{"id":"W1492951456","doi":"10.1002/rsa.20538","title":"On longest paths and diameter in random apollonian networks","year":2014,"lang":"en","type":"article","venue":"Random Structures and Algorithms","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto; University of Waterloo","funders":"Australian Research Council; Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Combinatorics; Vertex (graph theory); Mathematics; Planar graph; Random graph; Bounded function; Conjecture; Path (computing); Random walk; Plane (geometry); Triangulation; Graph; Discrete mathematics; Geometry; Computer science; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003792681,0.0006158967,0.001107655,0.002943692,0.001517068,0.001965658,0.002194698,0.001853514,0.003283873],"category_scores_gemma":[0.03195477,0.000891935,0.0006821875,0.001224414,0.003453074,0.005344937,0.0023758,0.001331622,0.0003391509],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002305433,"about_ca_system_score_gemma":0.0005923728,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001517485,"about_ca_topic_score_gemma":0.001571457,"domain_scores_codex":[0.9985884,0.0007082087,0.00005718823,0.0002875606,0.0001800907,0.0001786257],"domain_scores_gemma":[0.9645631,0.02789303,0.003091442,0.001476081,0.001272856,0.00170342],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0004803831,0.00007765547,0.008329854,0.0002947675,0.0001230012,0.0003662528,0.0007684638,0.2459675,0.004659102,0.7209257,0.004545581,0.01346165],"study_design_scores_gemma":[0.00006078584,0.00007908689,0.001418709,0.00007328152,0.00004293049,0.0002414049,0.0001378306,0.5894714,0.001151923,0.4050186,0.002260212,0.00004394805],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6797806,0.002297199,0.3055641,0.002577301,0.0001153117,0.00009172325,0.0005900287,0.0003259743,0.008657709],"genre_scores_gemma":[0.9627022,0.001499749,0.0323172,0.0002082904,0.0001698835,0.0002200406,0.0003991421,0.0001386563,0.002345002],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003792681,"threshold_uncertainty_score":0.02005792,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01312196339921286,"score_gpt":0.2678942400788881,"score_spread":0.2547722766796752,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}