Abelian quotients of monoids of homology cylinders

A homology cylinder over a surface consists of a homology cobordism between two copies of the surface and markings of its boundary. The set of isomorphism classes of homology cylinders over a fixed surface has a natural monoid structure and it is known that this monoid can be seen as an enlargement of the mapping class group of the surface. We now focus on abelian quotients of this monoid. We show that both the monoid of all homology cylinders and that of irreducible homology cylinders are not finitely generated and moreover they have big abelian quotients. These properties contrast with the fact that the mapping class group is perfect in general. The proof is given by applying sutured Floer homology theory to homologically fibered knots studied in a previous paper.     

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.     

Hadamard matrices of order 32 and extremal ternary self-dual codes

A ternary self-dual code can be constructed from a Hadamard matrix of order congruent to 8 modulo 12. In this paper, we show that the Paley–Hadamard matrix is the only Hadamard matrix of order 32 which gives an extremal self-dual code of length 64. This gives a coding theoretic characterization of the Paley–Hadamard matrix of order 32.     

Hydroxyl group recognition by hydrogen-bonding donor and acceptor sites embedded in a layered metal-organic framework

One of the dominant types of interactions between host and guest molecules is hydrogen-bonding, and these interactions can work selectively for a guest molecule. Here, we demonstrate a metal-organic framework (MOF) having both hydrogen-bonding donor and acceptor sites that are quite effective for selective sorption. The MOF selectively interacts with hydroxylic guests in contrast to aprotic hydrogen-bonding guests and shows a sorption selectivity for protic H(2)O, MeOH, and EtOH guests. Notably, this is the first compound that shows complete selectivity in adsorption not for MeCN and MeCHO but for EtOH, which has similar fundamental properties except for its proticity.     

Efficient excited energy transfer reaction in clay/porphyrin complex toward an artificial light-harvesting system

The quantitative excited energy transfer reaction between cationic porphyrins on an anionic clay surface was successfully achieved. The efficiency reached up to ca. 100% owing to the "Size-Matching Rule" as described in the text. It was revealed that the important factors for the efficient energy transfer reaction are (i) suppression of the self-quenching between adjacent dyes, and (ii) suppression of the segregated adsorption structure of two kinds of dyes on the clay surface. By examining many different kinds of porphyrins, we found that tetrakis(1-methylpyridinium-3-yl) porphyrin (m-TMPyP) and tetrakis(1-methylpyridinium-4-yl) porphyrin (p-TMPyP) are the suitable porphyrins to accomplish a quantitative energy transfer reaction. These findings indicate that the clay/porphyrin complexes are promising and prospective candidates to be used for construction of an efficient artificial light-harvesting system.     

Design of chemical shift-switching 19F magnetic resonance imaging probe for specific detection of human monoamine oxidase A

Monoamine oxidase (MAO) A is a flavoenzyme that catalyzes the oxidation of biologically important monoamines and is thought to be associated with psychiatric disorders. Here, we report a strategy for rationally designing a (19)F magnetic resonance imaging probe for the specific detection of human MAO-A (hMAO-A) activity. Our designed (19)F probe was oxidized expeditiously by hMAO-A to produce 2-fluoro-4-nitrophenol via a spontaneous β-elimination mechanism. Concomitant with the structural change of the probe to the product, the (19)F chemical shift changed by 4.2 ppm, which was enough to visualize the probe and enzymatic product separately. Importantly, our probe achieved excellent discrimination of hMAO-A from its isoform hMAO-B.     

From metal-organic framework to nanoporous carbon: toward a very high surface area and hydrogen uptake

In this work, with a zeolite-type metal-organic framework as both a precursor and a template and furfuryl alcohol as a second precursor, nanoporous carbon material has been prepared with an unexpectedly high surface area (3405 m(2)/g, BET method) and considerable hydrogen storage capacity (2.77 wt % at 77 K and 1 atm) as well as good electrochemical properties as an electrode material for electric double layer capacitors. The pore structure and surface area of the resultant carbon materials can be tuned simply by changing the calcination temperature.     

Confinement of photopolymerization and solidification with radiation pressure

Controlling chemical reactions within a small space is a significant issue in chemistry, and methods to induce reactions within a desired position have various potential applications. Here we demonstrate localized, efficient photopolymerization by radiation pressure. We induced a one-photon UV polymerization of liquid acrylate solutions in the optical-trapping potential of a focused near-IR (NIR) laser beam, leading to the confinement of solidification to a minute space with dimensions smaller or equal to one-fifth of the wavelength of the NIR laser. Our approach can produce solidification volumes smaller than those achievable with conventional one-photon polymerization, thus enabling the production of tiny polymeric structures that are smaller than the diffraction limit of the trapping light. This is the first demonstration of a radiation pressure effect on a photochemical reaction.     

Catalytic silicon-mediated carbon-carbon bond-forming reactions of unactivated amides

In the presence of catalytic amounts of trialkylsilyl triflate and triethylamine, unactivated amides react with imines to afford the corresponding Mannich-type adducts in high yields with high anti selectivities. While silicon enolates have been widely used in organic synthesis for four decades, this is the first example of the catalytic use of the silicon species, to the best of our knowledge. Moreover, it is noteworthy that unactivated simple amides bearing α-protons that are less acidic than those of ketones and aldehydes can be successfully used in catalytic direct-type addition reactions. Finally, a preliminary trial of an asymmetric catalytic version was conducted and showed promising enantioselectivity of the desired product.     

Quantitative evaluation of mechanosensing of cells on dynamically tunable hydrogels

Thin hydrogel films based on an ABA triblock copolymer gelator [where A is pH-sensitive poly(2-(diisopropylamino)ethyl methacrylate) (PDPA) and B is biocompatible poly(2-(methacryloyloxy)ethyl phosphorylcholine) (PMPC)] were used as a stimulus-responsive substrate that allows fine adjustment of the mechanical environment experienced by mouse myoblast cells. The hydrogel film elasticity could be reversibly modulated by a factor of 40 via careful pH adjustment without adversely affecting cell viability. Myoblast cells exhibited pronounced stress fiber formation and flattening on increasing the hydrogel elasticity. As a new tool to evaluate the strength of cell adhesion, we combined a picosecond laser with an inverted microscope and utilized the strong shock wave created by the laser pulse to determine the critical pressure required for cell detachment. Furthermore, we demonstrate that an abrupt jump in the hydrogel elasticity can be utilized to monitor how cells adapt their morphology to changes in their mechanical environment.