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.     

Adhesion of binary giant vesicles containing negative spontaneous curvature lipids induced by phase separation

We report the adhesion of binary giant vesicles composed of two types of phospholipids, one has negative spontaneous curvature which tends to bend toward the head group and the other has zero spontaneous curvature. In a homogeneous one-phase region, the giant vesicles do not adhere to each other, whereas in a coexisting two-phase region, the giant vesicles show adhesion. A fluorescence microscope observation reveals that the adhesion takes place through the domains rich in phospholipids having negative spontaneous curvature. We propose a phase separation induced hemifusion model where two apposed monolayers of adjacent vesicles are hemifused in order to reduce the bending energy of monolayers with negative spontaneous curvature and the boundary energy between the domains and matrix. We provide a strong evidence for the hemifusion model by lipid transfer experiments.     

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.     

Rheological properties of microfibrillar suspension of TEMPO-oxidized pulp

The rheology of cellulose microfibril suspensions from TEMPO-oxidized pulp was investigated. The suspension showed a pseudo-plastic and thixotropic behavior, slowly evolving with time under a given shear rate. The viscosity was proportional to the concentration up to the critical concentration of 0.23%. Above it, the viscosity followed a power law with exponents from 2 to 6 depending on the shear rate, and the system showed shear thinning behavior and behaved gel-like. Below this concentration, the system was more Newtonian. Birefringence measurement of 0.44% and 0.78% suspension showed that microfibrils alignment saturated at a small shear rate with a Herman’s orientation parameter below 0.65 probably due to the interconnection of microfibrils.     

Ising vectors and automorphism groups of commutant subalgebras related to root systems

In this article we study and obtain a classification of Ising vectors in vertex operator algebras (VOAs) associated to binary codes and times root lattices, where an Ising vector is a conformal vector with central charge 1/2 generating a simple Virasoro sub-VOA. Then we apply our results to study certain commutant subalgebras related to root systems. We completely classify all Ising vectors in such commutant subalgebras and determine their full automorphism groups. C. H. Lam was supported by NSC grant 93-2115-M-006-012 of Taiwan and National Center for Theoretical Sciences, Taiwan, S. Sakuma was supported by JSPS Research Fellowships for Young Scientists and H. Yamauchi was supported by JSPS Research Fellowships for Young Scientists