{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T12:30:37Z","timestamp":1772022637555,"version":"3.50.1"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Neur. Syst."],"published-print":{"date-parts":[[2005,8]]},"abstract":"<jats:p>Reconstruction of genetic regulatory networks from time series data of gene expression patterns is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been proposed as an effective model for gene regulatory networks. PBNs are able to cope with uncertainty, corporate rule-based dependencies between genes and discover the sensitivity of genes in their interactions with other genes. However, PBNs are unlikely to use directly in practice because of huge amount of computational cost for obtaining predictors and their corresponding probabilities. In this paper, we propose a multivariate Markov model for approximating PBNs and describing the dynamics of a genetic network for gene expression sequences. The main contribution of the new model is to preserve the strength of PBNs and reduce the complexity of the networks. The number of parameters of our proposed model is O(n<jats:sup>2<\/jats:sup>) where n is the number of genes involved. We also develop efficient estimation methods for solving the model parameters. Numerical examples on synthetic data sets and practical yeast data sequences are given to demonstrate the effectiveness of the proposed model.<\/jats:p>","DOI":"10.1142\/s0129065705000256","type":"journal-article","created":{"date-parts":[[2005,9,23]],"date-time":"2005-09-23T10:42:07Z","timestamp":1127472127000},"page":"297-310","source":"Crossref","is-referenced-by-count":42,"title":["ON CONSTRUCTION OF STOCHASTIC GENETIC NETWORKS BASED ON GENE EXPRESSION SEQUENCES"],"prefix":"10.1142","volume":"15","author":[{"given":"WAI-KI","family":"CHING","sequence":"first","affiliation":[{"name":"Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong, China"}]},{"given":"MICHAEL M.","family":"NG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, Hong Kong, China"}]},{"given":"ERIC S.","family":"FUNG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong, China"}]},{"given":"TATSUYA","family":"AKUTSU","sequence":"additional","affiliation":[{"name":"Institute for Chemical Research, Kyoto University, Gokasho Uji, Kyoto 611-0011, Japan, Kyoto, Japan"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/16.8.727"},{"key":"rf2","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/2018.001.0001","volume-title":"Computational Modeling of Genetic and Biochemical Networks","author":"Bower J.","year":"2001"},{"key":"rf3","volume-title":"Nonnegative Matrices in the Mathematical Sciences","author":"Berman A.","year":"1979"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1006\/jtbi.1996.0328"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1117\/12.281504"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1093\/imaman\/13.3.187"},{"key":"rf7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/978-3-540-28651-6_3","volume":"3177","author":"Ching W.","year":"2004"},{"key":"rf8","volume-title":"Linear Programming","author":"Chvatal V.","year":"1983"},{"key":"rf9","first-page":"69","volume":"9","author":"de Jong H.","journal-title":"J. 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