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X-WR-CALNAME:Institute of Mathematics and Informatics
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X-WR-CALDESC:Събития за Institute of Mathematics and Informatics
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DTSTART:20190331T010000
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DTSTART:20191027T010000
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DTSTART;TZID=Europe/Sofia:20190619T140000
DTEND;TZID=Europe/Sofia:20190619T160000
DTSTAMP:20260405T064246
CREATED:20190610T064406Z
LAST-MODIFIED:20190610T064406Z
UID:7048-1560952800-1560960000@math.bas.bg
SUMMARY:Национален семинар по стохастика
DESCRIPTION:Поредната сбирка на Националния семинар по стохастика ще се проведе на 19 юни 2019 г. (сряда) от 14:00 часа в зала 403 на ИМИ – БАН. Доклад на тема: \nA decomposable multi-type Bellman-Harris branching process\nwith mutations. Application in modeling of cancer evolution\nще изнесе Калоян Витанов (докторант във ФМИ-СУ). \nПоканват се всички интересуващи се. \nРезюме: A prominent feature of biological systems is their capacity to adapt and mutation is a key mechanism for achieving adaptation. As a continuation of [3] we propose a decomposable multi-type Bellman-Harris branching process\, which incorporates a possibility for mutation.\nMetastasis\, the spread of cancer cells from a primary tumour to secondary location(s) in the human organism\, is the ultimate cause of death for the majority of cancer patients. We consider a metastasized cancer cell population after some medical treatment (e.g. chemotherapy). Arriving in a dierent environment the cancer cells may change their characteristics concerning lifespan and reproduction\, thus they may dierentiate into dierent types. Even if the treatment is eective (resulting in subcritical reproduction of all cancer cell types)\, however\, it is possible during cell division for mutations to occur. These mutations can produce a new cancer cell type that is adapted to the treatment (having supercritical reproduction). Cancer cells from this new type may lead to a non-extinction process.\nWe model the above scenario with the proposed model. Expanding [1] and [2] we investigate relevant quantities such as the probability of extinction of the process until time t and as t approaches innity\, the number of occurred supercritical mutants until time t and as t approaches innity\, the time until the rst occurrence of a mutant starting a non-extinction process and the immediate risk for the process to escape extinction. We also propose numerical schemes for performing calculations.\nKeywords: Mutations\, Decomposable multi-type branching process\, Probability of extinction\, Waiting time to escape mutant\, Immediate risk of escaping extinction\nAcknowledgements: The research of these authors was supported\, in part\, by the Bulgarian National Science Fund at the Ministry of Science and Education\, Grant No. KP-06-H22/3.\nReferences\n[1] K. Vitanov\, M. Slavtchova-Bojkova\, Multitype branching processes in continuous time as models of cancer\, Annuaire de l’Universite de Soa \St. Kl. Ohridski”\, Fac. Math and Inf.\, 104\, 2017\, 193-200.\n[2] M. Slavtchova-Bojkova\, K. Vitanov\, Modelling cancer evolution by multi-type age-dependent branching processes\, Compt. rend. de l’acad. bulgare des Sci. 71\, 2018\, 1297{1305.\n[3] M. Slavtchova-Bojkova\, P. Trayanov\, S. Dimitrov\, Branching processes in continuous time as models of mutations: Computational approaches and algorithms\, Computational Statistics and Data Analysis\, 113\, 2017\, 111{124.
URL:https://math.bas.bg/event/%d0%bd%d0%b0%d1%86%d0%b8%d0%be%d0%bd%d0%b0%d0%bb%d0%b5%d0%bd-%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d1%81%d1%82%d0%be%d1%85%d0%b0%d1%81%d1%82%d0%b8%d0%ba%d0%b0-16/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%A1%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%20%D0%98%D0%B7%D1%81%D0%BB%D0%B5%D0%B4%D0%B2%D0%B0%D0%BD%D0%B5%20%D0%BD%D0%B0%20%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B8%D1%82%D0%B5%2C%20%D0%B2%D0%B5%D1%80%D0%BE%D1%8F%D1%82%D0%BD%D0%BE%D1%81%D1%82%D0%B8%20%D0%B8%20%D1%81%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0":MAILTO:jeni@math.bas.bg;
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