Mathematical Solutions

The development and application of mathematical solutions designed to solve specific client problems is at the heart of Quintessa. Problems are formulated in close harmony with clients and, where appropriate, are analysed from fundamentals in order to ensure that the most relevant conceptual, mathematical and numerical formulations are used.

The bespoke computer software developed by Quintessa can be applied in-house or transferred, with appropriate training and support, to clients.

The past two decades have witnessed a revolution in applied science. As successive generations of computers have become ever faster, more reliable, and more accessible, so scientists and engineers have focused upon problems and fields of increasing size, complexity and difficulty. The same developments in computer power have simultaneously fuelled an unprecedented expansion in the volume of data requiring analysis, for a wide range of topics.

At the heart of this new paradigm lie the disciplines of mathematical and numerical analysis.

The formulation and solution of problems is assisted by the constant expansion of relevant theory and the development of new mathematical and numerical techniques. In addition, the utility of such techniques allows the creative mathematician to make connections across diverse fields, for example using pattern recognition algorithms for elucidating supermarket shopping patterns or understanding the genetic causes of diseases.

At Quintessa we have a team of innovative mathematicians who are experienced in solving problems using whatever techniques are most appropriate to the problem at hand. Our problem-led approach provides a challenging working environment for our staff, who are encouraged to develop their expertise while working on different projects.

Quintessa staff have the capability to tackle each new problem from fundamentals if required, or to develop and apply existing techniques. Our innovative approach is designed to ensure that our clients obtain appropriate answers to their problems, even though they may be poorly defined at the outset.

While most mathematical modelling tools are aimed at specialist users, there is an increasing requirement for a wider group of stakeholders to understand environmental and energy issues from a quantitative perspective. To address this issue, Quintessa has developed a web site (www.quintessa-online.com) where user-friendly systems models can be used online. An example of such an online model is SafetyNet which can be used to assess the safety of near-surface disposal of low-level radioactive waste.

Project plans are tailored to each client's needs, although the following elements are common to many projects:

  • Client liaison and project planning;
  • Problem formulation;
  • Information gathering and interpretation;
  • Conceptual and mathematical model formulation;
  • Mathematical and numerical analysis;
  • Software development;
  • Verification and validation;
  • Application and assessment;
  • Synthesis and presentation;
  • Project review;
  • Training.

This general approach can be applied to the analysis of data from such diverse areas as:

  • Environmental protection;
  • Chemical and process engineering;
  • Operational research;
  • Biotechnology;
  • Remote sensing;
  • Radioactive waste disposal;
  • Nuclear reactor safety;
  • Financial and insurance services.

The mathematical and numerical techniques that can been applied by Quintessa staff and associates include:

  • Differential and algebraic equations;
  • Probabilistic analysis;
  • Statistics;
  • Pattern recognition;
  • Non-linear mathematics;
  • Optimisation;
  • Fuzzy logic;
  • Time-series analysis;
  • Finite-element and finite-difference methods;
  • Sensitivity and uncertainty analysis;
  • Agent-based modelling.

Quintessa staff have long experience in developing bespoke software packages that encapsulate the solutions to client problems. At the heart of all good software is an efficient numerical algorithm. Quintessa staff have wide experience in choosing, developing and refining numerical algorithms so that they are optimised for specific problems. Of course, modern software needs to be developed in a structured 'software engineered' fashion in order to ensure that it is properly specified and that the specifications are met. A related point is the pride that we take in producing clear and comprehensive documentation. Software is developed in frameworks such as .NET and a variety of languages appropriate to the problem at hand including:

  • C, C++, C#
  • Visual Basic
  • HTML, XML
  • Matlab
  • Perl
  • Excel

For examples of software developed by Quintessa staff please click here.

For more information on Quintessa's mathematical consultancy services, please contact Peter Robinson or Steven Benbow in the UK or Hiro Takase in Japan.