The degree distribution in bipartite planar maps: applications to the Ising model

We characterize the generating function of bipartite planar maps counted according to the degree distribution of their black and white vertices. This result is applied to the solution of the hard particle and Ising models on random planar lattices. We thus recover and extend some results previously obtained by means of matrix integrals. Proofs are purely combinatorial and rely on the idea that planar maps are conjugacy classes of trees. In particular, these trees explain why the solutions of the Ising and hard particle models on maps of bounded degree are always algebraic.Comment: 32 pages, 15 figure

Creating a center for global health at the University of Wisconsin-Madison.

Globalization, migration, and widespread health disparities call for interdisciplinary approaches to improve health care at home and abroad. Health professions students are pursuing study abroad in increasing numbers, and universities are responding with programs to address these needs. The University of Wisconsin (UW)-Madison schools of medicine and public health, nursing, pharmacy, veterinary medicine, and the division of international studies have created an interdisciplinary center for global health (CGH). The CGH provides health professions and graduate students with courses, field experiences, and a new Certificate in Global Health. Educational programs have catalyzed a network of enthusiastic UW global health scholars. Partnerships with colleagues in less economically developed countries provide the foundation for education, research, and service programs. Participants have collaborated to improve the education of health professionals and nutrition in Uganda; explore the interplay between culture, community development, and health in Ecuador; improve animal health and address domestic violence in Mexico; and examine successful public health efforts in Thailand. These programs supply students with opportunities to understand the complex determinants of health and structure of health systems, develop adaptability and cross-cultural communication skills, experience learning and working in interdisciplinary teams, and promote equity and reduce health disparities at home and abroad. Based on the principles of equity, sustainability, and reciprocity, the CGH provides a strong foundation to address global health challenges through networking and collaboration among students, staff, and faculty within the UW and beyond

Statistical properties of Kernel Prinicipal Component Analysis

International audienceWe study the properties of the eigenvalues of Gram matrices in a non-asymptotic setting. Using local Rademacher averages, we provide data-dependent and tight bounds for their convergence towards eigenvalues of the corresponding kernel operator. We perform these computations in a functional analytic framework which allows to deal implicitly with reproducing kernel Hilbert spaces of infinite dimension. This can have applications to various kernel algorithms, such as Support Vector Machines (SVM). We focus on Kernel Principal Component Analysis (KPCA) and, using such techniques, we obtain sharp excess risk bounds for the reconstruction error. In these bounds, the dependence on the decay of the spectrum and on the closeness of successive eigenvalues is made explicit

An alternative competing risk model to the Weibull distribution in lifetime data analysis

A simple competing risk distribution as a possible alternative to the Weibull distribution in lifetime analysis is proposed. This distribution corresponds to the minimum between exponential and Weibull distributions. Our motivation is to take account of both accidental and aging failures in lifetime data analysis. First, the main characteristics of this distribution are presented. Then the estimation of its parameters are considered through maximum likelihood and Bayesian inference. Decision tests to choose between an exponential, Weibull and this competing risk distribution are presented. And this alternative model is compared to the Weibull model from numerical experiments on both real and simulated data sets

Effect of Intraspecific Competition and Substrate Type on Terpene Emissions from Some Mediterranean Plant Species

International audienceCompetition is an important factor that has been extensively reported in the Mediterranean area. There is evidence that leaf terpene accumulation may vary between plants growing on calcareous and siliceous soils. In the present study, leaf terpene emissions from potted seedlings of Pinus halepensis, Cistus albidus, and Quercus coccifera, growing under natural environmental conditions on calcareous and siliceous substrates, were studied by using a bag enclosure method. In both substrates, seedlings were potted alone and in intraspecific competition, to examine the effect of substrate type and that of intraspecific competition on terpene emissions. The results showed that competition favored: (i) overall monoterpene and sesquiterpene emissions from Q. coccifera; (ii) overall monoterpene emissions from P. halepensis; (iii) overall sesquiterpene emissions from C. albidus. Substrate type affected terpene emissions to a limited extent and in a species-specific way. Whereas for Q. coccifera, the overall monoterpene emissions and that of Allo-aromadendrene were favored on siliceous substrate, no significant changes were found in emissions from P. halepensis. Only the release of AR-curcumene from C. albidus was higher on siliceous substrate. We also found high variability in terpene emission composition from the study species, particularly for P. halepensis and Q. coccifera. These two species released both monoterpenes and sesquiterpenes, instead of monoterpenes only, as shown in previous studies

Bayesian inference for inverse problems occurring in uncertainty analysis

The inverse problem considered here is to estimate the distribution of a non-observed random variable $X$ from some noisy observed data $Y$ linked to $X$ through a time-consuming physical model $H$. Bayesian inference is considered to take into account prior expert knowledge on $X$ in a small sample size setting. A Metropolis-Hastings within Gibbs algorithm is proposed to compute the posterior distribution of the parameters of $X$ through a data augmentation process. Since calls to $H$ are quite expensive, this inference is achieved by replacing $H$ with a kriging emulator interpolating $H$ from a numerical design of experiments. This approach involves several errors of different nature and, in this paper, we pay effort to measure and reduce the possible impact of those errors. In particular, we propose to use the so-called DAC criterion to assess in the same exercise the relevance of the numerical design and the prior distributions. After describing how computing this criterion for the emulator at hand, its behavior is illustrated on numerical experiments.Le problème inverse considéré est d'estimer la distribution d'une variable aléatoire non observée $X$ à partir d'observations bruitées $Y$, à l'aide d'un modèle physique d'obtention coûteuse $H$. Le cadre bayésien nous permet de prendre en compte les connaissances préalables d'experts surtout avec peu de données disponibles. Un échantillonneur de Gibbs combiné avec l'algorithme de Metropolis-Hastings est utilisé pour approcher la distribution a posteriori de $X$. La fonction coûteuse $H$ est remplacée par un émulateur de krigeage (méta-modèle) $\widehat{H}$ basé sur un plan d'expérience ({\it design}). Cette approche implique plusieurs erreurs de nature différente et, dans ce rapport, nous nous attachons à estimer et réduire l'impact de ces erreurs. En particulier, nous proposons d'utiliser le critère \DAC pour évaluer la qualité du design ainsi que le choix de la loi a priori. Après avoir décrit le calcul de ce critère, son comportement est illustré par les expériences numériques

SOFA: A Multi-Model Framework for Interactive Physical Simulation

International audienceSOFA (Simulation Open Framework Architecture) is an open-source C++ library primarily targeted at interactive computational medical simulation. SOFA facilitates collaborations between specialists from various domains, by decomposing complex simulators into components designed independently and organized in a scenegraph data structure. Each component encapsulates one of the aspects of a simulation, such as the degrees of freedom, the forces and constraints, the differential equations, the main loop algorithms, the linear solvers, the collision detection algorithms or the interaction devices. The simulated objects can be represented using several models, each of them optimized for a different task such as the computation of internal forces, collision detection, haptics or visual display. These models are synchronized during the simulation using a mapping mechanism. CPU and GPU implementations can be transparently combined to exploit the computational power of modern hardware architectures. Thanks to this flexible yet efficient architecture, \sofa{} can be used as a test-bed to compare models and algorithms, or as a basis for the development of complex, high-performance simulators