{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:CC2AVDE74DCYCJ4X2YHNRZVI7M","short_pith_number":"pith:CC2AVDE7","schema_version":"1.0","canonical_sha256":"10b40a8c9fe0c5812797d60ed8e6a8fb3ca40a903529e3a42a7d1163e2101f38","source":{"kind":"arxiv","id":"0910.3916","version":1},"attestation_state":"computed","paper":{"title":"Coupling algorithm for calculating sensitivities of Smoluchowski's coagulation equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ismael F. Bailleul, James R. Norris, Markus Kraft, Peter L.W. Man","submitted_at":"2009-10-20T17:13:07Z","abstract_excerpt":"In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new algorithms (called `Single' and `Double') work by coupling two Marcus-Lushnikov processes in such a way as to reduce the difference between their trajectories, thereby significantly reducing the variance of central difference estimators of the parametric derivatives. In the numerical results, the algorithms are shown have have a O(1/N) order of convergence a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0910.3916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-20T17:13:07Z","cross_cats_sorted":[],"title_canon_sha256":"ab03a75ae342b2a18edd1f2221cafc4f6f82e0a42d423b9823eb3cb951160221","abstract_canon_sha256":"5b99308d420a50af3274d6e7d05af93b0c4d071f383541273981d2701acd5910"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:59.612603Z","signature_b64":"gtU2znrBdu4xMdCR/cjZJ2Kx//U3oBA1sS1H8rT3g0hkqFPgjq6Ho//gAaqx8nYUGMzrXGR2TuT7Nz12y0yWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10b40a8c9fe0c5812797d60ed8e6a8fb3ca40a903529e3a42a7d1163e2101f38","last_reissued_at":"2026-05-18T01:04:59.611957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:59.611957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coupling algorithm for calculating sensitivities of Smoluchowski's coagulation equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ismael F. Bailleul, James R. Norris, Markus Kraft, Peter L.W. Man","submitted_at":"2009-10-20T17:13:07Z","abstract_excerpt":"In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new algorithms (called `Single' and `Double') work by coupling two Marcus-Lushnikov processes in such a way as to reduce the difference between their trajectories, thereby significantly reducing the variance of central difference estimators of the parametric derivatives. In the numerical results, the algorithms are shown have have a O(1/N) order of convergence a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3916","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0910.3916","created_at":"2026-05-18T01:04:59.612067+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.3916v1","created_at":"2026-05-18T01:04:59.612067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3916","created_at":"2026-05-18T01:04:59.612067+00:00"},{"alias_kind":"pith_short_12","alias_value":"CC2AVDE74DCY","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"CC2AVDE74DCYCJ4X","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"CC2AVDE7","created_at":"2026-05-18T12:25:59.703012+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M","json":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M.json","graph_json":"https://pith.science/api/pith-number/CC2AVDE74DCYCJ4X2YHNRZVI7M/graph.json","events_json":"https://pith.science/api/pith-number/CC2AVDE74DCYCJ4X2YHNRZVI7M/events.json","paper":"https://pith.science/paper/CC2AVDE7"},"agent_actions":{"view_html":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M","download_json":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M.json","view_paper":"https://pith.science/paper/CC2AVDE7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.3916&json=true","fetch_graph":"https://pith.science/api/pith-number/CC2AVDE74DCYCJ4X2YHNRZVI7M/graph.json","fetch_events":"https://pith.science/api/pith-number/CC2AVDE74DCYCJ4X2YHNRZVI7M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M/action/storage_attestation","attest_author":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M/action/author_attestation","sign_citation":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M/action/citation_signature","submit_replication":"https://pith.science/pith/CC2AVDE74DCYCJ4X2YHNRZVI7M/action/replication_record"}},"created_at":"2026-05-18T01:04:59.612067+00:00","updated_at":"2026-05-18T01:04:59.612067+00:00"}