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How to take into account dependence between the inputs: from interval computations to constraintrelated set computations, with potential applications to nuclear safety, bio and geosciences
 Proceedings of the Second International Workshop on Reliable Engineering Computing
"... In the traditional interval computations approach to handling uncertainty, we assume that we know the intervals xi of possible values of different parameters xi, and we assume that an arbitrary combination of these values is possible. In geometric terms, in the traditional interval computations appr ..."
Abstract

Cited by 12 (12 self)
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In the traditional interval computations approach to handling uncertainty, we assume that we know the intervals xi of possible values of different parameters xi, and we assume that an arbitrary combination of these values is possible. In geometric terms, in the traditional interval computations approach, the set of possible combinations x = (x1,..., xn) is a box x = x1 ×... × xn. In many reallife situations, in addition to knowing the intervals xi of possible values of each variable xi, we also know additional restrictions on the possible combinations of xi; in this case, the set x of possible values of x is a subset of the original box. For example, in addition to knowing the bounds on x1 and x2, we may also know that the difference between x1 and x2 cannot exceed a certain amount. Informally speaking, the parameters xi are no longer independent – in the sense that the set of possible values of xi may depend on the values of other parameters. In interval computations, we start with independent inputs; as we follow computations, we get dependent intermediate results: e.g., for x1 − x 2 1, the values of x1
Fast Quantum Algorithms for Handling Probabilistic and Interval Uncertainty
, 2003
"... this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time ..."
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Cited by 6 (6 self)
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this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time