Stabilization Coefficient of Random Variable

Coefficient of variation, standard deviation divided by mean, has some essential defects. Its density, expectation and variance are too complex to make the statistical inference for such a coefficient. The definition of stabilization coefficient is just the reciprocal of variation coefficient, mean divided by standard deviation. Such a coefficient has a simple expectation and a simple variance, and is an asymptotically unbiased estimator and a consistent estimator of its true value. Furthermore, coefficient of stabilization has an asymptotic normality. Due to its statistical advantages, coefficient of stabilization is easy to be tested statistically. In some applied fields, usually, there is an increasing standard deviation accompanying an increasing mean. Coefficient of stabilization can be practically used for some comparison studies in such fields. Illustrations about comparing microorganism strains are given in this paper. The robustness of stabilization coefficient is satisfactory.     

A Formula for the Gini Coefficient and its Decomposition

This paper is concerned with the Gini coefficient as a concentration measure of the distribution. The proposed formula for the computation of the Gini coefficient allows its decomposition according to different sub-groups of the initial population, either exactly or approximately.     

Rank of Correlation Coefficient as a Comparable Measure for Biological Significance of Gene Coexpression

Information regarding gene coexpression is useful to predict gene function. Several databases have been constructed for gene coexpression in model organisms based on a large amount of publicly available gene expression data measured by GeneChip platforms. In these databases, Pearson''s correlation coefficients (PCCs) of gene expression patterns are widely used as a measure of gene coexpression. Although the coexpression measure or GeneChip summarization method affects the performance of the gene coexpression database, previous studies for these calculation procedures were tested with only a small number of samples and a particular species. To evaluate the effectiveness of coexpression measures, assessments with large-scale microarray data are required. We first examined characteristics of PCC and found that the optimal PCC threshold to retrieve functionally related genes was affected by the method of gene expression database construction and the target gene function. In addition, we found that this problem could be overcome when we used correlation ranks instead of correlation values. This observation was evaluated by large-scale gene expression data for four species: Arabidopsis, human, mouse and rat.     

Interaction of enkephalin peptides with anionic model membranes

According to the model for passive transport across the membranes, the total flow of permeant molecules is related to the product of the water-membrane partition coefficient and the diffusion coefficient, and to the water-membrane interfacial barrier. The effect of membrane surface charge on the permeability and interaction of analgesic peptide ligands with model membranes was investigated. A mixture of zwitterionic phospholipids with cholesterol was used as a model membrane. The lipid membrane charge density was controlled by the addition of anionic 1-palmitoyl-2-oleoylphosphatidylserine. Two classes of highly potent analgesic peptides were studied, c[D-Pen²,D-Pen⁵]enkephalin (DPDPE) and biphalin, a dimeric analog of enkephalin. The effect of increased surface charge on the permeability of the zwitterionic DPDPE is a relatively modest decrease, that appears to be due to a diminished partition coefficient. On the other hand the binding of the dicationic biphalin ligands to membranes increases proportionally with increased negative surface charge. This effect translates into a significant reduction of biphalin permeability by reducing the diffusion of the peptide across the bilayer. These experiments show the importance of electrostatic effects on the peptide-membrane interactions and suggest that the negative charge naturally present in cell membranes may hamper the membrane transport of some peptide drugs, especially cationic ones, unless there are cationic transporters present.     

Accuracy Analysis with Special Reference to the Prediction of Grassland Yield

In this paper techniques are presented which allow the evaluation of accuracy of prediction methods, with special reference to the prediction of grassland yield. The more prominent methods of predicting grassland yield are discussed. Two coefficients, which are normalizations of the mean-squared-error, are proposed as measures of accuracy. It is shown that the mean-squared-error partitions into the sum of three meaningful components of error. The distribution of the components is discussed under the assumption that the actual and predicted yields have a bivariate normal distribution. The problem of accuracy analysis is addressed when one is only interested in ranking the yields of grassland areas. The ratio of the mean-squared-error for two competing prediction methods is investigated. Finally, a multiplicative model is studied which allows predicting ability to differ over time or over regions.     

The determination of desirable and nuisance plant levels in streams

To cope with luxuriant plant growth in the streams of southern Ontario, an approach to determine the desirable and nuisance plant levels was proposed.With a more intensive analysis of the assimilation efficiency of plant communities, which includes the fractionation of community respiration as well as compensation for the plant self-shading effect, the plant biomass of all species component expressed as chlorophyll a can be estimated from the modified growth equation, where B is the biomass, P_max is the photosynthetic growth rate at light saturation, A is the assimilation number and S is the plant shading coefficient. Once comparable biomass values are available, a desirable plant level relative to specified environmental standards can be determined.For instance, to meet the minimum dissolved oxygen criteria of 5 ppm, the desirable and the nuisance crop levels in the North Thames River, Ontario, were found to be 0.15 and 0.75 g chla/m² respectively.     

Effect of lipid membranes on the apparent pK of the local anesthetic tetracaine spin label and titration studies

Electrometric titrations and spin label data demonstrate changes in the experimentally determined apparent pK of an ionizable drug in the presence of membranes. This effect is attributed to the difference in partition coefficients for the charged and uncharged forms of the drug. Investigation of the binding of a local anesthetic, tetracaine, to egg phosphatidylcholine membranes indicates that the drug apparent pK decreases in the presence of membranes, the decrease being a function of membrane concentration. The agreement between titration and spin label studies is very good and could be simulated by calculating membrane-bound and free populations of charged and uncharged tetracaine from the independently-measured partition coefficients for the two forms.     

Analysis of multilocus fingerprinting data sets containing missing data

Missing data are commonly encountered using multilocus, fragment‐based (dominant) fingerprinting methods, such as random amplified polymorphic DNA (RAPD) or amplified fragment length polymorphism (AFLP). Data sets containing missing data have been analysed by eliminating those bands or samples with missing data, assigning values to missing data or ignoring the problem. Here, we present a method that uses random assignments of band presence–absence to the missing data, implemented by the computer program famd (available from http://homepage.univie.ac.at/philipp.maria.schlueter/famd.html ), for analyses based on pairwise similarity and Shannon's index. When missing values group in a data set, sample or band elimination is likely to be the most appropriate action. However, when missing values are scattered across the data set, minimum, maximum and average similarity coefficients are a simple means of visualizing the effects of missing data on tree structure. Our approach indicates the range of values that a data set containing missing data points might generate, and forces the investigator to consider the effects of missing values on data interpretation.     

Wave intensity amplification and attenuation in non-linear flow: Implications for the calculation of local reflection coefficients

Local reflection coefficients (R) provide important insights into the influence of wave reflection on vascular haemodynamics. Using the relatively new time-domain method of wave intensity analysis, R has been calculated as the ratio of the peak intensities (R_PI) or areas (R_CI) of incident and reflected waves, or as the ratio of the changes in pressure caused by these waves (R_ΔP). While these methods have not yet been compared, it is likely that elastic non-linearities present in large arteries will lead to changes in the size of waves as they propagate and thus errors in the calculation of R_PI and R_CI. To test this proposition, R_PI, R_CI and R_ΔP were calculated in a non-linear computer model of a single vessel with various degrees of elastic non-linearity, determined by wave speed and pulse amplitude (ΔP₊), and a terminal admittance to produce reflections. Results obtained from this model demonstrated that under linear flow conditions (i.e. as ΔP₊→0), R_ΔP is equivalent to the square-root of R_PI and R_CI (denoted by R_PI^p and R_CI^p). However for non-linear flow, pressure-increasing (compression) waves undergo amplification while pressure-reducing (expansion) waves undergo attenuation as they propagate. Consequently, significant errors related to the degree of elastic non-linearity arise in R_PI and R_CI, and also R_PI^p and R_CI^p, with greater errors associated with larger reflections. Conversely, R_ΔP is unaffected by the degree of non-linearity and is thus more accurate than R_PI and R_CI.