Physiological fractals: Visual and statistical evidence across timescales and experimental states

2020 ◽  
Author(s):  
Jeffrey J Kim
Keyword(s):  
Time Series ◽  
Published Data ◽  
Compassion Meditation ◽  
Open Questions ◽  
Mean And Variance ◽  
Time Series Analyses ◽  
The Mean ◽  
Highly Correlated ◽  
Mind Training ◽  
Stable Signal

A marker of engaging in compassion meditation and related processes is an increase in heart-rate variability (HRV), typically interpreted as a marker of parasympathetic nervous response. Whilst insightful, open questions remain. For example, which timescale is best to examine the effects of meditation and related practices on HRV? Furthermore, how might advanced time series analyses – such as stationarity – be able to examine dynamic changes in the mean and variance of the HRV signal across time? Here we apply such methods to previously published data, which measured HRV pre- and post- a two-week compassionate mind training (CMT) intervention. Inspection of these data reveal that a visualization of HRV correlations across resting and compassion meditation states, pre- and post- two-week training, is retained across numerous recording timescales. Here, the fractal-like nature of our data indicate that the accuracy of representing HRV data can exist across timescales, albeit with greater or lesser granularity. Interestingly, inspection of the HRV signal at Time 2 compassion meditation versus Time 1 revealed a more highly correlated (i.e., potentially more stable) signal. We followed up these results with tests of stationarity, which revealed Time 2 had a less stochastic (variable) signal than Time 1, and a measure of distance in the time series, which showed that Time 2 had less of an average difference between rest and meditation than at Time 1. Our results provide novel assessment of visual and statistical markers of HRV change across distinct experimental states.

scholarly journals Physiological fractals: visual and statistical evidence across timescales and experimental states

2020 ◽  
Vol 17 (167) ◽  
pp. 20200334 ◽  
Author(s):  
Jeffrey J. Kim ◽  
Stacey Parker ◽  
Trent Henderson ◽  
James N. Kirby
Keyword(s):  
Time Series ◽  
Parasympathetic Nervous System ◽  
System Response ◽  
Published Data ◽  
Compassion Meditation ◽  
Open Questions ◽  
Mean And Variance ◽  
Time Series Analyses ◽  
Highly Correlated ◽  
Mind Training

A marker of engaging in compassion meditation and related processes is an increase in heart-rate variability (HRV), typically interpreted as a marker of parasympathetic nervous system response. While insightful, open questions remain. For example, which timescale is best to examine the effects of meditation and related practices on HRV? Furthermore, how might advanced time-series analyses––such as stationarity––be able to examine dynamic changes in the mean and variance of the HRV signal across time? Here we apply such methods to previously published data, which measured HRV pre- and post- a two-week compassionate mind training (CMT) intervention. Inspection of these data reveals that a visualization of HRV correlations across resting and compassion meditation states, pre- and post-two-week training, is retained across numerous recording timescales. Here, the fractal-like nature of our data indicates that the accuracy of representing HRV data can exist across timescales, albeit with greater or lesser granularity. Interestingly, inspection of the HRV signal at Time 2 compassion meditation versus Time 1 revealed a more highly correlated (i.e. potentially more stable) signal. We followed up these results with tests of stationarity, which revealed Time 2 had a less stochastic (variable) signal than Time 1, and a measure of distance in the time series, which showed that Time 2 had less of an average difference between rest and meditation than at Time 1. Our results provide novel assessment of visual and statistical markers of HRV change across distinct experimental states.

The Initial Return and Its Conditional Return Volatility: Evidence from the Chinese IPO Market

2014 ◽  
Vol 17 (04) ◽  
pp. 1450022 ◽  
Author(s):  
M. Monica Hussein ◽  
Zhong-Guo Zhou
Keyword(s):  
Time Series ◽  
Linear Functions ◽  
Return Volatility ◽  
Cross Sectional ◽  
Variance Model ◽  
Initial Return ◽  
Traditional Market ◽  
Mean And Variance ◽  
The Mean ◽  
Sectional Analysis

This paper investigates the monthly initial return and its conditional return volatility for Chinese IPOs. We find that the mean initial return (IR) and cross-sectional return volatility are highly auto- and cross-correlated, and time-varying. We propose a system of two simultaneous equations: a GARCH-in-mean (GARCH-M) process with an ARMA(1,1) adjustment in the residuals for the IR and an EGARCH process for the conditional return volatility, assuming that the IR and its conditional return volatility are linear functions of the same market, firm- and offer-specific characteristics. We find that the model captures both time-series and cross-sectional correlations at the mean and variance levels. Our findings suggest that the conditional return volatility affects the IR positively and significantly, in addition to the traditional market, firm- and offer-specific characteristics. IPOs with higher conditional return volatility, as a proxy for information asymmetry, tend to be underpriced more. The paper demonstrates the merit of using a conditional variance model, along with time series and cross-sectional analysis to price Chinese IPOs.

Analysis of historic jack pine budworm outbreaks in the Prairie provinces of Canada

1988 ◽  
Vol 18 (9) ◽  
pp. 1152-1158 ◽  
Author(s):  
W. Jan A. Volney
Keyword(s):  
Time Series ◽  
Severity Index ◽  
Jack Pine ◽  
Stationary Time Series ◽  
Sufficient Information ◽  
Outbreak Area ◽  
Jack Pine Budworm ◽  
Annual Time Series ◽  
Time Series Analyses ◽  
Highly Correlated

The annual Forest Insect and Disease Survey reports of the Canadian Forestry Service were used to develop a jack pine budworm (Choristoneurapinus Freeman) defoliation severity index for a 50-year span. The region covered was the western half of the host's (Pinusbanksiana Lamb.) range. An interpretation of this record permitted the construction of an annual time series of the total area moderately to severely or severely defoliated. The area of outbreaks has increased over the period. This trend was removed from the data to obtain a stationary time series. Analyses of the time series showed that there was a statistically significant periodicity to the size of outbreaks. An examination of the sample autocorrelation function revealed that only the past year's outbreak area was significantly correlated with that of the current year's outbreak. The model identified by applying the Box–Jenkins methodology to these results was inadequate, indicating that the series itself does not contain sufficient information for predictions. Outbreak area and the total area burned in Manitoba and Saskatchewan 4–7 years previously were highly correlated. Despite the crudity of the data, these relations could be exploited to develop predictors of outbreak size and occurrence. The significance of these results for forest management in the region is discussed.

Selection for economic characters in Australian Merino sheep. 3. Inheritance of skin-fold score in Merino sheep and problems of scale.

1953 ◽  
Vol 4 (2) ◽  
pp. 204 ◽  
Author(s):  
FHW Morley
Keyword(s):  
Logarithmic Transformation ◽  
Published Data ◽  
Logarithmic Scale ◽  
Strongly Correlated ◽  
Merino Sheep ◽  
Skin Fold ◽  
Mean And Variance ◽  
The Mean ◽  
Breed Crosses ◽  
Accuracy Of Prediction

A study of published data on the fold scores of certain breed crosses, backcrosses, and filial generations suggests that causes of variation in skinfold score act geometrically. A logarithmic transformation increased the accuracy of prediction of F2 and backcross scores. Data from selection experiments on Merinos at Trangie were analysed using both arithmetic and logarithmic scales. Heritability of breech fold score was estimated as 0.45 on an arithmetic scale, 0.55 on the logarithmic scale. The mean and variance within groups of Merinos with different means were strongly correlated on the arithmetic scale, but this correlation was removed by the logarithmic transformation, resulting variances being approximately constant. Freedom from folds showed strong potence on both arithmetic and logarithmic scales. Theoretical implications of potence and geometric action appear to be confirmed by available data.

scholarly journals Consistency of Regions of Interest as nodes of fMRI functional brain networks

2017 ◽  
Vol 1 (3) ◽  
pp. 254-274 ◽  
Author(s):  
Onerva Korhonen ◽  
Heini Saarimäki ◽  
Enrico Glerean ◽  
Mikko Sams ◽  
Jari Saramäki
Keyword(s):  
Time Series ◽  
Pearson Correlation ◽  
Network Connectivity ◽  
Regions Of Interest ◽  
Brain Areas ◽  
Network Nodes ◽  
Functional Relationships ◽  
Functional Brain Networks ◽  
The Mean ◽  
Highly Correlated

The functional network approach, where fMRI BOLD time series are mapped to networks depicting functional relationships between brain areas, has opened new insights into the function of the human brain. In this approach, the choice of network nodes is of crucial importance. One option is to consider fMRI voxels as nodes. This results in a large number of nodes, making network analysis and interpretation of results challenging. A common alternative is to use predefined clusters of anatomically close voxels, Regions of Interest (ROIs). This approach assumes that voxels within ROIs are functionally similar. Because these two approaches result in different network structures, it is crucial to understand what happens to network connectivity when moving from the voxel level to the ROI level. We show that the consistency of ROIs, defined as the mean Pearson correlation coefficient between the time series of their voxels, varies widely in resting-state experimental data. Therefore the assumption of similar voxel dynamics within each ROI does not generally hold. Further, the time series of low-consistency ROIs may be highly correlated, resulting in spurious links in ROI-level networks. Based on these results, we recommend that averaging BOLD signals over anatomically defined ROIs should be carefully considered.

Changes in antibiotic usage and susceptibility in nosocomial Enterobacteriaceae and Pseudomonas isolates following the introduction of ertapenem to hospital formulary

2011 ◽  
Vol 140 (1) ◽  
pp. 115-125 ◽  
Author(s):  
C. J. GRABER ◽  
C. HUTCHINGS ◽  
F. DONG ◽  
W. LEE ◽  
J. K. CHUNG ◽  
...  
Keyword(s):  
Time Series ◽  
Linear Trend ◽  
Interrupted Time Series ◽  
Antibiotic Usage ◽  
Cross Resistance ◽  
Hospital Formulary ◽  
Time Series Analyses ◽  
The Mean ◽  
The Impact ◽  
Change In Mean

SUMMARYThere is concern that widespread usage of ertapenem may promote cross-resistance to other carbapenems. To analyse the impact that adding ertapenem to our hospital formulary had on usage of other broad-spectrum agents and on susceptibilities of nosocomial Enterobacteriaceae and Pseudomonas isolates, we performed interrupted time-series analyses to determine the change in linear trend in antibiotic usage and change in mean proportion and linear trend of susceptibility pre- (March 2004–June 2005) and post- (July 2005–December 2008) ertapenem introduction. Usage of piperacillin-tazobactam (P=0·0013) and ampicillin-sulbactam (P=0·035) declined post-ertapenem introduction. For Enterobacteriaceae, the mean proportion susceptible to ciprofloxacin (P=0·016) and piperacillin-tazobactam (P=0·038) increased, while the linear trend in susceptibility significantly increased for cefepime (P=0·012) but declined for ceftriaxone (P=0·0032). For Pseudomonas, the mean proportion susceptible to cefepime (P=0·011) and piperacillin-tazobactam (P=0·028) increased, as did the linear trend in susceptibility to ciprofloxacin (P=0·028). Notably, no significant changes in carbapenem susceptibility were observed.

scholarly journals A comparison of methods to estimate vertical land motion trends from GNSS and altimetry at tide gauge stations

Ocean Science ◽  
2018 ◽  
Vol 14 (2) ◽  
pp. 187-204 ◽  
Author(s):  
Marcel Kleinherenbrink ◽  
Riccardo Riva ◽  
Thomas Frederikse
Keyword(s):  
Time Series ◽  
Sea Level ◽  
Tide Gauge ◽  
Satellite System ◽  
Vertical Land Motion ◽  
Correlation Threshold ◽  
The Mean ◽  
Highly Correlated ◽  
Global Navigation Satellite ◽  
Along Track

Abstract. Tide gauge (TG) records are affected by vertical land motion (VLM), causing them to observe relative instead of geocentric sea level. VLM can be estimated from global navigation satellite system (GNSS) time series, but only a few TGs are equipped with a GNSS receiver. Hence, (multiple) neighboring GNSS stations can be used to estimate VLM at the TG. This study compares eight approaches to estimate VLM trends at 570 TG stations using GNSS by taking into account all GNSS trends with an uncertainty smaller than 1 mm yr−1 within 50 km. The range between the methods is comparable with the formal uncertainties of the GNSS trends. Taking the median of the surrounding GNSS trends shows the best agreement with differenced altimetry–tide gauge (ALT–TG) trends. An attempt is also made to improve VLM trends from ALT–TG time series. Only using highly correlated along-track altimetry and TG time series reduces the SD of ALT–TG time series by up to 10 %. As a result, there are spatially coherent changes in the trends, but the reduction in the root mean square (RMS) of differences between ALT–TG and GNSS trends is insignificant. However, setting correlation thresholds also acts like a filter to remove problematic TG time series. This results in sets of ALT–TG VLM trends at 344–663 TG locations, depending on the correlation threshold. Compared to other studies, we decrease the RMS of differences between GNSS and ALT–TG trends (from 1.47 to 1.22 mm yr−1), while we increase the number of locations (from 109 to 155), Depending on the methods the mean of differences between ALT–TG and GNSS trends vary between 0.1 and 0.2 mm yr−1. We reduce the mean of the differences by taking into account the effect of elastic deformation due to present-day mass redistribution. At varying ALT–TG correlation thresholds, we provide new sets of trends for 759 to 939 different TG stations. If both GNSS and ALT–TG trend estimates are available, we recommend using the GNSS trend estimates because residual ocean signals might correlate over long distances. However, if large discrepancies ( > 3 mm yr−1) between the two methods are present, local VLM differences between the TG and the GNSS station are likely the culprit and therefore it is better to take the ALT–TG trend estimate. GNSS estimates for which only a single GNSS station and no ALT–TG estimate are available might still require some inspection before they are used in sea level studies.

scholarly journals A comparison of data weighting methods to derive vertical land motion trends from GNSS and altimetry at tide gauge stations

2017 ◽  
Author(s):  
Marcel Kleinherenbrink ◽  
Riccardo Riva ◽  
Thomas Frederikse
Keyword(s):  
Time Series ◽  
Tide Gauge ◽  
Satellite System ◽  
Vertical Land Motion ◽  
Correlation Threshold ◽  
The Mean ◽  
Highly Correlated ◽  
Global Navigation Satellite ◽  
Along Track ◽  
Weighting Methods

Abstract. This study compares eight weighting techniques for Global Navigation Satellite System (GNSS)-derived Vertical Land Motion (VLM) trends at 570 tide gauge (TG) stations. The spread between the methods has a comparable size as the formal uncertainties of the GNSS trends. Taking the median of the surrounding GNSS trends shows the best agreement with differenced altimetry – tide gauge (ALT-TG) trends. An attempt is also made to improve VLM trends from ALT-TG time series. Only using highly correlated along-track altimetry and TG time series, reduces the standard deviation of ALT-TG time series up to 10 %. As a result, there are spatially coherent changes in the trends, but the reduction in the RMS of differences between ALT-TG and GNSS trends is insignificant. However, setting correlation thresholds also acts like a filter to remove problematic TG stations. This results in sets of ALT-TG VLM trends at 344–663 TG locations, depending on the correlation threshold. Compared to other studies, we decrease the RMS of differences between GNSS and ALT-TG trends (from 1.47 to 1.22 mm/yr), while we increase the number of locations (from 109 to 155), Depending on the weighting methods the mean of differences between ALT-TG and GNSS trends varies between 0.1–0.2 mm/yr. We reduce the mean of differences by taking into account the effect of elastic deformation due to present-day mass redistribution into account.

SIMULTANEOUS SPECIFICATION TESTING OF MEAN AND VARIANCE STRUCTURES IN NONLINEAR TIME SERIES REGRESSION

2011 ◽  
Vol 27 (4) ◽  
pp. 792-843 ◽  
Author(s):  
Song Xi Chen ◽  
Jiti Gao
Keyword(s):  
Time Series ◽  
Empirical Likelihood ◽  
Goodness Of Fit ◽  
Test Procedure ◽  
Single Pair ◽  
Test Statistic ◽  
Time Series Regression ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean

This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the variance components of the goodness-of-fit measure. To reduce the dependence of the test on a single pair of smoothing bandwidths, we construct an adaptive test by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. The test procedure is based on a bootstrap calibration to the distribution of the empirical likelihood test statistic. We demonstrate that the empirical likelihood test is able to distinguish local alternatives that are different from the null hypothesis at an optimal rate.

scholarly journals Statistical redundancy of instantaneous phases: theory and application to the seismic ambient wavefield

2015 ◽  
Vol 204 (2) ◽  
pp. 1159-1163 ◽  
Author(s):  
I. Gaudot ◽  
É. Beucler ◽  
A. Mocquet ◽  
M. Schimmel ◽  
M. Le Feuvre
Keyword(s):  
Time Series ◽  
Phase Coherence ◽  
Pairwise Comparisons ◽  
Gulf Of Guinea ◽  
Source Characterization ◽  
Second Moments ◽  
Mean And Variance ◽  
The Mean ◽  
Seismic Wavefield ◽  
Synchronous Time

Abstract In order to detect possible signal redundancies in the ambient seismic wavefield, we develop a new method based on pairwise comparisons among a set of synchronous time-series. This approach is based on instantaneous phase coherence statistics. The first and second moments of the pairwise phase coherence distribution are used to characterize the phase randomness. For perfect phase randomness, the theoretical values of the mean and variance are equal to 0 and $\sqrt{1-2/\pi }$, respectively. As a consequence, any deviation from these values indicates the presence of a redundant phase in the raw continuous signal. A previously detected microseismic source in the Gulf of Guinea is used to illustrate one of the possible ways of handling phase coherence statistics. The proposed approach allows us to properly localize this persistent source, and to quantify its contribution to the overall seismic ambient wavefield. The strength of the phase coherence statistics relies in its ability to quantify the redundancy of a given phase among a set of time-series with various useful applications in seismic noise-based studies (tomography and/or source characterization).

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