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101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aBranching Process Models of Cancer /$fby Richard Durrett
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (73 p.)
225 1 $aStochastics in Biological Systems,$x2364-2297 ;$v1.1
300   $aDescription based upon print version of record.
311   $a3-319-16064-8 
320   $aIncludes bibliographical references.
327   $aMultistage Theory of Cancer -- Mathematical Overview -- Branching Process Results -- Time for Z_0 to Reach Size M -- Time Until the First Type 1 -- Mutation Before Detection? -- Accumulation of Neutral Mutations -- Properties of the Gamma Function -- Growth of Z_1(t) -- Movements of Z_1(t) -- Luria-Delbruck Distributions -- Number of Type 1's at Time T_M -- Gwoth of Z_k(t) -- Transitions Between Waves -- Time to the First Type \tau_k, k \ge 2 -- Application: Metastasis -- Application: Ovarian Cancer -- Application: Intratumor Heterogeneity.
330   $aThis volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As a consequence, the authors calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the authors evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis. These notes should be accessible to students who are familiar with Poisson processes and continuous time. Richard Durrett is mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles, and has supervised more than 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.
410  0$aStochastics in Biological Systems,$x2364-2297 ;$v1.1
606   $aProbabilities
606   $aBiomathematics
606   $aCancer research
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aMathematical and Computational Biology$3https://scigraph.springernature.com/ontologies/product-market-codes/M31000
606   $aCancer Research$3https://scigraph.springernature.com/ontologies/product-market-codes/B11001
615  0$aProbabilities.
615  0$aBiomathematics.
615  0$aCancer research.
615 14$aProbability Theory and Stochastic Processes.
615 24$aMathematical and Computational Biology.
615 24$aCancer Research.
676   $a614.5999
700   $aDurrett$b Richard$4aut$4http://id.loc.gov/vocabulary/relators/aut$055577
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299775603321
996   $aBranching process models of cancer$91522586
997   $aUNINA