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Branching Brownian motion models for cell developmental trajectories Gadhiwala, Nitya
Abstract
Recent advances in single cell sequencing has led to the availability of gene expression data. We model the trajectories of cells in gene expression space using a diffusion and gradient drift process that also undergoes branching. We recover the law on paths of this process given time marginals using an entropy minimization problem. The optimization is over the set of all processes with the same branching mechanism and given marginals. We prove that among these the one which minimizes the relative entropy with respect to a reference branching Brownian motion is the ground truth. The above result has been proved earlier for models that don't consider branching. This thesis extends it for the case with branching.
Item Metadata
| Title |
Branching Brownian motion models for cell developmental trajectories
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| Creator | |
| Supervisor | |
| Publisher |
University of British Columbia
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| Date Issued |
2023
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| Description |
Recent advances in single cell sequencing has led to the availability of gene expression data. We model the trajectories of cells in gene expression space using a diffusion and gradient drift process that also undergoes branching. We recover the law on paths of this process given time marginals using an entropy minimization problem. The optimization is over the set of all processes with the same branching mechanism and given marginals. We prove that among these the one which minimizes the relative entropy with respect to a reference branching Brownian motion is the ground truth. The above result has been proved earlier for models that don't consider branching. This thesis extends it for the case with branching.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2023-08-30
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0435667
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2023-11
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International