8  cB211.072.64 d\Gamma/dq^2

theta_m <- function(x,s){
  return(  (exp(-x/s)-1)/(1/s+exp(x/s)+exp(-x/s))  )
}
theta_p <- function(x,s){
  return(  (1+s)/(1+s*exp(x/s))  )
}

theta <- function(x){
  r<-x*0
  l<-which(x<0)
  r[l]<-1
  return( r)
}
N<-200
x<-(c(0:N)-N/2)/(N/4)
y<-theta_m(x,0.5) 
gg<- myggplot(fill = FALSE, shape = FALSE)
gg<- gg + geom_line(aes(x=x, y=theta(x), color="$\\theta$"))
gg<- gg + geom_line(aes(x=x, y=theta_p(x,0.5), color="$\\theta_+(s=0.5)$"))
gg<- gg + geom_line(aes(x=x, y=theta_p(x,0.2), color="$\\theta_+(s=0.2)$"))
gg<- gg + geom_line(aes(x=x, y=theta_p(x,0.05), color="$\\theta_+(s=0.05)$"))
gg<- gg + geom_line(aes(x=x, y=theta_m(x,0.5), color="$\\theta_-(s=0.5)$"))
gg<- gg + geom_line(aes(x=x, y=theta_m(x,0.2), color="$\\theta_-(s=0.2)$"))
gg<- gg + geom_line(aes(x=x, y=theta_m(x,0.05), color="$\\theta_-(s=0.05)$"))

myplotly(gg)

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&lt;r &gt;

8.1 \sigma extrapolation

<r >

8.2 Stability

<r >

<r >

<r >

9 reconstruction th7

here we plot the smallest \sigma: 0.005000

here we plot the smallest \sigma: 0.005000

here we plot the smallest \sigma: 0.005000

<r > here we plot the smallest \sigma: 0.130000

here we plot the smallest \sigma: 0.130000

here we plot the smallest \sigma: 0.130000

<r > here we plot the smallest \sigma: 0.500000

here we plot the smallest \sigma: 0.500000

here we plot the smallest \sigma: 0.500000

<r >