Gravitational collapse of plasmas in General Relativity

We provide a covariant derivation of plasma physics coupled to gravitation by utilizing the 3+1 formulation of general relativity, including a discussion of the Lorentz force law. We then reduce the system to the spherically symmetric case and show that all regions of the spacetime can be represented in a single coordinate system, thus revoking the need for junction conditions. We further show that the region exterior to the collapsing region is naturally described by the charged Vaidya spacetime in non-null coordinates.Comment: Talk given at the Spanish Relativity Meeting, Tenerife, September 200

Spherically Symmetric Gravitational Collapse of Perfect Fluids

Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change on an initial spacelike hypersurface. Rather than specifying Schwarzschild coordinates for the exterior of the collapsing region, we let the interior dictate the form of the solution in the exterior, and thus both regions are found to be written in one coordinate patch. This not only alleviates the need for complicated matching schemes at the interface, but also finds a new coordinate system for the Schwarzschild spacetime expressed in generalized Painleve-Gullstrand coordinates.Comment: 3 pages, To appear in the proceedings of the eleventh Marcel Grossmann meeting on general relativity (MGXI), 23-29 July, 2006, Berli

Hematopoiesis: Wandering progenitor cells

AbstractThe generation of mice that are chimeric for expression of α4 integrin has revealed a critical role for this adhesion molecule, specifically in postnatal lymphopoiesis

Effects of predation and social interaction on spatial learning and brain cell proliferation in weakly electric fish, Apteronotus leptorhynchus

Previous studies have determined that the stress of predation inhibits brain cell proliferation in two species of weakly electric fish, including, Apteronotus leptorhynchus. In this thesis, three experiments examined how predator stimuli and social interaction affect brain cell proliferation and spatial learning in A. leptorhynchus. The three questions that were explored were: 1) Is the decrease in brain cell proliferation seen after tail amputation in weakly electric fish due to the actual predation injury event or the subsequent regenerative process of their tail? 2) Does social interaction influence the effect of predator stimuli on brain cell proliferation? 3) Do predator stimuli in the form of chasing affect the spatial learning ability of the fish? In the first experiment the action of amputating the tail of the fish caused a drastic significant decrease in brain cell proliferation as compared to the fish allowed long-term recovery (17-18d) and the intact fish. This indicates that the actual predation injury event causes the decrease in cell proliferation, not the regenerative process of the tail. In the second experiment social interaction mitigated the negative effects of stress on brain cell proliferation. Finally in the third experiment the decrease in brain cell proliferation associated with chasing had no apparent effect on the spatial learning behavior of the fish

The Impact of Cross-References on the Readability of the U.S. Internal Revenue Code

Scholars and practitioners have long argued that U.S. income tax law (“the Tax Code”) is excessively complex and difficult to understand, and hence imposes non-trivial adjudication, administration, planning, and compliance costs across the spectrum of income tax stakeholders: the courts, the Internal Revenue Service, tax practitioners, business managers, and individual taxpayers. Hence, there is considerable interest in reducing the effort needed to accurately understand and apply the provisions of income tax law. Prior scholarly work has strongly argued that exceptions to Tax Code provisions as expressed by cross-references embedded in the Tax Code text constitute a major source of reading complexity. The goal of the study was to gain a first empirical understanding about the readability impacts on users who encounter cross-references while reading Tax Code provisions. The study included a human subjects task performance experiment with 75 undergraduate and graduate accounting student participants who were completing or had completed an introductory level course in federal income taxation. Participants were presented with integrated tax scenarios and accompanying sets of scenario questions. Copies of several Tax Code sections were the only reference materials available to the study participants. The study was based on a within-subjects experimental design. To investigate the prior work argument, cross-references embedded in the Tax Code reference materials provided to study participants that expressed exceptions were all assigned to one cross-reference category, and all other cross-references that served different purposes were assigned to a second category. As responses to scenario questions were binary (correct/incorrect), logistic regression was used to test study hypotheses. The study’s major finding was that reading cross-references assigned to the exceptions category had a very strong negative effect on task performance, while reading cross-references assigned to the second category had a modest positive effect on task performance. The finding thus supports decades of analysis and argument that cross-references related to expressing exceptions are a major source of Tax Code reading complexity. This outcome warrants further research into statutory exception language, that subset of statutory language used to express exceptions. Such a subset will include cross-references as one of many language elements that are available for the purpose of expressing exceptions

Three-dimensional shapelets and an automated classification scheme for dark matter haloes

We extend the two-dimensional Cartesian shapelet formalism to d-dimensions. Concentrating on the three-dimensional case, we derive shapelet-based equations for the mass, centroid, root-mean-square radius, and components of the quadrupole moment and moment of inertia tensors. Using cosmological N-body simulations as an application domain, we show that three-dimensional shapelets can be used to replicate the complex sub-structure of dark matter halos and demonstrate the basis of an automated classification scheme for halo shapes. We investigate the shapelet decomposition process from an algorithmic viewpoint, and consider opportunities for accelerating the computation of shapelet-based representations using graphics processing units (GPUs).Comment: 19 pages, 11 figures, accepted for publication in MNRA

Development of an algorithm for the diagnosis of otitis media

Background: The relative importance of signs and symptoms in the diagnosis of otitis media has not been adequately evaluated. This has led to a large degree of variation in the criteria used to diagnose otitis media, which has resulted in inconsistencies in clinical care and discrepant research findings. Methods: A group of experienced otoscopists examined children presenting for primary care. We investigated the signs and symptoms that these otoscopists used to distinguish acute otitis media (AOM), otitis media with effusion (OME), and no effusion. We used recursive partitioning to develop a diagnostic algorithm. To assess the algorithm, we validated it in an independent dataset. Results: Bulging of the tympanic membrane (TM) was the main finding that otoscopists used to discriminate AOM from OME; information regarding the presence or absence of other signs and symptoms added little to the diagnostic process. Overall, 92% of children with AOM had a bulging TM compared with 0% of children with OME. Opacification and/or an air-fluid level was the main finding that the otoscopists used to discriminate OME from no effusion; 97% of children diagnosed with OME had an opaque TM compared with 5% of children diagnosed with no effusion. An algorithm that used bulging and opacification of the TM correctly classified 99% of ears in an independent dataset. Conclusions: Bulging of the TM was the finding that best discriminated AOM from OME. The algorithm developed here may prove to be useful in clinical care, research, and education concerning otitis media. Copyright © 2012 by Academic Pediatric Association

Spherically Symmetric Gravitational Collapse of General Fluids

We express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame, simply by designating specific equations of state. Furthermore, this reduces to the Schwarzschild spacetime when all matter variables vanish. We then describe the formulation of an initial value problem, whereby a general fluid ball with vacuum exterior is established on an initial spacelike slice. As the system evolves, the fluid ball collapses and emanates null radiation such that a region of Vaidya spacetime develops. Therefore, on any subsequent spacelike slice there exists three regions; general fluid, Vaidya and Schwarzschild, all expressed in a single coordinate patch with two free-boundaries determined by the equations. This implies complicated matching schemes are not required at the interfaces between the regions, instead, one simply requires the matter variables tend to the appropriate equations of state. We also show the reduction of the system of equations to the static cases, and show staticity necessarily implies zero ``heat flux''. Furthermore, the static equations include a generalization of the Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium to include anisotropic stresses in general coordinates.Comment: 11 pages, 3 figures, submitted to Phys. Rev.

Gravitational collapse of spherically symmetric plasmas in Einstein-Maxwell spacetimes

We utilize a recent formulation of a spherically symmetric spacetime endowed with a general decomposition of the energy momentum tensor [Phys. Rev. D, 75, 024031 (2007)] to derive equations governing spherically symmetric distributions of electromagnetic matter. We show the system reduces to the Reissner-Nordstrom spacetime in general, spherically symmetric coordinates in the vacuum limit. Furthermore, we show reduction to the charged Vaidya spacetime in non-null coordinates when certain equations of states are chosen. A model of gravitational collapse is discussed whereby a charged fluid resides within a boundary of finite radial extent on the initial hypersurface, and is allowed to radiate charged particles. Our formalism allows for the discussion of all regions in this model without the need for complicated matching schemes at the interfaces between successive regions. As further examples we consider the collapse of a thin shell of charged matter onto a Reissner-Nordstrom black hole. Finally, we reduce the entire system of equations to the static case such that we have the equations for hydrostatic equilibrium of a charged fluid.Comment: Accepted for publication in Phys. Rev.