Polychrony as Chinampas
Abstract
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.
Cite
@article{arxiv.2103.15265,
title = {Polychrony as Chinampas},
author = {Eric Dolores-Cuenca and Jose Antonio Arciniega-Nevarez and Anh Nguyen and Yitong Zou and Luke Van Popering and Nathan Crock and Gordon Erlebacher and Jose L. Mendoza-Cortes},
journal= {arXiv preprint arXiv:2103.15265},
year = {2026}
}
Comments
32 pages. We changed the exposition, removed unfinished work, and added bibliography. To appear on "Algorithms"