Multivariate Homogeneity Testing Using an Extended Concept of Nearest Neighbors

Given independent multivariate random samples {X_ij: j = 1, …, n_i} from F_i, for i = 1,2, a test is desired for H₀: F₁ = F₂ against general alternatives. Consider the k · (n₁ + n₂) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let S_k be the proportion of these choices in which the point and neighbor are in the same sample. Schilling (1986) proposed S_k as a test statistic, but did not indicate how to determine k. We suggest as test statistic W = N Σ kS_k, which we show is equivalent to a sum of N Wilcoxon rank sums, and also to a sum of two two-sample U-statistics of degrees (1, 2) and (2, 1). Simulation with multivariate normal data suggests that our test is generally more powerful than Schilling's test using k = 1, 2, or 3. We illustrate its use with Fisher's iris data.     

Synthesis,Molecular Docking,and Cytotoxicity Evaluation of New Khellinone Derivatives as Tyrosine Kinase Inhibitors

Russian Journal of Bioorganic Chemistry - A series of new benzofuran derivatives were synthesized using khellinone. The acetyl function of khellinone was converted into its corresponding enaminone,...     

Basal-cell adenoma of parotid. Difficulty of differentiation from adenoid cystic carcinoma on aspiration biopsy

Two cases of basal-cell adenoma (basaloid monomorphic adenoma, dermal analogue tumor) seen in a one-year period were subjected to fine needle aspiration biopsy and subsequent histologic confirmation. Two cases of adenoid cystic carcinoma occurring in the parotid region were selected for comparison; a great similarity between the two types of tumors was noted. On aspiration smear both lesions consisted of clusters and sheets of uniform, small, regular cells with scant basophilic cytoplasm and regular round or oval bland nuclei. The smears contained varying amounts of homogeneous, pale, eosinophilic stromal substance within and around the cell clusters. Individual cell differences between the two lesions were minimal, with the adenoid cystic carcinomas tending to exhibit more nuclear hyperchromatism and irregularity; the architectural arrangements of the cell clusters and the stromal substance permitted differentiation between the two lesions.