A non-adapted sparse approximation of PDEs with stochastic inputs

We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems (with slow decay in the spectrum)

«La relation de limitation et d’exception dans le français d’aujourd’hui : excepté, sauf et hormis comme pivots d’une relation algébrique »

L’analyse des emplois prépositionnels et des emplois conjonctifs d’ “excepté”, de “sauf” et d’ “hormis” permet d’envisager les trois prépositions/conjonctions comme le pivot d’un binôme, comme la plaque tournante d’une structure bipolaire. Placées au milieu du binôme, ces prépositions sont forcées par leur sémantisme originaire dûment métaphorisé de jouer le rôle de marqueurs d’inconséquence systématique entre l’élément se trouvant à leur gauche et celui qui se trouve à leur droite. L’opposition qui surgit entre les deux éléments n’est donc pas une incompatibilité naturelle, intrinsèque, mais extrinsèque, induite. Dans la plupart des cas (emplois limitatifs), cette opposition prend la forme d’un rapport entre une « classe » et le « membre (soustrait) de la classe », ou bien entre un « tout » et une « partie » ; dans d’autres (emplois exceptifs), cette opposition se manifeste au contraire comme une attaque de front portée par un « tout » à un autre « tout ». De plus, l’inconséquence induite mise en place par la préposition/conjonction paraît, en principe, tout à fait insurmontable. Dans l’assertion « les écureuils vivent partout, sauf en Australie » (que l’on peut expliciter par « Les écureuils vivent partout, sauf [qu’ils ne vivent pas] en Australie »), la préposition semble en effet capable d’impliquer le prédicat principal avec signe inverti, et de bâtir sur une telle implication une sorte de sous énoncé qui, à la rigueur, est totalement inconséquent avec celui qui le précède (si « les écureuils ne vivent pas en Australie », le fait qu’ils « vivent partout » est faux). Néanmoins, l’analyse montre qu’alors que certaines de ces oppositions peuvent enfin être dépassées, d’autres ne le peuvent pas. C’est, respectivement, le cas des relations limitatives et des relations exceptives. La relation limitative, impliquant le rapport « tout » - « partie », permet de résoudre le conflit dans les termes d’une somme algébrique entre deux sous énoncés pourvus de différent poids informatif et de signe contraire. Les valeurs numériques des termes de la somme étant déséquilibrées, le résultat est toujours autre que zéro. La relation exceptive, au contraire, qui n’implique pas le rapport « tout » - « partie », n’est pas capable de résoudre le conflit entre deux sous énoncés pourvus du même poids informatif et en même temps de signe contraire : les valeurs numériques des termes de la somme étant symétriques et égales, le résultat sera toujours équivalent à zéro

Prox-regularity of rank constraint sets and implications for algorithms

We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank exactly equal to $s$. The normal cone formula appears to be new. This allows for easy application of prior results guaranteeing local linear convergence of the fundamental alternating projection algorithm between sets, one of which is a rank constraint set. We apply this to show local linear convergence of another fundamental algorithm, approximate steepest descent. Our results apply not only to linear systems with rank constraints, as has been treated extensively in the literature, but also nonconvex systems with rank constraints.Comment: 12 pages, 24 references. Revised manuscript to appear in the Journal of Mathematical Imaging and Visio

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Metal free fluoroamination of allylsilanes: A route to 3-fluoropyrrolidines

The intramolecular fluoroamination of homoallylic amines activated by a triisopropylsilyl or p-tolyldiisopropylsilyl group was successfully performed in the presence of Selectfluor® in acetonitrile leading to anti or syn 3-fluoropyrrolidines. The stereochemical outcome of these fluorocyclizations is dictated by the geometry of the alkene precursor. In comparison with oxygen nucleophile, the use of N-tosyl or N-Boc nucleophiles benefits from superior control over stereoselectivity but suffers from competitive fluorodesilylation. © 2012 Elsevier B.V. All rights reserved

Model - based and Experimental Analysis of the Symmetry in Human Walking in Different Device Carrying Modes

The advent of embedded sensors and their low cost integration in handheld devices (e.g. smartphones) are making them increasingly aware of the human location and context. There have been attempts to extract certain gait features (e.g. step length, step frequency etc.) based on data recorded from handheld devices. However, these attempts have been mostly inspired from observations in biomechanics. Hence, there is a profound need to study the modeling of human walking gait cycle while taking into account the different device carrying modes. It is hypothesized that the presence of handheld device in one hand can alter the step level symmetry of human walking gait cycle without affecting the stride level symmetry. The aim of this paper is to present a model of human walking gait cycle in different device carrying modes over a stride, which is based on parametric optimization technique used in robotics motion generation and the results of a preliminary experimentation conducted using motion capture technology. Both simulation and pilot experiments confirm that the presence of a small mass in one hand can affect the step level symmetry of the human walking gait which constitutes the novel outcome of this paper. Overall, the model successfully captures human walking features and can stand useful for the enhancement of existing pedestrian navigation algorithms with handheld devices for an increased autonomy of elderly people and pedestrian's mobility in general

Conformational analysis of fluorinated pyrrolidines using 19F-1H scalar couplings and heteronuclear NOEs.

A series of 3-fluoropyrrolidines have been studied to investigate the influence of the stereoelectronic fluorine gauche effect on ring conformations in the solid state by single-crystal X-ray analysis and in solution phase by NMR spectroscopy. As part of these studies 1D (19)F-(1)H heteronuclear NOE (HOESY) experiments have been optimised for applications to small molecules and are described in detail. These have been employed to estimate (19)F-(1)H internuclear distances and were combined with vicinal (3)J(F,H) and (3)J(H,H) scalar coupling constants to analyse the ring conformations. Where possible the derived solution-phase structural data have been compared with those of the crystalline state. The results demonstrate the influence of the gauche effect in stabilising C(γ)-exo conformations of the fluorinated pyrrolidines. It was further shown that when steric interactions were also present, this conformational bias was diminished and the contribution of the alternative C(γ)-endo conformation was seen to increase in solution at lower sample temperatures