Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation

Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It is the purpose of this paper to develop these issues and find applications in GR. The applications center around the problem of extracting interior physical properties of an asymptotically flat space-time directly from the asymptotic gravitational (and Maxwell) field itself in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center of mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular momentum conservation law with well-defined flux terms. When a Maxwell field is present the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world-line and intrinsic magnetic dipole moment.Comment: 98 pages, 6 appendices. v2: typos corrected; v3: significant changes made to results section using simpler arguments, added discussion of real structures, additional references, 2 new appendice

Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

Total hip arthroplasty surgical approach does not alter postoperative gait mechanics one year after surgery

Objective: To investigate the differences in gait biomechanics on the basis of surgical approach 1 year after surgery. Design: This was a descriptive laboratory study to investigate the side-to-side differences in walking mechanics at a self-selected walking speed as well as a functional assessment 1year after total hip arthroplasty (THA). Temporospatial, kinetic, and kinematic data as well as functional outcomes were collected. Two-way analysis of variance was used to assess for between-group differences and limb-to-limb asymmetries. Setting: A controlled laboratory study. Participants: This study examined 35 patients with primary, unilateral THA. The THA surgical approaches that were used in these patients included 12 direct lateral, 18 posterior, and 11 anterolateral. All the patients were assessed 1 year after THA. Patients were excluded from the study if they had contralateral hip pain or pathology, or any prior lower extremity total joint replacements. Main Outcome Measurements: Three-dimensional lower extremity kinematics and kinetics as well as spatiotemporal variables were collected. In addition, a series of physical performance measures were collected. Results: No main effects for the physical performance measures or biomechanical variables were observed among the approach groups. Significant limb-to-limb asymmetries were observed among all the patients, with decreased sagittal plane range of motion, peak extension, and peak vertical ground reaction forces on the operative side. Conclusion: The results of this study indicated that no significant differences existed among the different surgical approach groups for any study variable. However, 1 year after THA, the patients demonstrated asymmetric gait patterns regardless of surgical approach, which indicated the potential need for continued intervention through physical therapy to regain normal side-to-side symmetry after THA. © 2014 American Academy of Physical Medicine and Rehabilitation

Prospectives

Tiré de: Prospectives, vol. 24, no 2, avril 1988.Titre de l'écran-titre (visionné le 24 janv. 2013

The Blind Watchmaker Network: Scale-freeness and Evolution

It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects an ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree distribution during evolution. The corresponding random network, here termed the blind watchmaker network has a power-law degree distribution with an exponent gamma >= 2. It is random with respect to a complete set of network states characterized by a description of which links are attached to a node as well as a time-ordering of these links. No a priory assumption of any growth mechanism or evolution process is made. It is found that the degree distribution of the blind watchmaker network agrees very precisely with that of the metabolic networks. This implies that the evolutionary pathway of the cell-metabolism, when projected onto a metabolic network representation, has remained statistically random with respect to a complete set of network states. This suggests that even a biological system, which due to natural selection has developed an enormous specificity like the cellular metabolism, nevertheless can, at the same time, display well defined characteristics emanating from the ubiquitous inherent random element of Darwinian evolution. The fact that also completely random networks may have scale-free node distributions gives a new perspective on the origin of scale-free networks in general.Comment: 5 pages, 3 figure

Understanding plant invasions: An example of working with citizen scientists to collect environmental data

Citizen science programs are useful tools for collecting important environmental science data. To ensure data quality, however, it must be shown that data collected by volunteers can produce reliable results. We engaged 143 volunteers over four years to map and estimate abundance of invasive plants in New York and New Jersey parklands. We found that off trail abundance of only a few of our targeted invasive species were positively correlated with on trail abundance. Our results support that citizen science programs can be a useful and sometimes a much needed addition to environmental science protocols

T-cell responses in oiled guillemots and swans in a rehabilitation setting

This article has been accepted for publication in the Archives of Environmental Contamination and Toxicology. The final version can be accessed from the link below.This article has been made available through the Brunel Open Access Publishing Fund.Aquatic birds are commonly affected by oil spills. Despite rehabilitation efforts, the majority of rehabilitated common guillemots (Uria aalge) do not survive, whereas mute swans (Cygnus olor) tend to have higher post-release survival. Polyaromatic hydrocarbons (PAHs) present in crude oil and diesel are immunotoxic in birds affecting cell-mediated responses to immunogens. Because it is a target of PAH toxicity, T-lymphocyte response to controlled mitogen administration (phytohemagglutinnin test) was investigated in a scoping study as a potentially useful minimally invasive in vivo test of cell-mediated immunity. The test was performed on 69 mute swans and 31 common guillemots stranded on the Norfolk and Lincolnshire coastline and inland waterways in England (UK)either due to injury or to contamination with crude or diesel oil. T-lymphocyte response was significantly decreased in swans with greater oil scores. T-lymphocyte responses were also decreased in guillemots, but this finding was not statistically significant

Black Holes in Modified Gravity (MOG)

The field equations for Scalar-Tensor-Vector-Gravity (STVG) or modified gravity (MOG) have a static, spherically symmetric black hole solution determined by the mass $M$ with two horizons. The strength of the gravitational constant is $G=G_N(1+\alpha)$ where $\alpha$ is a parameter. A regular singularity-free MOG solution is derived using a nonlinear field dynamics for the repulsive gravitational field component and a reasonable physical energy-momentum tensor. The Kruskal-Szekeres completion of the MOG black hole solution is obtained. The Kerr-MOG black hole solution is determined by the mass $M$, the parameter $\alpha$ and the spin angular momentum $J=Ma$. The equations of motion and the stability condition of a test particle orbiting the MOG black hole are derived, and the radius of the black hole photosphere and the shadows cast by the Schwarzschild-MOG and Kerr-MOG black holes are calculated. A traversable wormhole solution is constructed with a throat stabilized by the repulsive component of the gravitational field.Comment: 14 pages, 3 figures. Upgraded version of paper to match published version in European Physics Journal

Generalized Painleve-Gullstrand descriptions of Kerr-Newman black holes

Generalized Painleve-Gullstrand metrics are explicitly constructed for the Kerr-Newman family of charged rotating black holes. These descriptions are free of all coordinate singularities; moreover, unlike the Doran and other proposed metrics, an extra tunable function is introduced to ensure all variables in the metrics remain real for all values of the mass M, charge Q, angular momentum aM, and cosmological constant \Lambda > - 3/(a^2). To describe fermions in Kerr-Newman spacetimes, the stronger requirement of non-singular vierbein one-forms at the horizon(s) is imposed and coordinate singularities are eliminated by local Lorentz boosts. Other known vierbein fields of Kerr-Newman black holes are analysed and discussed; and it is revealed that some of these descriptions are actually not related by physical Lorentz transformations to the original Kerr-Newman expression in Boyer-Lindquist coordinates - which is the reason complex components appear (for certain ranges of the radial coordinate) in these metrics. As an application of our constructions the correct effective Hawking temperature for Kerr black holes is derived with the method of Parikh and Wilczek.Comment: 5 pages; extended to include application to derivation of Hawking radiation for Kerr black holes with Parikh-Wilczek metho

Kerr-Newman Black Hole Thermodynamical State Space: Blockwise Coordinates

A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner-Nordstrom and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr-Newman case's 3 by 3 thermodynamical state space metric.Comment: 4 pages incl 2 figs. Accepted by Gen. Rel. Grav. Replaced with Accepted version (minor corrections