We used a variety of statistical measures to identify the point process that describes the maintained discharge of retinal ganglion cells (RGC's) and neurons in the lateral geniculate nucleus (LGN) of the cat. These measures are based on both interevent intervals and event counts and include the interevent-interval histogram, rescaled range analysis, the event-number histogram, the Fano factor, Allan factor, and the periodogram. In addition, we applied these measures to surrogate versions of the data, generated by random shuffling of the order of interevent intervals. The continuing statistics reveal 1/f-type fluctuations in the data (long-duration power-law correlation), which are not present in the shuffled data. Estimates of the fractal exponents measured for RGC- and their target LGN-spike trains are similar in value, indicating that the fractal behavior either is transmitted form one cell to the other or has a common origin. The gamma-r renewal process model, often used in the analysis of visual-neuron interevent intervals, describes certain short-term features of the RGC and LGN data reasonably well but fails to account for the long-duration correlation. We present a new model for visual-system nerve-spike firings: a gamma-r renewal process whose mean is modulated by fractal binomial noise. This fractal, doubly stochastic point process characterizes the statistical behavior of both RGC and LGN data sets remarkably well.

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A method for the automatic processing of the electrocardiogram (ECG) for the detection of obstructive apnoea is presented. The method screens nighttime single-lead ECG recordings for the presence of major sleep apnoea and provides a minute-by-minute analysis of disordered breathing. A large independently validated database of 70 ECG recordings acquired from normal subjects and subjects with obstructive and mixed sleep apnoea, each of approximately eight hours in duration, was used throughout the study. Thirty-five of these recordings were used for training and 35 retained for independent testing. A wide variety of features based on heartbeat intervals and an ECG-derived respiratory signal were considered. Classifiers based on linear and quadratic discriminants were compared. Feature selection and regularization of classifier parameters were used to optimize classifier performance. Results show that the normal recordings could be separated from the apnoea recordings with a 100% success rate and a minute-by-minute classification accuracy of over 90% is achievable.

Stochastic fractal signals can be characterized by the Hurst coefficient H, which is related to the exponents of various power-law statistics characteristic of these processes. Two techniques widely used to estimate H are spectral analysis and detrended fluctuation analysis (DFA). This paper examines the analytical link between these two measures and shows that they are related through an integral transform. Numerical simulations confirm this relationship for ideal synthesized fractal signals. Their performance as estimators of H is compared based on a mean square error criterion and found to be similar. DFA measures are derived for physiological signals of heartbeat R-R intervals through the integral transform of a spectral density estimate. These agree with directly calculated DFA estimates, indicating that the relationship holds for signals with nonideal fractal properties. It is concluded that DFA and spectral measures provide equivalent characterizations of stochastic signals with long-term correlation.

Respiration rate, heart rate, and heart rate variability (HRV) are some health metrics that are easily measured by consumer devices, which can potentially provide early signs of illness. Furthermore, mobile applications that accompany wearable devices can be used to collect relevant self-reported symptoms and demographic data. This makes consumer devices a valuable tool in the fight against the COVID-19 pandemic. Data on 2745 subjects diagnosed with COVID-19 (active infection, PCR test) were collected from May 21 to September 11, 2020, consisting of PCR positive tests conducted between February 16 and September 9. Considering male (female) participants, 11.9% (11.2%) of the participants were asymptomatic, 48.3% (47.8%) recovered at home by themselves, 29.7% (33.7%) recovered at home with the help of someone else, 9.3% (6.6%) required hospitalization without ventilation, and 0.5% (0.4%) required ventilation. There were a total of 21 symptoms reported, and the prevalence of symptoms varies by sex. Fever was present in 59.4% of male subjects and in 52% of female subjects. Based on self-reported symptoms alone, we obtained an AUC of 0.82 ± 0.017 for the prediction of the need for hospitalization. Based on physiological signs, we obtained an AUC of 0.77 ± 0.018 for the prediction of illness on a specific day. Respiration rate and heart rate are typically elevated by illness, while HRV is decreased. Measuring these metrics, taken in conjunction with molecular-based diagnostics, may lead to better early detection and monitoring of COVID-19.

Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and sequences of neuronal action potentials.A particularly useful statistic of these processes is the fractal exponent α, which may be estimated for any FSPP or FRSPP by using a variety of statistical methods. Simulated FSPPs and FRSPPs consistently exhibit bias in this fractal exponent, however, rendering the study and analysis of these processes non-trivial. In this paper, we examine the synthesis and estimation of FRSPPs by carrying out a systematic series of simulations for several different types of FRSPP over a range of design values for α. The discrepancy between the desired and achieved values of α is shown to arise from finite data size and from the character of the 1 Corresponding author.

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A cardiorespiratory-based automatic sleep staging system for subjects with sleep-disordered breathing is described. A simplified three-state system is used: Wakefulness (W), rapid eye movement (REM) sleep (R), and non-REM sleep (S). The system scores the sleep stages in standard 30-s epochs. A number of features associated with the epoch RR-intervals, an inductance plethysmography estimate of rib cage respiratory effort, and an electrocardiogram-derived respiration (EDR) signal were investigated. A subject-specific quadratic discriminant classifier was trained, randomly choosing 20% of the subject's epochs (in appropriate proportions of W, S and R) as the training data. The remaining 80% of epochs were presented to the classifier for testing. An estimated classification accuracy of 79% (Cohen's kappa value of 0.56) was achieved. When a similar subject-independent classifier was trained, using epochs from all other subjects as the training data, a drop in classification accuracy to 67% (kappa = 0.32) was observed. The subjects were further broken in groups of low apnoea-hypopnea index (AHI) and high AHI and the experiments repeated. The subject-specific classifier performed better on subjects with low AHI than high AHI; the performance of the subject-independent classifier is not correlated with AHI. For comparison an electroencephalograms (EEGs)-based classifier was trained utilizing several standard EEG features. The subject-specific classifier yielded an accuracy of 87% (kappa = 0.75), and an accuracy of 84% (kappa = 0.68) was obtained for the subject-independent classifier, indicating that EEG features are quite robust across subjects. We conclude that the cardiorespiratory signals provide moderate sleep-staging accuracy, however, features exhibit significant subject dependence which presents potential limits to the use of these signals in a general subject-independent sleep staging system.