Mathematics for social phenomena
We explore mathematical solutions within criminology, politics and cognitive science.
Research leads
Professor Dorje Brody
Mathematics of Politics and Cognitive Science
Professor David Lloyd
Mathematical criminology
Dr Naratip Santitissadeekorn
Data assimilation methods for crime forecasting and influence networks
Mathematical criminology
Crime is rarely spatially or temporally constant and often occurs in spikes (in time) or hotspots (in space). The development of mechanistic dynamical models that can predict these spikes and hotspots is an emerging area in the field of mathematical criminology, where we develop a range of agent-based and partial-differential equations-based models to analyse the qualitative behaviour of crime and combine it with data. This work requires an interesting combination of mathematical modelling, dynamical systems analysis and Bayesian statistics.
This area of research is linked to the Centre for Criminology at the University of Surrey.
Modelling community and crime interaction
Understanding the formation of crime hotspots and their interaction with the community requires the development of continuum models that capture various criminological theories such as repeat victimisation, collective efficacy and social disorganisation. Such models can then be analysed using a variety of mathematical techniques from dynamical systems theory and numerical methods.
This area of work also looks at the interaction of these behaviours with the police, uncovering the phenomenology of when crime hotspots use a range of dynamical systems and PDE techniques.
This project, led by David Lloyd, is in collaboration with Ian Brunton-Smith (Department of Sociology, Surrey).
Modelling crime escalation and desistence
New data is becoming available which allows researchers to investigate why people desist from, or persist in, a life of crime – an area of work that has major implications for policy making and policing.
This project aims to carry out a data analysis and develop continuum models to understand and quantify transition rates from/to crime.
Designing continuum models that incorporate explanatory variables and stratified data (such as age/location) will help explore various interventions and assess their impact. This project, led by David Lloyd, is in collaboration with Ian Brunton-Smith (Department of Sociology, Surrey).
Data assimilation methods for crime forecasting and influence networks
David Lloyd and Naratip Santitissadeekorn are developing novel methods to combine data and models to improve short-term crime forecasting, with a focus on helping victims. This work combines dynamical systems models with Bayesian statistical methods to help quantify our uncertainty when making decisions.
An interesting application of these methods is to detect dynamic social influence in communication networks and gang violence. The project is a collaboration with Martin Short (Georgia Tech).
Mathematical politics
Modern politics is largely about the art of messaging to influence the public. The mathematical theory of messaging – information and communication theory – can turn this art into a precise analysis, both qualitative and quantitative, that enables us to gain retrospective understandings of past political events and to make forward-looking future predictions. This project is led by Dorje Brody.
Calculus for elections and referendums
By modelling how information is communicated to the electorates it is possible to arrive at formulae for the probability of a given candidate winning a future election. The model is sufficiently versatile to explore how the communication strategy and political positioning will affect the likelihood of winning a future election.
Modelling the impact of disinformation
If we can model how people respond to information, we can also model how an inclusion of disinformation affects how people behave. This leads to the first mathematical model that enables us to infer the impact of disinformation and how to tackle its dark force.
How to spot politicians who lie?
Imagine that you have a political leader who is determined not to reveal the truth that he is aware of. It turns out that the behaviour of a person who is genuinely unaware of the truth and that of someone who refuses to reveal the truth have strikingly different characteristics, to the extent that with a high level of statistical significance it is often possible to distinguish them. See here for an interview where Dorje Brody explains the idea and corresponding Conversation article.
