{"paper":{"title":"Optimal excitation and measurement patterns for networks with tree topology","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"For networks with tree topology, minimal excitation and measurement patterns selected via the partial information matrix optimize the trace of the asymptotic covariance matrix.","cross_cats":["cs.SY","eess.SY"],"primary_cat":"physics.soc-ph","authors_text":"Alexandre Sanfelici Bazanella, Eduardo Mapurunga","submitted_at":"2026-05-12T23:54:19Z","abstract_excerpt":"In this work we evaluate the excitation and measurement patterns (EMP) for networks with tree topology. \n  We investigate guidelines for the selection of the minimal EMPs, i.e. those with the least number of excited and measured nodes combined, for which\n  the accuracy obtained, in terms of the trace of the asymptotic covariance matrix, is optimal.\n  We introduce the concept of partial information matrix as a means to systematically obtain the information matrix for any dynamic network.\n  For a specific tree class, called cross, we show that the accuracy of a particular module depends on the m"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For networks with tree topology, minimal EMPs can be systematically selected using the partial information matrix concept such that the trace of the asymptotic covariance matrix is optimized, and for cross trees the accuracy of a module depends on the magnitude of its parameters.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The network is exactly a tree (no cycles) and the asymptotic covariance matrix derived from the information matrix accurately reflects finite-sample estimation error under the chosen excitation and measurement patterns.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Minimal excitation and measurement patterns for tree networks are selected via partial information matrices to optimize estimation accuracy, with module accuracy depending on parameter magnitudes in cross trees.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For networks with tree topology, minimal excitation and measurement patterns selected via the partial information matrix optimize the trace of the asymptotic covariance matrix.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"80fa6bc40b09d081d363cb1ddab7b97705b53bce4fce062352e59ba12b3622d8"},"source":{"id":"2605.12829","kind":"arxiv","version":1},"verdict":{"id":"885eaadb-069d-4736-bf71-68ebc51cd4ef","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:14:37.954390Z","strongest_claim":"For networks with tree topology, minimal EMPs can be systematically selected using the partial information matrix concept such that the trace of the asymptotic covariance matrix is optimized, and for cross trees the accuracy of a module depends on the magnitude of its parameters.","one_line_summary":"Minimal excitation and measurement patterns for tree networks are selected via partial information matrices to optimize estimation accuracy, with module accuracy depending on parameter magnitudes in cross trees.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The network is exactly a tree (no cycles) and the asymptotic covariance matrix derived from the information matrix accurately reflects finite-sample estimation error under the chosen excitation and measurement patterns.","pith_extraction_headline":"For networks with tree topology, minimal excitation and measurement patterns selected via the partial information matrix optimize the trace of the asymptotic covariance matrix."},"references":{"count":13,"sample":[{"doi":"","year":2020,"title":"Ravazzi, C., and Ye, M. (2020). Dynamical Networks of Social Influence: Modern Trends and Perspectives. IFAC-PapersOnLine, 53(2), 17616–17627","work_id":"b0c1e94a-7727-44fa-a9a2-7ba1a529e8df","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Bazanella, A.S., Gevers, M., and Hendrickx, J.M. (2019). Network identification with partial excitation and mea- surement. In2019 IEEE 58th Conference on Decision and Control (CDC), 5500–5506","work_id":"e5b8676d-8e77-4f85-bf9a-52badf9b0739","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"(2018).Lectures on Network Systems","work_id":"ed23f6d2-0eaf-485f-8244-144f91f21e4f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Tomlin, C.J. (2016). Reconstruction of Gene Regulatory Networks Based on Repairing Sparse Low-Rank Matrices. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 13(4), 767–777","work_id":"8976f6b9-fa5d-48b2-9e77-f43bc9350f2b","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"Gevers, M., Bazanella, A.S., and da Silva, G.V. (2018). A practical method for the consistent identification of a module in a dynamical network.IFAC-PapersOnLine, 51(15), 862–867","work_id":"24106702-4d07-4759-8507-307a2d48839d","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":13,"snapshot_sha256":"d0896e565b76277eb04b83fddc016e600b563595fb6ae892e6ecbfcca0028271","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"}