School of Mathematics

Collaborative Research

Case studies that highlight the breadth of work completed recently within the School of Mathematics that demonstrate impact in our wider society.

Global Food Solutions via Optimal Diet Formulations

what in a field with blue sky

Research Team: Julian Hall, Ken McKinnon, Andreas Grothey

Research Area(s): Optimization, Operational Research

Impact on food formulation: High performance optimization software is essential to the efficient formulation of food, particularly in the (farm) animal and pet food markets, but also in important areas of human food production.

Beneficiaries: The optimization solvers have been largely developed for Format Solutions, the world’s leading supplier of software for food formulation.                   

Significance and Reach: The reach is global. Significance is demonstrated by the dependence of Format Solutions on the Edinburgh technology when selling its software – in particular to a manufacturer producing more than half of the world’s pet food.

STACK - Computer Aided Assessment for Maths

Man studying on his computer

Research Lead: Chris Sangwin

Research Area(s): Technologically Enhanced Learning

STACK (a System for Teaching and Assessment with a Computer Algebra Kernel) is contemporary online assessment software, for mathematics and related STEM disciplines.The software accepts mathematical expressions from students and automatically assesses equivalence with the correct answer; thus students benefit from feedback and marks, and staff from the statistics generated. 

With a focus on university education, STACK is used by over 900 registered learning management systems (of 10,000+ students); is used at every university in Finland; at over 30 universities in Germany; and has been translated into multiple languages, enabling wide international use. The quality and impact of STACK is proved through its widespread adoption in the face of aggressively marked commercial alternatives.

The Evaluation and Interpretation of Evidence in Forensic Science Casework

pile of dollars spread out

Research Team: Colin Aitken, Amy Wilson

Research Area(s): Statistics

Our judicial system increasingly relies on the quantification of the value of evidence presented in court. As a result, advanced statistical methods have a strong impact on the administration of justice. The research team has applied Bayesian statistics to develop methodology for this quantification of evidence and has proposed and implemented procedures for the evaluation of forensic evidence from (i) multivariate hierarchical data and (ii) autocorrelated data (exemplified with work on drugs on banknotes). 

The procedures and methods developed are routinely used in forensic laboratories worldwide for casework, are recommended in international guidelines for forensic scientists, and have supported the accreditation of a UK laboratory. Research outputs have been cited in expert witness reports in court cases worldwide. Beneficiaries include both forensic scientists and the justice system.

Dynamic Centrality

Illustration of vivid coloured lines of purple and red

Research Lead: Des Higham

Research Area(s): Applied & Computational Mathematics

Identifying “highly influential” individuals in peer-to-peer networks is critical in sectors as varied as advertising media and security. Research by Grindrod and Higham – focused on mathematical modelling and analysis of evolving networks – has developed first-principles discrete time dynamical models for digital communications between people, putting forward a new theoretical framework for describing and analysing time-varying connectivity.

This work has led to algorithmic approaches to identifying strong influencers; proposes a tool that identifies key players in complex evolving networks; and opens up the possibility of real-time monitoring and prediction. The digital marketing agency Bloom (acquired by Jaywing Plc in 2016 ) used these ideas to launch ‘Whisper’: a commercially available, real time social planning software product that has been used in campaigns for high-profile clients such as Sky, Yorkshire Tea and KitKat.

Strengthening Asset Management by Building Diverse Portfolios

Image of computer programme modelling

Research Team: Sotirios Sabanis, Jacek Gondzio, Sergio García Quiles, Joerg Kalcsics

Research Area(s): Mathematical Finance, Optimization, Probability & Stochastic Analysis

Research was carried out in collaboration with Aberdeen Standard Investments (ASI), the investment arm of one of the largest asset managers in the UK and in Europe, namely Standard Life Aberdeen, for the design and implementation of new diversification algorithms, based on which multi-asset portfolios are created with better performance under adverse market conditions.

Direct beneficiaries of this work include ASI with the launch of a new product (fund) and their clients. Indirectly, increasing the resilience of UK’s asset management sector carries clear benefits both for the UK society and its economy.

HiGHS - High Performance Software for Linear Optimization

Logo of Highs project

Research Team: Julian Hall, Ivet Galabova, Leona Gottwald and Michael Feldmeier

Research Area(s): Optimization, Operational Research

HiGHS is an open-source software project that brings modern high performance solvers for linear optimization to the industrial and academic worlds. Building on the award-winning research work of Hall, HiGHS currently solves linear programming problems via the simplex and interior point methods, and mixed-integer programming problems; an active set solver for quadratic programming problems is under development.

These are the fundamental models for optimal decision-making. HiGHS is used by industrial partners such as Format Solutions (Cargill), and is being developed in collaboration with other companies. Beyond the commercial world, HiGHS provides the linear programming solvers in the SciPy system, and will soon be available within the popular modern Julia-based modelling and optimization systems JuMP and JuliaOpt. With a growing number of users, big and small, the goal of HiGHS is to become the world’s leading open-source resource for linear optimization.

Risk of the "lights going out"

Transmission towers

Research Lead: Chris Dent

Research Area(s): Optimization, Operational Research

Maxwell Institute researchers have advised the National Grid on development of methodology for assessing the risk of future electricity supply shortfalls (commonly known as ‘the lights going out’), and the amount of supply capacity which should be procured to keep this risk to an appropriate level. Recent topics have included how to compare contributions of new technologies (e.g. renewables and storage) on a fair basis with conventional generating capacity (gas, nuclear etc), and how to manage uncertainty in the future background against which capacity procurement decisions are taken.

Using Machine Learning to Predict Battery Performance with Dukosi

Electric car getting charged

Research Team: Gonçalo dos Reis, Miguel Anjos, Paula Fermin, Encarni Medina-Lopez

Research Area(s): Machine Learning

Lithium lon Cells are ubiquitous in Electric Vehicle and Energy Storage solutions but vary in life expectancy due to their source chemistry and usage patterns. Goncalo dos Reis was awarded an IAA Grant to develop and run advanced Machine Learning models to accurately predict the end of Lithium lon Cell’s useful life. An innovative new concept for battery management systems was built – called knee-onset – which gives a very early warning of rapid cell degradation.

Mathematical models were developed to identify knee points from capacity degradation curves and to predict when it will occur from a very early stage of the cell’s life. The methods used have significant positive commercial applications for the energy storage sector and are also of considerable academic interest, given the growing attention being devoted to the modelling of cell behaviour. A paper has appeared in ‘Energy and AI’.