deletions | additions       diff --git a/Trajectory spawning.tex b/Trajectory spawning.tex  index 64863b3..cdf923f 100644  --- a/Trajectory spawning.tex  +++ b/Trajectory spawning.tex 
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\subsection{trajectory spawning as message passing}  This can be re-formulated in the language of the message passing algorithm in which there are two types of nodes. The spawn surfaces are factor nodes, and the   trajectories are variable nodes (we'll call them trajectory nodes). The graph is bipartite, in that trajectory node are only connected to factor nodes and visa versa. Again, since we are only using local information, the graph will be a tree. The leaves will be nodes are created recursively by sweeping outwards from  the trajectories that encounter center of  the basin boundary before spawning. basin. The volume is computed by passing messages from outside in.  The messages from trajectory nodes to factor nodes will simply be the $\rho$ for that trajectory.   \begin{equation} 
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\right]  \end{equation}  The leaf nodes will be the trajectories that encounter the basin boundary before spawning. The incomming messages for those nodes $\mu_{f \to t}$ can be taken to be zero.  note:  At first I had the projection part, that includes the term $\vec{n}(x(0))$ as part of the factor node. It seemed logical because it is evaluated at the spawning surface (which is the factor). But I think computationally it will be simpler this way because the messages that are passed are simply numbers and all the computation involving the potential and high dimensional vectors can be done at runtime during the trajectory.