8,377 research outputs found
Diagnostic reasoning techniques for selective monitoring
An architecture for using diagnostic reasoning techniques in selective monitoring is presented. Given the sensor readings and a model of the physical system, a number of assertions are generated and expressed as Boolean equations. The resulting system of Boolean equations is solved symbolically. Using a priori probabilities of component failure and Bayes' rule, revised probabilities of failure can be computed. These will indicate what components have failed or are the most likely to have failed. This approach is suitable for systems that are well understood and for which the correctness of the assertions can be guaranteed. Also, the system must be such that changes are slow enough to allow the computation
Exact two-terminal reliability of some directed networks
The calculation of network reliability in a probabilistic context has long
been an issue of practical and academic importance. Conventional approaches
(determination of bounds, sums of disjoint products algorithms, Monte Carlo
evaluations, studies of the reliability polynomials, etc.) only provide
approximations when the network's size increases, even when nodes do not fail
and all edges have the same reliability p. We consider here a directed, generic
graph of arbitrary size mimicking real-life long-haul communication networks,
and give the exact, analytical solution for the two-terminal reliability. This
solution involves a product of transfer matrices, in which individual
reliabilities of edges and nodes are taken into account. The special case of
identical edge and node reliabilities (p and rho, respectively) is addressed.
We consider a case study based on a commonly-used configuration, and assess the
influence of the edges being directed (or not) on various measures of network
performance. While the two-terminal reliability, the failure frequency and the
failure rate of the connection are quite similar, the locations of complex
zeros of the two-terminal reliability polynomials exhibit strong differences,
and various structure transitions at specific values of rho. The present work
could be extended to provide a catalog of exactly solvable networks in terms of
reliability, which could be useful as building blocks for new and improved
bounds, as well as benchmarks, in the general case
Proof of finite surface code threshold for matching
The field of quantum computation currently lacks a formal proof of
experimental feasibility. Qubits are fragile and sophisticated quantum error
correction is required to achieve reliable quantum computation. The surface
code is a promising quantum error correction code, requiring only a physically
reasonable 2-D lattice of qubits with nearest neighbor interactions. However,
existing proofs that reliable quantum computation is possible using this code
assume the ability to measure four-body operators and, despite making this
difficult to realize assumption, require that the error rate of these operator
measurements is less than 10^-9, an unphysically low target. High error rates
have been proved tolerable only when assuming tunable interactions of strength
and error rate independent of distance, which is also unphysical. In this work,
given a 2-D lattice of qubits with only nearest neighbor two-qubit gates, and
single-qubit measurement, initialization, and unitary gates, all of which have
error rate p, we prove that arbitrarily reliable quantum computation is
possible provided p<7.4x10^-4, a target that many experiments have already
achieved. This closes a long-standing open problem, formally proving the
experimental feasibility of quantum computation under physically reasonable
assumptions.Comment: 5 pages, 4 figures, published versio
Exact solutions for the two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan
The two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the
generalized fan have been calculated exactly for arbitrary size as well as
arbitrary individual edge and node reliabilities, using transfer matrices of
dimension four at most. While the all-terminal reliabilities of these graphs
are identical, the special case of identical edge () and node ()
reliabilities shows that their two-terminal reliabilities are quite distinct,
as demonstrated by their generating functions and the locations of the zeros of
the reliability polynomials, which undergo structural transitions at
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