Minimal chordal sense of direction and circulant graphs

A sense of direction is an edge labeling on graphs that follows a globally consistent scheme and is known to considerably reduce the complexity of several distributed problems. In this paper, we study a particular instance of sense of direction, called a chordal sense of direction (CSD). In special, we identify the class of k-regular graphs that admit a CSD with exactly k labels (a minimal CSD). We prove that connected graphs in this class are Hamiltonian and that the class is equivalent to that of circulant graphs, presenting an efficient (polynomial-time) way of recognizing it when the graphs' degree k is fixed

In vivo assessment of the mechanical properties of the child cortical bone using quantitative computed tomography

The mechanical properties of the rib cortical bone are extremely rare on children due to difficulties to obtain specimens to perform conventional tests. Some recent studies used cadaveric bones or bone tissues collected during surgery but are limited by the number of samples that could be collected. A non-invasive technique could be extremely valuable to overcome this limitation. It has been shown that a relationship exists between the mechanical properties (apparent Young’s modulus and ultimate strength) and the bone mineral density (assessed using Quantitative Computed Tomography, QCT), for the femur and recently by our group for the adult ribs ex vivo. Thus the aim of this study was to assess the mechanical properties of the child rib cortical bone using both QCT images in vivo and the previous relationship between bone mineral density and mechanical properties of the rib cortical bone. Twenty-eight children were included in this study. Seven age-groups have been considered (1, 1.5, 3, 6, 10, 15, 18 years old). The QCT images were prescribed for various thoracic pathologies at the pediatric hospital in Lyon. A calibration phantom was added to the clinical protocol without any modifications for the patient. The protocol was approved by the ethical committee. A 3D reconstruction of each thorax was performed using the QCT images. A custom software was then used to obtain cross-sections to the rib midline. The mean bone mineral density was then computed by averaging the Hounsfield Units in a specific cross-section and by converting the mean value (Hounsfield Units) in bone mineral density using the calibration phantom. This bone mineral density was assessed for the 6th rib of each subject. Our relationship between the bone mineral density and the mechanical properties of the rib cortical bone was used to derive the mechanical properties of the child ribs in vivo. The results give values for the apparent Young’s modulus and the ultimate strength. The mechanical properties increase along growth. As an example the apparent Young’s modulus in the lateral region ranges from 7 GPa +/-3 at 1 year old up to 13 GPa +/- 2 at 18 years old. These data are in agreement with the few previous values obtained from child tissues. This methodology opens the way to in vivo measurement of the mechanical properties of the child cortical bone based on calibrated QCT images

Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph

Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely ADMs. We consider the case when the topology is a unidirectional ring. In graph-theoretical terms, the traffic grooming problem in this case consists in partitioning the edges of a request graph into subgraphs with a maximum number of edges, while minimizing the total number of vertices of the decomposition. We consider the case when the request graph has bounded maximum degree $\Delta$, and our aim is to design a network being able to support any request graph satisfying the degree constraints. The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and solve the cases $\Delta=2$ (for all values of $C$) and $\Delta = 3$ (except the case C=4). We also provide lower and upper bounds for the general case

What do Italian medical students read? A call for a library of good books on physicians for physicians

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Equilibrium crystal shapes in the Potts model

The three-dimensional $q$-state Potts model, forced into coexistence by fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of $q$. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing $q$, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length scale at the melting point.Comment: 6 pages, 3 figures, submitted to PR

Secondary contact and admixture between independently invading populations of the Western corn rootworm, diabrotica virgifera virgifera in Europe

The western corn rootworm, Diabrotica virgifera virgifera (Coleoptera: Chrysomelidae), is one of the most destructive pests of corn in North America and is currently invading Europe. The two major invasive outbreaks of rootworm in Europe have occurred, in North-West Italy and in Central and South-Eastern Europe. These two outbreaks originated from independent introductions from North America. Secondary contact probably occurred in North Italy between these two outbreaks, in 2008. We used 13 microsatellite markers to conduct a population genetics study, to demonstrate that this geographic contact resulted in a zone of admixture in the Italian region of Veneto. We show that i) genetic variation is greater in the contact zone than in the parental outbreaks; ii) several signs of admixture were detected in some Venetian samples, in a Bayesian analysis of the population structure and in an approximate Bayesian computation analysis of historical scenarios and, finally, iii) allelic frequency clines were observed at microsatellite loci. The contact between the invasive outbreaks in North-West Italy and Central and South-Eastern Europe resulted in a zone of admixture, with particular characteristics. The evolutionary implications of the existence of a zone of admixture in Northern Italy and their possible impact on the invasion success of the western corn rootworm are discussed

Vicinal silicon surfaces: from step density wave to faceting

This paper investigates faceting mechanisms induced by electromigration in the regime where atomic steps are transparent. For this purpose we study several vicinal orientations by means of in-situ (optical diffraction, electronic microscopy) as well as ex-situ (AFM, microprofilometry) visualization techniques. The data show that faceting proceeds in two stages. The first stage is short and leads to the appearance of a step density wave, with a wavelength roughly independent of the surface orientation. The second stage is much slower, and leads to the formation of a hill-and-valley structure, the period of which depends on the initial surface orientation. A simple continuum model enables us to point out why the wavelength of the step density wave does not depend on the microscale details of the surface. The final wavelength is controlled by the competition between elastic step-step interaction and facet edge energy cost. Finally, the surface stress angular dependence is shown to emerge as a coarsed-grained picture from the step model.Comment: 26 pages, 9 figure

Measuring the surface stress polar dependence

While measurements of the polar dependence of the surface free energy are easily available, measurements of the whole polar dependence of the surface stress of a crystal do not exist. In this paper is presented a new procedure that allows, for the first time, the experimental determination of the surface stress polar dependence of a crystal. For this purpose (1) electromigration is used to control the kinetic faceting of surface orientations that belong to the equilibrium shape of the crystal and (2) for each destabilised surface, the period of faceting as well as the crystallographic angles of the appearing facets are measured by AFM. The so-obtained data lead to a set of equations whose mathematical solution, compatible with physical constraints, gives access to the surface stress polar dependence of the whole crystal and thus to a better understanding of surface stress properties.Comment: 8 pages, 6 Figure