Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences

We show that for many moduli spaces M of torsion sheaves on K3 surfaces S, the functor D(S) -> D(M) induced by the universal sheaf is a P-functor, hence can be used to construct an autoequivalence of D(M), and that this autoequivalence can be factored into geometrically meaningful equivalences associated to abelian fibrations and Mukai flops. Along the way we produce a derived equivalence between two compact hyperkaehler 2g-folds that are not birational, for every g >= 2. We also speculate about an approach to showing that birational moduli spaces of sheaves on K3 surfaces are derived-equivalent.Comment: 28 pages. typos corrected. final version to appear in JLM

Dynamics of fuel in tanks

The validity of the available theory in determining the natural frequency of the fundamental fuel sloshing mode in a rectangular tank was experimentally investigated. The results were found to agree within 5% over the whole range, end were quite accurate in the extreme "shallow and deep water" regions. A. qualitative investigation into baffle types and positioning indicates that baffles should be positioned in a region of highest velocity such that the surface waves are trapped and the energy dissipated at the shallowest depth possible, This suggests that, for a tank with varying liquid depth, a multi-perforated baffle should be employed. A total orifice area of one quarter the baffle area is suggested

Dynamics of fuel in tanks

The validity of the available theory in determining the natural frequency of the fundamental fuel sloshing mode in a rectangular tank was experimentally investigated. The results were found to agree within 5% over the whole range, end were quite accurate in the extreme "shallow and deep water" regions. A. qualitative investigation into baffle types and positioning indicates that baffles should be positioned in a region of highest velocity such that the surface waves are trapped and the energy dissipated at the shallowest depth possible, This suggests that, for a tank with varying liquid depth, a multi-perforated baffle should be employed. A total orifice area of one quarter the baffle area is suggested

Novel Autism Subtype-Dependent Genetic Variants Are Revealed by Quantitative Trait and Subphenotype Association Analyses of Published GWAS Data

The heterogeneity of symptoms associated with autism spectrum disorders (ASDs) has presented a significant challenge to genetic analyses. Even when associations with genetic variants have been identified, it has been difficult to associate them with a specific trait or characteristic of autism. Here, we report that quantitative trait analyses of ASD symptoms combined with case-control association analyses using distinct ASD subphenotypes identified on the basis of symptomatic profiles result in the identification of highly significant associations with 18 novel single nucleotide polymorphisms (SNPs). The symptom categories included deficits in language usage, non-verbal communication, social development, and play skills, as well as insistence on sameness or ritualistic behaviors. Ten of the trait-associated SNPs, or quantitative trait loci (QTL), were associated with more than one subtype, providing partial replication of the identified QTL. Notably, none of the novel SNPs is located within an exonic region, suggesting that these hereditary components of ASDs are more likely related to gene regulatory processes (or gene expression) than to structural or functional changes in gene products. Seven of the QTL reside within intergenic chromosomal regions associated with rare copy number variants that have been previously reported in autistic samples. Pathway analyses of the genes associated with the QTL identified in this study implicate neurological functions and disorders associated with autism pathophysiology. This study underscores the advantage of incorporating both quantitative traits as well as subphenotypes into large-scale genome-wide analyses of complex disorders