# [R] Explain how it gets back out?

mousy0815 mousy0815 at gmail.com
Tue Jul 12 19:18:26 CEST 2011

```Probability <- function(N, f, m, b, x, t) {
#N is the number of lymph nodes
#f is the fraction of Dendritic cells (in the correct node) that have the
antigen
#m is the number of time steps
#b is the starting position (somewhere in the node or somewhere in the gap
between nodes. It is a number between 1 and (x+t))
#x is the number of time steps it takes to traverse the gap
#t is the number of time steps it takes to traverse a node.
A <- 1/N
B <- 1-A
C <- 1-f
D <- (((m+b-1)%%(x+t))+1)

if (b<=t) {########starts inside node
if (m<=(t-b)){return(B + A*(C^m))} # start & end in first node
if (D<=t) { # we finish in a node
a <- (B + A*(C^(t-b))) #first node
b <- ((B + A*(C^t))^(floor((m+b)/(x+t))-1))  # intermediate nodes (if
any)
c <- (B + A*(C^D))  # last node
d <- (a*b*c)
return(d)
} else {Probability(N, f, (m-1), b, x, t)} ## finish in a gap
} else {###### starts outside node
if (m<=(x+t-b)) {return(1)} #also end in the gap
if (D<=t) { #end in a node
b <- ((B + A*(C^t))^(floor((m/(x+t)))))
c <- (B + (A*(C^D)))
d <- (b*c)
return(d)
} else {Probability(N, f, (m-1), b, x, t)} #outside node
}
}

I have the following code and I know it works, but I need to explain what is
going on, particularly with the recursion.
Is it true that "when each call finishes - it will pass a quantity back to
the next generation above until you return to the start of the chain, then
outputs the final result."? If so, could someone explain it in a bit more
clearly? if not, how does the recursion work - how does it finally output a
value?

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