4,324 research outputs found
Partially-Static Data as Free Extension of Algebras
Partially-static data structures are a well-known technique for improving binding times. However, they are often defined in an ad-hoc manner, without a unifying framework to ensure full use of the equations associated with each operation. We present a foundational view of partially-static data structures as free extensions of algebras for suitable equational theories, i.e. the coproduct of an algebra and a free algebra in the category of algebras and their homomorphisms. By precalculating these free extensions, we construct a high-level library of partially-static data representations for common algebraic structures. We demonstrate our library with common use-cases from the literature: string and list manipulation, linear algebra, and numerical simplification.Supported by the European Research Council grant ‘events causality and symmetry Ð the next- generation semantics’; the Engineering and Physical Sciences Research Council grant EP/N007387/1 ‘Quantum computation as a programming language’, and a Balliol College Oxford Career Development Fellowshi
Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
We present some generalities of unfolded on-shell dynamics that are useful in
analysing the BMV conjecture for mixed-symmetry fields in constantly curved
backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra
modules generated from primary Weyl tensors of arbitrary mass and shape, and in
backgrounds with general values of the cosmological constant. We also discuss
the unfolded notion of local degrees of freedom in theories with and without
gravity and with and without massive deformation parameters, using the language
of Weyl zero-form modules and their duals.Comment: Corrected typos, references added, two figures, some remarks and two
subsections added for clarit
Modular nuclearity: A generally covariant perspective
A quantum field theory in its algebraic description may admit many irregular
states. So far, selection criteria to distinguish physically reasonable states
have been restricted to free fields (Hadamard condition) or to flat spacetimes
(e.g. Buchholz-Wichmann nuclearity). We propose instead to use a modular
l^p-condition, which is an extension of a strengthened modular nuclearity
condition to generally covariant theories.
The modular nuclearity condition was previously introduced in Minkowski
space, where it played an important role in constructive two dimensional
algebraic QFT's. We show that our generally covariant extension of this
condition makes sense for a vast range of theories, and that it behaves well
under causal propagation and taking mixtures. In addition we show that our
modular l^p-condition holds for every quasi-free Hadamard state of a free
scalar quantum field (regardless of mass or scalar curvature coupling).
However, our condition is not equivalent to the Hadamard condition.Comment: 42 page
The Ernst Equation on a Riemann Surface
The Ernst equation is formulated on an arbitrary Riemann surface.
Analytically, the problem reduces to finding solutions of the ordinary Ernst
equation which are periodic along the symmetry axis. The family of (punctured)
Riemann surfaces admitting a non-trivial Ernst field constitutes a ``partially
discretized'' subspace of the usual moduli space. The method allows us to
construct new exact solutions of Einstein's equations in vacuo with non-trivial
topology, such that different ``universes'', each of which may have several
black holes on its symmetry axis, are connected through necks bounded by cosmic
strings. We show how the extra topological degrees of freedom may lead to an
extension of the Geroch group and discuss possible applications to string
theory.Comment: 22 page
Design and Development of Software Tools for Bio-PEPA
This paper surveys the design of software tools for the Bio-PEPA process algebra. Bio-PEPA is a high-level language for modelling biological systems such as metabolic pathways and other biochemical reaction networks. Through providing tools for this modelling language we hope to allow easier use of a range of simulators and model-checkers thereby freeing the modeller from the responsibility of developing a custom simulator for the problem of interest. Further, by providing mappings to a range of different analysis tools the Bio-PEPA language allows modellers to compare analysis results which have been computed using independent numerical analysers, which enhances the reliability and robustness of the results computed.
A Survey of Languages for Specifying Dynamics: A Knowledge Engineering Perspective
A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machine
Thermodynamics of Higher Spin Black Holes in AdS
We discuss the thermodynamics of recently constructed three-dimensional
higher spin black holes in SL(N,R)\times SL(N,R) Chern-Simons theory with
generalized asymptotically-anti-de Sitter boundary conditions. From a
holographic perspective, these bulk theories are dual to two-dimensional CFTs
with W_N symmetry algebras, and the black hole solutions are dual to thermal
states with higher spin chemical potentials and charges turned on. Because the
notion of horizon area is not gauge-invariant in the higher spin theory, the
traditional approaches to the computation of black hole entropy must be
reconsidered. One possibility, explored in the recent literature, involves
demanding the existence of a partition function in the CFT, and consistency
with the first law of thermodynamics. This approach is not free from
ambiguities, however, and in particular different definitions of energy result
in different expressions for the entropy. In the present work we show that
there are natural definitions of the thermodynamically conjugate variables that
follow from careful examination of the variational principle, and moreover
agree with those obtained via canonical methods. Building on this intuition, we
derive general expressions for the higher spin black hole entropy and free
energy which are written entirely in terms of the Chern-Simons connections, and
are valid for both static and rotating solutions. We compare our results to
other proposals in the literature, and provide a new and efficient way to
determine the generalization of the Cardy formula to a situation with higher
spin charges.Comment: 30 pages, PDFLaTeX; v2: typos corrected, explicit expressions for the
free energy adde
Topological features of massive bosons on two dimensional Einstein space-time
In this paper we tackle the problem of constructing explicit examples of
topological cocycles of Roberts' net cohomology, as defined abstractly by
Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum
field theory on the two dimensional Einstein cylinder. After deriving some
crucial results of the algebraic framework of quantization, we address the
problem of the construction of the topological cocycles. All constructed
cocycles lead to unitarily equivalent representations of the fundamental group
of the circle (seen as a diffeomorphic image of all possible Cauchy surfaces).
The construction is carried out using only Cauchy data and related net of local
algebras on the circle.Comment: 41 pages, title changed, minor changes, typos corrected, references
added. Accepted for publication in Ann. Henri Poincare
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