Averaging and Deterministic Optimal Control

International audienceAveraging is often used in ordinary differential equations when dealing with fast periodic phenomena. It is shown here that it can be used efficiently in optimal control. As the period tends to zero, a limit or "averaged" problem is defined. The open loop optimal control of the limit problem induces a cost which is optimal up to the second order when evaluated through the original dynamics. The definition of the averaged problem is then generalized to the nonperiodic case. It is shown that the Bellman function of the original "fast" problem tends uniformly on any compact set to that of the averaged problem

The Averaging Homotopy

Classical averaging is an asymptotic theory in the sense that it con- siders the problem of finding a limit for a sequence of differential systems. We present here another formulation that is based on an homotopy be- tween any two vectorfields. This formulation accounts both for classical averaging and for regular perturbations. It can also be used to justify the use of numerical windowed averaging schemes without any asymptotic imbedding

Redundant wavelet filter banks on the half-axis with applications to signal denoising with small delays

International audienceA wavelet transform on the negative half real axis is developed using an average-interpolation scheme. This transform is redundant and can be used to perform causal wavelet processing, such as signal denoising, without delay. Nonetheless, in practice some boundary effects occur and thus a small amount of delay is required to reduce them. The theory is implemented on a challenging signal with large noise and sharp transients. Results from the experimental implementation of the proposed algorithm for the denoising of a feedback signal for controlling a three-phase permanent-magnet synchronous brushless DC motor are also presented

Redundant wavelet processing on the half-axis with applications to signal denoising with small delays: Theory and experiments

International audienceA wavelet transform on the negative half real axis is developed using an average-interpolation scheme. This transform is redundant and can be used to perform causal wavelet processing, such as on-line signal denoising, without delay. Nonetheless, in practice some boundary effects occur and thus a small amount of delay is required to reduce them. The effect of this delay is studied using a numerical example of a signal with large noise and sharp transients. It is shown that the delay required to obtain acceptable denoising levels is decreased by using the proposed redundant transform instead of a non-redundant one. We also present results from the experimental implementation of the proposed algorithm for the denoising of a feedback signal during the control of a three-phase permanent-magnet synchronous brushless DC motor

Thermal building model identification using time-scaled identification methods

International audienceThe aim of this paper is to propose a robust and accurate method for the parametric identification of the thermal behaviour of low consumption buildings. These buildings are known to have a two-time scale structure, which, if not handled properly, results in poor conditioning of the parametric identification. We compare three identification methods, one uses the data on the whole frequency domain (ARX) when the other methods use the same data but separated on local frequency domain (time scaled methods). All three methods identify a reduced second order model. Robustness is tested by corrupting the input and output before the identification, and comparing the simulation results for the various models and the original uncorrupted input. The numerical results clearly show that the time scaled methods are superior both in accuracy (noise free identification and simulation) and robustness (when identification is performed on corrupted data)

Generalization of the interaction between the Haar approximation and polynomial operators to higher order methods

International audienceIn applications it is useful to compute the local average of a function f(u) of an input u from empirical statistics on u. A very simple relation exists when the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation

The Adibox Study: Adiposity and Bone Metabolism: Effects of Exercise-induced Weight Loss in Adolescents with Obesity

Introduction: This program of research targeted the impact of an 8-month weight loss intervention induced by physical activity and nutrition on bone health in adolescents with obesity. The overall aim of this thesis was to examine the impact of a lifestyle weight loss intervention on the bone parameters in adolescents with obesity. Method: Sixty-five adolescents were recruited: 31 (6 males) adolescents with obesity in the weight loss intervention (age: 13.61 (1.27)), 23 normal weight (NW) adolescents (age: 15.90 (0.43)) and 11 (4 males) adolescents with obesity in another control group (14.02 (1.39)). Primary outcomes targeted bone densitometry (whole body, spine, hip DXA). Secondary outcomes included body composition, bone geometry and strength (hip structural analysis) and bone biomarkers (procollagen type 1 N-terminal propeptide (P1NP), C telopeptide (CTx) estradiol, leptin). Data were collected at baseline, 4 months and 8 months. Data were adjusted for body weight, fat mass and lean mass changes. Results: Compared with the NW controls, adolescents with obesity displayed lower unadjusted and adjusted bone density. Following successful weight loss (~ -11%) adolescents with obesity increased whole body (%Ob Δ 3.22 (3.58) pp<0.001) and lumbar spine (%Ob Δ 6.27 (12.45) p=0.014) BMD. However, values remain lower than their NW peers after adjustment to body weight changes. After the weight loss intervention, compromised estimates of fracture risk remained especially at the narrow neck (buckling ratio (BR) 8.25 (2.00) p=0.005), despite positive adaptations of some geometric properties (i.e. NN CSA, NN Z). Also, bone accretion changes in adolescents with obesity followed an androgen-like adaptation demonstrated by periosteal expansion (% NW Δ 0.69 (3.71); Ob Δ 1.67 (9.11)) and endocortical resorption (% NW Δ -2.11 (11.79); Ob Δ 4.42 (10.56)). Among the intervention group, differences in bone markers favoured formation during the first 4 months and favoured resorption in the remaining months. Conclusion: Bone fragility in adolescents with obesity was demonstrated by (1) baseline and post intervention lower whole body and regional BMD than NW controls, (2) post-intervention higher fracture risk index at the narrow neck, (3) bone biomarkers showing reduced z-scores, uncoupling indices and qualitative representations of the distribution of bone remodeling. Future investigations of links between bone and obesity during adolescence can be well informed by the results of this thesis

Writing in Britain and Ireland, c. 400 to c. 800

No abstract available

Une approche de modélisation de biologie des systèmes sur la spondylarthrite

Spondyloarthritis is a frequent chronic inflammatory rheumatism, with a prevalence of 0.43 % in France. This disease presents axial skeleton injuries, but also on peripheral joints, and can results in a total spinal and sacro-iliac motility loss. Extra-articular features including uveitis, psoriasis and inflammatory bowel disease are frequent. Current SpA treatments are only symptomatic, relieving inflammatory symptoms. SpA etiology is largely multifactorial with a genetic component dominated by the long-known strong association with the HLA-B27 allele. This allele, however, is not sufficient for the disease to occur. This thesis project objective was then to identify other genetic factors in the origin of SpA.My work was mainly divided in two complementary data analyses, in a way to get a systems biology approach. The first one consisted in proceed linking analyses on data from Affymetrix genotyping chips gathered from DNA of 1310 people grouped in 210 families. This study allowed notably to detect a new significantly linked region to SpA : 13q13, with an interval of 1.3 Mb. This part of genome is currently being sequenced to allow a better causal SNP identification.Secondly, an Affymetrix HumanGene 1.0 st transcriptomic chips analysis was performed on MD-DCs extracted from 68 people, stimulated or not by LPS during 6 or 24 hours. This cohort was grouped between 23 patients HLA-B27+, 23 healthy controls HLA-B27+ and 21 healthy controls HLA-B27-. I could notice that HLA-B27 allele is farly enough to considerably affect cell transcriptomic profiles, which encourages to include HLA-B27+ healthy controls. Otherwise, a gene network analysis allowed me to highlight on an inhibition of early steps of cholesterol biosyntthesis.La Spondyloarthrite (SpA) est un rhumatisme inflammatoire chronique fréquent, avec une prévalence de 0,43 % en France. Elle consiste en une atteinte prédominante du squelette axial, mais aussi des articulations périphériques, et peut conduire à une immobilité du rachis et des articulations sacro-iliaques. Des atteintes extra-articulaires sont fréquentes, telles qu'une uvéite, un psoriasis ou une maladie inflammatoire chronique de l'intestin. Les traitements actuels ne sont que symptomatiques, ciblant principalement les manifestations inflammatoires. L'étiologie de la SpA est multifactorielle avec une composante génétique dominée par l'association forte et bien connue avec l'allèle HLA-B27. Cependant, ce facteur génétique n'est clairement pas suffisant pour induire le développement de la maladie. L'objectif de ce projet de thèse était donc d'identifier d'autres facteurs génétiques à l'origine du développement de la SpA.Mon travail a porté sur l'analyse de deux jeux de données complémentaires, dans une perspective de biologie des systèmes. Dans une première partie, j'ai conduit une analyse de liaison dans 210 familles atteintes de la maladie représentant 1310 personnes génotypées avec des puces Affymetrix 250k. Une nouvelle région significativement liée à la SpA a été détectée en 13q13, avec un intervalle de 1,3 Mb défini par des haplotypes recombinants chez les patients.Ensuite, une analyse transcriptomique des cellules dendritiques dérivées des monocytes de 23 patients HLA-B27+, 23 témoins sains HLA-B27+ et 21 témoins sains HLA-B27-, et stimulées ou non par du LPS, a tenté de distinguer les gènes dont l'expression est modifiée par la maladie de ceux influencés par l'allèle HLA-B27 seul. L'annotation fonctionnelle et une analyse par réseau de gènes ont mis en évidence l'inhibition chez les patients des étapes précoces de la biosynthèse du cholestérol

The English Crown and the Election of Pope John XXII

This article investigates the involvement of Edward II in the negotiations that led to John XXII's election on 7 August 1316 after a two-year papal vacancy between 1314 and 1316. The main source for this analysis is a dossier of sixteen diplomatic documents, found among the Chancery records in The National Archives in London. The article concludes that Edward II tried to exploit the papal vacancy as a means to re-establish his international profile and seek support abroad in order to face opposition at home, thus ensuring a place for the English Crown within the European political milieu