Triangle percolation in mean field random graphs -- with PDE

We apply a PDE-based method to deduce the critical time and the size of the giant component of the ``triangle percolation'' on the Erd\H{o}s-R\'enyi random graph process investigated by Palla, Der\'enyi and VicsekComment: Summary of the changes made: We have changed a remark about k-clique percolation in the first paragraph. Two new paragraphs are inserted after equation (4.4) with two applications of the equation. We have changed the names of some variables in our formula

Exponential Upper Bounds via Martingales for Multiplexers with Markovian Arrivals.

We obtain explicit upper bounds in closed form for the queue length in a slotted time FCFS queue in which the service requirement is a sum of independent Markov processes on the state space {O, 1}, with integral service rate. The bound is of the form P[queue length ≥ b] ≤ cy^(-b) for any b ≥ 1 where c 1 are given explicitly in terms of the parameters of the model. The model can be viewed as an approximation for the burst-level component of the queue in an ATM multiplexer. We obtain heavy traffic bounds for the mean queue length and show that for typical parameters this far exceeds the mean queue length for independent arrivals at the same load. We compare our results on the mean queue length with an analytic expression for the case of unit service rate, and compare our results on the full distribution with computer simulations

Geodynamo alpha-effect derived from box simulations of rotating magnetoconvection

The equations for fully compressible rotating magnetoconvection are numerically solved in a Cartesian box assuming conditions roughly suitable for the geodynamo. The mean electromotive force describing the generation of mean magnetic flux by convective turbulence in the rotating fluid is directly calculated from the simulations, and the corresponding alpha-coefficients are derived. Due to the very weak density stratification the alpha-effect changes its sign in the middle of the box. It is positive at the top and negative at the bottom of the convection zone. For strong magnetic fields we also find a clear downward advection of the mean magnetic field. Both of the simulated effects have been predicted by quasi-linear computations (Soward, 1979; Kitchatinov and Ruediger, 1992). Finally, the possible connection of the obtained profiles of the EMF with mean-field models of oscillating alpha^2-dynamos is discussed.Comment: 17 pages, 9 figures, submitted to Phys. Earth Planet. Inte

Directed polymers on a Cayley tree with spatially correlated disorder

In this paper we consider directed walks on a tree with a fixed branching ratio K at a finite temperature T. We consider the case where each site (or link) is assigned a random energy uncorrelated in time, but correlated in the transverse direction i.e. within the shell. In this paper we take the transverse distance to be the hierarchical ultrametric distance, but other possibilities are discussed. We compute the free energy for the case of quenched disorder and show that there is a fundamental difference between the case of short range spatial correlations of the disorder which behaves similarly to the non-correlated case considered previously by Derrida and Spohn and the case of long range correlations which has a totally different overlap distribution which approaches a single delta function about q=1 for large L, where L is the length of the walk. In the latter case the free energy is not extensive in L for the intermediate and also relevant range of L values, although in the true thermodynamic limit extensivity is restored. We identify a crossover temperature which grows with L, and whenever T<T_c(L) the system is always in the low temperature phase. Thus in the case of long-ranged correlation as opposed to the short-ranged case a phase transition is absent.Comment: 23 pages, 1 figure, standard latex. J. Phys. A, accepted for publicatio

Pour un échantillonnage et un conseil agronomique raisonné, les outils d'aide à la décision

To a sampling and personal fertility advice, the tools for decision support. Environmental and agronomic issues require always more well thought and suited farmer management of agricultural inputs; soil analysis is therefore an essential tool to support decision. However, for a soil analysis to provide valuable information, it is essential for the sample to be representative of the studied field. Without this representativeness, an analytical result, as accurate as it could be, would not be of interest if it could mislead the farmer. In practice, the main difficulty for the sampler is the recognition of soil criteria which are essential to provide a fertility advice, especially in Wallonia (Belgium) where soil variability is very important. With the Digital Soil Map of Wallonia (DSMW), drowned at the scale 1/5,000, it seems appropriate to give these information to the samplers in an useful form for routine works. That is why a mapping tool for decision support, named REQUACARTO, was designed to be used for soil analysis by provincial laboratories, members of the REQUASUD laboratories network. This tool responds to a real requirement in Wallonia: achieving a quality sampling for the development of personalized soil fertility advice

Fractional moment bounds and disorder relevance for pinning models

We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(.) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form K(n)=n^{-\alpha-1}L(n), with L(.) slowly varying. The model undergoes a (de)-localization phase transition: the free energy (per unit length) is zero in the delocalized phase and positive in the localized phase. For \alpha<1/2 it is known that disorder is irrelevant: quenched and annealed critical points coincide for small disorder, as well as quenched and annealed critical exponents. The same has been proven also for \alpha=1/2, but under the assumption that L(.) diverges sufficiently fast at infinity, an hypothesis that is not satisfied in the (1+1)-dimensional wetting model considered by Forgacs et al. (1986) and Derrida et al. (1992), where L(.) is asymptotically constant. Here we prove that, if 1/21, then quenched and annealed critical points differ whenever disorder is present, and we give the scaling form of their difference for small disorder. In agreement with the so-called Harris criterion, disorder is therefore relevant in this case. In the marginal case \alpha=1/2, under the assumption that L(.) vanishes sufficiently fast at infinity, we prove that the difference between quenched and annealed critical points, which is known to be smaller than any power of the disorder strength, is positive: disorder is marginally relevant. Again, the case considered by Forgacs et al. (1986) and Derrida et al. (1992) is out of our analysis and remains open.Comment: 20 pages, 1 figure; v2: few typos corrected, references revised. To appear on Commun. Math. Phy

Traitement médical de l’endométriose douloureuse sans infertilité, RPC Endométriose CNGOF-HAS

OBJECTIVE: To provide clinical practice guidelines for the management of painful endometriosis in women without infertility. METHODS: Systematic review of the literature literature since 2006, level of evidence rating, external proofreading and grading of the recommendation grade by an expert group according to HAS methodology. RESULTS: Combined hormonal contraceptives (COP) and the levonorgestrel-releasing intra-uterin system (LNG-IUS) are recommended as first-line hormonal therapies for the treatment of painful endometriosis (grade B). Second-line therapy relies on oral desogestrel microprogestative, etonogestrel-releasing implant, GnRH analogs (GnRHa) and dienogest (grade C). It is recommended to use add-back therapy containing estrogen in association with GnRHa (grade B). After endometriosis surgery, hormonal treatment relying on COP or LNG-IUS is recommended to prevent pain recurrence (grade B). COP is recommended to reduce the risk of endometrioma recurrence after surgery (grade B) but the prescription of GnRHa is not recommended (grade C). Continuous COP is recommended in case of dysmenorrhea (grade B). GnRHa is not recommended as first line endometriosis treatment for adolescent girl because of the risk of bone demineralization (grade B). The management of endometriosis-induced chronic pain requires an interdisciplinary evaluation. Physical therapies improving the quality of life such as yoga, relaxation or osteopathy can be proposed (expert agreement). Promising medical alternatives are currently under preclinical and clinical evaluation

Gaussian field theories, random Cantor sets and multifractality

The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian field theories in terms of random Cantor sets and show how universal multifractal scaling exponents can be calculated. We use this approach to characterize the multifractal critical wave function of Dirac fermions interacting with a random vector potential in two spatial dimensions. We show that the multifractal scaling exponents are self-averaging.Comment: Extensive modifications of previous version; exact results replace numerical calculation

Instability of Bose-Einstein condensation into the one-particle ground state on quantum graphs under repulsive perturbations

In this Note we investigate Bose-Einstein condensation in interacting quantum many-particle systems on graphs. We extend previous results obtained for particles on an interval and show that even arbitrarily small repulsive two-particle interactions destroy a condensate in the non-interacting Bose gas. Our results also cover singular two-particle interactions, such as the well-known Lieb-Lininger model, in the thermodynamic limit

Deep subcutaneous application of poly-L-lactic acid as a filler for facial lipoatrophy in HIV-infected patients

Introduction: Facial lipoatrophy is a crucial problem of HIV-infected patients undergoing highly active antiretroviral therapy (HAART). Poly-L-lactic acid (PLA), provided as New-Fill(R)/Sculptra(TM), is known as one possible treatment option. In 2004 PLA was approved by the FDA as Sculptra(TM) for the treatment of lipoatrophy of the face in HIV-infected patients. While the first trials demonstrated relevant efficacy, this was to some extent linked to unwanted effects. As the depth of injection was considered relevant in this context, the application modalities of the preparation were changed. The preparation was to be injected more deeply into subcutaneous tissue, after increased dilution. Material and Methods: To test this approach we performed a pilot study following the new recommendations in 14 patients. Results: While the efficacy turned out to be about the same, tolerability was markedly improved. The increase in facial dermal thickness was particularly obvious in those patients who had suffered from lipoatrophy for a comparatively small period of time. Conclusion: With the new recommendations to dilute PLA powder and to inject it into the deeper subcutaneous tissue nodule formation is a minor problem. However, good treatment results can only be achieved if lipoatrophy is not too intense; treatment intervals should be about 2 - 3 weeks. Copyright (C) 2005 S. Karger AG, Basel