BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jiaxin Jin (University of Louisiana at Lafayette) DTSTART:20260326T160000Z DTEND:20260326T163000Z DTSTAMP:20260421T130004Z UID:MoRN/141 DESCRIPTION:Title: H omeostasis Patterns and Infinitesimal Homeostasis in Reaction Networks \nby Jiaxin Jin (University of Louisiana at Lafayette) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nHomeostasis is a re gulatory mechanism that keeps a specific variable close to a prescribed va lue as other variables fluctuate. This notion can be formulated rigorously when a system is modeled as an input-output network with distinguished in put and output nodes\, where the dynamics determine the corresponding inpu t-output function. In this setting\, homeostasis can be defined infinitesi mally\, namely when the derivative of the input-output function vanishes a t an isolated point. Combined with graph-theoretic ideas from combinatoria l matrix theory\, this provides a framework for computing homeostasis poin ts and classifying homeostasis types. \n\nIn the first part of the talk\, we introduce the notion of a homeostasis pattern\, a set of nodes that are simultaneously infinitesimally homeostatic\, and show that all such patte rns can be described using a combinatorial structure associated with the n etwork\, called the homeostasis pattern network. In the second part\, we s tudy infinitesimal homeostasis in chemical reaction networks\, where conse rvation laws complicate the standard analysis. We present criteria for the existence of infinitesimal homeostasis with and without conservation\, an d introduce the notion of infinitesimal concentration robustness\, where t he output remains nearly constant under perturbations of conserved quantit ies.\n LOCATION:https://researchseminars.org/talk/MoRN/141/ END:VEVENT END:VCALENDAR