The modal mu-calculus alternation hierarchy is strict

AbstractOne of the open questions about the modal mu-calculus is whether the alternation hierarchy collapses; that is, whether all modal fixpoint properties can be expressed with only a few alternations of least and greatest fixpoints. In this paper, we resolve this question by showing that the hierarchy does not collapse

Destruction of 18F via 18F(p,α) 15O burning through the Ec.m.=665 keV resonance

Knowledge of the astrophysical rate of the 18F(p,α)15O reaction is important for understanding the γ-ray emission expected from novae and heavy-element production in x-ray bursts. The rate of this reaction is dominated at temperatures above ∼0.4 GK by a resonance near 7.08 MeV excitation energy in 19Ne. The 18F(p,α)15O rate has been uncertain in part because of disagreements among previous measurements concerning the resonance strength and excitation energy of this state. To resolve these uncertainties, we have made simultaneous measurements of the 1H(18F,p)18F and 1H(18F,α)15O excitation functions using a radioactive 18F beam at the ORNL Holifield Radioactive Ion Beam Facility. A simultaneous fit of the data sets has been performed, and the best fit was obtained with a center-of-mass resonance energy of 664.7±1.6 keV (Ex = 7076±2 keV), a total width of 39.0±1.6 keV, a proton branching ratio of Γp/Γ = 0.39±0.02, and a resonance strength of ωγ= 6.2±0.3 keV

Kinematically complete measurement of the 1H(18F,p)18F excitation function for the astrophysically important 7.08-MeV state in 19Ne

Knowledge of the astrophysical [Formula Presented] rate is important for understanding gamma-ray emission from novae and heavy-element production in x-ray bursts. A state with [Formula Presented] in [Formula Presented] provides an s-wave resonance and, depending on its properties, could dominate the [Formula Presented] rate. By measuring a kinematically complete [Formula Presented] excitation function with a radioactive [Formula Presented] beam at the ORNL Holifield Radioactive Ion Beam Facility, we find that the [Formula Presented] state lies at a center-of-mass energy of [Formula Presented] has a total width of [Formula Presented] and a proton partial-width of [Formula Presented]

Associations of autozygosity with a broad range of human phenotypes

In many species, the offspring of related parents suffer reduced reproductive success, a phenomenon known as inbreeding depression. In humans, the importance of this effect has remained unclear, partly because reproduction between close relatives is both rare and frequently associated with confounding social factors. Here, using genomic inbreeding coefficients (F-ROH) for >1.4 million individuals, we show that F-ROH is significantly associated (p <0.0005) with apparently deleterious changes in 32 out of 100 traits analysed. These changes are associated with runs of homozygosity (ROH), but not with common variant homozygosity, suggesting that genetic variants associated with inbreeding depression are predominantly rare. The effect on fertility is striking: F-ROH equivalent to the offspring of first cousins is associated with a 55% decrease [95% CI 44-66%] in the odds of having children. Finally, the effects of F-ROH are confirmed within full-sibling pairs, where the variation in F-ROH is independent of all environmental confounding.Peer reviewe

Analysis of shared heritability in common disorders of the brain

Paroxysmal Cerebral Disorder

Open proofs and open terms: A basis for interactive logic

When proving a theorem, one makes intermediate claims, leaving parts temporarily unspecified. These ‘open’ parts may be proofs but also terms. In interactive theorem proving systems, one prominently deals with these ‘unfinished proofs’ and ‘open terms’. We study these ‘open phenomena’ from the point of view of logic. This amounts to finding a correctness criterion for ‘unfinished proofs’ (where some parts may be left open, but the logical steps that have been made are still correct). Furthermore we want to capture the notion of ‘proof state’. Proof states are the objects that interactive theorem provers operate on and we want to understand them in terms of logic. In this paper we define ‘open higher order predicate logic’, an extension of higher order logic with unfinished (open) proofs and open terms. Then we define a type theoretic variant of this open higher order logic together with a formulas-as-types embedding from open higher order logic to this type theory. We show how this type theory nicely captures the notion of ‘proof state’, which is now a type-theoretic context