A Simple Approach for the Computation of Multiple Periodicities in Biological Time Series

We have described a simple approach for the analysis and isolation of multiple periodicities from a biological time series. For the estimation of the periodicities, we used simulated data and data from ongoing experiments in our laboratory. Two time series were simulated, one which consisted of only white noise and the other consisted white noise along with periodicities of 6, 11, 17 and 23 h, to demonstrate that our method can successfully isolate multiple patterns in a time series. Our method of analysis is objective, simple, flexible and adaptive since it distinctly delineates the individual contribution from an overlap of multiple periodicities. The key features of our method are: (i) identification of a reliable phase reference point, (ii) scanning the time series using a moving window in increments, (iii) use of Siegel's modification of Fisher's method to detect significant periodicit(y)ies in the time series. The use of window sizes of increasing length to examine the time series elegantly reduces noise while identifying periodicities that are otherwise not apparent. Finally, the periodogram can be smoothed in order to normalize the contribution by attendant frequency components within the waveform. A minimum critical value for relative contribution of various frequencies was calculated to delineate the periodicities that contributed significantly to the time series. We executed this method of time series analysis using MS Excel and C.     

A Concordance Method For Analyzing Categorical Time Series. An Application For The Search of Periodicities

A simple method for searching for periods in biological series is proposed. Because it is based on an auto-comparison of the observations within a series we call it the concordance method. It requires few theoritical assumptions. In fact, even the ever present stationarity condition is not used. The method is compared with competing methods based on the khi-square periodogram. It is shown that the concordance method is much better for analyzing multimodal and noisy series. Rhythms presenting simultaneously circadian and ultradian components can also be analyzed with this method.     

A Concordance Method For Analyzing Categorical Time Series. An Application For The Search of Periodicities

A simple method for searching for periods in biological series is proposed. Because it is based on an auto-comparison of the observations within a series we call it the concordance method. It requires few theoritical assumptions. In fact, even the ever present stationarity condition is not used. The method is compared with competing methods based on the khi-square periodogram. It is shown that the concordance method is much better for analyzing multimodal and noisy series. Rhythms presenting simultaneously circadian and ultradian components can also be analyzed with this method.     

Some Tools to Analyze Changes of Rhythms in Biological Time Series

The moving window principle applied to the khi-square periodogram allows, through local successive examinations, a comprehensive study of the biological time series. This method puts forward several cases of transition linked to environmental or physiological changes. Furthermore, we applied the Grassberger and Procaccia method (1983) for the analysis of more complex transition problems. The method helps to detect chaotic properties in behavioral activity rhythms.     

Some Tools to Analyze Changes of Rhythms in Biological Time Series

The moving window principle applied to the khi-square periodogram allows, through local successive examinations, a comprehensive study of the biological time series. This method puts forward several cases of transition linked to environmental or physiological changes. Furthermore, we applied the Grassberger and Procaccia method (1983) for the analysis of more complex transition problems. The method helps to detect chaotic properties in behavioral activity rhythms.     

A Novel Approach to Quantify Time Series Differences of Gait Data Using Attractor Attributes

In this paper we introduce a new method to expressly use live/corporeal data in quantifying differences of time series data with an underlying limit cycle attractor; and apply it using an example of gait data. Our intention is to identify gait pattern differences between diverse situations and classify them on group and individual subject levels. First we approximated the limit cycle attractors, from which three measures were calculated: δM amounts to the difference between two attractors (a measure for the differences of two movements), δD computes the difference between the two associated deviations of the state vector away from the attractor (a measure for the change in movement variation), and δF, a combination of the previous two, is an index of the change. As an application we quantified these measures for walking on a treadmill under three different conditions: normal walking, dual task walking, and walking with additional weights at the ankle. The new method was able to successfully differentiate between the three walking conditions. Day to day repeatability, studied with repeated trials approximately one week apart, indicated excellent reliability for δM (ICC_ave > 0.73 with no differences across days; p > 0.05) and good reliability for δD (ICC_ave  =  0.414 to 0.610 with no differences across days; p > 0.05). Based on the ability to detect differences in varying gait conditions and the good repeatability of the measures across days, the new method is recommended as an alternative to expensive and time consuming techniques of gait classification assessment. In particular, the new method is an easy to use diagnostic tool to quantify clinical changes in neurological patients.     

A Novel Approach for Choosing Summary Statistics in Approximate Bayesian Computation

The choice of summary statistics is a crucial step in approximate Bayesian computation (ABC). Since statistics are often not sufficient, this choice involves a trade-off between loss of information and reduction of dimensionality. The latter may increase the efficiency of ABC. Here, we propose an approach for choosing summary statistics based on boosting, a technique from the machine-learning literature. We consider different types of boosting and compare them to partial least-squares regression as an alternative. To mitigate the lack of sufficiency, we also propose an approach for choosing summary statistics locally, in the putative neighborhood of the true parameter value. We study a demographic model motivated by the reintroduction of Alpine ibex (Capra ibex) into the Swiss Alps. The parameters of interest are the mean and standard deviation across microsatellites of the scaled ancestral mutation rate (θ_anc = 4N_eu) and the proportion of males obtaining access to matings per breeding season (ω). By simulation, we assess the properties of the posterior distribution obtained with the various methods. According to our criteria, ABC with summary statistics chosen locally via boosting with the L₂-loss performs best. Applying that method to the ibex data, we estimate θ^anc≈1.288 and find that most of the variation across loci of the ancestral mutation rate u is between 7.7 × 10⁻⁴ and 3.5 × 10⁻³ per locus per generation. The proportion of males with access to matings is estimated as ω^≈0.21, which is in good agreement with recent independent estimates.     

Computation of Time-Specified Tolerance Intervals for Hybrid Time Series with Nonequidistant Sampling,Illustrated for Plasma Growth Hormone

The ideal reference interval for a variable of clinical interest would be specific for all deterministic factors affecting that variable, including the time of sampling in relation to biological rhythms. In particular, growth hormone is characterized in children by circadian and ultradian variability, with high peaks of secretion occurring mainly during sleep. For clinical applications, the use of tolerance intervals has been recommended, and they should substitute, whenever possible, for prediction limits. In the case of hybrid data (time series of data collected from a group of subjects), such a tolerance interval could be very difficult to determine following a parametric approach similar to the procedure used for the computation of prediction intervals, especially when consideration of both within-subjects and among-subjects variances is wanted. Accordingly, we have developed a nonparametric method for the computation of such tolerance intervals. Because the method is based on bootstrap techniques, it does not require the assumption of normality or symmetry in the data and is also more appropriate when dealing with small samples. The method was used to establish time-qualified reference limits for a series of growth hormone sampled around the clock in groups of prepubertal children differentiated according to stature. The use of these tolerance intervals may eliminate many false-positive and false-negative diagnoses that might be obtained when relying on time-unspecified single samples. The provision of such tolerance limits introduces time-specification and time-structure evaluation into prevention, diagnosis, and treatment of growth disorders. (Chronobiology International, 14(4), 409–425, 1997)     

Classification of Time Series Gene Expression in Clinical Studies via Integration of Biological Network

The increasing availability of time series expression datasets, although promising, raises a number of new computational challenges. Accordingly, the development of suitable classification methods to make reliable and sound predictions is becoming a pressing issue. We propose, here, a new method to classify time series gene expression via integration of biological networks. We evaluated our approach on 2 different datasets and showed that the use of a hidden Markov model/Gaussian mixture models hybrid explores the time-dependence of the expression data, thereby leading to better prediction results. We demonstrated that the biclustering procedure identifies function-related genes as a whole, giving rise to high accordance in prognosis prediction across independent time series datasets. In addition, we showed that integration of biological networks into our method significantly improves prediction performance. Moreover, we compared our approach with several state-of–the-art algorithms and found that our method outperformed previous approaches with regard to various criteria. Finally, our approach achieved better prediction results on early-stage data, implying the potential of our method for practical prediction.     

A Four-Stage Hybrid Model for Hydrological Time Series Forecasting

Hydrological time series forecasting remains a difficult task due to its complicated nonlinear, non-stationary and multi-scale characteristics. To solve this difficulty and improve the prediction accuracy, a novel four-stage hybrid model is proposed for hydrological time series forecasting based on the principle of ‘denoising, decomposition and ensemble’. The proposed model has four stages, i.e., denoising, decomposition, components prediction and ensemble. In the denoising stage, the empirical mode decomposition (EMD) method is utilized to reduce the noises in the hydrological time series. Then, an improved method of EMD, the ensemble empirical mode decomposition (EEMD), is applied to decompose the denoised series into a number of intrinsic mode function (IMF) components and one residual component. Next, the radial basis function neural network (RBFNN) is adopted to predict the trend of all of the components obtained in the decomposition stage. In the final ensemble prediction stage, the forecasting results of all of the IMF and residual components obtained in the third stage are combined to generate the final prediction results, using a linear neural network (LNN) model. For illustration and verification, six hydrological cases with different characteristics are used to test the effectiveness of the proposed model. The proposed hybrid model performs better than conventional single models, the hybrid models without denoising or decomposition and the hybrid models based on other methods, such as the wavelet analysis (WA)-based hybrid models. In addition, the denoising and decomposition strategies decrease the complexity of the series and reduce the difficulties of the forecasting. With its effective denoising and accurate decomposition ability, high prediction precision and wide applicability, the new model is very promising for complex time series forecasting. This new forecast model is an extension of nonlinear prediction models.     

Sparse Spatial Sampling for the Computation of Motion in Multiple Stages

The avian retino-tecto-rotundal pathway plays a central role in motion analysis and features complex connectivity. Yet, the relation between the pathway’s structural arrangement and motion computation has remained elusive. For an important type of tectal wide-field neuron, the stratum griseum centrale type I (SGC-I) neuron, we quantified its structure and found a spatially sparse but extensive sampling of the retinal projection. A computational investigation revealed that these structural properties enhance the neuron’s sensitivity to change, a behaviorally important stimulus attribute, while preserving information about the stimulus location in the SGC-I population activity. Furthermore, the SGC-I neurons project with an interdigitating topography to the nucleus rotundus, where the direction of motion is computed. We showed that, for accurate direction-of-motion estimation, the interdigitating projection of tectal wide-field neurons requires a two-stage rotundal algorithm, where the second rotundal stage estimates the direction of motion from the change in the relative stimulus position represented in the first stage     

A Robust Measurement of Correlation in Dependent Time Series

A special problem in behavioral sciences are time series where the data points of one series are dependent on the just prior values of the other series. The data structure may additionally exhibit an interdependence between the variables that changes over time. Pfanzagl's T provides a robust test of trend independence between such data sets. At the same time the applicability of Pearson's r can be extended by using the statistical considerations for T. For this purpose, the time series are transformed into binary series, consisting either of the values 1 or 0. These series may show distinct trend patterns of consecutive data points with the value 1 or with the value 0. Data points belonging to the same trend pattern are regarded as cohering values for any further mathematical operation applied. Based on the trend identifcation the T-value is derived, providing information on the coherent development of trend patterns in the two series. Additionally Pearson's r together with a modified sampling theory offers a standard measure of linear association between the time series. The procedures are described and a computer program is provided, combining Pfanzagl's T and Pearson's r with a bootstrap procedure for the statistical evaluation of the correlation coefficients.     

A Method for Comparing Multivariate Time Series with Different Dimensions

In many situations it is desirable to compare dynamical systems based on their behavior. Similarity of behavior often implies similarity of internal mechanisms or dependency on common extrinsic factors. While there are widely used methods for comparing univariate time series, most dynamical systems are characterized by multivariate time series. Yet, comparison of multivariate time series has been limited to cases where they share a common dimensionality. A semi-metric is a distance function that has the properties of non-negativity, symmetry and reflexivity, but not sub-additivity. Here we develop a semi-metric – SMETS – that can be used for comparing groups of time series that may have different dimensions. To demonstrate its utility, the method is applied to dynamic models of biochemical networks and to portfolios of shares. The former is an example of a case where the dependencies between system variables are known, while in the latter the system is treated (and behaves) as a black box.     

A Simple Method for Multiple Modification of the Escherichia coli K-12 Chromosome

We developed a simple method of generating markerless deletions in the Escherichia coli chromosome. The method consists of two recombination events stimulated by λ Red recombinase. The first recombination replaced a target region with a marker cassette and the second then eliminated the marker cassette. The marker cassette included an antibiotic resistant gene and a negative selection marker (Bacillus subtilis sacB). Since sacB makes E. coli sensitive to sucrose, a markerless deletion strain was successfully selected using its sucrose-resistant phenotype. To stimulate these recombination events, 1-kbp homologous sequences adjacent to the target region were connected to both ends of the marker cassette or connected to each other by PCR. The average efficiency of the recombinations was 24% and 93% respectively. Eliminating the marker cassette with a fragment including an additional sequence, insertion was also possible. This markerless deletion method should be useful in creating a highly modified E. coli chromosome.     

A Simple Approach to Analyse Non-Orthogonal Data

The present paper deals with an alternative and simple procedure to analyse the non-orthogonal data. The procedure is general in nature but has some advantages for the non-orthogonal data due to some missing observations. The procedure is applied to (i) two way classification with unequal number of observations per cell; (ii) randomized block designs with some missing observations and (iii) balanced incomplete block designs and also illustrated with the help of numerical examples.     

时间序列数据记忆性的判别方法

目的：发展时间序列数据记忆的判别方法并用于离子通道数据记忆性的判别研究。方法：应用Pearson检验与曲线拟合的方法,识别数据的记忆性。结果：得到数据记忆性的判别方法,讨论了离子通道记忆性。结论：Pearson检验与曲线拟合法简单易用,离子通道具有记忆性。