Dynamic Boundary Projection: Refining Deterministic Approximations Of Stochastic Reaction Networks Through Dynamic Boundary Projection

Abstract: To exactly compute the mean dynamics of stochastic reaction networks, the solution of the Chemical Master Equation (CME) is rarely feasible. Deterministic rate equations (DRE), while proven to converge to the average population dynamics for infinite individuals, may exhibit significant discrepancies for finite populations, especially in the presence of intrinsic noise, unstable or multi-stable dynamics. Therefore, it is often necessary to resort to computationally expensive simulations. Dynamic Boundary Projection (DBP) is a method that couples together a truncated version of the CME, describing the evolution of a subset of states and a set of DREs, used to shift the observed subset across the state space. I will show how we can apply DBP to SRNs even when they exhibit oscillatory orbits, multi-scale populations, or multiple stable equilibria. Moreover, I will present an extension aiming at reducing the computational costs of the method by suitably defining a family of rescaled approximating processes.

The talk is based on joint work with Mirco Tribastone and Luca Bortolussi.

algebraic 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!

The organizers.

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