Polychrony as Chinampas
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...
| Main Authors: | , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-04-01
|
| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/16/4/193 |
| _version_ | 1797606685465903104 |
|---|---|
| author | Eric Dolores-Cuenca José Antonio Arciniega-Nevárez Anh Nguyen Amanda Yitong Zou Luke Van Popering Nathan Crock Gordon Erlebacher Jose L. Mendoza-Cortes |
| author_facet | Eric Dolores-Cuenca José Antonio Arciniega-Nevárez Anh Nguyen Amanda Yitong Zou Luke Van Popering Nathan Crock Gordon Erlebacher Jose L. Mendoza-Cortes |
| author_sort | Eric Dolores-Cuenca |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T05:18:34Z |
| format | Article |
| id | doaj.art-14fb5778e3c74e5b8f5ff03faad36349 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-11T05:18:34Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-14fb5778e3c74e5b8f5ff03faad363492023-11-17T17:59:04ZengMDPI AGAlgorithms1999-48932023-04-0116419310.3390/a16040193Polychrony as ChinampasEric Dolores-Cuenca0José Antonio Arciniega-Nevárez1Anh Nguyen2Amanda Yitong Zou3Luke Van Popering4Nathan Crock5Gordon Erlebacher6Jose L. Mendoza-Cortes7Department of Mathematics, Yonsei University, Seoul 03722, Republic of KoreaDivisión de Ingenierías, Campus Guanajuato, Universidad de Guanajuato, Guanajuato 36000, MexicoCollege of Arts and Sciences, Drexel University, Philadelphia, PA 19104, USADepartment of Mathematics, University of Michigan, Ann Arbor, MI 48104, USAEmelex, Tallahassee, FL 32308, USAEmelex, Tallahassee, FL 32308, USADepartment of Scientific Computing, Florida State University, Tallahassee, FL 32306, USADepartment of Chemical Engineering & Materials Science, Michigan State University, East Lansing, MI 48824, USAIn 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.https://www.mdpi.com/1999-4893/16/4/193polychronynonlinear signal flow graphcellular automatarule 192order polynomialsEhrhart series |
| spellingShingle | Eric Dolores-Cuenca José Antonio Arciniega-Nevárez Anh Nguyen Amanda Yitong Zou Luke Van Popering Nathan Crock Gordon Erlebacher Jose L. Mendoza-Cortes Polychrony as Chinampas Algorithms polychrony nonlinear signal flow graph cellular automata rule 192 order polynomials Ehrhart series |
| title | Polychrony as Chinampas |
| title_full | Polychrony as Chinampas |
| title_fullStr | Polychrony as Chinampas |
| title_full_unstemmed | Polychrony as Chinampas |
| title_short | Polychrony as Chinampas |
| title_sort | polychrony as chinampas |
| topic | polychrony nonlinear signal flow graph cellular automata rule 192 order polynomials Ehrhart series |
| url | https://www.mdpi.com/1999-4893/16/4/193 |
| work_keys_str_mv | AT ericdolorescuenca polychronyaschinampas AT joseantonioarcinieganevarez polychronyaschinampas AT anhnguyen polychronyaschinampas AT amandayitongzou polychronyaschinampas AT lukevanpopering polychronyaschinampas AT nathancrock polychronyaschinampas AT gordonerlebacher polychronyaschinampas AT joselmendozacortes polychronyaschinampas |