Multilinear Eigenfunction Estimates for the Harmonic Oscillator and the Nonlinear Schrödinger Equation with the Harmonic Potential

We consider the Cauchy problem for the cubic nonlinear Schr?dinger equation with the harmonic potential. We prove global well-posedness below the energy class in energy subcritical cases. The main ingredients for the proof are a multilinear eigenfunction estimate for the harmonic oscillator and the I-method. Submitted: January 13, 2008. Accepted: February 11, 2009.     

Asymmetric construction of quaternary carbon stereocenter by Pd-catalyzed intramolecular alpha-arylation

The catalyst comprised of Pd(OAc)(2) and H(8)-BINAP provides good reaction conversions for a catalytic enantioselective intramolecular alpha-arylation of N-(2-bromophenyl)-N-methyl-2-arylpropanamide to form the quaternary carbon with up to 68% enantioselectivity.     

Total Synthesis of (+)‐Dibromophakellin and (+)‐Dibromophakellstatin

A new method for the preparation of quaternary chiral aminals has been developed that employs an enamide‐type Overman rearrangement process. This methodology was applied to enantioselective total syntheses of (+)‐dibromophakellin and (+)‐dibromophakellstatin.     

Synthesis and biological evaluation of a beauveriolide analogue library

Synthesis of beauveriolide III (1b), which is an inhibitor of lipid droplet accumulation in macrophages, was achieved by solid-phase assembly of linear depsipeptide using a 2-chlorotrityl linker followed by solution-phase cyclization. On the basis of this strategy, a combinatorial library of beauveriolide analogues was carried out by radio frequency-encoded combinatorial chemistry. After automated purification using preparative reversed-phase HPLC, the library was tested for inhibitory activity of CE synthesis in macrophages to determine structure-activity relationships of beauveriolides. Among them, we found that diphenyl derivative 7{9,1} is 10 times more potent than 1b.     

Host–guest complexation‐triggered chiroptical change of poly(phenylacetylene)s bearing binaphthocrown ether moieties on the main chain

Diacetylene monomers with respective lengths of the oxyethylene chains were cyclopolymerized with a rhodium catalyst to produce novel poly(phenylacetylene)s bearing a different cavity size of the chiral crown ether in the repeating units ( 2a – c ). In the circular dichroism spectra of the resulting polymers, characteristic Cotton effects were observed in the range from 350 to 500 nm corresponding to the absorption of the conjugated polymer backbone, indicating that the polymers possessed a helical structure with an excess single screw sense induced by the covalently bonded binaphthyl units. The host–guest complexation of 2a – c with achiral guests produced a chiroptical change based on the fluctuation in the main chain conformation. The behavior of the complexation‐induced chiroptical change was essentially dictated by the cavity size of the binaphthocrown ether units. Additionally, a chirality‐responsive helicity change was observed in the case of the complexation of 2a – c with chiral guests, which also depended on the crown ether size. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1197–1206, 2010     

Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation

Estimation of the ratio of probability densities has attracted a great deal of attention since it can be used for addressing various statistical paradigms. A naive approach to density-ratio approximation is to first estimate numerator and denominator densities separately and then take their ratio. However, this two-step approach does not perform well in practice, and methods for directly estimating density ratios without density estimation have been explored. In this paper, we first give a comprehensive review of existing density-ratio estimation methods and discuss their pros and cons. Then we propose a new framework of density-ratio estimation in which a density-ratio model is fitted to the true density-ratio under the Bregman divergence. Our new framework includes existing approaches as special cases, and is substantially more general. Finally, we develop a robust density-ratio estimation method under the power divergence, which is a novel instance in our framework.