Fast rate of convergence in high dimensional linear discriminant analysis

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when dimension p is larger than sample size n. The corresponding theoretical results are non asymptotic lower bounds. On the other hand, we propose two discrimination procedures based on dimensionality reduction and provide associated rates of convergence which can be O(log(p)/n) under sparsity assumptions. Finally all our results rely on a theorem that provides simple sharp relations between the excess risk and an estimation error associated to the geometric parameters defining the used discrimination rule

Segmentation d'images hyper-spectrales

Ce travail a été effectué dans le cadre du projet "Méthode de Classification et Imagerie par Ondelettes : Aide au diagnostic pour les tumeurs cérébrales" financé par la région Rhône-Alpes et en collaboration avec l'INSERM Unité 594, et le service IRM du CHU de Grenoble.National audienceNous présentons un algorithme de segmentation d'images hyper-spectrales supposées constantes par régions. Cet algorithme est composé de trois phases. La première est une phase de débruitage inspirée d'une méthode adaptative de lissage pondéré fondée sur une segmentation par croissance de régions, la deuxième se sert des paramètres obtenus lors du débruitage de la première phase et a pour but de produire une estimation des contours des régions connexes issues du débruitage. La dernière étape de l'algorithme consiste à fusionner les régions issues de la deuxième phase en minimisant une version pénalisée de l'erreur quadratique de reconstruction. La méthodologie est illustrée sur des données simulées d'imagerie de résonance magnétique nucléaire

Courtly Love and Its Counterparts in the Medieval Mediterranean

At least since Stendhal\u27s De l\u27Amour, scholars have argued that the theories of courtly love expressed in the Old French literature of the High Middle Ages were inspired by or drew upon elements of Islamicate culture. In this dissertation, I explore the theories of love represented in works of literature, lover\u27s manuals and medical treatises composed in and around the late twelfth–century court of Marie de Champagne, which I read in conjunction with contemporaneous works from the Islamicate world, ranging from Al‑Andalus to Persia, in order to show how these works reflect the common cultural orientation of the medieval Mediterranean. By showing that the theories of amatory practice described in Andreas Capellanus\u27s De amore cannot be accounted for exclusively from within the Ovidian tradition, I posit that by viewing the Old French theories of courtly love as a synthesis of the earlier Ovidian and Islamicate traditions, as represented by Ibn Hazm’s Tawq al‑Hamāma, we can better understand the place of courtly love within the constellation of medieval Mediterranean cultures. This conclusion serves as the point of departure for my subsequent analyses as I endeavor to show that the Tristan legend drew heavily upon the Persianate epic, Vīs u Rāmīn, a claim I substantiate through a comparision between those two works and Chrétien de Troyes\u27s anti-Tristan, Cligès. Further, I maintain that the act of literary appropriation, whether through inspiration or translation, remained an active process that sought to recontextualize and adapt content to the needs of its new cultural milieu. I then focus on the routes of pilgrimage and trade that spanned and linked the fragmented spaces of Christian and Islamic Mediterraneans and that made such cultural and literary exchanges possible accross political, cultural, religion and linguistic borders. I do this through a study of the “Tale of Niʿma and Nuʿm” from the Alf Layla wa Layla and its old French adaptation, the Conte de Floire et Blancheflor by Robert d\u27Orbigny. There were, however, limits to the influence of Islamicate thought on the representation of love in Old French literature as is evinced in medical discourse: although theoretical medicine was revolutionized by the translation of medical treatises sich as Constantinus Africanus\u27s eleventh-century Viaticum peregrinantis, literary love-discourse resisted change. Even as theories of love and lovesickness were redefined in light of this new medical knowledge, I demonstrate that the literary representation of love medicine continued to cleave to older, Ovidian tropes through the middle of the thirteenth century. By focusing on theories of love, which intersect with as disparate domains as theology and law, politics and science, I am able to show the ways in which Old French literature engages with and extends contemporaneous cultural and literary trends within the Islamicate world, thereby resituating it in its Mediterranean context

Forecasting Uncertainty Related to Ramps of Wind Power Production

International audienceThe continuous improvement of the accuracy of wind power forecasts is motivated by the increasing wind power integration. Today forecasters are challenged in providing forecasts able to handle extreme situations. This paper presents two methods focusing on forecasting large and sharp variations in power output of a wind farm called ramps. The fi rst one provides probabilistic forecasts using large temporal scales information about ramps. The second method uses ensembles to generate con dence intervals allowing to better estimate the timing of ramps. The two methods are tested and results are given for a real case study

The impact of electricity market schemes on predictability being a decision factor in the wind farm investment phase

International audienceWind power production forecasts over the next hours to days ahead are a prerequisite for the secure and economic operation of power systems with high wind power penetration. For wind power producers who participate in a day-ahead electricity market, low predictability of wind production results in imbalance costs. This influences the revenue, and in turn, the pay back of the investment. The aim of this work is to evaluate the role of wind power predictability versus the traditional used criterion of capacity factor on the investment phase of a wind farm and on spatial planning in an electricity market context. The study cases of OMEL and PJM markets are considered to generalize the results of the West Denmark (DK1) case study in order to quantify the impact of predictability. In the three studies, we find that the role of capacity factor in explaining the revenue is greatly more important than the predictability (more than 99% in comparison with 0.05% for predictability in OMEL, 0.04% in NordPool and, in average, 0.001% for PJM)

Stochastic power generation

International audienceOur path towards decarbonisation involves the large-scale use of renewable sources - the most prominent contributions being from wind and solar, followed by biomass - to gradually replace fossil fuels for energy production, mainly in the form of heat and electricity. By June 2012, cumulative installed wind power capacity worldwide had reached 254 GW and was still increasing rapidly gives an extensive introduction to various forms of renewable energy sources among our potential options for the future ..

Assessment of wind power predictability as a decision factor in the investment phase of wind farms

International audienceThe ability to predict wind power production over the next few hours to days is prerequisites for the secure and economic operation of power systems with high wind power penetration. From the point of view of a producer participating in the day-ahead electricity market, lack of predictability at a wind power production site results in imbalance costs. This paper aims at quantifying the impact on market revenue of, respectively, the predictability and the capacity factor of a wind farm or a cluster of wind farms. This is done through a real-life case study in West Denmark, including wind farm production data and market data. Finally, we make a prospective analysis under the assumption that the imbalance price settlement mechanism will remain the sam

A Novel Methodology for comparison of different wind power ramp characterization approaches

International audienceWind power forecasting is recognized as a means to facilitate large scale wind power integration into power systems. Recently, focus has been given on developing dedicated short-term forecasting approaches for the case of large and sharp wind power variations, so-called ramps. Accurate forecasts of specific ramp characteristics (e.g. timing, probability of occurrence, etc) are important since the related forecast errors may lead to potentially large power imbalances, with high impact to the power system. Various works about ramps' periodicity or predictability have led to the development of new characterization approaches. The evaluation of these approaches has often been neglected, leading to potentially irrelevant conclusions on ramps characteristics, or ineffective forecasting approaches. In this work, we propose a comprehensive framework for evaluating and comparing different characterization approaches of wind power ramps

Wind farm strategic investment considering forecast errors penalties in a nodal prices market

International audienceIn this work, we determine the optimal investment strategy of a wind producer in a local prices environment, taking into account the penalties for real-time imbalances. We assume these imbal- ances come from forecast errors on the considered renewable production only. To do so, we solve a bilevel optimization problem. The upper level problem corresponds to the revenue of the con- sidered producer, and the lower level problems correspond to the market clearings, taking place a day ahead of operations and on real-time. Indeed, we consider that imbalances penalties cor- respond to real-time prices such as is done in the American market PJM. Indeed, in a local prices framework, using real-time prices is a simple way to recover the financial amounts corresponding to the imbalances in power

Multi-temporal Optimal Power Flow for Assessing the Renewable Generation Hosting Capacity of an Active Distribution System

International audienceThe detailed modeling of distribution grids is expected to be critical to understand the current functionality limits and necessary retrofits to satisfy integration of massive amounts of distributed generation, energy storage devices and the electric consumption demand of the future. Due to the highly dimensional non-convex characteristics of the power flow equations, convex relaxations have been used to ensure an efficient calculation time. However, these relaxations have been proven to be inexact during periods of high RES injection. In this paper additional linear constraints were introduced in the power flow formulation to guaranty an exact relaxation. This convex relaxation is then applied within a multi-temporal algorithm in order to evaluate the benefits of storage grid integration. The case study of a French medium voltage feeder is studied to evaluate the maximum capacity of the grid to host RES sources and the advantages of storage systems in reducing curtailment of RES