AN EXTENDED BLOCK RESTRICTED ISOMETRY PROPERTY FOR SPARSE RECOVERY WITH NON-GAUSSIAN NOISE

We study the recovery conditions of weighted mixed $\ell_2/\ell_p$ minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. We show theoretically that the extended block restricted isometry property can ensure robust recovery when the data fidelity constraint is expressed in terms of an $\ell_q$ norm of the residual error, thus establishing a setting wherein we are not restricted to Gaussian measurement noise. We illustrate the results with a series of numerical experiments.     

The length function and matrix algebras

By the length of a finite system of generators for a finite-dimensional associative algebra over an arbitrary field we mean the least positive integer k such that words of length not exceeding k span this algebra (as a vector space). The maximum length for the systems of generators of an algebra is referred to as the length of the algebra. In the present paper, we study the main ring-theoretical properties of the length function: the behavior of the length under unity adjunction, direct sum of algebras, passage to subalgebras and homomorphic images. We give an upper bound for the length of the algebra as a function of the nilpotency index of its Jacobson radical and the length of the quotient algebra. We also provide examples of length computation for certain algebras, in particular, for the following classical matrix subalgebras: the algebra of upper triangular matrices, the algebra of diagonal matrices, the Schur algebra, Courter’s algebra, and for the classes of local and commutative algebras.     

Shining Light on the Secreted Luciferases of Marine Copepods: Current Knowledge and Applications

Copepod luciferases—a family of small secretory proteins of 18.4–24.3 kDa, including a signal peptide—are responsible for bright secreted bioluminescence of some marine copepods. The copepod luciferases use coelenterazine as a substrate to produce blue light in a simple oxidation reaction without any additional cofactors. They do not share sequence or structural similarity with other identified bioluminescent proteins including coelenterazine‐dependent Renilla and Oplophorus luciferases. The small size, strong luminescence activity and high stability, including thermostability, make secreted copepod luciferases very attractive candidates as reporter proteins which are particularly useful for nondisruptive reporter assays and for high‐throughput format. The most known and extensively investigated representatives of this family are the first cloned GpLuc and MLuc luciferases from copepods Gaussia princeps and Metridia longa, respectively. Immediately after cloning, these homologous luciferases were successfully applied as bioluminescent reporters in vivo and in vitro, and since then, the scope of their applications continues to grow. This review is an attempt to systemize and critically evaluate the data scattered through numerous articles regarding the main structural features of copepod luciferases, their luminescent and physicochemical properties. We also review the main trends of their application as bioluminescent reporters in cell and molecular biology.     

Chemistry of 1,5-diketones: II. Specificity of transformations of polycyclic 1,5-diketones in acid media

2-(1,3-Diaryl-3-oxopropyl)cyclohexan-1-ones underwent carbo-and heterocyclization in a mixture of acetic acid with acetic anhydride in the presence of perchloric acid. The transformation of 2-(1,3-diaryl-3-oxopropyl)cyclohexan-1-ones into 2,4-diaryl-5,6,7,8-tetrahydrochromenylium salts was shown to involve intermediate 2,4-diarylbicyclo[3.3.1]non-2-en-9-ones. The structure of 2,4-diaryl-substituted bicyclo[3.3.1]non-2-en-9-ones and products of their reactions with halogens and hydroxylamine hydrochloride was confirmed by ¹H and ¹³C NMR spectroscopy.     

Synthesis of gasoline from syngas via dimethyl ether

Zeolite H-TsVM has been loaded with palladium by different methods. The properties of the resulting catalysts in gasoline synthesis from syngas via dimethyl ether depend on the way in which palladium was introduced. The catalysts have been characterized by ammonia temperature-programmed desorption (TPD), temperature-programmed reaction with hydrogen, and X-ray photoelectron spectroscopy. According to ammonia TPD data, use of a palladium ammine complex instead of palladium chloride reduces the concentration of strong acid sites and raises the concentration of medium-strength acid sites, thereby reducing the yield of C1–C4 hydrocarbons and increasing the yield of gasoline hydrocarbons. At T = 340°C, P = 100 atm, and GHSV = 2000 h^?1, the dimethyl ether conversion is 98–99%, the gasoline selectivity is >60%, the isoparaffin content of the product is ～61%, and the arene content is not higher than 29%.     

Application of the constant stoichiometry grouping concept to the Raman spectra of Pb(PO3)2-TeO2 glasses

Pb(PO₃)₂-TeO₂ glasses in the whole range of glass composition were first obtained and their properties (refractive index, density, T_g and light scattering losses) were determined. Based on the vibrational spectroscopy data a new approach was applied to investigate the interactions of initial oxides in melts resulted in so-called constant stoichiometry groupings (CSGs) formation symbolizing intermediate range order in glasses. Vibrational spectra of glasses are interpreted as a superposition of unchangeable spectral forms (principal spectral components (PSCs)) belonging to CSGs: PbO · P₂O₅, TeO₂ · 2PbO · 2P₂O₅, TeO₂ · PbO · P₂O₅, TeO₂, and possibly 2TeO₂ · PbO · P₂O₅ and 6TeO₂ · PbO · P₂O₅. In this work Multivariate Data Analysis has been applied as the independent mathematical tool to decompose Raman spectra of glasses and reveal the number of PSCs. It is shown that application of factor analysis results in the same five PSCs that confirms our data obtained from the CSG concept. This concept allows also the prediction of the existence of unknown compounds, and correspondingly some crystals (TeO₂⋅ 2PbO⋅2P₂O₅ and others) were revealed by XRPD of the crystallized glasses. The CSG concept opens the way for elaboration of low scattering glasses as candidates for Raman amplifiers. It is shown that Pb(PO₃)₂-TeO₂ glasses with small content of TeO₂ are of interest to photonic technology.     

Structure and properties of the surface alloy formed by irradiating a film/substrate system with a high-intensity electron beam

A film/substrate system has been treated with a submillisecond high-intensity electron beam. Examinations have shown that the electron-beam treatment of the film/substrate system resulted in alloying of the surface layer of the material throughout the melt which was accompanied by the formation of nanodimensional phases.