U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator

We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but an U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.Comment: 8 pages, 0 figures, pusblished in Physical Review Letters 95, 252501 (2005

Transparent interface between software and hardware versions of ADA compilation units

technical reportThe Ada-to-Silicon project at Utah is developing a methodology (and associated software and hardware) for the high level testing of Ada compilation units that are represented as hardware components (circuitry). There are two motivations for this research

Speckle interferometry at SOAR in 2015

The results of speckle interferometric observations at the SOAR telescope in 2015 are given, totalling 1303 measurements of 924 resolved binary and multiple stars and non-resolutions of 260 targets. The separations range from 12 mas to 3.37" (median 0.17"); the maximum measured magnitude difference is 6.7 mag. We resolved 27 pairs for the first time, including 10 as inner or outer subsystems in previously known binaries, e.g. the 50-mas pair in Epsilon Cha. Newly resolved pairs are commented upon. We discuss three apparently non-hierarchical systems discovered in this series, arguing that their unusual configuration results from projection. The resolved quadruple system HIP 71510 is studied as well.Comment: 10 pages, 8 figures. Accepted for publication in AJ. The online tables are not included, available from Tokovinin on request. arXiv admin note: text overlap with arXiv:1506.0571

Six-dimensional Davidson potential as a dynamical symmetry of the symplectic Interacting Vector Boson Model

A six-dimensional Davidson potential, introduced within the framework of the Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit transitional spectra between the purely rotational and vibrational limits of the theory. The results are shown to relate to a new dynamical symmetry that starts with the $Sp(12,R) \supset SU(1,1) \times SO(6)$ reduction. Exact solutions for the eigenstates of the model Hamiltonian in the basis defined by a convenient subgroup chain of SO(6) are obtained. A comparison of the theoretical results with experimental data for heavy nuclei with transitional spectra illustrates the applicability of the theory.Comment: 9 pages, 4 figure

Classification of states of single-jj fermions with JJ-pairing interaction

In this paper we show that a system of three fermions is exactly solvable for the case of a single-$j$ in the presence of an angular momentum-$J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-$j$ symbols. It is also found that the "non-integer" eigenvalues of three fermions with angular momentum $I$ around the maximum appear as "non-integer" eigenvalues of four fermions when $I$ is around (or larger than) $J_{\rm max}$ and the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J=J_{\rm max}=2j-1$. This pattern is also found in five and six fermion systems. A boson system with spin $l$ exhibits a similar pattern.Comment: to be published in Physical Review

Sleep, major depressive disorder and Alzheimer’s disease: a Mendelian randomisation study

Objective To explore the causal relationships between sleep, major depressive disorder (MDD), and Alzheimer’s disease (AD). Methods We conducted bi-directional two-sample Mendelian randomisation analyses. Genetic associations were obtained from the largest genome-wide association studies currently available in UK Biobank (N=446,118), the Psychiatric Genomics Consortium (N=18,759), and the International Genomics of Alzheimer’s Project (N=63,926). We used the inverse variance weighted Mendelian randomisation method to estimate causal effects, and weighted median and MR-Egger for sensitivity analyses to test for pleiotropic effects. Results We found that higher risk of AD was significantly associated with being a “morning person” (odds ratio (OR)=1.01, P=0.001), shorter sleep duration (self-reported: β=-0.006, P=1.9×10-4; accelerometer-based: β=-0.015, P=6.9×10-5), less likely to report long sleep (β=-0.003, P=7.3×10-7), earlier timing of the least active 5 hours (β=-0.024, P=1.7×10-13), and a smaller number of sleep episodes (β=-0.025, P=5.7×10-14) after adjusting for multiple comparisons. We also found that higher risk of AD was associated with lower risk of insomnia (OR=0.99, P=7×10-13). However, we did not find evidence either that these abnormal sleep patterns were causally related to AD or for a significant causal relationship between MDD and risk of AD. Conclusion We found that AD may causally influence sleep patterns. However, we did not find evidence supporting a causal role of disturbed sleep patterns for AD or evidence for a causal relationship between MDD and AD