A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks
Events
Loading … Spinner

Mendeley | Further Information

{"title"=>"A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks", "type"=>"journal", "authors"=>[{"first_name"=>"Ankit", "last_name"=>"Gupta", "scopus_author_id"=>"56531067600"}, {"first_name"=>"Corentin", "last_name"=>"Briat", "scopus_author_id"=>"33367554800"}, {"first_name"=>"Mustafa", "last_name"=>"Khammash", "scopus_author_id"=>"23012213900"}], "year"=>2014, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-84903397345", "sgr"=>"84903397345", "issn"=>"15537358", "arxiv"=>"arXiv:1304.5404v3", "doi"=>"10.1371/journal.pcbi.1003669", "pmid"=>"24968191", "pui"=>"373401402"}, "id"=>"91a44dbe-2b4b-3609-bcd1-34d91c960e27", "abstract"=>"Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed.", "link"=>"http://www.mendeley.com/research/scalable-computational-framework-establishing-longterm-behavior-stochastic-reaction-networks", "reader_count"=>46, "reader_count_by_academic_status"=>{"Unspecified"=>3, "Researcher"=>16, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>15, "Student > Postgraduate"=>2, "Student > Master"=>4, "Student > Bachelor"=>1, "Lecturer"=>1, "Professor"=>1}, "reader_count_by_user_role"=>{"Unspecified"=>3, "Researcher"=>16, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>15, "Student > Postgraduate"=>2, "Student > Master"=>4, "Student > Bachelor"=>1, "Lecturer"=>1, "Professor"=>1}, "reader_count_by_subject_area"=>{"Unspecified"=>6, "Agricultural and Biological Sciences"=>11, "Business, Management and Accounting"=>1, "Chemistry"=>1, "Computer Science"=>2, "Engineering"=>7, "Environmental Science"=>1, "Biochemistry, Genetics and Molecular Biology"=>4, "Mathematics"=>8, "Medicine and Dentistry"=>1, "Physics and Astronomy"=>2, "Social Sciences"=>1, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Mathematics"=>{"Mathematics"=>8}, "Unspecified"=>{"Unspecified"=>6}, "Environmental Science"=>{"Environmental Science"=>1}, "Engineering"=>{"Engineering"=>7}, "Chemistry"=>{"Chemistry"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>11}, "Computer Science"=>{"Computer Science"=>2}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>4}}, "reader_count_by_country"=>{"Sweden"=>1, "United States"=>3, "United Kingdom"=>1, "Slovenia"=>1, "France"=>1}, "group_count"=>0}

Scopus | Further Information

{"@_fa"=>"true", "link"=>[{"@_fa"=>"true", "@ref"=>"self", "@href"=>"https://api.elsevier.com/content/abstract/scopus_id/84903397345"}, {"@_fa"=>"true", "@ref"=>"author-affiliation", "@href"=>"https://api.elsevier.com/content/abstract/scopus_id/84903397345?field=author,affiliation"}, {"@_fa"=>"true", "@ref"=>"scopus", "@href"=>"https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84903397345&origin=inward"}, {"@_fa"=>"true", "@ref"=>"scopus-citedby", "@href"=>"https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84903397345&origin=inward"}], "prism:url"=>"https://api.elsevier.com/content/abstract/scopus_id/84903397345", "dc:identifier"=>"SCOPUS_ID:84903397345", "eid"=>"2-s2.0-84903397345", "dc:title"=>"A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks", "dc:creator"=>"Gupta A.", "prism:publicationName"=>"PLoS Computational Biology", "prism:issn"=>"1553734X", "prism:eIssn"=>"15537358", "prism:volume"=>"10", "prism:issueIdentifier"=>"6", "prism:pageRange"=>nil, "prism:coverDate"=>"2014-01-01", "prism:coverDisplayDate"=>"June 2014", "prism:doi"=>"10.1371/journal.pcbi.1003669", "citedby-count"=>"36", "affiliation"=>[{"@_fa"=>"true", "affilname"=>"ETH Zürich", "affiliation-city"=>"Zurich ZH,", "affiliation-country"=>"Switzerland"}], "pubmed-id"=>"24968191", "prism:aggregationType"=>"Journal", "subtype"=>"ar", "subtypeDescription"=>"Article", "article-number"=>"e1003669", "source-id"=>"4000151810", "openaccess"=>"1", "openaccessFlag"=>true}

Facebook

  • {"url"=>"http%3A%2F%2Fjournals.plos.org%2Fploscompbiol%2Farticle%3Fid%3D10.1371%252Fjournal.pcbi.1003669", "share_count"=>4, "like_count"=>4, "comment_count"=>0, "click_count"=>0, "total_count"=>8}

Counter

  • {"month"=>"6", "year"=>"2014", "pdf_views"=>"66", "xml_views"=>"6", "html_views"=>"663"}
  • {"month"=>"7", "year"=>"2014", "pdf_views"=>"114", "xml_views"=>"14", "html_views"=>"1157"}
  • {"month"=>"8", "year"=>"2014", "pdf_views"=>"14", "xml_views"=>"4", "html_views"=>"127"}
  • {"month"=>"9", "year"=>"2014", "pdf_views"=>"24", "xml_views"=>"1", "html_views"=>"83"}
  • {"month"=>"10", "year"=>"2014", "pdf_views"=>"31", "xml_views"=>"1", "html_views"=>"96"}
  • {"month"=>"11", "year"=>"2014", "pdf_views"=>"4", "xml_views"=>"2", "html_views"=>"46"}
  • {"month"=>"12", "year"=>"2014", "pdf_views"=>"14", "xml_views"=>"0", "html_views"=>"38"}
  • {"month"=>"1", "year"=>"2015", "pdf_views"=>"15", "xml_views"=>"0", "html_views"=>"66"}
  • {"month"=>"2", "year"=>"2015", "pdf_views"=>"14", "xml_views"=>"0", "html_views"=>"55"}
  • {"month"=>"3", "year"=>"2015", "pdf_views"=>"14", "xml_views"=>"0", "html_views"=>"47"}
  • {"month"=>"4", "year"=>"2015", "pdf_views"=>"13", "xml_views"=>"1", "html_views"=>"43"}
  • {"month"=>"5", "year"=>"2015", "pdf_views"=>"22", "xml_views"=>"0", "html_views"=>"67"}
  • {"month"=>"6", "year"=>"2015", "pdf_views"=>"17", "xml_views"=>"0", "html_views"=>"128"}
  • {"month"=>"7", "year"=>"2015", "pdf_views"=>"6", "xml_views"=>"0", "html_views"=>"22"}
  • {"month"=>"8", "year"=>"2015", "pdf_views"=>"3", "xml_views"=>"0", "html_views"=>"19"}
  • {"month"=>"9", "year"=>"2015", "pdf_views"=>"10", "xml_views"=>"0", "html_views"=>"32"}
  • {"month"=>"10", "year"=>"2015", "pdf_views"=>"24", "xml_views"=>"0", "html_views"=>"52"}
  • {"month"=>"11", "year"=>"2015", "pdf_views"=>"16", "xml_views"=>"0", "html_views"=>"45"}
  • {"month"=>"12", "year"=>"2015", "pdf_views"=>"4", "xml_views"=>"0", "html_views"=>"26"}
  • {"month"=>"1", "year"=>"2016", "pdf_views"=>"15", "xml_views"=>"0", "html_views"=>"51"}
  • {"month"=>"2", "year"=>"2016", "pdf_views"=>"9", "xml_views"=>"0", "html_views"=>"31"}
  • {"month"=>"3", "year"=>"2016", "pdf_views"=>"7", "xml_views"=>"0", "html_views"=>"55"}
  • {"month"=>"4", "year"=>"2016", "pdf_views"=>"21", "xml_views"=>"0", "html_views"=>"60"}
  • {"month"=>"5", "year"=>"2016", "pdf_views"=>"8", "xml_views"=>"0", "html_views"=>"25"}
  • {"month"=>"6", "year"=>"2016", "pdf_views"=>"22", "xml_views"=>"0", "html_views"=>"53"}
  • {"month"=>"7", "year"=>"2016", "pdf_views"=>"16", "xml_views"=>"0", "html_views"=>"41"}
  • {"month"=>"8", "year"=>"2016", "pdf_views"=>"14", "xml_views"=>"0", "html_views"=>"38"}
  • {"month"=>"9", "year"=>"2016", "pdf_views"=>"13", "xml_views"=>"0", "html_views"=>"41"}
  • {"month"=>"10", "year"=>"2016", "pdf_views"=>"10", "xml_views"=>"0", "html_views"=>"45"}
  • {"month"=>"11", "year"=>"2016", "pdf_views"=>"9", "xml_views"=>"0", "html_views"=>"63"}
  • {"month"=>"12", "year"=>"2016", "pdf_views"=>"10", "xml_views"=>"0", "html_views"=>"36"}
  • {"month"=>"1", "year"=>"2017", "pdf_views"=>"6", "xml_views"=>"1", "html_views"=>"34"}
  • {"month"=>"2", "year"=>"2017", "pdf_views"=>"19", "xml_views"=>"3", "html_views"=>"46"}
  • {"month"=>"3", "year"=>"2017", "pdf_views"=>"12", "xml_views"=>"0", "html_views"=>"37"}
  • {"month"=>"4", "year"=>"2017", "pdf_views"=>"10", "xml_views"=>"0", "html_views"=>"34"}
  • {"month"=>"5", "year"=>"2017", "pdf_views"=>"12", "xml_views"=>"1", "html_views"=>"54"}
  • {"month"=>"6", "year"=>"2017", "pdf_views"=>"7", "xml_views"=>"0", "html_views"=>"39"}
  • {"month"=>"7", "year"=>"2017", "pdf_views"=>"14", "xml_views"=>"1", "html_views"=>"29"}
  • {"month"=>"8", "year"=>"2017", "pdf_views"=>"23", "xml_views"=>"3", "html_views"=>"53"}
  • {"month"=>"9", "year"=>"2017", "pdf_views"=>"11", "xml_views"=>"1", "html_views"=>"34"}
  • {"month"=>"10", "year"=>"2017", "pdf_views"=>"15", "xml_views"=>"2", "html_views"=>"109"}
  • {"month"=>"11", "year"=>"2017", "pdf_views"=>"5", "xml_views"=>"1", "html_views"=>"87"}
  • {"month"=>"12", "year"=>"2017", "pdf_views"=>"13", "xml_views"=>"0", "html_views"=>"93"}
  • {"month"=>"1", "year"=>"2018", "pdf_views"=>"5", "xml_views"=>"0", "html_views"=>"51"}
  • {"month"=>"2", "year"=>"2018", "pdf_views"=>"5", "xml_views"=>"1", "html_views"=>"10"}
  • {"month"=>"3", "year"=>"2018", "pdf_views"=>"17", "xml_views"=>"0", "html_views"=>"37"}
  • {"month"=>"4", "year"=>"2018", "pdf_views"=>"8", "xml_views"=>"0", "html_views"=>"5"}
  • {"month"=>"5", "year"=>"2018", "pdf_views"=>"4", "xml_views"=>"0", "html_views"=>"9"}
  • {"month"=>"6", "year"=>"2018", "pdf_views"=>"11", "xml_views"=>"0", "html_views"=>"17"}
  • {"month"=>"7", "year"=>"2018", "pdf_views"=>"10", "xml_views"=>"3", "html_views"=>"27"}
  • {"month"=>"8", "year"=>"2018", "pdf_views"=>"8", "xml_views"=>"4", "html_views"=>"15"}
  • {"month"=>"9", "year"=>"2018", "pdf_views"=>"5", "xml_views"=>"0", "html_views"=>"9"}
  • {"month"=>"10", "year"=>"2018", "pdf_views"=>"26", "xml_views"=>"2", "html_views"=>"18"}
  • {"month"=>"11", "year"=>"2018", "pdf_views"=>"12", "xml_views"=>"0", "html_views"=>"10"}
  • {"month"=>"12", "year"=>"2018", "pdf_views"=>"12", "xml_views"=>"1", "html_views"=>"7"}
  • {"month"=>"1", "year"=>"2019", "pdf_views"=>"14", "xml_views"=>"0", "html_views"=>"16"}
  • {"month"=>"2", "year"=>"2019", "pdf_views"=>"4", "xml_views"=>"1", "html_views"=>"2"}
  • {"month"=>"3", "year"=>"2019", "pdf_views"=>"12", "xml_views"=>"4", "html_views"=>"9"}
  • {"month"=>"4", "year"=>"2019", "pdf_views"=>"14", "xml_views"=>"1", "html_views"=>"10"}
  • {"month"=>"5", "year"=>"2019", "pdf_views"=>"6", "xml_views"=>"1", "html_views"=>"2"}
  • {"month"=>"6", "year"=>"2019", "pdf_views"=>"6", "xml_views"=>"0", "html_views"=>"2"}
  • {"month"=>"7", "year"=>"2019", "pdf_views"=>"11", "xml_views"=>"0", "html_views"=>"9"}
  • {"month"=>"8", "year"=>"2019", "pdf_views"=>"13", "xml_views"=>"0", "html_views"=>"11"}
  • {"month"=>"9", "year"=>"2019", "pdf_views"=>"8", "xml_views"=>"0", "html_views"=>"9"}
  • {"month"=>"10", "year"=>"2019", "pdf_views"=>"15", "xml_views"=>"3", "html_views"=>"22"}
  • {"month"=>"11", "year"=>"2019", "pdf_views"=>"11", "xml_views"=>"1", "html_views"=>"26"}
  • {"month"=>"12", "year"=>"2019", "pdf_views"=>"12", "xml_views"=>"0", "html_views"=>"12"}
  • {"month"=>"1", "year"=>"2020", "pdf_views"=>"20", "xml_views"=>"1", "html_views"=>"26"}
  • {"month"=>"2", "year"=>"2020", "pdf_views"=>"23", "xml_views"=>"1", "html_views"=>"15"}
  • {"month"=>"3", "year"=>"2020", "pdf_views"=>"16", "xml_views"=>"0", "html_views"=>"9"}
  • {"month"=>"4", "year"=>"2020", "pdf_views"=>"16", "xml_views"=>"0", "html_views"=>"5"}
  • {"month"=>"5", "year"=>"2020", "pdf_views"=>"10", "xml_views"=>"2", "html_views"=>"4"}
  • {"month"=>"6", "year"=>"2020", "pdf_views"=>"19", "xml_views"=>"0", "html_views"=>"8"}
  • {"month"=>"7", "year"=>"2020", "pdf_views"=>"10", "xml_views"=>"1", "html_views"=>"8"}
  • {"month"=>"8", "year"=>"2020", "pdf_views"=>"7", "xml_views"=>"2", "html_views"=>"11"}
  • {"month"=>"9", "year"=>"2020", "pdf_views"=>"6", "xml_views"=>"1", "html_views"=>"10"}
  • {"month"=>"10", "year"=>"2020", "pdf_views"=>"10", "xml_views"=>"1", "html_views"=>"5"}
  • {"month"=>"11", "year"=>"2020", "pdf_views"=>"4", "xml_views"=>"2", "html_views"=>"3"}

Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1567580"], "description"=>"<p>Whereas the trajectory of the state of the deterministic model converges to a stationary value, the trajectory of the state of the stochastic model goes unbounded.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes", "deterministic", "markov", "describing"], "article_id"=>1084874, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Trajectory_of_the_state_of_the_deterministic_system_23_with_initial_condition_top_Sample_path_of_the_Markov_process_describing_the_network_22_with_initial_condition_bottom_/1084874", "title"=>"Trajectory of the state of the deterministic system (23) with initial condition (top); Sample path of the Markov process describing the network (22) with initial condition (bottom).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567586"], "description"=>"<p>We can see that while the deterministic trajectories converge to their equilibrium point, the first-order moments grow without bound.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes", "trajectories", "deterministic", "stochastic"], "article_id"=>1084876, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_the_trajectories_of_the_deterministic_and_stochastic_first_order_moments_models_of_the_reaction_network_22_with_initial_condition__and_for_the_deterministic_top_and_stochastic_dynamics_bottom_respectively_/1084876", "title"=>"Comparison of the trajectories of the deterministic and stochastic (first-order moments) models of the reaction network (22) with initial condition , , and for the deterministic (top) and stochastic dynamics (bottom), respectively.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567591"], "description"=>"<p>The trajectories converge to the unique steady-state value located inside the compact set (the surface below the dashed line), very close to the boundary.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes", "moments", "performed", "5000"], "article_id"=>1084877, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Trajectories_of_the_first_order_moments_and_of_network_29_for_different_initial_conditions_averaging_is_performed_over_5000_cells_/1084877", "title"=>"Trajectories of the first order moments and of network (29) for different initial conditions (averaging is performed over 5000 cells).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567594"], "description"=>"<p>Feedback loop with arbitrary feedback rule.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes", "arbitrary"], "article_id"=>1084880, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Feedback_loop_with_arbitrary_feedback_rule_/1084880", "title"=>"Feedback loop with arbitrary feedback rule.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567597"], "description"=>"<p>-gene repressilator.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes"], "article_id"=>1084882, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_gene_repressilator_/1084882", "title"=>"-gene repressilator.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567599"], "description"=>"<p>Circadian clock model of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003669#pcbi.1003669-Vilar1\" target=\"_blank\">[65]</a>.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes"], "article_id"=>1084884, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Circadian_clock_model_of_65_/1084884", "title"=>"Circadian clock model of [65].", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567601"], "description"=>"<p>Sample-path of the species of the circadian clock model.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes", "circadian"], "article_id"=>1084887, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Sample_path_of_the_species_of_the_circadian_clock_model_/1084887", "title"=>"Sample-path of the species of the circadian clock model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567605"], "description"=>"<p>The dashed-lines correspond to the (asymptotic) time-average.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes", "averages", "circadian", "cells"], "article_id"=>1084891, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Time_evolution_of_the_sample_averages_of_the_species_A_top_R_left_and_C_right_of_the_circadian_clock_model_2000_cells_averaging_/1084891", "title"=>"Time evolution of the sample averages of the species A (top), R (left) and C (right) of the circadian clock model (2000 cells averaging).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567606"], "description"=>"<p>The dashed lines correspond to the average trajectories computed over 1000 cells.</p>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes", "trajectories", "carcinogenesis"], "article_id"=>1084892, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669.g009"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_State_trajectories_of_the_carcinogenesis_model_41_with_the_parameters__and_/1084892", "title"=>"State trajectories of the carcinogenesis model (41) with the parameters , , , and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-06-26 02:57:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/1567611"], "description"=>"<div><p>Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed.</p></div>", "links"=>[], "tags"=>["Biochemistry", "Biochemical simulations", "Computational biology", "genome analysis", "Genetic networks", "Gene regulatory networks", "ecology", "Systems ecology", "genetics", "genomics", "Synthetic Biology", "systems biology", "Network Analysis", "Metabolic networks", "Regulatory networks", "Signaling networks", "mathematics", "algebra", "Linear algebra", "Probability theory", "Stochastic processes", "scalable", "computational", "establishing", "stochastic"], "article_id"=>1084897, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Ankit Gupta", "Corentin Briat", "Mustafa Khammash"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003669"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_Scalable_Computational_Framework_for_Establishing_Long_Term_Behavior_of_Stochastic_Reaction_Networks_/1084897", "title"=>"A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-06-26 02:57:18"}

PMC Usage Stats | Further Information

  • {"unique-ip"=>"12", "full-text"=>"14", "pdf"=>"5", "abstract"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"7"}
  • {"unique-ip"=>"6", "full-text"=>"4", "pdf"=>"3", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"8"}
  • {"unique-ip"=>"10", "full-text"=>"7", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"9"}
  • {"unique-ip"=>"11", "full-text"=>"7", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"2", "cited-by"=>"0", "year"=>"2014", "month"=>"10"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"3", "abstract"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"11"}
  • {"unique-ip"=>"6", "full-text"=>"5", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2014", "month"=>"12"}
  • {"unique-ip"=>"8", "full-text"=>"10", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"1"}
  • {"unique-ip"=>"6", "full-text"=>"5", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"2"}
  • {"unique-ip"=>"6", "full-text"=>"6", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"9", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"3"}
  • {"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"=>"2015", "month"=>"4"}
  • {"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"=>"2015", "month"=>"5"}
  • {"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"=>"6"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "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"=>"2015", "month"=>"8"}
  • {"unique-ip"=>"7", "full-text"=>"6", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"9"}
  • {"unique-ip"=>"7", "full-text"=>"5", "pdf"=>"4", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2015", "month"=>"10"}
  • {"unique-ip"=>"10", "full-text"=>"7", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2015", "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"=>"2015", "month"=>"12"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "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"=>"2016", "month"=>"2"}
  • {"unique-ip"=>"7", "full-text"=>"14", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"3"}
  • {"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"=>"2", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"5"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2016", "month"=>"6"}
  • {"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"=>"2016", "month"=>"7"}
  • {"unique-ip"=>"6", "full-text"=>"5", "pdf"=>"3", "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"=>"5", "full-text"=>"3", "pdf"=>"3", "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"=>"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"=>"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"=>"2017", "month"=>"3"}
  • {"unique-ip"=>"3", "full-text"=>"8", "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"=>"1", "full-text"=>"0", "pdf"=>"2", "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"=>"1", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"9"}
  • {"unique-ip"=>"4", "full-text"=>"1", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"1", "year"=>"2017", "month"=>"10"}
  • {"unique-ip"=>"7", "full-text"=>"7", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"11"}
  • {"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"=>"2018", "month"=>"3"}
  • {"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"=>"1"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"5"}
  • {"unique-ip"=>"1", "full-text"=>"0", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"4"}
  • {"unique-ip"=>"5", "full-text"=>"3", "pdf"=>"4", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"6"}
  • {"unique-ip"=>"3", "full-text"=>"1", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2018", "month"=>"7"}
  • {"unique-ip"=>"3", "full-text"=>"4", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"8"}
  • {"unique-ip"=>"1", "full-text"=>"2", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"9"}
  • {"unique-ip"=>"6", "full-text"=>"7", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"10"}
  • {"unique-ip"=>"3", "full-text"=>"2", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"0", "year"=>"2018", "month"=>"11"}
  • {"unique-ip"=>"5", "full-text"=>"4", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"12"}
  • {"unique-ip"=>"4", "full-text"=>"7", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
  • {"unique-ip"=>"5", "full-text"=>"6", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"1", "year"=>"2019", "month"=>"3"}
  • {"unique-ip"=>"6", "full-text"=>"7", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
  • {"unique-ip"=>"3", "full-text"=>"2", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}
  • {"unique-ip"=>"8", "full-text"=>"7", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"9"}
  • {"unique-ip"=>"7", "full-text"=>"7", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"10"}
  • {"unique-ip"=>"7", "full-text"=>"1", "pdf"=>"7", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"12"}
  • {"unique-ip"=>"8", "full-text"=>"6", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"1", "cited-by"=>"2", "year"=>"2020", "month"=>"2"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"3"}
  • {"unique-ip"=>"8", "full-text"=>"7", "pdf"=>"4", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"4"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"5"}
  • {"unique-ip"=>"4", "full-text"=>"3", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"6"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"7"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"8"}
  • {"unique-ip"=>"5", "full-text"=>"4", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2020", "month"=>"10"}

Relative Metric

{"start_date"=>"2014-01-01T00:00:00Z", "end_date"=>"2014-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Computational biology", "average_usage"=>[341, 529]}, {"subject_area"=>"/Biology and life sciences/Genetics", "average_usage"=>[306, 482]}, {"subject_area"=>"/Computer and information sciences", "average_usage"=>[327, 511]}, {"subject_area"=>"/Computer and information sciences/Systems science", "average_usage"=>[289, 462]}, {"subject_area"=>"/Physical sciences", "average_usage"=>[271]}, {"subject_area"=>"/Physical sciences/Mathematics", "average_usage"=>[286]}]}
Loading … Spinner
There are currently no alerts