The creation of Impact outside academia is a key priority of the Maxwell Institute, and examples of recent and current impact successes are listed below. To facilitate Impact there has been investment in Business Development Executives, consultancy units and support for individual researchers. The industry and agency partners contributing to the MAC-MIGS CDT are also enabling the Maxwell Institute to foster Impact. The main areas in which the Maxwell Institute is aiming to generate Impact are Finance, Energy, Pensions and Insurance, Software, Data Analytics, and Protecting the Natural Environment, but there will always remain scope for individual initiatives.
Global food solutions via optimal diet formulations

Research Team: Julian Hall, Ken McKinnon, Andreas Grothey, Ivet Galabova

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.

Understanding the Impact of Covid-19 on Life Insurance Portfolios

Research Lead: Andrew Cairns

Research Area: Actuarial Mathematics

Early in the 2020 pandemic Andrew Cairns was approached by the US-based multinational, Prudential Retirement to develop models that would help understand better the impact of Covid-19 on different sections of society. How much socio-economic inequality is there, and how much does mortality vary with age? How will it impact on life insurance liabilities for the survivors? The results of this research have proved to be of great interest to the insurance community generally with several invited presentations at industry conferences, specialist teams in international re-insurers and the French Institute of Actuaries.

STACK – Computer aided assessment for maths

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

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.

Helping to control the spread of Mycoplasma bovis in New Zealand

Research Team: Gavin Gibson and George Streftaris 

Research Area: Statistics

Methods for the simultaneous estimation of epidemic dynamics and pathogen evolution developed by Gibson, Streftaris and PhD student Lau were incorporated into a user-friendly computer package BORIS by scientists from the University of Melbourne.  From July 2018, the BORIS package has been used as an analytic tool within the New Zealand Ministry of Primary Industries (MPI) eradication programme for Mycoplama Bovis, a bacterial disease that affects dairy and beef cattle, estimated to cost NZD 886,000,000. Specifically, BORIS has been used to identify potential times and sources for observed infections so that risk factors for transmission, or potential failures in biosecurity can be identified. The eradication programme has been effective with only 4 premises out of more than 20,000 having active disease in July 2020.

Dynamic Centrality

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

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.

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HiGHS – high performance software for linear optimization

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 (LP) problems via the simplex and interior point methods, convex quadratic programming problems using an active set method, and mixed-integer programming (MIP) problems via branch-and-cut. These are the fundamental models for optimal decision-making. HiGHS is used by industrial partners such as Format Solutions (Cargill), and has been developed in collaboration with other companies. Beyond the commercial world, HiGHS provides the LP and MIP solvers in the popular Python (SciPy) and Julia (JuMP) software. With a growing number of users, big and small, HiGHS is the world’s best open-source resource for linear optimization.

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Risk of ‘the lights going out’

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.

Mathematical Modelling Protects the UK Red Squirrel Population

Research Lead: Andy White

Research Area: Mathematical Biology

Mathematical modelling was used to direct policy and practice to conserve red squirrels – a protected species in the UK – from squirrelpox, carried by invasive grey squirrels. The research demonstrated that the red squirrel conservation policy used up to 2015 was not sufficient to contain squirrelpox in the UK and was the trigger for a radical change in policy to protect red squirrels in UK priority areas, directly informing the ‘Scottish Strategy For Red Squirrel Conservation (2015)’ and the Red Squirrel Survival Trust policy to protect red squirrels on Anglesey. The research also evaluated red squirrel population viability under different forest management scenarios, underpinning commissioned reports for the Forestry Commission that have had a direct impact on current and future forest management practice in the UK. The techniques are also being used to develop disease control strategies for wild boar in Spain.

Mortality Models for the International Insurance and Pensions Industry

Research Lead: Andrew Cairns

Research Area: Actuarial Mathematics

Pension funds, life insurers and regulators are concerned about the financial consequences of longevity risk: the financial risk that people live longer than anticipated. Novel stochastic models for the assessment of longevity risk (the Cairns-Blake-Dowd – CBD – family) in life insurance and pensions have been widely adopted – in the UK and globally – by insurers, actuarial consultancies, insurance regulators, specialist software providers, and in professional education. The CBD models have played a central role in the transfer of 10’s of billions (GBP) pension liabilities from pension funds to multinational insurers including the £16bn transfer of BT pension liabilities in 2014. Use of the models provides an improved assessment of the financial consequences of longevity risk. This has enhanced the security of both pension funds and insurers and, through good risk management and regulation, has reduced the risk of insolvency.

Modelling Anomalies in Population Data

Research Team: Andrew Cairns and Torsten Kleinow

Research Area: Actuarial Mathematics

The 2011 UK census revealed accuracy issues with the underlying population data that were of considerable concern to the pensions and life insurance sectors. This led to a research project at the Maxwell Institute that developed methods for identifying anomalies in national population and mortality data. The work has impacted on institutions in the UK, US and France and has enabled insurers to reduce prices for the transfer of pension liabilities, saving UK pension funds between £330 million and £1 billion. It has persuaded actuaries to revise the mortality tables used for pricing and reserving, including changes in the methodology underpinning the UK actuaries’ Continuous Mortality Investigation mortality projection tables. The research team is also working with data in developing countries where census counts and death registrations are affected significantly by so-called “digit preference” (e.g. rounding ages to the nearest 0 or 5).

Using machine learning to predict battery performance with Dukosi

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’.

WEST Brewery

Research Lead: Ben Goddard

Research Area(s): Complex Fluids

Ben Goddard was awarded an EPSRC Impact Acceleration funding for his project ‘Development of Spectral Element Methods for Complex Fluids Modelling and Control’, carried out in conjunction with Heidi Beers. The project employed a postdoctoral researcher, Rory Mills-Williams, to implement numerical methods devised by Ben Goddard and John Pearson to tackle the optimization of processes in the brewing industry.

Non-stationary models within an automated machine learning framework

Research Team: Sara Wade, Karla Monterrubio-Gomez 

Research Area(s): Non-stationary Models, Machine Learning, AI

Wade and Monterrubio-Gomez were awarded an EPSRC IAA Secondment with Secondmind, an AI and machine learning start up. They worked with the company to integrate their research on non-stationary models within an automated machine learning framework; leading to improved forecasting tools for the company’s clients, as well as better automated-decisions through integration within the company’s decision-making platform.

Statistical learning for precision oncology

Research Lead: Timothy Cannings

Research Area(s): Statistics, Machine Learning, Precision Medicine, Cancer Genomics

Timothy Cannings was awarded an EPSRC IAA Secondmnet to Cambridge Cancer Genomics (, an AI startup working on personalized cancer treatment. Throughout 2019, he worked closely with industry experts at in order to help develop and improve their data-driven tool for precision oncology OncOS.

Interest Rate models with Moodys

Research Team: David Siska and Lukasz Szpruch

Research Area(s): Mathematical Finance

David Siska and Lukasz Szpruch were awarded part of the IAA fund as a follow up to a FinTech Aim day session with Moodys Analytics. The project employed a colleague from EPCC to work on applying algorithms developed by Dr. Siska and Dr. Szpruch to interest rate models and data provided by Moodys.

Statistical Consultancy Unit

Research Leads: Michael Allerhand, Gail Robertson

Research Area(s): Statistics

The Statistical Consultancy Unit (School of Maths, University of Edinburgh) have been involved in a range of impactful projects, from ‘Identifying offshore foraging areas used by seabirds’, to ‘Evaluating an instrument to assess delirium in patients in intensive care’, developed at Edinburgh Royal Infirmary.

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