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Simplification of SymbolicNumerical Interval Expressions
 in Gloor, O. (Ed.): Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, ACM
, 1998
"... Although interval arithmetic is increasingly used in combination with computer algebra and other methods, both approaches  symbolicalgebraic and intervalarithmetic  are used separately. Implementing symbolic interval arithmetic seems not suitable due to the exponential growth in the "si ..."
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Cited by 5 (2 self)
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;size" of the endpoints. In this paper we propose a methodology for "true" symbolicalgebraic manipulations on symbolicnumerical interval expressions involving interval variables instead of symbolic intervals. Due to the better algebraic properties, resembling to classical analysis, and the containment
Abstract Simplification of SymbolicNumerical Interval Expressions ∗
"... Although interval arithmetic is increasingly used in combination with computer algebra and other methods, both approaches — symbolicalgebraic and intervalarithmetic — are used separately. Implementing symbolic interval arithmetic seems not suitable due to the exponential growth in the “size ” of t ..."
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” of the endpoints. In this paper we propose a methodology for “true ” symbolicalgebraic manipulations on symbolicnumerical interval expressions involving interval variables instead of symbolic intervals. Due to the better algebraic properties, resembling to classical analysis, and the containment
Least squares quantization in pcm.
 Bell Telephone Laboratories Paper
, 1982
"... AbstractIt has long been realized that in pulsecode modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as t ..."
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Cited by 1362 (0 self)
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conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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the convergence the more exact the approximation. • If the hidden nodes are binary, then thresholding the loopy beliefs is guaranteed to give the most probable assignment, even though the numerical value of the beliefs may be incorrect. This result only holds for nodes in the loop. In the maxproduct (or "
Hierarchical Modelling and Analysis for Spatial Data. Chapman and Hall/CRC,
, 2004
"... Abstract Often, there are two streams in statistical research one developed by practitioners and other by main stream statisticians. Development of geostatistics is a very good example where pioneering work under realistic assumptions came from mining engineers whereas it is only now that statisti ..."
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Cited by 442 (45 self)
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in There is no doubt that the availability of cheap and powerful computers has increased the interest in ML applications. With spatially correlated data, the maximization of the likelihood requires considerable computer power mainly for two numerical operations: matrix inversion and maximization in multidimensional
Numerical interval simulation: combined qualitative and quantitative simulation to bound behaviors of nonmonotonic systems
 In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence
, 1995
"... Models of complex physical systems often cannot be defined precisely, either because of lack of knowledge or because the system parameters change over time according to unknown phenomena. Such systems can be represented by semiquantitative models that combine both qualitative and quantitative knowl ..."
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Cited by 9 (0 self)
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knowledge. This paper presents Numerical Interval Simulation, a method that can produce tight predictions of systems involving nonmonotonic functions. We present a successful application of NIS to predict the behavior of a complex process at a BrazilianJapanese steel company. We claim that such capability
Strictly Proper Scoring Rules, Prediction, and Estimation
, 2007
"... Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F if he ..."
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Cited by 373 (28 self)
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Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F
From Numerical Intervals to Set Intervals (IntervalRelated Results Presented at the First International Workshop on Applications and Theory of Random Sets)
, 1996
"... image set or not, these pixels form the desired set (image) S 0 . In real life, however, measurements are never absolutely accurate; as a result, we still get a set of pixels S, but the location of each point from the observed set S may 1 be slightly different from its location in the (unknown) act ..."
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image set or not, these pixels form the desired set (image) S 0 . In real life, however, measurements are never absolutely accurate; as a result, we still get a set of pixels S, but the location of each point from the observed set S may 1 be slightly different from its location in the (unknown) actual set S 0 . 1.2 How to describe the relationship between the observed set and the actual set: Hausdorff distance If we know the upper bound " ? 0 on the distance between the actual and mapped locations, then we can formulate the relationship between the known approximate set S and the actual (unknown) set S 0 as follows: ffl each "mapped" point s (i.e., a point from the "mapped" set S) is "\Gammaclose to some "actual" point (i.e., to some point from S<
Modeling and Robust Deflection Control of Piezoelectric microActuators modelled by ZeroOrder Numerator Interval System
, 2011
"... Piezoelectric actuators have received an increasing attention these last years thanks to the high resolution of displacement, high force density and fast response time that can offer piezoelectric materials. However, piezoelectric actuators are highly sensitive to environmental disturbances and ty ..."
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microsystems. This paper aims to design loworder controller ensuring robust performances for piezoelectric actuators. In the approach, first we use a linear model with uncertain parameters that are bounded by interval numbers. Then, on the basis of the interval model and the required performances, a low order
Spherical Wavelets: Efficiently Representing Functions on the Sphere
, 1995
"... Wavelets have proven to be powerful bases for use in numerical analysis and signal processing. Their power lies in the fact that they only require a small number of coefficients to represent general functions and large data sets accurately. This allows compression and efficient computations. Classic ..."
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Cited by 286 (14 self)
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Wavelets have proven to be powerful bases for use in numerical analysis and signal processing. Their power lies in the fact that they only require a small number of coefficients to represent general functions and large data sets accurately. This allows compression and efficient computations
Results 1  10
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4,825