{"paper":{"title":"Generation-by-Generation Dissection of the Response Function in Long Memory Epidemic Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.data-an","authors_text":"A. Saichev, D. Sornette","submitted_at":"2009-04-06T18:25:44Z","abstract_excerpt":"In a number of natural and social systems, the response to an exogenous shock relaxes back to the average level according to a long-memory kernel $\\sim 1/t^{1+\\theta}$ with $0 \\leq \\theta <1$. In the presence of an epidemic-like process of triggered shocks developing in a cascade of generations at or close to criticality, this \"bare\" kernel is renormalized into an even slower decaying response function $\\sim 1/t^{1-\\theta}$. Surprisingly, this means that the shorter the memory of the bare kernel (the larger $1+\\theta$), the longer the memory of the response function (the smaller $1-\\theta$). H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0872","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"}