Browse
Submit Data
Databases
API
Help

Dataset Information

18 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Effect of data length on time delay and embedding dimension for calculating the Lyapunov exponent in walking.

ABSTRACT: The Lyapunov exponent (LyE) is a trending measure for characterizing gait stability. Previous studies have shown that data length has an effect on the resultant LyE, but the origin of why it changes is unknown. This study investigates if data length affects the choice of time delay and embedding dimension when reconstructing the phase space, which is a requirement for calculating the LyE. The effect of three different preprocessing methods on reconstructing the gait attractor was also investigated. Lumbar accelerometer data were collected from 10 healthy subjects walking on a treadmill at their preferred walking speed for 30 min. Our results show that time delay was not sensitive to the amount of data used during calculation. However, the embedding dimension had a minimum data requirement of 200 or 300 gait cycles, depending on the preprocessing method used, to determine the steady-state value of the embedding dimension. This study also found that preprocessing the data using a fixed number of strides or a fixed number of data points had significantly different values for time delay compared to a time series that used a fixed number of normalized gait cycles, which have a fixed number of data points per stride. Thus, comparing LyE values should match the method of calculation using either a fixed number of strides or a fixed number of data points.

SUBMITTER: Hussain VS

PROVIDER: S-EPMC7423422 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Similar Datasets

The Maximum Lyapunov Exponent During Walking and Running: Reliability Assessment of Different Marker-Sets.

Project description:The maximum Lyapunov exponent (MLE) has often been suggested as the prominent measure for evaluation of dynamic stability of locomotion in pathological and healthy population. Although the popularity of the MLE has increased in the last years, there is scarce information on the reliability of the method, especially during running. The purpose of the current study was, thus, to examine the reliability of the MLE during both walking and running. Sixteen participants walked and ran on a treadmill completing two measurement blocks (i.e., two trials per day for three consecutive days per block) separated by 2 months on average. Six different marker-sets on the trunk were analyzed. Intraday, interday and between blocks reliability was assessed using the intraclass correlation coefficient (ICC) and the root mean square difference (RMSD). The MLE was on average significantly higher (p < 0.001) in running (1.836 ± 0.080) compared to walking (1.386 ± 0.207). All marker-sets showed excellent ICCs (>0.90) during walking and mostly good ICCs (>0.75) during running. The RMSD ranged from 0.023 to 0.047 for walking and from 0.018 to 0.050 for running. The reliability was better when comparing MLE values between blocks (ICCs: 0.965-0.991 and 0.768-0.961; RMSD: 0.023-0.034 and 0.018-0.027 for walking and running respectively), and worse when considering trials of the same day (ICCs: 0.946-0.980 and 0.739-0.844; RMSD: 0.042-0.047 and 0.045-0.050 for walking and running respectively). Further, different marker-sets affect the reliability of the MLE in both walking and running. Our findings provide evidence that the assessment of dynamic stability using the MLE is reliable in both walking and running. More trials spread over more than 1 day should be considered in study designs with increased demands of accuracy independent of the locomotion condition.

| S-EPMC6117405 | biostudies-literature

Selection Procedures for the Largest Lyapunov Exponent in Gait Biomechanics.

Project description:The present study was aimed at investigating the effectiveness of the Wolf et al. (LyE_W) and Rosenstein et al. largest Lyapunov Exponent (LyE_R) algorithms to differentiate data sets with distinctly different temporal structures. The three-dimensional displacement of the sacrum was recorded from healthy subjects during walking and running at two speeds; one low speed close to the preferred walking speed and one high speed close to the preferred running speed. LyE_R and LyE_W were calculated using four different time series normalization procedures. The performance of the algorithms were evaluated based on their ability to return relative low values for slow walking and fast running and relative high values for fast walking and slow running. Neither of the two algorithms outperformed the other; however, the effectiveness of the two algorithms was highly dependent on the applied time series normalization procedure. Future studies using the LyE_R should normalize the time series to a fixed number of strides and a fixed number of data points per stride or data points per time series while the LyE_W should be applied to time series normalized to a fixed number of data points or a fixed number of strides.

| S-EPMC6438190 | biostudies-literature

The evaluation of COVID-19 prediction precision with a Lyapunov-like exponent.

Project description:In the field of machine learning, building models and measuring their performance are two equally important tasks. Currently, measures of precision of regression models' predictions are usually based on the notion of mean error, where by error we mean a deviation of a prediction from an observation. However, these mean based measures of models' performance have two drawbacks. Firstly, they ignore the length of the prediction, which is crucial when dealing with chaotic systems, where a small deviation at the beginning grows exponentially with time. Secondly, these measures are not suitable in situations where a prediction is made for a specific point in time (e.g. a date), since they average all errors from the start of the prediction to its end. Therefore, the aim of this paper is to propose a new measure of models' prediction precision, a divergence exponent, based on the notion of the Lyapunov exponent which overcomes the aforementioned drawbacks. The proposed approach enables the measuring and comparison of models' prediction precision for time series with unequal length and a given target date in the framework of chaotic phenomena. Application of the divergence exponent to the evaluation of models' accuracy is demonstrated by two examples and then a set of selected predictions of COVID-19 spread from other studies is evaluated to show its potential.

| S-EPMC8162606 | biostudies-literature

A method of calculating the second dimension hold-up time for comprehensive two-dimensional gas chromatography.

Project description:A method of calculating the second dimension hold-up time for comprehensive two-dimensional gas chromatographic (GC×GC) data was developed by incorporating the temperature information of the second dimension column into the calculation model. The model was developed by investigating the relationship between the coefficients in each of six literature reported nonlinear models and the relationship between each coefficient and the second dimension column temperature. The most robust nonlinear function was selected and further used to construct the new model for calculation of the second dimension retention time, in which the coefficients that have significant correlation with the column temperature are replaced with expressions of column temperature. An advantage of the proposed equation is that eight parameters could explain the second dimension hold-up time as well as retention time corresponding to n-alkanes and column temperature in the entire chromatographic region, including the chromatographic region not bounded by the retention times of n-alkanes. To optimize the experimental design for collecting the isothermal data of n-alkanes to create the second dimension hold-up time model, the column temperature difference and the number of isothermal experiments should be considered simultaneously. It was concluded that a total of 5 or 6 isothermal experiments with temperature difference of 40 or 50 °C are enough to generate an accurate model. The test mean squared error (MSE) of those conditions ranges from 0.0428 to 0.0532 for calculation of the second dimension hold-up time for GC×GC data.

| S-EPMC3459176 | biostudies-literature

Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications.

Project description:Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ . Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ , only general recommendations such as N > > m ! , τ = 1 , or m = 3 , … , 7 . This paper deals specifically with the study of the practical implications of N > > m ! , since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real-world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N > > m ! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

| S-EPMC7514869 | biostudies-literature

Fractal dimension based geographical clustering of COVID-19 time series data.

Project description:Understanding the local dynamics of COVID-19 transmission calls for an approach that characterizes the incidence curve in a small geographical unit. Given that incidence curves exhibit considerable day-to-day variation, the fractal structure of the time series dynamics is investigated for the Flanders and Brussels Regions of Belgium. For each statistical sector, the smallest administrative geographical entity in Belgium, fractal dimensions of COVID-19 incidence rates, based on rolling time spans of 7, 14, and 21 days were estimated using four different estimators: box-count, Hall-Wood, variogram, and madogram. We found varying patterns of fractal dimensions across time and location. The fractal dimension is further summarized by its mean, variance, and autocorrelation over time. These summary statistics are then used to cluster regions with different incidence rate patterns using k-means clustering. Fractal dimension analysis of COVID-19 incidence thus offers important insight into the past, current, and arguably future evolution of an infectious disease outbreak.

| S-EPMC10016183 | biostudies-literature

Minimum embedding dimension analysis uncovers reduced network complexity during neuronal differentiation in autism spectrum disorder

Project description:Background: Neuronal activity can be modeled as a nonlinear dynamical system to yield novel measures of neuronal state and dysfunction. We hypothesized that electrical activity during neuronal differentiation would be marked by a reduction in dynamical complexity in autism spectrum disorder (ASD). Methods: Electrical activity of induced pluripotent stem cell (iPSC)-derived neurons from ASD patients and controls were recorded using a multielectrode array (MEA). Minimum embedding dimension (MED) analysis was performed to characterize the complexity present in the electrical recordings of the neuronal cultures during differentiation. Gene expression changes with respect to the MED were analyzed, and gene ontology analysis and the BrainSpan Atlas were used to identify gene enrichments in specific biological pathways, brain regions, and developmental stages. Results: We found that the MED showed a statistically significant deficit in the ASD samples, suggesting that, compared to controls, network complexity is reduced in ASD during neuronal differentiation. MED was correlated to clinical endpoints such as nonverbal intelligence and was associated with 53 differentially expressed genes. These differentially expressed genes were overrepresented in ASD gene lists and pathways related to neurodevelopment, cell morphology, and cell migration. Spatiotemporal analysis also showed a prenatal temporal enrichment in cortical and deep brain structures. Conclusion: Reduced network complexity in ASD was observed by MED analysis during neuronal differentiation, indicating deficits in integrated and synchronized firing. The results present nonlinear dynamical analysis of iPSC-derived neuronal electrical recordings as a new paradigm for the investigation of aberrant brain activity in neurodevelopmental disorders.

2020-05-18 | GSE125020 | GEO

Principled approach to the selection of the embedding dimension of networks.

Project description:Network embedding is a general-purpose machine learning technique that encodes network structure in vector spaces with tunable dimension. Choosing an appropriate embedding dimension - small enough to be efficient and large enough to be effective - is challenging but necessary to generate embeddings applicable to a multitude of tasks. Existing strategies for the selection of the embedding dimension rely on performance maximization in downstream tasks. Here, we propose a principled method such that all structural information of a network is parsimoniously encoded. The method is validated on various embedding algorithms and a large corpus of real-world networks. The embedding dimension selected by our method in real-world networks suggest that efficient encoding in low-dimensional spaces is usually possible.

| S-EPMC8213704 | biostudies-literature

Dimension reduction of microarray gene expression data: the accelerated failure time model.

Project description:The construction of the components of Partial Least Squares (PLS) is based on the maximization of the covariance/correlation between linear combinations of the predictors and the response. However, the usual Pearson correlation is influenced by outliers in the response or in the predictors. To cope with outliers, we replace the Pearson correlation with the Spearman rank correlation in the optimization criteria of PLS. The rank-based method of PLS is insensitive to outlying values in both the predictors and response, and incorporates the censoring information by using an approach of Nguyen and Rocke (2004) and two approaches of reweighting and mean imputation of Datta et al. (2007). The performance of the rank-based approaches of PLS, denoted by Rank-based Modified Partial Least Squares (RMPLS), Rank-based Reweighted Partial Least Squares (RRWPLS), and Rank-based Mean-Imputation Partial Least Squares (RMIPLS), is investigated in a simulation study and on four real datasets, under an Accelerated Failure Time (AFT) model, against their un-ranked counterparts, and several other dimension reduction techniques. The results indicate that RMPLS is a better dimension reduction method than other variants of PLS as well as other considered methods in terms of the minimized cross-validation error of fit and the mean squared error of fit in the presence of outliers in the response, and is comparable to other variants of PLS in the absence of outliers. Supplementary Materials are available at http://www.worldscinet.com/jbcb/

| S-EPMC2796584 | biostudies-literature

Embedding mRNA stability in correlation analysis of time-series gene expression data.

Project description:Current methods for the identification of putatively co-regulated genes directly from gene expression time profiles are based on the similarity of the time profile. Such association metrics, despite their central role in gene network inference and machine learning, have largely ignored the impact of dynamics or variation in mRNA stability. Here we introduce a simple, but powerful, new similarity metric called lead-lag R(2) that successfully accounts for the properties of gene dynamics, including varying mRNA degradation and delays. Using yeast cell-cycle time-series gene expression data, we demonstrate that the predictive power of lead-lag R(2) for the identification of co-regulated genes is significantly higher than that of standard similarity measures, thus allowing the selection of a large number of entirely new putatively co-regulated genes. Furthermore, the lead-lag metric can also be used to uncover the relationship between gene expression time-series and the dynamics of formation of multiple protein complexes. Remarkably, we found a high lead-lag R(2) value among genes coding for a transient complex.

| S-EPMC2453326 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data