On the Existence of Radiation Gauges in Petrov type II spacetimes

The radiation gauges used by Chrzanowski (his IRG/ORG) for metric reconstruction in the Kerr spacetime seem to be over-specified. Their specification consists of five conditions: four, which we treat here as valid gauge conditions, plus an additional condition on the trace of the metric perturbation. In this work, we utilize a newly developed form of the perturbed Einstein equations to establish a condition -- on a particular tetrad component of the stress-energy tensor -- under which the full IRG/ORG can be imposed. Using gauge freedom, we are able to impose the full IRG for Petrov type II and type D backgrounds, using a different tetrad for each case. As a specific example, we work through the process of imposing the IRG in a Schwarzschild background, using a more traditional approach. Implications for metric reconstruction using the Teukolsky curvature perturbations in type D spacetimes are briefly discussed.Comment: 21 pages, uses iop style files. v2: proved a stronger result for type II backgrounds, added a subsection on remaining gauge freedom in the full IRG and improved calrity and readability throughout due to insightful referee comments; published as Class. Quantum Grav. 24 (2007) 2367-238

CMB Lensing Reconstruction on the Full Sky

Gravitational lensing of the microwave background by the intervening dark matter mainly arises from large-angle fluctuations in the projected gravitational potential and hence offers a unique opportunity to study the physics of the dark sector at large scales. Studies with surveys that cover greater than a percent of the sky will require techniques that incorporate the curvature of the sky. We lay the groundwork for these studies by deriving the full sky minimum variance quadratic estimators of the lensing potential from the CMB temperature and polarization fields. We also present a general technique for constructing these estimators, with harmonic space convolutions replaced by real space products, that is appropriate for both the full sky limit and the flat sky approximation. This also extends previous treatments to include estimators involving the temperature-polarization cross-correlation and should be useful for next generation experiments in which most of the additional information from polarization comes from this channel due to sensitivity limitations.Comment: Accepted for publication in Phys. Rev. D; typos correcte

Nonlinear feedback oscillations in resonant tunneling through double barriers

We analyze the dynamical evolution of the resonant tunneling of an ensemble of electrons through a double barrier in the presence of the self-consistent potential created by the charge accumulation in the well. The intrinsic nonlinearity of the transmission process is shown to lead to oscillations of the stored charge and of the transmitted and reflected fluxes. The dependence on the electrostatic feedback induced by the self-consistent potential and on the energy width of the incident distribution is discussed.Comment: 10 pages, TeX, 5 Postscript figure

Spatial Mixing of Coloring Random Graphs

We study the strong spatial mixing (decay of correlation) property of proper $q$-colorings of random graph $G(n, d/n)$ with a fixed $d$. The strong spatial mixing of coloring and related models have been extensively studied on graphs with bounded maximum degree. However, for typical classes of graphs with bounded average degree, such as $G(n, d/n)$, an easy counterexample shows that colorings do not exhibit strong spatial mixing with high probability. Nevertheless, we show that for $q\ge\alpha d+\beta$ with $\alpha>2$ and sufficiently large $\beta=O(1)$, with high probability proper $q$-colorings of random graph $G(n, d/n)$ exhibit strong spatial mixing with respect to an arbitrarily fixed vertex. This is the first strong spatial mixing result for colorings of graphs with unbounded maximum degree. Our analysis of strong spatial mixing establishes a block-wise correlation decay instead of the standard point-wise decay, which may be of interest by itself, especially for graphs with unbounded degree

On the Number of Iterations for Dantzig-Wolfe Optimization and Packing-Covering Approximation Algorithms

We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$ variables, with high probability, any such algorithm requires $\Omega(\rho \log(m)/\epsilon^2)$ iterations to compute a $(1+\epsilon)$-approximate solution, where $\rho$ is the width of the input. The bound is tight for a range of the parameters $(m,n,\rho,\epsilon)$. The algorithms in the class include Dantzig-Wolfe decomposition, Benders' decomposition, Lagrangean relaxation as developed by Held and Karp [1971] for lower-bounding TSP, and many others (e.g. by Plotkin, Shmoys, and Tardos [1988] and Grigoriadis and Khachiyan [1996]). To prove the bound, we use a discrepancy argument to show an analogous lower bound on the support size of $(1+\epsilon)$-approximate mixed strategies for random two-player zero-sum 0/1-matrix games

Consequences of a Refuge for the Predator-Prey Dynamics of a Wolf-Elk System in Banff National Park, Alberta, Canada

Refugia can affect predator-prey dynamics via movements between refuge and non-refuge areas. We examine the influence of a refuge on population dynamics in a large mammal predator-prey system. Wolves (Canis lupus) have recolonized much of their former range in North America, and as a result, ungulate prey have exploited refugia to reduce predation risk with unknown impacts on wolf-prey dynamics. We examined the influence of a refuge on elk (Cervus elaphus) and wolf population dynamics in Banff National Park. Elk occupy the Banff townsite with little predation, whereas elk in the adjoining Bow Valley experience higher wolf predation. The Banff refuge may influence Bow Valley predator-prey dynamics through source-sink movements. To test this hypothesis, we used 26 years of wolf and elk population counts and the Delayed Rejection Adaptive Metropolis Markov chain Monte Carlo method to fit five predator-prey models: 1) with no source-sink movements, 2) with elk density-dependent dispersal from the refuge to the non-refuge, 3) with elk predation risk avoidance movements from the non-refuge to the refuge, 4) with differential movement rates between refuge and non-refuge, and 5) with short-term, source-sink wolf movements. Model 1 provided the best fit of the data, as measured by Akaike Information Criterion (AIC). In the top model, Banff and Bow Valley elk had median growth rates of 0.08 and 0.03 (95% credibility intervals [CIs]: 0.027–0.186 and 0.001–0.143), respectively, Banff had a median carrying capacity of 630 elk (95% CI: 471.9– 2676.9), Bow Valley elk had a median wolf encounter rate of 0.02 (95% CI: 0.013–0.030), and wolves had a median death rate of 0.23 (95% CI: 0.146–0.335) and a median conversion efficiency of 0.07 (95% CI: 0.031–0.124). We found little evidence for potential source-sink movements influencing the predator-prey dynamics of this system. This result suggests that the refuge was isolated from the non-refuge

Label-free detection of single nanoparticles and biological molecules using microtoroid optical resonators

Single-molecule detection is one of the fundamental challenges of modern biology. Such experiments often use labels that can be expensive, difficult to produce, and for small analytes, might perturb the molecular events being studied. Analyte size plays an important role in determining detectability. Here we use laser-frequency locking in the context of sensing to improve the signal-to-noise ratio of microtoroid optical resonators to the extent that single nanoparticles 2.5 nm in radius, and 15.5 kDa molecules are detected in aqueous solution, thereby bringing these detectors to the size limits needed for detecting the key macromolecules of the cell. Our results, covering several orders of magnitude of particle radius (100 nm to 2 nm), agree with the ‘reactive’ model prediction for the frequency shift of the resonator upon particle binding. This confirms that the main contribution of the frequency shift for the resonator upon particle binding is an increase in the effective path length due to part of the evanescent field coupling into the adsorbed particle. We anticipate that our results will enable many applications, including more sensitive medical diagnostics and fundamental studies of single receptor–ligand and protein–protein interactions in real time

Horizontal-Branch Models and the Second-Parameter Effect. IV. The Case of M3 and Palomar 3

We present a detailed analysis of the "second-parameter pair" of globular clusters M3 (NGC 5272) and Palomar 3. Our main results can be summarized as follows: i) The horizontal-branch (HB) morphology of M3 is significantly bluer in its inner regions (observed with the Hubble Space Telescope) than in the cluster outskirts (observed from the ground), i.e., M3 has an internal second parameter. Most plausibly the mass loss on the red giant branch (RGB) has been more efficient in the inner than in the outer regions of the cluster. ii) The dispersion in mass of the Pal 3 HB is found to be very small -- consistent with zero -- and we argue that this is unlikely to be due to a statistical fluctuation. It is this small mass dispersion that leads to the most apparent difference in the HB morphologies of M3 and Pal 3. iii) The relative HB types of M3 and Pal 3, as measured by mean colors or parameters involving the number of blue, variable, and red HB stars, can easily be accounted for by a fairly small difference in age between these clusters, of order 0.5-1 Gyr -- which is in good agreement with the relative age measurement, based on the clusters' turnoffs, by VandenBerg (2000).Comment: 20 pages, 12 figures, emulateapj5 style. The Astrophysical Journal, in press. Figs. 1, 6, 9, 10 are in png format. The preprint (postscript format) with full resolution (embedded) figures is available from http://www.astro.virginia.edu/~mc6v