Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

NASA's Understanding of Risk in Apollo and Shuttle

Mathematical risk analysis was used in Apollo, but it gave unacceptably pessimistic resultsand was discontinued. Shuttle was designed without using risk analysis, under the assumptionthat good engineering would make it very safe. This approach led to an unnecessarily riskydesign, which directly led to the Shuttle tragedies. Although the Challenger disaster wasdirectly due to a mistaken launch decision, it might have been avoided by a safer design. Theultimate cause of the Shuttle tragedies was the Apollo era decision to abandon risk analysis

First Stars. I. Evolution without mass loss

The first generation of stars was formed from primordial gas. Numerical simulations suggest that the first stars were predominantly very massive, with typical masses M > 100 Mo. These stars were responsible for the reionization of the universe, the initial enrichment of the intergalactic medium with heavy elements, and other cosmological consequences. In this work, we study the structure of Zero Age Main Sequence stars for a wide mass and metallicity range and the evolution of 100, 150, 200, 250 and 300 Mo galactic and pregalactic Pop III very massive stars without mass loss, with metallicity Z=10E-6 and 10E-9, respectively. Using a stellar evolution code, a system of 10 equations together with boundary conditions are solved simultaneously. For the change of chemical composition, which determines the evolution of a star, a diffusion treatment for convection and semiconvection is used. A set of 30 nuclear reactions are solved simultaneously with the stellar structure and evolution equations. Several results on the main sequence, and during the hydrogen and helium burning phases, are described. Low metallicity massive stars are hotter and more compact and luminous than their metal enriched counterparts. Due to their high temperatures, pregalactic stars activate sooner the triple alpha reaction self-producing their own heavy elements. Both galactic and pregalactic stars are radiation pressure dominated and evolve below the Eddington luminosity limit with short lifetimes. The physical characteristics of the first stars have an important influence in predictions of the ionizing photon yields from the first luminous objects; also they develop large convective cores with important helium core masses which are important for explosion calculations.Comment: 17 pages, 24 figures, 2 table

Magnetic Reconnection in Extreme Astrophysical Environments

Magnetic reconnection is a basic plasma process of dramatic rearrangement of magnetic topology, often leading to a violent release of magnetic energy. It is important in magnetic fusion and in space and solar physics --- areas that have so far provided the context for most of reconnection research. Importantly, these environments consist just of electrons and ions and the dissipated energy always stays with the plasma. In contrast, in this paper I introduce a new direction of research, motivated by several important problems in high-energy astrophysics --- reconnection in high energy density (HED) radiative plasmas, where radiation pressure and radiative cooling become dominant factors in the pressure and energy balance. I identify the key processes distinguishing HED reconnection: special-relativistic effects; radiative effects (radiative cooling, radiation pressure, and Compton resistivity); and, at the most extreme end, QED effects, including pair creation. I then discuss the main astrophysical applications --- situations with magnetar-strength fields (exceeding the quantum critical field of about 4 x 10^13 G): giant SGR flares and magnetically-powered central engines and jets of GRBs. Here, magnetic energy density is so high that its dissipation heats the plasma to MeV temperatures. Electron-positron pairs are then copiously produced, making the reconnection layer highly collisional and dressing it in a thick pair coat that traps radiation. The pressure is dominated by radiation and pairs. Yet, radiation diffusion across the layer may be faster than the global Alfv\'en transit time; then, radiative cooling governs the thermodynamics and reconnection becomes a radiative transfer problem, greatly affected by the ultra-strong magnetic field. This overall picture is very different from our traditional picture of reconnection and thus represents a new frontier in reconnection research.Comment: Accepted to Space Science Reviews (special issue on magnetic reconnection). Article is based on an invited review talk at the Yosemite-2010 Workshop on Magnetic Reconnection (Yosemite NP, CA, USA; February 8-12, 2010). 30 pages, no figure

Energy loss due to defect formation from 206Pb recoils in SuperCDMS germanium detectors

The Super Cryogenic Dark Matter Search experiment at the Soudan Underground Laboratory studied energy loss associated with defect formation in germanium crystals at mK temperatures using in situ 210Pb sources. We examine the spectrum of 206Pb nuclear recoils near its expected 103 keV endpoint energy and determine an energy loss of (6:08 ± 0:18)%, which we attribute to defect formation. From this result and using TRIM simulations, we extract the first experimentally determined average displacement threshold energy of 19.7+0.6−0.5 eV for germanium. This has implications for the analysis thresholds of future germanium-based dark matter searches

Clustered mutations in the GRIK2 kainate receptor subunit gene underlie diverse neurodevelopmental disorders

Kainate receptors (KARs) are glutamate-gated cation channels with diverse roles in the central nervous system. Bi-allelic loss of function of the KAR-encoding gene GRIK2 causes a nonsyndromic neurodevelopmental disorder (NDD) with intellectual disability and developmental delay as core features. The extent to which mono-allelic variants in GRIK2 also underlie NDDs is less understood because only a single individual has been reported previously. Here, we describe an additional eleven individuals with heterozygous de novo variants in GRIK2 causative for neurodevelopmental deficits that include intellectual disability. Five children harbored recurrent de novo variants (three encoding p.Thr660Lys and two p.Thr660Arg), and four children and one adult were homozygous for a previously reported variant (c.1969G>A [p.Ala657Thr]). Individuals with shared variants had some overlapping behavioral and neurological dysfunction, suggesting that the GRIK2 variants are likely pathogenic. Analogous mutations introduced into recombinant GluK2 KAR subunits at sites within the M3 transmembrane domain (encoding p.Ala657Thr, p.Thr660Lys, and p.Thr660Arg) and the M3-S2 linker domain (encoding p.Ile668Thr) had complex effects on functional properties and membrane localization of homomeric and heteromeric KARs. Both p.Thr660Lys and p.Thr660Arg mutant KARs exhibited markedly slowed gating kinetics, similar to p.Ala657Thr-containing receptors. Moreover, we observed emerging genotype-phenotype correlations, including the presence of severe epilepsy in individuals with the p.Thr660Lys variant and hypomyelination in individuals with either the p.Thr660Lys or p.Thr660Arg variant. Collectively, these results demonstrate that human GRIK2 variants predicted to alter channel function are causative for early childhood development disorders and further emphasize the importance of clarifying the role of KARs in early nervous system development.Genetics of disease, diagnosis and treatmen