How the Spatial Position of Individuals Affects Their Influence on Swarms: A Numerical Comparison of Two Popular Swarm Dynamics Models
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{"title"=>"How the Spatial Position of Individuals Affects Their Influence on Swarms: A Numerical Comparison of Two Popular Swarm Dynamics Models", "type"=>"journal", "authors"=>[{"first_name"=>"Allison", "last_name"=>"Kolpas", "scopus_author_id"=>"16678857600"}, {"first_name"=>"Michael", "last_name"=>"Busch", "scopus_author_id"=>"57198078427"}, {"first_name"=>"Hong", "last_name"=>"Li", "scopus_author_id"=>"57196359867"}, {"first_name"=>"Iain D.", "last_name"=>"Couzin", "scopus_author_id"=>"55889306800"}, {"first_name"=>"Linda", "last_name"=>"Petzold", "scopus_author_id"=>"7005581592"}, {"first_name"=>"Jeff", "last_name"=>"Moehlis", "scopus_author_id"=>"6602083356"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "pui"=>"368580210", "sgr"=>"84875347747", "doi"=>"10.1371/journal.pone.0058525", "scopus"=>"2-s2.0-84875347747", "isbn"=>"1932-6203", "pmid"=>"23555585"}, "id"=>"2ecdfe2e-6d5e-3066-b874-400d0340345f", "abstract"=>"Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual's Voronoi neighbors. The models include a tunable parameter that controls an individual's relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.", "link"=>"http://www.mendeley.com/research/spatial-position-individuals-affects-influence-swarms-numerical-comparison-two-popular-swarm-dynamic", "reader_count"=>58, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>9, "Student > Doctoral Student"=>6, "Researcher"=>10, "Student > Ph. D. Student"=>16, "Student > Master"=>6, "Student > Bachelor"=>6, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>9, "Student > Doctoral Student"=>6, "Researcher"=>10, "Student > Ph. D. Student"=>16, "Student > Master"=>6, "Student > Bachelor"=>6, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>2}, "reader_count_by_subject_area"=>{"Engineering"=>7, "Unspecified"=>2, "Environmental Science"=>1, "Mathematics"=>3, "Agricultural and Biological Sciences"=>25, "Medicine and Dentistry"=>1, "Physics and Astronomy"=>10, "Psychology"=>1, "Computer Science"=>5, "Earth and Planetary Sciences"=>3}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>7}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>10}, "Psychology"=>{"Psychology"=>1}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>25}, "Computer Science"=>{"Computer Science"=>5}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>2}, "Environmental Science"=>{"Environmental Science"=>1}}, "reader_count_by_country"=>{"Canada"=>1, "United States"=>5, "China"=>1, "Mexico"=>2, "France"=>1}, "group_count"=>3}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1008025"], "description"=>"<p>The density of a swarm can be determined by dividing the number of individuals in the swarm by the area of the bounding box that encloses the swarm, which is the same bounding box used to compute swarm elongation.</p>", "links"=>[], "tags"=>["swarm"], "article_id"=>668651, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.t004", "stats"=>{"downloads"=>0, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Delaunay_based_model_swarm_density_individuals_area_/668651", "title"=>"Delaunay-based model swarm density (individuals/area).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-21 02:24:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/1008008"], "description"=>"<p>Average number of neighbors for each individual, as a percentage of total population in Delaunay-based model.</p>", "links"=>[], "tags"=>["neighbors", "delaunay-based"], "article_id"=>668634, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.t002", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_number_of_neighbors_for_each_individual_as_a_percentage_of_total_population_in_Delaunay_based_model_/668634", "title"=>"Average number of neighbors for each individual, as a percentage of total population in Delaunay-based model.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-21 02:23:54"}
  • {"files"=>["https://ndownloader.figshare.com/files/994957"], "description"=>"<div><p>Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual's Voronoi neighbors. The models include a tunable parameter that controls an individual's relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.</p> </div>", "links"=>[], "tags"=>["spatial", "individuals", "numerical", "swarm", "models"], "article_id"=>657914, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/How_the_Spatial_Position_of_Individuals_Affects_Their_Influence_on_Swarms_A_Numerical_Comparison_of_Two_Popular_Swarm_Dynamics_Models__/657914", "title"=>"How the Spatial Position of Individuals Affects Their Influence on Swarms: A Numerical Comparison of Two Popular Swarm Dynamics Models", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-22 09:30:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/994952"], "description"=>"<p>Polarization and elongation are given as functions of <i>r</i>, the ratio of orientation to attraction weightings, for schools of size <i>N</i> = 25, 50, 100, 150 for the local Delaunay-based schooling model. The probability of fragmentation is zero for all values of <i>N</i> and <i>r</i>. For large values of <i>N</i>, a distinct phase transition occurs at , where the swarm becomes elongated and polarized. The standard deviation of polarization values is bounded by 0.16 for all values of <i>N</i>, while the standard deviation of elongation values are bounded by: , , , .</p>", "links"=>[], "tags"=>["polarization"], "article_id"=>657909, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.g004", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_group_polarization_and_elongation_/657909", "title"=>"Average group polarization and elongation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-22 09:29:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/994951"], "description"=>"<p>(A) <i>N</i> = 10, <i>r</i> = 4, (B) <i>N</i> = 10, <i>r</i> = 16, (C) <i>N</i> = 10, <i>r</i> = 64, (D) <i>N</i> = 25, <i>r</i> = 4, (E) <i>N</i> = 25, <i>r</i> = 16, (F) <i>N</i> = 25, <i>r</i> = 64, (G) <i>N</i> = 50, <i>r</i> = 4, (H) <i>N</i> = 50, <i>r</i> = 16, (I) <i>N</i> = 50, <i>r</i> = 64, (J) <i>N</i> = 100, <i>r</i> = 4, (K) <i>N</i> = 100, Ì,, <i>r</i> = 16, (L) <i>N</i> = 100, <i>r</i> = 64. Results are colored according to , averaged over each point on a lattice of width  = 1 at time step . Groups are oriented so their center of mass is at the origin, and rotated such that the average direction of orientation aligns with the vertical axis. The perturbation was performed by rotating an individual counterclockwise by 90 degrees from the swarm's average direction of orientation. Boxes are only given a color if at least 5 individuals were averaged to compute that box's value. Standard deviation values are bounded over all values of <i>N</i>, for each value of <i>r</i>: , , .</p>", "links"=>[], "tags"=>["groups", "perturbation", "zone-based"], "article_id"=>657908, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.g003", "stats"=>{"downloads"=>3, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_relative_response_of_groups_to_a_single_perturbation_for_the_zone_based_model_/657908", "title"=>"Average relative response of groups to a single perturbation for the zone-based model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-22 09:28:50"}
  • {"files"=>["https://ndownloader.figshare.com/files/994947"], "description"=>"<p>The Voronoi cell associated with an individual in the swarm is the region of space which contains points that are closer to that individual than any other individual, where the boundary of a Voronoi cell (dashed lines) specifies two neighboring individuals. Black dots show the locations of the individuals. A Delaunay Triangulation defines triangular regions that are formed by drawing edges (solid lines) to connect nearest Voronoi neighbors. Therefore, the collection of edges given by the Delaunay Triangulation defines the swarm communication network topology when individuals within a swarm are constrained to communicate only with their nearest neighbors, as defined by Voronoi partitioning.</p>", "links"=>[], "tags"=>["voronoi", "delaunay"], "article_id"=>657904, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.g001", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relationship_between_a_Voronoi_Cell_and_its_Delaunay_Triangulation_/657904", "title"=>"Relationship between a Voronoi Cell and its Delaunay Triangulation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-22 09:28:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/1007978"], "description"=>"<p>Average number of neighbors for each individual, as a percentage of total population in zone-based model.</p>", "links"=>[], "tags"=>["neighbors", "zone-based"], "article_id"=>668605, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.t001", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_number_of_neighbors_for_each_individual_as_a_percentage_of_total_population_in_zone_based_model_/668605", "title"=>"Average number of neighbors for each individual, as a percentage of total population in zone-based model.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-21 02:23:25"}
  • {"files"=>["https://ndownloader.figshare.com/files/1007994"], "description"=>"<p>The density of a swarm can be determined by dividing the number of individuals in the swarm by the area of the bounding box that encloses the swarm, which is the same bounding box used to compute swarm elongation.</p>", "links"=>[], "tags"=>["swarm"], "article_id"=>668619, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.t003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Zone_based_model_swarm_density_individuals_area_/668619", "title"=>"Zone-based model swarm density (individuals/area).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-21 02:23:39"}
  • {"files"=>["https://ndownloader.figshare.com/files/994954"], "description"=>"<p>(A) <i>N</i> = 10, <i>r</i> = 4, (B) <i>N</i> = 10, <i>r</i> = 16, (C) <i>N</i> = 10, <i>r</i> = 64, (D) <i>N</i> = 25, <i>r</i> = 4, (E) <i>N</i> = 25, <i>r</i> = 16, (F) <i>N</i> = 25, <i>r</i> = 64, (G) <i>N</i> = 50, <i>r</i> = 4, (H) <i>N</i> = 50, <i>r</i> = 16, (I) <i>N</i> = 50, <i>r</i> = 64, (J) <i>N</i> = 100, <i>r</i> = 4, (K) <i>N</i> = 100, Ì,, <i>r</i> = 16, (L) <i>N</i> = 100, <i>r</i> = 64. Results are colored according to , averaged over each point on a lattice of width  = 1 at time step . Groups are oriented so their center of mass is at the origin, and rotated such that the average direction of orientation aligns with the vertical axis. The perturbation was performed by rotating an individual counterclockwise by 90 degrees from the swarm's average direction of orientation. Boxes are only given a color if at least 5 individuals were averaged to compute that box's value. Standard deviation values are bounded over all values of <i>N</i>, for each value of <i>r</i>: , , .</p>", "links"=>[], "tags"=>["groups", "perturbation", "delaunay-based"], "article_id"=>657911, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.g005", "stats"=>{"downloads"=>3, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_relative_response_of_groups_to_a_single_perturbation_for_the_Delaunay_based_model_/657911", "title"=>"Average relative response of groups to a single perturbation for the Delaunay-based model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-22 09:29:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/994955"], "description"=>"<p>For the and parameter values of the Dealunay-based perturbation results depicted in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058525#pone-0058525-g005\" target=\"_blank\">Figure 5(G)</a>, the collection of swarms are separated into (a) leftward aligned and (b) rightward aligned swarms. Averaging (a) and (b) produces <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058525#pone-0058525-g005\" target=\"_blank\">Figure 5(G)</a>. Results are colored according to <i>C</i>, averaged over each point on a lattice of width  = 1 at time step .</p>", "links"=>[], "tags"=>["swarm"], "article_id"=>657912, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.g006", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Symmetry_of_swarm_influence_/657912", "title"=>"Symmetry of swarm influence.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-22 09:29:54"}
  • {"files"=>["https://ndownloader.figshare.com/files/994949"], "description"=>"<p>Polarization, elongation, and probability of fragmentation are given as functions of <i>r</i>, the ratio of orientation to attraction weightings, for schools of size for the local zone-based schooling model. For schools of size , the probability of fragmentation is zero for all values of <i>r</i>. The standard deviation of polarization values is bounded by 0.20 for all values of <i>N</i>, while the standard deviation of elongation values are bounded by: , , , .</p>", "links"=>[], "tags"=>["probability"], "article_id"=>657906, "categories"=>["Information And Computing Sciences", "Mathematics", "Neuroscience"], "users"=>["Allison Kolpas", "Michael Busch", "Hong Li", "Iain D. Couzin", "Linda Petzold", "Jeff Moehlis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0058525.g002", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_group_polarization_elongation_and_probability_of_fragmentation_/657906", "title"=>"Average group polarization, elongation, and probability of fragmentation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-22 09:28:12"}

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Relative Metric

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