  In this paper, we study the flow of signals through linear paths with the
nonlinear condition that a node emits a signal when it receives external
stimuli or when two incoming signals from other nodes arrive coincidentally
with a combined amplitude above a fixed threshold. Sets of such nodes form a
polychrony group and can sometimes lead to cascades. In the context of this
work, cascades are polychrony groups in which the number of nodes activated as
a consequence of other nodes is greater than the number of externally activated
nodes. The difference between these two numbers is the so-called profit.
  Given the initial conditions, we predict the conditions for a vertex to
activate at a prescribed time and provide an algorithm to efficiently
reconstruct a cascade. We develop a dictionary between polychrony groups and
graph theory. We call the graph corresponding to a cascade a chinampa. This
link leads to a topological classification of chinampas. We enumerate the
chinampas of profits zero and one and the description of a family of chinampas
isomorphic to a family of partially ordered sets, which implies that the
enumeration problem of this family is equivalent to computing the Stanley-order
polynomials of those partially ordered sets.

Combinatorics;Formal Languages and Automata Theory;Category Theory;Neurons and Cognition