{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:32:34Z","timestamp":1760236354105,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T00:00:00Z","timestamp":1637280000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti\u2019s Theorem. In its original form, it applies to infinite 0\u20131 valued sequences with the special property that the distribution is invariant to permutations (called an exchangeable sequence). Later it was extended and generalized in numerous directions. After reviewing this line of development, we present our new decomposition theorem, covering cases that have not been previously considered. We also introduce a novel way of applying these types of results in the analysis of random networks. For self-containment, we provide the introductory exposition in more detail than usual, with the intent of making it also accessible to readers who may not be closely familiar with the subject.<\/jats:p>","DOI":"10.3390\/a14110336","type":"journal-article","created":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T08:29:17Z","timestamp":1637310557000},"page":"336","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8952-6946","authenticated-orcid":false,"given":"Andr\u00e1s","family":"Farag\u00f3","sequence":"first","affiliation":[{"name":"Department of Computer Science, The University of Texas at Dallas, 800 W. Campbell Rd., Richardson, TX 75080, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lindsay, B.G. (1995). Mixture Models: Theory, Geometry and Applications, Institute of Mathematical Statistics.","DOI":"10.1214\/cbms\/1462106013"},{"key":"ref_2","first-page":"251","article-title":"Funzione Caratteristica di un Fenomeno Aleatorio","volume":"4","year":"1931","journal-title":"Cl. Sci. Fis. Math. Nat."},{"key":"ref_3","unstructured":"Stoyanov, J.M. (2014). Counterexamples in Probability, Dover Publications. [3rd ed.]. Dover Books on Mathematics."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.spl.2019.03.014","article-title":"An Elementary Proof of de Finetti\u2019s Theorem","volume":"151","author":"Kirsch","year":"2019","journal-title":"Stat. Probab. Lett."},{"key":"ref_5","unstructured":"(2021, November 01). 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