Affine modifications and affine hypersurfaces with a very transitive automorphism group

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface $X \subset C^{k+2}$ given by the equation $uv=p(x_1,...,x_k)$ where $p \in C[x_1,...,x_k],$ acts $m-$transitively on the smooth part reg$X$ of $X$ for any $m \in N.$ We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction

Spin dynamics in molecular ring nanomagnets: Significant effect of acoustic phonons and magnetic anisotropies

The nuclear spin-lattice relaxation rate 1/T_1_ is calculated for magnetic ring clusters by fully diagonalizing their microscopic spin Hamiltonians. Whether the nearest-neighbor exchange interaction J is ferromagnetic or antiferromagnetic, 1/T_1_ versus temperature T in ring nanomagnets may be peaked at around k_B_T=|J| provided the lifetime broadening of discrete energy levels is in proportion to T^3^. Experimental findings for ferromagnetic and antiferromagnetic Cu^II^ rings are reproduced with crucial contributions of magnetic anisotropies as well as acoustic phonons.Comment: 5 pages with 5 figures embedded, to be published in J. Phys. Soc. Jpn. 75, No. 10 (2006

An iPS-derived in vitro model of human atrial conduction

Atrial fibrillation (AF) is the most common arrhythmia in the United States, affecting approximately 1 in 10 adults, and its prevalence is expected to rise as the population ages. Treatment options for AF are limited; moreover, the development of new treatments is hindered by limited (1) knowledge regarding human atrial electrophysiological endpoints (e.g., conduction velocity [CV]) and (2) accurate experimental models. Here, we measured the CV and refractory period, and subsequently calculated the conduction wavelength, in vivo (four subjects with AF and four controls), and ex vivo (atrial slices from human hearts). Then, we created an in vitro model of human atrial conduction using induced pluripotent stem (iPS) cells. This model consisted of iPS-derived human atrial cardiomyocytes plated onto a micropatterned linear 1D spiral design of Matrigel. The CV (34-41 cm/s) of the in vitro model was nearly five times faster than 2D controls (7-9 cm/s) and similar to in vivo (40-64 cm/s) and ex vivo (28-51 cm/s) measurements. Our iPS-derived in vitro model recapitulates key features of in vivo atrial conduction and may be a useful methodology to enhance our understanding of AF and model patient-specific disease

Assessing the reactivity of sodium alkyl-magnesiates towards quinoxaline : single electron transfer (SET) vs. nucleophilic alkylation processes

By exploring the reactivity of sodium butyl-magnesiate (1) supported by the bulky chelating silyl(bisamido) ligand {Ph2Si(NAr*)2}(2-) (Ar* = 2,6-iPr2-C6H3) towards Quinoxaline (Qx), the ability of this bimetallic system to effectively promote SET processes has been disclosed. Thus 1 executes the single-electron reduction of Qx affording complex (2) whose structure in the solid state contains two quinaxolyl radical anions Qx˙ stabilised within a dimeric magnesiate framework. Combining multinuclear NMR and EPR measurements with DFT calculations, new insights into the constitution of 2 in solution and its magnetic behaviour have been gained. Further evidence on the SET reactivity of 1 was found when it was reacted with nitroxyl radical TEMPO which furnished contacted ion pair sodium magnesiate [(Ph2Si(NAr*)2)Mg(TEMPO(-))Na(THF)3] (4) where both metals are connected by an alkoxide bridge, resulting from reduction of TEMPO. The role that the different ligands present in 1 can play in these new SET reactions has also been assessed. Using an amination approach, the Bu group in 1 can be replaced by the more basic amide TMP allowing the isolation of (3) which was characterised by multinuclear NMR and X-ray crystallography. (1)H NMR monitoring of the reaction of 3 with Qx showed its conversion to 2, leaving the hydrogen atoms of the heterocycle untouched. Contrastingly, using sodium homoalkyl magnesiate [NaMg(CH2SiMe3)3] (5) led to the chemoselective C2 alkylation of this heterocycle, suggesting that the presence of the steric stabiliser {Ph2Si(NAr*)2}(2-) on the mixed-metal reagent is required in order to facilitate the Qx reduction