Quantitative Analysis of Single Particle Trajectories: Mean Maximal Excursion Method

An increasing number of experimental studies employ single particle tracking to probe the physical environment in complex systems. We here propose and discuss what we believe are new methods to analyze the time series of the particle traces, in particular, for subdiffusion phenomena. We discuss the statistical properties of mean maximal excursions (MMEs), i.e., the maximal distance covered by a test particle up to time t. Compared to traditional methods focusing on the mean-squared displacement we show that the MME analysis performs better in the determination of the anomalous diffusion exponent. We also demonstrate that combination of regular moments with moments of the MME method provides additional criteria to determine the exact physical nature of the underlying stochastic subdiffusion processes. We put the methods to test using experimental data as well as simulated time series from different models for normal and anomalous dynamics such as diffusion on fractals, continuous time random walks, and fractional Brownian motion.     

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.     

Surveillance in longitudinal models: detection of intrauterine growth restriction

A new methodology for online detection of intrauterine growth restriction (IUGR) is proposed where traditional methods for statistical surveillance are applied. Here, deficient growth rate is used to detect IUGR instead of the common surrogate measure "small for gestational age" (SGA). Fetal growth is estimated by repeated measurements of symphysis-fundus (SF) height. At each time point the new method, based on the Shiryaev-Roberts method, is used to evaluate the growth in SF height. We use Swedish data to model a normal growth pattern, which is used to evaluate the capability of the new method to detect IUGR in comparison with a method used in practice today. Results from simulations indicate that the new method performs considerably better than the method used today. We also illustrate the effect of some important factors which influence the detection ability and illuminate the tendency of the method used today to misclassify SGA cases as IUGR.     

Analyzing Single-Molecule Time Series via Nonparametric Bayesian Inference

The ability to measure the properties of proteins at the single-molecule level offers an unparalleled glimpse into biological systems at the molecular scale. The interpretation of single-molecule time series has often been rooted in statistical mechanics and the theory of Markov processes. While existing analysis methods have been useful, they are not without significant limitations including problems of model selection and parameter nonidentifiability. To address these challenges, we introduce the use of nonparametric Bayesian inference for the analysis of single-molecule time series. These methods provide a flexible way to extract structure from data instead of assuming models beforehand. We demonstrate these methods with applications to several diverse settings in single-molecule biophysics. This approach provides a well-constrained and rigorously grounded method for determining the number of biophysical states underlying single-molecule data.     

Effectiveness and utility of acoustic recordings for surveying tropical birds

ABSTRACT Although acoustic recordings have recently gained popularity as an alternative to point counts for surveying birds, little is known about the relative performance of the two methods for detecting tropical bird species across multiple vegetation types. During June and July 2008, we collected species detection/nondetection data to compare the performance of a quadraphonic acoustic recording system and point counts for estimating species richness and composition and detection probabilities of 15 rare, moderately common, and common tropical bird species across six structurally distinct vegetation types (coastal dune scrub, mangrove, low‐stature deciduous thorn forest, early and late successional medium‐stature semievergreen forest, and grazed pastures) in the northern Yucatan Peninsula. We selected five rare species endemic to the Yucatan Peninsula and 10 moderately common and common species that also occur in other tropical regions. Species richness and composition did not differ between survey methods in any of the vegetation types. At the population level, however, we found support for an effect of method on detection probability for most species. For 13 species, regardless of their abundance, acoustic recordings yielded detection probabilities as high as or higher than those for point counts across all vegetation types. The remaining two species were better detected by point counts in pastures and coastal scrub, where greater visibility likely improved sightings of these species. However, these species were detected as well as or better by acoustic recordings in forests and mangroves where detections were primarily auditory. In tropical regions where experienced field observers may not be available and funding for field surveys may be limited, acoustic recordings offer a practical solution for determining species richness and composition and the occupancy patterns of most species. However, for some species, a combination of methods will provide the most reliable data. Regardless of the method selected, analyses that account for variation in detection probability among vegetation types will be necessary because most species in our study demonstrated vegetation‐dependent detection probabilities.     

Drones and sound recorders increase the number of bird species identified: A combined surveys approach

Many studies have compared results from sound recordings and traditional point-count survey observer data when surveying avian communities. None have investigated the use of a moving sound recorder to replicate line-transect surveying.We conducted point-count surveys and line-transect surveys in four urban/peri-urban habitats in Darwin, tropical Australia, with stationary and moving sound recorders, respectively, to assess whether such a combination would result in more bird species being identified than with either technique alone.More bird species were identified using sound recordings than standard observer data. Further, the difference in the number of species identified between the observer and audio from point-count surveys was found to be significant with audio identification being more accurate; however, line-transect surveys showed no significant difference between the two identification methods. Overall, there was no statistical significance between using point-count surveys and line-transect surveys for total species identified.Linear mixed modelling found the interaction between habitat and survey type (point-count vs line-transect) was strongly significant, but not so that between habitat and survey method (sound recording vs human observation).Our results indicate that the integration of bioacoustic and drone technologies with traditional avian surveying techniques adds significant additional identifications when compiling a species list of an area.     

Detecting determinism in short time series, with an application to the analysis of a stationary EEG recording

We have developed a new method for detecting determinism in a short time series and used this method to examine whether a stationary EEG is deterministic or stochastic. The method is based on the observation that the trajectory of a time series generated from a differentiable dynamical system behaves smoothly in an embedded phase space. The angles between two successive directional vectors in the trajectory reconstructed from a time series at a minimum embedding dimension were calculated as a function of time. We measured the irregularity of the angle variations obtained from the time series using second-order difference plots and central tendency measures, and compared these values with those from surrogate data. The ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated time series, including data from Lorenz, R?ssler, and Van der Pol attractors, high-dimensional equations, and 1/f noise. We then applied this method to the analysis of stationary segments of EEG recordings consisting of 750 data points (6-s segments) from five normal subjects. The stationary EEG segments were not found to exhibit deterministic components. This method can be used to analyze determinism in short time series, such as those from physiological recordings, that can be modeled using differentiable dynamical processes.     

Ciclograma: a tool for detection of rhythmicities in sleep/wake cycles

The Fourier spectral analysis of binary time series (or rectangular signals) causes methodological problems, due to the fact that it is based on sinusoidal functions. We propose a new tool for the detection of periodicities in binary time series, focusing on sleep/wake cycles. This methodology is based on a weighted histogram of cycle durations. In this paper, we compare our methodology with the Fourier spectral analysis on the basis of simulated and real binary data sets of various lengths. We also provide an approach to statistical validation of the periodicities determined with our methodology. Furthermore, we analyze the discriminating power of both methods in terms of standard deviation. Our results indicate that the Ciclograma is much more powerful than Fourier analysis when applied on this type of time series.     

CICLOGRAMA: A TOOL FOR DETECTION OF RHYTHMICITIES IN SLEEP/WAKE CYCLES

The Fourier spectral analysis of binary time series (or rectangular signals) causes methodological problems, due to the fact that it is based on sinusoidal functions. We propose a new tool for the detection of periodicities in binary time series, focusing on sleep/wake cycles. This methodology is based on a weighted histogram of cycle durations. In this paper, we compare our methodology with the Fourier spectral analysis on the basis of simulated and real binary data sets of various lengths. We also provide an approach to statistical validation of the periodicities determined with our methodology. Furthermore, we analyze the discriminating power of both methods in terms of standard deviation. Our results indicate that the Ciclograma is much more powerful than Fourier analysis when applied on this type of time series.     

浅水湖泊生态系统稳态转换的阈值判定方法

浅水湖泊生态系统对人类干扰的反应会随着干扰力度的改变或增强而出现突然的变化,即发生稳态转换;对其机理和驱动机制的揭示将有助于对湖泊富营养化的控制及恢复.基于“多稳态”理论的稳态转换研究已广泛开展,但对浅水湖泊生态系统稳态转换的驱动机制结论各异,采用的阈值判定方法相差很大,主要有实验观测、模型模拟和统计分析3种.实验观测多关注少数特定指标,指标筛选过程复杂且工作量大;模型模拟虽能从较为全面的尺度上理解生态系统稳态变化的特征和主要机理过程,但在模型误差和不确定性的处理等问题上尚存在不足;统计分析方法基于对长时间序列数据的统计变化规律分析,用以判断或者预警稳态转换现象的发生,是目前最为常用的方法.目前稳态转换领域的研究大都是对已发生的稳态转换进行机制分析或过程反演,对未来预测与预警的问题仍然亟需加强.     

An online spike detection and spike classification algorithm capable of instantaneous resolution of overlapping spikes

For the analysis of neuronal cooperativity, simultaneously recorded extracellular signals from neighboring neurons need to be sorted reliably by a spike sorting method. Many algorithms have been developed to this end, however, to date, none of them manages to fulfill a set of demanding requirements. In particular, it is desirable to have an algorithm that operates online, detects and classifies overlapping spikes in real time, and that adapts to non-stationary data. Here, we present a combined spike detection and classification algorithm, which explicitly addresses these issues. Our approach makes use of linear filters to find a new representation of the data and to optimally enhance the signal-to-noise ratio. We introduce a method called “Deconfusion” which de-correlates the filter outputs and provides source separation. Finally, a set of well-defined thresholds is applied and leads to simultaneous spike detection and spike classification. By incorporating a direct feedback, the algorithm adapts to non-stationary data and is, therefore, well suited for acute recordings. We evaluate our method on simulated and experimental data, including simultaneous intra/extra-cellular recordings made in slices of a rat cortex and recordings from the prefrontal cortex of awake behaving macaques. We compare the results to existing spike detection as well as spike sorting methods. We conclude that our algorithm meets all of the mentioned requirements and outperforms other methods under realistic signal-to-noise ratios and in the presence of overlapping spikes.     

The Use of Automated Bioacoustic Recorders to Replace Human Wildlife Surveys: An Example Using Nightjars

To be able to monitor and protect endangered species, we need accurate information on their numbers and where they live. Survey methods using automated bioacoustic recorders offer significant promise, especially for species whose behaviour or ecology reduces their detectability during traditional surveys, such as the European nightjar. In this study we examined the utility of automated bioacoustic recorders and the associated classification software as a way to survey for wildlife, using the nightjar as an example. We compared traditional human surveys with results obtained from bioacoustic recorders. When we compared these two methods using the recordings made at the same time as the human surveys, we found that recorders were better at detecting nightjars. However, in practice fieldworkers are likely to deploy recorders for extended periods to make best use of them. Our comparison of this practical approach with human surveys revealed that recorders were significantly better at detecting nightjars than human surveyors: recorders detected nightjars during 19 of 22 survey periods, while surveyors detected nightjars on only six of these occasions. In addition, there was no correlation between the amount of vocalisation captured by the acoustic recorders and the abundance of nightjars as recorded by human surveyors. The data obtained from the recorders revealed that nightjars were most active just before dawn and just after dusk, and least active during the middle of the night. As a result, we found that recording at both dusk and dawn or only at dawn would give reasonably high levels of detection while significantly reducing recording time, preserving battery life. Our analyses suggest that automated bioacoustic recorders could increase the detection of other species, particularly those that are known to be difficult to detect using traditional survey methods. The accuracy of detection is especially important when the data are used to inform conservation.     

Signal localization: a new approach in signal discovery

A new approach for statistical association signal identification is developed in this paper. We consider a strategy for nonprecise signal identification by extending the well‐known signal detection and signal identification methods applicable to the multiple testing problem. Collection of statistical instruments under the presented approach is much broader than under the traditional signal identification methods, allowing more efficient signal discovery. Further assessments of maximal value and average statistics in signal discovery are improved. While our method does not attempt to detect individual predictors, it instead detects sets of predictors that are jointly associated with the outcome. Therefore, an important application would be in genome wide association study (GWAS), where it can be used to detect genes which influence the phenotype but do not contain any individually significant single nucleotide polymorphism (SNP). We compare power of the signal identification method based on extremes of single p‐values with the signal localization method based on average statistics for logarithms of p‐values. A simulation analysis informs the application of signal localization using the average statistics for wide signals discovery in Gaussian white noise process. We apply average statistics and the localization method to GWAS to discover better gene influences of regulating loci in a Chinese cohort developed for risk of nasopharyngeal carcinoma (NPC).     

A statistical approach to bioclimatic trend detection in the airborne pollen records of Catalonia (NE Spain)

Airborne pollen records are a suitable indicator for the study of climate change. The present work focuses on the role of annual pollen indices for the detection of bioclimatic trends through the analysis of the aerobiological spectra of 11 taxa of great biogeographical relevance in Catalonia over an 18-year period (1994–2011), by means of different parametric and non-parametric statistical methods. Among others, two non-parametric rank-based statistical tests were performed for detecting monotonic trends in time series data of the selected airborne pollen types and we have observed that they have similar power in detecting trends. Except for those cases in which the pollen data can be well-modeled by a normal distribution, it is better to apply non-parametric statistical methods to aerobiological studies. Our results provide a reliable representation of the pollen trends in the region and suggest that greater pollen quantities are being liberated to the atmosphere in the last years, specially by Mediterranean taxa such as Pinus, Total Quercus and Evergreen Quercus, although the trends may differ geographically. Longer aerobiological monitoring periods are required to corroborate these results and survey the increasing levels of certain pollen types that could exert an impact in terms of public health.     

An operational definition of a statistically meaningful trend

Linear trend analysis of time series is standard procedure in many scientific disciplines. If the number of data is large, a trend may be statistically significant even if data are scattered far from the trend line. This study introduces and tests a quality criterion for time trends referred to as statistical meaningfulness, which is a stricter quality criterion for trends than high statistical significance. The time series is divided into intervals and interval mean values are calculated. Thereafter, r(2) and p values are calculated from regressions concerning time and interval mean values. If r(2) ≥ 0.65 at p ≤ 0.05 in any of these regressions, then the trend is regarded as statistically meaningful. Out of ten investigated time series from different scientific disciplines, five displayed statistically meaningful trends. A Microsoft Excel application (add-in) was developed which can perform statistical meaningfulness tests and which may increase the operationality of the test. The presented method for distinguishing statistically meaningful trends should be reasonably uncomplicated for researchers with basic statistics skills and may thus be useful for determining which trends are worth analysing further, for instance with respect to causal factors. The method can also be used for determining which segments of a time trend may be particularly worthwhile to focus on.     

Using soundscape recordings to estimate bird species abundance, richness, and composition

ABSTRACT Point counts are the most frequently used technique for sampling bird populations and communities, but have well‐known limitations such as inter‐ and intraobserver errors and limited availability of expert field observers. The use of acoustic recordings to survey birds offers solutions to these limitations. We designed a Soundscape Recording System (SRS) that combines a four‐channel, discrete microphone system with a quadraphonic playback system for surveying bird communities. We compared the effectiveness of SRS and point counts for estimating species abundance, richness, and composition of riparian breeding birds in California by comparing data collected simultaneously using both methods. We used the temporal‐removal method to estimate individual bird detection probabilities and species abundances using the program MARK. Akaike's Information Criterion provided strong evidence that detection probabilities differed between the two survey methods and among the 10 most common species. The probability of detecting birds was higher when listening to SRS recordings in the laboratory than during the field survey. Additionally, SRS data demonstrated a better fit to the temporal‐removal model assumptions and yielded more reliable estimates of detection probability and abundance than point‐count data. Our results demonstrate how the perceptual constraints of observers can affect temporal detection patterns during point counts and thus influence abundance estimates derived from time‐of‐detection approaches. We used a closed‐population capture–recapture approach to calculate jackknife estimates of species richness and average species detection probabilities for SRS and point counts using the program CAPTURE. SRS and point counts had similar species richness and detection probabilities. However, the methods differed in the composition of species detected based on Jaccard's similarity index. Most individuals (83%) detected during point counts vocalized at least once during the survey period and were available for detection using a purely acoustic technique, such as SRS. SRS provides an effective method for surveying bird communities, particularly when most species are detected by sound. SRS can eliminate or minimize observer biases, produce permanent records of surveys, and resolve problems associated with the limited availability of expert field observers.     

Detecting Change in Biological Rhythms: A Multivariate Permutation Test Approach to Fourier‐Transformed Data

Treatment‐related changes in neurobiological rhythms are of increasing interest to psychologists, psychiatrists, and biological rhythms researchers. New methods for analyzing change in rhythms are needed, as most common methods disregard the rich complexity of biological processes. Large time series data sets reflect the intricacies of underlying neurobiological processes, but can be difficult to analyze. We propose the use of Fourier methods with multivariate permutation test (MPT) methods for analyzing change in rhythms from time series data. To validate the use of MPT for Fourier‐transformed data, we performed Monte Carlo simulations and compared statistical power and family‐wise error for MPT to Bonferroni‐corrected and uncorrected methods. Results show that MPT provides greater statistical power than Bonferroni‐corrected tests, while appropriately controlling family‐wise error. We applied this method to human, pre‐ and post‐treatment, serially‐sampled neurotransmitter data to confirm the utility of this method using real data. Together, Fourier with MPT methods provides a statistically powerful approach for detecting change in biological rhythms from time series data.     

Understanding relationship between sequence and functional evolution in yeast proteins

The underlying relationship between functional variables and sequence evolutionary rates is often assessed by partial correlation analysis. However, this strategy is impeded by the difficulty of conducting meaningful statistical analysis using noisy biological data. A recent study suggested that the partial correlation analysis is misleading when data is noisy and that the principal component regression analysis is a better tool to analyze biological data. In this paper, we evaluate how these two statistical tools (partial correlation and principal component regression) perform when data are noisy. Contrary to the earlier conclusion, we found that these two tools perform comparably in most cases. Furthermore, when there is more than one ‘true’ independent variable, partial correlation analysis delivers a better representation of the data. Employing both tools may provide a more complete and complementary representation of the real data. In this light, and with new analyses, we suggest that protein length and gene dispensability play significant, independent roles in yeast protein evolution. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Exploring the nonlinear dynamics of the brain.

The growing need for a better understanding of large-scale brain dynamics has stimulated in the last decade the development of new and more advanced data analysis techniques. Progress in this domain has greatly benefited from developments in nonlinear time series analysis. This review gives a short overview of some of the nonlinear properties one may wish to infer from brain recordings and presents some examples and recent applications.     

Hilbert phase entropy imaging of fMRI time series

Functional magnetic resonance imaging (fMRI) data-processing methods in the time domain include correlation analysis and the general linear model, among others. Virtually, many fMRI processing strategies utilise temporal information and ignore or pay little attention to phase information, resulting in an unnecessary loss of efficiency. We proposed a novel method named Hilbert phase entropy imaging (HPEI) that used the discrete Hilbert transform of the magnitude time series to detect brain functional activation. The data from two simulation studies and two in vivo fMRI studies that both contained block-design and event-related experiments revealed that the HPEI method enabled the effective detection of brain functional activation and the distinction of different response patterns. Our results demonstrate that this method is useful as a complementary analysis, but hypothesis-constrained, in revealing additional information regarding the complex nature of fMRI time series.