult Congolese Bantu related to sexual dimorphism. Lateral photographs stand thus as a relevant alternative tool in the assessement of reference values of the Congolese subject's facial skin profile for diagnosis and therapeutic purposes.  Contexte et objectif. En pratique orthodontique, les valeurs morpho-métriques de références de la face sont essentielles dans le diagnostic et la prise en charge thérapeutique des populations. Ces valeurs montrant une variabilité ethnique ne sont pas encore connues dans notre pays. La présente étude avait pour objectif de décrire les particularités morphologiques angulaires de la face et celles relatives aux analyses esthétiques du profil cutané du jeune adulte bantu congolais en normocclusion dentaire. Méthodes. Dans une étude descriptive transversale, des jeunes adultes bantus congolais sélectionnés aléatoirement parmi les étudiants de Médecine dentaire ayant une denture permanente complète et en occlusion dentaire de classe I molaire ont été examinés. Les paramètres d’intérêt comprenaient les données angulaires de la face et esthétiques. Des images photographiques latérales standardisées, ainsi que des mensurations photogrammétriques ont été réalisées. Le test de student a été utilisé pour les analyses statistiques selon le cas. Résultats. 156 étudiants ont été enrolés. Leur age moyen était de 24,5 ans (hommes 54,4%). Un dimorphisme sexuel a été observé dans dix des dix-sept variables évaluées. Une erreur de la méthode relativement importante a été observée pour les angles naso-labial (Pr-Sn-Ls) et labio-mentonnier (Li-Sm-Pog). Deux aires de fluctuation des valeurs moyennes suivant le sexe, sous forme de polygones, ont été proposées aux praticiens orthodontiques et pourront permettre de quantifier et localiser les dysmorphoses. Conclusion. La présente étude utilisant les données photogrammétriques du visage a illustré des particularités morphologiques faciales angulaires et esthétiques chez le jeune adulte bantu congolais liées au dimorphisme sexuel. Ainsi, les photographies latérales peuvent être une alternative fiable pour la détermination des valeurs normatives du profil cutané facial du sujet congolais et servir de référence pour la démarche diagnostique et thérapeutique

Parameterizing Path Partitions

We study the algorithmic complexity of partitioning the vertex set of a given (di)graph into a small number of paths. The Path Partition problem (PP) has been studied extensively, as it includes Hamiltonian Path as a special case. The natural variants where the paths are required to be either \emph{induced} (Induced Path Partition, IPP) or \emph{shortest} (Shortest Path Partition, SPP), have received much less attention. Both problems are known to be NP-complete on undirected graphs; we strengthen this by showing that they remain so even on planar bipartite directed acyclic graphs (DAGs), and that SPP remains \NP-hard on undirected bipartite graphs. When parameterized by the natural parameter ``number of paths'', both SPP and IPP are shown to be W{1}-hard on DAGs. We also show that SPP is in \XP both for DAGs and undirected graphs for the same parameter, as well as for other special subclasses of directed graphs (IPP is known to be NP-hard on undirected graphs, even for two paths). On the positive side, we show that for undirected graphs, both problems are in FPT, parameterized by neighborhood diversity. We also give an explicit algorithm for the vertex cover parameterization of PP. When considering the dual parameterization (graph order minus number of paths), all three variants, IPP, SPP and PP, are shown to be in FPT for undirected graphs. We also lift the mentioned neighborhood diversity and dual parameterization results to directed graphs; here, we need to define a proper novel notion of directed neighborhood diversity. As we also show, most of our results also transfer to the case of covering by edge-disjoint paths, and purely covering.Comment: 27 pages, 8 figures. A short version appeared in the proceedings of the CIAC 2023 conferenc

Determinants of contraceptive methods use after voluntary induced abortion at the Yaounde Central Hospital, Cameroon

Background: Abortion is the termination of pregnancy with expulsion of the product of conception before the age of fetal viability- 28 weeks. In Africa, 96% of abortions are unsafe and there is an estimated 1 death for 150 abortions. Few data are available in Cameroon on the determinants of contraception after a voluntary termination of pregnancy. The objective of this study to investigate the determinants of the use of contraceptive methods after a voluntary termination of pregnancy.Methods: The study was descriptive cross-sectional lasting 09 months in the gynecology and obstetrics unit of the Yaounde Central Hospital. We included women admitted to this unit who have already had at least one abortion. All women who did not give their consent were excluded. The data were entered and analyzed using the Epi-info software version 7.2.2.6. The tools used to express our results were the Student's and Whitney's test, the Wald test and the Odd ratios (OR) with their 95% confidence interval. The significance level was 5%.Results: Out of 139 participants, 86 (61.87%) had already used a modern contraceptive method after voluntary termination of pregnancy. The mean age was 27.13±6.16 years with extremes of 16 and 42 years. Being single and having unwanted pregnancies independently increased contraceptive method use after abortions.Conclusions: An intensification of campaigns for behaviour change and men's involvement would further improve the use of contraceptive methods after abortion