3,950 research outputs found
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
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