Spectral Analysis of Binary Time Series: Square Waves vs. Sinusoidal Functions

The analysis of signals consisting of discrete and irregular data causes methodological problems for the Fourier spectral Analysis: Since it is based on sinusoidal functions, rectangular signals with unequal periodicities cannot easily be replicated. The Walsh spectral Analysis is based on the so called "Walsh functions", a complete set of orthonormal, rectangular waves and thus seems to be the method of choice for analysing signals consisting of binary or ordinal data. The paper compares the Walsh spectral analysis and the Fourier spectral analysis on the basis of simulated and real binary data sets of various length. Simulated data were derived from signals with defined cyclic patterns that were noised by randomly generated signals of the same length. The Walsh and Fourier spectra of each set were determined and up to 25% of the periodogram coefficients were utilized as input for an inverse transform. Mean square approximation error (MSE) was calculated for each of the series in order to compare the goodness of fit between the original and the reconstructed signal. The same procedure was performed with real data derived from a behavioral observation in pigs. The comparison of the two methods revealed that, in the analysis of discrete and binary time series, Walsh spectral analysis is the more appropriate method, if the time series is rather short. If the length of the signal increases, the difference between the two methods is less substantial.     

Linear Discriminant Functions for Stationary Time Series

Optimal classification rules based on linear functions which maximize the Chernoff distance, or the Morisita distance, or the Kullback-Leibler distance are studied here. We obtain an expression for the optimal linear discriminant function and show that the resulting linear procedure belongs to the Anderson-Bahadur admissible class. For the comparison of discriminant rules we use some index which is the measure of the accuracy of a given class of discriminant procedures. The asymptotic form of the discriminant function is also studied.     

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.     

Spectral vs. compartmental averaging of VA/Q distributions: confidence limits

We have investigated the method of statistical averaging as a nonparametric approach to obtain a representative ventilation-perfusion (VA/Q) distribution that exemplifies the family of compatible solutions for multiple inert gas elimination data. The variability of the compatible solutions was examined by determining the standard deviation of the statistical average. For six inert gases, it can be predicted that a distribution with up to seven contiguous nonzero VA/Q compartments can be uniquely recovered, whereas the compatible family becomes more diverse, the broader the distribution. For a given compatible family consisting of multimodal distributions with various phase relationships, the average distribution was found to display an uncharacteristically unimodal shape as a result of modal smoothing. To avoid this possible artifact, an alternative approach was adopted in which statistical averaging was performed in the frequency domain. For both deterministic and empirical data, the energy spectra of all feasible VA/Q distributions displayed a well-defined low-frequency band that was invariant within the compatible family and with a bandwidth that approximated the predicted sampling cutoff frequency. The nonuniqueness of the result was ascribable to a variable high-frequency band that was due to an aliasing effect. For a wide range of clinical data, the representative distributions resulting from compartmental and spectral averaging were indistinguishable from each other and had little variability both in the VA/Q and frequency domains. For these cases, therefore, the resolving power of the recovery algorithm was not critical. Finally, an efficient method of finding the average distribution was proposed.     

Efficient Transfer Entropy Analysis of Non-Stationary Neural Time Series

Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of interest in neuroscience. Estimating transfer entropy from two processes requires the observation of multiple realizations of these processes to estimate associated probability density functions. To obtain these necessary observations, available estimators typically assume stationarity of processes to allow pooling of observations over time. This assumption however, is a major obstacle to the application of these estimators in neuroscience as observed processes are often non-stationary. As a solution, Gomez-Herrero and colleagues theoretically showed that the stationarity assumption may be avoided by estimating transfer entropy from an ensemble of realizations. Such an ensemble of realizations is often readily available in neuroscience experiments in the form of experimental trials. Thus, in this work we combine the ensemble method with a recently proposed transfer entropy estimator to make transfer entropy estimation applicable to non-stationary time series. We present an efficient implementation of the approach that is suitable for the increased computational demand of the ensemble method''s practical application. In particular, we use a massively parallel implementation for a graphics processing unit to handle the computationally most heavy aspects of the ensemble method for transfer entropy estimation. We test the performance and robustness of our implementation on data from numerical simulations of stochastic processes. We also demonstrate the applicability of the ensemble method to magnetoencephalographic data. While we mainly evaluate the proposed method for neuroscience data, we expect it to be applicable in a variety of fields that are concerned with the analysis of information transfer in complex biological, social, and artificial systems.     

Temporal Trend of Carpal Tunnel Release Surgery: A Population-Based Time Series Analysis

Background

Carpal tunnel release (CTR) is among the most common hand surgeries, although little is known about its pattern. In this study, we aimed to investigate temporal trends, age and gender variation and current practice patterns in CTR surgeries.

Methods

We conducted a population-based time series analysis among over 13 million residents of Ontario, who underwent operative management for carpal tunnel syndrome (CTS) from April 1, 1992 to March 31, 2010 using administrative claims data.

Results

The primary analysis revealed a fairly stable procedure rate of approximately 10 patients per 10,000 population per year receiving CTRs without any significant, consistent temporal trend (p = 0.94). Secondary analyses revealed different trends in procedure rates according to age. The annual procedure rate among those age >75 years increased from 22 per 10,000 population at the beginning of the study period to over 26 patients per 10,000 population (p<0.01) by the end of the study period. CTR surgical procedures were approximately two-fold more common among females relative to males (64.9% vs. 35.1 respectively; p<0.01). Lastly, CTR procedures are increasingly being conducted in the outpatient setting while procedures in the inpatient setting have been declining steadily – the proportion of procedures performed in the outpatient setting increased from 13% to over 30% by 2010 (p<0.01).

Conclusion

Overall, CTR surgical-procedures are conducted at a rate of approximately 10 patients per 10,000 population annually with significant variation with respect to age and gender. CTR surgical procedures in ambulatory-care facilities may soon outpace procedure rates in the in-hospital setting.     

Multi-locus Analysis of Genomic Time Series Data from Experimental Evolution

Genomic time series data generated by evolve-and-resequence (E&R) experiments offer a powerful window into the mechanisms that drive evolution. However, standard population genetic inference procedures do not account for sampling serially over time, and new methods are needed to make full use of modern experimental evolution data. To address this problem, we develop a Gaussian process approximation to the multi-locus Wright-Fisher process with selection over a time course of tens of generations. The mean and covariance structure of the Gaussian process are obtained by computing the corresponding moments in discrete-time Wright-Fisher models conditioned on the presence of a linked selected site. This enables our method to account for the effects of linkage and selection, both along the genome and across sampled time points, in an approximate but principled manner. We first use simulated data to demonstrate the power of our method to correctly detect, locate and estimate the fitness of a selected allele from among several linked sites. We study how this power changes for different values of selection strength, initial haplotypic diversity, population size, sampling frequency, experimental duration, number of replicates, and sequencing coverage depth. In addition to providing quantitative estimates of selection parameters from experimental evolution data, our model can be used by practitioners to design E&R experiments with requisite power. We also explore how our likelihood-based approach can be used to infer other model parameters, including effective population size and recombination rate. Then, we apply our method to analyze genome-wide data from a real E&R experiment designed to study the adaptation of D. melanogaster to a new laboratory environment with alternating cold and hot temperatures.     

Spectral Properties of Plasma Waves in Periodic Plasma-Filled Structures

The dispersion properties and field distribution of plasma waves in a periodic plasma-filled waveguide are correctly analyzed for the first time with allowance for all spatial harmonics. It is shown that the plasma wave spectrum has a zonal structure and a lower cutoff frequency. The widths of the forbidden bands and the lower cutoff frequency are determined by the waveguide corrugation depth. For a planar periodic plasma-filled waveguide, the allowed and forbidden frequency bands are evaluated analytically. The waveguide periodicity substantially influences the field of the plasma waves at frequencies close to the forbidden bands. This leads to the formation of regions in which the energy density of plasma waves exceeds the average level by more than one order of magnitude. This effect is related to the contribution from the higher spatial harmonics.     

时间序列的相似性测度

时间序列（time series）是指按时间顺序排列的观测值集合,在生物信息学研究领域中,DNA序列和基因表达数据都可以视为时间序列数据。时间序列分析中很重要的环节就是刻划两个时间序列或者时间子序列的相似性,用于序列比对等。时间序列的相似性测度是时间序列研究中的基础和重点,直接影响查询、聚类等后续计算的效率和精度,在高通量基因芯片数据分析、基因网络构建等研究中,具有重要的应用,目前已引起了众多研究人员的关注,在欧氏距离的基础上进行了大量的研究,本文综述了基于欧式距离和时间弯曲的时间序列相似性测度及其相关领域的研究进展,可作为进一步研究的参考。     

Analysis of Telemetric Time Series data for Periodic Components Using Dq-Fit

DQ-FIT and CV-SORT have been developed to facilitate the automatic analysis of data sampled by radiotelemetry, but they can also be used with other data sampled in chronobiological settings. After import of data, DQ-FIT performs conventional linear, as well as rhythm analysis according to user-defined specifications. Linear analysis includes calculation of mean values, load values (percentage of values above a defined limit), highest and lowest readings, and areas under the (parameter-time) curve (AUC). All of these parameters are calculated for the total sampling interval and for user-defined day and night periods. Rhythm analysis is performed by fitting of partial Fourier series with up to six harmonics. The contribution of each harmonic to the overall variation of data is tested statistically; only those components are included in the best-fit function that contribute significantly. Parameters calculated in DQ-FIT's rhythm analysis include mesor, amplitudes, and acrophases of all rhythmic components; significance and percentage rhythm of the combined best fit; maximum and minimum of the fitted curve and times of their occurrence. In addition, DQ-FIT uses the first derivative of the fitted curve (i.e., its slope) to determine the time and extent of maximal increases and decreases within the total sampling interval or user-defined intervals of interest, such as the times of lights on or off. CV-SORT can be used to create tables or graphs from groups of data sets analyzed by DQ-FIT. Graphs are created in CV-SORT by calculation of group mean profiles from individual best-fit curves rather than their curve parameters. This approach allows the user to combine data sets that differ in the number and/ or period length of harmonics included. In conclusion, DQ-FIT and CV-SORT can be helpful in the analysis of time-dependent data sampled by telemetry or other monitoring systems. The software can be obtained on request by every interested researcher. (Chronobiology International, 14(6), 561–574, 1997)     

Equidirection: A Measure of Similarity Among Time Series

In the present paper we investigate the concept of equidirection, i.e. similarity in the direction of variation, or parallelism in the broader sense, among m (m ≧ 2) times series, especially under the assumption that the time series are realizations of processes with independent increments. However, the processes need not be stationary. Furthermore, the probabilities for the direction of variation may be unstable, in which case only upper and lower bounds are known. A measure based on the concept of equidirection was developed that enables identification of clusters of similar time series and analysis of relationships among variables.     

Analysis of Multiple Surface Electromagnetic Waves on the Planner Interface of Hyperbolic Medium and Rugate Filter Having Sinusoidal Refractive Index Profile

Plasmonics - This paper presents a canonical boundary value problem to understand the behavior of electromagnetic surface waves propagated on the planar interface of rugate filter and hyperbolic...     

Thiol Metabolism and Redox Regulation of Cellular Functions. Series I: Life and Behavioural Sciences

α,β-Unsaturated carbonyl compounds have been implicated in a number of environmentally-related diseases. Often, the presence of α,β-unsaturated carbonyl functionality as part of either an aliphatic or cyclic structure is considered a structural alert for cytotoxicity. We examined the cytotoxicity of methyl vinyl ketone (MVK), an aliphatic, straight-chain α,β-unsaturated carbonyl compound, in murine GT1-7 hypothalamic neurons. In addition to its widespread environmental occurrence, MVK was selected due to its extensive use in the chemical industry. Also, MVK is a close structural analog of hydroxymethylvinyl ketone that, in part, mediates the cytotoxic effects of 1,3-butadiene in vivo. It was found that MVK at low micromolar concentrations induced extensive cell death that retained key features of apoptosis such as chromatin condensation and DNA fragmentation. The MVK-induced apoptosis was associated with depletion of glutathione, disruption of mitochondrial transmembrane potential, and increased generation of reactive oxygen species (ROS). Supplementation of neuronal cells with Trolox offered partial, but significant, protection against the MVK-induced cytotoxicity, presumably due to scavenging of ROS in situ. The suggested sequence of events in the MVK-induced apoptosis in neuronal cells involves the depletion of cellular glutathione followed by an increased generation of ROS and finally the loss of mitochondrial function.