New algorithms for discrete vector optimization based on the Graef-Younes method and cone-monotone sorting functions

Abstract

The well-known Jahn-Graef-Younes algorithm, proposed by Jahn in 2006, generates all minimal elements of a finite set with respect to an ordering cone. It consists of two Graef-Younes procedures, namely the forward iteration, which eliminates a part of the non-minimal elements, followed by the backward iteration, which is applied to the reduced set generated by the previous iteration. Without using the backward iteration, we develop new algorithms that also compute all minimal elements of the initial set, by combining the forward iteration with certain sorting procedures based on cone-monotone functions. In particular, when the ordering cone is polyhedral, computational results obtained in MATLAB allow us to compare our algorithms with the Jahn-Graef-Younes algorithm, within a bi-objective optimization problem.     

Nonlinear eigenvalue problems for quasilinear equations in unbounded domains

We prove the existence of a solution of the nonlinear equation in IR^N and in exterior domains, respectively. We concentrate to the case when p ≥ N and the nonlinearity f(x, · ) is “superlinear” and “subcritical”.     

Photochemical protection of amines with Cbz and Fmoc groups

The photochemical conversion of amines into carbamates was achieved using N-Cbz-, N-Fmoc-, and N-Boc-5,7-dinitroindolines. This reaction allows the protection of amines in neutral medium. Primary and unhindered secondary amines were protected to yield their benzyloxycarbonyl- and 9-fluorenylmethoxycarbonyl derivatives efficiently, whereas bulky amines or anilines gave low yields or no product. On the other hand, the formation of N-Boc compounds, although possible, proceeded only with low yields.     

An approach to the tricyclic core of madangamines based upon a biogenetic scheme

[reaction: see text] A short synthesis of intermediates possessing the tricyclic core of natural madangamines, bioactive alkaloids found in marine sponges, is described. The key reaction entails the condensation of the sodium salt of diethylacetonedicarboxylate with a dihydropyridinium salt derivative. This new approach is modeled on a biogenetic proposal linking madangamines to ircinals, related alkaloids occurring in sponges of the same order.     

Isolation and On‐Line LC/CD Analysis of 3,8″‐Linked Biflavonoids from Gnidia involucrata

Investigation of the methanol extract of the roots of Gnidia involucrata (Thymelaeaceae) led to the isolation and characterization of two new 3,8″‐biflavonoid diastereoisomers, named GB‐4 ( 6a ) and GB‐4a ( 6b ). Their absolute configurations were determined in mixture by on‐line LC/CD measurements, which also allowed the revision of absolute configurations of the biflavanoids GB‐1 and GB‐2, and the configurational assignment of GB‐3.     

Bio-dissolution of colloidal-size clay minerals entrapped in microporous silica gels

Four colloidal-size fractions of strongly anisotropic particles of nontronite (NAu-2) having different ratios of basal to edge surfaces were incubated in the presence of heterotrophic soil bacteria to evaluate how changes in mineral surface reactivity influence microbial dissolution rate of minerals. To avoid any particle aggregation, which could change the reactive surface area available for dissolution, NAu-2 particles were immobilized in a biocompatible TEOS-derived silica matrix. The resulting hybrid silica gels support bacterial growth with NAu-2 as the sole source of Fe and Mg. Upon incubation of the hybrid material with bacteria, between 0.3% and 7.5% of the total Fe included in the mineral lattice was released with a concomitant pH decrease. For a given pH value, the amount of released Fe varied between strains and was two to twelve-fold higher than under abiotic conditions. This indicates that complexing agents produced by bacteria play an important role in the dissolution process. However, in contrast with proton-promoted NAu-2 dissolution (abiotic incubations) that was negatively correlated with particle size, bacterial-enhanced dissolution was constant for all size fractions used. We conclude that bio-dissolution of nontronite particles under acidic conditions seems to be controlled by bacterial metabolism rather than by the surface reactivity of mineral.     

Reversible Mechanical Switching of Magnetic Interactions in a Molecular Shuttle

An acid–base switchable molecular shuttle based on a [2]rotaxane, incorporating stable radical units in both the ring and dumbbell components, is reported. The [2]rotaxane comprises a dibenzo[24]crown-8 ring (DB24C8) interlocked with a dumbbell component that possesses a dialkylammonium (NH₂⁺) and a 4,4′-bipyridinium (BPY²⁺) recognition site. Deprotonation of the rotaxane NH₂⁺ centers effects a quantitative displacement of the DB24C8 macroring to the BPY²⁺ recognition site, a process that can be reversed by acid treatment. Interaction between stable 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) radicals connected to the ring and dumbbell components could be switched between noncoupled (three-line electron paramagnetic resonance (EPR) spectrum) and coupled (five-line EPR spectrum) upon displacement of the spin-labelled DB24C8 macroring. The complete base- and acid-induced switching cycle of the EPR pattern was repeated six times without an appreciable loss of signal, highlighting the reversibility of the process. Hence, this molecular machine is capable of switching on/off magnetic interactions by chemically driven reversible mechanical effects. A system of this kind represents an initial step towards a new generation of nanoscale magnetic switches that may be of interest for a variety of applications.     

Rationally Designed Semisynthetic Natural Product Analogues for Stabilization of 14‐3‐3 Protein–Protein Interactions

The natural product family of fusicoccanes are stabilizers of 14‐3‐3 mediated protein–protein interactions (PPIs), some of which possess antitumor activity. In this study, the first use of molecular dynamics (MD) to rationally design PPI stabilizers with increased potency is presented. Synthesis of a focused library, with subsequent characterization by fluorescence polarization, mutational studies, and X‐ray crystallography confirmed the power of the MD‐based design approach, revealing the potential for an additional hydrogen bond with the 14‐3‐3 protein to lead to significantly increased potency. Additionally, these compounds exert their action in a cellular environment with increased potency. The newly found polar interaction could provide an anchoring point for new small‐molecule PPI stabilizers. These results facilitate the development of fusicoccanes towards drugs or tool compounds, as well as allowing the study of the fundamental principles behind PPI stabilization.