Mathematics & Scientific Computing
NPL is active in areas of mathematics and scientific computing which support measurement science, with research work carried out in the Mathematics & Modelling for Metrology (MMM).
All measurements are subject to uncertainty and a measured value is meaningless without a quantitative statement of its quality in the form of an uncertainty. NPL develops techniques and analysis methods to help ensure that uncertainties quoted are defensible. In particular, the application of Bayesian statistics and Monte Carlo methods to uncertainty evaluation are currently being studied. NPL plays in large role in the development of the Guide to the expression of uncertainty in Measurement (GUM) and its supplements as well as the analysis of data collected in international key comparisons of measurements made by National Metrology Institutes.
Mathematical modelling, from the macro- to the nano-scale, is widely used in science and engineering to predict the behaviour of components, systems and experiments. In many cases, the model relies on experimental data which is itself subject to measurement uncertainty. NPL is active in a range of projects with the general aim of assessing the reliability of modelling software packages and thereby improving users' confidence in the results they obtain. Case studies across all areas of metrology are undertaken to improve the state of the art and to develop best practice which is disseminated through publications and reports.
Experimental data, often collected in large quantities by data acquisition systems, is usually subject to further processing to deduce measurement results and in some cases to make decisions such as compliance with a specification. NPL is working on signal processing, data fitting and inverse modelling techniques with the aim of quantifying the effect these methods have on the overall accuracy of the final result. In addition, NPL is taking the lead in establishing best practice in the specification, production and testing of scientific software for metrology applications.
A particular, high profile example of this is Biometrics, where data such as a fingerprint or face image is used for automatic identification. NPL is a recognised source of advice on the evaluation of biometrics technologies and has run several trials under controlled conditions.
Mathematics & Scientific Computing science areas
- Biometric identification technologies, such as automatic face, fingerprint and iris recognition, are beginning to be used for user authentication in a variety of applications.
- During the second half of the twentieth century, the use of computers has transformed life in the developed world. NPL is one of the places that gave birth to modern computing with the development of the Pilot ACE and ACE computers.
- The Mathematics and Modelling for Metrology (MMM) programme is a metrology-focused programme, which is generic in the sense that it aims to meet the requirements of more than one of the other NMS programmes.
- All measurement data is subject to uncertainty and a measured value is only complete if it is accompanied by an appropriate statement of the associated uncertainty. Understanding and evaluating uncertainty is important to anyone wishing to make good quality measurement.
- A mathematical model is used to describe the behaviour of a physical system in terms of equations involving variables and parameters representing aspects of the system.
- NPL has been at forefront of numerical computation since the first computers in the world were developed here and elsewhere in the late 1940s. From that time, computers have always been used to perform numerical scientific calculations and NPL has developed hardware and software for computation to support scientific research and development.
- Signal processing, particularly digital signal processing (DSP), is ubiquitous in modern measurement science. Almost all physical events of interest to scientists are ultimately converted to an electrical signal which is then sampled, digitised and downloaded into a computer
- Scientific Computing and Mathematics and Modelling for Metrology training courses.