This is an introductory talk, and does not assume that you have any previous knowledge about the theory of reaction networks.
We will introduce and discuss reaction networks and reaction systems, especially as they are used in Mathematical Biology.
We will also emphasize the history of the development of key results and ideas about reaction systems, starting with ideas from...
Monte Carlo methods are among the most flexible tools for studying stochastic reaction networks, but they can be computationally expensive when exact simulation is used naively. In this talk, I will describe a general philosophy for improving such methods: exploit the structure inherent in the stochastic model itself. For reaction networks, that structure is often encoded through...
Stochastic reaction networks, modelled as continuous-time Markov chains, provide a principled framework for capturing the inherent randomness in biochemical and population systems. In this overview, I will introduce them and present the classical scaling limit, which establishes convergence to the deterministic reaction network model on compact time intervals as the system size grows. A...
Biochemical reaction networks are characterized by varying orders of abundance for different species types, as well as varying orders of magnitude for different reactions.
This feature allows one to reduce a complex model to a simpler one without losing the salient features of the dynamics. The model reduction can also lead to novel models that incorporate both stochastic and deterministic...
Let's imagine "CRN space", the set of all finite chemical reaction networks (CRNs), which can be visualised as an infinite set of digraphs. We can stratify CRN space in various ways: by molecularity, by number of species or reactions, by rank, by various equivalences, and so forth. Much of CRN theory consists of theorems linking network structure and network dynamics. Many classical and modern...
Multistability and oscillations are ubiquitous in nature, appearing in contexts ranging from biochemical reaction networks and cellular regulation to ecological and chemical processes. These phenomena are often associated with qualitative changes in system dynamics as parameters vary, making bifurcation analysis a fundamental tool for understanding the mechanisms that generate such...
This talk is concerned with quasi-stationary distributions (QSDs) of continuous-time Markov chains (CTMCs) with extinction in a setting that embraces reaction networks. QSDs describe the long-term behavior of such stochastic systems conditioned not to go extinct.
QSDs have a long history in probability theory, and this talk draws from this rich history. The focus is on CTMCs on the...
Abstract: This minisymposium, part of the Reaction Network subgroup, brings together leading experts to provide an accessible overview of the past, present, and future of chemical reaction network theory for a general SMB/ECMTB audience. Since its origins in the early 1970s, the field has aimed to understand chemical and biochemical systems through their network structure and species...
