On the Existence of the Quantum Action

We have previously proposed a conjecture stating that quantum mechanical transition amplitudes can be parametrized in terms of a quantum action. Here we give a proof of the conjecture and establish the existance of a local quantum action in the case of imaginary time in the Feynman-Kac limit (when temperature goes to zero). Moreover we discuss some symmetry properties of the quantum action.Comment: revised version, Text (LaTeX

Non-Linear Sigma Model on the Fuzzy Supersphere

In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S^(2,2). In hep-th/0212133 Bott projectors have been used to obtain the fuzzy CP^1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super) -projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model.Comment: 11 pages, LaTeX, corrected typo

Scalar Solitons on the Fuzzy Sphere

We study scalar solitons on the fuzzy sphere at arbitrary radius and noncommutativity. We prove that no solitons exist if the radius is below a certain value. Solitons do exist for radii above a critical value which depends on the noncommutativity parameter. We construct a family of soliton solutions which are stable and which converge to solitons on the Moyal plane in an appropriate limit. These solutions are rotationally symmetric about an axis and have no allowed deformations. Solitons that describe multiple lumps on the fuzzy sphere can also be constructed but they are not stable.Comment: 24 pages, 2 figures, typo corrected and stylistic changes. v3: reference adde

Space/Time Noncommutativity in String Theories without Background Electric Field

The appearance of space/time non-commutativity in theories of open strings with a constant non-diagonal background metric is considered. We show that, even if the space-time coordinates commute, when there is a metric with a time-space component, no electric field and the boundary condition along the spatial direction is Dirichlet, a Moyal phase still arises in products of vertex operators. The theory is in fact dual to the non-commutatitive open string (NCOS) theory. The correct definition of the vertex operators for this theory is provided. We study the system also in the presence of a $B$ field. We consider the case in which the Dirichlet spatial direction is compactified and analyze the effect of these background on the closed string spectrum. We then heat up the system. We find that the Hagedorn temperature depends in a non-extensive way on the parameters of the background and it is the same for the closed and the open string sectors.Comment: 18 pages, JHEP styl

Absorption of electromagnetic and gravitational waves by Kerr black holes

We calculate the absorption cross section for planar waves incident upon Kerr black holes, and present a unified picture for scalar, electromagnetic and gravitational waves. We highlight the spin-helicity effect that arises from a coupling between the rotation of the black hole and the helicity of a circularlypolarized wave. For the case of on-axis incidence, we introduce an extended ‘sinc approximation’ to quantify the spin-helicity effect in the strong-field regime

Conformal Affine Toda Soliton and Moduli of IIB Superstring on AdS5×S5AdS_5\times S^5

In this paper we interpret the hidden symmetry of the moduli space of IIB superstring on $AdS_{5}\times S^{5}$ in terms of the chiral embedding in $AdS_{5}$, which turns to be the $\mathbb{CP}^{3}$ conformal affine Toda model. We review how the position $\mu$ of poles in the Riemann-Hilbert formulation of dressing transformation and how the value of loop parameters $\mu$ in the vertex operator of affine algebra determines the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinize the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients $\mu$ of twistor.Comment: Final version, Misprints corrected, Note adde

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

Genome-wide by Environment Interaction Studies of Depressive Symptoms and Psychosocial Stress in UK Biobank and Generation Scotland

Stress is associated with poorer physical and mental health. To improve our understanding of this link, we performed genome-wide association studies (GWAS) of depressive symptoms and genome-wide by environment interaction studies (GWEIS) of depressive symptoms and stressful life events (SLE) in two UK population-based cohorts (Generation Scotland and UK Biobank). No SNP was individually significant in either GWAS, but gene-based tests identified six genes associated with depressive symptoms in UK Biobank (DCC, ACSS3, DRD2, STAG1, FOXP2 and KYNU; p < 2.77 x 10(-6)). Two SNPs with genome-wide significant GxE effects were identified by GWEIS in Generation Scotland: rs12789145 (53-kb downstream PIWIL4; p = 4.95 x 10(-9); total SLE) and rs17070072 (intronic to ZCCHC2; p = 1.46 x 10(-8); dependent SLE). A third locus upstream CYLC2 (rs12000047 and rs12005200, p < 2.00 x 10(-8); dependent SLE) when the joint effect of the SNP main and GxE effects was considered. GWEIS gene-based tests identified: MTNR1B with GxE effect with dependent SLE in Generation Scotland; and PHF2 with the joint effect in UK Biobank (p < 2.77 x 10(-6)). Polygenic risk scores (PRSs) analyses incorporating GxE effects improved the prediction of depressive symptom scores, when using weights derived from either the UK Biobank GWAS of depressive symptoms (p = 0.01) or the PGC GWAS of major depressive disorder (p = 5.91 x 10(-3)). Using an independent sample, PRS derived using GWEIS GxE effects provided evidence of shared aetiologies between depressive symptoms and schizotypal personality, heart disease and COPD. Further such studies are required and may result in improved treatments for depression and other stress-related conditions

Integrated analysis of environmental and genetic influences on cord blood DNA methylation in new-borns

Epigenetic processes, including DNA methylation (DNAm), are among the mechanisms allowing integration of genetic and environmental factors to shape cellular function. While many studies have investigated either environmental or genetic contributions to DNAm, few have assessed their integrated effects. Here we examine the relative contributions of prenatal environmental factors and genotype on DNA methylation in neonatal blood at variably methylated regions (VMRs) in 4 independent cohorts (overall n = 2365). We use Akaike’s information criterion to test which factors best explain variability of methylation in the cohort-specific VMRs: several prenatal environmental factors (E), genotypes in cis (G), or their additive (G + E) or interaction (GxE) effects. Genetic and environmental factors in combination best explain DNAm at the majority of VMRs. The CpGs best explained by either G, G + E or GxE are functionally distinct. The enrichment of genetic variants from GxE models in GWAS for complex disorders supports their importance for disease risk