Averages and moments associated to class numbers of imaginary quadratic fields

For any odd prime $\ell$, let $h_\ell(-d)$ denote the $\ell$-part of the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-d})$. Nontrivial pointwise upper bounds are known only for $\ell =3$; nontrivial upper bounds for averages of $h_\ell(-d)$ have previously been known only for $\ell =3,5$. In this paper we prove nontrivial upper bounds for the average of $h_\ell(-d)$ for all primes $\ell \geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\ell \geq 3$.Comment: 26 pages; minor edits to exposition and notation, to agree with published versio

Deformations of bordered Riemann surfaces and associahedral polytopes

We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface, relating it to the well-known phenomenon of bubbling. Our main result classifies all such spaces that can be realized as convex polytopes. A new polytope is introduced based on truncations of cubes, and its combinatorial and algebraic structures are related to generalizations of associahedra and multiplihedra.Comment: 25 pages, 31 figure

Simultaneous Integer Values of Pairs of Quadratic Forms

We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.Comment: 63 page

Thermionic reactor power system: Effects of radiation on integration with Manned Space Station

The application of a thermionic reactor power system to the modular space station is described. The nominal net power is 40 kWe, with the power system designed to be applicable over the power range from 25 to 60 kWe. The power system is designed to be launched by the space shuttle. Radiation protection is provided by LiH neutron shielding and W gamma shielding in a shaped 4 pion configuration, i.e., the reactor is shielded on all sides but not to equal extent. Isodose contours are presented for the region around the modular space station. Levels and spectral distribution of radiation are given for later evaluation of effects on space station experiments. Parametric data on the effects of separation distance on power system mass are presented

A Vaccine Against Group B Streptococcus: Recent Advances

Group B streptococcus (GBS) causes a high burden of neonatal and infant disease globally. Implementing a vaccine for pregnant women is a promising strategy to prevent neonatal and infant GBS disease and has been identified as a priority by the World Health Organisation (WHO). GBS serotype-specific polysaccharide – protein conjugate vaccines are at advanced stages of development, but a large number of participants would be required to undertake Phase III clinical efficacy trials. Efforts are therefore currently focused on establishing serocorrelates of protection in natural immunity studies as an alternative pathway for licensure of a GBS vaccine, followed by Phase IV studies to evaluate safety and effectiveness. Protein vaccines are in earlier stages of development but are highly promising as they might confer protection irrespective of serotype. Further epidemiological, immunological and health economic studies are required to enable the vaccine to reach its target population as soon as possible

The capacity to maintain ion and water homeostasis underlies interspecific variation in Drosophila cold tolerance

Many insects, including Drosophila, succumb to the physiological effects of chilling at temperatures well above those causing freezing. Low temperature causes a loss of extracellular ion and water homeostasis in such insects, and chill injuries accumulate. Using an integrative and comparative approach, we examined the role of ion and water balance in insect chilling susceptibility/ tolerance. The Malpighian tubules (MT), of chill susceptible Drosophila species lost [Na+] and [K+] selectivity at low temperatures, which contributed to a loss of Na+ and water balance and a deleterious increase in extracellular [K+]. By contrast, the tubules of chill tolerant Drosophila species maintained their MT ion selectivity, maintained stable extracellular ion concentrations, and thereby avoided injury. The most tolerant species were able to modulate ion balance while in a cold-induced coma and this ongoing physiological acclimation process allowed some individuals of the tolerant species to recover from chill coma during low temperature exposure. Accordingly, differences in the ability to maintain homeostatic control of water and ion balance at low temperature may explain large parts of the wide intra- and interspecific variation in insect chilling tolerance