{"paper":{"title":"Accuracy of reconstruction of spike-trains with two near-colliding nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrey Akinshin, Gil Goldman, Vladimir Golubyatnikov, Yosef Yomdin","submitted_at":"2017-01-05T21:25:01Z","abstract_excerpt":"We consider a signal reconstruction problem for signals $F$ of the form $ F(x)=\\sum_{j=1}^{d}a_{j}\\delta\\left(x-x_{j}\\right),$ from their moments $m_k(F)=\\int x^kF(x)dx.$ We assume $m_k(F)$ to be known for $k=0,1,\\ldots,N,$ with an absolute error not exceeding $\\epsilon > 0$.\n  We study the \"geometry of error amplification\" in reconstruction of $F$ from $m_k(F),$ in situations where two neighboring nodes $x_i$ and $x_{i+1}$ near-collide, i.e $x_{i+1}-x_i=h \\ll 1$. We show that the error amplification is governed by certain algebraic curves $S_{F,i},$ in the parameter space of signals $F$, alon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01482","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"}