Derivatives of the Incomplete Beta Function

The incomplete beta function is defined as where Beta(p, q) is the beta function. Dutka (1981) gave a history of the development and numerical evaluation of this function. In this article, an algorithm for computing first and second derivatives of Ix,p,q with respect to p and q is described. The algorithm is useful, for example, when fitting parameters to a censored beta, truncated beta, or a truncated beta-binomial model.

Second-Order Accurate Inference on Simple, Partial, and Multiple Correlations

This article develops confidence interval procedures for functions of simple, partial, and squared multiple correlation coefficients. It is assumed that the observed multivariate data represent a random sample from a distribution that possesses infinite moments, but there is no requirement that the distribution be normal. The coverage error of conventional one-sided large sample intervals decreases at rate 1√n as n increases, where n is an index of sample size. The coverage error of the proposed intervals decreases at rate 1/n as n increases. The results of a simulation study that evaluates the performance of the proposed intervals is reported and the intervals are illustrated on a real data set

Derivatives of the Incomplete Beta Function

The incomplete beta function is defined as where Beta(p, q) is the beta function. Dutka (1981) gave a history of the development and numerical evaluation of this function. In this article, an algorithm for computing first and second derivatives of Ix,p,q with respect to p and q is described. The algorithm is useful, for example, when fitting parameters to a censored beta, truncated beta, or a truncated beta-binomial model

A Comparative Survey of Leguminous Plants as Sources of the Isoflavones, Genistein and Daidzein: Implications for Human Nutrition and Health

Over 80 taxa of mostly agriculturally important legumes were surveyed as sources of the metabolites, genistein and daidzein. Remarkably high concentrations (over 2 g · kg–1 dry weight) of the anticancer metabolite, genistein, were found in the leaves of Psoralea corylifolia (Indian bread root). All other legumes, with the exception of fermented soybean miso, had genistein levels <400 mg · kg–1 dry weight. Concentrations of over 1 g · kg–1 dry weight and 0.95 g · kg–1 dry weight of the anticancer metabolite, daidzein, were found in the stems of the fava bean (Vicia faba) and roots of kudzu vine (Pueraria lobata)' respectively. From this survey, our results indicate that the legumes, lupine (Lupinus spp.), fava bean, (Vicia faha), soybeans (Glycine max), kudzu (Pueraria lobata), and psoralea (Psoralea corylifolia), are excellent food sources for both genistein and daidzein. Miso, a fermented soybean product, is also a rich source of both isoflavones.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63131/1/acm.1997.3.7.pd

A Comparison of the Wholesale Model and the Agency Model in Differentiated Markets

We compare the wholesale model and the agency model that characterise a vertical relation in a bilateral duopoly framework. Results suggest that the agency model may be regarded as an example of retailer power resale price maintenance and provide an economic view of why restraints of this kind should be evaluated under the rule of reason. While competition is more likely to be undercut under the agency model, relative to the wholesale model, the agency model benefits consumers by offering relatively lower retail prices and greater demand

Taking Ownership: Our Pledge to Educate All of Detroit's Children

Excellent Schools Detroit represents a broad and diverse cross section of Detroit's education, government, civic and community, parent, organized labor, and philanthropic leaders who are committed to ensuring that all Detroit children receive the great education they deserve. This citywide education plan reflects months of discussions and deliberations by coalition members, as well as a series of six community meetings in November and December, youth focus groups, small group discussions with multiple stakeholders, and other outreach efforts. We appreciate the thoughtful recommendations from the many Detroiters who are as passionate as we are about the need to prepare all students for college, careers, and life in the 21st century

Anticancer Activities of Six Selected Natural Compounds of Some Cameroonian Medicinal Plants

BACKGROUND: Natural products are well recognized as sources of drugs in several human ailments. In the present work, we carried out a preliminary screening of six natural compounds, xanthone V(1) (1); 2-acetylfuro-1,4-naphthoquinone (2); physcion (3); bisvismiaquinone (4); vismiaquinone (5); 1,8-dihydroxy-3-geranyloxy-6-methylanthraquinone (6) against MiaPaCa-2 pancreatic and CCRF-CEM leukemia cells and their multidrug-resistant subline, CEM/ADR5000. Compounds 1 and 2 were then tested in several other cancer cells and their possible mode of action were investigated. METHODOLOGY/FINDINGS: The tested compounds were previously isolated from the Cameroonian medicinal plants Vismia laurentii (1, 3, 4, 5 and 6) and Newbouldia laevis (2). The preliminary cytotoxicity results allowed the selection of xanthone V(1) and 2-acetylfuro-1,4-naphthoquinone, which were then tested on a panel of cancer cell lines. The study was also extended to the analysis of cell cycle distribution, apoptosis induction, caspase 3/7 activation and the anti-angiogenic properties of xanthone V(1) and 2-acetylfuro-1,4-naphthoquinone. IC(50) values around or below 4 µg/ml were obtained on 64.29% and 78.57% of the tested cancer cell lines for xanthone V(1) and 2-acetylfuro-1,4-naphthoquinone, respectively. The most sensitive cell lines (IC(50)<1 µg/ml) were breast MCF-7 (to xanthone V(1)), cervix HeLa and Caski (to xanthone V(1) and 2-acetylfuro-1,4-naphthoquinone), leukemia PF-382 and melanoma colo-38 (to 2-acetylfuro-1,4-naphthoquinone). The two compounds showed respectively, 65.8% and 59.6% inhibition of the growth of blood capillaries on the chorioallantoic membrane of quail eggs in the anti-angiogenic assay. Upon treatment with two fold IC(50) and after 72 h, the two compounds induced cell cycle arrest in S-phase, and also significant apoptosis in CCRF-CEM leukemia cells. Caspase 3/7 was activated by xanthone V(1). CONCLUSIONS/SIGNIFICANCE: The overall results of the present study provided evidence for the cytotoxicity of compounds xanthone V(1) and 2-acetylfuro-1,4-naphthoquinone, and bring supportive data for future investigations that will lead to their use in cancer therapy