Postcards from Network Theory I will show some postcards of the use of network theory for solving real-world problems. After a very brief introduction I will start by illustrating such postcards. The postcard 1 is about the study of protein-protein interaction (PPI) networks. The postcard 2 is about the use of networks to describe the 3-dimensional structure of biomacromolecules. In particular, I will develop the concept of network communicability and […]
Mathematical Modelling of the Sleep-wake Cycle: Light, Clocks and Societal Rhythms We’re all familiar with sleep, but how can we mathematically model it? And what determines how long and when we sleep? In this talk I’ll introduce the non-smooth coupled oscillator systems that form the basis of current models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we have used models to inform debates on societal questions such as whether to move school start time […]
A Fluid Mechanic’s Analysis of Tea-cup Singularity One of the most fundamental issues in fluid dynamics is whether or not an initially smooth fluid flow can evolve over time to arrive at a singularity — a state for which the classical equations of fluid mechanics break down and the flow field no longer makes physical sense. While proof remains an […]
Ergodic Theory Without Invariant Measures Ergodic theory deals with dynamical systems from a measurable point of view. One considers transformations of a probability space, like the rotation of a circle over a typically irrational angle. In general, one considers transformations that may or may not preserve the given probability measure, but that will always preserve sets of measure zero. Iterating […]
Approximating Real Numbers by Fractions How well can you approximate real numbers by rationals with denominators coming from a given set? Although this old question has applications in many areas, in general this question seems impossibly hard – we don’t even know whether e+pi is rational or not! If you allow for a tiny number of bad exceptions, then a beautiful […]
What Is the Best Super Power? If you could have any power as a super hero, what would it be? Would you choose to be able to use and interpret statistics? Statistics are an everyday part of life – in our social media feeds, news reports and conversations. It’s not always easy to know if we can trust the statistics […]
Symmetry and Enumeration of Fractals In this talk, it is discussed how a simple ‘iterated function system’ construction leads to large classes of self-similar fractals. It is described how a little group theory can be used to examine the symmetries of these fractals and to enumerate various classes, with pictorial examples.