Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation

We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural smoothness parameters of an associated Riemannian manifold. We then apply the method with the manifold defined by the log barrier function to the problems of (1) uniformly sampling a polytope and (2) computing its volume, the latter by extending Gaussian cooling to the manifold setting. In both cases, the total number of steps needed is O^{*}(mn^{\frac{2}{3}}), improving the state of the art. A key ingredient of our analysis is a proof of an analog of the KLS conjecture for Gibbs distributions over manifolds

Electrical transport in high contrast composite materials

Journal ArticleA broad range of problems in the physics of materials involve highly disordered media whose effective behavior depends critically on the connectedness, or percolation properties of a particular component. Examples include smart materials such as piezoresistors and thermistors, smart insulators, radar absorbing composites, cermets, porous media, doped semiconductors, thin metal films, and sea ice

Monthly variation in the probability of presence of adult Culicoides populations in nine European countries and the implications for targeted surveillance

Background: Biting midges of the genus Culicoides (Diptera: Ceratopogonidae) are small hematophagous insects responsible for the transmission of bluetongue virus, Schmallenberg virus and African horse sickness virus to wild and domestic ruminants and equids. Outbreaks of these viruses have caused economic damage within the European Union. The spatio-temporal distribution of biting midges is a key factor in identifying areas with the potential for disease spread. The aim of this study was to identify and map areas of neglectable adult activity for each month in an average year. Average monthly risk maps can be used as a tool when allocating resources for surveillance and control programs within Europe. Methods : We modelled the occurrence of C. imicola and the Obsoletus and Pulicaris ensembles using existing entomological surveillance data from Spain, France, Germany, Switzerland, Austria, Denmark, Sweden, Norway and Poland. The monthly probability of each vector species and ensembles being present in Europe based on climatic and environmental input variables was estimated with the machine learning technique Random Forest. Subsequently, the monthly probability was classified into three classes: Absence, Presence and Uncertain status. These three classes are useful for mapping areas of no risk, areas of high-risk targeted for animal movement restrictions, and areas with an uncertain status that need active entomological surveillance to determine whether or not vectors are present. Results: The distribution of Culicoides species ensembles were in agreement with their previously reported distribution in Europe. The Random Forest models were very accurate in predicting the probability of presence for C. imicola (mean AUC = 0.95), less accurate for the Obsoletus ensemble (mean AUC = 0.84), while the lowest accuracy was found for the Pulicaris ensemble (mean AUC = 0.71). The most important environmental variables in the models were related to temperature and precipitation for all three groups. Conclusions: The duration periods with low or null adult activity can be derived from the associated monthly distribution maps, and it was also possible to identify and map areas with uncertain predictions. In the absence of ongoing vector surveillance, these maps can be used by veterinary authorities to classify areas as likely vector-free or as likely risk areas from southern Spain to northern Sweden with acceptable precision. The maps can also focus costly entomological surveillance to seasons and areas where the predictions and vector-free status remain uncertain

APPROXIMATIONS FOR AND CONVEXITY OF PROBABILISTICALLY CONSTRAINED PROBLEMS WITH RANDOM RIGHT-HAND SIDES

Abstract. We consider probabilistically constrained problems, in which the multivariate random variables are located in the right-hand sides. The objective function is linear, and its optimization is subject to a set of linear constraints as well as a joint probabilistic constraint enforcing that the joint fulfillment of a system of linear inequalities with random right-hand side variables be above a prescribed probability level p. To deal with such complex problems, we describe a solving method based on the pefficiency concept for discretely distributed random variables, and also propose some alternative formulations applicable to both discrete and continuous probability distributions, and involving the substitution of the joint probabilistic constraint by a set of individual constraints, the Boole’s inequality, the binomial moment bounding scheme, and Slepian’s inequality, respectively. The common advantage of these formulations is that they involve the computation of joint probabilistic constraints of lower dimension than this of the joint probabilistic constraint included in the original formulation. We analyze their computational tractability, and evaluate their constraining power relying on three datasets, in which random variables have a normal distribution. We then prove that the function E [ ε −Txε − T x> 0] i i enforcing a reliability level di is concave except for very large (small) values of Tix (di). We study th