Detecting causality from short time-series data based on prediction of topologically equivalent attractors

Background

Detecting causality for short time-series data such as gene regulation data is quite important but it is usually very difficult. This can be used in many fields especially in biological systems. Recently, several powerful methods have been set up to solve this problem. However, it usually needs very long time-series data or much more samples for the existing methods to detect causality among the given or observed data. In our real applications, such as for biological systems, the obtained data or samples are short or small. Since the data or samples are highly depended on experiment or limited resource.

Results

In order to overcome these limitations, here we propose a new method called topologically equivalent position method which can detect causality for very short time-series data or small samples. This method is mainly based on attractor embedding theory in nonlinear dynamical systems. By comparing with inner composition alignment, we use theoretical models and real gene expression data to show the effectiveness of our method.

Conclusions

As a result, it shows our method can be effectively used in biological systems. We hope our method can be useful in many other fields in near future such as complex networks, ecological systems and so on.

     

Studying and modelling dynamic biological processes using time-series gene expression data

Biological processes are often dynamic, thus researchers must monitor their activity at multiple time points. The most abundant source of information regarding such dynamic activity is time-series gene expression data. These data are used to identify the complete set of activated genes in a biological process, to infer their rates of change, their order and their causal effects and to model dynamic systems in the cell. In this Review we discuss the basic patterns that have been observed in time-series experiments, how these patterns are combined to form expression programs, and the computational analysis, visualization and integration of these data to infer models of dynamic biological systems.     

Cycles in insect populations: delayed density dependence or exogenous driving variables?

Summary Delayed density dependence, and the cycles in insect populations that it can generate, are often investigated using time-series analysis. Recently, several authors have raised concerns about the validity of using time-series analysis to detect density dependence. One particular concern is the suggestion that exogenous driving variables, such as cyclic weather patterns, can lead to the spurious detection of density dependence in natural populations.
Using non-biological data (the electricity bills of one of the authors), we show how easy it is to be misled by the results of time-series analysis. We then present 16 years' data on the gall-forming sawfly, Euura lasiolepis (Hymenoptera: Tenthredinidae), and show that cycles in weather, specifically winter precipitation, lead to the spurious detection of density dependence in time-series analysis. We conclude that time-series analysis cannot stand alone as a method for inferring the action of density dependence, and urge further investigation of the effects of apparent cycles in abiotic forces on insect populations.     

Analysis of time-course microarray data: Comparison of common tools

High-throughput time-series data have a special value for studying the dynamism of biological systems. However, the interpretation of such complex data can be challenging. The aim of this study was to compare common algorithms recently developed for the detection of differentially expressed genes in time-course microarray data. Using different measures such as sensitivity, specificity, predictive values, and related signaling pathways, we found that limma, timecourse, and gprege have reasonably good performance for the analysis of datasets in which only test group is followed over time. However, limma has the additional advantage of being able to report significance cut off, making it a more practical tool. In addition, limma and TTCA can be satisfactorily used for datasets with time-series data for all experimental groups. These findings may assist investigators to select appropriate tools for the detection of differentially expressed genes as an initial step in the interpretation of time-course big data.     

Identifying predator-prey processes from time-series

The functional response is a key element in predator-prey models as well as in food chains and food webs. Classical models consider it as a function of prey abundance only. However, many mechanisms can lead to predator dependence, and there is increasing evidence for the importance of this dependence. Identification of the mathematical form of the functional response from real data is therefore a challenging task. In this paper we apply model-fitting to test if typical ecological predator-prey time series data, which contain both observation error and process error, can give some information about the form of the functional response. Working with artificial data (for which the functional response is known) we will show that with moderate noise levels, identification of the model that generated the data is possible. However, the noise levels prevailing in real ecological time-series can give rise to wrong identifications. We will also discuss the quality of parameter estimation by fitting differential equations to such time-series.     

The Lomb-Scargle Periodogram in Biological Rhythm Research: Analysis of Incomplete and Unequally Spaced Time-Series

This paper investigates the utility of the Lomb-Scargle periodogram for the analysis of biological rhythms. This method is particularly suited to detect periodic components in unequally sampled time-series and data sets with missing values, but restricts all calculations to actually measured values. The Lomb-Scargle method was tested on both real and simulated time-series with even and uneven sampling, and compared to a standard method in biomedical rhythm research, the Chi-square periodogram. Results indicate that the Lomb-Scargle algorithm shows a clearly better detection efficiency and accuracy in the presence of noise, and avoids possible bias or erroneous results that may arise from replacement of missing data by interpolation techniques. Hence, the Lomb-Scargle periodogram may serve as a useful method for the study of biological rhythms, especially when applied to telemetrical or observational time-series obtained from free-living animals, i.e., data sets that notoriously lack points.     

New insights into testing for density dependence

The reasons why tests for density dependence often differ in their results for a particular time-series were investigated using modelled time-series of 20 generations in lenght. The test of Pollard et al. (1987) is the most reliable; it had the greatest power with the three forms of density dependent data investigated (mean detection rates of 50.8–61.1%) and was least influenced by the form of the density dependence in time-series. Bulmer's first test (Bulmer 1975) had slightly lower power (mean detection rates of 27.4–56.8%) and was more affected by the form of density dependence present in the data. The mean power of the other tests was lower and detection rates were more variable. Rates were 24.6–46.2% for regression of k-value on abundance, 6.4–32.6% for regression of k-value on logarithmic abundance and 0.2–13.7% for Bulmer's second test (Bulmer 1975). Bulmer's second test is not useful because of low power. For one method, regression of k-value on abundance. density dependence was detected in 19.9% of timeseries generated using a random-walk model. For regression of k-value on logarithmically-transformed abundance the equivalent figure was 18.3% of series. These rates of spurious detection were significantly (P<0.001) greater than the generally accepted 5% level of type 1 errors and so these methods are not suitable for the analysis of time-series data for density dependence. Levels of spurious detection (from random-walk data) were around the 5% level and hence were acceptable for Bulmer's first test, Bulmer's second test, and the tests of Pollard et al. (1987), Reddinguis and den Boer (1989) and Crowley (1992). For all tests, except Bulmer's second test, the rate of detection and the amount of autocorrelation in time-series were negatively correlated. The degree of autocorrelation accounted for as much as 59.5–77.9% of the deviance in logit proportion detection for regression of k-value on abundance, Bulmer's first test, and the tests of Pollard et al. and Reddingius and den Boer. For regression of k-value on abundance this relationship accounted for less of the deviance (29.4%). Independent effects of density dependence were largely absent. It is concluded that these are tests of autocorrelation, not density dependence (or limitation). Autocorrelation was found to become positive (which is similar to values from random-walk data) as the intrinsic growth rate became either small or large. As the strength of density dependence (in the discrete exponential logistic equation) is dependent on the product of the intrinsic growth rate and the density dependent parameter it is unclear whether this is because of variation in the strength of density dependent mortality or reproduction per se. However, small values of the intrinsic grwoth rate cause the amount of variation in the data to become small, which might hinder detection of density dependence, and large values of the intrinsic growth rate are coincident with determinstic chaos which hinders detection. The user of these tests for density dependence should be aware of their potential weakness when variation within time-series is small (which itself is difficult to judge) or if the intrinsic growth rate is large so that chaotic dynamics might result. Power and levels of variability in rates of detection using Reddingius and den Boer's test were intermediate between those of the test of Pollard et al. and Bulmer's first test. This, combined with the strong relationship between rates of detection of limitation and the value of the autocorrelation coefficient, make testing for limitation similar to testing for density dependence. Crowley's test of attraction gave the widest range of mean detection rates from density dependent data of all the tests (20.4–60.6%). The relative rates of detection for the three forms of density dependent data were opposite to those found for Bulmer's first test and the test of Pollard et al. I conclude that testing for attraction is a complementary concept to testing for density dependence. As dynamics represented in time-series generated using a stochastic form of the exponential logistic equation became chaotic, Bulmer's first test, the test of Pollard et al. and regression of k on abundance failed to detect density dependence reliably. Conversely, Crowley's test was capable of detecting attraction with a power between 96 and 100% with time-series containing both stochastically and deterministically chaotic dynamics. This difference from other tests is in agreement with the lower influence of autocorrelation.     

Identifying Predator–Prey Processes from Time-Series

The functional response is a key element in predator–prey models as well as in food chains and food webs. Classical models consider it as a function of prey abundance only. However, many mechanisms can lead to predator dependence, and there is increasing evidence for the importance of this dependence. Identification of the mathematical form of the functional response from real data is therefore a challenging task. In this paper we apply model-fitting to test if typical ecological predator–prey time series data, which contain both observation error and process error, can give some information about the form of the functional response. Working with artificial data (for which the functional response is known) we will show that with moderate noise levels, identification of the model that generated the data is possible. However, the noise levels prevailing in real ecological time-series can give rise to wrong identifications. We will also discuss the quality of parameter estimation by fitting differential equations to such time-series.     

Avoiding erroneously high levels of detection in combinations of semi-independent tests

A randomization procedure is proposed which allows statistical tests to be combined into a single test to maintain specified and acceptable levels of false detection. This method was applied to the problem of detecting density dependence in 135 unpublished time-series (of 10 generations) from insect populations, and to simulated density-dependent and density-independent data, so that the correctness of observed levels of detection from the published data could be verified. To allow the application of the randomization procedure to Bulmer's (1975) tests and Varley and Gradwell's (1960) test, these were recast as randomization tests. The randomization procedure was tested with 39 combinations of tests for density dependence (and limitation/attraction); it generally producedcombined tests with levels of detection that were intermediate between detection levels of the constituent tests (and hence was limite by these). The specified rate of false detection (5%) was never exceeded (by more than 1%) when combined tests were applied to time-series from a random-walk model. Two different combinations of tests produced levels of detection from the published time-series which were slightly greater than their constituent tests when they were combined into single tests. These were the randomized form of Bulmer's (1975) first test with the tests of Pollard et al. (1987) and Reddingius and den Boer (1989) with the randomized form of Bulmer's second test. The combination of Bulmer's first and Pollard et al.'s test produced a greater level of detection (21.5%) than any other single test or combination of tests. These results were confirmed by the analysis of modelled density dependent data. Although the increase in power of combinations of tests over single tests is small with the data we used, the combined tests (listed above) had rates of detection that were less influenced by the form of data (of two forms of density-dependent data) than were their constituent tests. Hence, it appears that the combined tests are of greater generality than single test statistics. The method presented here for combining several statistical tests into a single randomization test is applicable in many other areas of ecology where we wish to apply several tests and take the most probable result of these; and if the tests being conducted are, or can be expressed as, randomization tests.     

Pattern Detection in Intensive Care Monitoring Time Series with Autoregressive Models: Influence of the Model Order

The detection of patterns in monitoring data of vital signs is of great importance for adequate bedside decision support in critical care. Currently used alarm systems, which are based on fixed thresholds and independency assumptions, are not satisfactory in clinical practice. Time series techniques such as AR‐models consider autocorrelations within the series, which can be used for pattern recognition in the data. For practical applications in intensive care the data analysis has to be automated. An important issue is the suitable choice of the model order which is difficult to accomplish online. In a comparative case‐study we analyzed 34564 univariate time series of hemodynamic variables in critically ill patients by autoregressive models of different orders and compared the results of pattern detection. AR(2)‐models seem to be most suitable for the detection of clinically relevant patterns, thus affirming that treating the data as independent leads to false alarms. Moreover, using AR(2)‐models affords only short estimation periods. These findings for pattern detection in intensive care data are of medical importance as they justify a preselection of a model order, easing further automated statistical online analysis.     

A two-stage virtual machine abnormal behavior-based anomaly detection mechanism

Virtual machine abnormal behavior detection is an effective way to help cloud platform administrators monitor the running status of cloud platform to improve the reliability of cloud platform, which has become one of the research hotspots in the field of cloud computing. Aiming at the problems of high computational complexity and high false alarm rate in the existing virtual machine anomaly monitoring mechanism of cloud platform, this paper proposed a two-stage virtual machine abnormal behavior-based detection mechanism. Firstly, a workload-based incremental clustering algorithm is used to monitor and analyze both the virtual machine workload information and performance index information. Then, an online anomaly detection mechanism based on the incremental local outlier factor algorithm is designed to enhance detection efficiency. By applying this two-phase detection mechanism, it can significantly reduce the computational complexity and meet the needs of real-time performance. The experimental results are verified on the mainstream Openstack cloud platform.

     

Tracking and forecasting ecosystem interactions in real time

Evidence shows that species interactions are not constant but change as the ecosystem shifts to new states. Although controlled experiments and model investigations demonstrate how nonlinear interactions can arise in principle, empirical tools to track and predict them in nature are lacking. Here we present a practical method, using available time-series data, to measure and forecast changing interactions in real systems, and identify the underlying mechanisms. The method is illustrated with model data from a marine mesocosm experiment and limnologic field data from Sparkling Lake, WI, USA. From simple to complex, these examples demonstrate the feasibility of quantifying, predicting and understanding state-dependent, nonlinear interactions as they occur in situ and in real time—a requirement for managing resources in a nonlinear, non-equilibrium world.     

An improved neutral landscape model for recreating real landscapes and generating landscape series for spatial ecological simulations

Many studies have assessed the effect of landscape patterns on spatial ecological processes by simulating these processes in computer‐generated landscapes with varying composition and configuration. To generate such landscapes, various neutral landscape models have been developed. However, the limited set of landscape‐level pattern variables included in these models is often inadequate to generate landscapes that reflect real landscapes. In order to achieve more flexibility and variability in the generated landscapes patterns, a more complete set of class‐ and patch‐level pattern variables should be implemented in these models. These enhancements have been implemented in Landscape Generator (LG), which is a software that uses optimization algorithms to generate landscapes that match user‐defined target values. Developed for participatory spatial planning at small scale, we enhanced the usability of LG and demonstrated how it can be used for larger scale ecological studies. First, we used LG to recreate landscape patterns from a real landscape (i.e., a mountainous region in Switzerland). Second, we generated landscape series with incrementally changing pattern variables, which could be used in ecological simulation studies. We found that LG was able to recreate landscape patterns that approximate those of real landscapes. Furthermore, we successfully generated landscape series that would not have been possible with traditional neutral landscape models. LG is a promising novel approach for generating neutral landscapes and enables testing of new hypotheses regarding the influence of landscape patterns on ecological processes. LG is freely available online.     

Estimating brain functional connectivity with sparse multivariate autoregression

There is much current interest in identifying the anatomical and functional circuits that are the basis of the brain's computations, with hope that functional neuroimaging techniques will allow the in vivo study of these neural processes through the statistical analysis of the time-series they produce. Ideally, the use of techniques such as multivariate autoregressive (MAR) modelling should allow the identification of effective connectivity by combining graphical modelling methods with the concept of Granger causality. Unfortunately, current time-series methods perform well only for the case that the length of the time-series Nt is much larger than p, the number of brain sites studied, which is exactly the reverse of the situation in neuroimaging for which relatively short time-series are measured over thousands of voxels. Methods are introduced for dealing with this situation by using sparse MAR models. These can be estimated in a two-stage process involving (i) penalized regression and (ii) pruning of unlikely connections by means of the local false discovery rate developed by Efron. Extensive simulations were performed with idealized cortical networks having small world topologies and stable dynamics. These show that the detection efficiency of connections of the proposed procedure is quite high. Application of the method to real data was illustrated by the identification of neural circuitry related to emotional processing as measured by BOLD.     

Similarity Ratio Analysis for Early Stage Fault Detection with Optical Emission Spectrometer in Plasma Etching Process

A Similarity Ratio Analysis (SRA) method is proposed for early-stage Fault Detection (FD) in plasma etching processes using real-time Optical Emission Spectrometer (OES) data as input. The SRA method can help to realise a highly precise control system by detecting abnormal etch-rate faults in real-time during an etching process. The method processes spectrum scans at successive time points and uses a windowing mechanism over the time series to alleviate problems with timing uncertainties due to process shift from one process run to another. A SRA library is first built to capture features of a healthy etching process. By comparing with the SRA library, a Similarity Ratio (SR) statistic is then calculated for each spectrum scan as the monitored process progresses. A fault detection mechanism, named 3-Warning-1-Alarm (3W1A), takes the SR values as inputs and triggers a system alarm when certain conditions are satisfied. This design reduces the chance of false alarm, and provides a reliable fault reporting service. The SRA method is demonstrated on a real semiconductor manufacturing dataset. The effectiveness of SRA-based fault detection is evaluated using a time-series SR test and also using a post-process SR test. The time-series SR provides an early-stage fault detection service, so less energy and materials will be wasted by faulty processing. The post-process SR provides a fault detection service with higher reliability than the time-series SR, but with fault testing conducted only after each process run completes.     

Ovitrap Monitor - Online application for counting mosquito eggs and visualisation toolbox in support of health services

Ovitraps are a widely used method for mosquito detection and monitoring, especially Aedes mosquitoes. Eggs present in ovitraps must be routinely counted to generate up-to-date information on potential spread of mosquito-borne diseases. This task is tedious, time consuming and prone to errors if done manually by eye counting. In this contribution, we introduce the Ovitrap Monitor, an online open source and user-friendly integrated application that semi-automatically counts mosquito eggs from low-medium resolution mobile phone pictures. A high correlation was found between counts performed manually by a technician and those obtained with the app using an extensive dataset of more than 750 ovitrap pictures. The application features an intuitive user interface and time-series plots and maps to facilitate data flow and speed up evidence-based decision-making within health organisations battling mosquito-borne diseases. Besides being open source, the Ovitrap Monitor is also backed by test data to guarantee its implementation through benchmarking and enforce research in the public health field.     

Group behavior time series anomaly detection in specific network space based on separation degree

Specific network space, including virtual space and practical space, is a space for executing group behavior on specified regions via network. Due to the variability and unpredictability of time series in group behavior in special network space, the detection of normal and abnormal borders faces significant challenges. The parameters in traditional time series mode need to be predefined such as clustering method and anomaly detection methods science the results influentially depend on the selection of parameters. According to the characteristics of data, this paper proposes an efficient method called separation degree algorithm that can construct the self-adaptive interval based on the separation degree model to filter out anomaly data in virtual and practical spaces. The advantage allows us to automatically find the self-adaptive interval to improve the accuracy and applicability of anomaly detection based on the characteristics of the data instead of set parameters of traditional methods in network space. The extensive experimental result shows that the proposed method can effectively detect anomaly data from different spaces.     

Research on spatial and temporal characteristics of drought based on GIS using Remote Sensing Big Data

Drought is a stochastic natural hazard that is caused by intense and persistent shortage of precipitation. Spatial and temporal patterns of drought have been analyzed by several methods, ranging from satellite images to historical records; however, drought is generally identified by climate elements. Drought indices are quantitative measures that characterize drought levels by assimilating data from one or several variables (indicators). A number of different indices have been developed to quantify droughts, each with its own strengths and weaknesses. In this paper, using the remote sensing image to acquire the vegetation cover data, and combined with meteorological data and the Geographic Information System (GIS) technology to discuss the spatial and temporal characteristics of the drought. Based on precipitation observations Pu’er City, Yunnan Province, ten counties (districts) ten meteorological observation stations from 1961 to 2010 monthly for 50 years, mainly in ArcGIS10.1 analysis platform, using Mann–Kendall nonparametric trend test method for time-series trends in precipitation was tested, using ArcGIS in inverse distance weighting interpolation tool were precipitation the amount and distribution of precipitation anomaly percentage. Finally, precipitation anomaly percentage grading standards drought intensity distribution of drought The results showed that: Pu’er City under the effect of temperature, altitude, vegetation cover, and many other factors, forming the situation that the rainfall is a little more in north–south and less in east–west, the drought incidence appears more in northwest and less in southeast, more in spring and winter and less in summer and fall.     

Combined static and dynamic analysis for determining the quality of time-series expression profiles

Expression profiling of time-series experiments is widely used to study biological systems. However, determining the quality of the resulting profiles remains a fundamental problem. Because of inadequate sampling rates, the effect of arrest-and-release methods and loss of synchronization, the measurements obtained from a series of time points may not accurately represent the underlying expression profiles. To solve this, we propose an approach that combines time-series and static (average) expression data analysis--for each gene, we determine whether its temporal expression profile can be reconciled with its static expression levels. We show that by combining synchronized and unsynchronized human cell cycle data, we can identify many cycling genes that are missed when using only time-series data. The algorithm also correctly distinguishes cycling genes from genes that specifically react to an environmental stimulus even if they share similar temporal expression profiles. Experimental validation of these results shows the utility of this analytical approach for determining the accuracy of gene expression patterns.     

Metal reduction kinetics in Shewanella

MOTIVATION: Metal reduction kinetics have been studied in cultures of dissimilatory metal reducing bacteria which include the Shewanella oneidensis strain MR-1. Estimation of system parameters from time-series data faces obstructions in the implementation depending on the choice of the mathematical model that captures the observed dynamics. The modeling of metal reduction is often based on Michaelis-Menten equations. These models are often developed using initial in vitro reaction rates and seldom match with in vivo reduction profiles. RESULTS: For metal reduction studies, we propose a model that is based on the power law representation that is effectively applied to the kinetics of metal reduction. The method yields reasonable parameter estimates and is illustrated with the analysis of time-series data that describes the dynamics of metal reduction in S.oneidensis strain MR-1. In addition, mixed metal studies involving the reduction of Uranyl (U(VI)) to the relatively insoluble tetravalent form (U(IV)) by S. alga strain (BR-Y) were studied in the presence of environmentally relevant iron hydrous oxides. For mixed metals, parameter estimation and curve fitting are accomplished with a generalized least squares formulation that handles systems of ordinary differential equations and is implemented in Matlab. It consists of an optimization algorithm (Levenberg-Marquardt, LSQCURVEFIT) and a numerical ODE solver. Simulation with the estimated parameters indicates that the model captures the experimental data quite well. The model uses the estimated parameters to predict the reduction rates of metals and mixed metals at varying concentrations. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.