= Parallel-bond ray with different site and bond thresholds
Take a <directed graph> with vertices $v_0,v_1,\ldots$ and $n+1$ parallel bonds from $v_n$ to $v_{n+1}$. This is a <locally finite graph>, although the incoming degrees are unbounded. For <bond percolation>, $\theta_b(p)=\prod_{n\ge0}(1-(1-p)^{n+1})>0$ whenever $p>0$: the failure <probabilities> are summable, so the <infinite product> is positive. For <site percolation>, survival requires every vertex of the ray to be open, which has <probability> zero for $p<1$. Thus the <survival and susceptibility thresholds for directed percolation> satisfy $p_H^b=0$ and $p_H^s=1$.
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