The object-oriented data model TM is a language that is based on the formal theory of FM, a typed language with object-oriented features such as attributes and methods in the presence of subtyping. The general (typed) set constructs of FM allow one to deal with (database) constraints in TM. The paper describes the theory of FM, and discusses the role that set expressions may play in conceptual ...

Density functional theory(DFT) has gained popularity because it can frequently give accurate energies and geometries. The evaluation of DFT integrals in a fully analytical manner is generally impossible; thus, most implementations use numerical quadrature over grid points. The grid-free approaches were developed as a viable alternative based upon the resolution of the identity (RI). Of particul...

Polarization consistent basis sets, optimized for density functional calculations, are proposed for the elements Si-Cl. Their performance for atomization energies, equilibrium geometries, harmonic vibrational frequencies, and associated infrared intensities is compared with other commonly used basis sets. Atomization energies can be predicted to within 0.01 kJ/mol per atom of the basis set limi...

Radial basis functions are powerful meshfree methods for multivariate interpolation for scattered data. But both the approximation quality and stability depend on the distribution of the center set. Many methods such as so called thinning algorithm, greedy algorithm, arclength equipartition like algorithm and k-means clustering algorithm are constructed for center choosing. But all these method...

Unsupervised lexicon learning techniques for audio-in-the-wild typically assume that only one of the lexical units is active at any given point in time (hard quantization) or use soft counts to avoid committing to one unit (soft quantization). In reality, the audio will usually be produced as a mixture of the different audio concepts in the lexicon. In this paper, we propose a model where the a...

It is shown how unbound electron wave functions can be expanded in a suitably chosen localized basis sets for any desired range of energies. In particular, we focus on the use of Gaussian basis sets, commonly used in first-principles codes. The possible usefulness of these basis sets in a first-principles description of field emission or scanning tunneling microscopy at large bias is illustrate...

Abst ract . The degree to which the genetic opt imizat ion process is transparent is in part determined by the form of th e object ive funct ion. We develop two forms from first principles: polynomial forms and basis sets. We characterize three function classes that are fully easy for the genetic algorithm in terms of the polynomial representation. We generate functions of varying degrees of de...

Finding the sparsest solution α for an under-determined linear system of equations Dα = s is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of α that allow its recovery using `1-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of D called the mutual-coherence. In this...

Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculate...

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