Cluster analysis of respiratory time series

We have investigated the respiratory control system with the hypothesis that, although many variables such as minute ventilation (V _I), tidal volume (V _T),breathing period (T _T),inspiratory duration (T _I),and exspiratory duration (T _E),may be observed, the controller functions more simply by manipulating only 2 or 3 of these. Thus, if tidal volume is the only independent variable, T _Ibeing determined by the off-switch threshold, these variables should have very similar time courses. Anesthetized dogs were subjected to CO₂ breathing and carotid sinus perfusion to stimulate both chemoreceptors. The time series of the variables V _I, V _T, T_T, T_Eand T _Ias well as P _{A CO 2}were determined on a breath by breath basis. Derived characteristics of these time series were compared using Cluster Analysis and the latent dimensionality of respiratory control determined by Factor Analysis. The characteristics of the time series clustered into 4 groups: magnitude (of the response), speed, variability and relative change. One respiratory factor accounted for 86% of the variance for the variability characteristics, 2 factors for magnitude (91%) and relative change (85%) and 3 factors for speed (89%). The respiratory variables were analysed for each of the 4 groups of characteristics with the following results: V _Tand T _I clustered together only for the magnitude and relative change characteristics where as T _Tand T _Eclustered closely for all four characteristics. One latent factor was associated with the [T _T-T_E]group and the other usually with P _{A CO 2}.Supported by USPHS 5t01 01919-05, NIH HL 12564 and GM 07033     

Autoregressive time series analysis via representatives

In any realization of an autoregressive time series there exist a few observations having a noticeable feature: they express the useful properties of the time series and, therefore, they represent the entire process. Such representative observations (or, simply, representatives) can be determined by an optimization procedure, provided that the absolute value criterion is used instead of the customary least squares. To achieve this, a special kind of optimization operator (optimator) which generate the parameters of the time series is considered. The concepts of strong and weak similarity of the time series are defined in terms of the representatives and sufficient conditions for both strong and weak similarity are derived. It is shown that there exists a subclass of strongly similar processes, say X, such that ordinary addition is a binary operation in X. An analogous result is shown to hold for weakly similar autoregressive processes. Some examples illustrating these results are given.     

Wavelet-based time series analysis of circadian rhythms

Analysis of circadian oscillations that exhibit variability in period or amplitude can be accomplished through wavelet transforms. Wavelet-based methods can also be used quite effectively to remove trend and noise from time series and to assess the strength of rhythms in different frequency bands, for example, ultradian versus circadian components in an activity record. In this article, we describe how to apply discrete and continuous wavelet transforms to time series of circadian rhythms, illustrated with novel analyses of 2 case studies involving mouse wheel-running activity and oscillations in PER2::LUC bioluminescence from SCN explants.     

林木生长的多维时间序列分析

利用多维时间序列分析方法,以影响杉木直径生长的五大主导气象要素作控制因子,建立杉木直径生长的ＣＡＲ模型,从而对杉木直径生长提前一年作预测,回验结果表明模型准确率很高,为林木生长预测预报提供了一种新方法．     

Spectral analysis of unequally spaced sampled time series

Abstract

The diurnal excretion patterns of several electrolytes and urea were studied in 5 freely moving rats on an elemental diet (Vivonex) administered either orally or as a continuous intragastric feeding; the lights were on from 07.00–19.00 h and off from 19.00–07.00 h. During continuous feeding the diurnal rhythms persisted, although the amplitude was lower than during oral feeding. The maximum excretion rates of potassium, phosphate and urea all coincided under both feeding regimens. The time of the maximum calcium excretion rate coincided with that of sodium during oral feeding but not during continuous feeding. During continuous feeding the maximum calcium excretion rate shifted from 04.00 to 10.00 h. The diurnal excretion of magnesium during continuous feeding was abolished, possibly as a result of the low calcium intake. From this study it can be concluded that duringcontinuous intragastric feeding all of the studied excretion patterns persist, with the exception of magnesium, which indicates that these rhythms are not merely the result of the intermittent intake of food and minerals.     

Nonlinear time series analysis of jerk congenital nystagmus

Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to recorded jerk CN waveforms, and also to simulated jerk waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the analysis were then interpreted within the framework of a generalised model of the unforced oculomotor system. This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems, rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test the first of these hypotheses. Action Editor: Peter Latham     

Extending nonlinear analysis to short ecological time series

Nonlinearity is important and ubiquitous in ecology. Though detectable in principle, nonlinear behavior is often difficult to characterize, analyze, and incorporate mechanistically into models of ecosystem function. One obvious reason is that quantitative nonlinear analysis tools are data intensive (require long time series), and time series in ecology are generally short. Here we demonstrate a useful method that circumvents data limitation and reduces sampling error by combining ecologically similar multispecies time series into one long time series. With this technique, individual ecological time series containing as few as 20 data points can be mined for such important information as (1) significantly improved forecast ability, (2) the presence and location of nonlinearity, and (3) the effective dimensionality (the number of relevant variables) of an ecological system.     

On-line estimation of the time constant of oxygen electrodes by time series analysis

Summary The time constant of an oxygen electrode was estimated on-line by fitting a first order autoregressive model to the normal process noise. The method allows the time constant to be determined under normal operating conditions, thus the effect of the outside liquid film can be accounted for. This has applications to the determination of K_La.     

Pergressive Fourier analysis of rapidly decaying oscillations in short time series

Abstract

A sample is used to demonstrate that with the aid of heuristic principles, based on the Pergressive Fourier Analysis, rapidly decaying oscillations can be identified in empirical graphs or data. The properties and advantages of this method are explained.     

Selecting EEG components using time series analysis in brain death diagnosis

In diagnosis of brain death for human organ transplant, EEG (electroencephalogram) must be flat to conclude the patient’s brain death but it has been reported that the flat EEG test is sometimes difficult due to artifacts such as the contamination from the power supply and ECG (electrocardiogram, the signal from the heartbeat). ICA (independent component analysis) is an effective signal processing method that can separate such artifacts from the EEG signals. Applying ICA to EEG channels, we obtain several separated components among which some correspond to the brain activities while others contain artifacts. This paper aims at automatic selection of the separated components based on time series analysis. In the flat EEG test in brain death diagnosis, such automatic component selection is helpful.     

Ecogeographic patterns of rabies in southern Ontario based on time series analysis

We describe a method based on time series analysis that divided the rabies enzootic area of southern Ontario into 13 regions using data collected at the township level, the smallest available geographical unit for Ontario (Canada). The intent was to discover ecogeographic patterns if such existed. For the period 1957-89, the quarterly time series of fox rabies cases for each of the 423 townships in the study area was correlated with the time series of its adjacent neighbors. Townships were then linked to adjacent townships provided the pair-wise correlations had significant correlation coefficients. This procedure produced 13 clusters that remained stable when additional lead/lag relationships between townships were examined. Furthermore, those clusters, which we then termed "rabies units," had different behaviors in terms of species distribution, persistence, and periodicity. Time series in adjacent units were not synchronous. We discuss how our findings influenced the rabies control program in Ontario, how they relate to recent findings about the distribution of fox rabies virus subtypes, and how they lend support for the role of metapopulation structulre in persistence of disease.