204,820 research outputs found
Refinement via interpretation
Traditional notions of refinement of algebraic specifications, based on signature morphisms, are often too rigid to capture a number of relevant transformations in the context of software design, reuse and adaptation. This paper proposes an alternative notion of specification refinement, building on recent work on logic interpretation. The concept is discussed, its theory partially developed, its use illustrated through a number of examples.This research was supported by FCT (the Portuguese Foundation for Science and Technology) under contracts PTDC/EIA/73252/2006, at Minho University, as well as PTDC/MAT/68723/2006 and the Unidade de Investigacao Matematica e Aplicaoes of University of Aveiro
Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
We point out that the entropy of (near) extremal black holes can be
interpreted as the entanglement entropy of dual conformal quantum mechanics via
AdS2/CFT1. As an explicit example, we study near extremal BTZ black holes and
derive this claim from AdS3/CFT2. We also analytically compute the entanglement
entropy in the two dimensional CFT of a free Dirac fermion compactified on a
circle at finite temperature. From this result, we clarify the relation between
the thermal entropy and entanglement entropy, which is essential for the
entanglement interpretation of black hole entropy.Comment: LaTeX, 32 pages, 7 figures; refinement in the organizatio
Set-free Markov state model building
Molecular dynamics (MD) simulations face challenging problems since the time
scales of interest often are much longer than what is possible to simulate;
and even if sufficiently long simulations are possible the complex nature of
the resulting simulation data makes interpretation difficult. Markov State
Models (MSMs) help to overcome these problems by making experimentally
relevant time scales accessible via coarse grained representations that also
allow for convenient interpretation. However, standard set-based MSMs exhibit
some caveats limiting their approximation quality and statistical
significance. One of the main caveats results from the fact that typical MD
trajectories repeatedly re-cross the boundary between the sets used to build
the MSM which causes statistical bias in estimating the transition
probabilities between these sets. In this article, we present a set-free
approach to MSM building utilizing smooth overlapping ansatz functions instead
of sets and an adaptive refinement approach. This kind of meshless
discretization helps to overcome the recrossing problem and yields an adaptive
refinement procedure that allows us to improve the quality of the model while
exploring state space and inserting new ansatz functions into the MSM
Grope cobordism of classical knots
We explain the notion of a grope cobordism between two knots in a 3-manifold.
Each grope cobordism has a type that can be described by a rooted unitrivalent
tree. By filtering these trees in different ways, we show how the
Goussarov-Habiro approach to finite type invariants of knots is closely related
to our notion of grope cobordism. Thus our results can be viewed as a geometric
interpretation of finite type invariants.
An interesting refinement we study are knots modulo symmetric grope cobordism
in 3-space. On one hand this theory maps onto the usual Vassiliev theory and on
the other hand it maps onto the Cochran-Orr-Teichner filtration of the knot
concordance group, via symmetric grope cobordism in 4-space. In particular, the
graded theory contains information on finite type invariants (with degree h
terms mapping to Vassiliev degree 2^h), Blanchfield forms or S-equivalence at
h=2, Casson-Gordon invariants at h=3, and for h=4 one has the new von Neumann
signatures of a knot.Comment: Final version. To appear in Topology. See
http://www.math.cornell.edu/~jconant/pagethree.html for a PDF file with
better figure qualit
Refinement by interpretation in {\pi}-institutions
The paper discusses the role of interpretations, understood as multifunctions
that preserve and reflect logical consequence, as refinement witnesses in the
general setting of pi-institutions. This leads to a smooth generalization of
the refinement-by-interpretation approach, recently introduced by the authors
in more specific contexts. As a second, yet related contribution a basis is
provided to build up a refinement calculus of structured specifications in and
across arbitrary pi-institutions.Comment: In Proceedings Refine 2011, arXiv:1106.348
Bounded Refinement Types
We present a notion of bounded quantification for refinement types and show
how it expands the expressiveness of refinement typing by using it to develop
typed combinators for: (1) relational algebra and safe database access, (2)
Floyd-Hoare logic within a state transformer monad equipped with combinators
for branching and looping, and (3) using the above to implement a refined IO
monad that tracks capabilities and resource usage. This leap in expressiveness
comes via a translation to "ghost" functions, which lets us retain the
automated and decidable SMT based checking and inference that makes refinement
typing effective in practice.Comment: 14 pages, International Conference on Functional Programming, ICFP
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