BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ruth J. Williams (University of California San Diego) DTSTART:20230126T163000Z DTEND:20230126T170000Z DTSTAMP:20260421T124323Z UID:MoRN/62 DESCRIPTION:Title: Co mparison Theorems for Stochastic Chemical Reaction Networks\nby Ruth J . Williams (University of California San Diego) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nContinuous-time Markov cha ins are frequently used as stochastic models for chemical reaction network s\, especially in the growing field of systems biology. A fundamental prob lem for these Stochastic Chemical Reaction Networks (SCRNs) is to understa nd the dependence of the stochastic behavior of these systems on the chemi cal reaction rate parameters. Towards solving this problem\, in this paper we develop theoretical tools called comparison theorems that provide stoc hastic ordering results for SCRNs. These theorems give sufficient conditio ns for monotonic dependence on parameters in these network models\, which allow us to obtain\, under suitable conditions\, information about transie nt and steady state behavior. These theorems exploit structural properties of SCRNs\, beyond those of general continuous-time Markov chains. Further more\, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values\, or with t he same parameters and different initial conditions. These tools are devel oped for SCRNs taking values in a generic (finite or countably infinite) s tate space and can also be applied for non-mass-action kinetics models. We illustrate our results with applications to models of chromatin regulatio n and enzymatic kinetics.\n\nThis is based on joint work with Felipe Campo s\, Simone Bruno\, Yi Fu and Domitilla Del Vecchio.\n LOCATION:https://researchseminars.org/talk/MoRN/62/ END:VEVENT END:VCALENDAR