TABLE 1.

Variables computed for CoP analysis

Description of CoP data obtained from force plate
Time series	Abbreviation		Unit	Description	Equation
Raw CoP time series (AP, ML)	AP0; ML0		mm	Time series describing the CoP path relative to the origin of the force platform in the anterior-posterior (AP; z-axis) and medial-lateral (ML; x-axis) directions	N.A. (directly recorded from force plate)
Signal filtered using 4th order Butterworth low pass filter with 5 Hz cutoff frequency (Prieto et al., 1996; Sun et al., 2018) First second (=1000 samples) of signal cut out to eliminate the filter transient effect.
CoP time series referenced to mean (AP, ML)	AP; ML		Mm	CoP path time series describing the change of CoP relative to the mean CoP value	AP= AP0 - mean(AP0)
					ML= ML0 - mean(ML0)
Resultant Distance time series (comb. AP and ML)	Rd		Mm	Resultant distance time series describing vector distance from mean CoP to pair of points in AP0 and ML0	$rd=\surd \left(A{P}^2+M{L}^2\right)$
Traditional CoP measures (Prieto et al., 1996)
Variable name	Abbreviation		Unit	Description	Equation
Fractal dimension - 95% Confidence Ellipse	Fd		-	Fractal dimension is a unitless measure of the degree to which a curve fills the metric space which it encompasses. Fractal dimension confidence ellipse models the area of the stabilogram with the 95% confidence ellipse	$fd=\log \left(N\right)/\log \left(\frac{N*d}{pathlength}\right)$
					$d=\surd \left(2a*2b\right)$
Mean Distance	Mdist		Mm	Mean resultant distance; average distance from the mean CoP	$mdist=mean\left(rd\right)$
Mean Distance AP	mdist_AP		Mm	Average AP distance from mean CoP	$mdist\_AP=mean\left(\left|AP\right|\right)$
Mean Distance ML	mdist_ML		Mm	Average ML distance from mean CoP	$mdist\_ML=mean\left(\left|ML\right|\right)$
Mean Frequency	mfreq		Hz	Mean frequency is the rotational frequency, in revolutions per second or Hz, of the CoP if it had traveled the total excursions around a circle with a radius of the mean distance	$mfreq=\frac{mvelo}{2\pi *mdist}$
Mean Velocity	mvelo		mm/s	Average velocity of resultant CoP	$mvelo=\frac{pathlengt\mathrm{h}}{T}$
Mean Velocity AP	mvelo_AP		mm/s	Average velocity of CoP path in the AP direction	$mvelo\_AP=\frac{pathlengt\mathrm{h}\_\text{AP}}{T}$
Mean Velocity ML	mvelo_ML		mm/s	Average velocity of CoP path in the ML direction	$mvelo\_ML=\frac{pathlengt\mathrm{h}\_\text{ML}}{T}$
Path Length	pathlength		Mm	Total length of resultant distance CoP path	$pathlengt\mathrm{h}=\sum \surd \left[{\left(AP\left(n+1\right)-AP\left(n\right)\right)}^2+{\left(ML\left(n+1\right)-ML\left(n\right)\right)}^2\right]$
Path Length AP	pathlength_AP		Mm	Total length of CoP path in the AP direction	$pathlength\_AP=\sum \left|AP\left(n+1\right)-AP\left(n\right)\right|$
Path Length ML	pathlength_ML		Mm	Total length of CoP path in the ML direction	$pathlength\_ML=\sum \left|ML\left(n+1\right)-ML\left(n\right)\right|$
Range	Range		Mm	Maximum distance between any 2 points on the CoP resultant distance	$range=\left|\max \left(rd\right)-\min \left(rd\right)\right|$
Range AP	range_AP		Mm	Maximum distance between any 2 points on the CoP path in the AP direction	$range\_AP=\left|\max \left(AP\right)-\min \left(AP\right)\right|$
Range ML	range_ML		Mm	Maximum distance between any 2 points on the CoP path in the ML direction	$range\_ML=\left|\max \left(ML\right)-\min \left(ML\right)\right|$
Root Mean Square distance	RMS_dist		Mm	RMS distance from mean CoP for resultant distance time series	$RMS\_dist=\surd \left(\frac{1}{N}\sum r{d}^2\right)$
Standard Deviation	SD		Mm	Standard deviation of resultant distance (rd) time series	$SD=\surd \left(\frac{1}{N}\sum {\left(rd-mdist\right)}^2\right)$
Standard Deviation AP	SD_AP		Mm	Standard deviation of AP time series	$SD\_AP=\surd \left(\frac{1}{N}\sum A{P}^2\right)$
Standard Deviation ML	SD_ML		Mm	Standard deviation of ML time series	$SD\_ML=\surd \left(\frac{1}{N}\sum M{L}^2\right)$
Sway Area	area_sw		mm2/s	Sway area estimates the area enclosed by the CoP path per unit of time. Approximated by summing the area of the triangles formed by two consecutive points on the CoP path and the mean CoP	$area\_sw=\frac{1}{2T}\sum \left|AP\left(n+1\right)ML\left(n\right)-AP\left(n\right)ML\left(n+1\right)\right|$
95% Confidence Ellipse Area	area_ce		mm2	The 95% confidence ellipse area is the area of the 95% bivariate confidence ellipse, which is expected to enclose approximately 95% of the points on the resultant distance CoP path	${\mathit{area}}_{\mathrm{ce}}=\pi ab$
					$a=\surd \left(F_{0.5\left[2,n-2\right]}\left(S{D}_{AP}^2+S{D}_{ML}^2+D\right)\right)$
					$b=\surd \left(F_{0.5\left[2,n-2\right]}\left(S{D}_{AP}^2+S{D}_{ML}^2-D\right)\right)$
					$D=\surd \left[\left(S{D}_{AP}^2+S{D}_{ML}^2\right)-4\left(S{D}_{AP}^{2}S{D}_{ML}^2-S{D}_{APML}^2\right)\right]$
					$S{D}_{APML}=\frac{1}{N}\sum AP\left(n\right)ML\left(n\right)$

Entropy measures
Variable name	Abbreviation	Unit		Description	Equation
Sample Entropy	SampEn	-		Measure of complexity and regularity of the magnitude of the resultant displacement time series	SampEn is defined as the logarithmic likelihood that the patterns of the data that are close to each other will remain close for the next comparison within a longer pattern. Algorithm from (Richman and Moorman, 2000).
Sample Entropy AP	SampEn_AP	-		Measure of complexity and regularity of the AP time series	Briefly: A template of defined length, m, is created from the first few data point in the time series. The template is then compared to successive data points in the time series and a match is counted if it is within a defined threshold, r, of the template.
Sample Entropy ML	SampEn_ML	-		Measure of complexity and regularity of the ML time series	Here, m = 2 and r = 0.01