A variable fixing version of the two-block nonlinear constrained Gauss–Seidel algorithm for \ell _1-regularized least-squares

The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields as e.g. signal/image processing and statistics. A standard tool for dealing with sparse recovery is the \(\ell _1\) -regularized least-squares approach that has recently attracted the attention of many researchers. In this paper, we describe a new version of the two-block nonlinear constrained Gauss–Seidel algorithm for solving \(\ell _1\) -regularized least-squares that at each step of the iteration process fixes some variables to zero according to a simple active-set strategy. We prove the global convergence of the new algorithm and we show its efficiency reporting the results of some preliminary numerical experiments.     

Absolute continuity of the law for the two dimensional stochastic Navier–Stokes equations

We consider the two dimensional Navier–Stokes equations in vorticity form with a stochastic forcing term given by a gaussian noise, white in time and colored in space. First, we prove existence and uniqueness of a weak (in the Walsh sense) solution process $\xi$ and we show that, if the initial vorticity ${\xi }_0$ is continuous in space, then there exists a space–time continuous version of the solution. In addition we show that the solution $\xi (t,x)$ (evaluated at fixed points in time and space) is locally differentiable in the Malliavin calculus sense and that its image law is absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}$.     

Modeling sequence evolution with kernel methods

We model the evolution of biological and linguistic sequences by comparing their statistical properties. This comparison is performed by means of efficiently computable kernel functions, that take two sequences as an input and return a measure of statistical similarity between them. We show how the use of such kernels allows to reconstruct the phylogenetic trees of primates based on the mitochondrial DNA (mtDNA) of existing animals, and the phylogenetic tree of Indo-European and other languages based on sample documents from existing languages. Kernel methods provide a convenient framework for many pattern analysis tasks, and recent advances have been focused on efficient methods for sequence comparison and analysis. While a large toolbox of algorithms has been developed to analyze data by using kernels, in this paper we demonstrate their use in combination with standard phylogenetic reconstruction algorithms and visualization methods.     

Austrodoral and austrodoric acid: nor-sesquiterpenes with a new carbon skeleton from the Antarctic nudibranch Austrodoris kerguelenensis

Two unprecedented nor-sesquiterpenes, austrodoral (4) and its oxidised derivative austrodoric acid (5), have been isolated from the skin of the marine dorid Austrodoris kerguelenensis, collected in Antarctica. The structures and the relative stereochemistry were elucidated on the basis of spectroscopic data. A role of stress-metabolites could be suggested for these compounds.     

Cellulose beads: a new versatile solid support for microwave- assisted synthesis. Preparation of pyrazole and isoxazole libraries

The synthesis of libraries of substituted pyrazoles and isoxazoles has been developed via in situ generation of polymer-bound enaminones. The synthetic protocol makes use of commercially available aniline cellulose, a low-cost and versatile biopolymer, under very mild conditions. This new support allowed us to carry out reactions in polar solvents under both conventional heating and MW irradiation without degradation of the polymer. The reaction between cellulose-bound enaminone and hydroxylamine or hydrazines to afford the target heterocycles in high yields directly in solution is the key step. The support can be conveniently recycled.     

Structural and stereochemical revision of isocyanide and isothiocyanate amphilectenes from the Caribbean marine sponge Cribochalina sp.

The absolute stereochemistry of amphilectene metabolites from Cribochalina sp. has been revised by a detailed NMR spectroscopic study of the Mosher ester derivatives of a related alcohol. The relative stereochemistry of the previously described amphilectenes has been reinvestigated and reassigned on the basis of the X-ray structural analysis carried out on one of them. The structure of a new amphilectene metabolite, which is an isothiocyanato analogue is also presented.     

Olefin metathesis: what have we learned about homogeneous and heterogeneous catalysts from surface organometallic chemistry?

Since its early days, olefin metathesis has been in the focus of scientific discussions and technology development. While heterogeneous olefin metathesis catalysts based on supported group 6 metal oxides have been used for decades in the petrochemical industry, detailed mechanistic studies and the development of molecular organometallic chemistry have led to the development of robust and widely used homogeneous catalysts based on well-defined alkylidenes that have found applications for the synthesis of fine and bulk chemicals and are also used in the polymer industry. The development of the chemistry of high-oxidation group 5–7 alkylidenes and the use of surface organometallic chemistry (SOMC) principles unlocked the preparation of so-called well-defined supported olefin metathesis catalysts. The high activity and stability (often superior to their molecular analogues) and molecular-level characterisation of these systems, that were first reported in 2001, opened the possibility for the first direct structure–activity relationships for supported metathesis catalysts. This review describes first the history of SOMC in the field of olefin metathesis, and then focuses on what has happened since 2007, the date of our last comprehensive reviews in this field.

Surface organometallic chemistry bridges the gap between homogeneous and heterogeneous olefin metathesis catalysts.