Visualizing the large-ZZ scaling of the kinetic energy density of atoms

The scaling of neutral atoms to large $Z$, combining periodicity with a gradual trend to homogeneity, is a fundamental probe of density functional theory, one that has driven recent advances in understanding both the kinetic and exchange-correlation energies. Although research focus is normally upon the scaling of energies, insights can also be gained from energy densities. We visualize the scaling of the positive-definite kinetic energy density (KED) in closed-shell atoms, in comparison to invariant quantities based upon the gradient and Laplacian of the density. We notice a striking fit of the KED within the core of any atom to a gradient expansion using both the gradient and the Laplacian, appearing as an asymptotic limit around which the KED oscillates. The gradient expansion is qualitatively different from that derived from first principles for a slowly-varying electron gas and is correlated with a nonzero Pauli contribution to the KED near the nucleus. We propose and explore orbital-free meta-GGA models for the kinetic energy to describe these features, with some success, but the effects of quantum oscillations in the inner shells of atoms makes a complete parametrization difficult. We discuss implications for improved orbital-free description of molecular properties.Comment: 17 pages, 11 figures; 56th Sanibel Symposiu

Locality of correlation in density functional theory

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi approximation in the non-relativistic semiclassical (or large-$Z$) limit for all matter, i.e, the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms supports the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that the correlation energy tends to $-A_c Z ln Z + B_c Z$ as $Z$ tends to infinity, where $Z$ is the atomic number, $A_c$ is known, and we estimate $B_c$ to be about 37 millihartrees. The local density approximation yields $A_c$ exactly, but a very incorrect value for $B_c$, showing that the local approximation is less relevant for correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-$Z$ limit generally takes this form, but with $B_c$ a functional of the TF density for the system. The implications for construction of approximate density functionals are discussed.Comment: 17 pages, 10 figure

DSpot: Test Amplification for Automatic Assessment of Computational Diversity

Context: Computational diversity, i.e., the presence of a set of programs that all perform compatible services but that exhibit behavioral differences under certain conditions, is essential for fault tolerance and security. Objective: We aim at proposing an approach for automatically assessing the presence of computational diversity. In this work, computationally diverse variants are defined as (i) sharing the same API, (ii) behaving the same according to an input-output based specification (a test-suite) and (iii) exhibiting observable differences when they run outside the specified input space. Method: Our technique relies on test amplification. We propose source code transformations on test cases to explore the input domain and systematically sense the observation domain. We quantify computational diversity as the dissimilarity between observations on inputs that are outside the specified domain. Results: We run our experiments on 472 variants of 7 classes from open-source, large and thoroughly tested Java classes. Our test amplification multiplies by ten the number of input points in the test suite and is effective at detecting software diversity. Conclusion: The key insights of this study are: the systematic exploration of the observable output space of a class provides new insights about its degree of encapsulation; the behavioral diversity that we observe originates from areas of the code that are characterized by their flexibility (caching, checking, formatting, etc.).Comment: 12 page

Applications of a System of Tools in the Construction and Implementation of Multimedia Courses

Los profesores tienen el reto de usar las NTIC de forma creativa. Muchos de ellos poseen materiales de instrucción en diferentes soportes, pero necesitan de herramientas que les faciliten la construcción de cursos multimedia interactivos. Este trabajo aborda la aplicación de un sistema de herramientas, que viabiliza la construcción y administración de cursos multimedia. El sistema ha sido aplicado por profesores y estudiantes de la Facultad de Economía de la UH, así como por profesores y estudiantes de la Facultad de Informática de la Universidad de Cienfuegos, en la construcción e implementación de cursos multimedia que han sido utilizados en el modelo de enseñanza presencial y semipresencial.The professors have the challenge of using the NTIC in a creative way. Many of them possess instruction materials in different supports, but they need of tools that facilitate them the construction of interactive multimedia courses. This work approaches the application of a system of tools that viabiliza the construction and administration of multimedia courses. The system has been applied by professors and students of the Economy Faculty of the Havana University, as well as for professors and students of the Computer science Faculty of the Cienfuegos University, in the construction and implementation of multimedia courses that have been used in the pattern of present teaching and semipresencial

The RUPTURE OF MODERNITY : A PARADOX FOR THE EMERGENCE OF DEMOCRACY

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