Research projects
This is a listing of current projects. Former projects can be found on an old webpage.
FWO project: Analysis and applications of orthogonal polynomials with zeros in the complex plane
Supervisors: Daan Huybrechs, Arno Kuijlaars
Duration: 01.01.2011 - 31.12.2014
The topic of the research project is a classical one: the determination of zeros of polynomials in the complex plane. Despite being an old problem, several important research questions remain unanswered in this setting. Quite surprisingly, the study of the polynomials in this project is a shared problem in two different areas of current and highly active international research: the theory of random matrices and the theory of highly oscillatory integrals. Both areas in turn have applications in diverse disciplines of science. Random matrices provide a statistical description of many physical systems and highly oscillatory integrals appear, e.g., in the numerical simulation of wave phenomena, such as those found in electromagnetics, quantum physics or acoustics.
The methodology of the project is based on a modern tool of analysis, namely the nonlinear steepest descent method for the asymptotic analysis of Riemann-Hilbert problems. Promising results have been obtained by the promotor and co-promotor using this approach for an initial special case. It is expected that these results can be significantly extended and generalized, with relevance simultaneously in both application areas. In particular, the proposed research contributes to the understanding and analysis of random matrices with external source and coupled random matrices. In addition, it contributes to the analysis and construction of numerical methods for the evaluation of highly oscillatory integrals based on Gaussian quadrature.
FWO project: Numerical simulation of highly oscillatory problems with applications
Supervisors: Stefan Vandewalle, Daan Huybrechs
Duration: 01.01.2010 - 31.12.2013
The research project aspires a new approach for the numerical simulation of physical processes and models that exhibit wave characteristics. The research consists of three major components. In the first component we study novel methods for the computation of highly oscillatory integrals. The second component deals with the development of novel algorithms for the solution of integral equations that model high frequency wave phenomena. In the third component of the project the new methods and models are applied to solve a number of specific technical and scientific problems.
OT project: Algorithmic advances based on low-discrepancy point sets
Supervisor: Ronald Cools
Duration: 1/10/2009 - 31/8/2013
The aim of this research project is to investigate shortcomings of existing computational techniques and to develop new algorithms, mainly based on low-discrepancy point sets, tailored for specific problems. Such techniques are called quasi-Monte Carlo methods, and, in contrast to the standard Monte Carlo method, use low-discrepancy point sets instead of random point sets.
The main applications that we will be looking at will be coming from financial mathematics and quantum physics. In both areas we are cooperating with domain experts. The typical problem from financial engineering is pricing of derivative contracts, where some nice quasi-Monte Carlo techniques have already been established. For quantum physics we are interested in multi particle systems. The usage in this domain is relatively new.
The main objectives of this project are the development of new algorithms related to low-discrepancy point sets and the development of end-user software for the application of low-discrepancy points.
FWO postdoc project: Advanced algorithms for optimal numerical integration
Dirk Nuyens
Duration: 01.10.2008 - 30.09.2011
This project concerns algorithms for the construction of lattice rules/sequences and polynomial lattice rules/sequences.
TELEX: Combining acoustic TEmplates en LEXical modeling
Promotor: Dirk Van Campernolle
Co-promotors: Ronald Cools and Patrick Wambacq
Duration: 01.01.2007 - 31.12.2010
The goal of this project is to combine bottom-up phonetic recognition and long span example based recognition into a single speech recognition architecture that beats mainstream state-of-the-art HMM systems in terms of performance, be it at a higher computational cost.
This project builds further on 2 predecessor projects. In het FLAVOR project we developed a high-quality bottom-up phonetic recognizer as an ideal first pass for complex speech recognition systems relying on a multitude of different knowledge sources. From the TEMPLATE project we know that template based recognition is more powerful than HMMs when long span contextual information can be used. However, when looking at single phonemes the statistical modeling in the HMMs typically outperforms the template formalism. In this project we want to combine the strengths of both approaches and explore if by long span modeling we can overcome the problems due to pronunciation variation.
In previous work we relied on a lexicon with canonical transcriptions with little or no modeling of pronunciation variation. In this setup a simple combination of HMM and DTW scores and only using the canonical transcription already leads to improvements over either system. Now we want to go further. The word level distance metric should be a combination of a phoneme based HMM score (given by the bottom-up recognizer) and a template score found by directly matching in the training database. This template score may be computed at multiple layers (phoneme, sub-word, word) and the mixing of the scores is determined by the origin of the phonetic transcription. We expect that the further the applied transcription deviates from the canonical one, the larger weight a word level template matching score should receive. The less the impact of the training database on the used transcription, the more one should rely on the generalizing phoneme HMM model for the score computation. Within this project there will be extensive cooperation with the Marie Curies Network Sound to Sense (S2S).
SRN WOG 2006-2010: Advanced Numerical Methods for Mathematical Modelling
Supervisor: Ronald Cools
Duration: 1/1/2004 - 31/12/2010
This is a network consisting of 12 research groups active in the field of numerical analysis and the application of numerical methods: 6 Flemish research groups, 2 groups from French-speaking universities, and 4 groups from abroad. Within the section "Numerical Analysis and Applied Mathematics" research focuses on numerical methods and software for quadrature and cubature; differential equations; nonlinear dynamical systems; numerical linear algebra; approximation theory; splines and applications.
See the website of this project.
FWO project: The development and implementation of quasi-Monte Carlo methods for large scale and real-time applications
Promotor: Ronald Cools
Co-promotor: Herman Bruyninckx
Duration: 01.01.2006 - 31.12.2009
Intelligent robots are equipped with sensors to monitor the environment. They processes these measurements using stochastic methods in which Bayesian statistics play an important role. In general this requires the numerical integration of multivariate probability density functions. The past years a number of important breakthroughs have been achieved using so-called quasi-Monte Carlo methods. The aim of this project is to study these techniques to make them applicable in the area of robotics.
