{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:11:03Z","timestamp":1680300663904},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"name":"NSF","award":["DMS-0710831, DMS-0410266"],"award-info":[{"award-number":["DMS-0710831, DMS-0410266"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper studies differential equation-based mathematical models\nand their numerical solutions for genetic regulatory network\nidentification. The primary objectives are to design, analyze,\nand test a general variational framework and numerical methods for seeking its\napproximate solutions for reverse engineering genetic regulatory\nnetworks from microarray datasets. In the proposed variational\nframework, no structure assumption on the genetic network is presumed,\ninstead, the network is solely determined by the microarray profile\nof the network components and is identified through a well chosen\nvariational principle which minimizes an energy functional.\nThe variational principle serves not only as a selection criterion\nto pick up the right solution of the underlying differential\nequation model but also provides an effective mathematical characterization\nof the small-world property of genetic regulatory networks which\nhas been observed in lab experiments. Five specific models\nwithin the variational framework and efficient numerical methods\nand algorithms for computing their solutions are proposed and\nanalyzed. Model validations using both synthetic\nnetwork datasets and subnetwork datasets of\n<jats:italic>Saccharomyces cerevisiae<\/jats:italic> (yeast) and <jats:italic>E. coli<\/jats:italic> are\nperformed on all five proposed variational models and\na performance comparison versus some existing genetic regulatory network\nidentification methods is also provided.<\/jats:p>","DOI":"10.1515\/cmam-2015-0019","type":"journal-article","created":{"date-parts":[[2015,8,20]],"date-time":"2015-08-20T09:03:58Z","timestamp":1440061438000},"page":"77-103","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Methods for Genetic Regulatory Network Identification Based on a Variational Approach"],"prefix":"10.1515","volume":"16","author":[{"given":"Xiaobing","family":"Feng","sequence":"first","affiliation":[{"name":"Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, USA"}]},{"given":"Miun","family":"Yoon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, USA"}]}],"member":"374","published-online":{"date-parts":[[2015,8,20]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/16\/1\/article-p77.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0019\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0019\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:34:13Z","timestamp":1680298453000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2015-0019\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,1]]},"published-print":{"date-parts":[[2016,1,1]]}},"alternative-id":["10.1515\/cmam-2015-0019"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2015-0019","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2015,8,20]]}}}