Random walk driven by the simple exclusion process

We prove a strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $\gamma$. First, we establish that if the asymptotic velocity of the walker is non-zero in the limiting case "$\gamma = \infty$", where the environment gets fully refreshed between each step of the walker, then, for $\gamma$ large enough, the walker still has a non-zero asymptotic velocity in the same direction. Second, we establish that if the walker is transient in the limiting case $\gamma = 0$, then, for $\gamma$ small enough but positive, the walker has a non-zero asymptotic velocity in the direction of the transience. These two limiting velocities can sometimes be of opposite sign. In all cases, we show that the fluctuations are normal.Comment: v2 -> v3: Figures and heuristic comments added. Various typos correcte

Multi-Paradigm Reasoning for Access to Heterogeneous GIS

Accessing and querying geographical data in a uniform way has become easier in recent years. Emerging standards like WFS turn the web into a geospatial web services enabled place. Mediation architectures like VirGIS overcome syntactical and semantical heterogeneity between several distributed sources. On mobile devices, however, this kind of solution is not suitable, due to limitations, mostly regarding bandwidth, computation power, and available storage space. The aim of this paper is to present a solution for providing powerful reasoning mechanisms accessible from mobile applications and involving data from several heterogeneous sources. By adapting contents to time and location, mobile web information systems can not only increase the value and suitability of the service itself, but can substantially reduce the amount of data delivered to users. Because many problems pertain to infrastructures and transportation in general and to way finding in particular, one cornerstone of the architecture is higher level reasoning on graph networks with the Multi-Paradigm Location Language MPLL. A mediation architecture is used as a “graph provider” in order to transfer the load of computation to the best suited component – graph construction and transformation for example being heavy on resources. Reasoning in general can be conducted either near the “source” or near the end user, depending on the specific use case. The concepts underlying the proposal described in this paper are illustrated by a typical and concrete scenario for web applications

Gradient Scan Gibbs Sampler: an efficient algorithm for high-dimensional Gaussian distributions

This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set of directions. The algorithm is proved to converge, i.e. the drawn samples are asymptotically distributed according to the target distribution. Our main motivation is in inverse problems related to general linear observation models and their solution in a hierarchical Bayesian framework implemented through sampling algorithms. It finds direct applications in semi-blind/unsupervised methods as well as in some non-Gaussian methods. The paper provides an illustration focused on the unsupervised estimation for super-resolution methods.Comment: 18 page

Coffee-stain growth dynamics on dry and wet surfaces

The drying of a drop containing particles often results in the accumulation of the particles at the contact line. In this work, we investigate the drying of an aqueous colloidal drop surrounded by a hydrogel that is also evaporating. We combine theoretical and experimental studies to understand how the surrounding vapor concentration affects the particle deposit during the constant radius evaporation mode. In addition to the common case of evaporation on an otherwise dry surface, we show that in a configuration where liquid is evaporating from a flat surface around the drop, the singularity of the evaporative flux at the contact line is suppressed and the drop evaporation is homogeneous. For both conditions, we derive the velocity field and we establish the temporal evolution of the number of particles accumulated at the contact line. We predict the growth dynamics of the stain and the drying timescales. Thus, dry and wet conditions are compared with experimental results and we highlight that only the dynamics is modified by the evaporation conditions, not the final accumulation at the contact line

Independent Resampling Sequential Monte Carlo Algorithms

Sequential Monte Carlo algorithms, or Particle Filters, are Bayesian filtering algorithms which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on Importance Sampling with a bootstrap resampling step which aims at struggling against weights degeneracy. However, in some situations (informative measurements, high dimensional model), the resampling step can prove inefficient. In this paper, we revisit the fundamental resampling mechanism which leads us back to Rubin's static resampling mechanism. We propose an alternative rejuvenation scheme in which the resampled particles share the same marginal distribution as in the classical setup, but are now independent. This set of independent particles provides a new alternative to compute a moment of the target distribution and the resulting estimate is analyzed through a CLT. We next adapt our results to the dynamic case and propose a particle filtering algorithm based on independent resampling. This algorithm can be seen as a particular auxiliary particle filter algorithm with a relevant choice of the first-stage weights and instrumental distributions. Finally we validate our results via simulations which carefully take into account the computational budget

Semi-independent resampling for particle filtering

Among Sequential Monte Carlo (SMC) methods,Sampling Importance Resampling (SIR) algorithms are based on Importance Sampling (IS) and on some resampling-based)rejuvenation algorithm which aims at fighting against weight degeneracy. However %whichever the resampling technique used this mechanism tends to be insufficient when applied to informative or high-dimensional models. In this paper we revisit the rejuvenation mechanism and propose a class of parameterized SIR-based solutions which enable to adjust the tradeoff between computational cost and statistical performances