Generic singularities of nilpotent orbit closures

According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity of the nilpotent cone, the closure of the minimal nilpotent orbit is also an isolated symplectic singularity, called a minimal singularity. For classical Lie algebras, Kraft and Procesi showed that these two types of singularities suffice to describe all generic singularities of nilpotent orbit closures: specifically, any such singularity is either a simple surface singularity, a minimal singularity, or a union of two simple surface singularities of type $A_{2k-1}$. In the present paper, we complete the picture by determining the generic singularities of all nilpotent orbit closures in exceptional Lie algebras (up to normalization in a few cases). We summarize the results in some graphs at the end of the paper. In most cases, we also obtain simple surface singularities or minimal singularities, though often with more complicated branching than occurs in the classical types. There are, however, six singularities which do not occur in the classical types. Three of these are unibranch non-normal singularities: an $SL_2(\mathbb C)$-variety whose normalization is ${\mathbb A}^2$, an $Sp_4(\mathbb C)$-variety whose normalization is ${\mathbb A}^4$, and a two-dimensional variety whose normalization is the simple surface singularity $A_3$. In addition, there are three 4-dimensional isolated singularities each appearing once. We also study an intrinsic symmetry action on the singularities, in analogy with Slodowy's work for the regular nilpotent orbit.Comment: 56 pages (5 figures). Minor corrections. Accepted in Advances in Mat

A Study of the Attitudes of the Adventist Church Members in Taiwan Toward the Support of Seventh-day Adventist Christian Education

Problem. The Seventh-day Adventist denomination has developed a school system to serve theindividual needs of its members and general needs of the church. From 1972 to 1986, the educational work of the Adventist church in Taiwan has declined steadily. This study was to investigate the attitudes of church members toward the support of Adventist education on relation to demographic and personal variables. Method. The Adventist Christian Education Attitude Scale measured (1) demographic characteristics; (2) 59 attitude statements, arranged in five scales, identified by factor analysis; and (3) the 13 reasons why church members did not attend or send their youth to Adventistschools. Questionnaires were mailed to 495 church members, 457 of whom responded. The 18 null hypothesis were tested by the t-test for independent means and one-way analysis ofvariance, each hypothesis was tested at an alpha level of.05. Results. This study revealed the following: (1) Of the five identified areas of church members\u27 attitude toward Adventist education, the Christ-centered education and character building of children and youth was ranked highest; the curriculum offering and teacher qualifications lowest. (2) There was a significant difference in attitudes toward the support of Adventist education inrelation to 17 demographic and personal characteristics. (3) The first five reasons why church members do not attend or do not send their youth to Adventist schools were: (a) the schools are not officially recognized by the Taiwan government; (b) opportunity to find a job after graduation is limited; (c) the cost for Adventist education is too burdensome; (d) the curriculum offering is limited; and (e) teachers are inadequately qualified. Conclusions. The major conclusions were: (1) Ministers and teachers had a more favorable attitude than members in other occupations toward the support of Adventist education. (2) Parents who were members of the Adventist church had a more positive attitude toward Adventist education than those parents who had other religious affiliations. (3) Church memberswho had attended an Adventist school for a longer period of time reported a higher degree of support for Adventist schools than those who had attended an Adventist school for a shorter period of time. (4) Church members who had attended an Adventist college had a more negative attitude toward the Adventist education than those who had not

Chip-based microcavities coupled to NV centers in single crystal diamond

Optical coupling of nitrogen vacancy centers in single-crystal diamond to an on-chip microcavity is demonstrated. The microcavity is fabricated from a hybrid gallium phosphide and diamond material system, and supports whispering gallery mode resonances with spectrometer resolution limited Q > 25000

Topological magnetic textures in magnetic topological insulators

The surfaces of intrinsic magnetic topological insulators (TIs) host magnetic moments exchange-coupled to Dirac electrons. We study the magnetic phases arising from tuning the electron density using variational and exact diagonalization approaches. In the dilute limit, we find that magnetic skrymions are formed which bind to electrons leading to a skyrmion Wigner crystal phase while at higher densities spin spirals accompanied by chiral 1d channels of electrons are formed. The binding of electrons to textures raises the possibility of manipulating textures with electrostatic gating. We determine the phase diagram capturing the competition of intrinsic spin-spin interactions and carrier density and comment on the possible application to experiments in magnetic TIs and spintronic devices such as skyrmion-based memory.Comment: v2: highlighted the 4-parameter parameterization of skyrmions and elaborated on skyrmion Wigner crystal phase v1: 6+3 pages, 5 figure

Nanocavity enhanced diamond nitrogen-vacancy center zero phonon line emission

Resonantly enhanced emission of the zero phonon line of a diamond nitrogen-vacancy center in single crystal diamond is demonstrated experimentally using a hybrid whispering gallery mode nanocavity

Genome informatics: advances in theory and practice

A report on the 20th International Conference on Genome Informatics, Yokohama, Japan, 14-16 December 2009

Mass-concentration relation of clusters of galaxies from CFHTLenS

Based on weak lensing data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), in this paper we study the mass-concentration ($M$-$c$) relation for $\sim 200$ redMaPPer clusters in the fields. We extract the $M$-$c$ relation by measuring the density profiles of individual clusters instead of using stacked weak lensing signals. By performing Monte Carlo simulations, we demonstrate that although the signal-to-noise ratio for each individual cluster is low, the unbiased $M$-$c$ relation can still be reliably derived from a large sample of clusters by carefully taking into account the impacts of shape noise, cluster center offset, dilution effect from member or foreground galaxies, and the projection effect. Our results show that within error bars the derived $M$-$c$ relation for redMaPPer clusters is in agreement with simulation predictions. There is a weak deviation in that the halo concentrations calibrated by Monte Carlo simulations are somewhat higher than that predicted from ${\it Planck}$ cosmology.Comment: Accepted for Publication in ApJ. 18 pages, 8 figures. Updated to match the published versio

Quantum Walk Inspired Dynamic Adiabatic Local Search

We investigate the irreconcilability issue that raises from translating the search algorithm from the Continuous-Time Quantum Walk (CTQW) framework to the Adiabatic Quantum Computing (AQC) framework. One major issue is the constant energy gap in the translated Hamiltonian throughout the AQC schedule. To resolve the issue in the initial investigation, we choose only Z operator as the catalyst Hamiltonian and show that this modification keeps the running time optimal. Inspired by this irreconcilability issue and our solution, we further investigate to find the proper timing for releasing the chosen catalyst Hamiltonian and the suitable coefficient function of the catalyst Hamiltonian in the AQC schedule to improve the Adiabatic local search.Comment: 9 pages, 8 figure