Penrose Limits and Spacetime Singularities

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyer ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction

Fermi Coordinates and Penrose Limits

We propose a formulation of the Penrose plane wave limit in terms of null Fermi coordinates. This provides a physically intuitive (Fermi coordinates are direct measures of geodesic distance in space-time) and manifestly covariant description of the expansion around the plane wave metric in terms of components of the curvature tensor of the original metric, and generalises the covariant description of the lowest order Penrose limit metric itself, obtained in hep-th/0312029. We describe in some detail the construction of null Fermi coordinates and the corresponding expansion of the metric, and then study various aspects of the higher order corrections to the Penrose limit. In particular, we observe that in general the first-order corrected metric is such that it admits a light-cone gauge description in string theory. We also establish a formal analogue of the Weyl tensor peeling theorem for the Penrose limit expansion in any dimension, and we give a simple derivation of the leading (quadratic) corrections to the Penrose limit of AdS_5 x S^5.Comment: 25 page

The Supply of Quality in Child Care Centers

We use data from a sample of day care centers to estimate the relationships between cost and the quality of the child care service provided, and between revenue and quality. We use a measure of child care quality derived from an instrument designed by developmental psychologists. This measure of quality has been found to be positively associated with child development. Taking the estimated cost-quality and revenue-quality relationships as given, we then estimate the objective functions of the firms and compute the supply function for quality. The results indicate that (1) the estimated cost function is inconsistent with the implications of cost-minimization; (2) for-profit firms operate at a positive level of marginal cost, but non-profit firms operate at zero or negative marginal cost; (3) revenue is positively but weakly associated with quality; and (4) the supply of quality is inelastic, with point estimates of the supply elasticity of .04-.05 for both for-profit and non-profit firms. Implications of the results for child care policy are discussed.

Symmetries and Observables for BF-theories in Superspace

The supersymmetric version of a topological quantum field theory describing flat connections, the super BF-theory, is studied in the superspace formalism. A set of observables related to topological invariants is derived from the curvature of the superspace. Analogously to the non-supersymmetric versions, the theory exhibits a vector-like supersymmetry. The role of the vector supersymmetry and an additional new symmetry of the action in the construction of observables is explained.Comment: 11 pages, LaTe

A Visual Query Language for Relational Knowledge Discovery

QGRAPH is a visual query language for knowledge discovery in relational data. Using QGRAPH, a user can query and update relational data in ways that support data exploration, data transformation, and sampling. When combined with modeling algorithms, such as those developed in inductive logic programming and relational learning, the language assists analysis of relational data, such as data drawn fromtheWeb, chemical structure-activity relationships, and social networks. Several features distinguish QGRAPH from other query languages such as SQL and Datalog. It is a visual language, so its queries are annotated graphs that reflect potential structures within a database. QGRAPH treats objects, links, and attributes as first-class entities, so its queries can dynamically alter a data schema by adding and deleting those entities. Finally, the language provides grouping and counting constructs that facilitate calculation of attributes that can capture features of local graph structure. We describe the language in detail, discuss key aspects of the underlying data model and implementation, and discuss several uses of QGRAPH for knowledge discovery

The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A "phenomenology" of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph

Computer program compatible with a laser nephelometer

The laser nephelometer data system was updated to provide magnetic tape recording of data, and real time or near real time processing of data to provide particle size distribution and liquid water content. Digital circuits were provided to interface the laser nephelometer to a Data General Nova 1200 minicomputer. Communications are via a teletypewriter. A dual Linc Magnetic Tape System is used for program storage and data recording. Operational programs utilize the Data General Real-Time Operating System (RTOS) and the ERT AIRMAP Real-Time Operating System (ARTS). The programs provide for acquiring data from the laser nephelometer, acquiring data from auxiliary sources, keeping time, performing real time calculations, recording data and communicating with the teletypewriter

g_contacts: Fast contact search in bio-molecular ensemble data.

Short-range interatomic interactions govern many bio-molecular processes. Therefore, identifying close interaction partners in ensemble data is an essential task in structural biology and computational biophysics. A contact search can be cast as a typical range search problem for which efficient algorithms have been developed. However, none of those has yet been adapted to the context of macromolecular ensembles, particularly in a molecular dynamics (MD) framework. Here a set-decomposition algorithm is implemented which detects all contacting atoms or residues in maximum O(Nlog(N)) run-time, in contrast to the O(N2) complexity of a brute-force approach

Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory.Comment: 72 pages (60 A4 pages), LaTeX (to appear in the Journal of Mathematical Physics Special Issue on Functional Integration (May 1995)

Dissipative Hydrodynamics and Heavy Ion Collisions

Recent discussions of RHIC data emphasized the exciting possibility that the matter produced in nucleus-nucleus collisions shows properties of a near-perfect fluid. Here, we aim at delineating the applicability of fluid dynamics, which is needed to quantify the size of corresponding dissipative effects. We start from the equations for dissipative fluid dynamics, which we derive from kinetic theory up to second order (Israel-Stewart theory) in a systematic gradient expansion. In model studies, we then establish that for too early initialization of the hydrodynamic evolution (\tau_0 \lsim 1 fm/c) or for too high transverse momentum (p_T \gsim 1 GeV) in the final state, the expected dissipative corrections are too large for a fluid description to be reliable. Moreover, viscosity-induced modifications of hadronic transverse momentum spectra can be accommodated to a significant degree in an ideal fluid description by modifications of the decoupling stage. We argue that these conclusions, drawn from model studies, can also be expected to arise in significantly more complex, realistic fluid dynamics simulations of heavy ion collisions.Comment: 18 pages, 5 figures, uses revtex4; v2: references added, typos correcte