Crystal structure of 11-(2,3-dimethoxy-phenyl)-14-methyl-12-oxa-8,14-diaza-tetracyclo[8.3.3.01,10.02,7]hexadeca-2(7),3,5-triene-9,13-dione

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Crystal structure of ethyl (2S,2′ R)-1′-benzyl-3-oxo-3H-dispiro[1-benzothio-phene-2,3′-pyrrolidine-2′,11″-indeno-[1,2-b]quinoxaline]-4′-carboxylate

The authors thank the TBI X-ray facility, CAS in Crystallography and BioPhysics, University of Madras, Chennai, India, for the data collection.Peer reviewedPublisher PD

Synthetic sequence generator for recommender systems - memory biased random walk on sequence multilayer network

Personalized recommender systems rely on each user's personal usage data in the system, in order to assist in decision making. However, privacy policies protecting users' rights prevent these highly personal data from being publicly available to a wider researcher audience. In this work, we propose a memory biased random walk model on multilayer sequence network, as a generator of synthetic sequential data for recommender systems. We demonstrate the applicability of the synthetic data in training recommender system models for cases when privacy policies restrict clickstream publishing.Comment: The new updated version of the pape

Ultraviolet Fe II Emission in Fainter Quasars: Luminosity Dependences, and the Influence of Environments

We investigate the strength of ultraviolet Fe II emission in fainter quasars com- pared with brighter quasars for 1.0 :( z :( 1.8, using the SDSS (Sloan Digital Sky Survey) DR7QSO catalogue and spectra of Schneider et al., and the SFQS (SDSS Faint Quasar Survey) catalogue and spectra of Jiang et al. We quantify the strength of the UV Fe II emission using the W 2400 equivalent width of Weymann et al., which is defined between two rest-frame continuum windows at 2240–2255 and 2665–2695 ˚A. The main results are the following. (1) We find that for W 2400 2: 25 ˚A there is a universal (i.e. for quasars in general) strengthening of W 2400 with decreasing intrinsic luminosity, L3000. (2) In conjunction with previous work by Clowes et al., we find that there is a further, differential, strengthening of W 2400 with decreasing L3000 for those quasars that are members of Large Quasar Groups (LQGs). (3) We find that increasingly strong W 2400 tends to be associated with decreasing FWHM of the neighbouring Mg II λ2798 broad emission line. (4) We suggest that the dependence of W 2400 on L3000 arises from Lyα fluorescence. (5) We find that stronger W 2400 tends to be associated with smaller virial estimates from Shen et al. of the mass of the central black hole, by a factor ∼ 2 between the ultrastrong emitters and the weak. Stronger W 2400 emission would correspond to smaller black holes that are still growing. The differential effect for LQG members might then arise from preferentially younger quasars in the LQG environments

Small oscillations and the Heisenberg Lie algebra

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra $\mathfrak g$ that admits an ad-invariant metric. Its quadratic induces the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that one on $\mathbb R^{2n}$. This system is a Lax pair equation whose solution can be computed with help of the Adjoint representation. For a certain class of functions, the Poisson commutativity on the coadjoint orbits in $\mathfrak g$ is related to the commutativity of a family of derivations of the 2n+1-dimensional Heisenberg Lie algebra $\mathfrak h_n$. Therefore the complete integrability is related to the existence of an n-dimensional abelian subalgebra of certain derivations in $\mathfrak h_n$. For instance, the motion of n-uncoupled harmonic oscillators near an equilibrium position can be described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of the AKS schem