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| Natura: | Preprint |
| Pubblicazione: |
2018
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| Accesso online: | https://arxiv.org/abs/1811.10176 |
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| _version_ | 1866929499271069696 |
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| author | Azencott, Robert Geiger, Brett Timofeyev, Ilya |
| author_facet | Azencott, Robert Geiger, Brett Timofeyev, Ilya |
| contents | Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. In this paper, we develop a theoretical large deviations framework for a class of Markov chains modeling the genetic evolution of bacteria such as E. coli. In particular, we develop the cost function for discrete-time Markov chains which describe the daily evolution of histograms of bacterial populations. We also develop explicit formulas that can be used to numerically quantify the most likely evolutionary trajectories connecting an initial histogram and the target histogram. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_10176 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Large Deviations Analysis for Stochastic Models of Bacterial Evolution Azencott, Robert Geiger, Brett Timofeyev, Ilya Probability 60F10, 60J20, 92D15 Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. In this paper, we develop a theoretical large deviations framework for a class of Markov chains modeling the genetic evolution of bacteria such as E. coli. In particular, we develop the cost function for discrete-time Markov chains which describe the daily evolution of histograms of bacterial populations. We also develop explicit formulas that can be used to numerically quantify the most likely evolutionary trajectories connecting an initial histogram and the target histogram. |
| title | Large Deviations Analysis for Stochastic Models of Bacterial Evolution |
| topic | Probability 60F10, 60J20, 92D15 |
| url | https://arxiv.org/abs/1811.10176 |