Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms

In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of c-atoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpoint-based semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negation-as-failure (naf) atoms, make use of an immediate consequence operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly well-supported models, are generalizations of the notion of well-supported models of normal logic programs to the case of programs with c-atoms. As for the case of fixpoint-based semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) well-supported models of a program, thus generalizing the theorem on the correspondence between stable models and well-supported models of a normal logic program to the class of programs with c-atoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone c-atoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with c-atoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature

Surface morphological evolutions on single crystal films by strong anisotropic drift-diffusion under the capillary and electromigration forces

The morphological evolution of voids at the unpassivated surfaces and the sidewalls of the single crystal metallic films are investigated via computer simulations by using the novel mathematical model developed by Ogurtani relying on the fundamental postulates of irreversible thermodynamics. The effects of the drift-diffusion anisotropy on the development of the surface morphological scenarios are fully explored under the action of the electromigration (EM) and capillary forces (CF), utilizing numerous combination of the surface textures and the directions of the applied electric field. The interconnect failure time due to the EM induced wedge shape internal voids and the incubation time of the oscillatory surface waves, under the severe instability regimes, are deduced by the novel renormalization procedures applied on the outputs of the computer simulation experiments.Comment: 41 pages, 18 figures. related simulation movies utilizing numerous combination of the surface texture, see http://www.csl.mete.metu.edu.tr/aytac/thesis/movies/index.ht

Key Findings From HSC's 2010 Site Visits: Health Care Markets Weather Economic Downturn, Brace for Health Reform

Presents findings about hospital payment rate increases, hospital-physician alignment, and insurance premiums, funding for safety-net providers, and their implications from HSC's site visits to twelve nationally representative metropolitan communities

Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor

The integrability of an m-component system of hydrodynamic type, u_t=V(u)u_x, by the generalized hodograph method requires the diagonalizability of the mxm matrix V(u). This condition is known to be equivalent to the vanishing of the corresponding Haantjes tensor. We generalize this approach to hydrodynamic chains -- infinite-component systems of hydrodynamic type for which the infinite matrix V(u) is `sufficiently sparse'. For such systems the Haantjes tensor is well-defined, and the calculation of its components involves finite summations only. We illustrate our approach by classifying broad classes of conservative and Hamiltonian hydrodynamic chains with the zero Haantjes tensor. We prove that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition for the integrability.Comment: 36 pages, the classification results and proofs are refined. A section on generating functions is adde

Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model

We propose 1D and 2D lattice wave functions constructed from the SU(n)_1 Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane-Shastry model as a special case. In 2D, we show that the wave function converges to a class of Halperin's multilayer fractional quantum Hall states and belongs to chiral spin liquids. Our result reveals a hidden SU(n) symmetry for this class of Halperin states. When the spins sit on bipartite lattices with alternating fundamental and conjugate representations, we provide numerical evidence that the state in 1D exhibits quantum criticality deviating from the expected behaviors of the SU(n)_1 WZW model, while in 2D they are chiral spin liquids being consistent with the prediction of the SU(n)_1 WZW model.Comment: 28 pages, 9 figures, published versio

Forecasting the equity risk premium: The role of technical indicators

Ministry of Education, Singapore under its Academic Research Funding Tier