Arrow in Sigma Notation?

Question

Working through a bioinformatics textbook currently, when I ran into this set of sigma equations:

$$\sum_jJ_{ij}S_j+h>0\to S_i(t+1)=1\\[5pt]\sum_jJ_{ij}S_j+h\le0\to S_i(t+1)=0$$

My interpretation of it is that it means if the sum from $j$ to $S_i(t+1)$ of $J_{ij}S_j + h$ is less than $0$, then the equation evaluates to a value of $1$. Similarly if it is less than or equal to $0$, it evaluates to $0$ (for the bottom one). Is that correct?

Answer 1

$p(x)\rightarrow q(x)$ is the logical operator if.

If p(x) is true, then q(x) is true

If p(x) is false, then q(x) is unknown(until you actually calculate it)

The logical operator iff(if and only if) is a stronger version of the operator if

$p(x)\leftrightarrow q(x)$ means

If and only if p(x) is true, q(x) is true

Answer 2

redo this. It should read like this,

if $$\Sigma_jJ_{ij}S_j=J_{i1}S_1+J_{i2}S_2+J_{i3}S_3+...>0$$

then $$S_i(t-1)=1$$