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.     

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.     

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.     

Universality properties of Gelfand–Tsetlin patterns

A standard Gelfand–Tsetlin pattern of depth n is a configuration of particles in ${\{1,\ldots,n\} \times \mathbb{R}}$ . For each ${r \in \{1, \ldots, n\}, \{r\} \times \mathbb{R}}$ is referred to as the rth level of the pattern. A standard Gelfand–Tsetlin pattern has exactly r particles on each level r, and particles on adjacent levels satisfy an interlacing constraint. Probability distributions on the set of Gelfand–Tsetlin patterns of depth n arise naturally as distributions of eigenvalue minor processes of random Hermitian matrices of size n. We consider such probability spaces when the distribution of the matrix is unitarily invariant, prove a determinantal structure for a broad subclass, and calculate the correlation kernel. In particular we consider the case where the eigenvalues of the random matrix are fixed. This corresponds to choosing uniformly from the set of Gelfand–Tsetlin patterns whose nth level is fixed at the eigenvalues of the matrix. Fixing ${q_n \in \{1,\ldots,n\}}$ , and letting n → ∞ under the assumption that ${\frac{q_n}n \to \alpha \in (0, 1)}$ and the empirical distribution of the particles on the nth level converges weakly, the asymptotic behaviour of particles on level q _n is relevant to free probability theory. Saddle point analysis is used to identify the set in which these particles behave asymptotically like a determinantal random point field with the Sine kernel.     

Superefficient drift estimation on the Wiener space

In the framework of a nonparametric functional estimation for the drift of a Brownian motion $X_t$ we construct Stein type estimators of the form $X_t+D_t\log F$ which are superefficient when $\sqrt{F}$ is a superharmonic functional on the Wiener space for the Malliavin derivative D. To cite this article: N. Privault, A. Réveillac, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Burstiness and fractional diffusion on complex networks

Many dynamical processes on real world networks display complex temporal patterns as, forinstance, a fat-tailed distribution of inter-events times, leading to heterogeneouswaiting times between events. In this work, we focus on distributions whose averageinter-event time diverges, and study its impact on the dynamics of random walkers onnetworks. The process can naturally be described, in the long time limit, in terms ofRiemann-Liouville fractional derivatives. We show that all the dynamical modes possess, inthe asymptotic regime, the same power law relaxation, which implies that the dynamics doesnot exhibit time-scale separation between modes, and that no mode can be neglected versusanother one, even for long times. Our results are then confirmed by numericalsimulations.     

Scattering of plane guided waves obliquely incident on a straight feature with uniform cross-section

A frequency-domain finite element (FE) method is presented for modeling the scattering of plane guided waves incident on an infinitely-long, straight feature with uniform cross-section in a planar host waveguide. The method utilizes a mesh of 2-dimensional finite elements with harmonic shape functions in the perpendicular direction. The model domain comprises a cross-section through the feature and short lengths of the adjoining host waveguide. A spatial frequency equal to the wavenumber of the desired incident mode multiplied by the sine of the desired incidence angle is prescribed for the element shape functions. An integral representation of the incident mode is used to determine a suitable system of harmonic forces to uniquely excite that mode. These are applied at nodes through the thickness of the host waveguide on one side of the feature. The displacement field is measured at nodes through the thickness of the host waveguide on either side of the feature and decomposed into reflected and transmitted modes. The cases of guided wave transmission in a featureless waveguide and the reflection of guided waves from a free-edge are examined as validation cases. Finally, the results for transmission at an adhesively-bonded stiffener are presented and compared with experimental measurements.     

Calculation of effective material parameters by field averaging over lattices with non-negligible unit cell size

The Pendry et?al. field averaging method for calculation of effective material parameters is reviewed and its limits explored. The method is then extended so that it can accurately calculate the effective material parameters of lattices where the unit cell size is appreciable but still quasistatic (d??0.1?? ₀). The new algorithm is verified by calculating the effective material properties of periodically placed particles suspended in free space, as the unit cell size becomes appreciable. Results of our proposed formulation are then compared with the Pendry et?al. and conventional volumetric averaging algorithms.