Normal heart function relies of the fine-tuned synchronization of cellular components. In healthy hearts, calcium oscillations and physical contractions are coupled across a synchronised network of 3 billion heart cells. When the process of functional isolation of rogue cells isn’t successful, the network becomes maladapted, resulting in cardiovascular diseases, including heart failure and arrythmia. To advance knowledge on this normal-to-disease transition we must first address the lack of a mechanistic understanding of the plastic readaptation of these networks. In this talk I will explore coupling and loss of synchronisation using a mathematical model of calcium oscillations informed by experimental data. I will show some preliminary results pointing at the heterogeneity hidden behind seemingly uniform cell populations, as a causative mechanism behind disrupted dynamics in maladapted networks.

Certain models of collective dynamics exhibit deceptively simple patterns that are surprisingly difficult to explain. These patterns often arise from phase transitions within the underlying dynamics. However, these phase transitions can be explained only when one derives continuum equations from the corresponding individual-based models. In this talk, I will explore this subtle yet rich phenomenon and discuss advances and open problems.

In this talk we present different modeling approaches to describe and analyse the dynamics of large pedestrian crowds. We start with the individual microscopic description and derive the respective partial differential equation (PDE) models for the crowd density. Hereby we are particularly interested in identifying the main driving forces, which relate to complex dynamics such as lane formation in bidirectional flows. We then analyse the time-dependent and stationary solutions to these models, and provide interesting insights into their behavior at bottlenecks. We conclude by discussing how the Bayesian framework can be used to estimate unknown parameters in PDE models using individual trajectory data.