{"paper":{"title":"Bootstrap percolation on spatial networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"physics.soc-ph","authors_text":"Jian Gao, Tao Zhou, Yanqing Hu","submitted_at":"2014-08-06T14:20:34Z","abstract_excerpt":"We numerically study bootstrap percolation on Kleinberg's spatial networks, in which the probability density function of a node to have a long-range link at distance $r$ scales as $P(r)\\sim r^{\\alpha}$. Setting the ratio of the size of the giant active component to the network size as the order parameter, we find a critical exponent $\\alpha_{c}=-1$, above which a hybrid phase transition is observed, with both the first-order and second-order critical points being constant. When $\\alpha<\\alpha_{c}$, the second-order critical point increases as the decreasing of $\\alpha$, and there is either abs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1290","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}