Small angle neutron scattering (SANS) is used to measure the density of heavy water contained in 1D cylindrical pores of mesoporous silica material MCM-41-S-15, with pores of diameter of 15 ؎ 1 Å. In these pores the homogenous nucleation process of bulk water at 235 K does not occur, and the liquid can be supercooled down to at least 160 K. The analysis of SANS data allows us to determine the absolute value of the density of D 2O as a function of temperature. We observe a density minimum at 210 ؎ 5 K with a value of 1.041 ؎ 0.003 g/cm 3 . We show that the results are consistent with the predictions of molecular dynamics simulations of supercooled bulk water. Here we present an experimental report of the existence of the density minimum in supercooled water, which has not been described previously.liquid-liquid critical point ͉ nanopores ͉ small angle neutron scattering ͉ Widom line O f the many remarkable physical properties of liquid water (1), the density maximum is probably the most well known. The density maximum of H 2 O at T max ϭ 277 K (284 K in D 2 O) is one of only a few liquid-state density maxima known (2) and the only one found to occur in the stable liquid phase above the melting temperature. Water's density maximum is a dramatic expression of the central role played by hydrogen bonding in determining the properties of this liquid: as temperature T decreases through the region of the density maximum, an increasingly organized and open four-coordinated network of hydrogen bonds expands the volume occupied by the liquid, overwhelming the normal tendency of the liquid to contract as it is cooled.The density of bulk supercooled liquid water decreases rapidly with T before the onset of homogeneous crystal nucleation (at Ϸ235 K) precludes further measurements. The density curve of ice Ih lies below that of the liquid and almost certainly sets a lower bound on the density that the supercooled liquid could attain if nucleation were avoided, because ice Ih represents the limiting case of a perfectly ordered tetrahedral network of hydrogen bonds. Significantly, the expansivity of ice Ih in this T range is positive (3); i.e., the density increases as T decreases (see Fig. 2). The low density amorphous (LDA) ice that forms from deeply supercooled liquid water at the (in this case extremely weak) glass transition approaches very closely the structure of a ''random tetrahedral network'' (RTN) and exhibits a number of ice-like properties, including a ''normal'' (i.e., positive) expansivity (4). If the structure of deeply supercooled water also approaches that of a RTN, it is therefore possible that a density minimum occurs in the supercooled liquid (5).Consistent with this possibility, a number of recent molecular dynamics (MD) computer simulation studies predict that a density minimum occurs in water (H 2 O) (5-10). These studies achieve deep supercooling without crystal nucleation due to the small system size and short observation time explored, compared with experiment. In the literature, the five-site transfer...

BackgroundIn designing genome-wide association (GWA) studies it is important to calculate statistical power. General statistical power calculation procedures for quantitative measures often require information concerning summary statistics of distributions such as mean and variance. However, with genetic studies, the effect size of quantitative traits is traditionally expressed as heritability, a quantity defined as the amount of phenotypic variation in the population that can be ascribed to the genetic variants among individuals. Heritability is hard to transform into summary statistics. Therefore, general power calculation procedures cannot be used directly in GWA studies. The development of appropriate statistical methods and a user-friendly software package to address this problem would be welcomed.ResultsThis paper presents GWAPower, a statistical software package of power calculation designed for GWA studies with quantitative traits, where genetic effect is defined as heritability. Based on several popular one-degree-of-freedom genetic models, this method avoids the need to specify the non-centrality parameter of the F-distribution under the alternative hypothesis. Therefore, it can use heritability information directly without approximation. In GWAPower, the power calculation can be easily adjusted for adding covariates and linkage disequilibrium information. An example is provided to illustrate GWAPower, followed by discussions.ConclusionsGWAPower is a user-friendly free software package for calculating statistical power based on heritability in GWA studies with quantitative traits. The software is freely available at: http://dl.dropbox.com/u/10502931/GWAPower.zip

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