國立虎尾科技大學 |

Branching Process Models of Cancer

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Branching Process Models of Cancer/ by Richard Durrett.
作者:	Durrett, Richard.
面頁冊數:	VII, 63 p. 6 illus., 2 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Probabilities. -
電子資源:	https://doi.org/10.1007/978-3-319-16065-8
ISBN:	9783319160658

Branching Process Models of Cancer
Durrett, Richard.

Branching Process Models of Cancer[electronic resource] /by Richard Durrett. - 1st ed. 2015. - VII, 63 p. 6 illus., 2 illus. in color.online resource. - Stochastics in Biological Systems,1.12364-2297 ;. - Stochastics in Biological Systems,1.1.

Multistage 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.

This 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.

ISBN: 9783319160658

Standard No.: 10.1007/978-3-319-16065-8doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Branching Process Models of Cancer
LDR:02885nam a22004215i 4500 001 963114
003 DE-He213
005 20200704120952.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319160658 $9 978-3-319-16065-8
024 7 $a 10.1007/978-3-319-16065-8 $2 doi
035 $a 978-3-319-16065-8
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a Durrett, Richard. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 683928
245 1 0 $a Branching Process Models of Cancer $h [electronic resource] / $c by Richard Durrett.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a VII, 63 p. 6 illus., 2 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Stochastics in Biological Systems, $x 2364-2297 ; $v 1.1
505 0 $a Multistage 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.
520 $a This 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.
650 0 $a Probabilities. $3 527847
650 0 $a Biomathematics. $3 527725
650 0 $a Cancer research. $3 1253664
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Mathematical and Computational Biology. $3 786706
650 2 4 $a Cancer Research. $3 668358
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319160665
776 0 8 $i Printed edition: $z 9783319160641
830 0 $a Stochastics in Biological Systems, $x 2364-2297 ; $v 1.1 $3 1258055
856 4 0 $u https://doi.org/10.1007/978-3-319-16065-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)