Fractional smoothness and applications in finance

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.Comment: Chapter of AMAMEF book. 20 pages

Matter wave functions and Yukawa couplings in F-theory Grand Unification

We study the local structure of zero mode wave functions of chiral matter fields in F-theory unification. We solve the differential equations for the zero modes derived from local Higgsing in the 8-dimensional parent action of F-theory 7-branes. The solutions are found as expansions both in powers and derivatives of the magnetic fluxes. Yukawa couplings are given by an overlap integral of the three wave functions involved in the interaction and can be calculated analytically. We provide explicit expressions for these Yukawas to second order both in the flux and derivative expansions and discuss the effect of higher order terms. We explicitly describe the dependence of the couplings on the U(1) charges of the relevant fields, appropriately taking into account their normalization. A hierarchical Yukawa structure is naturally obtained. The application of our results to the understanding of the observed hierarchies of quarks and leptons is discussed.Comment: Latex, 51 pages, 4 figures, typos corrected, note adde

Oral Condition and Incident Coronary Heart Disease: A Clustering Analysis

Poor oral health has been linked to coronary heart disease (CHD). Clustering clinical oral conditions routinely recorded in adults may identify their CHD risk profile. Participants from the Paris Prospective Study 3 received, between 2008 and 2012, a baseline routine full-mouth clinical examination and an extensive physical examination and were thereafter followed up every 2 y until September 2020. Three axes defined oral health conditions: 1) healthy, missing, filled, and decayed teeth; 2) masticatory capacity denoted by functional masticatory units; and 3) gingival inflammation and dental plaque. Hierarchical cluster analysis was performed with multivariate Cox proportional hazards regression models and adjusted for age, sex, smoking, body mass index, education, deprivation (EPICES score; Evaluation of Deprivation and Inequalities in Health Examination Centres), hypertension, type 2 diabetes, LDL and HDL serum cholesterol (low- and high-density lipoprotein), triglycerides, lipid-lowering medications, NT-proBNP and IL-6 serum level. A sample of 5,294 participants (age, 50 to 75 y; 37.10% women) were included in the study. Cluster analysis identified 3,688 (69.66%) participants with optimal oral health and preserved masticatory capacity (cluster 1), 1,356 (25.61%) with moderate oral health and moderately impaired masticatory capacity (cluster 2), and 250 (4.72%) with poor oral health and severely impaired masticatory capacity (cluster 3). After a median follow-up of 8.32 y (interquartile range, 8.00 to 10.05), 128 nonfatal incident CHD events occurred. As compared with cluster 1, the risk of CHD progressively increased from cluster 2 (hazard ratio, 1.45; 95% CI, 0.98 to 2.15) to cluster 3 (hazard ratio, 2.47; 95% CI, 1.34 to 4.57; P < 0.05 for trend). To conclude, middle-aged individuals with poor oral health and severely impaired masticatory capacity have more than twice the risk of incident CHD than those with optimal oral health and preserved masticatory capacity (ClinicalTrials.gov NCT00741728)

Typicality, Black Hole Microstates and Superconformal Field Theories

We analyze the structure of heavy multitrace BPS operators in N = 1 superconformal quiver gauge theories that arise on the worldvolume of D3-branes on an affine toric cone. We exhibit a geometric procedure for counting heavy mesonic operators with given U(1) charges. We show that for any fixed linear combination of the U(1) charges, the entropy is maximized when the charges are in certain ratios. This selects preferred directions in the charge space that can be determined with the help of a piece of string. We show that almost all heavy mesonic operators of fixed U(1) charges share a universal structure. This universality reflects the properties of the dual extremal black holes whose microstates they create. We also interpret our results in terms of typical configurations of dual giant gravitons in AdS space.Comment: 40 pages + 3 appendices, 11 figure

Restauration morpho-dynamique et redynamisation de la section court-circuitée du Rhin en aval du barrage de Kembs (projet INTERREG / EDF)

National audienceThe Upper Rhine River has been heavily impacted by channelization for flood protection and navigation, and then by damming for hydropower generation. In normal non flooding conditions, most of the flows are diverted in a canalized section whereas the regulated “old Rhine” bypassed reach runs a minimum flow. Between Huningue and Neuf-Brisach, engineering works induced simplification and stabilization of the channel pattern from a formerly braiding sector to a single incised channel, hydrological modifications, bottom armouring due to bedload decrease, and thus ecological alterations. Two complementary and interdisciplinary projects have been initiated to restore alluvial morphodynamics: i) the international “INTERREG IV - Redynamisation of the old Rhine” project (2009-2012) coordinated by the Alsace region, France; ii) the left bank “controlled erosion” project launched by Electricité de France (EDF) within Kembs hydroelectric station relicensing process since 2003-2004. The purpose of these projects is to evaluate the feasibility of an important hydro-morphological and ecological restoration plan on a 45 km long reach, through both field testing of bank erosion techniques at favourable locations, and artificial sediments input from right bank excavations. This will help define possible long term prospective scenarios, in order to restore sustainable sediment transport, morphodynamics variability and associated ecological functions. The study will involve historical analysis, hydro-morphological / hydraulic physical and numerical modelling, physical and ecological monitoring, and sociological aspectsLe Rhin alsacien-allemand a enregistré de profondes modifications morphologiques et hydrologiques à la suite de sa correction et de sa régularisation pour la protection contre les crues et la navigation, puis après la construction de barrages hydro-électriques. Les aménagements réalisés entre Huningue et Neuf-Brisach ont engendré une simplification et une stabilisation du style fluvial. Un fleuve en tresses a cédé la place à un chenal unique incisé. Le fond de chenal est devenu pavé à cause d’une diminution des apports de charge de fond et des altérations écologiques ont été observées (simplification des habitats aquatiques et riverains). Deux projets complémentaires et interdisciplinaires ont été engagés afin de restaurer une dynamique des formes alluviales : i) le projet international INTERREG IV – Redynamisation du Vieux Rhin (2009-2012) sous l’impulsion de la région Alsace ; ii) le projet d’érosion maitrisée des berges de la rive gauche conduit par Electricité de France (EDF) dans le cadre du renouvellement de la concession de l’aménagement de Kembs. L’objectif des deux projets est de définir un plan de restauration hydro-morphologique et écologique conduisant à la redynamisation d’un tronçon de 45 km. L’étude repose sur une analyse historique, l’exploitation de modèles à la fois physiques et numériques, et les suivis morphologiques in situ d’une recharge artificielle en sédiments et d’érosions de berge contrôlées. Ces études de faisabilité sont complétées par des analyses écologique et sociologique pour apprécier l’impact socio-environnemental de ces projets

Exact results for topological strings on resolved Y(p,q) singularities

We obtain exact results in \alpha' for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories. The toric Calabi-Yau's that we analyze are obtained as minimal resolution of cones over Y(p,q) manifolds and give rise via M-theory compactification to SU(p) gauge theories on R^4 x S^1. As an application we present a detailed study of the local F_2 case and compute open and closed genus zero Gromov-Witten invariants of the C^3/Z_4 orbifold. We also display the modular structure of the topological wave function and give predictions for higher genus amplitudes.The mirror curve in this case is the spectral curve of the relativistic A_1 Toda chain. Our results also indicate the existence of a wider class of relativistic integrable systems associated to generic Y(p,q) geometries.Comment: 54 pages, 10 figures; typos corrected, new section added. Version accepted for publication on Communications in Mathematical Physic

Genome-wide meta-analysis uncovers novel loci influencing circulating leptin levels.

Leptin is an adipocyte-secreted hormone, the circulating levels of which correlate closely with overall adiposity. Although rare mutations in the leptin (LEP) gene are well known to cause leptin deficiency and severe obesity, no common loci regulating circulating leptin levels have been uncovered. Therefore, we performed a genome-wide association study (GWAS) of circulating leptin levels from 32,161 individuals and followed up loci reaching P&lt;10(-6) in 19,979 additional individuals. We identify five loci robustly associated (P&lt;5 × 10(-8)) with leptin levels in/near LEP, SLC32A1, GCKR, CCNL1 and FTO. Although the association of the FTO obesity locus with leptin levels is abolished by adjustment for BMI, associations of the four other loci are independent of adiposity. The GCKR locus was found associated with multiple metabolic traits in previous GWAS and the CCNL1 locus with birth weight. Knockdown experiments in mouse adipose tissue explants show convincing evidence for adipogenin, a regulator of adipocyte differentiation, as the novel causal gene in the SLC32A1 locus influencing leptin levels. Our findings provide novel insights into the regulation of leptin production by adipose tissue and open new avenues for examining the influence of variation in leptin levels on adiposity and metabolic health

Associations of autozygosity with a broad range of human phenotypes

In many species, the offspring of related parents suffer reduced reproductive success, a phenomenon known as inbreeding depression. In humans, the importance of this effect has remained unclear, partly because reproduction between close relatives is both rare and frequently associated with confounding social factors. Here, using genomic inbreeding coefficients (F-ROH) for >1.4 million individuals, we show that F-ROH is significantly associated (p <0.0005) with apparently deleterious changes in 32 out of 100 traits analysed. These changes are associated with runs of homozygosity (ROH), but not with common variant homozygosity, suggesting that genetic variants associated with inbreeding depression are predominantly rare. The effect on fertility is striking: F-ROH equivalent to the offspring of first cousins is associated with a 55% decrease [95% CI 44-66%] in the odds of having children. Finally, the effects of F-ROH are confirmed within full-sibling pairs, where the variation in F-ROH is independent of all environmental confounding.Peer reviewe

The Influence of Age and Sex on Genetic Associations with Adult Body Size and Shape : A Large-Scale Genome-Wide Interaction Study

Genome-wide association studies (GWAS) have identified more than 100 genetic variants contributing to BMI, a measure of body size, or waist-to-hip ratio (adjusted for BMI, WHRadjBMI), a measure of body shape. Body size and shape change as people grow older and these changes differ substantially between men and women. To systematically screen for age-and/or sex-specific effects of genetic variants on BMI and WHRadjBMI, we performed meta-analyses of 114 studies (up to 320,485 individuals of European descent) with genome-wide chip and/or Metabochip data by the Genetic Investigation of Anthropometric Traits (GIANT) Consortium. Each study tested the association of up to similar to 2.8M SNPs with BMI and WHRadjBMI in four strata (men 50y, women 50y) and summary statistics were combined in stratum-specific meta-analyses. We then screened for variants that showed age-specific effects (G x AGE), sex-specific effects (G x SEX) or age-specific effects that differed between men and women (G x AGE x SEX). For BMI, we identified 15 loci (11 previously established for main effects, four novel) that showed significant (FDR= 50y). No sex-dependent effects were identified for BMI. For WHRadjBMI, we identified 44 loci (27 previously established for main effects, 17 novel) with sex-specific effects, of which 28 showed larger effects in women than in men, five showed larger effects in men than in women, and 11 showed opposite effects between sexes. No age-dependent effects were identified for WHRadjBMI. This is the first genome-wide interaction meta-analysis to report convincing evidence of age-dependent genetic effects on BMI. In addition, we confirm the sex-specificity of genetic effects on WHRadjBMI. These results may providefurther insights into the biology that underlies weight change with age or the sexually dimorphism of body shape.Peer reviewe