The Volume of the Past Light-Cone and the Paneitz Operator

We study a conjecture involving the invariant volume of the past light-cone from an arbitrary observation point back to a fixed initial value surface. The conjecture is that a 4th order differential operator which occurs in the theory of conformal anomalies gives $8\pi$ when acted upon the invariant volume of the past light-cone. We show that an extended version of the conjecture is valid for an arbitrary homogeneous and isotropic geometry. First order perturbation theory about flat spacetime reveals a violation of the conjecture which, however, vanishes for any vacuum solution of the Einstein equation. These results may be significant for constructing quantum gravitational observables, for quantifying the back-reaction on spacetime expansion and for alternate gravity models which feature a timelike vector field.Comment: 22 pages, no figures, 5 tables. Version 2 substantially extended to cover nonzero spatial curvature, and with simplified derivation

Specific paucity of unmyelinated C-fibers in cutaneous peripheral nerves of the African naked-mole rat: comparative analysis using six species of bathyergidae

In mammalian peripheral nerves, unmyelinated C-fibers usually outnumber myelinated A-fibers. Using transmission electron microscopy we recently showed that the saphenous nerve of the naked mole-rat (Heterocephalus glaber) has a C-fiber deficit manifested as a substantially lower C:A-fiber ratio compared to other mammals. Here we determined the uniqueness of this C-fiber deficit by performing a quantitative anatomical analysis of several peripheral nerves in five further members of the Bathyergidae mole-rat family: silvery (Heliophobius argenteocinereus), giant (Fukomys mechowii), Damaraland (Fukomys damarensis), Mashona (Fukomys darlingi) and Natal (Cryptomys hottentotus natalensis) mole-rats. In the largely cutaneous saphenous and sural nerves we found that the naked mole-rat had the lowest C:A-fiber ratio (~1.5:1 compared to ~3:1), whereas in nerves innervating both skin and muscle (common peroneal and tibial) or just muscle (lateral/medial gastrocnemius), this pattern was mostly absent. We asked whether lack of hair follicles alone accounts for the C-fiber paucity using a mouse model, which loses virtually all its hair as a consequence of conditional deletion of the beta-catenin gene in the skin. These beta-catenin loss-of function mice (beta-cat LOF mice) displayed only a mild decrease in C:A-fiber ratio compared to wild-type mice (4.42 compared to 3.81). We suggest that the selective cutaneous C-fiber deficit in the cutaneous nerves of naked mole-rats is unlikely to be primarily due to lack of skin hair follicles. Possible mechanisms contributing to this unique peripheral nerve anatomy are discussed

Toroidal mode number estimation of the edge-localized modes using the KSTAR 3-D electron cyclotron emission imaging system

A new and more accurate technique is presented for determining the toroidal mode number n of edge-localized modes (ELMs) using two independent electron cyclotron emission imaging (ECEI) systems in the Korea Superconducting Tokamak Advanced Research (KSTAR) device. The technique involves the measurement of the poloidal spacing between adjacent ELM filaments, and of the pitch angle ?? O of filaments at the plasma outboard midplane. Equilibrium reconstruction verifies that ?? O is nearly constant and thus well-defined at the midplane edge. Estimates of n obtained using two ECEI systems agree well with n measured by the conventional technique employing an array of Mirnov coils.open3

Universality in percolation of arbitrary Uncorrelated Nested Subgraphs

The study of percolation in so-called {\em nested subgraphs} implies a generalization of the concept of percolation since the results are not linked to specific graph process. Here the behavior of such graphs at criticallity is studied for the case where the nesting operation is performed in an uncorrelated way. Specifically, I provide an analyitic derivation for the percolation inequality showing that the cluster size distribution under a generalized process of uncorrelated nesting at criticality follows a power law with universal exponent $\gamma=3/2$. The relevance of the result comes from the wide variety of processes responsible for the emergence of the giant component that fall within the category of nesting operations, whose outcome is a family of nested subgraphs.Comment: 5 pages, no figures. Mistakes found in early manuscript have been remove

Simulations of denuded-zone formation during growth on surfaces with anisotropic diffusion

We have investigated the formation of denuded zones during epitaxial growth on surfaces exhibiting anisotropic diffusion of adparticles, such as Si(001)-2x1, using Monte Carlo simulations and a continuum model. In both the simulations, which were mainly for low-temperature cases (small critical clusters), and the continuum model, appropriate for high-temperature cases (large critical clusters), it was found that the ratio of denuded-zone widths Wf and Ws in the fast- and slow-diffusion directions scales with the ratio Df/Ds of the diffusion constants in the two directions with a power of 1/2, i.e., Wf/Ws ≈ (Df/Ds)1/2, independent of various conditions including the degree of diffusion anisotropy. This supplies the foundation of a method for extracting the diffusion anisotropy from the denuded zone anisotropy which is experimentally measurable. Further, we find that unequal probabilities of a diffusing particle sticking to different types of step edges [e.g., S A and SB steps on Si(001)] does not affect the relation Wf/Ws ≈ (Df/Ds)1/2 seriously unless the smaller of the two sticking probabilities is less than about 0.1. Finally, we examined the relation between the number of steps and the number of sites visited in anisotropic random walks, finding it is better described by a crossover from one-dimensional to two-dimensional behavior than by scaling behavior with a single exponent. This result has bearing on scaling arguments relating denuded-zone widths to diffusion constants for anisotropic diffusion.open7

Nursing and Environmental Health Roundtable: August 26-27, 2002, Research Triangle Park, North Carolina : final report

Environmental health nursing is being revitalized and strengthened. The recommendations outlined in this report can serve to better coordinate environmental health nursing research, education, and translation to advances in practice. If implemented, these recommendations will establish a strong foundation for environmental health nursing. This report is organized around the three roundtable themes: research, education, and translation to practice.edited by Teresa Nastoff ... [et al.].Includes bibliographical references

Rate-equation calculations of the current flow through two-site molecular device and DNA-based junction

Here we present the calculations of incoherent current flowing through the two-site molecular device as well as the DNA-based junction within the rate-equation approach. Few interesting phenomena are discussed in detail. Structural asymmetry of two-site molecule results in rectification effect, which can be neutralized by asymmetric voltage drop at the molecule-metal contacts due to coupling asymmetry. The results received for poly(dG)-poly(dC) DNA molecule reveal the coupling- and temperature-independent saturation effect of the current at high voltages, where for short chains we establish the inverse square distance dependence. Besides, we document the shift of the conductance peak in the direction to higher voltages due to the temperature decrease.Comment: 12 pages, 6 figure