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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Background and Purpose-Transcranial Doppler (TCD) can detect high-intensity transient signals (HITS) in the cerebralcirculation. HITS may correspond to artifacts or solid or gaseous emboli. The aim of this study was to develop an offline automated Doppler system allowing the classification of HITS. Methods-We studied 600 HITS in vivo, including 200 artifacts from normal subjects, 200 solid emboli from patients with symptomatic internal carotid artery stenosis, and 200 gaseous emboli in stroke patients with patent foramen ovale. The study was 2-fold, each part involving 300 HITS (100 of each type). The first 300 HITS (learning set) were used to construct an automated classification algorithm. The remaining 300 HITS (validation set) were used to check the validity of this algorithm. To classify HITS, we combined dual-gate TCD with a wavelet representation and compared it with the current "gold standard," the human experts. Results-A combination of the peak frequency of HITS and the time delay makes it possible to separate artifacts from emboli. On the validation set, we achieved a sensitivity of 97%, a specificity of 98%, a positive predictive value (PPV) of 99%, and a negative predictive value (NPV) of 94%. To distinguish between solid and gaseous emboli, where positive refers now to the solid emboli, we used the peak frequency, the relative power, and the envelope symmetry of HITS.On the validation set, we achieved a sensitivity of 89%, a specificity of 86%, a conditional PPV of 89%, and a conditional NPV of 89%. Conclusions-An

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