Building on Durham's strengths, work within this theme will include events, activities, and fellowships on the following sub-themes:
When we attempt to learn about complex processes through the development of mathematical models, then it is necessary for us to assess the uncertainty in our model based statements about the underlying phenomena. Such uncertainty derives from many sources, including uncertainty as to the initial conditions and to appropriate choices of model parameters, imperfect science, approximate solutions for the model equations and observational errors in data used to calibrate the model. Further, computer implementations of the models may be very time consuming to evaluate, even for a single choice of model input values, so that, in practice, we are uncertain about the functional form of the model itself.
There is a gowing interface between statistics and mathematical modelling, based around Bayesian analysis, which is aimed at developing and implementing an efficient technology that is capable of addressing all sources of uncertainty in model calibration, prediction, optimisation and validation, even for complex high dimensional models. This technology is of interest and importance for all modelling problems, and is a focus for much research in the Statistics group within Mathematical Sciences.
Modelling Climate Change
Climate change is a very broad church. To give focus this sub-theme will be given the title ‘Ice and Oceans' and will examine how models and modelling are helping us understand the complex processes, interactions and their influences on climate change.
Modelling Extreme Events
Extreme events, like tsunamis, financial meltdowns, extinctions, blockbuster movies, and radical innovations, are more common and intense than predicted by linear science. Extreme events generate a qualitative change in the system they act upon and reshape the world as we know it. Most of our theories are based on linear models; they derive averages and assume that deviations from averages predict future distribution. The problem is that by assuming such "science" reflects reality, extremes should be infinitely rare. They are not, dramatically. The discussion of extreme events plays a marginal role and is mostly fragmented even within single disciplines. The consequence is the lack of theories in many sciences that account for extreme events, and therefore the lack of preparedness to face extreme events' impact and consequences. Predicting extreme events is hard, some say impossible. However, extreme events show common dynamical patterns, and on the basis of these, we believe that useful anticipation - if not prediction - of extreme events events is possible.
Modelling and Representation
A conventional view of modelling may see it as a prerogative of the hard sciences. Models are used in physics, biology, chemistry, astronomy and many other areas still to try to understand a bewildering array of phenomena, from earthquakes to fabric distortion, from climate change to stock market crashes. But the uses - and misuses - of models also raise a series of more general questions for the human and social sciences that are at once historical and contemporary. A model, seen from one perspective, is a scientific tool, an instrument of understanding. Seen from another, it is a symbolic system whose production and application needs to be understood in a multiplicity of dimensions: ethical, political, metaphysical, linguistic, rhetorical, aesthtic. Whether they are used to plan cities or to predict the occurrence of extreme events, the construction of models is inseparable from a complex set of issues relating to processes of representation. In short, whatever scientific models chart, plot or predict, they call for a broader interrogation of the relationship of models to the human.
As models of physical and biological systems become ever more widespread it is tempting to try to model human society in similar ways, namely by treating humans as elementary particles that behave in linear ways and that only need to be "scaled up" for households, societies and cities to be created. Unfortunately (or fortunately) humans behave in idiosyncratic, non-linear, or perverse ways that often defy the operation of physical models. However, new technologies such as agent-based models and other simulation frameworks allow us to capture some aspects of human behaviour and create artificial societies from individuals (or agents) who react with or against each other. This sub-theme will examine how the emerging field of simulations and social models can contribute to the development and growth of larger structures resembling human settlements and ultimately cities. There remains the problem of scaling up from the individual to the city, but some agent-based modellers are confident that it is indeed possible to scale up from the small to the large without losing the fine granulated behaviour that is inherent in individual behaviours.
The scale of detail required varies from one model to another, while issues of granularity and resolution remain of paramount importance in modelling, impacting on the degree of uncertainty inherent in the model itself. This sub-theme will focus on the mathematical and computational principles underpinning multi-scale methods.