{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:37:59Z","timestamp":1760240279878,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,20]],"date-time":"2019-04-20T00:00:00Z","timestamp":1555718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["17-11-01220"],"award-info":[{"award-number":["17-11-01220"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The paper suggests a randomized model for dynamic migratory interaction of regional systems. The locally stationary states of migration flows in the basic and immigration systems are described by corresponding entropy operators. A soft randomization procedure that defines the optimal probability density functions of system parameters and measurement noises is developed. The advantages of soft randomization with approximate empirical data balance conditions are demonstrated, which considerably reduces algorithmic complexity and computational resources demand. An example of migratory interaction modeling and testing is given.<\/jats:p>","DOI":"10.3390\/e21040424","type":"journal-article","created":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T11:02:53Z","timestamp":1555930973000},"page":"424","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Soft Randomized Machine Learning Procedure for Modeling Dynamic Interaction of Regional Systems"],"prefix":"10.3390","volume":"21","author":[{"given":"Yuri S.","family":"Popkov","sequence":"first","affiliation":[{"name":"Federal Research Center \u201cComputer Science and Control\u201d of Russian Academy of Sciences, 119333 Moscow, Russia"},{"name":"Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia"},{"name":"Department of Software Engineering, ORT Braude College, 216100 Karmiel, Israel"},{"name":"Yugra Research Institute for Information Technologies, 628011 Khanty-Mansiysk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1080\/1369183X.2017.1300225","article-title":"Introduction: International academic mobility and inequalities","volume":"43","author":"Bilecen","year":"2017","journal-title":"J. Ethic Migr. Stud."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Penninx, R., Berger, M., and Kraal, K. (2006). Migration and development: Causes and consequences. The Dynamics of International Migration and Settlement in Europe: A State of the Art, Amsterdam University Press.","DOI":"10.5117\/9789053568668"},{"key":"ref_3","unstructured":"Wilson, A.G. (1975). Modeling of stochastic communication systems. Entropy Methods for Complex Systems Modeling, Nauka."},{"key":"ref_4","unstructured":"Heide, H., and Willekens, F. (1984). Structural analysis of interregional and intraregional migration patterns. Demographic Research and Spatial Policy, Academic Press."},{"key":"ref_5","first-page":"3","article-title":"Dynamic entropy model for migratory interaction of regional systems","volume":"2","author":"Popkov","year":"2018","journal-title":"Tr. Inst. Sist. Analiz. Ross. Akad. 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The Indirect Estimation of Migration: Methods for Dealing with Irregular, Inadequate, and Missing Data, Springer Science & Business Media.","DOI":"10.1007\/978-90-481-8915-1"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.na.2017.02.024","article-title":"Interaction of human migration and wealth distribution","volume":"150","author":"Volpert","year":"2017","journal-title":"Nonlinear Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0895-7177(94)90014-0","article-title":"Using Markov chains to model human migration in a network equilibrium framework","volume":"19","author":"Pan","year":"1994","journal-title":"Math. Comput. Model."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s10680-015-9362-0","article-title":"Decision-making in agent-based models of migration: State of the art and challenges","volume":"32","author":"Klabunde","year":"2016","journal-title":"Eur. J. Popul."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1080\/00324728.2017.1350281","article-title":"Multistable modelling extended by behavioural rules. An application to migration","volume":"71","author":"Klabunde","year":"2017","journal-title":"Popul. Stud."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1134\/S1064562418070293","article-title":"Soft randomized machine learning","volume":"98","author":"Popkov","year":"2018","journal-title":"Doklady Math."},{"key":"ref_16","unstructured":"Voevodin, V.V., and Kuznetsov, Y.A. (1984). Matrices and Calculations, Nauka. (In Russian)."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/4\/424\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:47:01Z","timestamp":1760186821000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/4\/424"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,20]]},"references-count":16,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["e21040424"],"URL":"https:\/\/doi.org\/10.3390\/e21040424","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,4,20]]}}}