random seed 42 👎👎👎 random seed 69 👍👍👍

👼🏻

(extremely over engineered with no comments or documentation)

you’re on thin ice here bb

anyway, like i said, this is a step towards that goal, just laying the ground work for interpreting and visualizing transcriptional dynamics using simple tools such as kNN graphs. but with some more time and effort, this bridge can be completed! i'd be happy to work with anyone interested 6/6

however one can take a fully stochastic model and, using the same techniques, turn it into a graph that could be fed into a UMAP, for instance, that could yield be used to accurately visualize transcription dynamics! up to some error that could probably be quantified. 5/

the backward Kolmogorov operator associated to the CRN. here, I take a data driven approach and define a particular SDE that gives rise to the observed data distribution (via the kNN estimate of the sampling density) and use the diffusion map as a basis for clustering. 4/

importantly the weights of the graph define exactly what operator is, and knowing the continuum operator is the most important part for being able interpret the results. we wanted to model the dynamics of chemical reaction networks (CRN) so the correct operator is the Fokker-Planck equation OR 3/

my goal was to bridge commonly used continuum tools of scRNA-seq (diffusion maps, UMAP, etc) with more mechanistic stochastic models. the main idea comes from the insight that markov chains on nearest neighbor graphs are generators for certain operators in the continuum limit. 2/

me reading ur posts

melville: AND THEYRE KISSING