Costly information and the CRA

Community Reinvestment Act of 1977

A market-based approach to CRA

Community Reinvestment Act of 1977

Imperfect information and the Community Reinvestment Act

Community Reinvestment Act of 1977

Pro-p groups of positive deficiency

Let \Gamma be a finitely presentable pro-p group with a nontrivial finitely generated closed normal subgroup N of infinite index. Then def(\Gamma)\leq 1, and if def(\Gamma)=1 then \Gamma is a pro-p duality group of dimension 2, N is a free pro-p group and \Gamma/N is virtually free. In particular, if the centre of \Gamma is nontrivial and def(\Gamma)\geq 1, then def(\Gamma)=1, cd G \leq 2 and \Gamma is virtually a direct product F \times Z_p, with F a finitely generated free pro-p group.Comment: final version, to appear in Bull. LM

A Surrogate Model of Gravitational Waveforms from Numerical Relativity Simulations of Precessing Binary Black Hole Mergers

We present the first surrogate model for gravitational waveforms from the coalescence of precessing binary black holes. We call this surrogate model NRSur4d2s. Our methodology significantly extends recently introduced reduced-order and surrogate modeling techniques, and is capable of directly modeling numerical relativity waveforms without introducing phenomenological assumptions or approximations to general relativity. Motivated by GW150914, LIGO's first detection of gravitational waves from merging black holes, the model is built from a set of $276$ numerical relativity (NR) simulations with mass ratios $q \leq 2$, dimensionless spin magnitudes up to $0.8$, and the restriction that the initial spin of the smaller black hole lies along the axis of orbital angular momentum. It produces waveforms which begin $\sim 30$ gravitational wave cycles before merger and continue through ringdown, and which contain the effects of precession as well as all $\ell \in \{2, 3\}$ spin-weighted spherical-harmonic modes. We perform cross-validation studies to compare the model to NR waveforms \emph{not} used to build the model, and find a better agreement within the parameter range of the model than other, state-of-the-art precessing waveform models, with typical mismatches of $10^{-3}$. We also construct a frequency domain surrogate model (called NRSur4d2s_FDROM) which can be evaluated in $50\, \mathrm{ms}$ and is suitable for performing parameter estimation studies on gravitational wave detections similar to GW150914.Comment: 34 pages, 26 figure

Designing Improved Sediment Transport Visualizations

Monitoring, or more commonly, modeling of sediment transport in the coastal environment is a critical task with relevance to coastline stability, beach erosion, tracking environmental contaminants, and safety of navigation. Increased intensity and regularity of storms such as Superstorm Sandy heighten the importance of our understanding of sediment transport processes. A weakness of current modeling capabilities is the ability to easily visualize the result in an intuitive manner. Many of the available visualization software packages display only a single variable at once, usually as a two-dimensional, plan-view cross-section. With such limited display capabilities, sophisticated 3D models are undermined in both the interpretation of results and dissemination of information to the public. Here we explore a subset of existing modeling capabilities (specifically, modeling scour around man-made structures) and visualization solutions, examine their shortcomings and present a design for a 4D visualization for sediment transport studies that is based on perceptually-focused data visualization research and recent and ongoing developments in multivariate displays. Vector and scalar fields are co-displayed, yet kept independently identifiable utilizing human perception\u27s separation of color, texture, and motion. Bathymetry, sediment grain-size distribution, and forcing hydrodynamics are a subset of the variables investigated for simultaneous representation. Direct interaction with field data is tested to support rapid validation of sediment transport model results. Our goal is a tight integration of both simulated data and real world observations to support analysis and simulation of the impact of major sediment transport events such as hurricanes. We unite modeled results and field observations within a geodatabase designed as an application schema of the Arc Marine Data Model. Our real-world focus is on the Redbird Artificial Reef Site, roughly 18 nautical miles offshor- Delaware Bay, Delaware, where repeated surveys have identified active scour and bedform migration in 27 m water depth amongst the more than 900 deliberately sunken subway cars and vessels. Coincidently collected high-resolution multibeam bathymetry, backscatter, and side-scan sonar data from surface and autonomous underwater vehicle (AUV) systems along with complementary sub-bottom, grab sample, bottom imagery, and wave and current (via ADCP) datasets provide the basis for analysis. This site is particularly attractive due to overlap with the Delaware Bay Operational Forecast System (DBOFS), a model that provides historical and forecast oceanographic data that can be tested in hindcast against significant changes observed at the site during Superstorm Sandy and in predicting future changes through small-scale modeling around the individual reef objects

Bulk phase behaviour of binary hard platelet mixtures from density functional theory

We investigate isotropic-isotropic, isotropic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom and radial size ratios $\lambda$ up to 5. A fundamental measure density functional theory, previously used for the one-component model, is proposed and results are compared against those from Onsager theory as a benchmark. For $\lambda \leq 1.7$ the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of $\lambda$. For size ratios $\lambda \geq 2$, we find demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of $\lambda$ than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles