A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary

We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use the Abstract Boundary to describe the structure of the `edge' of our manifold without resorting to structures external to the manifold itself. This is particularly important in the study of singularities within General Relativity where singularities lie on this `edge'. The ability to talk about the same objects, e.g., singularities, via different structures provides alternative routes for investigation which can be invaluable in the pursuit of physically motivated problems where certain types of information are unavailable or difficult to use.Comment: 23 page

The Cost of Complexity in Federal Student Aid: Lessons from Optimal Tax Theory and Behavioral Economics

The federal system for distributing student financial aid rivals the tax code in its complexity. Both have been a source of frustration and a focus of reform efforts for decades, yet the complexity of the student aid system has received comparatively little attention from economists. We describe the complexity of the aid system, and apply lessons from optimal tax theory and behavioral economics to show that complexity is a serious obstacle to both efficiency and equity in the distribution of student aid. We show that complexity disproportionately burdens those with the least ability to pay and undermines redistributive goals. We use detailed data from federal student aid applications to show that a radically simplified aid process can reproduce the current distribution of aid using a fraction of the information now collected.

Generalizations of the Abstract Boundary singularity theorem

The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.Comment: 24 page

Are drug therapies effective in treating Bell's palsy?

Early use of corticosteroid therapy results in less autonomic synkinesis and possibly improved rates of recovery in adults (strength of recommendation: C); there is no proven benefit in children (SOR: B). Adding acyclovir (Zovirax) to prednisone therapy may improve recovery rates compared with prednisone alone (SOR: C). The results of 1 nonblinded study indicate that intramuscular methylcobalamin (vitamin B12) used alone or in combination with prednisone may shorten time to recovery (SOR: C)

Does neonatal circumcision decrease morbidity?

Evidence suggests that neonatal circumcision decreases the incidence of childhood urinary tract infections, phimosis, paraphimosis, balanitis and other genital dermatoses, invasive penile cancer, and the sexually transmitted diseases human papilloma virus (HPV) and HIV (strength of recommendation [SOR]: B, based on case control and cohort studies). The benefits of decreased incidence of HPV and HIV infections go beyond the index patient and have public health implications on the transmission of these diseases (SOR: B). Further, a decrease in HPV incidence and transmission may lead to a lower incidence of cervical cancer (SOR: B). While there appears to be some evidence for reduced morbidity with routine circumcision, decisions regarding routine neonatal circumcision requires balancing risks and benefits of the procedure with the alternatives in the context of social, familial, and religious beliefs

Numerical wave optics and the lensing of gravitational waves by globular clusters

We consider the possible effects of gravitational lensing by globular clusters on gravitational waves from asymmetric neutron stars in our galaxy. In the lensing of gravitational waves, the long wavelength, compared with the usual case of optical lensing, can lead to the geometrical optics approximation being invalid, in which case a wave optical solution is necessary. In general, wave optical solutions can only be obtained numerically. We describe a computational method that is particularly well suited to numerical wave optics. This method enables us to compare the properties of several lens models for globular clusters without ever calling upon the geometrical optics approximation, though that approximation would sometimes have been valid. Finally, we estimate the probability that lensing by a globular cluster will significantly affect the detection, by ground-based laser interferometer detectors such as LIGO, of gravitational waves from an asymmetric neutron star in our galaxy, finding that the probability is insignificantly small.Comment: To appear in: Proceedings of the Eleventh Marcel Grossmann Meetin

The Apollo Capsule Optimization for Improved Stability and Computational/Experimental Data Comparisons

Numerical optimization was employed on the Apollo Command Module to modify its external shape. The Apollo Command Module (CM) that was used on all NASA human space flights during the Apollo Space Program is stable and trimmed in an apex forward (alpha of approximately 40 to 80 degrees) position. This poses a safety risk if the CM separates from the launch tower during abort. Optimization was employed on the Apollo CM to remedy the undesirable stability characteristics of the configuration. Geometric shape changes were limited to axisymmetric modifications that altered the radius of the apex (R(sub A)), base radius (R(sub O)), corner radius (R(sub C)), and the cone half angle (theta), while the maximum diameter of the CM was held constant. The results of multipoint optimization on the CM indicated that the cross-range performance can be improved while maintaining robust apex-aft stability with a single trim point. Navier-Stokes computations were performed on the baseline and optimized configurations and confirmed the Euler-based optimization results. Euler Analysis of ten alternative CM vehicles with different values of the above four parameters are compared with the published experimental results of numerous wind tunnel tests during the late 1960's. These comparisons cover a wide Mach number range and a full 180-degree pitch range and show that the Euler methods are capable of fairly accurate force and moment computations and can separate the vehicle characteristics of these ten alternative configurations

The Reliability and Validity of the Physical Therapy Outpatient Satisfaction Survey: A Replication Study

Objective: The study re-examined the validity and reliability of the Physical Therapy Outpatient Satisfaction Survey (PTOPS) using a geographically different and larger patient population, random sampling, and mail survey methodology. Background: Measurement of patient satisfaction in physical therapy is in tis infancy. Development and refinement of theory and measurement methodology are imperative. Replication of reliability and validity is an important component of questionnaire development. Design: This study used a methodological design with descriptive elements. It employed a survey of a random sampling of subjects from 20 outpatient clinics throughout the Gulf South United States. Method: 2,309 patients 21 years of age or older who lived in Mississippi, Alabama, Florida and Louisiana were mailed PTOPS questionnaire, yielding 1,175 usable responses and a 60% usable response rate. Principal components analysis explored the dimensions of satisfaction, and Cronbach alpha scores investigated inter-item reliability. Regression analysis investigated predictive validity. Results: The construct of four original dimensions found in the PTOPS (Enhancers, Detractors, Costs, Location) remained consistent with this sample and methodology. Cronbach alpha scores indicated high levels of inter-item reliability. Regression analysis suggested that all four dimensions were predictive of overall patient satisfaction. Conclusion: The PTOPS retained excellent reliability and validity when used in a different locale, with a mail survey methodology, and when using retrospective study techniques