An ordering of dependence for contingency tables

A majorization ordering is defined on matrices with the same row and column sums. This ordering is used as an ordering of dependence for contingency tables. Results are derived for maximal and minimal matrices with respect to the majorization ordering. This theory can be used to maximize and minimize Schur concave functions defined over matrices, when there are row and column sum constraints; in this paper, it is applied to the algorithm of Mehta and Patel (1983) for finding the P-value of Fisher's exact test.     

Barycentric coordinates for convex polytopes

An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, theadjoint of the polytope, generalizes a previous two-dimensional construction described by Wachspress. The barycentric coordinate functions for the polytope are rational combinations of adjoints of various dual cones associated with the polytope.     

The cell Reynolds number myth

The commonly accepted linear stability analysis for the forward-time centred-space (FTCS) algorithm applied to the transport equation has led to the concept of a cell Reynolds number restriction on the spatial grid size. This paper shows where the commonly accepted original analysis is in error and presents the correct stability restrictions, which are restrictions on the time step, not the spatial grid size. There is no cell Reynolds number restriction. The results are confirmed by numerical computations for the two-dimensional driven cavity problem.     

Quantum dots-based reverse phase protein microarray

CdSe nanocrystals, also called quantum dots (Qdots) are a novel class of fluorophores, which have a diameter of a few nanometers and possess high quantum yield, tunable emission wavelength and photostability. They are an attractive alternative to conventional fluorescent dyes. Quantum dots can be silanized to be soluble in aqueous solution under biological conditions, and thus be used in bio-detection. In this study, we established a novel Qdot-based technology platform that can perform accurate and reproducible quantification of protein concentration in a crude cell lysate background. Protein lysates have been spiked with a target protein, and a dilution series of the cell lysate with a dynamic range of three orders of magnitude has been used for this proof-of-concept study. The dilution series has been spotted in microarray format, and protein detection has been achieved with a sensitivity that is at least comparable to standard commercial assays, which are based on horseradish peroxidase (HRP)-catalyzed diaminobenzidine (DAB) chromogenesis. The data obtained through the Qdot method has shown a close linear correlation between relative fluorescence unit and relative protein concentration. The Qdot results are in almost complete agreement with data we obtained with the well-established HRP-DAB colorimetric array (R² = 0.986). This suggests that Qdots can be used for protein quantification in microarray format, using the platform presented here.     

Practical asymmetric synthesis of alpha-branched 2-piperazinylbenzylamines by 1,2-additions of organometallic reagents to N-tert-butanesulfinyl imines

[reaction: see text] 2-[4-(tert-Butoxycarbonyl)piperazinyl]benzylidene-tert-butanesulfinamides underwent nucleophilic 1,2-addition with different organometallic reagents to give highly diastereomerically enriched adducts. X-ray crystallography of the resulting alpha-branched N-Boc-2-piperazinylbenzyl-tert-butanesulfinamides confirms different mechanisms depending on the organometallic reagent used. Differential deprotection of the N-Boc and the tert-butanesulfinamides was investigated, and the dehydration byproducts have been identified and characterized. To avoid the formation of byproducts in the acidic deprotection step, the N-tert-butanesulfinamide group was converted to the corresponding N-tert-butanesulfonamide (Bus), which allowed for clean orthogonal deprotection. The efficient synthesis and deprotection of the N-Boc-2-piperazinylbenzyl-tert-butanesulfinamides herein described constitutes an attractive method for extensive structure-activity studies in the search for novel ligands of the human melanocortin 4 receptor.