Multiple Window and Cluster Size Scan Procedures

Researchers apply scan statistics to test for unusually large clusters of events within a time window of specified length w, or alternatively an unusually small window w that contains a specified number of events. In some cases, the researcher is interested in testing for a range of specified window lengths, or a set of several specified number of events k (cluster sizes). In this paper, we derive accurate approximations for the joint distributions of scan statistics for a range of values of w, or of k, that can be used to set an experiment-wide level of significance that takes into account the multiple comparisons involved. We use these methods to compare different ways of choosing the window sizes for the different cluster sizes. One special case is a multiple comparison procedure based on a generalized likelihood ratio test (GLRT) for a range of window sizes. We compare the power of the GLRT with another method for allocating the window sizes. We find that the GLRT is sensitive for very small window sizes at the expense of moderate and larger window sizes. We illustrate these results on two examples, one involving clustering of translocation breakpoints in DNA, and the other involving disease clusters.     

MULTIPLE EMULSIONS STABILIZED BY COLLOIDAL MICROGRYSTALLINE CELLULOSE

Multiple emulsions stabilized by colloidal microcrystalline cellulose (CMCC, Avicel RC591) at the w/o and o/w interfaces, and by the addition of Span 80 or Span 85 at the w/o interface, were studied by means of brightfield microscopy, freeze-etch electron microscopy, droplet size distribution analysis and rheologic measurements. Stable multiple emulsions were prepared by incorporation of sodium chloride in the innermost aqueous phase, thereby creating an osmotic gradient preventing loss of the inner aqueous phase to the external aqueous phase. Freeze-etch electron microscopy of the multiple emulsions indicated the presence of a network of microcrystalline cellulose at the outer o/w interface. It may be assumed that the surfactant directly stabilized the w/o interface by adsorption at the interface, as well as indirectly by facilitating wetting of the microcrystalline cellulose by the oil. From rheologic measurements, the existence of a three-dimensional network in the external aqueous phase was indicated by the considerable degrees of thlxotropy and significant static yield values of these multiple emulsions.     

Determining membrane capacitance by dynamic control of droplet interface bilayer area

By making dynamic changes to the area of a droplet interface bilayer (DIB), we are able to measure the specific capacitance of lipid bilayers with improved accuracy and precision over existing methods. The dependence of membrane specific capacitance on the chain-length of the alkane oil present in the bilayer is similar to that observed in black lipid membranes. In contrast to conventional artificial bilayers, DIBs are not confined by an aperture, which enables us to determine that the dependence of whole bilayer capacitance on applied potential is predominantly a result of a spontaneous increase in bilayer area. This area change arises from the creation of new bilayer at the three phase interface and is driven by changes in surface tension with applied potential that can be described by the Young-Lippmann equation. By accounting for this area change, we are able to determine the proportion of the capacitance dependence that arises from a change in specific capacitance with applied potential. This method provides a new tool with which to investigate the vertical compression of the bilayer and understand the changes in bilayer thickness with applied potential. We find that, for 1,2-diphytanoyl-sn-glycero-3-phosphocholine membranes in hexadecane, specific bilayer capacitance varies by 0.6-1.5% over an applied potential of ±100 mV.     

Jacobi matrices for sums of weight functions

Orthogonal polynomials are conveniently represented by the tridiagonal Jacobi matrix of coefficients of the recurrence relation which they satisfy. LetJ ₁ andJ ₂ be finite Jacobi matrices for the weight functionsw ₁ andw ₂, resp. Is it possible to determine a Jacobi matrix \(\tilde J\) , corresponding to the weight functions \(\tilde w\) =w ₁+w ₂ using onlyJ ₁ andJ ₂ and if so, what can be said about its dimension? Thus, it is important to clarify the connection between a finite Jacobi matrix and its corresponding weight function(s). This leads to the need for stable numerical processes that evaluate such matrices. Three newO(n ²) methods are derived that “merge” Jacobi matrices directly without using any information about the corresponding weight functions. The first can be implemented using any of the updating techniques developed earlier by the authors. The second new method, based on rotations, is the most stable. The third new method is closely related to the modified Chebyshev algorithm and, although it is the most economical of the three, suffers from instability for certain kinds of data. The concepts and the methods are illustrated by small numerical examples, the algorithms are outlined and the results of numerical tests are reported.     

FORMATION OF OIL IN GLYCEROIVWATER EMULSIONS: EFFECT OF SURFACTANT ETHYLENE OXIDE CONTENT

Oil-in-glycerol/water emulsions at various ratios of water to glycerol in the external phase were prepared with polyoxyethylated octylphenols and light mineral oil. As the water concentration in the external phase decreased, oil droplet size decreased down to a minimum size beyond which oil separation occurred. Also, the cloud points of various surfactants were depressed toward room temperature as the water content of the glycerol/water mixtures decreased. It was possible therefore to correlate the concentration of water needed for formation of the smallest droplets to the concentration of water needed for depression of the cloud point of each surfactant to room temperature.     

Drug Release From Emulsions Stabilized by Colloidal Macrocrystalline Cellulose

Drug release from water-in oil-in water (w/o/w)multiple emulsions stabilized with colloidal microcrystal-line cellulose and various surface-active agents has been studied in vitro. Lidocaine hydrochloride and lidocaine base were used as model drugs for these studies. Drug concentrations were measured by HPLC, and effective diffusion coefficients were determined.     

Nonsymmetric Lanczos and finding orthogonal polynomials associated with indefinite weights

The nonsymmetric Lanczos algorithm reduces a general matrix to tridiagonal by generating two sequences of vectors which satisfy a mutual bi-orthogonality property. The process can proceed as long as the two vectors generated at each stage are not mutually orthogonal, otherwise the process breaks down. In this paper, we propose a variant that does not break down by grouping the vectors into clusters and enforcing the bi-orthogonality property only between different clusters, but relaxing the property within clusters. We show how this variant of the matrix Lanczos algorithm applies directly to a problem of computing a set of orthogonal polynomials and associated indefinite weights with respect to an indefinite inner product, given the associated moments. We discuss the close relationship between the modified Lanczos algorithm and the modified Chebyshev algorithm. We further show the connection between this last problem and checksum-based error correction schemes for fault-tolerant computing.The research reported by this author was supported in part by NSF grant CCR-8813493.The research reported by this author was supported in part by ARO grant DAAL03-90-G-0105 and in part by NSF grant DCR-8412314.     

Jacobi matrices for measures modified by a rational factor

This paper describes how, given the Jacobi matrixJ for the measure d(t), it is possible to produce the Jacobi matrix for the measurer(t)d(t) wherer(t) is a quotient of polynomials. The method uses a new factoring algorithm to generate the Jacobi matrices associated with the partial fraction decomposition ofr(t) and then applies a previously developed summing technique to merge these Jacobi matrices. The factoring method performs best just where Gautschi's minimal solution method for this problem is weakest and vice versa. This suggests a hybrid strategy which is believed to be the most powerful yet for solving this problem. The method is demonstrated on a simple example and some numerical tests illustrate its performance characteristics.     

Conformational dependence of serotonin theoretical pKa prediction

In the present work we used quantum mechanics calculations to predict the two pK_a’s of 5-hydrotryptamine (5-HT). Proton dissociation reaction succeeded to predict the experimental pK_a1 corresponding to ionization of the protonated amine group but failed for pK_a2 corresponding to ionization of the 5-hydroxyl group. For pK_a2, a cluster-continuum model including three water molecules in the first hydration shell around 5-hydroxyl and 5-hydroxide groups enabled us to reproduce the experimental pK_a2 value. Furthermore, we demonstrated that specific conformations of acid/base pair of 5-HT is critical to predict accurately the experimental pK_a’s of the flexible 5-HT molecule.     

Adams-Harbertson protein precipitation-based wine tannin method found invalid

The poor precision of the Adams-Harbertson wine tannin assay which was proposed for commercial winemaking, thereby creating the real possibility of quality control problems, is documented. The method is a version of the Hagerman and Butler protein precipitation-based tannin method. An extensive invalidation of the assay results with luxury wine data shows that the assay cannot distinguish bottled wine with reasonable accuracy. Five laboratories used Adams-Harbertson to assay 9 replicates each, of 3 bottled wines (n = 135) found in California supermarkets, with tannin concentrations of nominally 500 and 1000 ppm by high-performance liquid chromatography (HPLC). Reliability exceeded the +/-5% industry requirement by nominally 5 times (z-score based on 5% distribution). Coefficient of variation was +/-27%, making the standard deviation range 54% for Pinot Noir, 34% for Merlot, and 44% for Cabernet Sauvignon. Validity exceeded the 100% requirement. Intralaboratory validity recovery was 55-63%. Interwinery validity was 71-178% of the mean for Pinot Noir, 81-144% for Merlot, and 83-164% for Cabernet Sauvignon. Range as a function of the mean was 89% for Pinot Noir, 55% for Merlot, and 67% for Cabernet Sauvignon. Expect intermethod validity to be nominally 50%, i.e., percent recovery to HPLC. These statistically significant errors were predicted by the literature. First-order error is related to the tannin-protein equilibrium constant (Ka), as suggested by the original author, Hagerman, and the protein equivalence point error as suggested by Silber. This does not obviate second-order errors for tannin-protein analytical chemistry. Winemakers using the measurements risk making wines that are relatively more tannic than the measurements report.