Linear LL-positive sets and their polar subspaces

In this paper, we define a Banach SNL space to be a Banach space with a certain kind of linear map from it into its dual, and we develop the theory of linear $L$-positive subsets of Banach SNL spaces with Banach SNL dual spaces. We use this theory to give simplified proofs of some recent results of Bauschke, Borwein, Wang and Yao, and also of the classical Brezis-Browder theorem.Comment: 11 pages. Notational changes since version

Quantum Phase Transitions in Bosonic Heteronuclear Pairing Hamiltonians

We explore the phase diagram of two-component bosons with Feshbach resonant pairing interactions in an optical lattice. It has been shown in previous work to exhibit a rich variety of phases and phase transitions, including a paradigmatic Ising quantum phase transition within the second Mott lobe. We discuss the evolution of the phase diagram with system parameters and relate this to the predictions of Landau theory. We extend our exact diagonalization studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising critical exponents for the longitudinal and transverse magnetic susceptibilities within the second Mott lobe. The numerical results for the ground state energy and transverse magnetization are in good agreement with exact solutions of the Ising model in the thermodynamic limit. We also provide details of the low-energy spectrum, as well as density fluctuations and superfluid fractions in the grand canonical ensemble.Comment: 11 pages, 14 figures. To appear in Phys. Rev.

Feshbach Resonance in Optical Lattices and the Quantum Ising Model

Motivated by experiments on heteronuclear Feshbach resonances in Bose mixtures, we investigate s-wave pairing of two species of bosons in an optical lattice. The zero temperature phase diagram supports a rich array of superfluid and Mott phases and a network of quantum critical points. This topology reveals an underlying structure that is succinctly captured by a two-component Landau theory. Within the second Mott lobe we establish a quantum phase transition described by the paradigmatic longitudinal and transverse field Ising model. This is confirmed by exact diagonalization of the 1D bosonic Hamiltonian. We also find this transition in the homonuclear case.Comment: 5 pages, 4 figure

Learning Visual Question Answering by Bootstrapping Hard Attention

Attention mechanisms in biological perception are thought to select subsets of perceptual information for more sophisticated processing which would be prohibitive to perform on all sensory inputs. In computer vision, however, there has been relatively little exploration of hard attention, where some information is selectively ignored, in spite of the success of soft attention, where information is re-weighted and aggregated, but never filtered out. Here, we introduce a new approach for hard attention and find it achieves very competitive performance on a recently-released visual question answering datasets, equalling and in some cases surpassing similar soft attention architectures while entirely ignoring some features. Even though the hard attention mechanism is thought to be non-differentiable, we found that the feature magnitudes correlate with semantic relevance, and provide a useful signal for our mechanism's attentional selection criterion. Because hard attention selects important features of the input information, it can also be more efficient than analogous soft attention mechanisms. This is especially important for recent approaches that use non-local pairwise operations, whereby computational and memory costs are quadratic in the size of the set of features.Comment: ECCV 201

Class struggles in America

https://stars.library.ucf.edu/prism/1082/thumbnail.jp

Tail States in Disordered Superconductors with Magnetic Impurities: the Unitarity Limit

When subject to a weak magnetic impurity distribution, the order parameter and quasi-particle energy gap of a weakly disordered bulk s-wave superconductor are suppressed. In the Born scattering limit, recent investigations have shown that `optimal fluctuations' of the random impurity potential can lead to the nucleation of `domains' of localised states within the gap region predicted by the conventional Abrikosov-Gor'kov mean-field theory, rendering the superconducting system gapless at any finite impurity concentration. By implementing a field theoretic scheme tailored to the weakly disordered system, the aim of the present paper is to extend this analysis to the consideration of magnetic impurities in the unitarity scattering limit. This investigation reveals that the qualitative behaviour is maintained while the density of states exhibits a rich structure.Comment: 18 pages AMSLaTeX (with LaTeX2e), 6 eps figure

Diseases of winter linseed : occurrence, effects and importance

In 1998, a survey of the incidence and severity of diseases was carried out on 30 crops of winter linseed at early flowering and again at crop maturity. Five crops each were selected in south west, east, east Midlands, west Midlands and north of England and from Scotland. Crops were predominantly cv. Oliver (90% crops), grown from certified seed (83%) and sown in September (97%). Pasmo (Mycosphaerella) was the most important disease, affecting leaves of 73% crops at early flowering and 90% crops at maturity. Powdery mildew (70% crops), Alternaria (30% crops) on leaves and Botrytis on capsules (70% crops) were also common. Regional differences were apparent for powdery mildew, which was present in all regions except the southwest, whilst Alternaria predominated in the Midlands. Half of the crops surveyed had received fungicide sprays, but this appeared to have made limited impact on disease severity. Pasmo is a new threat to UK linseed crops and this raises concerns about the threat it poses to spring linsee

Polaritons and Pairing Phenomena in Bose--Hubbard Mixtures

Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the problem of a two-band Bose--Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the non-trivial interplay between Mott insulating behavior and superfluidity. The model displays a global U(1) X U(1) symmetry which supports the coexistence of Mott insulating and superfluid phases, and yields a rich phase diagram with multicritical points. This symmetry property is shared by several other problems of current experimental interest, including two-component Bose gases in optical lattices, and the bosonic BEC-BCS crossover problem for atom-molecule mixtures induced by a Feshbach resonance. We corroborate our findings by numerical simulations.Comment: 4 pages, 3 figure

Critical States in Disordered Superconducting Films

When subject to a pair-breaking perturbation, the pairing susceptibility of a disordered superconductor exhibits substantial long-ranged mesoscopic fluctuations. Focusing on a thin film subject to a parallel magnetic field, it is proposed that the quantum phase transition to the bulk superconducting condensate may be preempted by the formation of a glass-like phase with multi-fractal correlations of a complex order parameter. Although not universal, we argue that such behavior may be a common feature of quantum critical phenomena in disordered environments.Comment: 7 pages, 1 eps figur