Multiplicity one theorems: the Archimedean case

Let $G$ be one of the classical Lie groups \GL_{n+1}(\R), \GL_{n+1}(\C), \oU(p,q+1), \oO(p,q+1), \oO_{n+1}(\C), \SO(p,q+1), \SO_{n+1}(\C), and let $G'$ be respectively the subgroup \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \oO(p,q), \oO_n(\C), \SO(p,q), \SO_n(\C), embedded in $G$ in the standard way. We show that every irreducible Casselman-Wallach representation of $G'$ occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of $G$. Similar results are proved for the Jacobi groups \GL_{n}(\R)\ltimes \oH_{2n+1}(\R), \GL_{n}(\C)\ltimes \oH_{2n+1}(\C), \oU(p,q)\ltimes \oH_{2p+2q+1}(\R), \Sp_{2n}(\R)\ltimes \oH_{2n+1}(\R), \Sp_{2n}(\C)\ltimes \oH_{2n+1}(\C), with their respective subgroups \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \Sp_{2n}(\R), \Sp_{2n}(\C).Comment: To appear in Annals of Mathematic

Four-qubit entanglement from string theory

We invoke the black hole/qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D=4 to D=3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references adde

Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices

This paper is mainly a review of the multi--Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include master symmetries, recursion operators, higher Poisson brackets, invariants and group symmetries for the systems. In addition to the positive hierarchy we also consider the negative hierarchy which is crucial in establishing the bi--Hamiltonian structure for each particular simple Lie group. Finally, we include some results on point and Noether symmetries and an interesting connection with the exponents of simple Lie groups. The case of exceptional simple Lie groups is still an open problem.Comment: 65 pages, 67 reference

Mapping epilepsy-specific patient-reported outcome measures for children to a proposed core outcome set for childhood epilepsy

This is the final version. Available on open access from Elsevier via the DOI in this recordObjective: The objectives of the study were to (1) map questions in epilepsy-specific patient-reported outcome measures (PROMs) of children's health-related quality of life (HRQoL) to a proposed core outcome set (COS) for childhood epilepsy research and (2) gain insight into the acceptability of two leading candidate PROMs. Method: We identified 11 epilepsy-specific PROMs of children's HRQoL (17 questionnaire versions) in a previous systematic review. Each item from the PROMs was mapped to 38 discrete outcomes across 10 domains of the COS: seizures, sleep, social functioning, mental health, cognition, physical functioning, behavior, adverse events, family life, and global quality of life. We consulted with three children with epilepsy and six parents of children with epilepsy in Patient Public Involvement and Engagement (PPIE) work to gain an understanding of the acceptability of the two leading PROMs from our review of measurement properties: Quality of Life in Childhood Epilepsy (QOLCE-55) and Health-Related Quality of Life Measure for Children with Epilepsy (CHEQOL). Results: Social Functioning is covered by all PROMs except DISABKIDS and G-QOLCE and Mental Health is covered by all PROMs except G-QOLCE and Hague Restrictions in Childhood Epilepsy Scale (HARCES). Only two PROMs (Epilepsy and Learning Disability Quality of Life (ELDQOL) and Glasgow Epilepsy Outcome Scale (GEOS-YP)) have items that cover the Seizure domain. The QOLCE-55 includes items that cover the domains of Physical Functioning, Social Functioning, Behavior, Mental Health, and Cognition. The CHEQOL parent and child versions cover the same domains as QOLCE-55 except for Physical Functioning and Behavior, and the child version has one item that covers the discrete outcome of Overall Quality of Life and one item that covers the discrete outcome of Relationship with parents and siblings. The QOLCE-55 parent version was acceptable to the parents we consulted with, and CHEQOL parent and child versions were described as acceptable to our child and parent advisory panel members. Significance: Mapping items from existing epilepsy-specific PROMs for children is an important step in operationalizing our COS for childhood epilepsy research, alongside evaluation of their measurement properties. Two leading PROMS, QOLCE-55 and CHEQOL, cover a wide range of domains from our COS and would likely be used in conjunction with assessment tools selected for specific study objectives. The PPIE work provided practical insights into the administration and acceptability of candidate PROMs in appropriate context. We promote our COS as a framework for selecting outcomes and PROMs for future childhood epilepsy evaluative research.National Institute for Health Research (NIHR)Canadian Institutes of Health ResearchWaterloo FoundationCharles Sykes Epilepsy Research Trus

Feasibility and Informative Value of Environmental Sample Collection in the National Children\u27s Vanguard Study

Background: Birth cohort studies provide the opportunity to advance understanding of the impact of environmental factors on childhood health and development through prospective collection of environmental samples. Methods: We evaluated the feasibility and informative value of the environmental sample collection methodology in the initial pilot phase of the National Children\u27s Study, a planned U.S. environmental birth cohort study. Environmental samples were collected from January 2009–September 2010 at up to three home visits: pre-pregnancy (n¼306), pregnancy (n¼807), and 6-months postnatal (n¼117). Collections included air for particulate matter r2.5 mm (PM2.5), nitrogen dioxide, ozone, volatile organic compounds (VOCs), and carbonyls; vacuum dust for allergens/endotoxin; water for VOCs, trihalomethanes (THMs), and haloacetic acids (HAAs); and wipe samples for pesticides, semi-volatile organics, and metals. We characterized feasibility using sample collection rates and times and informative value using analyte detection frequencies (DF). Results: Among the 1230 home visits, environmental sample collection rates were high across all sample types (mean¼89%); all samples except the air PM2.5 samples had collection times o30 min. Informative value was low for water VOCs (median DF¼0%) and pesticide floor wipes (median DF¼5%). Informative value was moderate for air samples (median DF¼35%) and high for water THMs and HAAs (median DF¼91% and 75%, respectively). Conclusions: Though collection of environmental samples was feasible, some samples (e.g., wipe pesticides and water VOCs) yielded limited information. These results can be used in conjunction with other study design considerations, such as target population size and hypotheses of interest, to inform the method selection of future environmental health birth cohort studies

An exploration of the effectiveness of artificial mini-magnetospheres as a potential solar storm shelter for long term human space missions

If mankind is to explore the solar system beyond the confines of our Earth and Moon the problem of radiation protection must be addressed. Galactic cosmic rays and highly variable energetic solar particles are an ever-present hazard in interplanetary space. Electric and/or magnetic fields have been suggested as deflection shields in the past, but these treated space as an empty vacuum. In fact it is not empty. Space contains a plasma known as the solar wind; a constant flow of protons and electrons coming from the Sun. In this paper we explore the effectiveness of a “mini-magnetosphere” acting as a radiation protection shield. We explicitly include the plasma physics necessary to account for the solar wind and its induced effects. We show that, by capturing/containing this plasma, we enhance the effectiveness of the shield. Further evidence to support our conclusions can be obtained from studying naturally occurring “mini-magnetospheres” on the Moon. These magnetic anomalies (related to “lunar swirls”) exhibit many of the effects seen in laboratory experiments and computer simulations. If shown to be feasible, this technology could become the gateway to manned exploration of interplanetary space

Non-Supersymmetric Attractor Flow in Symmetric Spaces

We derive extremal black hole solutions for a variety of four dimensional models which, after Kaluza-Klein reduction, admit a description in terms of 3D gravity coupled to a sigma model with symmetric target space. The solutions are in correspondence with certain nilpotent generators of the isometry group. In particular, we provide the exact solution for a non-BPS black hole with generic charges and asymptotic moduli in N=2 supergravity coupled to one vector multiplet. Multi-centered solutions can also be generated with this technique. It is shown that the non-supersymmetric solutions lack the intricate moduli space of bound configurations that are typical of the supersymmetric case.Comment: 50 pages, 4 figures; v2: Reference added. To appear in JHE

On the application of radio frequency voltages to ion traps via helical resonators

Ions confined using a Paul trap require a stable, high voltage and low noise radio frequency (RF) potential. We present a guide for the design and construction of a helical coil resonator for a desired frequency that maximises the quality factor for a set of experimental constraints. We provide an in-depth analysis of the system formed from a shielded helical coil and an ion trap by treating the system as a lumped element model. This allows us to predict the resonant frequency and quality factor in terms of the physical parameters of the resonator and the properties of the ion trap. We also compare theoretical predictions with experimental data for different resonators, and predict the voltage applied to the ion trap as a function of the Q-factor, input power and the properties of the resonant circuit