An effective criterion for multiple positive solutions of vertical systems

Abstract: We present a criterion for determining when a vertically parametrized polynomial system admits multiple positive zeros for some parameter values. Our approach is based on the higher deficiency algorithms from chemical reaction network theory. Under certain assumptions, these algorithms reduce the problem to checking the feasibility of a linear system of equalities and inequalities (polyhedral cones). Our criterion requires that the linear part of the system (stoichiometric matrix) has a row reduction whose underlying graph is a forest, implying a highly structured pattern of zeros, which is often realized in steady state varieties. Using the same polyhedral cones, we also provide sufficient conditions to derive connectivity of the parameter region yielding multiple positive solutions and to guarantee the existence of a pair of distinct nondegenerate positive zeros. This is joint work with Elisenda Feliu.

chemical biologychemical kineticsalgebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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