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.     

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 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 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.     

Biological Time Series Analysis Using a Context Free Language: Applicability to Pulsatile Hormone Data

We present a novel approach for analyzing biological time-series data using a context-free language (CFL) representation that allows the extraction and quantification of important features from the time-series. This representation results in Hierarchically AdaPtive (HAP) analysis, a suite of multiple complementary techniques that enable rapid analysis of data and does not require the user to set parameters. HAP analysis generates hierarchically organized parameter distributions that allow multi-scale components of the time-series to be quantified and includes a data analysis pipeline that applies recursive analyses to generate hierarchically organized results that extend traditional outcome measures such as pharmacokinetics and inter-pulse interval. Pulsicons, a novel text-based time-series representation also derived from the CFL approach, are introduced as an objective qualitative comparison nomenclature. We apply HAP to the analysis of 24 hours of frequently sampled pulsatile cortisol hormone data, which has known analysis challenges, from 14 healthy women. HAP analysis generated results in seconds and produced dozens of figures for each participant. The results quantify the observed qualitative features of cortisol data as a series of pulse clusters, each consisting of one or more embedded pulses, and identify two ultradian phenotypes in this dataset. HAP analysis is designed to be robust to individual differences and to missing data and may be applied to other pulsatile hormones. Future work can extend HAP analysis to other time-series data types, including oscillatory and other periodic physiological signals.     

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.     

Biological Invasions in Austria: Patterns and Case Studies

This paper provides a review of the first national inventory of non-indigenous species in Austria. In summary, 1110 vascular plant species (27 of the entire flora), 83 mycetes and at least 500 animal species (approximately 1 of the entire fauna) were documented for Austria, which are introduced intentionally or unintentionally by humans after 1492 and reported from the wild. About 25 of non-indigenous vascular plant species have become naturalized. Most non-indigenous vascular plants are native to the Palaearctic region (55%; with 33% originating from the Mediterranean subregion) and North America (20%). More than 90% of non-indigenous plant species are confined to naturally and anthropogenically disturbed (ruderal, urban, arable land, and riverine) habitats. Aquatic ecosystems are more affected and vulnerable to changes in their animal species composition. The current data demonstrate that non-indigenous species continue to invade and disperse and it also emphasize the necessity and responsibility to develop scientific strategies to minimize the impact of biological invasions and to raise public awareness of the problem.     

Frequent Pattern Discovery in Multiple Biological Networks: Patterns and Algorithms

The rapid accumulation of biological network data is creating an urgent need for computational methods capable of integrative network analysis. This paper discusses a suite of algorithms that we have developed to discover biologically significant patterns that appear frequently in multiple biological networks: coherent dense subgraphs, frequent dense vertex-sets, generic frequent subgraphs, differential subgraphs, and recurrent heavy subgraphs. We demonstrate these methods on gene co-expression networks, using the identified patterns to systematically annotate gene functions, map genome to phenome, and perform high-order cooperativity analysis.     

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.     

FTSPlot: Fast Time Series Visualization for Large Datasets

The analysis of electrophysiological recordings often involves visual inspection of time series data to locate specific experiment epochs, mask artifacts, and verify the results of signal processing steps, such as filtering or spike detection. Long-term experiments with continuous data acquisition generate large amounts of data. Rapid browsing through these massive datasets poses a challenge to conventional data plotting software because the plotting time increases proportionately to the increase in the volume of data. This paper presents FTSPlot, which is a visualization concept for large-scale time series datasets using techniques from the field of high performance computer graphics, such as hierarchic level of detail and out-of-core data handling. In a preprocessing step, time series data, event, and interval annotations are converted into an optimized data format, which then permits fast, interactive visualization. The preprocessing step has a computational complexity of ; the visualization itself can be done with a complexity of and is therefore independent of the amount of data. A demonstration prototype has been implemented and benchmarks show that the technology is capable of displaying large amounts of time series data, event, and interval annotations lag-free with ms. The current 64-bit implementation theoretically supports datasets with up to bytes, on the x86_64 architecture currently up to bytes are supported, and benchmarks have been conducted with bytes/1 TiB or double precision samples. The presented software is freely available and can be included as a Qt GUI component in future software projects, providing a standard visualization method for long-term electrophysiological experiments.     

Ecological Patterns and Biological Invasions: Using Regional Species Inventories in Macroecology

Macroecology depends heavily on a comparative methodology in order to identify large-scale patterns and to test alternative hypotheses that might generate such patterns. With the advent and accessibility of large electronic databases of species and their life history and ecological attributes, ecologists have begun seeking generalities, and examining large-scale ecological hypotheses involving core themes of range, abundance and diversity. For example, combinations of ecological, life history and phylogenetic data have been analysed using large species sets to test hypotheses in invasion biology. Analysis of regional species inventories can contribute cogently to our understanding of invasions. Here we examine several ways in which database analysis is effective. We review 19 studies of comparative invasions biology, each using >100 species of plants in their analyses, and show that invader success is linked to seven correlates: short life cycle, abiotic (mostly wind) dispersal, large native range size, non-random taxonomic patterns (emphasizing certain families or orders), presence of clonal organs, occupying disturbed habitats, and earlier time of introduction. These phylogenetically influenced, comparative analyses using regional species inventories are only just beginning and have much potential.     

Social Jetlag: Misalignment of Biological and Social Time

Humans show large differences in the preferred timing of their sleep and activity. This so‐called “chronotype” is largely regulated by the circadian clock. Both genetic variations in clock genes and environmental influences contribute to the distribution of chronotypes in a given population, ranging from extreme early types to extreme late types with the majority falling between these extremes. Social (e.g., school and work) schedules interfere considerably with individual sleep preferences in the majority of the population. Late chronotypes show the largest differences in sleep timing between work and free days leading to a considerable sleep debt on work days, for which they compensate on free days. The discrepancy between work and free days, between social and biological time, can be described as ‘social jetlag.’ Here, we explore how sleep quality and psychological wellbeing are associated with individual chronotype and/or social jetlag. A total of 501 volunteers filled out the Munich ChronoType Questionnaire (MCTQ) as well as additional questionnaires on: (i) sleep quality (SF‐A), (ii) current psychological wellbeing (Basler Befindlichkeitsbogen), (iii) retrospective psychological wellbeing over the past week (POMS), and (iv) consumption of stimulants (e.g., caffeine, nicotine, and alcohol). Associations of chronotype, wellbeing, and stimulant consumption are strongest in teenagers and young adults up to age 25 yrs. The most striking correlation exists between chronotype and smoking, which is significantly higher in late chronotypes of all ages (except for those in retirement). We show these correlations are most probably a consequence of social jetlag, i.e., the discrepancies between social and biological timing rather than a simple association to different chronotypes. Our results strongly suggest that work (and school) schedules should be adapted to chronotype whenever possible.     

Identifying Signatures of Selection in Genetic Time Series

Both genetic drift and natural selection cause the frequencies of alleles in a population to vary over time. Discriminating between these two evolutionary forces, based on a time series of samples from a population, remains an outstanding problem with increasing relevance to modern data sets. Even in the idealized situation when the sampled locus is independent of all other loci, this problem is difficult to solve, especially when the size of the population from which the samples are drawn is unknown. A standard χ²-based likelihood-ratio test was previously proposed to address this problem. Here we show that the χ²-test of selection substantially underestimates the probability of type I error, leading to more false positives than indicated by its P-value, especially at stringent P-values. We introduce two methods to correct this bias. The empirical likelihood-ratio test (ELRT) rejects neutrality when the likelihood-ratio statistic falls in the tail of the empirical distribution obtained under the most likely neutral population size. The frequency increment test (FIT) rejects neutrality if the distribution of normalized allele-frequency increments exhibits a mean that deviates significantly from zero. We characterize the statistical power of these two tests for selection, and we apply them to three experimental data sets. We demonstrate that both ELRT and FIT have power to detect selection in practical parameter regimes, such as those encountered in microbial evolution experiments. Our analysis applies to a single diallelic locus, assumed independent of all other loci, which is most relevant to full-genome selection scans in sexual organisms, and also to evolution experiments in asexual organisms as long as clonal interference is weak. Different techniques will be required to detect selection in time series of cosegregating linked loci.