Topological data analysis of biological aggregation models.
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2015-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC4430537?pdf=render |
| _version_ | 1819050823605288960 |
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| author | Chad M Topaz Lori Ziegelmeier Tom Halverson |
| author_facet | Chad M Topaz Lori Ziegelmeier Tom Halverson |
| author_sort | Chad M Topaz |
| collection | DOAJ |
| description | We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti numbers over simulation time and topological persistence scale. We compare our topological results to order parameters typically used to quantify the global behavior of aggregations, such as polarization and angular momentum. The topological calculations reveal events and structure not captured by the order parameters. |
| first_indexed | 2024-12-21T11:54:10Z |
| format | Article |
| id | doaj.art-7c5d43e2fc1047c2ae49e698285f18b2 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-21T11:54:10Z |
| publishDate | 2015-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-7c5d43e2fc1047c2ae49e698285f18b22022-12-21T19:04:58ZengPublic Library of Science (PLoS)PLoS ONE1932-62032015-01-01105e012638310.1371/journal.pone.0126383Topological data analysis of biological aggregation models.Chad M TopazLori ZiegelmeierTom HalversonWe apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti numbers over simulation time and topological persistence scale. We compare our topological results to order parameters typically used to quantify the global behavior of aggregations, such as polarization and angular momentum. The topological calculations reveal events and structure not captured by the order parameters.http://europepmc.org/articles/PMC4430537?pdf=render |
| spellingShingle | Chad M Topaz Lori Ziegelmeier Tom Halverson Topological data analysis of biological aggregation models. PLoS ONE |
| title | Topological data analysis of biological aggregation models. |
| title_full | Topological data analysis of biological aggregation models. |
| title_fullStr | Topological data analysis of biological aggregation models. |
| title_full_unstemmed | Topological data analysis of biological aggregation models. |
| title_short | Topological data analysis of biological aggregation models. |
| title_sort | topological data analysis of biological aggregation models |
| url | http://europepmc.org/articles/PMC4430537?pdf=render |
| work_keys_str_mv | AT chadmtopaz topologicaldataanalysisofbiologicalaggregationmodels AT loriziegelmeier topologicaldataanalysisofbiologicalaggregationmodels AT tomhalverson topologicaldataanalysisofbiologicalaggregationmodels |