Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

A simple abstraction of arrays and maps by program translation

We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,.. .). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the " Dutch flag " algorithm

High-pressure annealing of a prestructured nanocrystalline precursor to obtain tetragonal and orthorhombic polymorphs of Hf3N4

Transition metal nitrides containing metal ions in high oxidation states are a significant goal for the discovery of new families of semiconducting materials. Most metal nitride compounds prepared at high temperature and high pressure from the elements have metallic bonding. However amorphous or nanocrystalline compounds can be prepared via metal-organic chemistry routes giving rise to precursors with a high nitrogen:metal ratio. Using X-ray diffraction in parallel with high pressure laser heating in the diamond anvil cell this work highlights the possibility of retaining the composition and structure of a metastable nanocrystalline precursor under high pressure-temperature conditions. Specifically, a nanocrystalline Hf3N4 with a tetragonal defect-fluorite structure can be crystallized under high-P,T conditions. Increasing the pressure and temperature of crystallization leads to the formation of a fully recoverable orthorhombic (defect cottunite-structured) polymorph. This approach identifies a novel class of pathways to the synthesis of new crystalline nitrogen-rich transition metal nitrides

Does current UK research address priorities in palliative and end-of-life care?

The Palliative and end of life care Priority Setting Partnership uncovered 83 unanswered research questions. Florence Todd Fordham, Bridget Candy, Stevie McMillan and Sabine Best show that, as current UK research starts to address some of these questions, UK open grant data have the potential to encourage collaboratio

Properties of the superconducting state in a two-band model

Eliashberg theory is used to investigate the range of thermodynamic properties possible within a two-band model for s-wave superconductivity and to identify signatures of its two-band nature. We emphasize dimensionless BCS ratios (those for the energy gaps, the specific heat jump and the negative of its slope near Tc, the thermodynamic critical field Hc(0), and the normalized slopes of the critical field and the penetration depth near Tc), which are no longer universal even in weak coupling. We also give results for temperature-dependent quantities, such as the penetration depth and the energy gap. Results are presented both for microscopic parameters appropriate to MgB2 and for variations away from these. Strong coupling corrections are identified and found to be significant. Analytic formulas are provided which show the role played by the anisotropy in coupling in some special limits. Particular emphasis is placed on small interband coupling and on the opposite limit of no diagonal coupling. The effect of impurity scattering is considered, particularly for the interband case.Comment: 20 pages, 14 figures, final version accepted in PR

Non-Universal Fractional Quantum Hall States in a Quantum wire

The ground state as well as low-lying excitations in a 2D electron system in strong magnetic fields and a parabolic potential is investigated by the variational Monte Calro method. Trial wave functions analogous to the Laughlin state are used with the power-law exponent as the variational parameter. Finite size scaling of the excitation energy shows that the correlation function at long distance is characterized by anon-universal exponent in sharp contrast to the standard Laughlin state.The Laughlin-type state becomes unstable depending on strength of the confining potential.Comment: 10 pages, REVTE

Temperature-tuning of near-infrared monodisperse quantum dot solids at 1.5 um for controllable Forster energy transfer

We present the first time-resolved cryogenic observations of Forster energy transfer in large, monodisperse lead sulphide quantum dots with ground state transitions near 1.5 um (0.83 eV), in environments from 160 K to room temperature. The observed temperature-dependent dipole-dipole transfer rate occurs in the range of (30-50 ns)^(-1), measured with our confocal single-photon counting setup at 1.5 um wavelengths. By temperature-tuning the dots, 94% efficiency of resonant energy transfer can be achieved for donor dots. The resonant transfer rates match well with proposed theoretical models