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Viability and Resilience of Languages in Competition

Publication Date: January 26, 2010
Journal: PLOS ONE
Authors: Laetitia Chapel, Xavier Castelló, Claire Bernard, Guillaume Deffuant, et al
Volume: 5
Issue: 1
Pages: e8681
DOI: https://dx.plos.org/10.1371/journal.pone.0008681
Publisher URL: http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0008681
PubMed: http://www.ncbi.nlm.nih.gov/pubmed/20126655
PubMed Central: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2811194
Europe PMC: http://europepmc.org/abstract/MED/20126655
Web of Science: 000273896500003
Scopus: 77749245889
Mendeley: http://www.mendeley.com/research/viability-resilience-languages-competition

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Figshare 6202 May 18:40 UTC

Figshare

{"files"=>["https://ndownloader.figshare.com/files/866128"], "description"=>"The continuous grey line represents stable fixed points and the dotted grey line unstable fixed points.", "links"=>[], "tags"=>["examples", "trajectories"], "article_id"=>536584, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008681.g004", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Left_panel_Examples_of_trajectories_in_green_starting_from_an_initial_state_for_three_values_of__and_and_right_panel_evolution_of_the_control_with_/536584", "title"=>"(Left panel) Examples of trajectories (in green) starting from an initial state for three values of (, and ), and (right panel) evolution of the control, with .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-26 01:49:44"}
{"files"=>["https://ndownloader.figshare.com/files/866230"], "description"=>"Viability kernel is in dark blue.", "links"=>[], "tags"=>["non", "resilient", "states", "eqn"], "article_id"=>536682, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008681.g005", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Resilient_blue_and_non_resilient_states_in_white_in_the_model_associated_to_dynamics_Eqn_9_with_constraint_set_Eqn_10_for_three_values_of__/536682", "title"=>"Resilient (blue) and non resilient states (in white) in the model associated to dynamics Eqn 9 with constraint set Eqn 10, for three values of : , , .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-26 01:51:22"}
{"files"=>["https://ndownloader.figshare.com/files/865958"], "description"=>"The viability kernels are represented in blue and stable attractors (if any) by dots. Arrows represent the field direction and the controls to choose. For , any control is convenient because they lead the system to a stable fixed point. For and , when trajectory lead to a point located outside the viability kernel, the control value must be changed in order to ensure coexistence.", "links"=>[], "tags"=>["kernels", "trajectories", "viable"], "article_id"=>536408, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008681.g002", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Viability_kernels_and_trajectories_that_maintain_the_system_viable_for_and_/536408", "title"=>"Viability kernels and trajectories that maintain the system viable for , and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-26 01:46:48"}
{"files"=>["https://ndownloader.figshare.com/files/866427"], "description"=>"The continuous grey line represents stable fixed points and the dotted grey line unstable fixed points. Note that for an initial state located inside but outside , the trajectory crosses the viability constraint set boundaries before reaching .", "links"=>[], "tags"=>["trajectories", "viability", "eqn"], "article_id"=>536881, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008681.g007", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_trajectories_in_green_starting_from_a_point_during_time_steps_that_allow_the_system_to_restore_its_viability_at_the_minimal_cost_of_restoration_using_cost_function_Eqn_12_/536881", "title"=>"Examples of trajectories (in green) starting from a point during time steps, that allow the system to restore its viability at the minimal cost of restoration, using cost function Eqn 12.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-26 01:54:41"}
{"files"=>["https://ndownloader.figshare.com/files/866329"], "description"=>"In dark blue, the viability kernel; between the level lines (light blue area), the cost of restoration is finite (one level line corresponds to a cost of 4.8 and the darker the line, the higher the cost); in the white area, the cost is infinite and the resilience is zero. (Left panel) Cost function (Eqn 11); (Right panel) cost function (Eqn 12).", "links"=>[], "tags"=>["abrams-strogatz"], "article_id"=>536789, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008681.g006", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Resilience_values_of_the_Abrams_Strogatz_model_/536789", "title"=>"Resilience values of the Abrams-Strogatz model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-26 01:53:09"}
{"files"=>["https://ndownloader.figshare.com/files/866533"], "description"=>"Boundaries of the viability kernel for the dynamics associated to system Eqn 7 and Eqn 8.", "links"=>[], "tags"=>["viability", "kernel", "eqn"], "article_id"=>536983, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008681.t001", "stats"=>{"downloads"=>6, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Boundaries_of_the_viability_kernel_for_the_dynamics_associated_to_system_Eqn_7_and_Eqn_8_/536983", "title"=>"Boundaries of the viability kernel for the dynamics associated to system Eqn 7 and Eqn 8.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-01-26 01:56:23"}
{"files"=>["https://ndownloader.figshare.com/files/865892"], "description"=>"Case of socially equivalent languages (). Marginal volatility (, solid line), high volatility regime (, dashed line), and low volatility regime (, dotted line).", "links"=>[], "tags"=>["volatility", "parameter", "probability"], "article_id"=>536344, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008681.g001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dependence_on_the_volatility_parameter_for_the_transition_probability_to_change_from_state_to_state_/536344", "title"=>"Dependence on the volatility parameter for the transition probability to change from state to state , .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-26 01:45:44"}
{"files"=>["https://ndownloader.figshare.com/files/866045"], "description"=>"The continuous black lines represent the theoretical curves of the viability kernel, and the area in blue the approximation. The continuous grey line represents stable fixed points and the dotted grey lines unstable fixed points.", "links"=>[], "tags"=>["kernel", "abrams-strogatz"], "article_id"=>536501, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008681.g003", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Viability_kernel_for_the_Abrams_Strogatz_model_with_and_/536501", "title"=>"Viability kernel for the Abrams-Strogatz model, with and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-26 01:48:21"}
{"files"=>["https://ndownloader.figshare.com/files/429690", "https://ndownloader.figshare.com/files/429729"], "description"=>"<div>We study the viability and resilience of languages, using a simple dynamical model of two languages in competition. Assuming that public action can modify the prestige of a language in order to avoid language extinction, we analyze two cases: (i) the prestige can only take two values, (ii) it can take any value but its change at each time step is bounded. In both cases, we determine the viability kernel, that is, the set of states for which there exists an action policy maintaining the coexistence of the two languages, and we define such policies. We also study the resilience of the languages and identify configurations from where the system can return to the viability kernel (finite resilience), or where one of the languages is lead to disappear (zero resilience). Within our current framework, the maintenance of a bilingual society is shown to be possible by introducing the prestige of a language as a control variable.</div>", "links"=>[], "tags"=>["viability", "resilience", "languages"], "article_id"=>144831, "categories"=>["Mathematics", "Information And Computing Sciences"], "users"=>["Laetitia Chapel", "Xavier Castelló", "Claire Bernard", "Guillaume Deffuant", "Victor M. Eguiluz", "Sophie Martin", "Maxi San Miguel"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0008681.s001", "https://dx.doi.org/10.1371/journal.pone.0008681.s002"], "stats"=>{"downloads"=>14, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Viability_and_Resilience_of_Languages_in_Competition/144831", "title"=>"Viability and Resilience of Languages in Competition", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2010-01-26 01:20:31"}

PMC Usage Stats 75717 Jan 15:16 UTC

PMC Usage Stats | Further Information

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Relative Metric 35663010 May 16:17 UTC

Relative Metric

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F1000Prime13 Jan 12:06 UTC

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