Analysis and application of kinetic flow models

Abstract: In this contribution, nonnegative flow models in kinetic and compartmental form will be studied. The motivation of the research came from the results on ribosome flow models (RFMs) which are deterministic dynamical systems used to describe ribosome movement during mRNA translation. Over the past 15 years or so, many of the advantageous properties and applications of these models have been demonstrated in the literature. In the talk, an essential generalization of RFMs will be presented. The class of systems we propose can handle arbitrary directed network (graph) structures and general nonlinear (even time-varying) cell transition rates in contrast to the simpler structures and transition rates studied previously. Under the general assumptions, important properties of the models (e.g. stability, monotonicity, passivity, Hamiltonian structure) can be shown, which can be well exploited in dynamical analysis and control design. The basis of the analysis is the theory of chemical reaction networks and compartmental systems. Of further interest, a special spatial discretization of flow models used in vehicle flow modelling can be shown to belong to the generalized RFMs. This opens up an exciting opportunity to study the links between biochemical reaction networks and certain transportation models.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

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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