Sparse blind deconvolution and demixing through <Emphasis Type="Italic">ℓ</Emphasis><Subscript>1,2</Subscript>-minimization

This paper concerns solving the sparse deconvolution and demixing problem using ? _1,2-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and Strohmer (Inverse Probl. 31, 115002 2015), and in particular theoretically explain certain experimental findings from that paper. Our results do not only apply to the deconvolution and demixing problem, but to recovery of column-sparse matrices in general.     

Extreme value copula estimation based on block maxima of a multivariate stationary time series

The core of the classical block maxima method consists of fitting an extreme value distribution to a sample of maxima over blocks extracted from an underlying series. In asymptotic theory, it is usually postulated that the block maxima are an independent random sample of an extreme value distribution. In practice however, block sizes are finite, so that the extreme value postulate will only hold approximately. A more accurate asymptotic framework is that of a triangular array of block maxima, the block size depending on the size of the underlying sample in such a way that both the block size and the number of blocks within that sample tend to infinity. The copula of the vector of componentwise maxima in a block is assumed to converge to a limit, which, under mild conditions, is then necessarily an extreme value copula. Under this setting and for absolutely regular stationary sequences, the empirical copula of the sample of vectors of block maxima is shown to be a consistent and asymptotically normal estimator for the limiting extreme value copula. Moreover, the empirical copula serves as a basis for rank-based, nonparametric estimation of the Pickands dependence function of the extreme value copula. The results are illustrated by theoretical examples and a Monte Carlo simulation study.     

A Carbene‐Extended ATRA Reaction

Atom‐transfer radical addition (ATRA) reactions have gained a strong foothold in organic synthesis by virtue of their operational simplicity, synthetic versatility, and perfect atom economy. A rich chemical space can be accessed through clever combinations of the simple starting materials. Many variations of this general motif have been reported. However, the vast majority involve the addition of an organic halide across a C=C double bond, resulting in the formation of 1,2‐bifunctional products. This report introduces a significant expansion of this general reactivity concept to give 1,3‐bifunctional adducts through the combination of 1,1‐ATRA to a carbenoid and 1,2‐ATRA to an alkyne. Both processes operate under mild conditions (RT, 5 h) with the same commercial catalyst (CoBr₂, dppbz).     

Synthese,Struktur und einige Reaktionen [N-(N′,N′,N″,N″-tetramethyl)-guanidinyl]-substituierter Phosphorylverbindungen

Synthesis, Structure, and some Reactions of N-(N′,N′,N″,N″-tetramethyl)guanidinyl-substituted Phosphoryl Compounds The tetramethylguanidinyl-substituted phosphoryl compounds 1 – 10 were prepared in the reaction of the appropriate chlorophosphoryl compounds with either N′,N′,N″,N″-tetramethylguanidine (HTMG) or N-trimethylsilyl-(N′,N′,N″,N″-tetramethyl)guanidine (TMSTMG). With methyl iodide 1 reacted with N-alkylation to give the ammonium salt 11. 1 reacted with BF₃ · Et₂O at both imino nitrogen atoms with formation of the bis-BF₃-adduct 12 . The X-ray structure determination of phenylphosphonic acid-bis(N′,N′,N″,N″-tetramethylguanidinide) 3 shows shortened PN-bonds and widened PNC-angles, consistent with the partial double bond character of the PN-bond.     

Capillary electrophoresis with end-capillary potentiometric detection using a copper electrode.

Potentiometric end-capillary detection in capillary electrophoresis has the advantage of relatively easy miniaturisation without having to compromise the concentration sensitivity. Potentiometric end-capillary detection using a copper electrode is also attractive because of the sensitive detection of many inorganic and organic UV-transparent ions and the ability to work in both direct and indirect mode. In this work, detection of a number of common anions in a tartrate electrolyte at pH 3 was studied. The influence of the end-capillary detection geometry on the detection performance was investigated. An end-capillary detection cell allowing the separation capillary to be changed without the need to realign the detection electrode was constructed and fitted into a commercial CE apparatus. Under the optimal configuration, which was a 25 microm diameter copper electrode aligned coaxially with a 25 microm capillary and positioned at a distance of about 25 microm from the capillary end, excellent peak shapes were achieved and comparison with simultaneous on-capillary photometric detection showed no additional peak broadening. Good sensitivity was obtained, resulting in concentration limits of detection (LODs) in the low microM range and mass LODs in the low amol range. Examples of separations of inorganic and organic anions are presented and the analytical potential of the detection method is assessed.     

Heterometallic 3d–4f coordination polymers: Synthesis,characterization and magnetic properties of 1D zigzag chains containing samarium and terbium

Reaction of the copper precursor [Cu(MeOsaltn)(H₂O)] (H₂MeOsaltn = N,N′-bis(3-methoxysalicylidene)-1,3-diaminopropane) with Ln(NO₃)₃·6H₂O (Ln = Sm and Tb) and pyrazine-2,3-dicarboxylic acid (H₂pyrdic) results in the formation of 1D zigzag chains with the general formula of [Cu(MeOsaltn)Ln(NO₃)(pyrdic)]_n·nDMF. X-ray crystal structures reveal that the samarium and terbium compounds are isostructural and crystalize in the orthorhombic space group Pbcn. The chains are composed of heterodinuclear copper–lanthanide building blocks which are linked by the pyrazine-2,3-dicarboxylate bridging units. Temperature-dependent susceptibility measurements indicate antiferromagnetic exchange interactions for the samarium–copper chain whereas for the terbium–copper compound ferromagnetic interactions are observed.     

Diastereoselective Photochemical Synthesis of α-Amino-β-hydroxyketones by Photocycloaddition of Carbonyl Compounds to 2,5-Dimethyl-4-isobutyloxazole

Summary. The photocycloaddition of aldehydes and α-ketoesters to 2,5-dimethyl-4-isobutyloxazole leads to bicyclic oxetanes with high to moderate (exo) diastereoselectivity that can be easily ring-opened to give α-amino-β-hydroxyketones.     

Synthesis and Structure of Monomeric,Trimeric, and Mixed Phenylcyanamides

In a new synthetic approach phenylcyanamide (Hpca) was synthesized by methylation of phenylthiourea followed by a basic work‐up. All products along the synthetic route have been fully characterized by means of NMR, IR, and X‐ray studies. The first structural report of neutral mixed crystals of phenylcyanamide containing monomeric and trimeric Hpca is presented. Examination of these intriguing mixed crystals revealed the formation of distinct layers of monomeric and trimeric Hpca. These layers are interconnected by weak hydrogen bonds. The trimer represents triphenylisomelamine, which readily isomerizes to the triphenylmelamine in the melt, in accord with computations at the B3LYP level, indicating an exothermic process (ΔH=?49.4 kcal mol^?1). Pure trimeric Hpca (triphenylisomelamine) was obtained either by recrystallization of the mixed crystals from boiling water or by trimerization of monomeric Hpca in isopropanol for 12 h under reflux conditions. For comparison tritylcyanamide (Htca) and potassium phenylcyanamide as an [18]crown‐6 complex [K([18]crown‐6)pca] have been synthesized, and the solid‐state structures were determined using X‐ray diffraction techniques. The thermal behavior was studied by thermo‐analytical experiments. In agreement with the experimental results, computations predict an exothermic cyclotrimerization process for Hpca (ΔH=?41.3 kcal mol^?1).     

Inverse temperature transition of a biomimetic elastin model: reactive flux analysis of folding/unfolding and its coupling to solvent dielectric relaxation

The inverse temperature transition (ITT) of a biomimetic model for elastin, capped GVG(VPGVG) in liquid water, is investigated by a comprehensive classical molecular dynamics study. The temperature dependence of the solvation structure and dynamics of the octapeptide are compared using three common force fields, CHARMM, GROMOS, and OPLS. While these force fields differ in quantitative detail, they all predict this octapeptide to undergo a "folding transition" to closed conformations upon heating and a subsequent "unfolding transition" to open conformations at still higher temperatures, thus reproducing the ITT scenario. The peptide kinetics is analyzed within the reactive flux formalism applied to the largest-amplitude mode extracted from principal component analysis, and the solvent's dielectric fluctuations are obtained from the total water dipole autocorrelations. Most importantly, preliminary evidence for an intimate coupling of peptide folding/unfolding dynamics, and thus the ITT, and dielectric relaxation of bulk water is given, possibly being consistent with a "slave mode" picture.