Researcher portrait, 2009-11-18

Using mathematical tools to understand complex processes

Processes in everything from engineering to biology can be studied using mathematical models. Building up models that describe complex systems help both to understand these processes and to manage them. Claire Tomlin, this year´s Tage Erlander Professor, is one of the leading researchers in this field and also develops, in addition to basic mathematical models, applications for air traffic control and cell research.
In order to study complex systems, mathematical models are built up based on assumptions about how the system behaves. They are controlled partly by continuously measured quantities such as speed, voltage or temperature, and partly by discrete events such as interruptions of operations or faults.

Systems in which these elements interact are called, within research, hybrid systems. In order to be able to describe different types of constructions in one of these, a well-functioning model must coordinate multiple mathematical solutions. Hybrid models make it possible to control processes so that they meet required standards of quality, safety or other specifications.

Reliable models that can handle uncertainty


Claire Tomlin leads research into automatic control, intelligent systems and robotics at the University of California, Berkeley. She is one of the foremost researchers in the field of developing, testing and applying hybrid systems. One challenge presented by complex systems is to build mathematical models that describe the process very accurately and reliably, and at the same time are flexible enough to cope with the uncertainties that arise.

Claire Tomlin has made several important contributions to the research field in terms of both the theoretical framework for determining when disturbances may occur and simulations of control systems that enable the system to act within certain safe limits.

Practical tools for air traffic control and systems biology


The hybrid systems Claire Tomlin is studying have a particular application within the aviation sector. For example, she has developed an autopilot with an anti-collision system. In addition to speed, elevation and other physical parameters controlling the airplane, the system can handle the appropriate evasive manoeuvres necessary to fly around bad weather or keep the proper distance from other planes.

Systems biology is another research area where Claire Tomlin is involved. Mathematical modelling makes it possible to study biological processes all the way from how proteins interact at the cellular level to the tissue characteristics that arise. Her models include those that describe cell differentiation that controls how cells develop. These may help to understand how different organs are formed and how disruption can cause cancer and other diseases.

About Claire Tomlin


Claire Tomlin was born in Britain in 1969 but moved early on to Canada where she studied electrical engineering. She obtained a Ph.D. in 1998 from the University of California, Berkeley and then went on do research at Stanford University, where she has been a Professor of Aeronautics and Astronautics. Claire now primarily works at UC Berkeley, where she is Professor of Electrical Engineering and Computer Sciences.

She has received numerous awards and honours, including the prestigious MacArthur Fellowship in 2006 for young scientists. During her time in Sweden Claire will mainly to collaborate with researchers at the Royal Institute of Technology, including the Linnaeus Access Centre that is directed by Professor Karl Henrik Johansson and that brings together researchers in the field of signals and systems, funded by the Swedish Research Council.

Tage Erlander Guest Professorship


Internationally eminent Swedish or foreign researchers are afforded the opportunity, via the Tage Erlander Guest Professorship, to spend a year at a university, college or research institute in Sweden. This professorship was established in 1981 by the Swedish Parliament in honour of the former Prime Minister Tage Erlander on his 80th birthday. The subject focus of the professorship varies and as long as Tage Erlander was alive, the choice was always made in consultation with him.

The holder of the chair is appointed by invitation from the Swedish Research Council. Proposals are drawn up by the Council committees for the various disciplines. Deans at mathematics, science and technical departments of universities are also asked to nominate candidates, individual researchers are also able to make proposals.

Over the years, the Tage Erlander Guest Professorship has developed into an important instrument for bringing internationally prominent scientists to Sweden in the various scientific and engineering disciplines. The holder of the Chair is selected from among internationally eminent scientists. Clear proof of this is that two of the previous holders have been awarded the Nobel Prize, Roald Hoffmann 1981 Paul Crutzen in 1995, both in chemistry.

By Andreas Nilsson

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