UK Nonlinear News,
The Algebraic Approach to
Performance Evaluation of
an European Community Research Network
The European Community has recently approved the Research Network
ALAPEDES, under the Training and Mobility of Researchers scheme. It is
expected that up to 8 postdoctoral or PhD positions will become
available among the nodes of the network, which are located in
Belgium, England, France, and Holland. Positions are likely to start
in October 1996 and last for periods varying from 2 to 4 years.
Discrete event systems are systems whose behaviour consists of the
repeated occurrence of collections of events. Examples include a
digital circuit, in which an event might be a voltage transition on a
wire, or a distributed computer system, in which an event might be the
receipt of a message. From a mathematical standpoint, such systems may
be modelled as deterministic or stochastic dynamical systems.
Typically, they are extremely nonlinear in character. From a practical
standpoint, one would like to understand the asymptotic behaviour of
the system. Does it reach an equilibrium or settle into some periodic
regime? Is this regime stable with respect to change of parameters?
How quickly is equilibrium reached? What happens as the size of the
system goes to infinity?
The algebraic approach to discrete event systems, is based on the
observation that certain basic systems can be regarded as linear over
suitable semirings in which the addition operation is idempotent.
Surprisingly, many of the classical results of linear algebra and
analysis have analogues over these idempotent semirings, giving rise
to the subject of "idempotent analysis". Many of the questions rasied
above can now be solved by idempotent linear techniques. However,
these have not yet been applied to industrial scale problems and have
not yet been incorporated in design tools for engineering use.
Idempotent analysis turns out to have important implications for a
wide variety of subjects: algebric automata theory, particularly
decision problems relating to distance automata; viscosity solutions
of nonlinear partial differential equations, particularly the
Hamilton-Jacobi-Bellman equation; optimisation theory, where an
idempotent measure theory appears as the large deviation limit of
classical probability theory; fixed point problems for mappings which
are nonexpansive with respect to the supremum norm. These, and other,
directions are under intensive investigation at the various nodes of
this Research Network.
The challenge for the algebraic approach is threefold:
to explore the many ramifications of idempotent analysis;
to make idempotent methods usable at an industrial scale;
to extend the existing theory beyond the linear regime to a wider
class of systems.
The purpose of the Research Network is to address these challenges.
The 8 nodes of the Research Network are listed below.
It is expected that up to 8 postdoctoral or PhD positions will become
available in October 1996 at the various nodes of ALAPEDES. Because of
the multidisciplinary nature of this Network, the positions will be
attractive to candidates from a wide range of backgrounds in
mathematics, computer science or engineering. Candidates should take
note of the following restrictions imposed by the European Commission.
- Delft University of Technology, Delft, Holland
Faculty of Technical Mathematics and Informatics
Teamleader and Network Coordinator: Geert-Jan Olsder
- Ecole Nationale Supérieure des Mines de Paris,
Centre Automatique et Systèmes
Teamleader: Guy Cohen
ENSMP research interests in Alapedes
- INRIA Sophia-Antipolis, Sophia-Antipolis, France
Teamleader: Francois Baccelli
INRIA Rocquencourt, Rocquencourt, France
Teamleader: Jean-Pierre Quadrat
- Catholic University of Leuven, Leuven, Belgium
Department of Electrical Engineering
Teamleader: Bart de Moor
- Hewlett-Packard Laboratories, Bristol, England
Basic Research Institute in the Mathematical Sciences (BRIMS)
Teamleader: Jeremy Gunawardena
[Synopsis of BRIMS research interests in Alapedes]
- Laboratoire Informatique Théorique et Programmation
Université Pierre et Marie Curie, Paris, France
Teamleader: Daniel Krob
- University of Groningen, Groningen, Holland
Research Institute of Mathematics and Computing Science
Teamleader: Reinder Smedinga
- Université de Liège, Liège, Belgium
Institute de Mathématique
Teamleader: Vincent Blondel
A candidates must be a national of a member state of the
EC or of an associated state.
A candidate must not be a national of the state in which
he or she takes up an appointment.
To apply for a position, or to seek further information regarding
ALAPEDES, please contact Geert-Jan Olsder, the Network Coordinator.
Delft University of Technology
Faculty of Technical mathematics and Informatics
PO Box 5031, 2600 GA Delft, Holland
Tel: +31 15 278 1912
Fax: +31 15 278 7209
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Last Updated: 1st May 1996.