sMLE {musclesyneRgies}

Short-term maximum Lyapunov exponents

Description

Short-term maximum Lyapunov exponents

Usage

sMLE(synergies, mean_period, future_pts, norm, pts, R2_threshold = 0.9)

Arguments

synergies

A musclesyneRgies object

mean_period

To locate the nearest neighbour of each point on the state space trajectory

future_pts

To limit the number of points "in the future" that are being searched

norm

Type of normalisation ("u" for minimum subtraction and normalisation to the maximum, "z" for subtracting the mean and then divide by the standard deviation)

pts

Minimum number of points needed to linearly approximate the first part of the divergence curve

R2_threshold

Threshold for calculating the slope of the divergence curve

Details

The mean period is intended to exclude temporally close points. In gait, values are usually plus/minus half gait cycle. Future points usually correspond in gait to one to two gait cycles. Please consider that a sufficient amount of cycles in order to compute meaningful sMLE. For locomotor primitives, 30 gait cycles have been shown to be sensitive to perturbations (Santuz et al. 2020). However, in the more classical and widespread use on kinematic data, more are usually needed (Kang and Dingwell, 2006).

Value

A list with elements:

• divergences containing the average logarithmic divergence curve
  

• sMLE the short-term Maximum Lyapunov exponent
  

• R2 the goodness of fit of the most linear part of the divergence curve

References

Rosenstein, M.T., Collins, J.J., and De Luca, C.J. (1993). A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D 65, 117–134.

Santuz A, Brüll L, Ekizos A, Schroll A, Eckardt N, Kibele A, et al. Neuromotor Dynamics of Human Locomotion in Challenging Settings. iScience. 2020;23: 100796.

Kang H.G., and Dingwell J.B. (2006). Intra-session reliability of local dynamic stability of walking. Gait Posture. 24(3) 386-390.

Examples

# Load some primitives
data("primitives")
# Calculate sMLE of motor primitives in the muscle synergy space
short_term_MLE <- sMLE(primitives,
  mean_period = 80,
  future_pts = 200,
  norm = "z",
  pts = 30
)