# 15 June 2017: Academic Speed Dating Event

The idea behind this event, taking place in Durham, is to bring together members from other Durham and Newcastle departments to make 10 minute presentations about aspects of their research where a potential collaboration with Mathematicians or Computer Scientists might be beneficial. The audience comprises members of our Department of Mathematical Sciences and colleagues from Computer Science. The format is ALL presentations followed by the opportunity for further informal discussions and refreshments.

## Timetable:

**Thursday, 15 June
**

- 14.00-15.15 (Room CG83): Presentations by
- Halim Kusumaatmaja (Durham Physics):
*Some Problems Involving Geometry And Optimization In Soft Matter And Biophysics* - Marco Nardini and James Negen (Durham Psychology):
*Spatial Memory and Multisensory Perception in Children and Adults* - Mark Miller (Durham Chemistry):
*Mathematical Aspects of Computational Chemistry* - Stacey Aston (Newcastle Neurosciences):
*What we know and what we don’t about the mathematics of colour vision* - Pascal Mossay (Newcastle Business School):
*On Social Interactions in Cities*

- Halim Kusumaatmaja (Durham Physics):
- 15.15-16.30 Scarborough Dining Hall: Informal Discussions with Refreshments

**Abstracts:**

**Halim Kusumaatmaja: Some Problems Involving Geometry And Optimization In Soft Matter And Biophysics**

My group works on the physics of soft matter and biological systems, and we are often interested in phenomena where geometry is a key feature and/or the problem can be mapped to an optimization exercise involving a large number of degrees of freedom. To illustrate this, I will briefly highlight two ongoing projects. The first project involves demixing and liquid-gas phase transition on curved surfaces. In the second project we design super liquid-repellent surfaces by turning the problem into finding minima and saddle points in high-dimensional energy landscapes with O(1 million) degrees of freedom.

**Maco Nardini and James Negen: Spatial Memory and Multisensory Perception in Children and Adults**

Marko Nardini and James Negen use immersive virtual reality to study human spatial memory (roughly, how you use landmarks to remember where things were) and multisensory integration (roughly, how you use two senses like vision and hearing together to locate a nearby object) in both adults and children. In most perceptual and cognitive research of this kind, quite simple metrics are used to measure and compare performance. For example, one can ask how the precision of spatial memory changes during childhood by comparing different ages on their average distance error (remembered vs correct location). One can also determine at which ages and under which conditions average error is better than predicted by chance (random guessing).

We have been using Bayesian cognitive models to go beyond these kinds of summary measures and analyse distributions of responses. For example, in a recent re-analysis of previous data (Negen & Nardini, PLOS ONE 2015) we looked at a task on which 4-year-olds’ average error would seem to reflect completely random guessing. A closer look with a Bayesian cognitive model suggests that actually some of the 4-year-old participants were completing the task in a very accurate way, balanced out by a near-equal number of participants who using a systematically-incorrect strategy, worse than just guessing. This kind of result tells a new and very different story about the trajectories of cognitive development at this age range. We want to continue applying mathematical models to different spatial memory and multisensory integration tasks to see if we can actually predict response distributions (not just average error amount on each trial) and thus gain insight into the underlying cognitive processes and make testable predictions about future data.

**Mark Miller: Mathematical Aspects of Computational Chemistry**

Mathematical concepts underlie many of the tools that computational chemists use on a daily basis. When tackling unusual problems, it is often necessary to revisit these foundations or to bring in other mathematical ideas altogether. In this talk I will give a brief taste of why stochastic (Monte Carlo) sampling is a powerful and versatile tool in classical (as opposed to quantum mechanical) simulations, and I will outline two areas where interactions with members of the Department of Mathematical Sciences have already been very helpful: the topology of knots, and an application of constrained integer optimisation.

**Stacey Aston: What we know and what we don’t about the mathematics of colour vision**

Mathematics is an essential tool in neuroscience for describing the computations that happen in the brain. This statement is especially true in vision science where many features of visual processing can be described by complex computational algorithms. In addition, probabilistic models are successful in modelling the predictive nature of perception. In colour vision research, an added layer of complexity arises when parameterising colour stimuli. In this talk, I’ll give a brief introduction to the colour spaces that are used to represent colour stimuli, an overview of what we know about processing of colour in the brain and talk about the biggest computational challenge that our visual systems face when perceiving colour – colour constancy.

**Pascal Mossay: On Social Interactions in Cities**

In this talk I will present a research looking at how social interactions in cities affect housing prices. I will discuss a spatial model of social interactions between individuals. The spatial equilibria of the economy correspond to the Nash equilibria of a game with a continuum of individuals. In the case of a single group of individuals, these equilibria are shown to derive from a potential functional. I will explain how displacement convexity is helpful in this context to understand the structure of equilibria. Some examples will be used for illustration.

**Snapshots:**