4,583 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
The Gap Function Phi(k,w) for a Two-leg t-J Ladder and the Pairing Interaction
The gap function phi(k,omega), determined from a Lanczos calculation for a
doped 2-leg t-J ladder, is used to provide insight into the spatial and
temporal structure of the pairing interaction. It implies that this interaction
is a local near-neighbor coupling which is retarded. The onset frequency of the
interaction is set by the energy of an S=1 magnon-hole-pair and it is spread
out over a frequency region of order the bandwith
Star cluster ecology IVa: Dissection of an open star cluster---photometry
The evolution of star clusters is studied using N-body simulations in which
the evolution of single stars and binaries are taken self-consistently into
account. Initial conditions are chosen to represent relatively young Galactic
open clusters, such as the Pleiades, Praesepe and the Hyades. The calculations
include a realistic mass function, primordial binaries and the external
potential of the parent Galaxy. Our model clusters are generally significantly
flattened in the Galactic tidal field, and dissolve before deep core collapse
occurs. The binary fraction decreases initially due to the destruction of soft
binaries, but increases later because lower mass single stars escape more
easily than the more massive binaries. At late times, the cluster core is quite
rich in giants and white dwarfs. There is no evidence for preferential
evaporation of old white dwarfs, on the contrary the formed white dwarfs are
likely to remain in the cluster. Stars tend to escape from the cluster through
the first and second Lagrange points, in the direction of and away from the
Galactic center. Mass segregation manifests itself in our models well within an
initial relaxation time. As expected, giants and white dwarfs are much more
strongly affected by mass segregation than main-sequence stars. Open clusters
are dynamically rather inactive. However, the combined effect of stellar mass
loss and evaporation of stars from the cluster potential drives its dissolution
on a much shorter timescale than if these effects are neglected. The often-used
argument that a star cluster is barely older than its relaxation time and
therefore cannot be dynamically evolved is clearly in error for the majority of
star clusters.Comment: reduced abstract, 33 pages (three separate color .jpg figures),
submitted to MNRA
Binary--single-star scattering VI. Automatic Determination of Interaction Cross Sections
Scattering encounters between binaries and single stars play a central role
in determining the dynamical evolution of a star cluster. In addition,
three-body scattering can give rise to many interesting exceptional objects:
merging can produce blue stragglers; exchange can produce binaries containing
millisecond pulsars in environments quite different from those in which the
pulsars were spun up; various types of X-ray binaries can be formed, and their
activity can be either shut off or triggered as a result of triple
interactions.
To date, all published results on three-body scattering have relied on human
guidance for determining the correct parameter range for the envelope within
which to perform Monte--Carlo scattering experiments. In this paper, we
describe the first fully automatic determination of cross sections and reaction
rates for binary--single-star scattering. Rather than relying on human
inspection of pilot calculations, we have constructed a feedback system that
ensures near-optimal coverage of parameter space while guaranteeing
completeness. We illustrate our approach with a particular example, in which we
describe the results of a three-body encounter between three main-sequence
stars of different masses. We provide total cross sections, as well as
branching ratios for the various different types of two-body mergers,
three-body mergers, and exchanges, both non-resonant and resonant. The
companion paper in this series, Paper VII, provides a full survey of
unequal-mass three-body scattering for hard binaries in the point-mass limit.Comment: 20 pages, TeX + 5 ps-figures, to appear in Ap
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