Several approaches can be used to estimate neural activity. The main differences between them concern the a priori information used and its sensitivity to high noise levels. Empirical mode decomposition (EMD) has been recently applied to electroencephalography EEG-based neural activity reconstruction to provide a priori time-frequency information to improve the estimation of neural activity. EMD has the specific ability to identify independent oscillatory modes in non-stationary signals with multiple oscillatory components. However, attempts to use EMD in EEG analysis have not yet provided optimal reconstructions, due to the intrinsic mode-mixing problem of EMD. Several studies have used single-channel analysis, whereas others have used multiple-channel analysis for other applications. Here, we present the results of multiple-channel analysis using multivariate empirical mode decomposition (MEMD) to reduce the mode-mixing problem and provide useful a priori time-frequency information for the reconstruction of neuronal activity using several low-density EEG electrode montages. The methods were evaluated using real and synthetic EEG data, in which the reconstructions were performed using the multiple sparse priors (MSP) algorithm with EEG electrode montages of 32, 16, and 8 electrodes. The quality of the source reconstruction was assessed using the Wasserstein metric. A comparison of the solutions without pre-processing and those after applying MEMD showed the source reconstructions to be improved using MEMD as a priori information for the low-density montages of 8 and 16 electrodes. The mean source reconstruction error on a real EEG dataset was reduced by 59.42 and 66.04% for the 8 and 16 electrode montages, respectively, and that on a simulated EEG with three active sources, by 87.31 and 31.45% for the same electrode montages.
High-density Electroencephalography (HD-EEG) has proven to be the EEG montage that estimates the neural activity inside the brain with highest accuracy. Multiple studies have reported the effect of electrode number on source localization for specific sources and specific electrode configurations. The electrodes for these configurations are often manually selected to uniformly cover the entire head, going from 32 to 128 electrodes, but electrode configurations are not often selected according to their contribution to estimation accuracy. In this work, an optimization-based study is proposed to determine the minimum number of electrodes that can be used and to identify the optimal combinations of electrodes that can retain the localization accuracy of HD-EEG reconstructions. This optimization approach incorporates scalp landmark positions of widely used EEG montages. In this way, a systematic search for the minimum electrode subset is performed for single- and multiple-source localization problems. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) combined with source reconstruction methods is used to formulate a multi-objective optimization problem that concurrently minimizes (1) the localization error for each source and (2) the number of required EEG electrodes. The method can be used for evaluating the source localization quality of low-density EEG systems (e.g. consumer-grade wearable EEG). We performed an evaluation over synthetic and real EEG datasets with known ground-truth. The experimental results show that optimal subsets with 6 electrodes can attain an equal or better accuracy than HD-EEG (with more than 200 channels) for a single source case. This happened when reconstructing a particular brain activity in more than 88% of the cases in synthetic signals and 63% in real signals, and in more than 88% and 73% of cases when considering optimal combinations with 8 channels. For a multiple-source case of three sources (only with synthetic signals), it was found that optimized combinations of 8, 12 and 16 electrodes attained an equal or better accuracy than HD-EEG with 231 electrodes in at least 58%, 76%, and 82% of cases respectively. Additionally, for such electrode numbers, lower mean errors and standard deviations than with 231 electrodes were obtained.
In nuclear safety analysis, it is very important to be able to simulate the different transients that can occur in a nuclear power plant with a very high accuracy. Although the best estimate codes can simulate the transients and provide realistic system responses, the use of nonexact models, together with assumptions and estimations, is a source of uncertainties which must be properly evaluated. This paper describes a Rod Ejection Accident (REA) simulated using the coupled code RELAP5/PARCSv2.7 with a perturbation on the cross-sectional sets in order to determine the uncertainties in the macroscopic neutronic information. The procedure to perform the uncertainty and sensitivity (U&S) analysis is a sampling-based method which is easy to implement and allows different procedures for the sensitivity analyses despite its high computational time. DAKOTA-Jaguar software package is the selected toolkit for the U&S analysis presented in this paper. The size of the sampling is determined by applying the Wilks’ formula for double tolerance limits with a 95% of uncertainty and with 95% of statistical confidence for the output variables. Each sample has a corresponding set of perturbations that will modify the cross-sectional sets used by PARCS. Finally, the intervals of tolerance of the output variables will be obtained by the use of nonparametric statistical methods.
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