{"paper":{"title":"Upper-bounding $\\ell_1$-optimization sectional thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"Mihailo Stojnic","submitted_at":"2013-06-17T09:01:07Z","abstract_excerpt":"In this paper we look at a particular problem related to under-determined linear systems of equations with sparse solutions. $\\ell_1$-minimization is a fairly successful polynomial technique that can in certain statistical scenarios find sparse enough solutions of such systems. Barriers of $\\ell_1$ performance are typically referred to as its thresholds. Depending if one is interested in a typical or worst case behavior one then distinguishes between the \\emph{weak} thresholds that relate to a typical behavior on one side and the \\emph{sectional} and \\emph{strong} thresholds that relate to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3778","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"}