Principal points of a multivariate mixture distribution

A set of n-principal points of a distribution is defined as a set of n points that optimally represent the distribution in terms of mean squared distance. It provides an optimal n-point-approximation of the distribution. However, it is in general difficult to find a set of principal points of a multivariate distribution. Tarpey et al. [T. Tarpey, L. Li, B. Flury, Principal points and self-consistent points of elliptical distributions, Ann. Statist. 23 (1995) 103-112] established a theorem which states that any set of n-principal points of an elliptically symmetric distribution is in the linear subspace spanned by some principal eigenvectors of the covariance matrix. This theorem, called a “principal subspace theorem”, is a strong tool for the calculation of principal points. In practice, we often come across distributions consisting of several subgroups. Hence it is of interest to know whether the principal subspace theorem remains valid even under such complex distributions. In this paper, we define a multivariate location mixture model. A theorem is established that clarifies a linear subspace in which n-principal points exist.     

Synthesis and pharmacological evaluation of 1-isopropyl-1,2,3,4-tetrahydroisoquinoline derivatives as novel antihypertensive agents

A series of 1-isopropyl-1,2,3,4-tetrahydroisoquinoline derivatives were synthesized and their bradycardic activities were evaluated in isolated guinea pig right atria. Structure-activity relationship studies revealed that the introduction of an appropriate substituent and its position on the 1,2,3,4-tetrahydroisoquinoline ring are essential for potent in vitro activity. Furthermore, the tether between the piperidyl moiety and the terminal aromatic ring is important for potent antihypertensive activity. Oral administration of 6-fluoro-1-isopropyl-2-{[1-(2-phenylethyl)piperidin-4-yl]carbonyl}-1,2,3,4-tetrahydroisoquinoline (3b) to spontaneously hypertensive rats (SHR) elicited antihypertensive effects without inducing reflex tachycardia, which is often caused by traditional L-type Ca2? channel blockers.     

Synthesis and pharmacological evaluation of 1-alkyl-N-[(1R)-1-(4-fluorophenyl)-2-methylpropyl]piperidine-4-carboxamide derivatives as novel antihypertensive agents

We synthesized and evaluated inhibitory activity against T-type Ca(2+) channels for a series of 1-alkyl-N-[(1R)-1-(4-fluorophenyl)-2-methylpropyl]piperidine-4-carboxamide derivatives. Structure-activity relationship studies have revealed that the isopropyl substituent at the benzylic position plays an important role in exerting potent inhibitory activity, and the absolute configuration of the benzylic position was found to be opposite that of mibefradil, which was first launched as a new class of T-type Ca(2+) channel blocker. Oral administration of N-[(1R)-1-(4-fluorophenyl)-2-methylpropyl]-1-[2-(3-methoxyphenyl)ethyl]piperidine-4-carboxamide (17f) lowered blood pressure in spontaneously hypertensive rats without inducing reflex tachycardia, an adverse effect often caused by traditional L-type Ca(2+) channel blockers.     

Reaction-diffusion phenomena in a PDMS matrix can modify its topography

Various reagents and solvents can be absorbed into polydimethylsiloxane (PDMS), which may be a concern for many applications. We hypothesize that these absorbed reagents can also react with each other within the elastomer matrix. Here we demonstrate this phenomenon and use it as a means to physically modify the surface topography of the PDMS by generating wrinkles or pores.     

Dynamical spin susceptibility of the d–p model in the over doping region

Dynamical spin susceptibility χ^s(q,ω) of the d–p model in the over doping region is investigated by using the auxiliary boson technique. It includes higher order terms of the 1/N-expansion within the random phase approximation (RPA) of the local vertex, where frequency dependence of the quasi-particle interaction is taken into account. The incommensurate spin fluctuation is obtained due to the nesting effect in the low energy region (ωω^*), whereas the commensurate one in the high energy region (ωω^*), the characteristic energy ω^* is estimated to be about 30 meV. Both of the spin–lattice relaxation rate 1/T₁ and the spin–spin relaxation rate 1/T_g monotonically increase as T decreases, while the spin Knight shift K is almost independent of T.     

Adsorption behavior of metal ions onto a bovine serum albumin (BSA) membrane monitored by means of an electrode-separated piezoelectric quartz crystal.

The interaction between metal ions and bovine serum albumin (BSA) was studied by using a piezoelectric quartz crystal (PQC) arranged in the electrode-separated configuration. A silanized surface of the PQC was coated with a BSA membrane via a coupling reaction with glutaraldehyde. The frequency shifts obtained from PQC coated with a BSA membrane suggested that various kinds of metal ions could be adsorbed onto the BSA membrane from aqueous solutions containing a low concentration of metal ions (2 or 10 micromol dm(-3)), only when the BSA was denatured with an alkaline solution. Anionic species of Pt(IV) and Au(III) were adsorbed onto the denatured BSA membrane from an acetic acid solution at pH 2.2, and cationic species of Cd(II), Zn(II), Co(II), Ni(II), Cu(II), and Ag(I), and cations, such as Ca2+, Ba2+, and Mg2+, were adsorbed from ammonia buffer at pH 9.5, whereas Al(III), Cr(III), Fe(III), Hg(II), and Pb(II) were hardly adsorbed. The adsorption mechanisms of these metal ions are discussed, based on the electrostatic interaction between the metal ions and the denatured BSA membrane, and complex formation between the metal ions and amino acid residues of the denatured BSA. Further, the PQC coated with a denatured BSA membrane was applied to the determination of Pt and Cd, using large frequency shifts for Pt(IV) and Cd(II).