{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:02:14Z","timestamp":1760148134227,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T00:00:00Z","timestamp":1680480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Korea (NRF)","award":["2020R1C1C1A01008261"],"award-info":[{"award-number":["2020R1C1C1A01008261"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/a16040193","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T02:10:13Z","timestamp":1680487813000},"page":"193","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Polychrony as Chinampas"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3909-5580","authenticated-orcid":false,"given":"Eric","family":"Dolores-Cuenca","sequence":"first","affiliation":[{"name":"Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2639-0540","authenticated-orcid":false,"given":"Jos\u00e9 Antonio","family":"Arciniega-Nev\u00e1rez","sequence":"additional","affiliation":[{"name":"Divisi\u00f3n de Ingenier\u00edas, Campus Guanajuato, Universidad de Guanajuato, Guanajuato 36000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anh","family":"Nguyen","sequence":"additional","affiliation":[{"name":"College of Arts and Sciences, Drexel University, Philadelphia, PA 19104, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amanda Yitong","family":"Zou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Michigan, Ann Arbor, MI 48104, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luke","family":"Van Popering","sequence":"additional","affiliation":[{"name":"Emelex, Tallahassee, FL 32308, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nathan","family":"Crock","sequence":"additional","affiliation":[{"name":"Emelex, Tallahassee, FL 32308, USA"},{"name":"Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gordon","family":"Erlebacher","sequence":"additional","affiliation":[{"name":"Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5184-1406","authenticated-orcid":false,"given":"Jose L.","family":"Mendoza-Cortes","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering & Materials Science, Michigan State University, East Lansing, MI 48824, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1162\/089976606775093882","article-title":"Polychronization: Computation with spikes","volume":"18","author":"Izhikevich","year":"2006","journal-title":"Neural Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1109\/JRPROC.1953.274449","article-title":"Feedback Theory-Some Properties of Signal Flow Graphs","volume":"41","author":"Mason","year":"1953","journal-title":"Proc. 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