Accession Number : AD0430995


Title :   ON AGE DEPENDENT BRANCHING PROCESSES


Corporate Author : STANFORD UNIV CA


Personal Author(s) : Weiner, Howard


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/430995.pdf


Report Date : 27 Jan 1964


Pagination or Media Count : 83


Abstract : This paper deals with asymptotic properties of various models of age- dependent branching processes. Cell growth is considered in which a cell proceeds in a sequential manner through n independent states, state R with its life distribution FR, R=1,2,...,n. At the end of mitosis, the nth state, the cell divides into similar cells, the number of which is governed by a generating function h, independent of the time and other cells of the process. A variation of the given model treats cell growth in which the cell proceeds from state to state according to a general semi-Markov process until the mitotic state is completed, when division into similar cells in accord with h occurs. The random variable is considered in a simple age dependent branching process for m 1. Another case is that of two types of cells, of which only one type may divide while the other either accumulates or is eventually absorbed in the medium. An example of this is the production of stem cells and red blood cells from parent stem cells. Two related models are considered, both examples of the 'reducible case'. Increasing cell populations are considered. A binary fission case of each model may be represented schematically to indicate the various combinations of cell births with corresponding probabilities. (Author)


Descriptors :   *STATISTICAL PROCESSES , *MITOSIS , MATHEMATICAL MODELS , STOCHASTIC PROCESSES , PROBABILITY , DIFFERENCE EQUATIONS , MOMENTS , POPULATION , MATHEMATICAL ANALYSIS , DIFFERENTIAL EQUATIONS , STATISTICAL DISTRIBUTIONS , CORRELATION TECHNIQUES , MEDICAL RESEARCH , INTEGRAL TRANSFORMS , GROWTH(PHYSIOLOGY)


Subject Categories : Statistics and Probability
      Biomedical Instrumentation and Bioengineering


Distribution Statement : APPROVED FOR PUBLIC RELEASE