Phase drift on networks of coupled crystal oscillators for precision timing.

Precise time dissemination and synchronization have been some of the most important technological tasks for several centuries. Since the early 1800s, it was realized that precise time-keeping devices having the same stable frequency and precisely synchronized can have important applications in navigation. In modern times, satellite-based global positioning and navigation systems such as the GPS use the same principle.

Pattern formation in a nonlocal mathematical model for the multiple roles of the TGF-β pathway in tumour dynamics.

The growth and invasion of cancer cells are very complex processes, which can be regulated by the cross-talk between various signalling pathways, or by single signalling pathways that can control multiple aspects of cell behaviour. TGF-β is one of the most investigated signalling pathways in oncology, since it can regulate multiple aspects of cell behaviour: cell proliferation and apoptosis, cell-cell adhesion and epithelial-to-mesenchimal transition via loss of cell adhesion. In this study, we use a mathematical modelling approach to investigate the complex roles of TGF-β signalling pathways on the inhibition and growth of tumours, as well as on the epithelial-to-mesenchimal transition involved in the metastasis of tumour cells.

A spatial theory for characterizing predator-multiprey interactions in heterogeneous landscapes.

Trophic interactions in multiprey systems can be largely determined by prey distributions. Yet, classic predator-prey models assume spatially homogeneous interactions between predators and prey. We developed a spatially informed theory that predicts how habitat heterogeneity alters the landscape-scale distribution of mortality risk of prey from predation, and hence the nature of predator interactions in multiprey systems.

Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation.

The study of self-organised collective animal behaviour, such as swarms of insects or schools of fish, has become over the last decade a very active research area in mathematical biology. Parabolic and hyperbolic models have been used intensively to describe the formation and movement of various aggregative behaviours. While both types of models can exhibit aggregation-type patterns, studies on hyperbolic models suggest that these models can display a larger variety of spatial and spatio-temporal patterns compared to their parabolic counterparts.

Movement responses of caribou to human-induced habitat edges lead to their aggregation near anthropogenic features.

The assessment of disturbance effects on wildlife and resulting mitigation efforts are founded on edge-effect theory. According to the classical view, the abundance of animals affected by human disturbance should increase monotonically with distance from disturbed areas to reach a maximum at remote locations. Here we show that distance-dependent movement taxis can skew abundance distributions toward disturbed areas.