Non-uniqueness in conformal formulations of the Einstein constraints

Standard methods in non-linear analysis are used to show that there exists a parabolic branching of solutions of the Lichnerowicz-York equation with an unscaled source. We also apply these methods to the extended conformal thin sandwich formulation and show that if the linearised system develops a kernel solution for sufficiently large initial data then we obtain parabolic solution curves for the conformal factor, lapse and shift identical to those found numerically by Pfeiffer and York. The implications of these results for constrained evolutions are discussed.Comment: Arguments clarified and typos corrected. Matches published versio

Adsorption models of hybridization and post-hybridisation behaviour on oligonucleotide microarrays

Analysis of data from an Affymetrix Latin Square spike-in experiment indicates that measured fluorescence intensities of features on an oligonucleotide microarray are related to spike-in RNA target concentrations via a hyperbolic response function, generally identified as a Langmuir adsorption isotherm. Furthermore the asymptotic signal at high spike-in concentrations is almost invariably lower for a mismatch feature than for its partner perfect match feature. We survey a number of theoretical adsorption models of hybridization at the microarray surface and find that in general they are unable to explain the differing saturation responses of perfect and mismatch features. On the other hand, we find that a simple and consistent explanation can be found in a model in which equilibrium hybridization followed by partial dissociation of duplexes during the post-hybridization washing phase.Comment: 26 pages, 6 figures, some rearrangement of sections and some additions. To appear in J.Phys.(condensed matter

Gating-by-tilt of mechanosensitive membrane channels

We propose an alternative mechanism for the gating of biological membrane channels in response to membrane tension that involves a change in the slope of the membrane near the channel. Under biological membrane tensions we show that the energy difference between the closed (tilted) and open (untilted) states can far exceed kBT and is comparable to what is available under simple ilational gating. Recent experiments demonstrate that membrane leaflet asymmetries (spontaneous curvature) can strong effect the gating of some channels. Such a phenomenon would be more easy to explain under gating-by-tilt, given its novel intrinsic sensitivity to such asymmetry.Comment: 10 pages, 2 figure

On rationality of the intersection points of a line with a plane quartic

We study the rationality of the intersection points of certain lines and smooth plane quartics C defined over F_q. For q \geq 127, we prove the existence of a line such that the intersection points with C are all rational. Using another approach, we further prove the existence of a tangent line with the same property as soon as the characteristic of F_q is different from 2 and q \geq 66^2+1. Finally, we study the probability of the existence of a rational flex on C and exhibit a curious behavior when the characteristic of F_q is equal to 3.Comment: 17 pages. Theorem 2 now includes the characteristic 2 case; Conjecture 1 from the previous version is proved wron

Initial data for fluid bodies in general relativity

We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary. PACS: 04.20.Ex, 04.40.Nr, 02.30.JrComment: 38 pages, LaTeX 2e, no figures. Accepted for publication in Phys. Rev.

A genome-wide scan for common alleles affecting risk for autism

Although autism spectrum disorders (ASDs) have a substantial genetic basis, most of the known genetic risk has been traced to rare variants, principally copy number variants (CNVs). To identify common risk variation, the Autism Genome Project (AGP) Consortium genotyped 1558 rigorously defined ASD families for 1 million single-nucleotide polymorphisms (SNPs) and analyzed these SNP genotypes for association with ASD. In one of four primary association analyses, the association signal for marker rs4141463, located within MACROD2, crossed the genome-wide association significance threshold of P < 5 × 10−8. When a smaller replication sample was analyzed, the risk allele at rs4141463 was again over-transmitted; yet, consistent with the winner's curse, its effect size in the replication sample was much smaller; and, for the combined samples, the association signal barely fell below the P < 5 × 10−8 threshold. Exploratory analyses of phenotypic subtypes yielded no significant associations after correction for multiple testing. They did, however, yield strong signals within several genes, KIAA0564, PLD5, POU6F2, ST8SIA2 and TAF1C

Full Waveform Modelling for Converted Waves Seismic Reflections in Mountainous and Marine Environment

The application of seismic waves allows us to achieve adequate results by compressional wave (P-wave) surveys alone. However, in the presence of gas P-wave transmission disrupts and obscures underlying targets. Many reservoirs don’t present sufficient impedance contrast to the overburden and not reflect P-wave strongly to produce an impedance image. High impedance rock such as basalt or hard volcanic rocks are difficult to image with P-wave. To overcome these challenges shear-wave (S-wave) or converted wave (P-S) surveys are usedfor last 20 years by making the use of down going P waves converting to upcoming S waves at the mode conversion boundaries.The processing of converted waves requires studying asymmetric reflection at the conversion point, difference in geometries and conditions of source and receiver, and the partitioning of energy into orthogonally polarized components. Interpretation of P-S sections incorporates the identification of P-S waves, full waveform modelling, correlation with P-wave sections and depth migration.The objectives of this study is to model P-S wave reflections in onshore and offshore environment and to examine the major differences in processing of P and P-S wave surveys together with the identifying converted mode reflections by P-wave sources in anisotropic media. To achieve these, realistic mountainous and marine environment models have been developed and synthetic seismograms are generated by full waveform modelling technique. First a mountain foothill model was studied. A Kirchhoff-based technique that includes anisotropic velocities is used for depth migration of P-S waves. The results from depth imaging show that P-S section help in distinguishing amplitude associated with hydrocarbons from those caused by localized stratigraphic changes. Marine model shows a good correlation with identified converted waves. In addition, the full waveform elastic modellingproves useful in finding an appropriate balance between capturing high-quality P-wave data as well as P-S data challenges in a survey.Key Words: Converted-waves (P-S); P-S Wave; Kirchhoff migration; Depth migration; Gas clouds; Shale diaper

Emission of non‐thermal microwave radiation by a Martian dust storm

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94934/1/grl26053.pd