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Single-cell sequencing technology allows the dissection of genomic heterogeneity at the single-cell level, thereby providing important evolutionary information about cancer cells. In contrast to traditional bulk sequencing, single-cell sequencing requires the amplification of the whole genome of a single cell to accumulate enough samples for sequencing. However, the amplification process inevitably introduces amplification bias, resulting in an over-dispersing portion of the sequencing data. Recent study has manifested that the over-dispersed portion of the single-cell sequencing data could be well modelled by negative binomial distributions.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Results<\/jats:title>\n                <jats:p>We developed a read-depth based method, <jats:italic>nbCNV<\/jats:italic> to detect the copy number variants (CNVs). The nbCNV method uses two constraints-sparsity and smoothness to fit the CNV patterns under the assumption that the read signals are negatively binomially distributed. The problem of CNV detection was formulated as a quadratic optimization problem, and was solved by an efficient numerical solution based on the classical alternating direction minimization method.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Conclusions<\/jats:title>\n                <jats:p>Extensive experiments to compare nbCNV with existing benchmark models were conducted on both simulated data and empirical single-cell sequencing data. The results of those experiments demonstrate that nbCNV achieves superior performance and high robustness for the detection of CNVs in single-cell sequencing data.<\/jats:p>\n              <\/jats:sec>","DOI":"10.1186\/s12859-016-1239-7","type":"journal-article","created":{"date-parts":[[2016,9,17]],"date-time":"2016-09-17T11:19:32Z","timestamp":1474111172000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["nbCNV: a multi-constrained optimization model for discovering copy number variants in single-cell sequencing data"],"prefix":"10.1186","volume":"17","author":[{"given":"Changsheng","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2747-7234","authenticated-orcid":false,"given":"Hongmin","family":"Cai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingying","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,9,17]]},"reference":[{"issue":"6","key":"1239_CR1","doi-asserted-by":"publisher","first-page":"974","DOI":"10.1101\/gr.114876.110","volume":"21","author":"A Abyzov","year":"2011","unstructured":"Abyzov A, Urban AE, Snyder M, Gerstein M. 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