Decomposition tables for experiments. II. Two--one randomizations

We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.Comment: Published in at http://dx.doi.org/10.1214/09-AOS785 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Decomposition tables for experiments I. A chain of randomizations

One aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space. Initially we establish the notation and methods for evaluating an experiment with a single randomization. Starting with two structures, or orthogonal decompositions of the data space, we describe how to combine them to form the overall decomposition for a single-randomization experiment that is ``structure balanced.'' The relationships between the two structures are characterized using efficiency factors. The decomposition is encapsulated in a decomposition table. Then, for experiments that involve multiple randomizations forming a chain, we take several structures that pairwise are structure balanced and combine them to establish the form of the orthogonal decomposition for the experiment. In particular, it is proven that the properties of the design for such an experiment are derived in a straightforward manner from those of the individual designs. We show how to formulate an extended decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated.Comment: Published in at http://dx.doi.org/10.1214/09-AOS717 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Is the shell-focusing singularity of Szekeres space-time visible?

The visibility of the shell-focusing singularity in Szekeres space-time - which represents quasi-spherical dust collapse - has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second non-parallel radial geodesic, then the space-time is spherically symmetric, and so is a Lema\^{\i}tre-Tolman-Bondi (LTB) space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for non-radial null geodesics in the axially symmetric case and in the general (non-axially symmetric) case, and suggest a possible approach.Comment: 10 page

Cell proliferation and differentiation kinetics during spermatogenesis in Hydra carnea

Spermatogenesis inHydra carnea was investigated. The cell proliferation and differentiation kinetics of intermediates in the spermatogenesis pathway were determined, using quantitative determinations of cell abundance, pulse and continuous labelling with3H-thymidine and nuclear DNA measurements. Testes develop in the ectoderm of male hydra as a result of interstitial cell proliferation. Gonial stem cells and proliferating spermatogonia have cell cycles of 28 h and 22 h, respectively. Stem cells undergo four, five or six cell divisions prior to meiosis which includes a premeiotic S+G2 phase of 20 h followed by a long meiotic prophase (22 h). Spermatid differentiation requires 12–29 h. When they first appear, testes contain only proliferating spermatogonia; meiotic and postmeiotic cells appear after 2 and 3 days, respectively and release of mature sperm begins after 4 days. Mature testes produce about 27,000 sperm per day over a period of 4–6 days: about 220 gonial stem cells per testis are required to support this level of sperm differentiation. Further results indicate that somatic (e.g. nematocyte) differentiation does not occur in testes although it continues normally in ectodermal tissue outside testes. Our results support the hypothesis that spermatogenesis is controlled locally in regions of the ectoderm where testes develop

Odd-parity perturbations of self-similar Vaidya spacetime

We carry out an analytic study of odd-parity perturbations of the self-similar Vaidya space-times that admit a naked singularity. It is found that an initially finite perturbation remains finite at the Cauchy horizon. This holds not only for the gauge invariant metric and matter perturbation, but also for all the gauge invariant perturbed Weyl curvature scalars, including the gravitational radiation scalars. In each case, `finiteness' refers to Sobolev norms of scalar quantities on naturally occurring spacelike hypersurfaces, as well as pointwise values of these quantities.Comment: 28 page

Solute Concentrations Influence Microbial Methanogenesis in Coal-bearing Strata of the Cherokee Basin, USA

Microorganisms have contributed significantly to subsurface energy resources by converting organic matter in hydrocarbon reservoirs into methane, the main component of natural gas. In this study, we consider environmental controls on microbial populations in coal-bearing strata of the Cherokee basin, an unconventional natural gas resource in southeast Kansas, USA. Pennsylvanian-age strata in the basin contain numerous thin (0.4-1.1 m) coalbeds with marginal thermal maturities (0.5-0.7% Ro) that are interbedded with shale and sandstone. We collected gas, water, and microbe samples from 16 commercial coalbed methane wells for geochemical and microbiological analysis. The water samples were Na-Cl type with total dissolved solids (TDS) content ranging from 34.9 to 91.3 g L?1. Gas dryness values [C1/(C2 + C3)] averaged 2640 and carbon and hydrogen isotope ratios of methane differed from those of carbon dioxide and water, respectively, by an average of 65 and 183%. These values are thought to be consistent with gas that formed primarily by hydrogenotrophic methanogenesis. Results from cultivation assays and taxonomic analysis of 16S rRNA genes agree with the geochemical results. Cultivable methanogens were present in every sample tested, methanogen sequences dominate the archaeal community in each sample (avg 91%), and few archaeal sequences (avg 4.2%) were classified within Methanosarcinales, an order of methanogens known to contain methylotrophic methanogens. Although hydrogenotrophs appear dominant, geochemical and microbial analyses both indicate that the proportion of methane generated by acetoclastic methanogens increases with the solute content of formation water, a trend that is contrary to existing conceptual models. Consistent with this trend, beta diversity analyses show that archaeal diversity significantly correlates with formation water solute content. In contrast, bacterial diversity more strongly correlates with location than solute content, possibly as a result of spatial variation in the thermal maturity of the coalbeds.Citation: Kirk MF, Wilson BH, Marquart KA, Zeglin LH, Vinson DS and Flynn TM (2015) Solute Concentrations Influence Microbial Methanogenesis in Coal-bearing Strata of the Cherokee Basin, USA. Front. Microbiol. 6:1287. doi: 10.3389/fmicb.2015.0128

Cohabitation, Marriage, and Divorce in a Model of Match Quality

The objective of this research is to develop and estimate an economic model of nonmarital cohabitation, marriage, and divorce that is consistent with current data on the formation and dissolution of relationships. Jovanovic's (1979) theoretical matching model is extended to help explain household formation and dissolution behavior. Implications of the model reveal what factors influence the decision to start a relationship, what form this relationship will take, and the relative stability of the various types of unions. The structural parameters of the model are estimated using longitudinal data from a sample of female high school seniors from the U.S. New numerical methods are developed to reduce computational costs associated with estimation. The empirical results are mostly consistent with previous literature but have interesting interpretations given the structural model.