| Título: | The Aldous-Shields model revisited with application to cellular ageing |
| Autores: |
Best, Katharina; University of Freiburg Pfaffelhuber, Peter; University of Freiburg |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Random tree; cellular senescence; telomere; Hayflick limit 60K35; 92D20; 60J85; 05C0 |
| Descripción: | 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 $h$. |
| Idioma: | No aplica |
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