| Autor: |
Eric Dolores-Cuenca, José Antonio Arciniega-Nevárez, Anh Nguyen, Amanda Yitong Zou, Luke Van Popering, Nathan Crock, Gordon Erlebacher, Jose L. Mendoza-Cortes |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Algorithms, Vol 16, Iss 4, p 193 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
1999-4893 |
| DOI: |
10.3390/a16040193 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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