74 citations · 224 across the 8 of their papers we have counts for
9 papers
Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution
John J. Vastola, Gennady Gorin, Lior Pachter +1
The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to so…
The chemical Langevin equation: a path integral view of Gillespie's derivation
John J. Vastola, William R. Holmes
In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it yield a valid approximation of the chemical master…
Stochastic path integrals can be derived like quantum mechanical path integrals
John J. Vastola, William R. Holmes
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to…
Optimal models of decision-making in dynamic environments
Zachary P. Kilpatrick, William R. Holmes, Tahra L. Eissa +1
Nature is in constant flux, so animals must account for changes in their environment when making decisions. How animals learn the timescale of such changes and adapt their decision…
The Impact of Speed and Bias on the Cognitive Processes of Experts and Novices in Medical Image Decision-making
Jennifer S. Trueblood, William R. Holmes, Adam C. Seegmiller +6
Training individuals to make accurate decisions from medical images is a critical component of education in diagnostic pathology. We describe a joint experimental and computational…
A mechano-chemical feedback underlies co-existence of qualitatively distinct cell polarity patterns within diverse cell populations
JinSeok Park, William R. Holmes, Sung-Hoon Lee +7
Cell polarization and directional cell migration can display random, persistent and oscillatory dynamic patterns. However, it is not clear if these polarity patterns can be explain…