English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a method to sample Markov-chain trajectories constrained to boththe initial and final conditions, which we term Markov bridges. Thetrajectories are conditioned to end in a specific state at a given time. Wederive the master equation for Markov bridges, which exhibits the originaltransition rates scaled by a time-dependent factor. Trajectories can then begenerated using a refined version of the Gillespie algorithm. We illustrate thebenefits of our method by sampling trajectories in the M\"uller-Brownpotential. This allows us to generate transition paths which would otherwise beobtained at a high computational cost with standard Kinetic Monte Carlo methodsbecause commitment to a transition path is essentially a rare event. We thenapply our method to a single-cell RNA sequencing dataset from mouse pancreaticcells to investigate the cell differentiation pathways of endocrine-cellprecursors. By sampling Markov bridges for a specific differentiation pathwaywe obtain a time-resolved dynamics that can reveal features such as cell typeswhich behave as bottlenecks. The ensemble of trajectories also givesinformation about the fluctuations around the most likely path. For example, wequantify the statistical weights of different branches in the differentiationpathway to alpha cells.

Markov-bridge generation of transition paths and its application to cell-fate choice