Time-distributed effect of exposure and infectious outbreaks

Extreme weather affects the timing and intensity of infectious outbreaks, the resurgence and redistribution of infections, and it causes disturbances in human-environment interactions. Environmental stressors with high thermoregulatory demands require susceptible populations to undergo physiological adaptive processes potentially compromising immune function and increasing susceptibility to infection. In assessing associations between environmental exposures and infectious diseases, failure to account for a latent period between time of exposure and time of disease manifestation may lead to severe underestimation of the effects. In a population, health effects of an episode of exposure are distributed over a range of time lags. To consider such time-distributed lags is a challenging task given that the length of a latent period varies from hours to months and depends on the type of pathogen, individual susceptibility to the pathogen, dose of exposure, route of transmission, and many other factors. The two main objectives of this communication are to introduce an approach to modeling time-distributed effect of exposures to infection cases and to demonstrate this approach in an analysis of the association between high ambient temperature and daily incidence of enterically transmitted infections. The study is supplemented with extensive simulations to examine model sensitivity to response magnitude, exposure frequency, and extent of latent period.

Multiscale complex network of protein conformational fluctuations in single-molecule time series

Conformational dynamics of proteins can be interpreted as itinerant motions as the protein traverses from one state to another on a complex network in conformational space or, more generally, in state space. Here we present a scheme to extract a multiscale state space network (SSN) from a single-molecule time series. Analysis by this method enables us to lift degeneracy--different physical states having the same value for a measured observable--as much as possible. A state or node in the network is defined not by the value of the observable at each time but by a set of subsequences of the observable over time. The length of the subsequence can tell us the extent to which the memory of the system is able to predict the next state. As an illustration, we investigate the conformational fluctuation dynamics probed by single-molecule electron transfer (ET), detected on a photon-by-photon basis. We show that the topographical features of the SSNs depend on the time scale of observation; the longer the time scale, the simpler the underlying SSN becomes, leading to a transition of the dynamics from anomalous diffusion to normal Brownian diffusion.

Time Series Forecasting Energy-efficient Organization of Wireless Sensor Networks

Due to their wide potential applications, wireless sensor networks have recently received tremendous attention. The strict energy constraints of sensor nodes result in the great challenges for energy efficiency. This paper investigates the energy efficiency problem and proposes an energy-efficient organization method with time series forecasting. The organization of wireless sensor networks is formulated for target tracking. Target model, multi-sensor model and energy model are defined accordingly. For the target tracking application, target localization is achieved by collaborative sensing with multi-sensor fusion. The historical localization results are utilized for adaptive target trajectory forecasting. Empirical mode decomposition is implemented to extract the inherent variation modes in the time series of a target trajectory. Future target position is derived from autoregressive moving average (ARMA) models, which forecast the decomposition components, respectively. Moreover, the energy-efficient organization method is presented to enhance the energy efficiency of wireless sensor networks. The sensor nodes implement sensing tasks according to the probability awakening in a distributed manner. When the sensor nodes transfer their observations to achieve data fusion, the routing scheme is obtained by ant colony optimization. Thus, both the operation and communication energy consumption can be minimized. Experimental results verify that the combination of the ARMA model and empirical mode decomposition can estimate the target position efficiently and energy saving is achieved by the proposed organization method in wireless sensor networks.

Procedures for numerical analysis of circadian rhythms

This article reviews various procedures used in the analysis of circadian rhythms at the populational, organismal, cellular and molecular levels. The procedures range from visual inspection of time plots and actograms to several mathematical methods of time series analysis. Computational steps are described in some detail, and additional bibliographic resources and computer programs are listed.

The spectra and periodograms of anti-correlated discrete fractional Gaussian noise

Discrete fractional Gaussian noise (dFGN) has been proposed as a model for interpreting a wide variety of physiological data. The form of actual spectra of dFGN for frequencies near zero varies as f(1-2H), where 0 < H < 1 is the Hurst coefficient; however, this form for the spectra need not be a good approximation at other frequencies. When H approaches zero, dFGN spectra exhibit the 1 - 2H power-law behavior only over a range of low frequencies that is vanishingly small. When dealing with a time series of finite length drawn from a dFGN process with unknown H, practitioners must deal with estimated spectra in lieu of actual spectra. The most basic spectral estimator is the periodogram. The expected value of the periodogram for dFGN with small H also exhibits non-power-law behavior. At the lowest Fourier frequencies associated with a time series of N values sampled from a dFGN process, the expected value of the periodogram for H approaching zero varies as f(0) rather than f(1-2H). For finite N and small H, the expected value of the periodogram can in fact exhibit a local power-law behavior with a spectral exponent of 1 - 2H at only two distinct frequencies.

Evaluating maximum likelihood estimation methods to determine the Hurst coeficient

A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5 < H <1, characterizes long memory time series by quantifying the rate of decay of the autocorrelation function. S-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 2(10). A modified method is proposed to correct for this bias. It gives reliable estimates of H for both fd and fGn processes of length greater than or equal to 2(11).

Low doses of ethanol reduce evidence for nonlinear structure in brain activity

Recent theories of the effects of ethanol on the brain have focused on its direct actions on neuronal membrane proteins. However, neuromolecular mechanisms whereby ethanol produces its CNS effects in low doses typically used by social drinkers (e.g., 2-3 drinks, 10-25 mM, 0.05-0.125 gm/dl) remain less well understood. We propose the hypothesis that ethanol may act by introducing a level of randomness or "noise" in brain electrical activity. We investigated the hypothesis by applying a battery of tests originally developed for nonlinear time series analysis and chaos theory to EEG data collected from 32 men who had participated in an ethanol/placebo challenge protocol. Because nonlinearity is a prerequisite for chaos and because we can detect nonlinearity more reliably than chaos, we concentrated on a series of measures that quantitated different aspects of nonlinearity. For each of these measures the method of surrogate data was used to assess the significance of evidence for nonlinear structure. Significant nonlinear structure was found in the EEG as evidenced by the measures of time asymmetry, determinism, and redundancy. In addition, the evidence for nonlinear structure in the placebo condition was found to be significantly greater than that for ethanol. Nonlinear measures, but not spectral measures, were found to correlate with a subject's overall feeling of intoxication. These findings are consistent with the notion that ethanol may act by introducing a level of randomness in neuronal processing as assessed by EEG nonlinear structure.

Evaluation of the dispersional analysis method for fractal time series

Fractal signals can be characterized by their fractal dimension plus some measure of their variance at a given level of resolution. The Hurst exponent, H, is < 0.5 for rough anticorrelated series, > 0.5 for positively correlated series, and = 0.5 for random, white noise series. Several methods are available: dispersional analysis, Hurst rescaled range analysis, autocorrelation measures, and power special analysis. Short data sets are notoriously difficult to characterize; research to define the limitations of the various methods is incomplete. This numerical study of fractional Brownian noise focuses on determining the limitations of the dispersional analysis method, in particular, assessing the effects of signal length and of added noise on the estimate of the Hurst coefficient, H, (which ranges from 0 to 1 and is 2 - D, where D is the fractal dimension). There are three general conclusions: (i) pure fractal signals of length greater than 256 points give estimates of H that are biased but have standard deviations less than 0.1; (ii) the estimates of H tend to be biased toward H = 0.5 at both high H (> 0.8) and low H (< 0.5), and biases are greater for short time series than for long; and (iii) the addition of Gaussian noise (H = 0.5) degrades the signals: for those with negative correlation (H < 0.5) the degradation is great, the noise has only mild degrading effects on signals with H > 0.6, and the method is particularly robust for signals with high H and long series, where even 100% noise added has only a few percent effect on the estimate of H. Dispersional analysis can be regarded as a strong method for characterizing biological or natural time series, which generally show long-range positive correlation.

Estimating Time From Atomic Clocks

A Kalman recursive algorithm for estimating time from an ensemble of atomic clocks has been developed. The algorithm allows for the addition or deletion of clocks at any time, and provides automatic error detection and correction. The observations consist of time differences between clocks and may be taken at unequally spaced time points. Maximum likelihood estimates of the unknown parameters are obtained with confidence intervals, as well as hypothesis tests to determine whether the estimated parameters are significantly different from zero. The program is operational on the National Bureau of Standards' Time and Frequency Division's PDP 11/70.

Estimation of Parameters in Models for Cesium Beam Atomic Clocks

This paper is intended to serve as an introduction to the use of the Kalman filter in modeling atomic clocks and obtaining maximum likelihood estimates of the model paramaters from data on an ensemble of clocks. Tests for the validity of the model and confidence intervals for the parameter estimates are discussed. Techniques for dealing with unequally spaced and partially or completely missing multivariate data are described. The existence of deterministic frequency drifts in clocks is established and estimates of the drifts are obtained.