Asymptotic Expansions of Posterior Distributions in Nonregular Cases

We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Characterization and reactivity study of non-heme high-valent iron–hydroxo complexes

A terminal Fe^IIIOH complex, [Fe^III(L)(OH)]²⁻ (1), has been synthesized and structurally characterized (H₄L = 1,2-bis(2-hydroxy-2-methylpropanamido)benzene). The oxidation reaction of 1 with one equiv. of tris(4-bromophenyl)ammoniumyl hexachloroantimonate (TBAH) or ceric ammonium nitrate (CAN) in acetonitrile at −45 °C results in the formation of a Fe^IIIOH ligand radical complex, [Fe^III(L˙)(OH)]⁻ (2), which is hereby characterized by UV-visible, ¹H nuclear magnetic resonance, electron paramagnetic resonance, and X-ray absorption spectroscopy techniques. The reaction of 2 with a triphenylcarbon radical further gives triphenylmethanol and mimics the so-called oxygen rebound step of Cpd II of cytochrome P450. Furthermore, the reaction of 2 was explored with different 4-substituted-2,6-di-tert-butylphenols. Based on kinetic analysis, a hydrogen atom transfer (HAT) mechanism has been established. A pK_a value of 19.3 and a BDFE value of 78.2 kcal/mol have been estimated for complex 2.

One-electron oxidation of an Fe^III–OH complex (1) results in the formation of a Fe^III–OH ligand radical complex (2). Its reaction with (C₆H₅)₃C˙ results in the formation of (C₆H₅)₃COH, which is a functional mimic of compound II of cytochrome P450.     

A Facile One‐Pot Synthesis of Pyrrolo[1, 2‐a] Indoles by Intramolecular 1,3‐Dipolar Cycloaddition under Neat‐Microwave Irradiation

A straightforward and general approach for the stereoselective synthesis of fused pyrrolo[1,2‐a] indoles frameworks from>intramolecular 1,3‐dipolar cycloaddition using N‐alkylated Baylis–Hillman derivatives is presented. It was found that the cycloaddition proceeded efficiently under microwave irradiation in solvent‐free condition to afford highly stereoselective cycloadducts in good yield.     

Approximation of the Posterior Distribution in a Change-Point Problem

We consider a family of models that arise in connection with sharp change in hazard rate corresponding to high initial hazard rate dropping to a more stable or slowly changing rate at an unknown change-point . Although the Bayes estimates are well behaved and are asymptotically efficient, it is difficult to compute them as the posterior distributions are generally very complicated. We obtain a simple first order asymptotic approximation to the posterior distribution of . The accuracy of the approximation is judged through simulation. The approximation performs quite well. Our method is also applied to analyze a real data set.     

On existence of undominated pure strategy Nash equilibria in anonymous nonatomic games: a generalization

In this paper, we generalize the exitence result for pure strategy Nash equilibria in anonymous nonatomic games. By working directly on integrals of pure strategies, we also generalize, for the same class of games, the existence result for undominated pure strategy Nash equilibria even though, in general, the set of pure strategy Nash equilibria may fail to be weakly compact. Received August 2001     

An efficient total synthesis of the anticancer agent (+)-spisulosine (ES-285) from Garner’s aldehyde

An efficient total synthesis of (+)-spisulosine (ES-285) was completed in nine steps from (S)-Garner’s aldehyde. The vicinal amino alcohol moiety with anti-configuration was achieved by a highly diastereoselective addition of vinyl magnesium bromide to Garner’s aldehyde. The long hydrocarbon chain of the antitumor natural product was installed via olefin cross metathesis of the benzyl-protected allylic alcohol with an appropriate olefin counterpart followed by hydrogenation.