172,921 research outputs found
A Fair Power Domain for Actor Computations
This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Office of Naval Research of the Department of Defense under Contract N00014-75-C-0522.Actor-based languages feature extreme concurrency, allow side effects, and specify a form of fairness which permits unbounded nondeterminism. This makes it difficult to provide a satisfactory mathematical foundation for the semantics.
Due to the high degree of parallelism, an oracle semantics would be intractable. A weakest precondition semantics is out of the question because of the possibility of unbounded nondeterminism. The most attractive approach, fixed point semantics using power domains, has not been helpful because the available power domain constructions, although very general, seemed to deal inadequately with fairness.
By taking advantage of the relatively complex structure of the actor computation domain C, however, a power domain P(C) can be defined which is similar to Smyth's weak power domain but richer. Actor systems, which are collections of mutually recursive primitive actors with side effects, may be assigned meanings as least fixed points of their associated continuous functions acting on this power domain. Given a denotation A ∈ P(C), the set of possible complete computations of the actor system it represents is the set of least upper bounds of a certain set of "fair" chain in A, and this set of chains is definable within A itself without recourse to oracles or an auxiliary interpretive semantics.
It should be emphasized that this power domain construction is not nearly as generally applicable as those of the Plotkin [Pl] and Smyth [Sm], which can be used with any complete partial order. Fairness seems to require that the domain from which the power domain is to be constructed contain sufficient operational information.Department of Defense Office of Naval Researc
Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames
We consider the problem of designing spectral graph filters for the
construction of dictionaries of atoms that can be used to efficiently represent
signals residing on weighted graphs. While the filters used in previous
spectral graph wavelet constructions are only adapted to the length of the
spectrum, the filters proposed in this paper are adapted to the distribution of
graph Laplacian eigenvalues, and therefore lead to atoms with better
discriminatory power. Our approach is to first characterize a family of systems
of uniformly translated kernels in the graph spectral domain that give rise to
tight frames of atoms generated via generalized translation on the graph. We
then warp the uniform translates with a function that approximates the
cumulative spectral density function of the graph Laplacian eigenvalues. We use
this approach to construct computationally efficient, spectrum-adapted, tight
vertex-frequency and graph wavelet frames. We give numerous examples of the
resulting spectrum-adapted graph filters, and also present an illustrative
example of vertex-frequency analysis using the proposed construction
Generalized Satisfiability Problems via Operator Assignments
Schaefer introduced a framework for generalized satisfiability problems on
the Boolean domain and characterized the computational complexity of such
problems. We investigate an algebraization of Schaefer's framework in which the
Fourier transform is used to represent constraints by multilinear polynomials
in a unique way. The polynomial representation of constraints gives rise to a
relaxation of the notion of satisfiability in which the values to variables are
linear operators on some Hilbert space. For the case of constraints given by a
system of linear equations over the two-element field, this relaxation has
received considerable attention in the foundations of quantum mechanics, where
such constructions as the Mermin-Peres magic square show that there are systems
that have no solutions in the Boolean domain, but have solutions via operator
assignments on some finite-dimensional Hilbert space. We obtain a complete
characterization of the classes of Boolean relations for which there is a gap
between satisfiability in the Boolean domain and the relaxation of
satisfiability via operator assignments. To establish our main result, we adapt
the notion of primitive-positive definability (pp-definability) to our setting,
a notion that has been used extensively in the study of constraint satisfaction
problems. Here, we show that pp-definability gives rise to gadget reductions
that preserve satisfiability gaps. We also present several additional
applications of this method. In particular and perhaps surprisingly, we show
that the relaxed notion of pp-definability in which the quantified variables
are allowed to range over operator assignments gives no additional expressive
power in defining Boolean relations
On the commutativity of the powerspace constructions
We investigate powerspace constructions on topological spaces, with a
particular focus on the category of quasi-Polish spaces. We show that the upper
and lower powerspaces commute on all quasi-Polish spaces, and show more
generally that this commutativity is equivalent to the topological property of
consonance. We then investigate powerspace constructions on the open set
lattices of quasi-Polish spaces, and provide a complete characterization of how
the upper and lower powerspaces distribute over the open set lattice
construction
The Body In Question: Review Of The Anatomy Of Power: European Constructions Of The African Body By A. Butchart
Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte, 201
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