Catalytic Hydroetherification of Unactivated Alkenes Enabled by Proton-Coupled Electron Transfer

We report a catalytic, light-driven method for the intramolecular hydroetherification of unactivated alkenols to furnish cyclic ether products. These reactions occur under visible-light irradiation in the presence of an Ir^III-based photoredox catalyst, a Brønsted base catalyst, and a hydrogen-atom transfer (HAT) co-catalyst. Reactive alkoxy radicals are proposed as key intermediates, generated by direct homolytic activation of alcohol O−H bonds through a proton-coupled electron-transfer mechanism. This method exhibits a broad substrate scope and high functional-group tolerance, and it accommodates a diverse range of alkene substitution patterns. Results demonstrating the extension of this catalytic system to carboetherification reactions are also presented.     

Exciton Interactions,Excimer Formation,and [2π+2π] Photodimerization in Nonconjugated Curcuminoid-BF2 Dimers

We describe the synthesis of a series of covalently linked dimers of quadrupolar curcuminoid-BF₂ dyes and the detailed investigation of their solvent-dependent spectroscopic and photophysical properties. In solvents of low polarity, intramolecular folding induces the formation of aggregated chromophores, the UV/Vis absorption spectra of which display the optical signature characteristic of weakly-coupled H-aggregates. The extent of folding and, in turn, of ground-state aggregation is strongly dependent on the nature of the flexible linker. Steady-state and time-resolved fluorescence emission spectroscopies show that the Frenkel exciton relaxes into a fluorescent symmetrical excimer state with a long lifetime. Furthermore, our in-depth studies show that a weakly emitting excimer lies on the pathway toward a photocyclomer. Two-dimensional ¹H NMR spectroscopy and density functional theory (DFT) allowed the structure of the photoproduct to be established. To our knowledge, this represents the first example of a [2π+2π] photodimerization of the curcuminoid chromophore.     

Recent advances in the asymmetric catalytic synthesis of chiral 3-hydroxy and 3-aminooxindoles and derivatives: Medicinally relevant compounds

Several oxindole derivatives, of natural or synthetic origin, have been identified as medicinally appealing compounds, with a plethora of bioactivities reported. Chiral 3-hydroxy and 3-aminooxindole scaffolds have captured the attention of several research groups, due to their importance in drug discovery. In this review, we systematically address the wide variety of asymmetric catalytic methodologies employed in the preparation of these relevant chiral scaffolds, present in many biologically active compounds and/or natural products. Special focus will be given to the nature of the catalyst used.     

The computation of characteristic classes of lattice gauge fields

AGL(p,C)-valued lattice gauge fieldu on a simplicial complex determines a principalGL(p,C)-bundle if the plaquette products are sufficiently small with respect to the maximum distortion coefficient of the transporters. A representative cocyclec _q for theq ^th Chern class of can be computed on each 2q-simplex by takingc _q() to be the intersection number of a certain singular 2q-cubeM with a Schubert-type variety _q in the space of allp×p matrices. This reduces to the solution of polynomial equations with coefficients coming fromu and thus avoids numerical integration or cooling-type procedures. An application of this method is suggested for the computation of the topological charge of anSU(3)-valued lattice gauge field on a 4-complex.Partially supported by NSF grant DMS 8607168Partially supported by PSC-CUNY and by NSF grant DMS 8805485     

Monte Carlo approximation through Gibbs output in generalized linear mixed models

Geyer (J. Roy. Statist. Soc. 56 (1994) 291) proposed Monte Carlo method to approximate the whole likelihood function. His method is limited to choosing a proper reference point. We attempt to improve the method by assigning some prior information to the parameters and using the Gibbs output to evaluate the marginal likelihood and its derivatives through a Monte Carlo approximation. Vague priors are assigned to the parameters as well as the random effects within the Bayesian framework to represent a non-informative setting. Then the maximum likelihood estimates are obtained through the Newton Raphson method. Thus, out method serves as a bridge between Bayesian and classical approaches. The method is illustrated by analyzing the famous salamander mating data by generalized linear mixed models.     

The hilbert function and the minimal free resolution of some gorenstein ideals of codimension 4

We give a construction for Gorenstein ideals of codimension 4 which we believe have maximal graded Betti numbers for their Hilbert function.     

Localization algebras and deformations of Koszul algebras

We show that the center of a flat graded deformation of a standard Koszul algebra A behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed point set. In particular, the center of A acts by characters on the deformed standard modules, providing a “localization map”. We construct a universal graded deformation of A and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming from the algebra Koszul dual to A. This is an algebraic version of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers; we recover and generalize their result by showing that the center of the universal deformation for the ring governing a block of parabolic category O{\mathcal{O}} for \mathfrakgl_n{\mathfrak{gl}_n} is isomorphic to the equivariant cohomology of a Spaltenstein variety. We also identify the center of the deformed version of the “category O{\mathcal{O}}” of a hyperplane arrangement (defined by the authors in a previous paper) with the equivariant cohomology of a hypertoric variety.     

A directed topic model applied to call center improvement

We propose subject matter expert refined topic (SMERT) allocation, a generative probabilistic model applicable to clustering freestyle text. SMERT models are three‐level hierarchical Bayesian models in which each item is modeled as a finite mixture over a set of topics. In addition to discrete data inputs, we introduce binomial inputs. These ‘high‐level’ data inputs permit the ‘boosting’ or affirming of terms in the topic definitions and the ‘zapping’ of other terms. We also present a collapsed Gibbs sampler for efficient estimation. The methods are illustrated using real world data from a call center. Also, we compare SMERT with three alternative approaches and two criteria. Copyright © 2015 John Wiley & Sons, Ltd.     

Infinite Random Geometric Graphs

We introduce a new class of countably infinite random geometric graphs, whose vertices V are points in a metric space, and vertices are adjacent independently with probability p ? (0, 1){p \in (0, 1)} if the metric distance between the vertices is below a given threshold. For certain choices of V as a countable dense set in \mathbbRⁿ{\mathbb{R}^n} equipped with the metric derived from the L _∞-norm, it is shown that with probability 1 such infinite random geometric graphs have a unique isomorphism type. The isomorphism type, which we call GR _n , is characterized by a geometric analogue of the existentially closed adjacency property, and we give a deterministic construction of GR _n . In contrast, we show that infinite random geometric graphs in \mathbbR²{\mathbb{R}^{2}} with the Euclidean metric are not necessarily isomorphic.