Nonrandom variability in respiratory cycle parameters of humans during stage 2 sleep

We analyzed breath-to-breath inspiratory time (TI), expiratory time (TE), inspiratory volume (VI), and minute ventilation (Vm) from 11 normal subjects during stage 2 sleep. The analysis consisted of 1) fitting first- and second-order autoregressive models (AR1 and AR2) and 2) obtaining the power spectra of the data by fast-Fourier transform. For the AR2 model, the only coefficients that were statistically different from zero were the average alpha 1 (a1) for TI, VI, and Vm (a1 = 0.19, 0.29, and 0.15, respectively). However, the power spectra of all parameters often exhibited peaks at low frequency (less than 0.2 cycles/breath) and/or at high frequency (greater than 0.2 cycles/breath), indicative of periodic oscillations. After accounting for the corrupting effects of added oscillations on the a1 estimates, we conclude that 1) breath-to-breath fluctuations of VI, and to a lesser extent TI and Vm, exhibit a first-order autoregressive structure such that fluctuations of each breath are positively correlated with those of immediately preceding breaths and 2) the correlated components of variability in TE are mostly due to discrete high- and/or low-frequency oscillations with no underlying autoregressive structure. We propose that the autoregressive structure of VI, TI, and Vm during spontaneous breathing in stage 2 sleep may reflect either a central neural mechanism or the effects of noise in respiratory chemical feedback loops; the presence of low-frequency oscillations, seen more often in Vm, suggests possible instability in the chemical feedback loops. Mechanisms of high-frequency periodicities, seen more often in TE, are unknown.     

Heart rate variability signal processing: A quantitative approach as an aid to diagnosis in cardiovascular pathologies

The heart rate variability (HRV) signal carries important information about the systems controlling heat rate and blood pressure, mainly elicited by autonomic nervous system (sympathetic and parasympathetic) controls. The present paper illustrates methods of HRV signal processing by using autoregressive (AR) modeling and power spectral density estimate. The information enhanced in this way seems to be particularly sensitive in discriminating various cardiovascular pathologies (hypertension, myocardial infarction, diabetic neuropathy, etc.). This method provides a simple non-invasive analysis, based on the processing of spontaneous oscillations in heart rate. Particular emphasis is directed to the algorithms used and to their direct application by using proper computerized techniques: only a few paradigmatical examples will be illustrated as preliminary results.     

Short-window spectral analysis using AMVAR and multitaper methods: a comparison

We compare two popular methods for estimating the power spectrum from short data windows, namely the adaptive multivariate autoregressive (AMVAR) method and the multitaper method. By analyzing a simulated signal (embedded in a background Ornstein–Uhlenbeck noise process) we demonstrate that the AMVAR method performs better at detecting short bursts of oscillations compared to the multitaper method. However, both methods are immune to jitter in the temporal location of the signal. We also show that coherence can still be detected in noisy bivariate time series data by the AMVAR method even if the individual power spectra fail to show any peaks. Finally, using data from two monkeys performing a visuomotor pattern discrimination task, we demonstrate that the AMVAR method is better able to determine the termination of the beta oscillations when compared to the multitaper method.     

Estimation of changes in instantaneous aortic blood flow by the analysis of arterial blood pressure

The purpose of this study was to introduce and validate a new algorithm to estimate instantaneous aortic blood flow (ABF) by mathematical analysis of arterial blood pressure (ABP) waveforms. The algorithm is based on an autoregressive with exogenous input (ARX) model. We applied this algorithm to diastolic ABP waveforms to estimate the autoregressive model coefficients by requiring the estimated diastolic flow to be zero. The algorithm incorporating the coefficients was then applied to the entire ABP signal to estimate ABF. The algorithm was applied to six Yorkshire swine data sets over a wide range of physiological conditions for validation. Quantitative measures of waveform shape (standard deviation, skewness, and kurtosis), as well as stroke volume and cardiac output from the estimated ABF, were computed. Values of these measures were compared with those obtained from ABF waveforms recorded using a Transonic aortic flow probe placed around the aortic root. The estimation errors were compared with those obtained using a windkessel model. The ARX model algorithm achieved significantly lower errors in the waveform measures, stroke volume, and cardiac output than those obtained using the windkessel model (P < 0.05).     

Bayesian time-varying autoregressive models of COVID-19 epidemics

The COVID-19 pandemic has highlighted the importance of reliable statistical models which, based on the available data, can provide accurate forecasts and impact analysis of alternative policy measures. Here we propose Bayesian time-dependent Poisson autoregressive models that include time-varying coefficients to estimate the effect of policy covariates on disease counts. The model is applied to the observed series of new positive cases in Italy and in the United States. The results suggest that our proposed models are capable of capturing nonlinear growth of disease counts. We also find that policy measures and, in particular, closure policies and the distribution of vaccines, lead to a significant reduction in disease counts in both countries.     

Analysis of the Temporal Organization of Sleep Spindles in the Human Sleep EEG Using a Phenomenological Modeling Approach

The sleep electroencephalogram (EEG) is characterized by typical oscillatory patterns such as sleep spindles and slow waves. Recently, we proposed a method to detect and analyze these patterns using linear autoregressive models for short (≈?1 s) data segments. We analyzed the temporal organization of sleep spindles and discuss to what extent the observed interevent intervals correspond to properties of stationary stochastic processes and whether additional slow processes, such as slow oscillations, have to be assumed. We have found evidence for such an additional slow process, most pronounced in sleep stage 2.     

Acoustical detection of coronary occlusions using neural networks

A nonlinear neural network classifier was applied to noninvasive acoustic detection of coronary artery disease; the classifier included a feature vector, derived from diastolic heart sounds, and a multi-layered network trained by the backpropagation. The feature vector is based on the linear prediction coefficients of the autoregressive method after an adaptive line enhancement method was used as the input pattern to the neural network. One hundred and twelve recordings (70 abnormal, 42 normal) were studied and the network was trained on a randomly chosen set of six abnormal and six normal patients. It was tested on a database consisting of 100 recordings to which it had not been exposed. The network correctly identified 50 of the 64 patients with coronary artery disease and 32 of the 36 patients without any coronary artery occlusions. These results showed that this neural network is capable of distinguishing normal patients from abnormal patients. In addition, the diagnostic capability of this approach is much better than any other available noninvasive approach.     

Quantifying Intracellular Particle Flows by DIC Object Tracking

Label-free imaging techniques such as differential interference contrast (DIC) allow the observation of cells and large subcellular structures in their native, unperturbed states with minimal exposure to light. The development of robust computational image-analysis routines is vital to quantitative label-free imaging. The reliability of quantitative analysis of time-series microscopy data based on single-particle tracking relies on accurately detecting objects as distinct from the background, i.e., segmentation. Typical approaches to segmenting DIC images either involve converting images to those resembling phase contrast, mimicking the optics of DIC object formation, or using the morphological properties of objects. Here, we describe MATLAB based, single-particle tracking tool with a GUI for mobility analysis of objects from in vitro and in vivo DIC time-series microscopy. The tool integrates contrast enhancement with multiple modified Gaussian filters, automated threshold detection for segmentation and minimal distance-based two-dimensional single-particle tracking. We compare the relative performance of multiple filters and demonstrate the utility of the tool for DIC object tracking (DICOT). We quantify subcellular dynamics of a time series of Caenorhabditis elegans embryos in the one-celled stage by detecting birefringent yolk granules in the cytoplasm with high precision. The resulting two-dimensional map of oscillatory dynamics of granules quantifies the cytoplasmic flows driven by anaphasic spindle oscillations. The frequency of oscillations across the anterior-posterior (A-P) and transverse axes of the embryo correspond well with the reported frequency of spindle oscillations. We validate the quantitative accuracy of our method by tracking the in vitro diffusive mobility of micron-sized beads in glycerol solutions. Estimates of the diffusion coefficients of the granules are used to measure the viscosity of a dilution series of glycerol. Thus, our computational method is likely to be useful for both intracellular mobility and in vitro microrheology.     

Unequally spaced longitudinal data with AR(1) serial correlation

This paper discusses longitudinal data analysis when each subject is observed at different unequally spaced time points. Observations within subjects are assumed to be either uncorrelated or to have a continuous-time first-order autoregressive structure, possibly with observation error. The random coefficients are assumed to have an arbitrary between-subject covariance matrix. Covariates can be included in the fixed effects part of the model. Exact maximum likelihood estimates of the unknown parameters are computed using the Kalman filter to evaluate the likelihood, which is then maximized with a nonlinear optimization program. An example is presented where a large number of subjects are each observed at a small number of observation times. Hypothesis tests for selecting the best model are carried out using Wald's test on contrasts or likelihood ratio tests based on fitting full and restricted models.     

Two-stage biometric authentication method using thought activity brain waves

Brain waves are proposed as a biometric for verification of the identities of individuals in a small group. The approach is based on a novel two-stage biometric authentication method that minimizes both false accept error (FAE) and false reject error (FRE). These brain waves (or electroencephalogram (EEG) signals) are recorded while the user performs either one or several thought activities. As different individuals have different thought processes, this idea would be appropriate for individual authentication. In this study, autoregressive coefficients, channel spectral powers, inter-hemispheric channel spectral power differences, inter-hemispheric channel linear complexity and non-linear complexity (approximate entropy) values were used as EEG features by the two-stage authentication method with a modified four fold cross validation procedure. The results indicated that perfect accuracy was obtained, i.e. the FRE and FAE were both zero when the proposed method was tested on five subjects using certain thought activities. This initial study has shown that the combination of the two-stage authentication method with EEG features from thought activities has good potential as a biometric as it is highly resistant to fraud. However, this is only a pilot type of study and further extensive research with more subjects would be necessary to establish the suitability of the proposed method for biometric applications.     

Autoregressive models for capture-recapture data: a Bayesian approach

In this article, we incorporate an autoregressive time-series framework into models for animal survival using capture-recapture data. Researchers modeling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next. This may not be realistic for some populations. Using a Gibbs sampling approach, we can estimate covariate coefficients and autoregressive parameters for survival models. The procedure is illustrated with a waterfowl band recovery dataset for northern pintails (Anas acuta). The analysis shows that the second lag autoregressive coefficient is significantly less than 0, suggesting that there is a triennial relationship between survival probabilities and emphasizing that modeling survival rates as independent random variables may be unrealistic in some cases. Software to implement the methodology is available at no charge on the Internet.     

Deterministic and stochastic features of rhythmic human movement

The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method’s merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions.     

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture–recapture data

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.     

Comparison of different methods of time shift measurement in EEG

Digital signal processing techniques are often used for measurement of small time shifts between EEG signals. In our work we tested properties of linear cross-correlation and phase/coherence method. The last mentioned method was used in two versions. The first version used fast Fourier transform (FFT) algorithm and the second was based on autoregressive modeling with fixed or adaptive model order. Methods were compared on several testing signals mimicking real EEG signals. The accuracy index for each method was computed. Results showed that for long signal segments all methods bring comparably good results. Accuracy of FFT phase/coherence method significantly decreased when very short segments were used and also decreased with an increasing level of the additive noise. The best results were obtained with autoregressive version of phase/coherence. This method is more reliable and may be used with high accuracy even in very short signals segments and it is also resistant to additive noise.     

Yeast glycolytic oscillations that are not controlled by a single oscillophore: a new definition of oscillophore strength

Biochemical oscillations, such as glycolytic oscillations, are often believed to be caused by a single so-called ‘oscillophore’. The main characteristics of yeast glycolytic oscillations, such as frequency and amplitude, are however controlled by several enzymes. In this paper, we develop a method to quantify to which extent any enzyme determines the occurrence of oscillations. Principles extrapolated from metabolic control analysis are applied to calculate the control exerted by individual enzymes on the real and imaginary parts of the eigenvalues of the Jacobian matrix. We propose that the control exerted by an enzyme on the real part of the smallest eigenvalue, in terms of absolute value, quantifies to which extent that enzyme contributes to the emergence of instability. Likewise the control exerted by an enzyme on the imaginary part of complex eigenvalues may serve to quantify the extent to which that enzyme contributes to the tendency of the system to oscillate. The method was applied both to a core model and to a realistic model of yeast glycolytic oscillations. Both the control over stability and the control over oscillatory tendency were distributed among several enzymes, of which glucose transport, pyruvate decarboxylase and ATP utilization were the most important. The distributions of control were different for stability and oscillatory tendency, showing that control of instability does not imply control of oscillatory tendency nor vice versa. The control coefficients summed up to 1, suggesting the existence of a new summation theorem. These results constitute proof that glycolytic oscillations in yeast are not caused by a single oscillophore and provide a new, subtle, definition for the oscillophore strength of an enzyme.     

AN EIGENVECTOR METHOD FOR ESTIMATING PHYLOGENETIC INERTIA

We propose a new method to estimate and correct for phylogenetic inertia in comparative data analysis. The method, called phylogenetic eigenvector regression (PVR) starts by performing a principal coordinate analysis on a pairwise phylogenetic distance matrix between species. Traits under analysis are regressed on eigenvectors retained by a broken-stick model in such a way that estimated values express phylogenetic trends in data and residuals express independent evolution of each species. This partitioning is similar to that realized by the spatial autoregressive method, but the method proposed here overcomes the problem of low statistical performance that occurs with autoregressive method when phylogenetic correlation is low or when sample size is too small to detect it. Also, PVR is easier to perform with large samples because it is based on well-known techniques of multivariate and regression analyses. We evaluated the performance of PVR and compared it with the autoregressive method using real datasets and simulations. A detailed worked example using body size evolution of Carnivora mammals indicated that phylogenetic inertia in this trait is elevated and similarly estimated by both methods. In this example, Type I error at α = 0.05 of PVR was equal to 0.048, but an increase in the number of eigenvectors used in the regression increases the error. Also, similarity between PVR and the autoregressive method, defined by correlation between their residuals, decreased by overestimating the number of eigenvalues necessary to express the phylogenetic distance matrix. To evaluate the influence of cladogram topology on the distribution of eigenvalues extracted from the double-centered phylogenetic distance matrix, we analyzed 100 randomly generated cladograms (up to 100 species). Multiple linear regression of log transformed variables indicated that the number of eigenvalues extracted by the broken-stick model can be fully explained by cladogram topology. Therefore, the broken-stick model is an adequate criterion for determining the correct number of eigenvectors to be used by PVR. We also simulated distinct levels of phylogenetic inertia by producing a trend across 10, 25, and 50 species arranged in “comblike” cladograms and then adding random vectors with increased residual variances around this trend. In doing so, we provide an evaluation of the performance of both methods with data generated under different evolutionary models than tested previously. The results showed that both PVR and autoregressive method are efficient in detecting inertia in data when sample size is relatively high (more than 25 species) and when phylogenetic inertia is high. However, PVR is more efficient at smaller sample sizes and when level of phylogenetic inertia is low. These conclusions were also supported by the analysis of 10 real datasets regarding body size evolution in different animal clades. We concluded that PVR can be a useful alternative to an autoregressive method in comparative data analysis.     

Stabilometry as a diagnostic tool in clinical medicine.

Stabilomety, a method of measuring stability of stance or postural equilibrium in man, consists of transforming the mechanical oscillations of man''s "physiologic gravicentre" into electric signals, then amplifying, recording and analysing the signals. The frequency, duration and mean and maximum amplitudes of oscillations, and coefficients reflecting the influence of vision, differ in patients with various neurologic diseases and from values in healthy subjects. The method is highly sensitive and accurate, simple and rapid to use, lacks danger and discomfort and permits screening of a large number of people in a short time.     

High-frequency oscillations in a pulse wave signal and their relation to differential blood count leucocytes

High-frequency oscillations in a pulse wave signal in the range of 1-50 Hz and their relation to differential blood count leucocytes have been investigated. It is shown that the correlation coefficients grow in the frequency range of 1-12.5 Hz between high-frequency oscillations in a pulse wave signal and stab neutrophils, monocytes and segmented granulocytes. The procedure of smoothing the coefficients of harmonic variation has been proposed.