{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:J5JKRCIZTPBKZ23UIDEDZTF7RF","short_pith_number":"pith:J5JKRCIZ","schema_version":"1.0","canonical_sha256":"4f52a889199bc2aceb7440c83cccbf894f93f09c1bfdd99cc7066bbe2eb2511b","source":{"kind":"arxiv","id":"2201.00001","version":3},"attestation_state":"computed","paper":{"title":"Modeling Advection on Directed Graphs using Mat\\'ern Gaussian Processes for Traffic Flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Danielle C Maddix, Nadim Saad, Yuyang Wang","submitted_at":"2021-12-14T23:57:39Z","abstract_excerpt":"The transport of traffic flow can be modeled by the advection equation. Finite difference and finite volumes methods have been used to numerically solve this hyperbolic equation on a mesh. Advection has also been modeled discretely on directed graphs using the graph advection operator [4, 18]. In this paper, we first show that we can reformulate this graph advection operator as a finite difference scheme. We then propose the Directed Graph Advection Mat\\'ern Gaussian Process (DGAMGP) model that incorporates the dynamics of this graph advection operator into the kernel of a trainable Mat\\'ern G"},"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":"2201.00001","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-12-14T23:57:39Z","cross_cats_sorted":["cs.NA","stat.ML"],"title_canon_sha256":"b3e4f37162c3aa2ff68a92616ae15bb04dd7d11ab9faa11136d98d32365b1d10","abstract_canon_sha256":"a01cd46f719e28620514453d290e02590f01422e33471aaf08dedde8d1874c72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:58:05.687261Z","signature_b64":"XXPoXkW3S3NmX0ROHisyjy0rFlEdVwz9yiH3FBE6d7x1zNDhdkX6NJtOxOJaNvtj8ZwuueX3Yuh0Um0f/xMeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f52a889199bc2aceb7440c83cccbf894f93f09c1bfdd99cc7066bbe2eb2511b","last_reissued_at":"2026-07-05T03:58:05.686866Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:58:05.686866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modeling Advection on Directed Graphs using Mat\\'ern Gaussian Processes for Traffic Flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Danielle C Maddix, Nadim Saad, Yuyang Wang","submitted_at":"2021-12-14T23:57:39Z","abstract_excerpt":"The transport of traffic flow can be modeled by the advection equation. Finite difference and finite volumes methods have been used to numerically solve this hyperbolic equation on a mesh. Advection has also been modeled discretely on directed graphs using the graph advection operator [4, 18]. In this paper, we first show that we can reformulate this graph advection operator as a finite difference scheme. We then propose the Directed Graph Advection Mat\\'ern Gaussian Process (DGAMGP) model that incorporates the dynamics of this graph advection operator into the kernel of a trainable Mat\\'ern G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.00001","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.00001/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2201.00001","created_at":"2026-07-05T03:58:05.686924+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.00001v3","created_at":"2026-07-05T03:58:05.686924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.00001","created_at":"2026-07-05T03:58:05.686924+00:00"},{"alias_kind":"pith_short_12","alias_value":"J5JKRCIZTPBK","created_at":"2026-07-05T03:58:05.686924+00:00"},{"alias_kind":"pith_short_16","alias_value":"J5JKRCIZTPBKZ23U","created_at":"2026-07-05T03:58:05.686924+00:00"},{"alias_kind":"pith_short_8","alias_value":"J5JKRCIZ","created_at":"2026-07-05T03:58:05.686924+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.19305","citing_title":"Mat\\'ern Noise for Triangulation-Agnostic Flow Matching on Meshes","ref_index":50,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF","json":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF.json","graph_json":"https://pith.science/api/pith-number/J5JKRCIZTPBKZ23UIDEDZTF7RF/graph.json","events_json":"https://pith.science/api/pith-number/J5JKRCIZTPBKZ23UIDEDZTF7RF/events.json","paper":"https://pith.science/paper/J5JKRCIZ"},"agent_actions":{"view_html":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF","download_json":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF.json","view_paper":"https://pith.science/paper/J5JKRCIZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.00001&json=true","fetch_graph":"https://pith.science/api/pith-number/J5JKRCIZTPBKZ23UIDEDZTF7RF/graph.json","fetch_events":"https://pith.science/api/pith-number/J5JKRCIZTPBKZ23UIDEDZTF7RF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF/action/storage_attestation","attest_author":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF/action/author_attestation","sign_citation":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF/action/citation_signature","submit_replication":"https://pith.science/pith/J5JKRCIZTPBKZ23UIDEDZTF7RF/action/replication_record"}},"created_at":"2026-07-05T03:58:05.686924+00:00","updated_at":"2026-07-05T03:58:05.686924+00:00"}