Estimating cellular redundancy in networks of genetic expression.

Networks of genetic expression can be modeled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e.

Geometry and symmetry in biochemical reaction systems.

Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species and so are not well suited to modelling complex sets of reactions that may involve numerous reactants and/or products.

Coupled dynamics on hypergraphs: Master stability of steady states and synchronization.

In the study of dynamical systems on networks or graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that, instead of microscopic details of the individual nodes or vertices, rather make the influence of the network coupling topology visible. The master stability function is an important such tool to achieve this goal.