Interests

Envelopes

In some sense, this area shaped Andrew’s fascination with systems – especially the contrast in their behaviour at different scales of interest.  As you can see here, wonderful curves can emerge from the overlap of lines, sparking one of Andrew’s great passions: Visual Perception.

An ellipse (red) and some of its normals (blue). A new curve emerges from the overlap of the normals – this is called an envelope (Image by Andrew Irving, 2014 – please do not use without credit).”

Biological Networks

Just as people are at the root of social networks, products of genes underpin regulatory networks.   Although they do so very differently to people, such gene products interact with each other, producing proteins that ensure an organism’s well-being for example.  These interaction networks invariably involve feedback loops whose biological significance is wonderfully demonstrated in the following animation.

Playing Dice

Understandably, most people think of playing dice as a model of fairness, but what exactly do we mean by this term `fair’?  This is an area that has captured the imagination of many and led Andrew to employ Markov processes as well as combinatorics for the first time.

Collective Behaviour

Consider a flock of birds and their characteristic swirling waves.  Faced with such a system, is the whole greater than the sum of its parts?  This has dominated Andrew’s thinking in his investigations.  How can we relate the behaviour of an individual parts (e.g. a single bird) to the flock’s fluid motion?

Using visual phenomena as toy models, exploring this area has introduced him to aliasing (a feature of signal processing), aggregate motions (as used in engineering) and even the behaviour of electrons.  Broadly, it has shown him the omnipresence of waves.

Close Packing

The manner in which particles combine to form bigger structures is not always well understood.  On a simple level, if we allow that particles are spherical then how many particles can surround or encase a single particle?  Although the question is simple enough, the solution is not so and poses an exceptional open mathematical challenge.

Much of Andrew’s current work is collaborative.

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