Packing and Hausdorff measures of stable trees

In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991) which corresponds to the Brownian case. We provide results for the whole stable trees and for their level sets that are the sets of points situated at a given distance from the root. We first show that there is no exact packing measure for levels sets. We also prove that non-Brownian stable trees and their level sets have no exact Hausdorff measure with regularly varying gauge function, which continues previous results from a joint work with J-F Le Gall (2006).Comment: 40 page

Influence of the common mode impedance paths on the design of the EMI filters used with SiC-buck converter

This paper deals the design of EMI filter associated with buck converter using fast semiconductors silicon carbide SiC (diode and transistor JFET). To comply with EMC standards, a filter design method based on an equivalent electrical circuit is proposed. The aim is to identify the different values of the EMI filter elements but also to obtain the limits values of the parasitic elements of the passive components which have a major influence on the attenuation of the filters. The purpose is to study the influence of the modification of the common mode propagation paths before and after the installation of the filter. A solution is also proposed to reduce the conducted disturbances that occur at high frequency caused by the fast SiC components.The comparison of the simulation results with the measurements data carried out on a DC-DC converter without and with the EMI filter, shows the effectiveness of the proposed design approach

Ischiofemoral impingement: the evolutionary cost of pelvic obstetric adaptation.

Funder: Flemmish research foundationThe risk for ischiofemoral impingement has been mainly related to a reduced ischiofemoral distance and morphological variance of the femur. From an evolutionary perspective, however, there are strong arguments that the condition may also be related to sexual dimorphism of the pelvis. We, therefore, investigated the impact of gender-specific differences in anatomy of the ischiofemoral space on the ischiofemoral clearance, during static and dynamic conditions. A random sampling Monte-Carlo experiment was performed to investigate ischiofemoral clearance during stance and gait in a large (n = 40 000) virtual study population, while using gender-specific kinematics. Subsequently, a validated gender-specific geometric morphometric analysis of the hip was performed and correlations between overall hip morphology (statistical shape analysis) and standard discrete measures (conventional metric approach) with the ischiofemoral distance were evaluated. The available ischiofemoral space is indeed highly sexually dimorphic and related primarily to differences in the pelvic anatomy. The mean ischiofemoral distance was 22.2 ± 4.3 mm in the females and 29.1 ± 4.1 mm in the males and this difference was statistically significant (P < 0.001). Additionally, the ischiofemoral distance was observed to be a dynamic measure, and smallest during femoral extension, and this in turn explains the clinical sign of pain in extension during long stride walking. In conclusion, the presence of a reduced ischiofemroal distance and related risk to develop a clinical syndrome of ischiofemoral impingement is strongly dominated by evolutionary effects in sexual dimorphism of the pelvis. This should be considered when female patients present with posterior thigh/buttock pain, particularly if worsened by extension. Controlled laboratory study

Dual random fragmentation and coagulation and an application to the genealogy of Yule processes

The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the description of the genealogy of Yule processes.Comment: 14 page

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

The backbone decomposition for spatially dependent supercritical superprocesses

Consider any supercritical Galton-Watson process which may become extinct with positive probability. It is a well-understood and intuitively obvious phenomenon that, on the survival set, the process may be pathwise decomposed into a stochastically `thinner' Galton-Watson process, which almost surely survives and which is decorated with immigrants, at every time step, initiating independent copies of the original Galton-Watson process conditioned to become extinct. The thinner process is known as the backbone and characterizes the genealogical lines of descent of prolific individuals in the original process. Here, prolific means individuals who have at least one descendant in every subsequent generation to their own. Starting with Evans and O'Connell, there exists a cluster of literature describing the analogue of this decomposition (the so-called backbone decomposition) for a variety of different classes of superprocesses and continuous-state branching processes. Note that the latter family of stochastic processes may be seen as the total mass process of superprocesses with non-spatially dependent branching mechanism. In this article we consolidate the aforementioned collection of results concerning backbone decompositions and describe a result for a general class of supercritical superprocesses with spatially dependent branching mechanisms. Our approach exposes the commonality and robustness of many of the existing arguments in the literature

On Exceptional Times for generalized Fleming-Viot Processes with Mutations

If $\mathbf Y$ is a standard Fleming-Viot process with constant mutation rate (in the infinitely many sites model) then it is well known that for each $t>0$ the measure $\mathbf Y_t$ is purely atomic with infinitely many atoms. However, Schmuland proved that there is a critical value for the mutation rate under which almost surely there are exceptional times at which $\mathbf Y$ is a finite sum of weighted Dirac masses. In the present work we discuss the existence of such exceptional times for the generalized Fleming-Viot processes. In the case of Beta-Fleming-Viot processes with index $\alpha\in\,]1,2[$ we show that - irrespectively of the mutation rate and $\alpha$ - the number of atoms is almost surely always infinite. The proof combines a Pitman-Yor type representation with a disintegration formula, Lamperti's transformation for self-similar processes and covering results for Poisson point processes

Effect of binder on performance of intumescent coatings

This study investigates the role of the polymeric binder on the properties and performance of an intumescent coating. Waterborne resins of different types (vinylic, acrylic, and styrene-acrylic) were incorporated in an intumescent paint formulation, and characterized extensively in terms of thermal degradation behavior, intumescence thickness, and thermal insulation. Thermal microscopy images of charred foam development provided further information on the particular performance of each type of coating upon heating. The best foam expansion and heat protection results were obtained with the vinyl binders. Rheological measurements showed a complex evolution of the viscoelastic characteristics of the materials with temperature. As an example, the vinyl binders unexpectedly hardened significantly after thermal degradation. The values of storage moduli obtained at the onset of foam blowing (melamine decomposition) were used to explain different intumescence expansion behaviors.Funding for this work was provided by FCT-Fundacao para a Ciencia e Tecnologia (Project PTDC/EQU-EQU/65300/2006), and by FEDER/QREN (project RHED) in the - framework of Programa Operacional Factor de Competitividade-COMPETE. Joana Pimenta thanks FCT for PhD Grant SFRH/BDE/33431/2008

The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences

We define three hard problems in the theory of elliptic divisibility sequences (EDS Association, EDS Residue and EDS Discrete Log), each of which is solvable in sub-exponential time if and only if the elliptic curve discrete logarithm problem is solvable in sub-exponential time. We also relate the problem of EDS Association to the Tate pairing and the MOV, Frey-R\"{u}ck and Shipsey EDS attacks on the elliptic curve discrete logarithm problem in the cases where these apply.Comment: 18 pages; revised version includes some small mathematical corrections, reformatte

A simple proof of Duquesne's theorem on contour processes of conditioned Galton-Watson trees

We give a simple new proof of a theorem of Duquesne, stating that the properly rescaled contour function of a critical aperiodic Galton-Watson tree, whose offspring distribution is in the domain of attraction of a stable law of index $\theta \in (1,2]$, conditioned on having total progeny $n$, converges in the functional sense to the normalized excursion of the continuous-time height function of a strictly stable spectrally positive L\'evy process of index $\theta$. To this end, we generalize an idea of Le Gall which consists in using an absolute continuity relation between the conditional probability of having total progeny exactly $n$ and the conditional probability of having total progeny at least $n$. This new method is robust and can be adapted to establish invariance theorems for Galton-Watson trees having $n$ vertices whose degrees are prescribed to belong to a fixed subset of the positive integers.Comment: 16 pages, 2 figures. Published versio