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Maurício Resende, AT&T, USA
Title:
Combinatorial
Optimization in Telecommunications |
Synopsis:
Combinatorial optimization problems are abundant in the telecommunications
industry. In this tutorial, we present four real-world telecommunications
applications where combinatorial optimization plays a major
role. The first problem concerns the optimal location of modem
pools for an internet service provider. The second problem deals
with the optimal routing of permanent virtual circuits for a
frame relay service. In the third problem, one seeks to optimally
design a SONET ring network. The last problem comes up when
one wants to determine optimal link weights in internet OSPF
routing.
Joana Soares, Universidade do Minho, Portugal
Title:
Transforms,
Algorithms and Applications |
Synopsis:
Fourier transforms and other related transforms are an essential
tool in applications of science, engineering and technology.
In fact, much of the work currently being done in mathematics,
physics and engineering has its roots in Fouriers pioneering
idea of representing an arbitrary function as the sum of a trigonometric
series. The main purpose of this course is to give an overview
of Fourier?related transforms, namely: continuous Fourier transform,
discrete Fourier transform, fast Fourier transform (FFT), discrete
sine and cosine transforms (DST, DCT), local sine and cosine
transforms, Fourier series, Z?transform, windowed Fourier transform,
continuous and discrete wavelet transforms. Applications of
the transforms to telecommunications will be emphasized and
fast algorithms for the computation of discrete transforms will
be presented.
Enrique Zuazua, Universidad Autdnoma de Madrid, Spain
Title:
Controllability
of PDE's and its discrete approximations |
Synopsis:
In this series of lectures we shall discuss several topics related
with the analysis, numerical simulation and control of Partial
Differential Equations arising in various contexts of Science
and Technology. We shall focus mainly on wave-like phenomena.
In particular, we shall discuss the controllability of planar
networks of vibrating strings that undergo transversal deformations,
based on recent joint work with R. Dager. We shall also discuss
the problem of numerical approximation and, in particular, we
shall try to answer to the question of whether the processes
of control and numerical discretization conmute. As we shall
see, the answer depends in a very sensitive way on the type
of control problem under consideration and also on the model
one is considering. We shall discuss this problem both for the
wave and Schrödinger equations.
Eckart Zitzler, Swiss Federal Institute of Technology, Switzerland
Title:
Evolutionary
Algorithms, Multiobjective Optimization, and Applications |
Synopsis:
The term evolutionary algorithm (EA) stands for a class of stochastic
optimization methods that simulate the process of natural evolution:
a set of candidate solutions repeatedly undergoes selection
and variation in order to generate better solutions. Although
the underlying principles are simple, these algorithms have
proven themselves as a general, robust and powerful search mechanism.
In particular, they possess characteristics that are desirable
with optimization problems involving multiple objectives.
This lecture consists of three parts. The first parts gives
an introduction to evolutionary computation covering historical
roots, basic principles, as well as practical and theoretical
aspects. The second part focuses on optimization, in particular
in the presence of multiple optimization criteria, and the application
of evolutionary algorithms to multiobjective optimization problems
in general. Finally, it is demonstrated how evolutionary multiobjective
optimization is used in the field of telecommunications and
related areas.
Ivete Gomes, Universidade de Lisboa, Portugal
Title:
Stochastic
Processes in Telecommunication Traffic |
Synopsis:
The main goal of this short course is to review various models,
within the queueing framework, which have been suggested for
tele-traffic data.
Those models intend to capture the specific features of the
data, such as variability of arrival rates, heavy-taildeness
of on-periods and off-periods, as well as long-range dependence
in teletraffic transmission. Some of the topics we intend to
cover are:
1. Poisson arrivals;
2. Renewal arrival streams;
3. A Markov modulated Poisson process as an
arrival process;
4. Efficient techniques for the analysis of
Quasi-Birth-Death processes;
5. Classical models without long range dependence
and delays' underestimation;
6. Network self similarity and heavy tailed
transmission times: subexponentiality.
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