A nonconvex formulation for low rank subspace clustering: algorithms and convergence analysis

We consider the problem of subspace clustering with data that is potentially corrupted by both dense noise and sparse gross errors. In particular, we study a recently proposed low rank subspace clustering approach based on a nonconvex modeling formulation. This formulation includes a nonconvex spectral function in the objective function that makes the optimization task challenging, e.g., it is unknown whether the alternating direction method of multipliers (ADMM) framework proposed to solve the nonconvex model formulation is provably convergent. In this paper, we establish that the spectral function is differentiable and give a formula for computing the derivative. Moreover, we show that the derivative of the spectral function is Lipschitz continuous and provide an explicit value for the Lipschitz constant. These facts are then used to provide a lower bound for how the penalty parameter in the ADMM method should be chosen. As long as the penalty parameter is chosen according to this bound, we show that the ADMM algorithm computes iterates that have a limit point satisfying first-order optimality conditions. We also present a second strategy for solving the nonconvex problem that is based on proximal gradient calculations. The convergence and performance of the algorithms is verified through experiments on real data from face and digit clustering and motion segmentation.     

An efficient synthesis and cytotoxic activity of 2‐(4‐chlorophenyl)‐1H–benzo[d]imidazole obtained using a magnetically recyclable Fe3O4 nanocatalyst‐mediated white tea extract

A simple and efficient procedure has been developed for the synthesis of biologically relevant 2‐substituted benzimidazoles through a one‐pot condensation of o‐phenylenediamines with aryl aldehydes catalysed by iron oxide magnetic nanoparticles (Fe₃O₄ MNPs) in short reaction times with excellent yields. In the present study, Fe₃O₄ MNPs synthesized in a green manner using aqueous extract of white tea (Camelia sinensis) (Wt‐Fe₃O₄ MNPs) were applied as a magnetically separable heterogeneous nanocatalyst to synthesize 2‐(4‐chlorophenyl)‐1H–benzo[d]imidazole which has potential application in pharmacology and biological systems. Fourier transform infrared and NMR spectroscopies were used to characterize the 2‐(4‐chlorophenyl)‐1H–benzo[d]imidazole. In vitro cytotoxicity studies on MOLT‐4 cells showed a dose‐dependent toxicity with non‐toxic effect of 2‐(4‐chlorophenyl)‐1H–benzo[d]imidazole, up to a concentration of 0.147 µM. The green synthesized Wt‐Fe₃O₄ MNPs as recyclable nanocatalyst could be used for further research on the synthesis of therapeutic materials, particularly in nanomedicine, to assist in the treatment of cancer.     

Laser stabilization to an atomic transition using an optically generated dispersive line shape

We report a simple and robust technique to generate a dispersive signal which serves as an error signal to electronically stabilize a monomode continuous-wave laser emitting around an atomic resonance. We explore nonlinear effects in the laser beam propagation through a resonant vapor by way of spatial filtering. The performance of this technique is validated by locking semiconductor lasers to the cesium and rubidium D₂ lines and observing long-term reduction of the emission frequency drifts, making the lasers well adapted for many atomic physics applications.     

Polyarginine nanocapsules: a new platform for intracellular drug delivery

This report describes the development of a new nanocarrier, named as polyarginine (PArg) nanocapsules, specifically designed for overcoming cellular barriers. These nanocapsules are composed of an oily core and a PArg corona. The attachment of the PArg corona was mediated by its interaction with the oily core, which was conveniently stabilized with phosphatidylcholine. Hybrid PArg/PEG nanocapsules could also be obtained by introducing PEG-stearate in the nanocapsules formation process. The nanocapsules had an average size in the range of 120–160 nm, and a positive surface charge, which varied between +56 and +28 mV for PArg and PArg/PEG nanocapsules, respectively. They could accommodate significant amounts of lipophilic drugs, i.e., docetaxel, in their core, and also polar negatively charged molecules, i.e., plasmid DNA, on their coating. As a preliminary proof-of-principle, we explored the ability of these nanocarriers to enter cancer cells and to inhibit proliferation in the non-small cell lung cancer NCI-H460 cell line, using flow cytometry and confocal microscopy analysis. The results indicated that PArg nanocapsules are rapidly and massively accumulated into the NCI-H460 cells and that the PArg shell plays a critical role in the internalization process. Moreover, the incubation with docetaxel-loaded nanocapsules with NCI-H460 cells led to an enhanced inhibition of their proliferation, as compared to the free drug. Overall, this is the first report of the potential of PArg nanocapsules as intracellular drug delivery vehicles.

     

An efficient and scalable block parallel algorithm of Neville elimination as a tool for the CMB maps problem

This paper analyses the performance of several versions of a block parallel algorithm in order to apply Neville elimination in a distributed memory parallel computer. Neville elimination is a procedure to transform a square matrix A into an upper triangular one. This analysis must take into account the algorithm behaviour as far as execution time, efficiency and scalability are concerned. Special attention has been paid to the study of the scalability of the algorithms trying to establish the relationship existing between the size of the block and the performance obtained in this metric. It is important to emphasize the high efficiency achieved in the studied cases and that the experimental results confirm the theoretical approximation. Therefore, we have obtained a high predicting ability tool of analysis. Finally, we will present the elimination of Neville as an efficient tool in detecting point sources in cosmic microwave background maps.     

A New Approach to the Intensity of the Secondary Transition of the Benzene Chromophore with-CH3,-OH,-OCH3, Substituents

Since the beginning of the UV absorption spectroscopy, the intensity of the secondary transition of the benzene chromophore in organic derivatives has been a puzzling challenge. The well known vector model has led to some qualitative evaluation of intensity, but accuracy is very low, and sometimes leads to no less than 50% or 100% error. ^1–8 It is designed for very weak perturbations only, as in methylbenzenes. But, even in that latter case, it is not completely satisfactory. Nevertheless, that model is very easy to use; it allows to determine the sensitive positions around the benzene nucleus: those which could enhance or quench intensity for a given pattern of substitution. On that ground it has been of much help for qualitative evaluations. With SCF methods and CI calculations, evaluation of transition moments for several benzene derivatives has been possible on a firmer ground. In fact, such an approach is useful mainly from a theoretical point of view, when accuracy is not the first aim, for some choosen molecules at the same time, since the involvement of computation is far from being negligible, and since the method is not part of the ones that are of common use in organic chemistry ^9,10 (for a recent example on oscillator strength calculations of π systems see:¹¹). In other words, it is not perfectly valuable on a large scale and routine approach and, from that point of view, UV spectroscopy of benzene derivatives appeared sometimes, from 1965 till now, as being in a cul-de-sac, although it was under thorough examination (for example: 12–30). Until recently ab initio calculations have failed to reach a fit with experiment better than 1 eV for the spectrum of the benzene molecule^31–32)     

Accessing Extended Fused Isoindolinones Via Sequential Anionic Intramolecular Cyclizations

Sequential anionic intramolecular cyclizations and modelling were used for the first time to access unusual fused heterocyclic frameworks in excellent yields. 5-Exo-dig cyclizations yielded isoindolinone motifs and a subsequent 6-exo- and 7-endo-dig cyclization was directed to provide either fused isoquinoline or azepine frameworks. Regioselectivities were controlled by exploiting stereoelectronic effects via n_C−→π*_(Ph) interactions, and modelling studies provided reaction scope.     

Synthesis of N,N'-Disubstituted α,ω-Alkanediamines,Precursors of Linear bisDithiocarbamates

Linear bis dithiocarbamates are conveniently obtained from symmetrical disubstituted α,ω-alkanediamines whose preparation is reported.