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

Unparticle Self-Interactions and Their Collider Implications

In unparticle physics, operators of the conformal sector have self-interactions, and these are unsuppressed for strong coupling. The 3-point interactions are completely determined by conformal symmetry, up to a constant. We do not know of any theoretical upper bounds on this constant. Imposing current experimental constraints, we find that these interactions mediate spectacular collider signals, such as $pp -> U -> UU -> \gamma \gamma \gamma \gamma$, $\gamma \gamma ZZ$, $ZZZZ$, $\gamma \gamma l^+ l^-$, $ZZ l^+ l^-$, and $4l$, with cross sections of picobarns or larger at the Large Hadron Collider. Self-interactions may therefore provide the leading discovery prospects for unparticle physics.Comment: 12 pages, 5 figures; v2: published versio

The Extreme Ultraviolet and X-Ray Sun in Time: High-Energy Evolutionary Tracks of a Solar-Like Star

Aims. We aim to describe the pre-main sequence and main-sequence evolution of X-ray and extreme-ultaviolet radiation of a solar mass star based on its rotational evolution starting with a realistic range of initial rotation rates. Methods. We derive evolutionary tracks of X-ray radiation based on a rotational evolution model for solar mass stars and the rotation-activity relation. We compare these tracks to X-ray luminosity distributions of stars in clusters with different ages. Results. We find agreement between the evolutionary tracks derived from rotation and the X-ray luminosity distributions from observations. Depending on the initial rotation rate, a star might remain at the X-ray saturation level for very different time periods, approximately from 10 Myr to 300 Myr for slow and fast rotators, respectively. Conclusions. Rotational evolution with a spread of initial conditions leads to a particularly wide distribution of possible X-ray luminosities in the age range of 20 to 500 Myrs, before rotational convergence and therefore X-ray luminosity convergence sets in. This age range is crucial for the evolution of young planetary atmospheres and may thus lead to very different planetary evolution histories.Comment: 4 pages, 4 figures, accepted for publication in A&

Size-Dependent Tile Self-Assembly: Constant-Height Rectangles and Stability

We introduce a new model of algorithmic tile self-assembly called size-dependent assembly. In previous models, supertiles are stable when the total strength of the bonds between any two halves exceeds some constant temperature. In this model, this constant temperature requirement is replaced by an nondecreasing temperature function $\tau : \mathbb{N} \rightarrow \mathbb{N}$ that depends on the size of the smaller of the two halves. This generalization allows supertiles to become unstable and break apart, and captures the increased forces that large structures may place on the bonds holding them together. We demonstrate the power of this model in two ways. First, we give fixed tile sets that assemble constant-height rectangles and squares of arbitrary input size given an appropriate temperature function. Second, we prove that deciding whether a supertile is stable is coNP-complete. Both results contrast with known results for fixed temperature.Comment: In proceedings of ISAAC 201

Cholesterol-directed nanoparticle assemblies based on single amino acid peptide mutations activate cellular uptake and decrease tumor volume.

Peptide drugs have been difficult to translate into effective therapies due to their low in vivo stability. Here, we report a strategy to develop peptide-based therapeutic nanoparticles by screening a peptide library differing by single-site amino acid mutations of lysine-modified cholesterol. Certain cholesterol-modified peptides are found to promote and stabilize peptide α-helix formation, resulting in selectively cell-permeable peptides. One cholesterol-modified peptide self-assembles into stable nanoparticles with considerable α-helix propensity stabilized by intermolecular van der Waals interactions between inter-peptide cholesterol molecules, and shows 68.3% stability after incubation with serum for 16 h. The nanoparticles in turn interact with cell membrane cholesterols that are disproportionately present in cancer cell membranes, inducing lipid raft-mediated endocytosis and cancer cell death. Our results introduce a strategy to identify peptide nanoparticles that can effectively reduce tumor volumes when administered to in in vivo mice models. Our results also provide a simple platform for developing peptide-based anticancer drugs

Microscopic models for Kitaev's sixteenfold way of anyon theories

In two dimensions, the topological order described by $\mathbb{Z}_2$ gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number $\nu$ is classified by $\nu \; \mathrm{mod}\; 16$ as predicted by Kitaev [Ann. Phys. 321, 2 (2006)]. Here we provide a systematic and complete construction of microscopic models realizing this so-called sixteenfold way of anyon theories. These models are defined by $\Gamma$ matrices satisfying the Clifford algebra, enjoy a global $\mathrm{SO}(\nu)$ symmetry, and live on either square or honeycomb lattices depending on the parity of $\nu$. We show that all these models are exactly solvable by using a Majorana representation and characterize the topological order by calculating the topological spin of an anyonic quasiparticle and the ground-state degeneracy. The possible relevance of the $\nu=2$ and $\nu=3$ models to materials with Kugel-Khomskii-type spin-orbital interactions is discussed.Comment: 6+9 pages, 2+1 figures, published versio

Chirality Dependence of the KK-Momentum Dark Excitons in Carbon Nanotubes

Using a collection of twelve semiconducting carbon nanotube samples, each highly enriched in a single chirality, we study the chirality dependence of the $K$-momentum dark singlet exciton using phonon sideband optical spectroscopy. Measurements of bright absorptive and emissive sidebands of this finite momentum exciton identify its energy as 20 - 38 meV above the bright singlet exciton, a separation that exhibits systematic dependencies on tube diameter, $2n+m$ family, and semiconducting type. We present calculations that explain how chiral angle dependence in this energy separation relates to the Coulomb exchange interaction, and elaborate the dominance of the $K_{A_1'}$ phonon sidebands over the zone-center phonon sidebands over a wide range of chiralities. The Kataura plot arising from these data is qualitatively well described by theory, but the energy separation between the sidebands shows a larger chiral dependence than predicted. This latter observation may indicate a larger dispersion for the associated phonon near the $K$ point than expected from finite distance force modeling.Comment: 24 pages, 12 figures, 1 table; slight title change, Figures 1 and 11 added, reference added, presentation improved throughout documen