Robust-to-outliers square-root LASSO, simultaneous inference with a MOM approach

We consider the least-squares regression problem with unknown noise variance, where the observed data points are allowed to be corrupted by outliers. Building on the median-of-means (MOM) method introduced by Lecue and Lerasle Ann.Statist.48(2):906-931(April 2020) in the case of known noise variance, we propose a general MOM approach for simultaneous inference of both the regression function and the noise variance, requiring only an upper bound on the noise level. Interestingly, this generalization requires care due to regularity issues that are intrinsic to the underlying convex-concave optimization problem. In the general case where the regression function belongs to a convex class, we show that our simultaneous estimator achieves with high probability the same convergence rates and a similar risk bound as if the noise level was unknown, as well as convergence rates for the estimated noise standard deviation. In the high-dimensional sparse linear setting, our estimator yields a robust analog of the square-root LASSO. Under weak moment conditions, it jointly achieves with high probability the minimax rates of estimation $s^{1/p} \sqrt{(1/n) \log(p/s)}$ for the $\ell_p$-norm of the coefficient vector, and the rate $\sqrt{(s/n) \log(p/s)}$ for the estimation of the noise standard deviation. Here $n$ denotes the sample size, $p$ the dimension and $s$ the sparsity level. We finally propose an extension to the case of unknown sparsity level $s$, providing a jointly adaptive estimator $(\widetilde \beta, \widetilde \sigma, \widetilde s)$. It simultaneously estimates the coefficient vector, the noise level and the sparsity level, with proven bounds on each of these three components that hold with high probability.Comment: 70 page

The Interaction Between the Urinary Trypsin Inhibitor and Trypsin

Gel filtration and disc electrophoresis were used as simple and fast techniques for the investigation of the interaction and stoichiometry between UTI and trypsin. UTI appears to possess only a single trypsin binding site. The nature of the interaction between the inhibitor and enzyme appears to be dependent on the concentration ratio of the reactants. When UTI is in excess molar concentration, a single binary complex with trypsin of mol. wt. 95,000 is observed. In the presence of a molar excess of enzyme, this macromolecule is no longer observed, but proteins of mol. wt. 41,000 and 20,000 result. The possibility that UTI may be hydrolyzed to a partially degraded active fragment by the excess enzyme resulting in the formation of a modified inhibitor enzyme complex is proposed

Bioactive phenolic acids from Scorzonera radiata Fisch.

Chromatographic separation of the crude extract obtained from the aerial parts of the Mongolian medicinal plant Scorzonera radiata yielded five new dihydrostilbenes [4], two new flavonoids, one new quinic acid derivative, as well as twenty known compounds including eight quinic acid derivatives, four flavonoids, two coumarins, five simple benzoic acids, and one monoterpene glycoside. We present here results on isolation and structural identification some active phenolic compounds from the Scorzonera radiata - eight quinic acid derivatives (quinic acid, 4,5-dicaffeoylquinic acid, 4,5-dicaffeoyl-epi-quinic acid, 3,5-dicaffeoylquinic acid, 3,5-dicaffeoyl-epi-quinic acid, chlorogenic acid, 5-p-coumaroylquinic acid (trans), 5-p-coumaroylquinic acid (cis)). Quinic acid derivatives exhibited antioxidative activity.DOI: http://dx.doi.org/10.5564/mjc.v12i0.177 Mongolian Journal of Chemistry Vol.12 2011: 78-8

How chromophore labels shape the structure and dynamics of a peptide hydrogel

Biocompatible and functionalizable hydrogels have a wide range of (potential) medicinal applications. In contrast to conventional hydrogels formed by interconnected or interlocked polymer chains, self-assembled hydrogels form from small building blocks like short peptide chains. This has the advantage that the building blocks can be functionalized separately and then mixed to obtain the desired properties. However, the hydrogelation process for these systems, especially those with very low polymer weight percentage (< 1 wt%), is not well understood, and therefore it is hard to predict whether a given molecular building block will self-assemble into a hydrogel. This severely hinders the rational design of self-assembled hydrogels. In this study, we demonstrate the impact of an N-terminal chromophore label amino-benzoic acid on the self-assembly and rheology of hydrogel hFF03 (hydrogelating, fibril forming) using molecular dynamics simulations, which self-assembles into {\alpha}-helical coiled-coils. We find that the chromophore and even its specific regioisomers have a significant influence on the microscopic structure and dynamics of the self-assembled fibril, and on the macroscopic mechanical properties. This is because the chromophore influences the possible salt-bridges which form and stabilize the fibril formation. Furthermore we find that the solvation shell fibrils by itself cannot explain the viscoelasticity of hFF03 hydrogels. Our atomistic model of the hFF03 fibril formation enables a more rational design of these hydrogels. In particular, altering the N-terminal chromophore emergesas a design strategy to tune the mechanic properties of these self-assembled peptide hydrogels.Comment: 15 pages, 15 including appendi

Cytotoxic labdane diterpenes and bisflavonoid atropisomers from leaves of Araucaria bidwillii

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Induced secondary metabolites from the endophytic fungus Aspergillus versicolor through bacterial co-culture and OSMAC approaches

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Xanthones and sesquiterpene derivatives from a marine-derived fungus Scopulariopsis sp.

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