Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation

We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation's gradient flow structure with respect to the Wasserstein distance. The scheme inherits various properties of the continuous flow, like entropy monotonicity, mass preservation, metric contraction and minimum/maximum principles. As the main result, we give a proof of convergence in the limit of vanishing mesh size under a CFL-type condition. We also present results from numerical experiments.Comment: 28 pages, 6 figure

Catalytic C-H oxidation reactions for the synthesis and diversification of hydroxyamino acid motifs

Hydroxyamino acid motifs are well-represented structures in natural products and pharmaceuticals, and are widely employed as synthetic building blocks in organic synthesis. In nature, such compounds are often synthesized via enzymatic C-H oxidation of simple amino acid precursors. Inspired by such processes, small molecule catalysts have been developed to perform a variety of C-H oxidation reactions, which have increased the efficiency of synthetic routes and allowed for late-stage diversification of complex molecules. This work describes the development and application of two transition metal catalyzed C-H oxidation reactions for the synthesis and diversification of hydroxyamino acids and related molecules. α-Hydroxy-β-amino acids are an important subclass of the hydroxyamino acid family, examples of which are found in pharmaceutical agents including taxol and bestatin. Current synthetic methods for the construction of these molecules often rely on the use of pre-oxidized fragments or harsh reagents. This work reports the merging of Brønsted acid catalysis with Pd(II)/bis-sulfoxide catalyzed allylic C-H oxidation to achieve the synthesis of vinyl-oxazolidinones from simple homoallylic, N-Boc protected amines. It is shown that utilization of dibutylphosphate as a co-catalyst with a Pd(II)/bis-sulfoxide catalyst produces optimal reactivity, affording anti¬-vinyl-oxazolidinones. These products are versatile synthetic intermediates, and their synthetic derivatization into α-hydroxy-β-amino acids as well as intermediates to amino sugars is demonstrated. Furthermore, the high functional group tolerance of the reaction enabled late-stage cyclization on a leucine-β-allylglycine dipeptide substrate to install a vinyl oxazolidinone moiety. Mechanistic investigations into the role of the dibutylphosphate co-catalyst revealed that it may play multiple roles beyond promoting formation of a cationic π-allylPd intermediate, including serving as an anionic ligand to palladium capable of performing allylic C-H cleavage. Natural products of nonribosomal peptide synthetase (NRPS) origin posses complex topologies and diverse functional group arrays that lead to varied and impressive therapeutic potential. The structural diversity achieved among these natural products is due in large part to a biosynthetic strategy that employs pre- and post-assembly oxidative modifications of individual amino acid building blocks and fully assembled peptide chains, exemplified in the biosynthesis of vancomycin. In many cases, diversification is achieved via enzymatic hydroxylation of amino acids to form unnatural amino acids that are incorporated into a larger peptide structure, or are intermediates for further diversification of an amino acid. Here we report a strategy inspired by the elegant approach of NRPS biosynthetic systems, wherein small molecule iron catalysts Fe(PDP) and Fe(CF3PDP) enable the oxidative diversification of amino acids and peptides. In particular, a highly chemoselective hydroxylation at C5 of proline residues produces the versatile 5-hydroxyproline derivative, enabling further transformations to rapidly diversify amino acid and proline-containing peptide structures. In total, four chiral pool amino acids (proline, valine, leucine, and norvaline) are rapidly converted to twenty-one unnatural amino acid residues representing seven distinct functional group classes, and a single proline-containing tripeptide is transformed into eight sequences spanning five distinct functional group classes. Finally, the high efficiency and chemoselectivity of the iron catalyst is demonstrated by the chemoselective, late-stage transformation of a proline residue pentapeptide macrocycle to an unnatural residue

Recent Applications of Diversity-Oriented Synthesis Toward Novel, 3-Dimensional Fragment Collections

Fragment-based drug discovery (FBDD) is a well-established approach for the discovery of novel medicines, illustrated by the approval of two FBBD-derived drugs. This methodology is based on the utilization of small “fragment” molecules (<300 Da) as starting points for drug discovery and optimization. Organic synthesis has been identified as a significant obstacle in FBDD, however, in particular owing to the lack of novel 3-dimensional (3D) fragment collections that feature useful synthetic vectors for modification of hit compounds. Diversity-oriented synthesis (DOS) is a synthetic strategy that aims to efficiently produce compound collections with high levels of structural diversity and three-dimensionality and is therefore well-suited for the construction of novel fragment collections. This Mini-Review highlights recent studies at the intersection of DOS and FBDD aiming to produce novel libraries of diverse, polycyclic, fragment-like compounds, and their application in fragment-based screening projects

Preoperative Voice Parameters Affect the Postoperative Speech Intelligibility in Patients with Cochlear Implantation

ObjectivesVerbal communication depends on a good function of voice and speech organs. Some of the voice characteristics of deaf people differ considerably from those of speakers with normal hearing. After cochlear implantation (CI), auditory control of voice production is possible and the quality of the voice is improved. CI improves quality of voice, speech and hearing with deafness. The aim of our study was to investigate the relationship between acoustic analysis before CI and the speech intelligibility before and after CI.MethodsTwelve prelingually deafened children implanted unilaterally at the age of 3.4-9 years were included in the study. For all of the children an acoustic analysis of the Slovene vowel 'a' was performed before CI. The fundamental frequency (F0), jitter, shimmer and noise-to-harmonic ratio (NHR) were studied before the implantation. For all of the children the speech intelligibility was performed before and 12 months after CI. Preoperative hearing was divided on existing residual hearing. The results of the acoustic analyses and speech intelligibility before and after CI were compared for preoperative hearing. The results of the speech intelligibility were compared for the age of operation and preoperative acoustic analysis (F0, jitter, shimmer, NHR).ResultsPreoperative hearing had no influence on preoperative voice analysis. The children with residual hearing had a high grade of speech intelligibility before and after CI. The preoperative shimmer had positive correlation with postoperative 12 month speech intelligibility (r=0.618, P=0.032). The preoperative jitter had positive correlation with postoperative 12 month speech intelligibility, but was not statistically significant (r=0.479, P=0.116).ConclusionShimmer on preoperative voice analyses had influence on speech intelligibility after CI

A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes

A Lagrangian numerical scheme for solving nonlinear degenerate Fokker{Planck equations in space dimensions d>2 is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies and given external potentials, e.g. the porous medium equation and the fast diffusion equation. The key ingredient in our approach is the gradient ow structure of the dynamics. For discretization of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. Thanks to that time discretisation, the fully discrete solution inherits energy estimates from the original gradient ow, and these lead to weak compactness of the trajectories in the continuous limit. Consistency is analyzed in the planar situation, d = 2. A variety of numerical experiments for the porous medium equation indicates that the scheme is well-adapted to track the growth of the solution's support

- COMPORTAMIENTO DE PRECIOS EN LA INDUSTRIA EUROPEA DE PAVIMENTOS Y REVESTIMIENTOS CERÁMICOS

This paper constitutes an approach to the behavior of prices of the main exporters of tiles in the European markets. As in prior research studies, the analysis is based on the control of marginal costs, cross section data, and the data at an industry level, but with the particularity that the statistic information allows for testing the strategic interdependence among the groups that compete with each other. The analysis has been undertaken for the main exporter countries, namely Spain and Italy. From the behavior of prices it comes off the existence of product differentiation among the exporters' groups. We observe a similar evolution of the costs of production, interdependence absence in prices and the presence of strategies of pricing to market which try to reduce the losses of relative competitiveness of a group in front of their closest competitor. This strategy, based on the stabilization of prices in terms of the currency of each one of the markets of destination in those that converge, implies segmentation of the European markets and exporters' market power. Este trabajo constituye una aproximación al comportamiento de precios de los principales exportadores de pavimentos cerámicos en los mercados europeos en los que concurren. Como en trabajos anteriores, el análisis se basa en el control de los costes marginales, el detalle de datos a nivel de industria y la variación transversal de los datos, pero con la particularidad de que la información estadística que se dispone permite contrastar la posibilidad de interdependencia estratégica entre los grupos que compiten. El análisis se ha llevado a término para los principales países exportadores, es decir para los españoles e italianos. Del comportamiento de precios se desprende la existencia de diferenciación de productos entre grupos de exportadores, evolución similar de los costes de producción, ausencia de interdependencia en precios, y presencia de estrategias de Pricing to Market que tratan de reducir las pérdidas de competitividad relativa de un grupo frente a su competidor más cercano. Dicha estrategia, basada en la estabilización de precios en términos de la moneda de cada uno de los mercados de destino en los que concurren, implica segmentación de los mercados europeos y poder de mercado de las empresas exportadoras.Exportadores españoles, exportadores italianos, paralelismo de precios. Spanish exporters, Italian exporters and parallelism of prices.

Arylative intramolecular allylation of ketones with 1,3-enynes enabled by catalytic alkenyl-to-allyl 1,4-Rh(I) migration

Alkenyl-to-allyl 1,4-Rh(I) migration enables the generation of nucleophilic allylrhodium(I) species by remote C–H activation. This new mode of reactivity was employed in the diastereoselective reaction of arylboron reagents with substrates containing a 1,3-enyne tethered to a ketone, to give products containing three contiguous stereocenters. The products can be obtained in high enantioselectivities using a chiral sulfur–alkene ligand

Impact of Hydrogen Bonding on the Susceptibility of Peptides to Oxidation

The tendency of peptides to be oxidized is intimately connected with their function and even their ability to exist in an oxidative environment. Here we report high-level theoretical studies that show that hydrogen bonding can alter the susceptibility of peptides to oxidation, with complexation to a hydrogen-bond acceptor facilitating oxidation, and vice versa, impacting the feasibility of a diverse range of biological processes. It can even provide an energetically viable mechanistic alternative to direct hydrogen-atom abstraction. We find that hydrogen bonding to representative reactive groups leads to a broad (?400?kJ?mol?1) spectrum of ionization energies in the case of model amide, thiol and phenol systems. While some of the oxidative processes at the extreme ends of the spectrum are energetically prohibitive, subtle environmental and solvent effects could potentially mitigate the situation, leading to a balance between hydrogen bonding and oxidative susceptibility