Large systems of path-repellent Brownian motions in a trap at positive temperature

We study a model of $N$ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from escaping to infinity, and a pair-interaction Hamiltonian, which imposes a repellency of the $N$ paths. In fact, this interaction is an $N$-dependent regularisation of the Brownian intersection local times, an object which is of independent interest in the theory of stochastic processes. The time horizon (interpreted as the inverse temperature) is kept fixed. We analyse the model for diverging number of Brownian motions in terms of a large deviation principle. The resulting variational formula is the positive-temperature analogue of the well-known Gross-Pitaevskii formula, which approximates the ground state of a certain dilute large quantum system; the kinetic energy term of that formula is replaced by a probabilistic energy functional. This study is a continuation of the analysis in \cite{ABK04} where we considered the limit of diverging time (i.e., the zero-temperature limit) with fixed number of Brownian motions, followed by the limit for diverging number of motions. \bibitem[ABK04]{ABK04} {\sc S.~Adams, J.-B.~Bru} and {\sc W.~K\"onig}, \newblock Large deviations for trapped interacting Brownian particles and paths, \newblock {\it Ann. Probab.}, to appear (2004)

Tesserae: A Search Engine for Allusion

The Tesserae Project is an interdisciplinary research effort employing computational methods to detect and analyze literary allusion (a form of text reuse) currently focusing on Latin and ancient Greek. The Project seeks funding to create a fully-functional, publicly available tool to detect similar phrases in two texts at rates that approach those of literary commentators. To this end, funding will support adding sensitivity to word meaning, phrase context, and sound similarity. Detection rate improvements will be measured against a set of 3000 parallel phrases previously graded for literary significance. A revised website will inform researchers of research results and new functions of the tool. The project team will give presentations and produce publications explaining the function, results, and theoretical consequences of the fully operational tool. This work is preliminary to an out-year Implementation Phase that will see the addition of English, French, Italian, and Spanish

Modeling the Role of Polysemy in Verb Categorization

Recent work has indicated that static word embeddings can predict human semantic categories (Majewska et al. 2021). In this paper, we consider the role of polysemy in semantic categorization, by comparing sense-level embeddings with previously studied static embeddings in their prediction of human-produced categories. We find that the polysemy is crucial for predicting human categories; sense-level embeddings dramatically outperform static embeddings in predicting semantic categories. Our findings highlight the role of polysemy in semantic categorization that is exclusively based on linguistic input

Oxygen reduction at thin dense La0.52Sr0.48Co0.18Fe0.82O3- δ electrodes: Part I: Reaction model and faradaic impedance

The faradaic impedance of oxygen reduction has been simulated for thin dense two-dimensional $${\text{La}}_{{0.52}} {\text{Sr}}_{{0.48}} {\text{Co}}_{{0.18}} {\text{Fe}}_{{0.82}} {\text{O}}_{{3 - \delta }}$$ electrodes in air at 600°C. The reaction model accounts for the defect chemistry of the ceramic films and includes bulk and surface pathways. It was demonstrated that the contribution of the surface pathway to the reaction was negligible due to the small length of triple phase boundary gas/electrode/electrolyte. The diffusion of oxygen in the bulk of $${\text{La}}_{{0.52}} {\text{Sr}}_{{0.48}} {\text{Co}}_{{0.18}} {\text{Fe}}_{{0.82}} {\text{O}}_{{3 - \delta }}$$ (LSCF) can be evidenced by measuring the polarization resistance as a function of the electrode thickness that ranged between 10 and 800nm. When recorded as a function of the electrode potential and thickness, the frequency response exhibited features that were specific to the rate-determining steps of the reaction. The oxygen reduction mechanism and kinetics can therefore be identified by means of impedance spectroscopy. The faradaic impedances calculated for realistic values of the rate constants exhibited a noteworthy large faradaic capacitanc

Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes

International audienceWe present a new method of magnification for textured images featuring scale invariance properties. This work is originally motivated by an application to astronomical images. One goal is to propose a method to quantitatively predict statistical and visual properties of images taken by a forthcoming higher resolution telescope from older images at lower resolution. This is done by performing a virtual super resolution using a family of scale invariant stochastic processes, namely compound Poisson cascades, and fractional integration. The procedure preserves the visual aspect as well as the statistical properties of the initial image. An augmentation of information is performed by locally adding random small scale details below the initial pixel size. This extrapolation procedure yields a potentially infinite number of magnified versions of an image. It allows for large magnification factors (virtually infinite) and is physically conservative: zooming out to the initial resolution yields the initial image back. The (virtually) super resolved images can be used to predict the quality of future observations as well as to develop and test compression or denoising techniques

Amélioration virtuelle de la résolution d'images du Soleil par augmentation d'information invariante d'échelle

4 pagesNational audienceCurrent images of the quiet Sun from the spatial telescope EIT are such that 1 pixel = (1800km)2 whereas the smallest physical scales would be of about 100 m. The design of a high resolution spatial telescope where 1 pixel = (80 km)2 is planned. With a resolution 25 times finer, the images may be under-exposed or even useless. The point is to predict at best the quality of these images from the current observations. We exploit the scale invariance properties of images currently available to suggest a method to artificially improve (of a potentially infinite factor) the current images resolution by integrating details from a multifractal stochastic model. Quiet Sun images are magnified by a factor 32 while preserving the multiscale properties (spectrum, multiscaling) and assuring that reducing the magnified image gives the initial image back. We deduce from that an extrapolation of histograms of high resolution images allowing a prediction of the quality of images from a future high resolution telescope

Multipath study on the airport surface

International audienceAirport Navigation will require more stringent localization performance requirements than in-flight navigation [1]. GNSS signals (Global Navigation Satellites Systems) can be envisaged to elaborate the aircraft estimate position on the airport surface. To improve the performance of localization on the airport, the errors on GNSS signals particular to the airport environment must be characterized. Most of these errors are well known such as ionosphere error, troposphere error, etc, and do not depend on the airport environment. But to achieve the expected sub-metric performance, it is necessary to better model multipath error for which a model already exists but is valid for operations from en-route down to CAT I only. In this paper, an analysis of real GPS measurements (using code pseudo range measurement, carrier phase measurement, Doppler measurement and the estimate C/N0 ratio measurement) during taxiing operation on the airport surface is conducted. The goal of this paper is to evaluate when multipath occurs and to compare the multipath model (elaborated from the standard deviation of the measurement errors due to multipath) based on those collected measurements in the airport with different models proposed in the literature (not necessary proposed for airport navigation)