Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics

Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest value among a set of random variables) may also play a role in the statistics of global quantities, in a direct or indirect way. This review discusses different connections that may appear between problems of sums and of extreme values of random variables, and emphasizes physical situations in which such connections are relevant. Along this line of thought, standard convergence theorems for sums and extreme values of independent and identically distributed random variables are recalled, and some rigorous results as well as more heuristic reasonings are presented for correlated or non-identically distributed random variables. More specifically, the role of extreme values within sums of broadly distributed variables is addressed, and a general mapping between extreme values and sums is presented, allowing us to identify a class of correlated random variables whose sum follows (generalized) extreme value distributions. Possible applications of this specific class of random variables are illustrated on the example of two simple physical models. A few extensions to other related classes of random variables sharing similar qualitative properties are also briefly discussed, in connection with the so-called BHP distribution.Comment: 58 pages, final version, typo corrected in Theorem

Fatigue cracks initiation in a low alloy steel: Impact of hydrogen on plasticity

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One year OSIRHYS IV project synthesis: mechanical behaviour of 700 bar type iv high pressure vessel code qualification.

International audienceIn this paper we present results of the OSIRHYS IV French project which aims to develop andvalidate models and methods for composite high pressure design and optimization withbehavior uncertainties knowledge. Models of the five partners of this project are presentedand burst simulation results are compared for three test temperatures (-40°C, 15°C and85°C)

Generalised extreme value statistics and sum of correlated variables

We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and (generally) correlated random variables with a sum distributed according to one of the three (k-dependent) asymptotic distributions of extreme value statistics, namely the Gumbel, Frechet and Weibull distributions. These classes, as well as the limit distributions, are naturally extended to real values of k, thus providing a clear interpretation to the onset of Gumbel distributions with non-integer index k in the statistics of global observables. This is one of the very few known generalisations of the central limit theorem to non-independent random variables. Finally, in the context of a simple physical model, we relate the index k to the ratio of the correlation length to the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.

Applicability of in vivo staging of regional amyloid burden in a cognitively normal cohort with subjective memory complaints: the INSIGHT-preAD study.

BACKGROUND:Current methods of amyloid PET interpretation based on the binary classification of global amyloid signal fail to identify early phases of amyloid deposition. A recent analysis of 18F-florbetapir PET data from the Alzheimer's disease Neuroimaging Initiative cohort suggested a hierarchical four-stage model of regional amyloid deposition that resembles neuropathologic estimates and can be used to stage an individual's amyloid burden in vivo. Here, we evaluated the validity of this in vivo amyloid staging model in an independent cohort of older people with subjective memory complaints (SMC). We further examined its potential association with subtle cognitive impairments in this population at elevated risk for Alzheimer's disease (AD). METHODS:The monocentric INSIGHT-preAD cohort includes 318 cognitively intact older individuals with SMC. All individuals underwent 18F-florbetapir PET scanning and extensive neuropsychological testing. We projected the regional amyloid uptake signal into the previously proposed hierarchical staging model of in vivo amyloid progression. We determined the adherence to this model across all cases and tested the association between increasing in vivo amyloid stage and cognitive performance using ANCOVA models. RESULTS:In total, 156 participants (49%) showed evidence of regional amyloid deposition, and all but 2 of these (99%) adhered to the hierarchical regional pattern implied by the in vivo amyloid progression model. According to a conventional binary classification based on global signal (SUVRCereb = 1.10), individuals in stages III and IV were classified as amyloid-positive (except one in stage III), but 99% of individuals in stage I and even 28% of individuals in stage II were classified as amyloid-negative. Neither in vivo amyloid stage nor conventional binary amyloid status was significantly associated with cognitive performance in this preclinical cohort. CONCLUSIONS:The proposed hierarchical staging scheme of PET-evidenced amyloid deposition generalizes well to data from an independent cohort of older people at elevated risk for AD. Future studies will determine the prognostic value of the staging approach for predicting longitudinal cognitive decline in older individuals at increased risk for AD

Short-Term Efficacy of Rofecoxib and Diclofenac in Acute Shoulder Pain: A Placebo-Controlled Randomized Trial

OBJECTIVES: To evaluate the short-term symptomatic efficacy of rofecoxib and diclofenac versus placebo in acute episodes of shoulder pain. DESIGN: Randomized controlled trial of 7 days. SETTING: Rheumatologists and/or general practitioners totaling 47. PARTICIPANTS: Acute shoulder pain. INTERVENTIONS: Rofecoxib 50 mg once daily, diclofenac 50 mg three times daily, and placebo. OUTCOME MEASURES: Pain, functional impairment, patient's global assessment of his/her disease activity, and local steroid injection requirement for persistent pain. The primary variable was the Kaplan-Meier estimates of the percentage of patients at day 7 fulfilling the definition of success (improvement in pain intensity and a low pain level sustained to the end of the 7 days of the study; log-rank test). RESULTS: There was no difference in the baseline characteristics between the three groups (rofecoxib n = 88, placebo n = 94, and diclofenac n = 89). At day 7, the Kaplan-Meier estimates of successful patients was higher in the treatment groups than in the placebo (54%, 56%, and 38% in the diclofenac, rofecoxib, and placebo groups respectively, p = 0.0070 and p = 0.0239 for placebo versus rofecoxib and diclofenac, respectively). During the 7 days of the study, there was a statistically significant difference between placebo and both active arms (rofecoxib and diclofenac) in all the evaluated outcome measures A local steroid injection had to be performed in 33 (35%) and 19 (22%) patients in the placebo and rofecoxib group respectively. Number needed to treat to avoid such rescue therapy was 7 patients (95% confidence interval 5–15). CONCLUSION: This study highlights the methodological aspects of clinical trials, e.g., eligibility criteria and outcome measures, in acute painful conditions. The data also establish that diclofenac and rofecoxib are effective therapies for the management of acute painful shoulder and that they reduce the requirement for local steroid injection

Fatigue thermomécanique de multicouches polymères/composites

Cette thèse porte sur l'étude du remplissage rapide de réservoirs d'hydrogène sous haute pression (700 bars). Durant cette phase, se produisent simultanément une augmentation de la température du gaz et des contraintes internes dues à la pression. Un banc de fatigue thermomécanique instrumenté a été développé afin de simuler ce remplissage rapide sur des éprouvettes simples composées d'un liner en polyuréthane et d'une coque composite carbone/époxy, matériaux constitutifs des réservoirs étudiés. La validation thermique de ce banc a permis de montrer que le polyuréthane est une bonne barrière thermique. Une première étude sur un drapage composite non optimisé a permis de montrer l'influence néfaste de la température et d'un palier de maintien à la charge maximale sur le comportement du multicouche polymère/composite ainsi que l'effet bénéfique de l'alternance des plis du stratifié composite ; des couches épaisses conduisent à une apparition plus précoce de l'endommagement et à des durées de vie plus faibles. Un drapage ‘‘représentatif'' des conditions de service du réservoir a été optimisé par calcul analytique et par éléments finis afin d'atteindre les mêmes niveaux de contraintes maximales dans l'éprouvette sollicitée sur le banc de fatigue thermomécanique que ceux atteint dans le réservoir sous pression. Ces éprouvettes ‘‘représentatives'' conduisent néanmoins à des contraintes de cisaillement plus élevées que dans le réservoir et présentent des effets de bord qui n'existent pas dans le réservoir bobiné. Comme pour les drapages non optimisés, la fatigue thermomécanique conduit à des durées de vie plus faibles qu'en fatigue purement mécanique à 1Hz. L'observation par microscopie optique et par radiographie X des échantillons sollicités montre, en fatigue thermomécanique, une localisation des endommagements dans la partie la plus chauffée du composite alors qu'en fatigue mécanique à 1Hz, les endommagements sont répartis sur toute la longueur des éprouvettes. De plus, la fatigue thermomécanique conduit préférentiellement à des délaminages par rapport aux résultats obtenus en fatigue mécanique à 1Hz. Des mesures de champs de déplacement par corrélation d'images ont permis de mettre en évidence des concentrations de cisaillement sur le drapage ‘‘représentatif'' ainsi qu'un comportement viscoélastique, accentué en présence de cyclage thermique, qui seraient à l'origine des endommagements constatés

Extreme statistics and volume fluctuations in a confined one-dimensional gas

15 pages, 2 figuresInternational audienceWe consider the statistics of volume fluctuations in a one-dimensional classical gas of non-interacting particles confined by a piston, and subjected to an arbitrary external potential. We show that despite the absence of interactions between particles, volume fluctuations of the gas are non-Gaussian, and are described by generalized extreme value distributions. The continuous shape parameter of these distributions is related to the ratio between the force acting on the piston, and the force acting on the particles. Gaussian fluctuations are recovered in the strong compression limit, when the effect of the external potential becomes negligible. Consequences for the thermodynamics are also discussed