arXiv subjects

Ester Livshits

Publications and source records attributed to Ester Livshits.

21 records · Page 2Linked to original sources

arXiv2016

Unambiguous Prioritized Repairing of Databases

In its traditional definition, a repair of an inconsistent database is a consistent database that differs from the inconsistent one in a "minimal way". Often, repairs are not equally legitimate, as it is desired to prefer one over another; for example, one fact is regarded more reliable than another, or a more recent fact should be preferred to an earlier one. Motivated by these considerations, researchers have introduced and investigated the framework of preferred repairs, in the context of denial constraints and subset repairs. There, a priority relation between facts is lifted towards a priority relation between consistent databases, and repairs are restricted to the ones that are optimal in the lifted sense. Three notions of lifting (and optimal repairs) have been proposed: Pareto, global, and completion. In this paper we investigate the complexity of deciding whether the priority relation suffices to clean the database unambiguously, or in other words, whether there is exactly one optimal repair. We show that the different lifting semantics entail highly different complexities. Under Pareto optimality, the problem is coNP-complete, in data complexity, for every set of functional dependencies (FDs), except for the tractable case of (equivalence to) one FD per relation. Under global optimality, one FD per relation is still tractable, but we establish $Π^{p}_{2}$-completeness for a relation with two FDs. In contrast, under completion optimality the problem is solvable in polynomial time for every set of FDs. In fact, we present a polynomial-time algorithm for arbitrary conflict hypergraphs. We further show that under a general assumption of transitivity, this algorithm solves the problem even for global optimality. The algorithm is extremely simple, but its proof of correctness is quite intricate.

cs.DB↗

arXiv2008

A density functional theory for symmetric radical cations from bonding to dissociation

It is known for quite some time that approximate density functional (ADF) theories fail disastrously when describing the dis-sociative symmetric radical cations R2+. Considering this dissociation limit, previous work has shown that Hartree-Fock (HF) theory favors the R+1--R0 charge distribution while DF approximations favor the R+0.5 -- R+0.5. Yet, general quantum mechanical principles indicate that both these (as well as all intermediate) average charge distributions are asymptotically energy degenerate. Thus HF and ADF theories mistakenly break the symmetry but in a contradicting way. In this letter we show how to construct system-dependent long-range corrected (LC) density functionals that can successfully treat this class of molecules, avoiding the spurious symmetry breaking. Examples and comparisons to experimental data is given for R=H, He and Ne and it is shown that the new LC theory improves considerably the theoretical description of the R2+ bond properties, the long range form of the asymptotic potential curve as well as the atomic polarizability. The broader impact of this finding is discussed as well and it is argued that the widespread semi-empirical approach which advocates treating the LC parameter as a system-independent parameter is in fact inappropriate under general circumstances.

cond-mat.mtrl-sci↗

arXiv2007

A well-tempered density functional theory of electrons in molecules

Reporting extensions of a recently developed approach to density functional theory with correct long-range be-havior (Phys. Rev. Lett. 94, 043002 (2005)). The central quantities are a splitting functional gamma[n] and a complementary exchange-correlation functional. We give a practical method for determining the value of γin molecules, assuming an approximation for XC energy is given. The resulting theory shows good ability to reproduce the ionization potentials for various molecules. However it is not of sufficient accuracy for forming a satisfactory framework for studying molecular properties. A somewhat different approach is then adopted, which depends on a density-independent γand an additional parameter w eliminating part of the local exchange functional. The values of these two parameters are obtained by best-fitting to experimental atomization energies and bond-lengths of the molecules in the G2(1) database. The optimized values are gamma=0.5 a_0^{-1} and w=0.1 . We then examine the performance of this slightly semi-empirical functional for a variety of molecular properties, comparing to related works and to experiment. We show that this approach can be used for describing in a satisfactory manner a broad range of molecular properties, be they static or dynamic. Most satisfactory is the ability to describe valence, Rydberg and inter-molecular charge-transfer excitations.

cond-mat.mtrl-sci↗