{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BI6RISLTYRVP2UUGM4ALMMOFOF","short_pith_number":"pith:BI6RISLT","schema_version":"1.0","canonical_sha256":"0a3d144973c46afd52866700b631c5714bfaa03d35ab7592eec9b60bbe48426e","source":{"kind":"arxiv","id":"1411.7983","version":2},"attestation_state":"computed","paper":{"title":"Localized numerical impulses solutions in diffuse neural networks modeled by the complex fractional Ginzburg-Landau equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alain Mvogo, Antoine Tambue, G.H. Ben-Bolie, T.C. Kofane","submitted_at":"2014-11-28T19:36:24Z","abstract_excerpt":"We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave number $k\\rightarrow 0$) can be governed by the complex fractional Ginzburg-Landau (CFGL) equation. According to the stiffness of the system, we propose both the semi and the linearly implicit Riesz fractional finite-difference schemes to solve efficiently the CFGL equation. The obtained fractional numerical solutions for the nerve impulse reveal localized short"},"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":"1411.7983","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-28T19:36:24Z","cross_cats_sorted":[],"title_canon_sha256":"af109497ec58911c334a375a132d5162fefb05aaeee6c0dd0c27897f9a5fa160","abstract_canon_sha256":"d82ed7526ad92b1bb10546b3302114df6e4d40bbbc0c8a71b47a3e258eb274d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:21.501367Z","signature_b64":"fqyZLo8W1NTL3e7i3jH2Dtdi6Pxc3BQI5rn507wwj1cYbWBCzS/2+LD3izYkwrwwqML/y/8E8KU0mWlXlq1fDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a3d144973c46afd52866700b631c5714bfaa03d35ab7592eec9b60bbe48426e","last_reissued_at":"2026-05-18T01:12:21.501027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:21.501027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Localized numerical impulses solutions in diffuse neural networks modeled by the complex fractional Ginzburg-Landau equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alain Mvogo, Antoine Tambue, G.H. Ben-Bolie, T.C. Kofane","submitted_at":"2014-11-28T19:36:24Z","abstract_excerpt":"We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave number $k\\rightarrow 0$) can be governed by the complex fractional Ginzburg-Landau (CFGL) equation. According to the stiffness of the system, we propose both the semi and the linearly implicit Riesz fractional finite-difference schemes to solve efficiently the CFGL equation. The obtained fractional numerical solutions for the nerve impulse reveal localized short"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7983","kind":"arxiv","version":2},"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":"1411.7983","created_at":"2026-05-18T01:12:21.501078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.7983v2","created_at":"2026-05-18T01:12:21.501078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7983","created_at":"2026-05-18T01:12:21.501078+00:00"},{"alias_kind":"pith_short_12","alias_value":"BI6RISLTYRVP","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BI6RISLTYRVP2UUG","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BI6RISLT","created_at":"2026-05-18T12:28:22.404517+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/BI6RISLTYRVP2UUGM4ALMMOFOF","json":"https://pith.science/pith/BI6RISLTYRVP2UUGM4ALMMOFOF.json","graph_json":"https://pith.science/api/pith-number/BI6RISLTYRVP2UUGM4ALMMOFOF/graph.json","events_json":"https://pith.science/api/pith-number/BI6RISLTYRVP2UUGM4ALMMOFOF/events.json","paper":"https://pith.science/paper/BI6RISLT"},"agent_actions":{"view_html":"https://pith.science/pith/BI6RISLTYRVP2UUGM4ALMMOFOF","download_json":"https://pith.science/pith/BI6RISLTYRVP2UUGM4ALMMOFOF.json","view_paper":"https://pith.science/paper/BI6RISLT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.7983&json=true","fetch_graph":"https://pith.science/api/pith-number/BI6RISLTYRVP2UUGM4ALMMOFOF/graph.json","fetch_events":"https://pith.science/api/pith-number/BI6RISLTYRVP2UUGM4ALMMOFOF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BI6RISLTYRVP2UUGM4ALMMOFOF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BI6RISLTYRVP2UUGM4ALMMOFOF/action/storage_attestation","attest_author":"https://pith.science/pith/BI6RISLTYRVP2UUGM4ALMMOFOF/action/author_attestation","sign_citation":"https://pith.science/pith/BI6RISLTYRVP2UUGM4ALMMOFOF/action/citation_signature","submit_replication":"https://pith.science/pith/BI6RISLTYRVP2UUGM4ALMMOFOF/action/replication_record"}},"created_at":"2026-05-18T01:12:21.501078+00:00","updated_at":"2026-05-18T01:12:21.501078+00:00"}