Optimal local laws and CLT for the circular Riesz gas

We study the long-range one-dimensional Riesz gas on the circle, a continuous system of particles interacting through a Riesz (i.e inverse power) kernel. We establish near-optimal rigidity estimates on gaps valid at any scale. Leveraging on these local laws and using a Stein method, we provide a quantitative Central Limit Theorem for linear statistics. The proof is based on a mean-field transport and on a fine analysis of the fluctuations of local error terms through the study of Helffer-Sj\"ostrand equations. The method can handle very singular test-functions, including characteristic functions of intervals, using a comparison principle for the Helffer-Sj\"ostrand equation

Quelques problèmes de mécanique statistique pour les gaz de Coulomb et de Riesz

This thesis is devoted to the analysis of different problems concerning the statistical mechanics of a family of interacting particles systems, named Coulomb and Riesz gases. We begin by studying the mixing time of the Dyson Brownian motion with quadratic confinement, whose invariant measure is the Hermite beta-ensemble. We establish a cutoff phenomenon for the mixing time in a variety of distances and divergences, when the number of particles tend to infinity. We then consider the fluctuations and correlations of the circular Riesz gas in the long-range regime. First, we quantify the fluctuations of gaps and give a central limit theorem for linear statistics allowing very singular test-functions. Second, one shows an optimal estimate on the decay of gaps correlations, allowing one to prove the uniqueness of the infinite volume measure.The rest of the manuscript is devoted to the study of the two-dimensional two-component plasma in a law temperature regime where the partition function diverges. After proposing an efficient way to renormalize the model, we derive an asymptotic expression for the partition function as the truncation parameter tends to zero, some estimates on the number and size of neutral dipoles and an energetic control on the fluctuations.Cette thèse se propose d'étudier divers problèmes de mécanique statistique pour une famille de systèmes de particules en interaction, appelés gaz de Coulomb et de Riesz. Nous commençons par examiner le temps de mélange du mouvement Brownien de Dyson avec confinement quadratique, dont la mesure invariante est donnée par le beta-ensemble d'Hermite. Nous établissons un résultat de cutoff pour le temps de mélange du système dans une variété de distances et de divergences, lorsque le nombre de particules tend vers l'infini. Nous considérons ensuite les fluctuations et corrélations du gaz de Riesz circulaire dans le régime longue portée. Tout d'abord, nous quantifions les fluctuations des espacements entre particules et énonçons un théorème central limite pour les statistiques linéaires valables pour des fonctions-tests possiblement très singulières. Puis nous montrons une estimée optimale sur la décroissance de la corrélation des gaps, qui nous permet de montrer l'unicité du processus limite en volume infini. La suite de ce manuscrit est consacrée à l'étude du gaz de Coulomb bi-dimensionnel à deux composantes dans un régime de basse température où la fonction de partition diverge. Après avoir proposé une renormalisation efficace du modèle, nous donnons un développement asymptotique de la fonction de partition lorsque le paramètre de troncature tend vers zéro, des estimées sur le nombre et la taille de dipôles neutres ainsi qu'un contrôle énergétique sur les fluctuations

Some problems of statistical mechanics for Coulomb and Riesz gases

Cette thèse se propose d'étudier divers problèmes de mécanique statistique pour une famille de systèmes de particules en interaction, appelés gaz de Coulomb et de Riesz. Nous commençons par examiner le temps de mélange du mouvement Brownien de Dyson avec confinement quadratique, dont la mesure invariante est donnée par le beta-ensemble d'Hermite. Nous établissons un résultat de cutoff pour le temps de mélange du système dans une variété de distances et de divergences, lorsque le nombre de particules tend vers l'infini. Nous considérons ensuite les fluctuations et corrélations du gaz de Riesz circulaire dans le régime longue portée. Tout d'abord, nous quantifions les fluctuations des espacements entre particules et énonçons un théorème central limite pour les statistiques linéaires valables pour des fonctions-tests possiblement très singulières. Puis nous montrons une estimée optimale sur la décroissance de la corrélation des gaps, qui nous permet de montrer l'unicité du processus limite en volume infini. La suite de ce manuscrit est consacrée à l'étude du gaz de Coulomb bi-dimensionnel à deux composantes dans un régime de basse température où la fonction de partition diverge. Après avoir proposé une renormalisation efficace du modèle, nous donnons un développement asymptotique de la fonction de partition lorsque le paramètre de troncature tend vers zéro, des estimées sur le nombre et la taille de dipôles neutres ainsi qu'un contrôle énergétique sur les fluctuations.This thesis is devoted to the analysis of different problems concerning the statistical mechanics of a family of interacting particles systems, named Coulomb and Riesz gases. We begin by studying the mixing time of the Dyson Brownian motion with quadratic confinement, whose invariant measure is the Hermite beta-ensemble. We establish a cutoff phenomenon for the mixing time in a variety of distances and divergences, when the number of particles tend to infinity. We then consider the fluctuations and correlations of the circular Riesz gas in the long-range regime. First, we quantify the fluctuations of gaps and give a central limit theorem for linear statistics allowing very singular test-functions. Second, one shows an optimal estimate on the decay of gaps correlations, allowing one to prove the uniqueness of the infinite volume measure.The rest of the manuscript is devoted to the study of the two-dimensional two-component plasma in a law temperature regime where the partition function diverges. After proposing an efficient way to renormalize the model, we derive an asymptotic expression for the partition function as the truncation parameter tends to zero, some estimates on the number and size of neutral dipoles and an energetic control on the fluctuations

Multi-spectral investigation of ozone : Part I. Setup & uncertainty budget

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Factors Associated with Myocardial Uptake on Oncologic Somatostatin PET Investigations and Differentiation from Myocardial Uptake of Acute Myocarditis

International audienceMyocardial somatostatin-PET uptake is observed in most patients with acute myocarditis (AM) but also in some oncology patients referred for routine somatostatin-PET. This raises concerns about the specificity of somatostatin-PET for detecting myocarditis. The current study aims to identify (i) factors associated with the detection of myocardial uptake on somatostatin-PET recorded for oncology indications and (ii) differential PET criteria that characterize myocardial uptake in AM patients.Methods. We analyzed i) factors associated with the detection of myocardial [68Ga]Ga-DOTA-TOC uptake in 508 [68Ga]Ga-DOTA-TOC PETs from 178 patients, performed for a confirmed or suspected oncologic disease (Onc-PET group) and ii) PET criteria that could differentiate myocardial [68Ga]Ga-DOTA-TOC uptake in 31 patients with an MRI-ascertained AM (AM-PET group) from the Onc-PET group.Results. Significant myocardial uptake was detected in 137 (26.9%) Onc-PETs and was independently associated with somatostatin analog treatment (Exp(Beta) (95 %CI): 0.805 (0.728-0.890), p<0.001) and age (1.005 (1.001-1.009), p=0.012). A comparable model was selected for predicting the myocardial/blood SUVmax ratio (i.e. somatostatin analog treatment (p<0.001) and history of coronary artery disease (CAD) p=0.022)). Myocardial uptake was detected in 12.9% (25/193) of Onc-PETs from patients treated with somatostatin analogs but in 43.4% (59/136) of untreated patients over the median of 64 years of age. Myocardial uptake was apparent in all 31 AM-PETs, with volume and intensity of uptake dramatically higher than in the 137 Onc-PETs showing myocardial uptake. A myocardial/blood SUVmax ratio threshold of 2.20 provided a sensitivity of 87% (27/31) and a specificity of 88% (44/50) for differentiating myocardial uptake between AM-PETs and an Onc-PET group restricted to patients with comparable clinical characteristics to the AM group (≤ 64 years of age, no CAD history, no somatostatin agonists). A myocardial uptake volume threshold of 18 cm3 provided a comparable diagnostic accuracy (sensitivity: 84% (26/31), specificity: 94% (47/50)).Conclusion. Myocardial uptake is detected in 26.9% of somatostatin-PETs recorded for oncology indications. This rate is decreased by somatostatin analog treatments and increased in older individuals. However, somatostatin-PET, analyzed with the quantitative criterion of uptake intensity or volume, is able to identify acute myocarditis and to differentiate it from myocardial uptake of other origins

Using deep-neural-network-driven facial recognition to identify distinct Kabuki syndrome 1 and 2 gestalt

International audienceKabuki syndrome (KS) is a rare genetic disorder caused by mutations in two major genes, KMT2D and KDM6A, that are responsible for Kabuki syndrome 1 (KS1, OMIM147920) and Kabuki syndrome 2 (KS2, OMIM300867), respectively. We lack a description of clinical signs to distinguish KS1 and KS2. We used facial morphology analysis to detect any facial morphological differences between the two KS types. We used a facial-recognition algorithm to explore any facial morphologic differences between the two types of KS. We compared several image series of KS1 and KS2 individuals, then compared images of those of Caucasian origin only (12 individuals for each gene) because this was the main ethnicity in this series. We also collected 32 images from the literature to amass a large series. We externally validated results obtained by the algorithm with evaluations by trained clinical geneticists using the same set of pictures. Use of the algorithm revealed a statistically significant difference between each group for our series of images, demonstrating a different facial morphotype between KS1 and KS2 individuals (mean area under the receiver operating characteristic curve = 0.85 [p = 0.027] between KS1 and KS2). The algorithm was better at discriminating between the two types of KS with images from our series than those from the literature (p = 0.0007). Clinical geneticists trained to distinguished KS1 and KS2 significantly recognised a unique facial morphotype, which validated algorithm findings (p = 1.6e-11). Our deep-neural-network-driven facial-recognition algorithm can reveal specific composite gestalt images for KS1 and KS2 individuals

Growth charts in Kabuki syndrome 1

Kabuki syndrome (KS, KS1: OMIM 147920 and KS2: OMIM 300867) is caused by pathogenic variations in KMT2D or KDM6A. KS is characterized by multiple congenital anomalies and neurodevelopmental disorders. Growth restriction is frequently reported. Here we aimed to create specific growth charts for individuals with KS1, identify parameters used for size prognosis and investigate the impact of growth hormone therapy on adult height. Growth parameters and parental size were obtained for 95 KS1 individuals (41 females). Growth charts for height, weight, body mass index (BMI) and occipitofrontal circumference were generated in standard deviation values for the first time in KS1. Statural growth of KS1 individuals was compared to parental target size. According to the charts, height, weight, BMI, and occipitofrontal circumference were lower for KS1 individuals than the normative French population. For males and females, the mean growth of KS1 individuals was -2 and -1.8 SD of their parental target size, respectively. Growth hormone therapy did not increase size beyond the predicted size. This study, from the largest cohort available, proposes growth charts for widespread use in the management of KS1, especially for size prognosis and screening of other diseases responsible for growth impairment beyond a calculated specific target size.status: publishe

Growth charts in Kabuki syndrome 1

International audienceKabuki syndrome (KS, KS1: OMIM 147920 and KS2: OMIM 300867) is caused by pathogenic variations in KMT2D or KDM6A. KS is characterized by multiple congenital anomalies and neurodevelopmental disorders. Growth restriction is frequently reported. Here we aimed to create specific growth charts for individuals with KS1, identify parameters used for size prognosis and investigate the impact of growth hormone therapy on adult height. Growth parameters and parental size were obtained for 95 KS1 individuals (41 females). Growth charts for height, weight, body mass index (BMI) and occipitofrontal circumference were generated in standard deviation values for the first time in KS1. Statural growth of KS1 individuals was compared to parental target size. According to the charts, height, weight, BMI, and occipitofrontal circumference were lower for KS1 individuals than the normative French population. For males and females, the mean growth of KS1 individuals was -2 and -1.8 SD of their parental target size, respectively. Growth hormone therapy did not increase size beyond the predicted size. This study, from the largest cohort available, proposes growth charts for widespread use in the management of KS1, especially for size prognosis and screening of other diseases responsible for growth impairment beyond a calculated specific target size

Immunopathological manifestations in Kabuki syndrome: a registry study of 177 individuals

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