Metastability and Eye Movements: A Dynamical‑Systems Interpretation

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  1. Why metastability is a natural language for gaze behavior The idea that perception, attention, and neural activity evolve through transiently stable states has deep roots in cognitive science and neuroscience. Concepts such as attractors , basins , noise‑induced transitions , and escape times appear in work on perceptual switching, decision‑making, and neural population dynamics (Kelso, 1995; Rabinovich et al., 2008; Deco & Jirsa, 2012). Eye movements, especially the alternation between fixations and saccades ,   fit remarkably well into this metastable picture. The Freidlin–Wentzell theory of rare events (Freidlin & Wentzell, 2012) provides a rigorous mathematical language for these intuitions. 2. Fixations as metastable states  Consider the gaze position X t as the state of a stochastic dynamical system. During a fixation the  gaze remains confined to a small region, microsaccades and noise generate small fluctuations, and the gaze tends to return...
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R function prevalenceCI

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prevalenceCI calculates the confidence interval for prevalence study. The function takes four arguments:


  • x: number of positive cases.
  • n: sample size.
  • ci.lev: level of confidence.
  • ci.method: confidence interval calculation method (default=“all”, alternatives=“agresti.coull”,“exact”,“Jeffreys”,“Wald”,“Wilson”).

The function uses the prevalence package and returns the confidence interval for prevalence study using different methods.


prevalenceCI<-function(x,n,ci.lev=0.95,ci.method="all") {

#x:number of positive cases

#n:sample size

#ci.lev:level of confidence

#ci.method:confidence interval calculation method (default="all", alternatives="agresti.coull","exact","Jeffreys","Wald","Wilson")

library(prevalence)

results<- propCI(x,n)

tem=NULL

ifelse(ci.method=="agresti.coull",tem<-results[1,],

ifelse(ci.method=="exact",tem<-results[2,],

ifelse(ci.method=="",tem<-results[3,],

ifelse(ci.method=="",tem<-results[4,],

ifelse(ci.method=="",tem<-results[5,],

tem<- results)))))

return(tem)

}


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