Significance of trends in gait dynamics

Trends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The averages of scaling exponents of ST and SL MARS residuals are slightly smaller than 0.5. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. 10.1371/journal.pcbi.1000856.

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Significance of trends in gait dynamics

10.1101/677948 ◽

2019 ◽

Cited By ~ 2

Author(s):

Klaudia Kozlowska ◽

Miroslaw Latka ◽

Bruce J. West

Keyword(s):

Large Scale ◽

Stride Length ◽

Human Gait ◽

Small Scale ◽

Strongly Correlated ◽

Scaling Exponents ◽

Treadmill Speed ◽

Gait Parameters ◽

Instantaneous Values ◽

Spatio Temporal

AbstractTrends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The group-averaged values of scaling exponents of ST and ST MARS residuals are slightly smaller than 0.5, indicating weak anti-persistence. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. doi:10.1371/journal.pcbi.1000856.Author summaryDuring treadmill walking, the subject’s stride time (ST) and stride length (SL) must yield a stride speed which can fluctuate over a narrow range centered on the treadmill belt’s speed. The fact that both ST and SL are persistent is an intriguing property of human gait. For persistent fluctuations any deviation from the mean value is likely to be followed by a deviation in the same direction. To trace the origin of such persistence, we used a novel approach to determine trends in spatio-temporal gait parameters. We find that the trends of ST and SL of a subject are strongly correlated and are statistically independent of their corresponding residuals. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The persistence of gait parameters stems from superposition of large scale trends and small scale fluctuations.

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Solar cycle changes in the geo-effectiveness of small-scale solar wind turbulence measured by Wind and ACE at 1 AU

Annales Geophysicae ◽

10.5194/angeo-25-1183-2007 ◽

2007 ◽

Vol 25 (5) ◽

pp. 1183-1197 ◽

Cited By ~ 3

Author(s):

M. L. Parkinson ◽

R. C. Healey ◽

P. L. Dyson

Keyword(s):

Solar Wind ◽

Solar Cycle ◽

Solar Minimum ◽

Large Scale ◽

Small Scale ◽

Scaling Exponent ◽

Mhd Turbulence ◽

Scaling Exponents ◽

Solar Wind Turbulence ◽

Wind Turbulence

Abstract. Multi-scale structure of the solar wind in the ecliptic at 1 AU undergoes significant evolution with the phase of the solar cycle. Wind spacecraft measurements during 1995 to 1998 and ACE spacecraft measurements during 1997 to 2005 were used to characterise the evolution of small-scale (~1 min to 2 h) fluctuations in the solar wind speed vsw, magnetic energy density B2, and solar wind ε parameter, in the context of large-scale (~1 day to years) variations. The large-scale variation in ε most resembled large-scale variations in B2. The probability density of large fluctuations in ε and B2 both had strong minima during 1995, a familiar signature of solar minimum. Generalized Structure Function (GSF) analysis was used to estimate inertial range scaling exponents aGSF and their evolution throughout 1995 to 2005. For the entire data set, the weighted average scaling exponent for small-scale fluctuations in vsw was aGSF=0.284±0.001, a value characteristic of intermittent MHD turbulence (>1/4), whereas the scaling exponents for corresponding fluctuations in B2 and ε were aGSF=0.395±0.001 and 0.334±0.001, respectively. These values are between the range expected for Gaussian fluctuations (1/2) and Kolmogorov turbulence (1/3). However, the scaling exponent for ε changed from a Gaussian-Kolmogorov value of 0.373±0.005 during 1997 (end of solar minimum) to an MHD turbulence value of 0.247±0.004 during 2003 (recurrent fast streams). Changes in the characteristics of solar wind turbulence may be reproducible from one solar cycle to the next.

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Multifractal Cross Correlation Analysis of Agro-Meteorological Datasets (Including Reference Evapotranspiration) of California, United States

Atmosphere ◽

10.3390/atmos11101116 ◽

2020 ◽

Vol 11 (10) ◽

pp. 1116

Author(s):

Adarsh Sankaran ◽

Jaromir Krzyszczak ◽

Piotr Baranowski ◽

Archana Devarajan Sindhu ◽

Nandhineekrishna Kumar ◽

...

Keyword(s):

Time Series ◽

Cross Correlation ◽

Reference Evapotranspiration ◽

Multifractal Spectrum ◽

Fluctuation Analysis ◽

Scaling Exponent ◽

Scaling Exponents ◽

Multifractal Detrended Fluctuation Analysis ◽

Cross Correlation Analysis ◽

The Individual

The multifractal properties of six acknowledged agro-meteorological parameters, such as reference evapotranspiration (ET0), wind speed (U), incoming solar radiation (SR), air temperature (T), air pressure (P), and relative air humidity (RH) of five stations in California, USA were examined. The investigation of multifractality of datasets from stations with differing terrain conditions using the Multifractal Detrended Fluctuation Analysis (MFDFA) showed the existence of a long-term persistence and multifractality irrespective of the location. The scaling exponents of SR and T time series are found to be higher for stations with higher altitudes. Subsequently, this study proposed using the novel multifractal cross correlation (MFCCA) method to examine the multiscale-multifractal correlations properties between ET0 and other investigated variables. The MFCCA could successfully capture the scale dependent association of different variables and the dynamics in the nature of their associations from weekly to inter-annual time scales. The multifractal exponents of P and U are consistently lower than the exponents of ET0, irrespective of station location. This study found that joint scaling exponent was nearly the average of scaling exponents of individual series in different pairs of variables. Additionally, the α-values of joint multifractal spectrum were lower than the α values of both of the individual spectra, validating two universal properties in the MFCCA studies for agro-meteorological time series. The temporal evolution of cross-correlation determined by the MFCCA successfully captured the dynamics in the nature of associations in the P-ET0 link.

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Persistence and anti-persistence in treadmill walking

10.1101/2021.04.12.439523 ◽

2021 ◽

Author(s):

Klaudia Kozlowska ◽

Miroslaw Latka ◽

Bruce J. West

Keyword(s):

Large Scale ◽

Research Question ◽

Random Noise ◽

Cauchy Distribution ◽

Multivariate Adaptive Regression Splines ◽

Small Scale ◽

Scaling Exponents ◽

Belt Speed ◽

Gait Parameters ◽

All Speeds

AbstractBackgroundLong-range persistent correlations in stride time (ST) and length (SL) are the fundamental traits of treadmill gait. Our recent work showed that the ST and SL time series’ statistical properties originated from the superposition of large-scale trends and small-scale fluctuations (residuals). Trends served as the control manifolds about which ST and SL fluctuated. The scaling exponents of the residuals were slightly smaller than 0.5.Research questionDo random changes in treadmill belt speed affect the trend properties and scaling exponents of ST/SL residuals?MethodsWe used Multivariate Adaptive Regression Splines (MARS) to determine gait trends during a walk on a treadmill whose belt speed was perturbed by a strong random noise. Then, we calculated the scaling exponents of MARS residuals with the madogram estimator.ResultsExcept for the ST at the lowest treadmill speed v = 0.8 m/s, the normalized trend duration was at least three times greater than that for the unperturbed walk. The Cauchy distribution scale parameter, which served as a measure of the width of SL and ST trend slope distributions, was at v = 1.2 m/s, almost 50% and 25% smaller than the unperturbed values. The differences were even greater at v = 1.6 m/s: 73% and 83%. For all speeds, the ST and SL MARS residuals were strongly anti-persistent. At v = 1.2 m/s, the corresponding scaling exponents were equal to 0.37±0.10 and 0.25±0.09. Apart from ST at v = 0.8 m/s, the ST/SL scaling indices were close to 0.5.SignificancePersistence of gait parameters is closely related to the properties of their trends. Longer trends with a gentle slope and strong anti-persistence of ST/SL residuals are the manifestations or tight control required during the perturbed treadmill walk.

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Multifractal Cross Correlation Analysis of Agro-meteorological Datasets (Including Reference Evapotranspiration) of California, United States

10.20944/preprints202010.0123.v1 ◽

2020 ◽

Author(s):

Adarsh Sankaran ◽

Jaromir Krzyszczak ◽

Piotr Baranowski ◽

Archana Devarajan Sindhu ◽

Nandhinee Krishna Pradeep ◽

...

Keyword(s):

Time Series ◽

Los Angeles ◽

Cross Correlation ◽

Reference Evapotranspiration ◽

Fluctuation Analysis ◽

Scaling Exponent ◽

Air Humidity ◽

Scaling Exponents ◽

Relative Air Humidity ◽

Cross Correlation Analysis

This paper examined the multifractal properties of six acknowledged agro-meteorological parameters, such as reference evapotranspiration (ET0), wind speed (U), incoming solar radiation (SR), air temperature (T), air pressure (P), and relative air humidity (RH) of five stations in California, USA. The investigation of multifractality of datasets from stations with differing terrain conditions: Dagget, Bakersfield, Santa Maria, Los Angeles and San Diego using the Multifractal Detrended Fluctuation Analysis showed the existence of a long term persistence and multifractality irrespective of the location. The scaling exponents of SR and ET0 time series are found to be higher for stations with higher altitudes. Subsequently, this study proposed using the novel multifractal cross correlation (MFCCA) method to examine the multiscale-multifractal correlations properties between ET0 and other investigated variables. MFCCA could successfully capture the scale dependent association of different variables and the dynamics in the nature of their associations from seasonal to multi-annual time scale. The multifractal exponents of pressure and relative air humidity are consistently lower than the exponents of ET0, irrespective of station location. This study found that joint scaling exponent was nearly the average of scaling exponents of individual series in different pairs of variables. Additionally, the α-values of joint multifractal spectrum were lower than the α values of both of the individual spectra, validating two universal properties in the mutifractal cross correlation studies for agro-meteorological time series. The temporal evolution of cross-correlation showed similar pattern for all pair-wise associations involving ET0, except for the RH-ET0 link.

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Self-Supervised Pre-Training of Transformers for Satellite Image Time Series Classification

10.36227/techrxiv.13025039.v1 ◽

2020 ◽

Author(s):

Yuan Yuan ◽

Lei Lin

Keyword(s):

Time Series ◽

Deep Learning ◽

Large Scale ◽

Temporal Structure ◽

Satellite Image ◽

Fine Tuning ◽

Small Scale ◽

Model Parameters ◽

Learning Approaches ◽

Wide Range

Satellite image time series (SITS) classification is a major research topic in remote sensing and is relevant for a wide range of applications. Deep learning approaches have been commonly employed for SITS classification and have provided state-of-the-art performance. However, deep learning methods suffer from overfitting when labeled data is scarce. To address this problem, we propose a novel self-supervised pre-training scheme to initialize a Transformer-based network by utilizing large-scale unlabeled data. In detail, the model is asked to predict randomly contaminated observations given an entire time series of a pixel. The main idea of our proposal is to leverage the inherent temporal structure of satellite time series to learn general-purpose spectral-temporal representations related to land cover semantics. Once pre-training is completed, the pre-trained network can be further adapted to various SITS classification tasks by fine-tuning all the model parameters on small-scale task-related labeled data. In this way, the general knowledge and representations about SITS can be transferred to a label-scarce task, thereby improving the generalization performance of the model as well as reducing the risk of overfitting. Comprehensive experiments have been carried out on three benchmark datasets over large study areas. Experimental results demonstrate the effectiveness of the proposed method, leading to a classification accuracy increment up to 1.91% to 6.69%. <div><b>This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.</b></div>

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Instantaneous variance scaling of AIRS profiles using a circular area Monte Carlo approach

10.5194/amt-2017-463 ◽

2018 ◽

Author(s):

Jesse Dorrestijn ◽

Brian H. Kahn ◽

João Teixeira ◽

Fredrick W. Irion

Keyword(s):

Monte Carlo ◽

Water Vapor ◽

Large Scale ◽

Large Temperature ◽

Scaling Exponent ◽

Circular Area ◽

Scaling Exponents ◽

Monte Carlo Approach ◽

The Tropics ◽

Scale Break

Abstract. Satellite observations are used to study the variance scaling of temperature and water vapor in the atmosphere. A high resolution of 13.5 km at nadir, instead of 45 km as in previous Atmospheric Infrared Sounder (AIRS) studies, enables the derivation of the variance-scaling exponents down to length scales of ~ 55 km.With the variable-size circular area Monte Carlo approach the exponents can be computed instantaneously along the track of Aqua, which gives more insight into the scaling behavior of the atmospheric variables in individual Level 2 satellite granules. Scaling exponents are shown to fluctuate heavily between β = −1 and β = −3 at the larger scales, while at the smaller scales they are often closer to β = −2, and they decrease a bit for moisture at the smallest scales that are considered. Outside the tropics, the temperature large-scale variance-scaling exponent is often close to −3 due to large temperature slopes that are present along the track of Aqua, likely as a result of geostrophic turbulence. Around the tropics, this exponent is often closer to −1, because the tropical atmosphere is dominated by smaller-scale processes such as moist convection, leading to an observable reverse scale break. In contrast, water vapor is shown to have large-scale exponents often close to −3 around the tropics, because there, large-scale water vapor slopes are common along the Aqua track. Furthermore, the scale-break length scale turns out to be highly variable and shows a large spread. The presented variance-scaling results are of importance for cloud parameterization purposes.

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Self-Supervised Pre-Training of Transformers for Satellite Image Time Series Classification

10.36227/techrxiv.13025039.v3 ◽

2020 ◽

Author(s):

Yuan Yuan ◽

Lei Lin

Keyword(s):

Time Series ◽

Deep Learning ◽

Large Scale ◽

Temporal Structure ◽

Satellite Image ◽

Fine Tuning ◽

Small Scale ◽

Model Parameters ◽

Learning Approaches ◽

Wide Range

<div>Satellite image time series (SITS) classification is a major research topic in remote sensing and is relevant for a wide range of applications. Deep learning approaches have been commonly employed for SITS classification and have provided state-of-the-art performance. However, deep learning methods suffer from overfitting when labeled data is scarce. To address this problem, we propose a novel self-supervised pre-training scheme to initialize a Transformer-based network by utilizing large-scale unlabeled data. In detail, the model is asked to predict randomly contaminated observations given an entire time series of a pixel. The main idea of our proposal is to leverage the inherent temporal structure of satellite time series to learn general-purpose spectral-temporal representations related to land cover semantics. Once pre-training is completed, the pre-trained network can be further adapted to various SITS classification tasks by fine-tuning all the model parameters on small-scale task-related labeled data. In this way, the general knowledge and representations about SITS can be transferred to a label-scarce task, thereby improving the generalization performance of the model as well as reducing the risk of overfitting. Comprehensive experiments have been carried out on three benchmark datasets over large study areas. Experimental results demonstrate the effectiveness of the proposed method, leading to a classification accuracy increment up to 2.38% to 5.27%. The code and the pre-trained model will be available at https://github.com/linlei1214/SITS-BERT upon publication.</div><div><b>This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.</b></div>

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Evidence for fractal correlation properties in variations of peripheral arterial tone during REM sleep

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00336.2001 ◽

2002 ◽

Vol 283 (1) ◽

pp. H434-H439 ◽

Cited By ~ 18

Author(s):

I. Dvir ◽

Y. Adler ◽

D. Freimark ◽

P. Lavie

Keyword(s):

Time Series ◽

Rem Sleep ◽

Pulse Wave ◽

Sleep Stages ◽

Fluctuation Analysis ◽

Sympathetic Activation ◽

Scaling Exponents ◽

Fractal Scaling ◽

Peripheral Arterial ◽

Arterial Tone

Previous studies utilizing detrended fluctuation analysis (DFA) of heart rate variability during sleep revealed a higher fractal exponent during rapid eye movement (REM) sleep than non-REM sleep. The aim of this study was to determine whether the same difference exists in the variations of peripheral arterial tone (PAT). Finger pulse wave measured by a novel plethysmographic technique was monitored during sleep in 12 chronic heart failure patients, 8 heavy snorers, and 12 healthy volunteers. For each subject, at least two 15-min time series were constructed from the interpulse intervals and from pulse wave amplitudes during REM and non-REM sleep. Fractal scaling exponents of both types of time series were significantly higher for REM than non-REM sleep in all groups. In each of the groups and in both sleep stages, the fractal scaling exponents based on pulse wave amplitude were significantly higher than those based on pulse rate variability. A repeat of the analysis for short-, intermediate-, and long-term intervals revealed that the fractallike exponents were evident only in the short- and intermediate-term intervals. Because PAT is a surrogate of sympathetic activation, our results indicate that variations in sympathetic activation during REM sleep have a fractallike behavior.

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Instantaneous variance scaling of AIRS thermodynamic profiles using a circular area Monte Carlo approach

Atmospheric Measurement Techniques ◽

10.5194/amt-11-2717-2018 ◽

2018 ◽

Vol 11 (5) ◽

pp. 2717-2733

Author(s):

Jesse Dorrestijn ◽

Brian H. Kahn ◽

João Teixeira ◽

Fredrick W. Irion

Keyword(s):

Monte Carlo ◽

Large Scale ◽

Specific Humidity ◽

Time Variability ◽

Small Scale ◽

Circular Area ◽

Scaling Exponents ◽

Cloud Parameterization ◽

Non Gaussian ◽

The Tropics

Abstract. Satellite observations are used to obtain vertical profiles of variance scaling of temperature (T) and specific humidity (q) in the atmosphere. A higher spatial resolution nadir retrieval at 13.5 km complements previous Atmospheric Infrared Sounder (AIRS) investigations with 45 km resolution retrievals and enables the derivation of power law scaling exponents to length scales as small as 55 km. We introduce a variable-sized circular-area Monte Carlo methodology to compute exponents instantaneously within the swath of AIRS that yields additional insight into scaling behavior. While this method is approximate and some biases are likely to exist within non-Gaussian portions of the satellite observational swaths of T and q, this method enables the estimation of scale-dependent behavior within instantaneous swaths for individual tropical and extratropical systems of interest. Scaling exponents are shown to fluctuate between β=-1 and −3 at scales ≥500 km, while at scales ≤500 km they are typically near β≈-2, with q slightly lower than T at the smallest scales observed. In the extratropics, the large-scale β is near −3. Within the tropics, however, the large-scale β for T is closer to −1 as small-scale moist convective processes dominate. In the tropics, q exhibits large-scale β between −2 and −3. The values of β are generally consistent with previous works of either time-averaged spatial variance estimates, or aircraft observations that require averaging over numerous flight observational segments. The instantaneous variance scaling methodology is relevant for cloud parameterization development and the assessment of time variability of scaling exponents.

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