{"paper":{"title":"Properties of networks with partially structured and partially random connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.NC","authors_text":"Francesco Fumarola, Kenneth D. Miller, Yashar Ahmadian","submitted_at":"2013-11-19T09:47:23Z","abstract_excerpt":"We provide a general formula for the eigenvalue density of large random $N\\times N$ matrices of the form $A = M + LJR$, where $M$, $L$ and $R$ are arbitrary deterministic matrices and $J$ is a random matrix of zero-mean independent and identically distributed elements. For $A$ nonnormal, the eigenvalues do not suffice to specify the dynamics induced by $A$, so we also provide general formulae for the transient evolution of the magnitude of activity and frequency power spectrum in an $N$-dimensional linear dynamical system with a coupling matrix given by $A$. These quantities can also be though"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4672","kind":"arxiv","version":6},"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"}