Estimating an initial telomere length distribution from the Laplace transform of its senescence times distribution
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914431393333248 |
|---|---|
| author | Olayé, Jules |
| author_facet | Olayé, Jules |
| contents | This work follows from a previous study on the estimation of an initial distribution of telomere length from a senescence times distribution done in [10.1051/m2an/2026022, J. Olay{é}]. In this previous study, we have presented an estimation method based on the fact that our telomere shortening model can be approximated by a transport equation. This method has encouraging results, but fails to provide a good estimation when the variability of the initial telomere length distribution is too small. We improve here this method by approximating our model with an advection-diffusion equation, which allows us to better take into account the randomness of the shortening values. We show that under this approximation, there exists a simple link between the Laplace transform of the initial telomere length distribution and that of the senescence times distribution. Then, by using a numerical method for inverting Laplace transforms called Gaver-Stehfest algorithm, we exploit this link to construct a new estimator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27875 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Estimating an initial telomere length distribution from the Laplace transform of its senescence times distribution Olayé, Jules Analysis of PDEs This work follows from a previous study on the estimation of an initial distribution of telomere length from a senescence times distribution done in [10.1051/m2an/2026022, J. Olay{é}]. In this previous study, we have presented an estimation method based on the fact that our telomere shortening model can be approximated by a transport equation. This method has encouraging results, but fails to provide a good estimation when the variability of the initial telomere length distribution is too small. We improve here this method by approximating our model with an advection-diffusion equation, which allows us to better take into account the randomness of the shortening values. We show that under this approximation, there exists a simple link between the Laplace transform of the initial telomere length distribution and that of the senescence times distribution. Then, by using a numerical method for inverting Laplace transforms called Gaver-Stehfest algorithm, we exploit this link to construct a new estimator. |
| title | Estimating an initial telomere length distribution from the Laplace transform of its senescence times distribution |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.27875 |