Gell-Mann and Low Formula for Degenerate Unperturbed States

The Gell-Mann and Low switching allows to transform eigenstates of an unperturbed Hamiltonian H ₀ into eigenstates of the modified Hamiltonian H ₀ + V. This switching can be performed when the initial eigenstate is not degenerate, under some gap conditions with the remainder of the spectrum. We show here how to extend this approach to the case when the ground state of the unperturbed Hamiltonian is degenerate. More precisely, we prove that the switching procedure can still be performed when the initial states are eigenstates of the finite rank self-adjoint operator P₀VP₀{\mathcal{P}_{0}V\mathcal{P}_{0}} , where P₀{\mathcal{P}_0} is the projection onto a degenerate eigenspace of H ₀.     

Fast and accurate predictions of binding free energies using MM‐PBSA and MM‐GBSA

In the drug discovery process, accurate methods of computing the affinity of small molecules with a biological target are strongly needed. This is particularly true for molecular docking and virtual screening methods, which use approximated scoring functions and struggle in estimating binding energies in correlation with experimental values. Among the various methods, MM‐PBSA and MM‐GBSA are emerging as useful and effective approaches. Although these methods are typically applied to large collections of equilibrated structures of protein‐ligand complexes sampled during molecular dynamics in water, the possibility to reliably estimate ligand affinity using a single energy‐minimized structure and implicit solvation models has not been explored in sufficient detail. Herein, we thoroughly investigate this hypothesis by comparing different methods for the generation of protein‐ligand complexes and diverse methods for free energy prediction for their ability to correlate with experimental values. The methods were tested on a series of structurally diverse inhibitors of Plasmodium falciparum DHFR with known binding mode and measured affinities. The results showed that correlations between MM‐PBSA or MM‐GBSA binding free energies with experimental affinities were in most cases excellent. Importantly, we found that correlations obtained with the use of a single protein‐ligand minimized structure and with implicit solvation models were similar to those obtained after averaging over multiple MD snapshots with explicit water molecules, with consequent save of computing time without loss of accuracy. When applied to a virtual screening experiment, such an approach proved to discriminate between true binders and decoy molecules and yielded significantly better enrichment curves. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Kinetics of chalcone oxidation by peroxide anion catalysed by poly-l-leucine

An insight into the kinetics, mechanism and optimum reaction conditions of the Julia-Colonna epoxidation has been gained using a soluble polyleucine catalyst.     

Butadienic building blocks from 2-nitrothiophene as precursors of nitrogen heterocycles: intriguing dichotomic behavior

With the goal of their exploitation for the synthesis of heterocycles, sulfides 10 and sulfones 11, derived from the initial ring-opening of 2-nitrothiophene (5) with pyrrolidine/AgNO3 in EtOH, were reacted with diazomethane. Interesting dichotomic behavior was found to yield pyrazolines 17 from 10 and isoxazolines 18 (as the main products) from 11. Intriguingly enough, in the latter case, an unexpected apparent C-C methylene insertion was also observed, leading to the homologous cyclopropanes 19 as secondary products.     

Ruthenium(II) Tris-Pyrazolylmethane Complexes in Transfer Hydrogenation Reactions

While ruthenium(II) arene complexes have been widely investigated for their potential in catalytic transfer hydrogenation, studies on homologous compounds replacing the arene ligand with the six-electron donor tris(1-pyrazolyl)methane (tpm) are almost absent in the literature. The reactions of [RuCl(κ³-tpm)(PPh₃)₂]Cl, 1 , with a series of nitrogen ligands (L) proceeded with selective PPh₃ mono-substitution, affording the novel complexes [RuCl(κ³-tpm)(PPh₃)(L)]Cl (L=NCMe, 2 ; NCPh, 3 ; imidazole, 4 ) in almost quantitative yields. Products 2 – 4 were fully characterized by IR and multinuclear NMR spectroscopy, moreover the molecular structure of 4 was ascertained by single crystal X-ray diffraction. Compounds 2 – 4 were evaluated as catalytic precursors in the transfer hydrogenation of a series of ketones with isopropanol as the hydrogen source, and 2 exhibited the highest activity. Extensive NMR experiments and DFT calculations allowed to elucidate the mechanism of the transfer hydrogenation process, suggesting the crucial role played by the tpm ligand, reversibly switching from tri- to bidentate coordination during the catalytic cycle.     

Symmetry and Localization for Magnetic Schrödinger Operators: Landau Levels,Gabor Frames and All That

We investigate the relation between broken time-reversal symmetry and localization of the electronic states, in the explicitly tractable case of the Landau model. We first review, for the reader’s convenience, the symmetries of the Landau Hamiltonian and the relation of the latter with the Segal-Bargmann representation of Quantum Mechanics. We then study the localization properties of the Landau eigenstates by applying an abstract version of the Balian-Low Theorem to the operators corresponding to the coordinates of the centre of the cyclotron orbit in the classical theory. Our proof of the Balian-Low Theorem, although based on Battle’s main argument, has the advantage of being representation-independent.

     

Subagging for credit scoring models

The logistic regression framework has been for long time the most used statistical method when assessing customer credit risk. Recently, a more pragmatic approach has been adopted, where the first issue is credit risk prediction, instead of explanation. In this context, several classification techniques have been shown to perform well on credit scoring, such as support vector machines among others. While the investigation of better classifiers is an important research topic, the specific methodology chosen in real world applications has to deal with the challenges arising from the real world data collected in the industry. Such data are often highly unbalanced, part of the information can be missing and some common hypotheses, such as the i.i.d. one, can be violated. In this paper we present a case study based on a sample of IBM Italian customers, which presents all the challenges mentioned above. The main objective is to build and validate robust models, able to handle missing information, class unbalancedness and non-iid data points. We define a missing data imputation method and propose the use of an ensemble classification technique, subagging, particularly suitable for highly unbalanced data, such as credit scoring data. Both the imputation and subagging steps are embedded in a customized cross-validation loop, which handles dependencies between different credit requests. The methodology has been applied using several classifiers (kernel support vector machines, nearest neighbors, decision trees, Adaboost) and their subagged versions. The use of subagging improves the performance of the base classifier and we will show that subagging decision trees achieve better performance, still keeping the model simple and reasonably interpretable.     

DNS of buoyancy-dominated turbulent flows on a bluff body using the immersed boundary method

A novel immersed boundary (IB) method has been developed for simulating multi-material heat transfer problem – a cylinder in a channel heated from below with mixed convection. The method is based on a second-order velocity/scalar reconstruction near the IB. A novel algorithm has been developed for the IB method to handle conjugate heat transfer. The fluid–solid interface is constructed as a collection of disjoint faces of control volumes associated to different material zones. Coupling conditions for the material zones have been developed such that continuity and conservation of the scalar flux are satisfied by a second-order interpolation. Predictions of the local Nusselt number on the cylinder surface show good agreement with the experimental data. The effect of the Boussinesq approximation on this problem was also investigated. Comparison with the variable density formulation suggests that, in spite of a small thermal expansion coefficient of water, the variable density formulation in a transitional flow with mixed convection is preferable.     

Synthesis of 1H-pyrazino[1,2-a]pyrido[2,3-e]pyrazine and 2H-Pyrano[2,3-b]pyrido[2,3-e]pyrazine Derivatives

With a continuing interest on heteropolycyclic structures which may show biological activities, we synthesized new tricyclic derivatives in which the pyridopyrazine skeleton is fused with pyrazine 7 and 8, B , n = 1. However, the initial design of obtaining also the cyclohomologous structure B (n = 2) produced instead a pyranopyridopyrazine derivative 11 . Thus during the attempt to prepare a pyridodiazepine intermediate, beside a very small amount of the desired product 10 , the pyridopyrazine 9 was obtained. The latter compound reacted with chloroacetyl chloride/chloroketene to give 4-carbethoxy-10-(chloroacetyl)-5,10-dihydro-5-methyl-2H-pyrano[2,3-b]pyrido[2,3-e]pyrazin-2-one ( 11 ). In studying the behavior of this derivative, compounds 12–14 were obtained. Compounds 4b,c, 5a,b, 7, 8, 9 and 14 have been submitted to preliminary pharmacological screening as CNS depressant agents.