Automorphic forms: a physicist's survey

Motivated by issues in string theory and M-theory, we provide a pedestrian introduction to automorphic forms and theta series, emphasizing examples rather than generality.Comment: 22 pages, to appear in the Proceedings of Les Houches Winter School ``Frontiers in Number Theory, Physics and Geometry'', March 9-21, 2003; v2: minor changes and clarifications, section 3.5 on pure spinors has been rewritte

New Hampshire: Baseline Report - State Level Field Network Study of the Implementation of the Affordable Care Act

This report is part of a series of 21 state and regional studies examining the rollout of the ACA. The national network -- with 36 states and 61 researchers -- is led by the Rockefeller Institute of Government, the public policy research arm of the State University of New York, the Brookings Institution, and the Fels Institute of Government at the University of Pennsylvania.New Hampshire's experience with implementing the ACA in 2013 and 2014 underscores the state's "wait and see" approach to health care reform. Since the passage of the ACA in March 2010, a wide range of national polls demonstrated that the public remains fundamentally split about the law and its effects; unlike other major health care reforms (e.g., the Medicare Modernization Act of 2003) the public has not warmed to the ACA over time. The stability of public attitudes towards the ACA is striking; despite month-to-month variations, surveys by the Kaiser Family Foundation, Gallup, and other major polling organizations reveal that public views of the ACA have changed little over the past four years. This ongoing partisan and policy divide is evident in the Granite State, as Republicans continue to oppose the ACA, while Democrats embrace reform -- on New Hampshire's terms

A Bayesian Updating Framework for Simulating Marine Energy Converter Drive Train Reliability

This is the author accepted manuscript. The final version is available from METSINTRODUCTION: Accurately quantifying and assessing the reliability of Marine Energy Converters (MEC’s) is critical for the successful commercialization of the industry. Without improvements in reliability and hence reductions in operation & maintenance (O&M) costs, the industry will struggle to reach competitive Levelised Cost of Energy (LCoE). At present, due to the nascent stage of the industry and commercial sensitivities there is very little reliability field data available. This presents an issue: how can the reliability of MEC devices be accurately assessed and predicted with a lack of specific reliability data? [...]The support of the ETI and RCUK Energy Program funding for IDCORE (EP/J500847/1) is gratefully acknowledged

Minimal representations, spherical vectors, and exceptional theta series I

Theta series for exceptional groups have been suggested as a possible description of the eleven-dimensional quantized BPS membrane. We present explicit formulae for these automorphic forms whenever the underlying Lie group $G$ is simply laced. Specifically, we review and construct explicitly the minimal representation of $G$ which generalizes the Schr\"odinger representation of symplectic groups. The real spherical vector invariant under the maximal compact subgroup is computed in this representation and yields the action appearing in the summand of the automorphic theta series. The summation measure can be obtained from the p-adic form of the spherical vector and is left to the sequel of this paper. The simplicity of our result is suggestive of a new Born-Infeld-like description of the membrane where U-duality is realized non-linearly. Our results may also be used in constructing quantum mechanical systems with hidden non-compact symmetries

Quantum Cosmology and Conformal Invariance

According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal mechanical models first introduced by de Alfaro, Fubini and Furlan (DFF). The deformation used by DFF to render the spectrum discrete corresponds to a negative cosmological constant. The wave function of the universe is the zero-energy eigenmode of the Hamiltonian, also known as the spherical vector of the representation of the conformal group SO(1,2). A new class of conformal quantum mechanical models is constructed, based on the quantization of nilpotent coadjoint orbits, where the conformal group is enhanced to an ADE non-compact group for which the spherical vector is known.Comment: 4 pages, latex2e, uses revtex

Complex microwave conductivity of Pr1.85_{1.85}Ce0.15_{0.15}CuO4−δ_{4-\delta} thin films using a cavity perturbation method

We report a study of the microwave conductivity of electron-doped Pr$_{1.85}$Ce$_{0.15}$CuO$_{4-\delta}$ superconducting thin films using a cavity perturbation technique. The relative frequency shifts obtained for the samples placed at a maximum electric field location in the cavity are treated using the high conductivity limit presented recently by Peligrad $\textit{et}$ $\textit{al.}$ Using two resonance modes, TE$_{102}$ (16.5 GHz) and TE$_{101}$ (13 GHz) of the same cavity, only one adjustable parameter $\Gamma$ is needed to link the frequency shifts of an empty cavity to the ones of a cavity loaded with a perfect conductor. Moreover, by studying different sample configurations, we can relate the substrate effects on the frequency shifts to a scaling factor. These procedures allow us to extract the temperature dependence of the complex penetration depth and the complex microwave conductivity of two films with different quality. Our data confirm that all the physical properties of the superconducting state are consistent with an order parameter with lines of nodes. Moreover, we demonstrate the high sensitivity of these properties on the quality of the films

Perspectives of Fitness and Health in College Men and Women

Because many college students engage in low levels of physical activity, the current study used a qualitative framework to interview 11 college students to examine the meaning physically active college students assign to the practice of fitness and health. Students discussed the importance of healthy eating, but that it was difficult to accomplish at college. Additionally, students intertwined health and fitness with physical appearance and attractiveness. In particular, the media shaped many of their perceptions of health and fitness. Implications of these findings to policy making in higher education, in particular wellness programming, are highlighted

The influence of goal-state access cost on planning during problem solving

Two problem-solving experiments investigated the relationship between planning and the cost of accessing goal-state information using the theoretical framework of the soft constraints hypothesis (Gray & Fu, 2004; Gray, Simms, Fu, & Schoelles, 2006). In Experiment 1, 36 participants were allocated to low, medium, and high access cost conditions and completed a problem-solving version of the Blocks World Task. Both the nature of planning (memory based or display based) and its timing (before or during action) changed with high goal-state access cost (a mouse movement and a 2.5-s delay). In this condition more planning before action was observed, with less planning during action, evidenced by longer first-move latencies, more moves per goal-state inspection, and more short (≤0.8 s) and long (>8 s) “preplanned” intermove latencies. Experiment 2 used an eight-puzzle-like transformation task and replicated the effect of goal-state access cost when more complex planning was required, also confirmed by sampled protocol data. Planning before an episode of move making increased with higher goal-state access cost, and planning whilst making moves increased with lower access cost. These novel results are discussed in the context of the soft constraints hypothesis

R4R^4 couplings, the fundamental membrane and exceptional theta correspondences

This letter is an attempt to carry out a first-principle computation in M-theory using the point of view that the eleven-dimensional membrane gives the fundamental degrees of freedom of M-theory. Our aim is to derive the exact BPS $R^4$ couplings in M-theory compactified on a torus $T^{d+1}$ from the toroidal BPS membrane, by pursuing the analogy with the one-loop string theory computation. We exhibit an Sl(3,\Zint) modular invariance hidden in the light-cone gauge (but obvious in the Polyakov approach), and recover the correct classical spectrum and membrane instantons; the summation measure however is incorrect. It is argued that the correct membrane amplitude should be given by an exceptional theta correspondence lifting Sl(3,\Zint) modular forms to \exc(\Zint) automorphic forms, generalizing the usual theta lift between Sl(2,\Zint) and SO(d,d,\Zint) in string theory. The exceptional correspondence $Sl(3)\times E_{6(6)}\subset E_{8(8)}$ offers the interesting prospect of solving the membrane small volume divergence and unifying membranes with five-branes