3,251 research outputs found
On Measuring Non-Recursive Trade-Offs
We investigate the phenomenon of non-recursive trade-offs between
descriptional systems in an abstract fashion. We aim at categorizing
non-recursive trade-offs by bounds on their growth rate, and show how to deduce
such bounds in general. We also identify criteria which, in the spirit of
abstract language theory, allow us to deduce non-recursive tradeoffs from
effective closure properties of language families on the one hand, and
differences in the decidability status of basic decision problems on the other.
We develop a qualitative classification of non-recursive trade-offs in order to
obtain a better understanding of this very fundamental behaviour of
descriptional systems
Nonlocality and information flow: The approach of Deutsch and Hayden
Deutsch and Hayden claim to have provided an account of quantum mechanics
which is particularly local, and which clarifies the nature of information
transmission in entangled quantum systems. In this paper, a perspicuous
description of their formalism is offered and their claim assessed. It proves
essential to distinguish, as Deutsch and Hayden do not, between two ways of
interpreting the formalism. On the first, conservative, interpretation, no
benefits with respect to locality accrue that are not already available on
either an Everettian or a statistical interpretation; and the conclusions
regarding information flow are equivocal. The second, ontological,
interpretation, offers a framework with the novel feature that global
properties of quantum systems are reduced to local ones; but no conclusions
follow concerning information flow in more standard quantum mechanics.Comment: 26 pages, LaTeX, uses amsmath; 4 .eps figure
Anytime Hierarchical Clustering
We propose a new anytime hierarchical clustering method that iteratively
transforms an arbitrary initial hierarchy on the configuration of measurements
along a sequence of trees we prove for a fixed data set must terminate in a
chain of nested partitions that satisfies a natural homogeneity requirement.
Each recursive step re-edits the tree so as to improve a local measure of
cluster homogeneity that is compatible with a number of commonly used (e.g.,
single, average, complete) linkage functions. As an alternative to the standard
batch algorithms, we present numerical evidence to suggest that appropriate
adaptations of this method can yield decentralized, scalable algorithms
suitable for distributed/parallel computation of clustering hierarchies and
online tracking of clustering trees applicable to large, dynamically changing
databases and anomaly detection.Comment: 13 pages, 6 figures, 5 tables, in preparation for submission to a
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Comparing test sets and criteria in the presence of test hypotheses and fault domains
A number of authors have considered the problem of comparing test sets and criteria. Ideally
test sets are compared using a preorder with the property that test set T1 is at least as strong
as T2 if whenever T2 determines that an implementation p is faulty, T1 will also determine that
p is faulty. This notion can be extended to test criteria. However, it has been noted that very
few test sets and criteria are comparable under such an ordering; instead orderings are based
on weaker properties such as subsumes. This paper explores an alternative approach, in which
comparisons are made in the presence of a test hypothesis or fault domain. This approach allows
strong statements about fault detecting ability to be made and yet for a number of test sets and
criteria to be comparable. It may also drive incremental test generation
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