1,511 research outputs found

    Integrable deformations of the Bogoyavlenskij-Itoh Lotka-Volterra systems

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    We construct a family of integrable deformations of the Bogoyavlenskij-Itoh systems and construct a Lax operator with spectral parameter for it. Our approach is based on the construction of a family of compatible Poisson structures for the undeformed system, whose Casimirs are shown to yield a generating function for the integrals in involution of the deformed systems. We show how these deformations are related to the Veselov-Shabat systems.Comment: 23 pages, 14 reference

    Structural and Sequence Similarity Makes a Significant Impact on Machine-Learning-Based Scoring Functions for Protein–Ligand Interactions

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    The prediction of protein–ligand binding affinity has recently been improved remarkably by machine-learning-based scoring functions. For example, using a set of simple descriptors representing the atomic distance counts, the RF-Score improves the Pearson correlation coefficient to about 0.8 on the core set of the PDBbind 2007 database, which is significantly higher than the performance of any conventional scoring function on the same benchmark. A few studies have been made to discuss the performance of machine-learning-based methods, but the reason for this improvement remains unclear. In this study, by systemically controlling the structural and sequence similarity between the training and test proteins of the PDBbind benchmark, we demonstrate that protein structural and sequence similarity makes a significant impact on machine-learning-based methods. After removal of training proteins that are highly similar to the test proteins identified by structure alignment and sequence alignment, machine-learning-based methods trained on the new training sets do not outperform the conventional scoring functions any more. On the contrary, the performance of conventional functions like X-Score is relatively stable no matter what training data are used to fit the weights of its energy terms

    Synthesis of Phosphine-Functionalized Silicon Cubane and Its Oxidative Addition, Giving a Bis(silyl)copper Complex

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    A new strategy for the introduction of a second type of Si atom to silicon cubanes has been developed starting from the tricyclic hexasilane dianion [Ar6Si6]2– (Ar = 2,4,6-Me3C6H2). Treatment of the dianion with Ar′SiCl3, followed by KC8, gave new types of octasilacubanes Ar6Ar′2Si8 [Ar′ = 2,4,6-iPr2C6H2 (3a), 2-Ph2PC6H4 (3b)] in high yields. Remarkably, treatment of cubane 3b bearing with two phosphine groups with 2 equiv of CuCl in CH2Cl2 yielded the bis(silyl)copper complex via the selective oxidative addition of the newly formed Si–Si bond to Cu ion. Single-crystal X-ray analysis indicated the unique square-planar, four-coordinate Cu cation paired with the [CuCl2]− counteranion

    Theoretical Prediction of Activation Free Energies of Various Hydride Self-Exchange Reactions in Acetonitrile at 298 K

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    Hydride transfer reactions are very important chemical reactions in organic chemistry. It has been a chemist’s dream to predict the rate constants of hydride transfer reactions by only using the physical parameters of the reactants. To realize this dream, we have developed a kinetic equation (Zhu equation) in our previous papers to predict the activation free energies of various chemical reactions using the activation free energies of the corresponding self-exchange reactions and the related bond dissociation energies or redox potentials of the reactants. Because the activation free energy of the hydride self-exchange reaction is difficult to measure using the experimental method, in this study, the activation free energies of 159 hydride self-exchange reactions in acetonitrile at 298 K were systematically computed using an accurately benchmarked density functional theory method with a precision of 1.1 kcal mol<sup>–1</sup>. The results show that the range of the activation free energies of the 159 hydride self-exchange reactions is from 16.1 to 46.6 kcal mol<sup>–1</sup>. The activation free energies of 25 122 hydride transfer reactions in acetonitrile at 298 K can be estimated using the activation free energies of the 159 hydride self-exchange reactions and the corresponding heterolytic bond dissociation free energies of the reactants. The effects of the heteroatom, substituent, and aromaticity on the activation free energies of hydride self-exchange reactions were examined. The results show that heteroatoms, substituents at the reaction center, and the aromaticity of reactants, all have remarkable effects on the activation free energy of hydride self-exchange reactions. All kinetic information provided in this work on the hydride self-exchange reactions in acetonitrile at 298 K should be very useful in chemical labs and chemical industry

    Gold(III)-Catalyzed Intramolecular Cyclization of α‑Pyrroles to Pyrrolopyridinones and Pyrroloazepinones: A DFT Study

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    Density functional theory calculations were carried out to study the mechanisms of gold-catalyzed intramolecular cyclization reactions of terminal alkyne and phenyl-substituted alkyne tethered pyrroles leading to pyrrolopyridinones and pyrroloazepinones, respectively. The calculation results indicate that the reaction mechanisms mainly involve metal-coordination of a substrate molecule (alkyne tethered pyrrole) through the alkyne moiety, nucleophilic attack of the pyrrole’s α-carbon on the metal-coordinated alkyne, and 1,2-migration of either the carbonyl carbon or an alkenyl carbon (derived from the alkyne moiety) from the pyrrole’s α-carbon to the β-carbon, followed by a series of protodeaurylation to finally give cyclization products. Through the detailed mechanistic study, we have explained the regioselectivity and rationalized the major/minor products observed in the gold-catalyzed intramolecular cyclization reactions of alkyne-tethered pyrroles

    Robust Variable and Interaction Selection for Logistic Regression and General Index Models

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    <p>Under the logistic regression framework, we propose a forward-backward method, SODA, for variable selection with both main and quadratic interaction terms. In the forward stage, SODA adds in predictors that have significant overall effects, whereas in the backward stage SODA removes unimportant terms to optimize the extended Bayesian information criterion (EBIC). Compared with existing methods for variable selection in quadratic discriminant analysis, SODA can deal with high-dimensional data in which the number of predictors is much larger than the sample size and does not require the joint normality assumption on predictors, leading to much enhanced robustness. We further extend SODA to conduct variable selection and model fitting for general index models. Compared with existing variable selection methods based on the sliced inverse regression (SIR), SODA requires neither linearity nor constant variance condition and is thus more robust. Our theoretical analysis establishes the variable-selection consistency of SODA under high-dimensional settings, and our simulation studies as well as real-data applications demonstrate superior performances of SODA in dealing with non-Gaussian design matrices in both logistic and general index models. Supplementary materials for this article are available online.</p

    Visible-Light Photoredox-Catalyzed Decarboxylation of α‑Oxo Carboxylic Acids to C1-Deuterated Aldehydes and Aldehydes

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    The synthesis of high-value-added C1-deuterated aldehydes would improve the availability of deuterated lead compounds for deuterium-labeled drug discovery. Herein, we develop a metal-free synthesis of C1-deuterated aldehydes with D2O from α-oxo carboxylic acids at ambient temperature. Via visible-light photoredox-catalyzed decarboxylation, stoichiometric reductants and oxidants were avoided. Various functional groups were tolerated and resulted in C1-deuterium aldehydes in up to 92% yield and 91–97% D incorporation under mild conditions. This method is also applied to the synthesis of various aldehydes. Primary mechanistic studies indicate that the catalytic pathway occurs via a reductive quenching pathway followed by hydrogen atom transfer

    Gold(III)-Catalyzed Intramolecular Cyclization of α‑Pyrroles to Pyrrolopyridinones and Pyrroloazepinones: A DFT Study

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    Density functional theory calculations were carried out to study the mechanisms of gold-catalyzed intramolecular cyclization reactions of terminal alkyne and phenyl-substituted alkyne tethered pyrroles leading to pyrrolopyridinones and pyrroloazepinones, respectively. The calculation results indicate that the reaction mechanisms mainly involve metal-coordination of a substrate molecule (alkyne tethered pyrrole) through the alkyne moiety, nucleophilic attack of the pyrrole’s α-carbon on the metal-coordinated alkyne, and 1,2-migration of either the carbonyl carbon or an alkenyl carbon (derived from the alkyne moiety) from the pyrrole’s α-carbon to the β-carbon, followed by a series of protodeaurylation to finally give cyclization products. Through the detailed mechanistic study, we have explained the regioselectivity and rationalized the major/minor products observed in the gold-catalyzed intramolecular cyclization reactions of alkyne-tethered pyrroles

    Transient stable case.

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    <p>Transient stable case.</p
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