{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T08:08:40Z","timestamp":1770278920881,"version":"3.49.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,5,13]]},"abstract":"<jats:p>An open stochastic system \u00e0 la Jan Willems is a system affected by two qualitatively different kinds of uncertainty: one is probabilistic fluctuation, and the other one is nondeterminism caused by a fundamental lack of information. We present a formalization of open stochastic systems in the language of category theory. Central to this is the notion of copartiality which models how the lack of information propagates through a system (corresponding to the coarseness of sigma-algebras in Willems' work). As a concrete example, we study extended Gaussian distributions, which combine Gaussian probability with nondeterminism and correspond precisely to Willems' notion of Gaussian linear systems. We describe them both as measure-theoretic and abstract categorical entities, which enables us to rigorously describe a variety of phenomena like noisy physical laws and uninformative priors in Bayesian statistics. The category of extended Gaussian maps can be seen as a mutual generalization of Gaussian probability and linear relations, which connects the literature on categorical probability with ideas from control theory like signal-flow diagrams.<\/jats:p>","DOI":"10.46298\/lmcs-21(3:11)2025","type":"journal-article","created":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T08:30:06Z","timestamp":1753777806000},"source":"Crossref","is-referenced-by-count":1,"title":["A Categorical Treatment of Open Linear Systems"],"prefix":"10.46298","volume":"Volume 21, Issue 3","author":[{"given":"Dario","family":"Stein","sequence":"first","affiliation":[]},{"given":"Richard","family":"Samuelson","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,7,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2403.03934v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2403.03934v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T08:30:06Z","timestamp":1753777806000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/13188"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(3:11)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2403.03934v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2403.03934v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2403.03934","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2403.03934","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,29]]},"article-number":"13188"}}