A Semiparametric Two-Sample Hypothesis Testing Problem for Random Graphs

Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this article, we consider a semiparametric problem of two-sample hypothesis testing for a class of latent position random graphs. We formulate a notion of consistency in this context and propose a valid test for the hypothesis that two finite-dimensional random dot product graphs on a common vertex set have the same generating latent positions or have generating latent positions that are scaled or diagonal transformations of one another. Our test statistic is a function of a spectral decomposition of the adjacency matrix for each graph and our test procedure is consistent across a broad range of alternatives. We apply our test procedure to real biological data: in a test-retest dataset of neural connectome graphs, we are able to distinguish between scans from different subjects; and in the C. elegans connectome, we are able to distinguish between chemical and electrical networks. The latter example is a concrete demonstration that our test can have power even for small-sample sizes. We conclude by discussing the relationship between our test procedure and generalized likelihood ratio tests. Supplementary materials for this article are available online.     

A method for overcoming the surface tension time step constraint in multiphase flows II

A method for overcoming the surface tension time step constraint is presented. The algorithm presented in this work is an improvement on the work presented by Sussman and Ohta (SIAM J Sci Comput 2009). In this work, the method of Sussman and Ohta is extended in order to treat problems with contact angle dynamics. Furthermore, this work presents a more efficient method for computing volume‐preserving motion by mean curvature than the method presented previously. The new method is tested on the following four 2D problems: (1) 3D axisymmetric (r?z) surface tension driven zero gravity droplet oscillation, (2) measurement of the magnitude of parasitic currents for a droplet on a substrate initialized in static equilibrium, (3) relaxation of a 2D droplet on a substrate to static shape, and (3) relaxation of a 2D bubble on a substrate to static shape. Copyright © 2011 John Wiley & Sons, Ltd.     

Gravitational collapse of a magnetized fermion gas with finite temperature

The four LEP collaborations, ALEPH, DELPHI, L3 and OPAL, have searched for pair-produced charged Higgs bosons in the framework of Two Higgs Doublet Models (2HDMs). The data of the four experiments have been statistically combined. The results are interpreted within the 2HDM for Type I and Type II benchmark scenarios. No statistically significant excess has been observed when compared to the Standard Model background prediction, and the combined LEP data exclude large regions of the model parameter space. Charged Higgs bosons with mass below 80  ${\rm GeV}/c^{2}$ (Type II scenario) or 72.5 ${\rm GeV}/c^{2}$ (Type I scenario, for pseudo-scalar masses above 12 ${\rm GeV}/c^{2}$ ) are excluded at the 95 % confidence level.     

Conformal structure of a Schwarzschild black hole immersed in a Friedman universe

The evolution of a Schwarzschild black hole in an expanding Friedman universe is described using the same coordinate patch for both geometries. Comoving and extended Kruskal coordinates are considered and compared for the casesk=0 andk=1. The conformal structure and some global topological aspects of the Schwarzschild-Friedman system are examined with the help of diagrams in comoving and extended Kruskal coordinates.     

Hydrogen bond. Environmental effects on proton potential curves. An SCRF MO CNDO/2 calculation of a water dimer

A solvent and/or environmental effect has been introduced into the MO CNDO/2 calculation of a model hydrogen bonded system. Proton potential curves, potential energy, dipole moments, the polarizability component parallel to the reaction field, and the second order perturbation effects associated to the dispersion forces, have been studied as a function of a solute-solvent coupling parameter. This parameter may be related, through the self-consistent reaction field theory of solvent effects, to both the macroscopic dielectric properties of the solvent and to the local order (if any) around the solute. Numerical results corresponding to a water dimer are discussed.     

The sialoglycoprotein subunits of human placental brush border membranes characterized by two-two-dimensional electrophoresis

A brush border membrane enriched fraction was isolated from human full-term placenta. This membrane fraction exhibited large membrane fragments with microvilli projecting from the basal membrane in electron micrographs and was enriched tenfold in alkaline phosphatase, a brush border enzyme marker. The sialoglycoproteins associated with this membrane fraction were tritiated by mild periodate oxidation of sialic acid and reduction with tritiated NaBH4. The membranes were solubilized in 8 M urea, 2 percent Triton X-100, and the tritiated glycoprotein subunits were reduced with beta-mercaptoethanol and characterized by 2-dimensional poly-acrylamide gel electrophoresis using a method similar to that described by O'Farrell and Bhakdi, Knüferman, and Wallach. The tritiated subunits were detected in the gels by autofluorography. The 2-dimensional subunit "maps" resolved at least 17 major sialoglycoprotein subunits whereas only 10 major periodate-Schiff reagent staining components were resolved by 1-dimensional SDS polyacrylamide gel electrophoresis. Placental alkaline phosphatase (PAP) was identified on the subunit maps by inclusion of 32P-labeled PAP in the tritiated membrane sample. The 32P-labeled PAP corresponded to a major tritiated sialoglycoprotein subunit, which was heterogeneous with respect to charge as demonstrated by 3 closely running spots of the same molecular weight.     

Impaired intracellular Ca2+ dynamics in live cardiomyocytes revealed by rapid line scan confocal microscopy.

Altered intracellular Ca2+ dynamics are characteristically observed in cardiomyocytes from failing hearts. Studies of Ca2+ handling in myocytes predominantly use Fluo-3 AM, a visible light excitable Ca2+ chelating fluorescent dye in conjunction with rapid line-scanning confocal microscopy. However, Fluo-3 AM does not allow for traditional ratiometric determination of intracellular Ca2+ concentration and has required the use of mathematic correction factors with values obtained from separate procedures to convert Fluo-3 AM fluorescence to appropriate Ca2+ concentrations. This study describes methodology to directly measure intracellular Ca2+ levels using inactivated, Fluo-3-AM-loaded cardiomyocytes equilibrated with Ca2+ concentration standards. Titration of Ca2+ concentration exhibits a linear relationship to increasing Fluo-3 AM fluorescence intensity. Images obtained from individual myocyte confocal scans were recorded, average pixel intensity values were calculated, and a plot is generated relating the average pixel intensity to known Ca2+ concentrations. These standard plots can be used to convert transient Ca2+ fluorescence obtained with experimental cells to Ca2+ concentrations by linear regression analysis. Standards are determined on the same microscope used for acquisition of unknown Ca2+ concentrations, simplifying data interpretation and assuring accuracy of conversion values. This procedure eliminates additional equipment, ratiometric imaging, and mathematic correction factors and should be useful to investigators requiring a straightforward method for measuring Ca2+ concentrations in live cells using Ca2+-chelating dyes exhibiting variable fluorescence intensity.     

Switched wave packets: a route to nonperturbative quantum control

The dynamic Stark effect due to a strong nonresonant but nonionizing laser field provides a route to quantum control via the creation of novel superposition states. We consider the creation of a field-free "switched" wave packet through adiabatic turn-on and sudden turn-off of a strong dynamic Stark interaction. There are two limiting cases for such wave packets. The first is a Raman-type coupling, illustrated by the creation of field-free molecular axis alignment. An experimental demonstration is given. The second case is that of dipole-type coupling, illustrated by the creation of charge localization in an array of quantum wells.