This thesis presents a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphical models for probability density and mass functions, in a CDN, the marginal...

Toggle switch as a common phenomenon in gene regulatory networks has been recognized important for biological functions. Despite much effort dedicated to understanding the toggle switch and designing synthetic biology circuit to achieve the biological function, we still lack a comprehensive...

Transcriptional regulation is subject to significant stochasticity due partly to the random waiting times among synthesis and degradation reactions involving a finite collection of transcripts. Additional stochasticity is attributable to the random transitions among the discrete operator states...