On homogeneous warped product Einstein metrics

In this article we study homogeneous warped product Einstein metrics and its connections with homogeneous Ricci solitons. We show that homogeneous $(\lambda,n+m)$-Einstein manifolds (which are the bases of homogeneous warped product Einstein metrics) are one-dimensional extensions of algebraic solitons. This answers a question from a paper of C. He, P. Petersen and W. Wylie, where they prove the converse statement. Our proof is strongly based on their results, but it also makes use of sharp tools from the theory of homogeneous Ricci solitons. As an application, we obtain that any homogeneous warped product Einstein metric with homogeneous base is diffeomorphic to a product of homogeneous Einstein manifolds.Comment: 9 page

Immortal homogeneous Ricci flows

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.Comment: Final version, to appear in Invent. Mat

RELATIVISTIC-DFT STUDY OF THE ELECTRONIC STRUCTURE, BONDING AND ENERGETIC OF THE [ReF8]־ AND [UF8]2- IONS

Indexación: Web of Science; Scielo.In this study we evaluated the importance of the relativistic effects (scalar and spin-orbit) on the description of the electronic structure, bonding and the energetic of the [ReF8]- and [UF8]2- ions. We described the bonding interaction between ligands and metal center using the energy decomposition analysis (EDA) proposed by Morokuma and Ziegler, in which it can be appreciated a strong ionic behavior for both ions since the electrostatic interaction energy (∆Ezlestat) is greater than the orbitalic interaction energy (∆EOrb). Furthermore, a qualitative analysis using the mapping of the electrostatic potential over the total electronic density evidence an increase of the ionic character, as well as, the polarization of the electronic density as U > Re. The electron localization function (ELF) corroborates the bonding analysis because of the lack of di-synaptic basins on the metal-ligand bonding region.http://ref.scielo.org/jcbd4

Improving Missing Data Imputation with Deep Generative Models

Datasets with missing values are very common on industry applications, and they can have a negative impact on machine learning models. Recent studies introduced solutions to the problem of imputing missing values based on deep generative models. Previous experiments with Generative Adversarial Networks and Variational Autoencoders showed interesting results in this domain, but it is not clear which method is preferable for different use cases. The goal of this work is twofold: we present a comparison between missing data imputation solutions based on deep generative models, and we propose improvements over those methodologies. We run our experiments using known real life datasets with different characteristics, removing values at random and reconstructing them with several imputation techniques. Our results show that the presence or absence of categorical variables can alter the selection of the best model, and that some models are more stable than others after similar runs with different random number generator seeds

Exact predictions from Edwards ensemble vs. realistic simulations of tapped narrow two-dimensional granular columns

We simulate via a Discrete Element Method the tapping of a narrow column of disk under gravity. For frictionless disks, this system has a simple analytic expression for the density of states in the Edwards volume ensemble. We compare the predictions of the ensemble at constant compactivity against the results for the steady states obtained in the simulations. We show that the steady states cannot be properly described since the microstates sampled are not in correspondence with the predicted distributions, suggesting that the postulates of flat measure and ergodicity are, either or both, invalid for this simple realization of a static granular system. However, we show that certain qualitative features of the volume fluctuations difficult to predict from simple arguments are captured by the theory.Comment: 11 pages, 6 figure

On the reduction of 4-oxo-4h-benzopyran-3-carbaldehydes : global and local electrophilicity patterns

The theoretical global and local electrophilicity patterns of substituted and chelated 4-oxo-4H-benzopyran-3-carbaldehydes (formylchromones) have been evaluated using the electrophilicity index proposed by Parr et al [J. Am. Chem. Soc. 1999, 121, 1922]. The complexation of formylchromones with aluminum predicts a strong electrophilic character of these compounds against nucleophiles. Local response at the active sites may also be assessed in terms of a global contribution described by the global electrophilicity, and a local contribution described by the variations in electrophilic Fukui function at those sites. The highest local electrophilicity is found at the formyl group of the chelated formylchromones, in spite of that, the highest positive charge is located on the pyrone carbonyl group. This result is consistent with the experimental observed reactivity displayed by 4-oxo-4H-benzopyran-3-carbaldehydes in the presence of 2-propanol and alumina