{"paper":{"title":"Construction of quasi-potentials for stochastic dynamical systems: an optimization approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","q-bio.QM"],"primary_cat":"math.OC","authors_text":"Andrew Wynn, Michael P H Stumpf, Rowan D Brackston","submitted_at":"2018-05-18T15:44:10Z","abstract_excerpt":"The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing and complex problem. In many situations, the dynamics may be described by a Langevin equation while constructing a landscape comes down to obtaining the quasi-potential, a scalar function that quantifies the likelihood of reaching each point in the state-space. In this work we provide a novel method for constructing such landscapes by extending a tool from control theory: the Sum-of-Squares method for generating Lyapunov functions. Applicable to any system described by polynomia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07273","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"}