The geometrical structure of the parameter space of the two-dimensional normal distribution

The differential geometrical consideration of the parameter space, especially as a Riemannian geometry, was initiated by C.R. Rao in 1945. This approach appears to be important for the problem of estimation and test of hypotheses as well as for applications to physical problems. It has been shown that the parameter spaces of univariate normal distribution, univariate exponential distribution and multinomial distribution are Riemannian spaces of constant curvature. In the present paper the discussion is confined to the parameter space of the two-dimensional normal distribution. It has been shown that in general the parameter space is not necessarily of a constant curvature and that, if the correlation coefficient vanishes, the parameter space becomes an Einstein space. In addition, some invariant quantities, as sectional curvature, mean curvature and scalar curvature, have been calculated.     

Suppression of MeIQ-induced SOS response by allylbenzenes from Asiasarum heterotropoides in the Salmonella typhimurium OY1001/1A2 umu test

Three allylbenzenes from Asiasarum heterotropoides, methyleugenol (1), elemicin (2) and gamma-asaron (3) showed suppressive effects on umu gene expression of the SOS response in the Salmonella typhimurium OY1001/1A2 umu test against the mutagen 2-amino-3,4-dimethylimidazo[4,5-f ]quinoline (MeIQ). Gene expression was suppressed 70.0, 75.9 and 81.7% at a concentration of 0.4 mM, respectively. The ID50 values (50% inhibition dose) of these compounds were 0.125, 0.098 and 0.059 mM, respectively. On the other hand, compounds 1-3 showed weak suppressive effects of the SOS-inducing activity on activated MeIQ.     

Criticality and phase transition in stock-price fluctuations

We analyze the behavior of the U.S. S&P 500 index from 1984 to 1995, and characterize the non-Gaussian probability density functions (PDF) of the log returns. The temporal dependence of fat tails in the PDF of a ten-minute log return shows a gradual, systematic increase in the probability of the appearance of large increments on approaching black Monday in October 1987, reminiscent of parameter tuning towards criticality. On the occurrence of the black Monday crash, this culminates in an abrupt transition of the scale dependence of the non-Gaussian PDF towards scale-invariance characteristic of critical behavior. These facts suggest the need for revisiting the turbulent cascade paradigm recently proposed for modeling the underlying dynamics of the financial index, to account for time varying-phase transitionlike and scale invariant-critical-like behavior.     

On dual of square free modules

A module M is said to be square free if whenever its submodule is isomorphic to N² = N⊕N for some module N, then N = 0. Dually, a module M is said to be d-square free (dual square free) if whenever its factor module is isomorphic to N² for some module N, then N = 0. In this paper, we give some fundamental properties of d-square free modules and study rings whose d-square free modules are closed under submodules or essential extensions.     

Abdominal apparent diffusion coefficient measurements: effect of diffusion-weighted image quality and usefulness of anisotropic images

This study aimed to assess the effect of diffusion-weighted image (DWI) quality on abdominal apparent diffusion coefficient (ADC) measurements and the usefulness of anisotropic images. Twenty-six patients (10 men and 16 women; mean, 58.1 years) who underwent DW imaging and were diagnosed not to have any abdominal diseases were analyzed. Single-shot spin-echo echo-planar DW imaging was performed, and one isotropic and three orthogonal anisotropic images were created. ADCs were calculated for liver (four segments), spleen, pancreas (head, body, tail) and renal parenchyma. Image quality for each organ part was scored visually. We estimated the correlation between ADC and image quality and evaluated the feasibility of using anisotropic images. ADCs and image quality were affected by motion probing gradient directions in the liver and pancreas. A significant inverse correlation was found between ADC and image quality. The r values for isotropic images were −.46, −.48, −.70 and −.28 for the liver, spleen, pancreas and renal parenchyma, respectively. Anisotropic images had the best quality and lowest ADC in at least one organ part in 17 patients. DWIs with the best quality among isotropic and anisotropic images should be used in the liver and pancreas.     

Counting restricted orientations of random graphs

We count orientations of avoiding certain classes of oriented graphs. In particular, we study , the number of orientations of the binomial random graph in which every copy of is transitive, and , the number of orientations of containing no strongly connected copy of . We give the correct order of growth of and up to polylogarithmic factors; for orientations with no cyclic triangle, this significantly improves a result of Allen, Kohayakawa, Mota, and Parente. We also discuss the problem for a single forbidden oriented graph, and state a number of open problems and conjectures.     

The size Ramsey number of short subdivisions of bounded degree graphs

For graphs G and F, write if any coloring of the edges of G with colors yields a monochromatic copy of the graph F. Suppose is obtained from a graph S with s vertices and maximum degree d by subdividing its edges h times (that is, by replacing the edges of S by paths of length h + 1). We prove that there exists a graph G with no more than edges for which holds, provided that . We also extend this result to the case in which Q is a graph with maximum degree d on q vertices with the property that every pair of vertices of degree greater than 2 are distance at least h + 1 apart. This complements work of Pak regarding the size Ramsey number of “long subdivisions” of bounded degree graphs.     

TEMPO/NaIO4-SiO2: a catalytic oxidative rearrangement of tertiary allylic alcohols to beta-substituted alpha,beta-unsaturated ketones

The novel catalytic method for the oxidative rearrangement of tertiary allylic alcohols to beta-substituted alpha,beta-unsaturated ketones is described. TEMPO/NaIO4-SiO2 causes facile and efficient oxidative rearrangement of various acyclic substrates as well as medium-sized and macrocyclic substrates.     

In vitro and in vivo evaluation of microparticulate drug delivery systems composed of macromolecular prodrugs

Macromolecular prodrugs are very useful systems for achieving controlled drug release and drug targeting. In particular, various macromolecule-antitumor drug conjugates enhance the effectiveness and improve the toxic side effects. Also, polymeric micro- and nanoparticles have been actively examined and their in vivo behaviors elucidated, and it has been realized that their particle characteristics are very useful to control drug behavior. Recently, researches based on the combination of the concepts of macromolecular prodrugs and micro- or nanoparticles have been reported, although they are limited. Macromolecular prodrugs enable drugs to be released at a certain controlled release rate based on the features of the macromolecule-drug linkage. Micro- and nanoparticles can control in vivo behavior based on their size, surface charge and surface structure. These merits are expected for systems produced by the combination of each concept. In this review, several micro- or nanoparticles composed of macromolecule-drug conjugates are described for their preparation, in vitro properties and/or in vivo behavior.     

Oxidative rearrangement of tertiary allylic alcohols employing oxoammonium salts

Practical and highly efficient methods for oxidative rearrangement of tertiary allylic alcohols to beta-substituted alpha,beta-unsaturated carbonyl compounds employing oxoammonium salts are described. The methods developed are applicable to acyclic substrates as well as medium membered ring substrates and macrocyclic substrates. The counteranion of the oxoammonium salt plays crucial roles on this oxidative rearrangement.