Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices

We propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-diagonal elements of the inverse correlation matrix to zero and this sparsity structure is modeled using a decomposable graphical model. We propose an efficient Markov chain Monte Carlo algorithm relying on a parameter expansion scheme to sample from the resulting posterior distribution. This algorithm updates the correlation matrix within a simple Gibbs sampling framework and allows us to infer the correlation structure from the data, generalizing methods used for inference in decomposable Gaussian graphical models to multivariate binary observations. We demonstrate the performance of this model and of the Markov chain Monte Carlo algorithm on simulated and real datasets. This article has online supplementary materials.     

MRICOM–MRI COntrast Modelling using 2D T1–T2 correlation spectra and relaxation signatures

Image contrast is calculated by inputting experimental 2D T₁–T₂ relaxation spectra into the ODIN software interface. The method involves characterising a magnetic resonance imaging pulse sequence with a “relaxation signature” which describes the sensitivity of the sequence to relaxation and is independent of sample parameters. Maximising (or minimising) the overlap between the experimental 2D T₁–T₂ relaxation spectra and the relaxation signature can then be used to maximise image contrast. The concept is illustrated using relaxation signatures for the echo planar imaging and Turbo spin-echo imaging sequences, together with in-vitro 2D T₁–T₂ spectra for liver and cartilage.     

The third homology of the special linear group of a field

We prove that for any infinite field F, the map is an isomorphism for all n≥3. When n=2 the cokernel of this map is naturally isomorphic to , where is the nth Milnor K-group of F. We deduce that the natural homomorphism from to the indecomposable K₃ of F, , is surjective for any infinite field F.     

Sharp probability estimates for random walks with barriers

We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,∞) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.     

Aryl vinyl cyclopropane Cope rearrangements

While the divinyl cyclopropane Cope rearrangement is well-known, and has been broadly applied in synthesis, examples of the aryl vinyl cyclopropane Cope rearrangement are less common and generally limited in scope or reaction yield. The aryl vinyl cyclopropane Cope rearrangement gives access to the benzocycloheptene scaffold, which is present in a variety of naturally occurring and medicinally relevant products. Herein we report a method to obtain either of two regioisomeric benzocycloheptene products via an aryl vinyl cyclopropane Cope rearrangement, featuring additive-controlled regioselectivity. Mechanistic studies indicate a dynamic equilibration of cyclopropane stereoisomers, followed by rearrangement of the cis diastereomer.     

Synthesis,Antiprotozoal Activity,and Cheminformatic Analysis of 2-Phenyl-2H-Indazole Derivatives

Indazole is an important scaffold in medicinal chemistry. At present, the progress on synthetic methodologies has allowed the preparation of several new indazole derivatives with interesting pharmacological properties. Particularly, the antiprotozoal activity of indazole derivatives have been recently reported. Herein, a series of 22 indazole derivatives was synthesized and studied as antiprotozoals. The 2-phenyl-2H-indazole scaffold was accessed by a one-pot procedure, which includes a combination of ultrasound synthesis under neat conditions as well as Cadogan’s cyclization. Moreover, some compounds were derivatized to have an appropriate set to provide structure-activity relationships (SAR) information. Whereas the antiprotozoal activity of six of these compounds against E. histolytica, G. intestinalis, and T. vaginalis had been previously reported, the activity of the additional 16 compounds was evaluated against these same protozoa. The biological assays revealed structural features that favor the antiprotozoal activity against the three protozoans tested, e.g., electron withdrawing groups at the 2-phenyl ring. It is important to mention that the indazole derivatives possess strong antiprotozoal activity and are also characterized by a continuous SAR.     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

Photophysical characterization of a highly conjugated bipyridyl-based dye synthesized by a unique two-step approach

In this article, we present a new and simple, yet efficient, two-step approach to synthesize 4,4'-bis(dibutylaminostyrylstyryl)-2,2'-bipyridine with high yield, as well as its linear and nonlinear optical characterizations in THF and toluene solutions. We show that its one- and two-photon absorption spectra are similar in both solvents. Nevertheless, the relaxation processes of this compound exhibit dependence on the solvent polarity. The one- and two-photon induced fluorescence signal of this molecule in solution reveals that its excited state is highly stabilized in THF solution rather than in toluene. Analysis of the fluorescence quantum yield, lifetime, and radiative and nonradiative decay rates are in agreement with Lippert's model for solute-solvent interactions. The optical measurements demonstrate that this dye is a promising candidate for multiphoton fluorescence imaging, optical limiting, and dye lasers.