Analysis functions
For example, one can measure the full width at half maximum (FWHM) of the activation patterns or their centre of activity (CoA).
# Load a typical activation pattern of 30 cycles (from locomotion)
data("act_pattern")
# Reduce activation pattern to the first cycle
act_sub <- act_pattern$signal[
1:which(act_pattern$time == max(act_pattern$time))[1]
]
# Calculate FWHM and CoA
act_sub_FWHM <- FWHM(act_sub)
act_sub_CoA <- CoA(act_sub)
# Express results relative to the cycle
n <- length(act_sub)
cycle <- 100 * (seq_len(n) - 1) / n
FWHM_percent <- 100 * act_sub_FWHM / n
CoA_percent <- 100 * (act_sub_CoA - 1) / n
# Half-maximum threshold
hm <- min(act_sub) + (max(act_sub) - min(act_sub)) / 2
# Keep the half-maximum line only where activation is above threshold
hm_plot <- rep(NA_real_, n)
hm_plot[act_sub > hm] <- hm
# Plot activation pattern
plot(
cycle,
act_sub,
type = "l",
xlab = "Cycle (%)",
ylab = "Amplitude",
xlim = c(0, 100)
)
# FWHM: portions above half maximum
lines(
cycle,
hm_plot,
lwd = 3,
col = "red"
)
# CoA
graphics::abline(
v = CoA_percent,
lwd = 2,
col = "blue"
)
# Labels
text(
64,
max(act_sub) * 0.95,
paste0("FWHM = ", round(FWHM_percent, 1), "%"),
adj = 0,
col = "red"
)
text(
64,
max(act_sub) * 0.85,
paste0("CoA = ", round(CoA_percent, 1), "%"),
adj = 0,
col = "blue"
)
Or perhaps one might want to investigate the nonlinear behaviour of a long activation pattern.
act <- act_pattern$signal
# Calculate the local complexity or Higuchi's fractal dimension (HFD)
nonlin_HFD <- HFD(act)$Higuchi
# Calculate the global complexity or Hurst exponent (H)
nonlin_H <- Hurst(act, min_win = max(act_pattern$time))$Hurst
message("Higuchi's fractal dimension: ", round(nonlin_HFD, 3))
#> Higuchi's fractal dimension: 1.047
message("Hurst exponent: ", round(nonlin_H, 3))
#> Hurst exponent: 0.338