Statistique d’extrêmes de variables aléatoires fortement corrélées

Extreme value statistics plays a keyrole in various scientific contexts. Although the description of the statistics of a global extremum is certainly an important feature, it focuses on the fluctuations of a single variable among many others. A natural question that arises is then the following: is this extreme value lonely at the top or, on the contrary, are there many other variables close to it ? A natural and useful quantity to characterize the crowding is the density of states near extremes. For this quantity, there exist very few exact results for strongly correlated variables, which is however the case encountered in many situations. Two physical models of strongly correlated variables have attracted much attention because they can be studied analytically : the positions of a random walker and the eigenvalues of a random matrix. This thesis is devoted to the study of the statistics near the maximum of these two ensembles of strongly correlated variables.In the first part, I study the case where the collection of random variables is the position of a Brownian motion, which may be constrained to be periodic or positive. This Brownian motion is seen as the limit of a classical random walker after a large number of steps. It is then possible to interpret this problem as a quantum particle in a potential which allows us to use powerful methods from quantum mechanics as propagators and path integral. These tools are used to calculate the average density from the maximum for different constrained Brownian motions and the complete distribution of this observable in certain cases. It is also possible to generalize this approach to the study of several random walks, independent or with interaction, as well as to the study of other functional of the maximum.In the second part, I study the case of the eigenvalues of random matrices, belonging to both Gaussian and Wishart ensembles. The study near the maximal eigenvalues for both models is performed using a method based on semi-classical orthogonal polynomials. In the case of Gaussian unitary matrices, I have obtained an analytical formula for the density near the maximum as well as a new expression for the distribution of the gap between the two largest eigenvalues. These results, and in particular their generalizations to different Gaussian ensembles, are then applied to the relaxational dynamics of a mean-field spin glass model. Finally, for the case of Wishart matrices I proposed a new derivation of the distribution of the smallest eigenvalue using orthogonal polynomials. In addition, I proved a conjecture on the first finite size correction of this distribution in the «hard edge» limit.La statistique des valeurs extrêmes est une question majeure dans divers contextes scientifiques. Cependant, bien que la description de la statistique d'un extremum global soit certainement une caractéristique importante, celle-ci ne se concentre que sur une seule variable parmi un grand nombre de variables aléatoires. Une question naturelle qui se pose alors est la suivante: ces valeurs extrêmes sont-elles isolées, loin des autres variables ou bien au contraire existe-t-il un grand nombre d'autres variables proches de ces valeurs extrêmes ? Ces questions ont suscité l'étude de la densité d'état de ces événements quasi-extrêmes. Il existe pour cette quantité peu de résultats pour des variables fortement corrélées, qui est pourtant le cas rencontré dans de nombreux modèles fondamentaux. Deux pistes de modèles physiques de variables fortement corrélées pouvant être étudiés analytiquement se démarquent alors: les positions d’une marche aléatoire et les valeurs propres de matrice aléatoire. Cette thèse est ainsi consacrée à l’étude de statistique d’extrêmes pour ces deux modèles de variables fortement corrélées.Dans une première partie, j’étudie le cas où la collection de variables aléatoires est la position au cours du temps d’un mouvement brownien, qui peut être contraint à être périodique, positif... Ce mouvement brownien est vu comme la limite d’un marcheur aléatoire classique après un grand nombre de pas. Il est alors possible d’interprèter ce problème comme celui d’une particule quantique dans un potentiel ce qui permet d’utiliser des méthodes puissantes issues de la mécanique quantique comme l’utilisation de propagateurs et de l’intégrale de chemin. Ces outils permettent de calculer la densité moyenne à partir du maximum pour les différents mouvements browniens contraints et même la distribution complète de cette quantité pour certains cas. Il est également possible de généraliser cette démarche à l’étude de plusieurs marches aléatoires indépendantes ou avec interaction. Cette démarche permet également d’effectuer une étude temporelle, ainsi que de généraliser à l’étude d’autres fonctionnelle du maximum.Dans la seconde partie, j’étudie le cas où la collection de variables aléatoires est composée des valeurs propres d’une matrice aléatoire. Ce travail se concentre sur l’études des matrices des ensembles gaussiens (GOE, GUE et GSE) ainsi qu’à l’étude des matrices de Wishart. L’étude du voisinage de la valeur propre maximale pour ces deux modèles est faite en utilisant une méthode fondée sur les propriétés des polynômes orthogonaux. Dans le cas des matrices gaussiennes unitaires GUE, j’ai obtenu une formule analytique pour la distribution à partir du maximum ainsi qu’une nouvelle expression de la statistique du gap entre les deux plus grandes valeurs propres en termes d’une fonction transcendante de Painlevé. Ces résultats, et plus particulièrement leurs généralisations aux cas GOE, sont alors appliqués à un modèle de verre de spin sphérique en champs moyen. Dans le cas des matrices de Wishart, l’analyse des polynômes orthogonaux dans le régime de double échelle m’a permis de retrouver les différentes statistiques de la valeur propre minimale et également de prouver une conjecture sur la première correction de taille finie pour des grandes matrices de la distribution de la valeur propre minimale dans la limite dite de «hard edge»

Super-Rough Glassy Phase of the Random Field XY Model in Two Dimensions

We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the critical temperature $T_c$, the disorder and thermally averaged correlation function $B(r)$ of the phase field $\theta(x)$, $B(r) = \bar{}$ behaves, for $r \gg a$, as $B(r) \simeq A(\tau) \ln^2 (r/a)$ where $r = |r|$ and $a$ is a microscopic length scale. We derive the RG equations up to cubic order in $\tau = (T_c-T)/T_c$ and predict the universal amplitude ${A}(\tau) = 2\tau^2-2\tau^3 + {\cal O}(\tau^4)$. The universality of $A(\tau)$ results from nontrivial cancellations between nonuniversal constants of RG equations. Using an exact polynomial algorithm on an equivalent dimer version of the model we compute ${A}(\tau)$ numerically and obtain a remarkable agreement with our analytical prediction, up to $\tau \approx 0.5$.Comment: 5 pages, 3 figure

Ecosystems monitoring powered by environmental genomics: a review of current strategies with an implementation roadmap

A decade after environmental scientists integrated high-throughput sequencing technologies in their toolbox, the genomics-based monitoring of anthropogenic impacts on the biodiversity and functioning of ecosystems is yet to be implemented by regulatory frameworks. Despite the broadly acknowledged potential of environmental genomics to this end, technical limitations and conceptual issues still stand in the way of its broad application by end-users. In addition, the multiplicity of potential implementation strategies may contribute to a perception that the routine application of this methodology is premature or “in development”, hence restraining regulators from binding these tools into legal frameworks. Here, we review recent implementations of environmental genomics-based methods, applied to the biomonitoring of ecosystems. By taking a general overview, without narrowing our perspective to particular habitats or groups of organisms, this paper aims to compare, review and discuss the strengths and limitations of four general implementation strategies of environmental genomics for monitoring: (a) Taxonomy-based analyses focused on identification of known bioindicators or described taxa; (b) De novo bioindicator analyses; (c) Structural community metrics including inferred ecological networks; and (d) Functional community metrics (metagenomics or metatranscriptomics). We emphasise the utility of the three latter strategies to integrate meiofauna and microorganisms that are not traditionally utilised in biomonitoring because of difficult taxonomic identification. Finally, we propose a roadmap for the implementation of environmental genomics into routine monitoring programmes that leverage recent analytical advancements, while pointing out current limitations and future research needs.publishedVersio

The MOBILIZE Boston Study: Design and methods of a prospective cohort study of novel risk factors for falls in an older population

<p>Abstract</p> <p>Background</p> <p>Falls are the sixth leading cause of death in elderly people in the U.S. Despite progress in understanding risk factors for falls, many suspected risk factors have not been adequately studied. Putative risk factors for falls such as pain, reductions in cerebral blood flow, somatosensory deficits, and foot disorders are poorly understood, in part because they pose measurement challenges, particularly for large observational studies.</p> <p>Methods</p> <p>The MOBILIZE Boston Study (MBS), an NIA-funded Program Project, is a prospective cohort study of a unique set of risk factors for falls in seniors in the Boston area. Using a door-to-door population-based recruitment, we have enrolled 765 persons aged 70 and older. The baseline assessment was conducted in 2 segments: a 3-hour home interview followed within 4 weeks by a 3-hour clinic examination. Measures included pain, cerebral hemodynamics, and foot disorders as well as established fall risk factors. For the falls follow-up, participants return fall calendar postcards to the research center at the end of each month. Reports of falls are followed-up with a telephone interview to assess circumstances and consequences of each fall. A second assessment is performed 18 months following baseline.</p> <p>Results</p> <p>Of the 2382 who met all eligibility criteria at the door, 1616 (67.8%) agreed to participate and were referred to the research center for further screening. The primary reason for ineligibility was inability to communicate in English. Results from the first 600 participants showed that participants are largely representative of seniors in the Boston area in terms of age, sex, race and Hispanic ethnicity. The average age of study participants was 77.9 years (s.d. 5.5) and nearly two-thirds were women. The study cohort was 78% white and 17% black. Many participants (39%) reported having fallen at least once in the year before baseline.</p> <p>Conclusion</p> <p>Our results demonstrate the feasibility of conducting comprehensive assessments, including rigorous physiologic measurements, in a diverse population of older adults to study non-traditional risk factors for falls and disability. The MBS will provide an important new data resource for examining novel risk factors for falls and mobility problems in the older population.</p

A Historiometric Examination of Machiavellianism and a New Taxonomy of Leadership

Although researchers have extensively examined the relationship between charismatic leadership and Machiavellianism (Deluga, 2001; Gardner & Avolio, 1995; House & Howell, 1992), there has been a lack of investigation of Machiavellianism in relation to alternative forms of outstanding leadership. Thus, the purpose of this investigation was to examine the relationship between Machiavellianism and a new taxonomy of outstanding leadership comprised of charismatic, ideological, and pragmatic leaders. Using an historiometric approach, raters assessed Machiavellianism via the communications of 120 outstanding leaders in organizations across the domains of business, political, military, and religious institutions. Academic biographies were used to assess twelve general performance measures as well as twelve general controls and five communication specific controls. The results indicated that differing levels of Machiavellianism is evidenced across the differing leader types as well as differing leader orientation. Additionally, Machiavellianism appears negatively related to performance, though less so when type and orientation are taken into account.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

RANTES/CCL5 and Risk for Coronary Events: Results from the MONICA/KORA Augsburg Case-Cohort, Athero-Express and CARDIoGRAM Studies

BACKGROUND: The chemokine RANTES (regulated on activation, normal T-cell expressed and secreted)/CCL5 is involved in the pathogenesis of cardiovascular disease in mice, whereas less is known in humans. We hypothesised that its relevance for atherosclerosis should be reflected by associations between CCL5 gene variants, RANTES serum concentrations and protein levels in atherosclerotic plaques and risk for coronary events. METHODS AND FINDINGS: We conducted a case-cohort study within the population-based MONICA/KORA Augsburg studies. Baseline RANTES serum levels were measured in 363 individuals with incident coronary events and 1,908 non-cases (mean follow-up: 10.2±4.8 years). Cox proportional hazard models adjusting for age, sex, body mass index, metabolic factors and lifestyle factors revealed no significant association between RANTES and incident coronary events (HR [95% CI] for increasing RANTES tertiles 1.0, 1.03 [0.75-1.42] and 1.11 [0.81-1.54]). None of six CCL5 single nucleotide polymorphisms and no common haplotype showed significant associations with coronary events. Also in the CARDIoGRAM study (&gt;22,000 cases, &gt;60,000 controls), none of these CCL5 SNPs was significantly associated with coronary artery disease. In the prospective Athero-Express biobank study, RANTES plaque levels were measured in 606 atherosclerotic lesions from patients who underwent carotid endarterectomy. RANTES content in atherosclerotic plaques was positively associated with macrophage infiltration and inversely associated with plaque calcification. However, there was no significant association between RANTES content in plaques and risk for coronary events (mean follow-up 2.8±0.8 years). CONCLUSIONS: High RANTES plaque levels were associated with an unstable plaque phenotype. However, the absence of associations between (i) RANTES serum levels, (ii) CCL5 genotypes and (iii) RANTES content in carotid plaques and either coronary artery disease or incident coronary events in our cohorts suggests that RANTES may not be a novel coronary risk biomarker. However, the potential relevance of RANTES levels in platelet-poor plasma needs to be investigated in further studies