4,725 research outputs found
The nuclear dimension of graph C*-algebras
Consider a graph C*-algebra C*(E) with a purely infinite ideal I (possibly
all of C*(E)) such that I has only finitely many ideals and C*(E)/I is
approximately finite dimensional. We prove that the nuclear dimension of C*(E)
is 1. If I has infinitely many ideals, then the nuclear dimension of C*(E) is
either 1 or 2.Comment: 24 pages; this version to appear in Adv. Mat
A Provenance Tracking Model for Data Updates
For data-centric systems, provenance tracking is particularly important when
the system is open and decentralised, such as the Web of Linked Data. In this
paper, a concise but expressive calculus which models data updates is
presented. The calculus is used to provide an operational semantics for a
system where data and updates interact concurrently. The operational semantics
of the calculus also tracks the provenance of data with respect to updates.
This provides a new formal semantics extending provenance diagrams which takes
into account the execution of processes in a concurrent setting. Moreover, a
sound and complete model for the calculus based on ideals of series-parallel
DAGs is provided. The notion of provenance introduced can be used as a
subjective indicator of the quality of data in concurrent interacting systems.Comment: In Proceedings FOCLASA 2012, arXiv:1208.432
A Homological Approach to Factorization
Mott noted a one-to-one correspondence between saturated multiplicatively
closed subsets of a domain D and directed convex subgroups of the group of
divisibility D. With this, we construct a functor between inclusions into
saturated localizations of D and projections onto partially ordered quotient
groups of G(D). We use this functor to construct many cochain complexes of
o-homomorphisms of po-groups. These complexes naturally lead to some
fundamental structure theorems and some natural homology theory that provide
insight into the factorization behavior of D.Comment: Submitted for publication 12/15/201
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