Abstract-We demonstrate that it is possible to approximate the mutual information arbitrarily closely in probability by calculating relative frequencies on appropriate partitions and achieving conditional independence on the rectangles of which the partitions are made. Empirical results, including a comparison with maximum-likelihood estimators, are presented.

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Obstructive sleep apnea syndrome: effect of respiratory events and arousal on pulse wave amplitude measured by photoplethysmography in NREM sleep Abstract The objective of the study is to evaluate changes in finger pulse wave amplitude (PWA), as measured by photoplethysmography, and heart rate (HR), related to obstructive respiratory events and associated arousals during sleep. We analyzed 1,431 respiratory events in NREM sleep from 12 patients according to (1) the type of event (apnea, hypopnea, upper airway resistance episode) and (2) the duration of the associated EEG arousal (>10, 3-10, <3 s). Obstructive respiratory events provoked a relative bradycardia and vasodilation followed by HR increase and vasoconstriction. Relative PWA changes were significantly greater than HR changes. These responses differed significantly according to EEG-arousal grades (time×arousal interaction, p<0.0001), with longer arousals producing greater responses, but not to the type of respiratory event (time×event interaction, p = ns). Obstructive respiratory events provoke HR and PWA changes, the magnitude seemingly related to the intensity of central nervous activation, with PWA changes greater than HR. PWA obtained from a simple pulse oxymeter might be a valuable method to evaluate sleep fragmentation in sleep breathing disorders.

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