Quasi-optimal multiplication of linear differential operators

We show that linear differential operators with polynomial coefficients over a field of characteristic zero can be multiplied in quasi-optimal time. This answers an open question raised by van der Hoeven.Comment: To appear in the Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS'12

Chebyshev Expansions for Solutions of Linear Differential Equations

A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation lets us give a simple view of previous algorithms, analyze their complexity, and design a faster one for large orders

Présentation de la Maquette Retraites MARS-2003

This paper describes the model MARS, which is the shared property of the DP and the DSS. Currently, MARS aims at planning the general evolution of the first pillar pension scheme for private sector wage-earners, based on macroeconomic and demographic data. It allows to evaluate the impact of changing the parameters used when calculating one’s annuities, or changing general hypotheses. The model provides results which deal with the dynamics of the average annuity and the financial sustainability of the pension scheme. MARS relies on a macroeconomic approach and aims at forecasting the life cycle of average individuals representing their generation. In concrete terms, each generation is represented by two agents (a man and a woman), whose behaviour is supposed to match the average economic and demographic characteristics of their peers (as far as fertility, activity and employment are concerned). In addition, another source of heterogeneity is acknowledged in the model concerning the retirement age, the distribution of which is determined endogenously. Then the evolution of the representative annuity, calculated on the basis of these data, is considered to reflect the dynamics of the average annuity – and at this stage, sustainability indicators for the pension scheme can be inferred. First, the document introduces the demographic and macroeconomic framework of the model, which basically relies on the population and labour force projections of the INSEE, and takes the Conseil d’Orientation des Retraites scenario as a benchmark for the evolution of real wages and unemployment. The making of the retirement decision is a key feature of the model : it is assumed that men will retire when reaching entitlement to the full rate, and that the male and female distributions of retirement ages will match from the 1970 generation onwards. On the basis of these hypotheses, the average pension and the financing requirement of the pension scheme can be evaluated. As an illustration, the results of two variants are displayed: one deals with the impact of the lengthening of the contribution period which results from the August 2003 Act, the other one shows the sensitiveness of the results to alternative demographic scenarios. We conclude about the weaknesses of the model, which is based on the lifecycle of average individuals, and the flaws associated to a macroeconomic approach, versus a dynamic microsimulation one. Besides, MARS should encounter new limits, due to non-linear effects and deeper uncertainty associated to changes in the method used to calculate pensions after the 2003 reform. This paper is written in French.long term forecast, modeling of pay as you go pension schemes

Model Driven Mutation Applied to Adaptative Systems Testing

Dynamically Adaptive Systems modify their behav- ior and structure in response to changes in their surrounding environment and according to an adaptation logic. Critical sys- tems increasingly incorporate dynamic adaptation capabilities; examples include disaster relief and space exploration systems. In this paper, we focus on mutation testing of the adaptation logic. We propose a fault model for adaptation logics that classifies faults into environmental completeness and adaptation correct- ness. Since there are several adaptation logic languages relying on the same underlying concepts, the fault model is expressed independently from specific adaptation languages. Taking benefit from model-driven engineering technology, we express these common concepts in a metamodel and define the operational semantics of mutation operators at this level. Mutation is applied on model elements and model transformations are used to propagate these changes to a given adaptation policy in the chosen formalism. Preliminary results on an adaptive web server highlight the difficulty of killing mutants for adaptive systems, and thus the difficulty of generating efficient tests.Comment: IEEE International Conference on Software Testing, Verification and Validation, Mutation Analysis Workshop (Mutation 2011), Berlin : Allemagne (2011

Automatic difference measure between movies using dissimilarity measure fusion and rank correlation coefficients

International audienceWhen considering multimedia database growth, one current challenging issue is to design accurate navigation tools. End user basic needs, such as exploration, similarity search and favorite suggestions, lead to investigate how to find semantically resembling media. One way is to build numerous continuous dissimilarity measures from low-level image features. In parallel, an other way is to build discrete dissimilarities from textual information which may be available with video sequences. However, how such different measures should be selected as relevant and be fused ? To this aim, the purpose of this paper is to compare all those various issimilarities and to propose a suitable ranking fusion method for several dissimilarities. Subjective tests with human observers on the CITIA animation movie database have been carried out to validate the model

Analyse de trajectoires pour l'indexation sémantique des vidéos à grande échelle

National audienceL'indexation sémantique automatique de grandes collections vidéo est un problème complexe qui ne peut se limiter à l'analyse de mots clefs saisis par les utilisateurs. L'extraction de descripteurs spatiaux et temporels à partir du contenu est devenu indispensable pour appréhender la grande richesse des contenus. Cependant, le coût de calcul associé à l'extraction de descriptions temporelles est bloquant et les systèmes actuels se limitent souvent au traitement de l'information spatiale. Dans ces travaux, nous proposons une méthode d'analyse de trajectoires de points caractéristiques. Ses besoins en ressources de calcul sont faibles et s'adaptent facilement à de grandes collections vidéo. Partant d'une description des trajectoires de points d'intérêt utilisant l'analyse du flot optique, une batterie de descripteurs basés sur les modèles Sac de Mots sont calculés pour représenter les vidéos. L'approche est évaluée dans le contexte difficile du challenge TRECVid Semantic INdexing (SIN)

Intervalles de prévision de vente de produit avec historique nul ou limité

Cet article introduit une méthode de calcul d’intervalles de prévision de vente pour des nouveaux produits sans historique de vente avant leur mise en marché et dont la chronique se construit progressivement au fil des jours dès l’amorce de la saison de vente. Cette méthode permet d’estimer, à l’aide d’un intervalle, les ventes futures d’un nouveau produit pour toute la saison de vente, notamment dans le but d’aider la prise de décision de réapprovisionnement visant à maximiser les ventes et la profitabilité

Asteroid Taxonomy from Cluster Analysis of Spectrometry and Albedo

The classification of the minor bodies of the Solar System based on observables has been continuously developed and iterated over the past 40 years. While prior iterations followed either the availability of large observational campaigns or new instrumental capabilities opening new observational dimensions, we see the opportunity to improve primarily upon the established methodology. We developed an iteration of the asteroid taxonomy which allows the classification of partial and complete observations (i.e. visible, near-infrared, and visible-near-infrared spectrometry) and which reintroduces the visual albedo into the classification observables. The resulting class assignments are given probabilistically, enabling the uncertainty of a classification to be quantified. We built the taxonomy based on 2983 observations of 2125 individual asteroids, representing an almost tenfold increase of sample size compared with the previous taxonomy. The asteroid classes are identified in a lower-dimensional representation of the observations using a mixture of common factor analysers model. We identify 17 classes split into the three complexes C, M, and S, including the new Z-class for extremely-red objects in the main belt. The visual albedo information resolves the spectral degeneracy of the X-complex and establishes the P-class as part of the C-complex. We present a classification tool which computes probabilistic class assignments within this taxonomic scheme from asteroid observations. The taxonomic classifications of 6038 observations of 4526 individual asteroids are published. The ability to classify partial observations and the reintroduction of the visual albedo provide a taxonomy which is well suited for the current and future datasets of asteroid observations, in particular provided by the Gaia, MITHNEOS, NEO Surveyor, and SPHEREx surveys.Comment: Published in Astronomy and Astrophysics. The table of asteroid classifications and the templates of the defined taxonomic classes are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/665/A2