Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori where the Schrodinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density $\rho(p,q,t)$ going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.Comment: 36 pages, RevTex preprint forma

Decay of Classical Chaotic Systems - the Case of the Bunimovich Stadium

The escape of an ensemble of particles from the Bunimovich stadium via a small hole has been studied numerically. The decay probability starts out exponentially but has an algebraic tail. The weight of the algebraic decay tends to zero for vanishing hole size. This behaviour is explained by the slow transport of the particles close to the marginally stable bouncing ball orbits. It is contrasted with the decay function of the corresponding quantum system.Comment: 16 pages, RevTex, 3 figures are available upon request from [email protected], to be published in Phys.Rev.

Identification of common genetic risk variants for autism spectrum disorder

Autism spectrum disorder (ASD) is a highly heritable and heterogeneous group of neurodevelopmental phenotypes diagnosed in more than 1% of children. Common genetic variants contribute substantially to ASD susceptibility, but to date no individual variants have been robustly associated with ASD. With a marked sample-size increase from a unique Danish population resource, we report a genome-wide association meta-analysis of 18,381 individuals with ASD and 27,969 controls that identified five genome-wide-significant loci. Leveraging GWAS results from three phenotypes with significantly overlapping genetic architectures (schizophrenia, major depression, and educational attainment), we identified seven additional loci shared with other traits at equally strict significance levels. Dissecting the polygenic architecture, we found both quantitative and qualitative polygenic heterogeneity across ASD subtypes. These results highlight biological insights, particularly relating to neuronal function and corticogenesis, and establish that GWAS performed at scale will be much more productive in the near term in ASD.Peer reviewe

Discovery of the first genome-wide significant risk loci for attention deficit/hyperactivity disorder.

Attention deficit/hyperactivity disorder (ADHD) is a highly heritable childhood behavioral disorder affecting 5% of children and 2.5% of adults. Common genetic variants contribute substantially to ADHD susceptibility, but no variants have been robustly associated with ADHD. We report a genome-wide association meta-analysis of 20,183 individuals diagnosed with ADHD and 35,191 controls that identifies variants surpassing genome-wide significance in 12 independent loci, finding important new information about the underlying biology of ADHD. Associations are enriched in evolutionarily constrained genomic regions and loss-of-function intolerant genes and around brain-expressed regulatory marks. Analyses of three replication studies: a cohort of individuals diagnosed with ADHD, a self-reported ADHD sample and a meta-analysis of quantitative measures of ADHD symptoms in the population, support these findings while highlighting study-specific differences on genetic overlap with educational attainment. Strong concordance with GWAS of quantitative population measures of ADHD symptoms supports that clinical diagnosis of ADHD is an extreme expression of continuous heritable traits