2,366 research outputs found
Nominal Logic Programming
Nominal logic is an extension of first-order logic which provides a simple
foundation for formalizing and reasoning about abstract syntax modulo
consistent renaming of bound names (that is, alpha-equivalence). This article
investigates logic programming based on nominal logic. We describe some typical
nominal logic programs, and develop the model-theoretic, proof-theoretic, and
operational semantics of such programs. Besides being of interest for ensuring
the correct behavior of implementations, these results provide a rigorous
foundation for techniques for analysis and reasoning about nominal logic
programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as
of July 23, 200
Fitting theories of nuclear binding energies
In developing theories of nuclear binding energy such as density-functional
theory, the effort required to make a fit can be daunting due to the large
number of parameters that may be in the theory and the large number of nuclei
in the mass table. For theories based on the Skyrme interaction, the effort can
be reduced considerably by using the singular value decomposition to reduce the
size of the parameter space. We find that the sensitive parameters define a
space of dimension four or so, and within this space a linear refit is adequate
for a number of Skyrme parameters sets from the literature. We do not find
marked differences in the quality of the fit between the SLy4, the Bky4 and SkP
parameter sets. The r.m.s. residual error in even-even nuclei is about 1.5 MeV,
half the value of the liquid drop model. We also discuss an alternative norm
for evaluating mass fits, the Chebyshev norm. It focuses attention on the cases
with the largest discrepancies between theory and experiment. We show how it
works with the liquid drop model and make some applications to models based on
Skyrme energy functionals. The Chebyshev norm seems to be more sensitive to new
experimental data than the root-mean-square norm. The method also has the
advantage that candidate improvements to the theories can be assessed with
computations on smaller sets of nuclei.Comment: 17 pages and 4 figures--version encorporates referee's comment
Tropical range extension for the temperate, endemic South-Eastern Australian Nudibranch Goniobranchus splendidus (Angas, 1864)
In contrast to many tropical animals expanding southwards on the Australian coast concomitant with climate change, here we report a temperate endemic newly found in the tropics. Chromodorid nudibranchs are bright, colourful animals that rarely go unnoticed by divers and underwater photographers. The discovery of a new population, with divergent colouration is therefore significant. DNA sequencing confirms that despite departures from the known phenotypic variation, the specimen represents northern Goniobranchus splendidus and not an unknown close relative. Goniobranchus tinctorius represents the sister taxa to G. splendidus. With regard to secondary defences, the oxygenated terpenes found previously in this specimen are partially unique but also overlap with other G. splendidus from southern Queensland (QLD) and New South Wales (NSW). The tropical specimen from Mackay contains extracapsular yolk like other G. splendidus. This previously unknown tropical population may contribute selectively advantageous genes to cold-water species threatened by climate change. Competitive exclusion may explain why G. splendidus does not strongly overlap with its widespread sister taxon
Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices
Super-resolution is a fundamental task in imaging, where the goal is to
extract fine-grained structure from coarse-grained measurements. Here we are
interested in a popular mathematical abstraction of this problem that has been
widely studied in the statistics, signal processing and machine learning
communities. We exactly resolve the threshold at which noisy super-resolution
is possible. In particular, we establish a sharp phase transition for the
relationship between the cutoff frequency () and the separation ().
If , our estimator converges to the true values at an inverse
polynomial rate in terms of the magnitude of the noise. And when no estimator can distinguish between a particular pair of
-separated signals even if the magnitude of the noise is exponentially
small.
Our results involve making novel connections between {\em extremal functions}
and the spectral properties of Vandermonde matrices. We establish a sharp phase
transition for their condition number which in turn allows us to give the first
noise tolerance bounds for the matrix pencil method. Moreover we show that our
methods can be interpreted as giving preconditioners for Vandermonde matrices,
and we use this observation to design faster algorithms for super-resolution.
We believe that these ideas may have other applications in designing faster
algorithms for other basic tasks in signal processing.Comment: 19 page
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Negative thermal expansion of MgB in the superconducting state and anomalous behavior of the bulk Gr\"uneisen function
The thermal expansion coefficient of MgB is revealed to change
from positive to negative on cooling through the superconducting transition
temperature . The Gr\"uneisen function also becomes negative at
followed by a dramatic increase to large positive values at low temperature.
The results suggest anomalous coupling between superconducting electrons and
low-energy phonons.Comment: 5 figures. submitted to Phys. Rev. Let
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