Statistical Measures for the Computer-Aided Diagnosis of Mammographic Masses

Abstract

We propose statistical measures for finding masses in mammograms. The measures are based on fitting broken line regressions to local intensity plots of the images. The method is illustrated on a small database of mammograms that have been read by a radiologist and confirmed by operative data. This work illustrates some of the statistical challenges in working with large diagnostic images     

Euler polynomials,Bernoulli polynomials,and Lévyʼs stochastic area formula

In 1951, P. Lévy represented the Euler and Bernoulli numbers in terms of the moments of Lévy?s stochastic area. Recently the authors extended his result to the case of Eulerian polynomials of types A and B. In this paper, we continue to apply the same method to the Euler and Bernoulli polynomials, and will express these polynomials with the use of Lévy?s stochastic area. Moreover, a natural problem, arising from such representations, to calculate the expectations of polynomials of the stochastic area and the norm of the Brownian motion will be solved.     

Calorimetric Study of Micelle Formation in Polyethylene Glycol Monooctyl Ether Solution

The micellar solutions of polyethylene glycol monooctyl ethers C8Ej (j = 3,4,5) were investigated by employing the high-precision isothermal titration microcalorimeter at seven temperatures from 10^° to 40^°C. From the thermodynamic analysis of the experimental results, the differential enthalpies of solution of monomer and micelle of C8Ej were obtained separately; they are negative and increase with increasing temperature and decrease with the number j. It was found that C8Ej molecules interact with water molecules more strongly in the monomeric than in micellar state. The enthalpy of micelle formation of C8Ej was positive and decreased with rising temperature, while they increased slightly with increasing j. By comparing the results of ethylene glycol oligomers (C0Ej) with those of C8Ej, it seems reasonable to suppose that the driving force of micelle formation of C8Ej is mainly the increment of entropy caused by dehydration of hydrophilic parts at higher temperatures, while the increment caused by dehydration of hydrophobic parts becomes dominant at lower temperatures in the micellization process.     

Acid-Mediated Specific α,α-Diarylation And A-Monoarylation Reactions Of Pyruvic Acid With/Without Decarbonylation

Pyruvic acid (3) was found to be arylated chemoselectively at the a-ketocarbonyl carbon in P₂O₅-MsOH affording decarbonylative α,α-diarylated products 5, decarbonylative a-monoarylated compounds 6, or non-decarbonylative α,α-diarylated adducts 7 depending on the reactivity of arenes (4a-g), in contrast to Lewis acid-catalyzed reaction of its acid chloride (2).     

Rapid and Convenient Thioester Synthesis Under Phase-Transfer Catalysis Conditions

Various thioesters were obtained through an efficient phase-transfer catalysis method, by treating several thiophenols with different acyl chlorides, in a biphasic system composed of 10% aqueous NaOH and dichloromethane in the presence of tetrabutylammonium chloride. The thiolation reaction was complete in only 5 minutes, at 0°C.