The empirical process on Gaussian spherical harmonics

We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literature, in connection with the statistical analysis of cosmic microwave background radiation

Moduli of sheaves and the Chow group of K3 surfaces

Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c_X on X of degree 1: it is represented by any point lying on a rational curve in X. Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of the Beauville-Voisin class c_X if certain hypotheses hold and he conjectured that the additional hypotheses are unnecessary. We believe that the following generalization of Huybrechts' conjecture holds. Let M and N be moduli spaces of stable pure sheaves on X (with fixed cohomological Chern characters) and suppose that they have the same dimension: then the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) is equal to the set whose elements are second Chern classes of sheaves parametrized by the closure of N after a translation by a suitable multiple of c_X (so that degrees match). We will prove that the above statement holds under some additional assumptions.Comment: Deleted a footnote and replaced it by a sentence in the main body of the pape

Periods of Double EPW-sextics

We study the indeterminacy locus of the period map for double EPW-sextics. We recall that double EPW-sextics are parametrized by lagrangian subspaces of the third wedge-product of a 6-dimensional complex vector-space. The indeterminacy locus is contained in the set of lagrangians containing a decomposable vector. The projectivization of the 3-dimensional support of such a decomposable vector contains a degeneracy subscheme which is either all of the plane or a sextic curve. We show that the period map is regular on any lagrangian A such that for all decomposables in A the corresponding degeneracy subscheme is a GIT-semistable sextic curve whose closure (in the semistable locus) does not contain a triple conic.Comment: We added a proof that the the period map of double EPW-sextics with isolated singularities is an open embedding into the complement of four explicit arithmetic divisors in the period space. Gave precise references to results of "Moduli of double EPW-sextics" (latest arXiv version) which will appear in Memoirs of the AM

Lattice Gauge Fixing for Parameter Dependent Covariant Gauges

We propose a non-perturbative procedure to fix generic covariant gauges on the lattice. Varying the gauge parameter, this gauge fixing provides a concrete method to check numerically the gauge dependence of correlators measured on the lattice. The new algorithm turns out to converge with a good efficiency. As a preliminary physical result, we find a sensitive dependence of the gluon propagator on the gauge parameter.Comment: 10 pages (LaTeX2e), 5 eps figure

Comorbid depressive disorders in ADHD. the role of ADHD severity, subtypes and familial psychiatric disorders

ObjectiveaaTo evaluate the presence of Major Depressive Disorder (MDD) and Dysthymic Disorder (DD) in a sample of Italian children with Attention Deficit Hyperactivity Disorder (ADHD) and to explore specific features of comorbid depressive disorders in ADHD. MethodsaaThree hundred and sixty-six consecutive, drug-naïve Caucasian Italian outpatients with ADHD were recruited and comorbid disorders were evaluated using DSM-IV-TR criteria. To evaluate ADHD severity, parents of all children filled out the ADHD Rating Scale. Thirty-seven children with comorbid MDD or DD were compared with 118 children with comorbid conduct disorder and 122 without comorbidity for age, sex, IQ level, family psychiatric history, and ADHD subtypes and severity. Resultsaa42 of the ADHD children displayed comorbid depressive disorders: 16 exhibited MDD, 21 DD, and 5 both MDD and DD. The frequency of hyperactive-impulsive subtypes was significantly lower in ADHD children with depressive disorders, than in those without any comorbidity. ADHD children with depressive disorders showed a higher number of familial psychiatric disorders and higher score in the Inattentive scale of the ADHD Rating Scale, than children without any comorbidity. No differences were found for age, sex and IQ level between the three groups. Conclusions: Consistent with previous studies in other countries, depressive disorders affect a significant proportion of ADHD children in Italy. Patient assessment and subsequent treatment should take into consideration the possible presence of this comorbidity, which could specifically increase the severity of ADHD attention problems