ChemInform Abstract: An ab initio Theoretical Study of the Electronic Structure of UO2+ and [UO2(CO3)3]5‐.

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Smoothing nonlinear subdivision schemes by averaging

In the theory of linear subdivision algorithms, it is well-known that the regularity of a linear subdivision scheme can be elevated by one order (say, from C ^k to C ^k+1) by composing it with an averaging step (equivalently, by multiplying to the subdivision mask a(z) a (1 + z) factor. In this paper, we show that the same can be done to nonlinear subdivision schemes: by composing with it any nonlinear, smooth, 2-point averaging step, the lifted nonlinear subdivision scheme has an extra order of regularity than the original scheme. A notable application of this result shows that the classical Lane-Riesenfeld algorithm for uniform B-Spline, when extended to Riemannian manifolds based on geodesic midpoint, produces curves with the same regularity as their linear counterparts. (In particular, curvature does not obstruct the nonlinear Lane-Riesenfeld algorithm to inherit regularity from the linear algorithm.) Our main result uses the recently developed technique of differential proximity conditions.     

Direct Likelihood Evaluation for the Renewal Hawkes Process

An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley, Filimonov, and Sornette, which has the potential to significantly widen the application domains of the self-exciting point processes. However, they claimed that computation of the likelihood of the RHawkes process requires exponential time and therefore is practically impossible. They proposed two expectation–maximization (EM) type algorithms to compute the maximum likelihood estimator (MLE) of the model parameters. Because of the fundamental role of likelihood in statistical inference, a practically feasible method for likelihood evaluation is highly desirable. In this article, we provide an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley, Filimonov, and Sornette. We demonstrate the superior performance of the resulting MLEs of the model relative to the EM estimators through simulations. We also present a computationally efficient procedure to calculate the Rosenblatt residuals of the process for goodness-of-fit assessment, and a simple yet efficient procedure for future event prediction. The proposed methodologies were applied on real data from seismology and finance. An R package implementing the proposed methodologies is included in the supplementary materials.     

Phospholipid Bilayers as Molecular Models for Drug-Cell Membrana Interactions. The Case of the Antiinflamatory Drug Diclofenac

Phospholipids are amphipatic molecules with long hydrophobic acyl chains and zwitterionic polar heads which assemble into different types of molecular aggregates. The most relevant is the bilayer because of its relation with cell membranes, which are very complex entities. For this reason, simpler molecular models based on phospholipids bilayers are widely used. We have determined the bilayer structure of phospholipids located in the outer and inner monolayers of most cell membranes, and use them as molecular models to study the way different chemicals of biological interest interact with cell membranes. We present the results of our studies on the nonsteroidal anti-inflammatory drug diclofenac, from which little is known about its effects on human erythrocytes. This report presents the following evidence that diclofenac interacts with the human red cell membrane: a) X-ray diffraction and fluorescence spectroscopy of phospholipids bilayers show that diclofenac interacts with a class of lipids found in the outer moiety of the erythrocyte membrane; b) in isolated unsealed human erythrocyte membranes the drug induced a disordering effect on the acyl chains of the membrane lipid bilayer; c) in scanning electron microscopy studies on human erythrocytes it was observed that the drug induced morphological changes different from their normal biconcave shape.     

Limitations of learning in automata-based systems

In this article, we aim to analyze the limitations of learning in automata-based systems by introducing the L⁺$L^{+}$ algorithm to replicate quasi-perfect learning, i.e., a situation in which the learner can get the correct answer to any of his queries. This extreme assumption allows the generalization of any limitations of the learning algorithm to less sophisticated learning systems. We analyze the conditions under which the L⁺$L^{+}$ infers the correct automaton and when it fails to do so. In the context of the repeated prisoners’ dilemma, we exemplify how the L⁺$L^{+}$ may fail to learn the correct automaton. We prove that a sufficient condition for the L⁺$L^{+}$ algorithm to learn the correct automaton is to use a large number of look-ahead steps. Finally, we show empirically, in the product differentiation problem, that the computational time of the L⁺$L^{+}$ algorithm is polynomial on the number of states but exponential on the number of agents.     

Quantum chemical study on the coordination environment of the catalytic zinc ion in matrix metalloproteinases

X-ray analyses of matrix metalloproteinases (MMPs) have shown that the catalytic zinc ion (Zn1) can bind to one to three water molecules in addition to three conserved histidine residues. To estimate the relative stability of the possible Zn1 coordination structures in the active site of the MMPs, we carry out computational analyses on the coordination environment of the Zn1 ion in the gelatinase A enzyme (or matrix metalloproteinase 2; MMP-2). Four-, five-, and six-coordinated complexes representative of the Zn1 site are fully characterized by means of quantum mechanical (QM) methodologies. On one hand, B3LYP/LACVP* minimizations of various cluster models of the MMP-2 active site show that the trigonal bipyramidal geometry is energetically favored in the gas phase and that continuum solvent effects stabilize preferentially the tetrahedral complexes. On the other hand, B3LYP/OPLS-AA hybrid QM/molecular mechanical calculations in the solvated catalytic domain of the MMP-2 enzyme complemented with electrostatic Poisson-Boltzmann calculations show that the mature enzyme presents most likely a Zn1 ion coordinated by three histidine residues and two water molecules, while the active site glutamic acid is negatively charged. In consonance with X-ray diffraction data, other possible Zn1 configurations, a six-coordinated structure with Zn1-water as well as four- and five-coordinated complexes with a Zn1-bound hydroxide, are predicted to be very close in energy.     

Stereoselective synthesis of eight-membered cyclic ethers by tandem Nicholas reaction/ring-closing metathesis: a short synthesis of (+)-cis-Lauthisan

[STRUCTURE: SEE TEXT] Cis-2,8-disubstituted oxocanes and the parent unsaturated precursors were prepared from the corresponding Co2(CO)6-cycloalkynic ethers. Key steps in such synthesis were the ether linkage formation by intermolecular Nicholas reaction, RCM of the suitable acyclic dienyl ether and montmorillonite K-10 induced isomerization of the complexed cycloalkyne. A short synthesis of (+)-cis-lauthisan taking advantage of the developed methodology is described.     

On the maximal operator associated with certain rotational invariant measures

The aim of this work is to investigate the integrability properties of the maximal operator Mu,associated with a non-doubling measure μ defined on Rn. We start by establishing for a wide class of radial and increasing measures μ that Mu is bounded on all the spaces Lu^p（R^n）,P〉1.Also,we show that there is a radial and increasing measure p for which Mμ does not map Lμ^p（R^n） into weak Lμ^p（R^n）,1≤p〈∞.