FCT

R&D Institutions

Resultado da avaliação 2007 na área de Matemática

Unidade de I&D

Centro de Matemática e Aplicações - CEMAT [MATH-LVT-Lisboa-822] visitada em 21/02/2008

Classificação: Very Good

Comentários do painel de avaliação
Sobre a unidade
This unit is the result of the downsizing and restructuring of the former CEMAT, with the group in Mathematical Physics merging with another group in the same area in the Center for Analysis, Geometry, and Dynamical Systems at the IST, and the groups in Operator Theory, Banach Algebras and Applications joining Harmonic Analysis, Operator Theory and Applications to form CEAF with main focus on Functional Analysis.

CEMAT is now unified in the pursue of strengthening the applications of numerical analysis, statistics and stochastic processes to Engineering and Biosystems. In particular, CEMAT is one of the founding members of the consortium for Biomedical Engineering that integrates R&D groups at IST involved in research and training in biomedical engineering.

Currently CEMAT has three groups on Statistics and Stochastic Processes, Applied and Numerical Analysis,
Applications in Engineering and Biosystems. There is considerable overlap between the last two groups, not only in the membership but also in the research interests, projects, funding, etc. The level of interdisciplinary and collaborative activities is prominent, including interactions with health sciences, engineering, and telecommunications. These interactions are supported by international and national research awards, and involve research collaborations and training.

The CEMAT is actively engaged in the training of young researchers. It has created recently a PhD in Statistics and Stochastic Processes at the IST, its members are involved in the IST-UT Austin PhD in Computational Engineering and in the Information and Communication Technologies Institute (ICTI) CMU-Portugal program in Applied Mathematics.

The CEMAT has a very active participation in outreach activities, including in the program Ciência Viva.
Sobre os grupos de investigação
Applications in Engineering and Biosystems [RG-MATH-LVT-Lisboa-822-2547]
This is a large group.
The group has a variety of objectives, and its tools and methods range from applied mathematics, computer science, biology, to biomechanics.
From the computational mathematics point of view, the work on meshless and other methods for inverse problems is quite innovative and may have substantial impact on, for example, crack detection. Future research plans are also wide in scope, and, at least those involving computational issues are interesting and should lead to useful results. The proposed projects, such as the heart valve project, are very challenging.
The group has very good contacts with national and international researchers in the field, including a cardiologist. Even so, the panel encourages the group to include experts in mechanics and computer science.
International visibility of the group is very good, and team members are very active and cooperate with researches in many countries. The panel looks forward to seeing publications in the best journals.
The group has invested strongly in the organization of meetings, workshops and conferences. This is an excellent effort, and the panel is aware of how time-consuming this effort can be.
The level of training is quite good.
The group has excellent external funding (ten projects).

Recommendations:

Parallel computing power with large memory and software, to be used by the whole unit.

Applied and Numerical Analysis [RG-MATH-LVT-Lisboa-822-1764]
This is a medium-sized group.
The productivity of the group in analysis, applied analysis and mathematical modeling is very good, with :publications appearing in international journals (Advances in Computational Mathematics, Com. in Pure and Applied Analysis, Inverse problems, A.R.M.A., Mathematical Methods in the Applied Sciences, Math. Nachrichten, etc.). The research topics have been carefully chosen, including singular initial and boundary value problems with application to nonlinear field theory and hydrodynamics, spline collocation methods for singular Volterra integral equations, inverse problems for the detection of sources and cracks, fundamental solutions for acoustic and elastic scattering, and meshless methods for resonance poles.
This group is working on subjects of high scientific importance and has ideas for pursuing them. There is potential, and the team members are encouraged to bring the mathematical work to a new level by seeking to establish the stability of the numerical schemes of the visco-elastic non-Newtonian models.
Good research collaborations have been established with researchers in many countries (France, USA, Estonia, Switzerland, Germany, Austria, Lithuania, Russia, Slovania, Morocco,) The impact of this work outside of the mathematics community requires the engagement in truly interdisciplinary projects and collaborations; this team is urged to enhance existing collaborations and pursue new ones with this goal in mind.
The group has invested strongly in the organization of meetings, workshops and conferences. This is an excellent effort, and the panel is aware of how time-consuming this effort can be.
The proposed projects for future years seem to continue the group's past work. The computational projects on fluid dynamics and meshless methods have a broad scope and focus on issues that are important to practical computations. This numerical analysis of non-Newtonian flows is challenging, and important new ideas will be needed.
This group has a solid training of master and PhD theses.
The external funding for the group is quite strong.
Harmonic Analysis, Operator Theory and Applications [RG-X-MATH-Algarve-Faro-822-753]
This is a small group, most of whom are active in publication. The research includes operator theory in function spaces with non-standard growth, singular integral operators and factorization, and integrable systems. The group has made progress in these areas and a list of highlights is given in their proposal. The group produced a reasonable number of PhD students and has reasonable international activity. This group is to be discontinued.
Mathematical Physics [RG-X-MATH-LVT-Lisboa-822-754]
The mathematical physics group of the unit is constituted by 8 Ph.D. members and 5 non Ph.D. members. They cover a range of mathematics as well as theoretical physics including the following topics: Topological Quantum Field Theory, Quantum Gravitation, and others. Their study requires the following mathematics: algebraic geometry, abelian varieties, knot theory, Chern-Simons theory and topology. The production of the participant is uneven and the publications are concentrated in few (good) journals. The international activity is good; the group participates to or organizes important workshops. The training activity is reasonable.
The group has recently moved to the CAMGSD.
Operator Theory, Banach Algebras and Applications [RG-X-MATH-LVT-Lisboa-822-428]
The research of the group is in the area of operator theory with a special emphasis on Toeplitz operators and Wiener-Hopf factorizations. They study the links with C*-algebras and with boundary value problems, such as Riemann-Hilbert problems. They developed a symbol calculus for certain C*-algebras and also developed new constructive factorization methods.
This group has an impressive output of significant research publications.
Several members have strong international reputations and have been actively involved in the organization of international conferences
The group is seriously engaged in training. This group is to be discontinued.

Summary:

This group does serious Mathematics and contributes to producing a skills base in Portugal in an important area of pure and applied mathematics. Their subject is one which has been and continues to be seen as of major significance. The group has produced an impressive amount of high quality research.
Statistics and Stochastic Processes [RG-MATH-LVT-Lisboa-822-2462]
This medium-sized group has three main areas of emphasis, two in statistics and the third in applied probability (queuing theory).
The publications list shows ten papers in top journals (Advances in Applied Probability, Journal of Multivariate Analysis, Theoretical Computer Science, Pattern Recognition Letters,).
The probability work is focused on stochastic processes, especially queuing theory, and the development of stochastic orderings for so-called skip-free processes. There is an interest in the development of probability models for telecommunications. This remains a highly topical field of research with considerable potential for future development.
The main emphasis of the statistics research is robust methods for multivariate data. There is a slight danger here that the work could become over-specialized, but the group seems to recognize this and is taking a broad viewpoint of the work, including the development of computational procedures in the statistical programming language R.
The group has a long list of international collaborations in Europe, South America and the USA. This collaboration is solidified by many joint publications, participations to the Scientific Committees of 5 international conferences and workshops (Belgium, July 2003, UK, April 2005, Finland, June 2005, Italy, June 2005, Lisbon June 2006), and participation to the editorial board of REVSTAT.
The group has two industrial contracts, one with Newvision (forecasting of customer waiting time at public services) and one with Portugal Airports (air traffic modelling at Lisbon's International Airport).
There is an excellent output of students including six PhDs.
The group’s future plans include making a stronger effort to integrate the stochastic processes and multivariate analysis components. It is not clear that this is necessary, since each of the two subgroups is doing very well on its own. The panel would encourage further diversification of the group’s efforts, but not at the expense of the existing very strong activity.