On Singularities and Black Holes in Combination-Driven Models of Technological Innovation Networks
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{"title"=>"On singularities and black holes in combination-driven models of technological innovation networks", "type"=>"journal", "authors"=>[{"first_name"=>"Ricard", "last_name"=>"Solé", "scopus_author_id"=>"7004381560"}, {"first_name"=>"Daniel R.", "last_name"=>"Amor", "scopus_author_id"=>"35228454300"}, {"first_name"=>"Sergi", "last_name"=>"Valverde", "scopus_author_id"=>"7006393703"}], "year"=>2016, "source"=>"PLoS ONE", "identifiers"=>{"arxiv"=>"1407.6890", "issn"=>"19326203", "pui"=>"608273544", "sgr"=>"84959010765", "scopus"=>"2-s2.0-84959010765", "pmid"=>"26821277", "doi"=>"10.1371/journal.pone.0146180"}, "id"=>"2435d416-aea6-3bbb-8a4e-e009bfff92da", "abstract"=>"It has been suggested that innovations occur mainly by combination: the more inventions accumulate, the higher the probability that new inventions are obtained from previous designs. Additionally, it has been conjectured that the combinatorial nature of innovations naturally leads to a singularity: at some finite time, the number of innovations should diverge. Although these ideas are certainly appealing, no general models have been yet developed to test the conditions under which combinatorial technology should become explosive. Here we present a generalised model of technological evolution that takes into account two major properties: the number of previous technologies needed to create a novel one and how rapidly technology ages. Two different models of combinatorial growth are considered, involving different forms of ageing. When long-range memory is used and thus old inventions are available for novel innovations, singularities can emerge under some conditions with two phases separated by a critical boundary. If the ageing has a characteristic time scale, it is shown that no singularities will be observed. Instead, a \"black hole\" of old innovations appears and expands in time, making the rate of invention creation slow down into a linear regime.", "link"=>"http://www.mendeley.com/research/singularities-black-holes-combinationdriven-models-technological-innovation-networks", "reader_count"=>26, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Librarian"=>1, "Researcher"=>5, "Student > Ph. D. Student"=>7, "Student > Master"=>5, "Other"=>4, "Student > Bachelor"=>2, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Librarian"=>1, "Researcher"=>5, "Student > Ph. D. Student"=>7, "Student > Master"=>5, "Other"=>4, "Student > Bachelor"=>2, "Professor"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>3, "Unspecified"=>1, "Environmental Science"=>2, "Mathematics"=>3, "Agricultural and Biological Sciences"=>2, "Business, Management and Accounting"=>2, "Psychology"=>1, "Social Sciences"=>5, "Computer Science"=>6, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>3}, "Social Sciences"=>{"Social Sciences"=>5}, "Psychology"=>{"Psychology"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>2}, "Computer Science"=>{"Computer Science"=>6}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>2}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>1}, "Environmental Science"=>{"Environmental Science"=>2}}, "reader_count_by_country"=>{"United States"=>1, "Finland"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/4280610"], "description"=>"<p>The white area includes all parameter combinations allowing a singularity to emerge through a hyperbolic growth process.</p>", "links"=>[], "tags"=>["generalised model", "Technological Innovation Networks", "combinatorial technology", "technology ages", "combinatorial nature", "combinatorial growth", "invention creation", "singularitie", "Black Holes", "time scale", "ageing", "novel innovations"], "article_id"=>2629682, "categories"=>["Biochemistry", "Evolutionary Biology", "Environmental Sciences not elsewhere classified", "Biological Sciences not elsewhere classified"], "users"=>["Ricard Solé", "Daniel R. Amor", "Sergi Valverde"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146180.g002", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Two_phases_predicted_by_the_generalised_model_of_technological_evolution_with_power_law_ageing_/2629682", "title"=>"Two phases predicted by the generalised model of technological evolution with power law ageing.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 04:12:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/4280606"], "description"=>"<p>The main plot (a) shows the accelerated increase of the total number patents <i>N</i>(<i>t</i>) as provided by the USPTO dataset. In (b) we show the same data in linear-log form. As an alternative illustration, we also display the spindle diagrams for <i>N</i>(<i>t</i>) associated to (c) the overall pattern and (d) the early development linked to the Industrial Revolution [corresponding to the period indicated by the open square in (a)].</p>", "links"=>[], "tags"=>["generalised model", "Technological Innovation Networks", "combinatorial technology", "technology ages", "combinatorial nature", "combinatorial growth", "invention creation", "singularitie", "Black Holes", "time scale", "ageing", "novel innovations"], "article_id"=>2629676, "categories"=>["Biochemistry", "Evolutionary Biology", "Environmental Sciences not elsewhere classified", "Biological Sciences not elsewhere classified"], "users"=>["Ricard Solé", "Daniel R. Amor", "Sergi Valverde"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146180.g001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Evolution_of_technological_diversity_/2629676", "title"=>"Evolution of technological diversity.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 04:12:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/4280620"], "description"=>"<p>In (a) we show the different dynamics of <i>N</i>(<i>t</i>) for different aging decays affecting the hyperbolic (<i>k</i> = 2) term. The corresponding <i>γ</i><sub><i>H</i></sub> values are indicated in the legend. The rest of the parameter values are: <i>μ</i><sub><i>M</i></sub> = 8.5 × 10<sup>−2</sup>, <i>γ</i><sub><i>M</i></sub> = 1.5 × 10<sup>−4</sup> and <i>μ</i><sub><i>H</i></sub> = 5 × 10<sup>−7</sup>. In (b) we show again the case <i>γ</i><sub><i>H</i></sub> = 2 × 10<sup>−5</sup> (triangles), and the accumulated contribution of the Malthusian (<i>k</i> = 1) recombination to the total patent number <i>N</i>. At any time, the accumulated number of patents that have been generated by hyperbolic (<i>k</i> = 2) recombination corresponds to the difference between the two curves. The red line corresponds to an exponential fit to the first part (up to <i>t</i> = 50) of the time series.</p>", "links"=>[], "tags"=>["generalised model", "Technological Innovation Networks", "combinatorial technology", "technology ages", "combinatorial nature", "combinatorial growth", "invention creation", "singularitie", "Black Holes", "time scale", "ageing", "novel innovations"], "article_id"=>2629694, "categories"=>["Biochemistry", "Evolutionary Biology", "Environmental Sciences not elsewhere classified", "Biological Sciences not elsewhere classified"], "users"=>["Ricard Solé", "Daniel R. Amor", "Sergi Valverde"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146180.g004", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Innovation_dynamics_of_the_bimodal_recombination_model_/2629694", "title"=>"Innovation dynamics of the bimodal recombination model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 04:12:16"}
  • {"files"=>["https://ndownloader.figshare.com/files/4280616"], "description"=>"<p>In (a) we display our predicted growth curve <i>N</i>(<i>t</i>) and two approximations considering short time (dotted line) and long term (dashed line) scales. The effective kernels for these two scales are displayed in the inset plots (b) and (c). The maximum value displayed in the <i>τ</i> axis of insets (b) and (c) corresponds to <i>N</i>(<i>t</i>) at times <i>t</i> = 213 and <i>t</i> = 270, respectively. The characteristic scale of ageing imposed by the kernel implies that there is a time horizon beyond which no connections among inventions can be made. This is illustrated schematically in (d) where we show the spindle diagram of the whole system <i>π</i> along with a subset <i>ψ</i>(<i>t</i>), first appearing at the characteristic time <i>t</i><sub>1/2</sub> where the probability of citing the oldest invention <i>π</i><sub>1</sub> is half the maximum. All inventions within this “black hole” will be disconnected from the rest. In the present (top large circle) only new inventions (filled circles) occupying the outer part of the circle can connect among them whereas they cannot link (light lines) with those in the black hole (open circles). The parameter values used in (a)-(c) correspond to <i>μ</i>′ = 2 × 10<sup>5</sup>, <i>t</i><sub>0</sub> = 0, <i>N</i><sub>0</sub> = 5000, and <i>γ</i> = 2 × 10<sup>−6</sup>.</p>", "links"=>[], "tags"=>["generalised model", "Technological Innovation Networks", "combinatorial technology", "technology ages", "combinatorial nature", "combinatorial growth", "invention creation", "singularitie", "Black Holes", "time scale", "ageing", "novel innovations"], "article_id"=>2629686, "categories"=>["Biochemistry", "Evolutionary Biology", "Environmental Sciences not elsewhere classified", "Biological Sciences not elsewhere classified"], "users"=>["Ricard Solé", "Daniel R. Amor", "Sergi Valverde"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0146180.g003", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Transient_hyperbolic_growth_and_blackholes_in_combination_models_with_limited_memory_/2629686", "title"=>"Transient hyperbolic growth and blackholes in combination models with limited memory.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2016-01-28 04:12:16"}

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Relative Metric

{"start_date"=>"2016-01-01T00:00:00Z", "end_date"=>"2016-12-31T00:00:00Z", "subject_areas"=>[]}
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