When Two Become One: The Limits of Causality Analysis of Brain Dynamics
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{"title"=>"When two become one: The limits of causality analysis of brain dynamics", "type"=>"journal", "authors"=>[{"first_name"=>"Daniel", "last_name"=>"Chicharro", "scopus_author_id"=>"26657805900"}, {"first_name"=>"Anders", "last_name"=>"Ledberg", "scopus_author_id"=>"6602403928"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"doi"=>"10.1371/journal.pone.0032466", "sgr"=>"84858425279", "issn"=>"19326203", "pui"=>"364461139", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "pmid"=>"22438878", "scopus"=>"2-s2.0-84858425279"}, "id"=>"d08f12f1-4812-3c34-b89c-78f9de5bad55", "abstract"=>"Biological systems often consist of multiple interacting subsystems, the brain being a prominent example. To understand the functions of such systems it is important to analyze if and how the subsystems interact and to describe the effect of these interactions. In this work we investigate the extent to which the cause-and-effect framework is applicable to such interacting subsystems. We base our work on a standard notion of causal effects and define a new concept called natural causal effect. This new concept takes into account that when studying interactions in biological systems, one is often not interested in the effect of perturbations that alter the dynamics. The interest is instead in how the causal connections participate in the generation of the observed natural dynamics. We identify the constraints on the structure of the causal connections that determine the existence of natural causal effects. In particular, we show that the influence of the causal connections on the natural dynamics of the system often cannot be analyzed in terms of the causal effect of one subsystem on another. Only when the causing subsystem is autonomous with respect to the rest can this interpretation be made. We note that subsystems in the brain are often bidirectionally connected, which means that interactions rarely should be quantified in terms of cause-and-effect. We furthermore introduce a framework for how natural causal effects can be characterized when they exist. Our work also has important consequences for the interpretation of other approaches commonly applied to study causality in the brain. Specifically, we discuss how the notion of natural causal effects can be combined with Granger causality and Dynamic Causal Modeling (DCM). Our results are generic and the concept of natural causal effects is relevant in all areas where the effects of interactions between subsystems are of interest.", "link"=>"http://www.mendeley.com/research/two-become-one-limits-causality-analysis-brain-dynamics", "reader_count"=>74, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>1, "Librarian"=>1, "Researcher"=>26, "Student > Ph. D. Student"=>22, "Student > Postgraduate"=>4, "Student > Master"=>9, "Other"=>1, "Student > Bachelor"=>1, "Lecturer"=>2, "Professor"=>5}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>1, "Librarian"=>1, "Researcher"=>26, "Student > Ph. D. Student"=>22, "Student > Postgraduate"=>4, "Student > Master"=>9, "Other"=>1, "Student > Bachelor"=>1, "Lecturer"=>2, "Professor"=>5}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Engineering"=>3, "Materials Science"=>1, "Mathematics"=>5, "Medicine and Dentistry"=>5, "Agricultural and Biological Sciences"=>11, "Neuroscience"=>7, "Philosophy"=>1, "Sports and Recreations"=>1, "Physics and Astronomy"=>10, "Psychology"=>15, "Computer Science"=>11}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>3}, "Materials Science"=>{"Materials Science"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>5}, "Neuroscience"=>{"Neuroscience"=>7}, "Sports and Recreations"=>{"Sports and Recreations"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>10}, "Psychology"=>{"Psychology"=>15}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>11}, "Computer Science"=>{"Computer Science"=>11}, "Mathematics"=>{"Mathematics"=>5}, "Unspecified"=>{"Unspecified"=>4}, "Philosophy"=>{"Philosophy"=>1}}, "reader_count_by_country"=>{"United States"=>1, "United Kingdom"=>2, "Belarus"=>1, "Switzerland"=>1, "Spain"=>1, "Greece"=>1, "Cuba"=>1, "Canada"=>2, "Netherlands"=>1, "Finland"=>2, "France"=>2, "Peru"=>1, "Germany"=>3}, "group_count"=>3}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/667005"], "description"=>"<p>Causal graphs represent two subsystems with unidirectional causal connections from to (A–C), or bidirectional causal connections (D–F). From left to right the scale of the graphs changes from a microscopic level, representing the dynamic, to a macroscopic one, in which each subsystem is represented by a single node.</p>", "links"=>[], "tags"=>["causal", "connections", "subsystems"], "article_id"=>337500, "categories"=>["Mathematics", "Neuroscience"], "users"=>["Daniel Chicharro", "Anders Ledberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0032466.g003", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Graphical_representation_of_causal_connections_for_subsystems_changing_in_time_/337500", "title"=>"Graphical representation of causal connections for subsystems changing in time.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-03-16 02:05:00"}
  • {"files"=>["https://ndownloader.figshare.com/files/341253"], "description"=>"<div><p>Biological systems often consist of multiple interacting subsystems, the brain being a prominent example. To understand the functions of such systems it is important to analyze if and how the subsystems interact and to describe the effect of these interactions. In this work we investigate the extent to which the cause-and-effect framework is applicable to such interacting subsystems. We base our work on a standard notion of causal effects and define a new concept called natural causal effect. This new concept takes into account that when studying interactions in biological systems, one is often not interested in the effect of perturbations that alter the dynamics. The interest is instead in how the causal connections participate in the generation of the observed natural dynamics. We identify the constraints on the structure of the causal connections that determine the existence of natural causal effects. In particular, we show that the influence of the causal connections on the natural dynamics of the system often cannot be analyzed in terms of the causal effect of one subsystem on another. Only when the causing subsystem is autonomous with respect to the rest can this interpretation be made. We note that subsystems in the brain are often bidirectionally connected, which means that interactions rarely should be quantified in terms of cause-and-effect. We furthermore introduce a framework for how natural causal effects can be characterized when they exist. Our work also has important consequences for the interpretation of other approaches commonly applied to study causality in the brain. Specifically, we discuss how the notion of natural causal effects can be combined with Granger causality and Dynamic Causal Modeling (DCM). Our results are generic and the concept of natural causal effects is relevant in all areas where the effects of interactions between subsystems are of interest.</p> </div>", "links"=>[], "tags"=>["limits", "causality"], "article_id"=>127454, "categories"=>["Mathematics", "Neuroscience"], "users"=>["Daniel Chicharro", "Anders Ledberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0032466", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/When_Two_Become_One_The_Limits_of_Causality_Analysis_of_Brain_Dynamics/127454", "title"=>"When Two Become One: The Limits of Causality Analysis of Brain Dynamics", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-03-16 02:04:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/666956"], "description"=>"<p>Examples of causal graphs illustrating when the effect of the influence of on can be interpreted as a natural causal effect (<b>A</b>) and when it cannot (<b>B</b>).</p>", "links"=>[], "tags"=>["causal"], "article_id"=>337459, "categories"=>["Mathematics", "Neuroscience"], "users"=>["Daniel Chicharro", "Anders Ledberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0032466.g002", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Natural_causal_effects_/337459", "title"=>"Natural causal effects.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-03-16 02:04:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/666916"], "description"=>"<p><b>A</b>: Graph showing a case where the statistical dependence between and is (partly) due to a causal interaction from to . <b>B</b>: Graph showing a case where the statistical dependence between and is induced solely by the confounding variable . <b>C</b>: Graph corresponding to the intervention in the causal graph shown in <b>A</b>. <b>D</b>: Graph corresponding to the intervention in the causal graph shown in <b>B</b>.</p>", "links"=>[], "tags"=>["graphs", "illustrating"], "article_id"=>337404, "categories"=>["Mathematics", "Neuroscience"], "users"=>["Daniel Chicharro", "Anders Ledberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0032466.g001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Causal_graphs_illustrating_the_effect_of_interventions_/337404", "title"=>"Causal graphs illustrating the effect of interventions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-03-16 02:03:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/667077"], "description"=>"<p>Information theoretic measures used for the inference of causality and the analysis of causal effects calculated for a bivariate binary stationary Markov process of order . See the text for a description of the process. The measures are calculated analytically using time lags to account for the past and . The results are shown for (blue), (green), and (red), where is the probability that . A: Transfer entropy (Eq. 15). B: Jensen-Shannon divergence (Eq. 21). C: Jensen-Shannon divergence .</p>", "links"=>[], "tags"=>["binary", "markov"], "article_id"=>337567, "categories"=>["Mathematics", "Neuroscience"], "users"=>["Daniel Chicharro", "Anders Ledberg"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0032466.g004", "stats"=>{"downloads"=>1, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Causality_analysis_in_a_binary_Markov_process_/337567", "title"=>"Causality analysis in a binary Markov process.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-03-16 02:06:07"}

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  • {"unique-ip"=>"4", "full-text"=>"3", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"4"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"4"}
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  • {"unique-ip"=>"6", "full-text"=>"4", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2014", "month"=>"7"}
  • {"unique-ip"=>"12", "full-text"=>"6", "pdf"=>"6", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"8"}
  • {"unique-ip"=>"2", "full-text"=>"1", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"9"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"10"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"2"}
  • {"unique-ip"=>"4", "full-text"=>"3", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2014", "month"=>"11"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"12"}
  • {"unique-ip"=>"5", "full-text"=>"4", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"1"}
  • {"unique-ip"=>"5", "full-text"=>"3", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2015", "month"=>"11"}
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  • {"unique-ip"=>"1", "full-text"=>"0", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"4"}
  • {"unique-ip"=>"2", "full-text"=>"0", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"6"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"7"}
  • {"unique-ip"=>"6", "full-text"=>"5", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"8"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"9"}
  • {"unique-ip"=>"2", "full-text"=>"0", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"10"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"11"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"12"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"1"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"2"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"3"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"5"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"6"}
  • {"unique-ip"=>"2", "full-text"=>"1", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"7"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"8"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"9"}
  • {"unique-ip"=>"2", "full-text"=>"1", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"10"}
  • {"unique-ip"=>"2", "full-text"=>"1", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"11"}
  • {"unique-ip"=>"3", "full-text"=>"2", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"1"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"3"}
  • {"unique-ip"=>"10", "full-text"=>"11", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"1"}
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  • {"unique-ip"=>"8", "full-text"=>"7", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"5"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"10"}
  • {"unique-ip"=>"5", "full-text"=>"3", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2018", "month"=>"7"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"8"}
  • {"unique-ip"=>"11", "full-text"=>"11", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"5", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"9"}
  • {"unique-ip"=>"4", "full-text"=>"3", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2018", "month"=>"11"}
  • {"unique-ip"=>"14", "full-text"=>"15", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"12"}
  • {"unique-ip"=>"6", "full-text"=>"6", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
  • {"unique-ip"=>"8", "full-text"=>"8", "pdf"=>"4", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2019", "month"=>"3"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
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Relative Metric

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