Lab · Diffusion扩散实验 · 扩散
When does the clinic notice reach Arts?诊所通知什么时候到得了文学院？
The same 40 students. One Engineering student posts a campus-clinic notice. Each day the notice can pass along a recorded conversation, with the transmission probability, and it does not expire. If Engineering fills up, it is easy to tell the clinic that every student will have seen it. Arts still never sees it when no conversation crosses the faculties. That missing cross-talk is a bridge.还是这 40 名学生。工程学院的一名学生发出一则校园诊所通知。每一天，通知可以沿一条已记录的谈话传过去，概率就是传播概率，而且通知不会过期。工程学院如果传满了，就容易告诉诊所“每个学生都会看到”。没有跨学院的谈话时，文学院仍然谁也看不到。那条缺失的跨组谈话就是桥。
Why this matters.为何重要。 The notice moves along recorded talks. If no talk crosses the faculties, Arts never receives it, however easily it passes inside Engineering. The blank between the clouds is not what stops it. A missing talk is.通知沿已记录的谈话走。如果没有谈话跨过学院，文学院永远收不到，无论它在工程学院内部传得多容易。挡住它的不是两团之间的空白，而是缺失的谈话。
Try this试一试 Set Arts–Engineering talks to zero and watch the Arts squares. Then raise those talks, and leave the chance of passing along a talk where it is. Does the notice reach Arts?把跨学院的谈话设为零，看文学院的方。再把那些谈话调高，沿谈话传递的机会先不动。通知到得了文学院吗？
Read the chart读这张图
If you misread this读错了会怎样
If the clinic sees Engineering filled in and tells the university every student will have the notice, Arts can be left off the poster run. The notice can reach every Engineering student it can reach and still stop where no talk crosses to Arts.如果诊所看见工程学院已经传满，就告诉大学每个学生都会看到通知，文学院可能会被拿掉海报发放。通知可以传到它到得了的每一个工程学院学生，然后停在没有通向文学院的谈话的地方。
Enough, and not enough够用，以及不够
Enough to see that a missing Arts–Engineering talk, not only a low chance of passing the notice, stops it.够用来看见：挡住通知的，不只是传递机会低，还有文学院和工程学院之间缺失的谈话。
Not enough for a notice plan. It still needs the talks that were actually recorded, and a way to separate passing-along from students who would have heard about the clinic anyway.不够写一份通知计划。计划仍需要实际记下的谈话，以及把“沿谈话传递”和“这些学生本来就会听说诊所”分开的办法。
Equations, assumptions, and limits方程、假设与限度
The graph is the two-block model from the other network lab: each possible edge is an independent Bernoulli draw. Diffusion is a susceptible–infected process in discrete time. The index case is node 1 in group A. At each step, every infected node transmits independently along each edge to a susceptible neighbor with probability β. There is no recovery and no spontaneous infection.图是另一个网络实验里的两块模型：每条可能的边是一次独立的伯努利抽取。扩散是离散时间的易感—感染过程。指示病例是 A 组的 1 号节点。每一步，每个感染节点沿每条边独立地以概率 β 传给易感邻居。没有恢复，也没有自发感染。
The outbreak cannot leave the index case’s component. A between-group probability of zero means every draw has no bridge, so group B stays susceptible. A small probability can still draw zero bridges by chance. Transmission coins are drawn once per edge, direction, and step for the current seed, so raising β can infect more nodes without redrawing the graph. Changing a tie probability does redraw the graph.疫情不能离开指示病例所在的连通分量。组间概率为零意味着每一次抽样都没有桥，所以 B 组保持易感。概率很小的时候仍可能碰巧没有桥。对当前种子，每条边、每个方向、每一步的传播随机数只抽一次，所以提高 β 可以感染更多节点而不重画图。改变连边概率则会重画图。
Common pitfall.常见陷阱。 A large outbreak inside group A is not evidence that the process is about to jump. It can infect everyone it can reach and still stop at a missing bridge. Another pitfall is to read the gap between the two circles of nodes as the barrier. That gap is the layout. The barrier is the edge list. A third is to treat one run as the typical cascade. The next seed can cross on a different bridge.A 组内部疫情很大，并不能说明过程即将跳过去。它可以感染所有到得了的节点，然后停在一条缺失的桥上。另一个陷阱是把两圈节点之间的空隙当成障碍。那个空隙是布局。障碍是边的清单。第三个陷阱是把一次运行当成典型级联。下一个种子可能从另一条桥跨过去。