{"paper":{"title":"Metric Entropy and the Optimal Prediction of Chaotic Signals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Divakar Viswanath, Kirill Serkh, Xuan Liang","submitted_at":"2011-02-15T22:53:49Z","abstract_excerpt":"Suppose we are given a time series or a signal $x(t)$ for $0\\leq t\\leq T$. We consider the problem of predicting the signal in the interval $T<t\\leq T+t_{f}$ from a knowledge of its history and nothing more. We ask the following question: what is the largest value of $t_{f}$ for which a prediction can be made? We show that the answer to this question is contained in a fundamental result of information theory due to Wyner, Ziv, Ornstein, and Weiss. In particular, for the class of chaotic signals, the upper bound is $t_{f}\\leq\\log_{2}T/H$ in the limit $T\\rightarrow\\infty$, with $H$ being entropy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3202","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"}