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The Aldous-Shields model revisited with application to cellular ageing


 
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1. Title Title of document The Aldous-Shields model revisited with application to cellular ageing
 
2. Creator Author's name, affiliation, country Katharina Best; University of Freiburg
 
2. Creator Author's name, affiliation, country Peter Pfaffelhuber; University of Freiburg
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random tree; cellular senescence; telomere; Hayflick limit
 
3. Subject Subject classification 60K35; 92D20; 60J85; 05C0
 
4. Description Abstract In Aldous and Shields (1988) a model for a rooted, growing random binary tree with edge lengths 1 was presented. For some $c>0$, an external vertex splits at rate $c^{-i}$ (and becomes internal) if its distance from the root (depth) is $i$. We reanalyse the tree profile for $c>1$, i.e. the numbers of external vertices in depth $i=1,2,...$. Our main result are concrete formulas for the expectation and covariance-structure of the profile. In addition, we present the application of the model to cellular ageing. Here, we say that nodes in depth $h+1$ are senescent, i.e. do not split. We obtain a limit result for the proportion of non-senesced vertices for large $h$.
 
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7. Date (YYYY-MM-DD) 2010-10-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1581
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1581
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 15
 
12. Language English=en
 
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