Weak Liouville-Arnold Theorems & Their Implications

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two theorems reminiscent of the Liouville-Arnold theorem. Moreover, we also obtain results on the structure of the configuration spaces of such systems that are reminiscent of results on the configuration space of completely integrable Tonelli Hamiltonians.Comment: 24 pages, 1 figure; v2 corrects typo in online abstract; v3 includes new title (was: A Weak Liouville-Arnold Theorem), re-arrangement of introduction, re-numbering of main theorems; v4 updates the authors' email and physical addresses, clarifies notation in section 4. Final versio

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Which antidepressants have demonstrated superior efficacy? A review of the evidence

A review of published evidence of superior efficacy of a particular antidepressant in major depressive disorder may assist clinicians in making considered treatment choices. To identify such candidates, an international group of experts met to assess published evidence (identified through searches in Medline and Embase databases and discussions with experts in the field) from randomized, controlled trials and meta-analyses comparing two antidepressants under conditions of fair comparison. Criteria were defined to judge the strength of evidence. Two pivotal studies in moderate-to-severe major depressive disorder that demonstrate superiority on the primary efficacy measure, or alternatively one pivotal study supported by consistent results from meta-analyses, was considered to constitute evidence for definite superiority. Three antidepressants met these criteria: clomipramine, venlafaxine, and escitalopram. Three antidepressants were found to have probable superiority: milnacipran, duloxetine, and mirtazapine. Only escitalopram was found to have definite superiority in the treatment of severe depression; probable superiority was identified for venlafaxine and possible superiority for milnacipran and clomipramine. This review of published data found evidence that only a very few antidepressants are shown to be more effective than other

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Meta-analysis of genome-wide association studies of anxiety disorders.

Anxiety disorders (ADs), namely generalized AD, panic disorder and phobias, are common, etiologically complex conditions with a partially genetic basis. Despite differing on diagnostic definitions based on clinical presentation, ADs likely represent various expressions of an underlying common diathesis of abnormal regulation of basic threat-response systems. We conducted genome-wide association analyses in nine samples of European ancestry from seven large, independent studies. To identify genetic variants contributing to genetic susceptibility shared across interview-generated DSM-based ADs, we applied two phenotypic approaches: (1) comparisons between categorical AD cases and supernormal controls, and (2) quantitative phenotypic factor scores (FS) derived from a multivariate analysis combining information across the clinical phenotypes. We used logistic and linear regression, respectively, to analyze the association between these phenotypes and genome-wide single nucleotide polymorphisms. Meta-analysis for each phenotype combined results across the nine samples for over 18 000 unrelated individuals. Each meta-analysis identified a different genome-wide significant region, with the following markers showing the strongest association: for case-control contrasts, rs1709393 located in an uncharacterized non-coding RNA locus on chromosomal band 3q12.3 (P=1.65 × 10(-8)); for FS, rs1067327 within CAMKMT encoding the calmodulin-lysine N-methyltransferase on chromosomal band 2p21 (P=2.86 × 10(-9)). Independent replication and further exploration of these findings are needed to more fully understand the role of these variants in risk and expression of ADs.Molecular Psychiatry advance online publication, 12 January 2016; doi:10.1038/mp.2015.197

Novel loci affecting iron homeostasis and their effects in individuals at risk for hemochromatosis

Variation in body iron is associated with or causes diseases, including anaemia and iron overload. Here, we analyse genetic association data on biochemical markers of iron status from 11 European-population studies, with replication in eight additional cohorts (total up to 48,972 subjects). We find 11 genome-wide-significant (P<5 × 10(-8)) loci, some including known iron-related genes (HFE, SLC40A1, TF, TFR2, TFRC, TMPRSS6) and others novel (ABO, ARNTL, FADS2, NAT2, TEX14). SNPs at ARNTL, TF, and TFR2 affect iron markers in HFE C282Y homozygotes at risk for hemochromatosis. There is substantial overlap between our iron loci and loci affecting erythrocyte and lipid phenotypes. These results will facilitate investigation of the roles of iron in disease

Linear Collider Physics Resource Book for Snowmass 2001, 3: Studies of Exotic and Standard Model Physics

This Resource Book reviews the physics opportunities of a next-generation e+e- linear collider and discusses options for the experimental program. Part 3 reviews the possible experiments on that can be done at a linear collider on strongly coupled electroweak symmetry breaking, exotic particles, and extra dimensions, and on the top quark, QCD, and two-photon physics. It also discusses the improved precision electroweak measurements that this collider will make available.This Resource Book reviews the physics opportunities of a next-generation e+e- linear collider and discusses options for the experimental program. Part 3 reviews the possible experiments on that can be done at a linear collider on strongly coupled electroweak symmetry breaking, exotic particles, and extra dimensions, and on the top quark, QCD, and two-photon physics. It also discusses the improved precision electroweak measurements that this collider will make available

Meta-analysis of Genome-Wide Association Studies for Extraversion: Findings from the Genetics of Personality Consortium

Extraversion is a relatively stable and heritable personality trait associated with numerous psychosocial, lifestyle and health outcomes. Despite its substantial heritability, no genetic variants have been detected in previous genome-wide association (GWA) studies, which may be due to relatively small sample sizes of those studies. Here, we report on a large meta-analysis of GWA studies for extraversion in 63,030 subjects in 29 cohorts. Extraversion item data from multiple personality inventories were harmonized across inventories and cohorts. No genome-wide significant associations were found at the single nucleotide polymorphism (SNP) level but there was one significant hit at the gene level for a long non-coding RNA site (LOC101928162). Genome-wide complex trait analysis in two large cohorts showed that the additive variance explained by common SNPs was not significantly different from zero, but polygenic risk scores, weighted using linkage information, significantly predicted extraversion scores in an independent cohort. These results show that extraversion is a highly polygenic personality trait, with an architecture possibly different from other complex human traits, including other personality traits. Future studies are required to further determine which genetic variants, by what modes of gene action, constitute the heritable nature of extraversion