Plan of Activities - CMat

Transcrição

Research Centre of Mathematics - CMAT
Plan of Activities
Universidade do Minho
2009
Contents
1
Introduction
1
2 General Activities
4
3 Strategic Activities
7
4 Algebra, Logic and Computation (ALC)
14
5 Computational Mathematics and Applications (COMAPP)
21
6 Geometry and Analysis - Theory, History and Applications (GATHA)
35
7 Mathematical Physics and Modelling (MathPhys)
49
8 Statistics and Applied Probability (SAAP)
58
9 List of members of the Research Unit on December 31st
67
i
1
Introduction
The Centre of Mathematics (CMAT) is a research unit of the University of Minho that
aims at promoting the development of scientific research in Mathematics and its applications. The Unit has been supported by FCT pluriannual funding programmes for portuguese
research units since 1994. For the purpose of the application to the 2007-10 programme,
CMAT merged with Officina Mathematica, also a research unit of both the University of
Minho and FCT. This application was successful and a rating of Very Good was awarded to
CMAT in December of 2008. The consolidation of scientifically coherent research groups with
appropriate critical mass was a fundamental strategic goal of the merger. As a consequence,
the Unit was reorganised in accordance with scientific affinities and the following research
groups were defined:
• Algebra, Logic and Computation (ALC);
• Computational Mathematics and Applications (COMAPP);
• Geometry and Analysis: Theory, History and Applications (GATHA);
• Mathematical Physics and Modelling (MathPhys);
• Statistics and Applied Probabilities (SAAP).
The new organisation, implemented in January of 2008, has already contributed to an increase of scientific activity in these research areas, fostering closer collaborations between the
members. Apart from promoting the research in well-established areas of Pure Mathematics,
the Unit also devotes attention to applications of Mathematics in other scientific and technological domains. As can be seen in sections 4 to 8, all research groups have some of their
objectives orientated towards applications, involving, in some cases, multidisciplinary teams.
Research on Dynamical Systems (GATHA) and Kinetic Theory (MathPhys), for example,
has applications in Engineering, Financial Mathematics, Medical Sciences, Combustion and
Chemical Technologies.
In order to be a Full-Time Equivalent member of CMAT (FTE member) it is necessary
to have, at least, one refereed paper published or accepted for publication in the last three
years. The list of members of CMAT is subject to annual revision. On 31/December of 2008
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the Unit had 45 FTE members. A list of the 79 members of the Unit (45 FTE, 10 PhD
collaborators and 24 PhD students) can be found in section IX.
The activity planned for 2009, essentially organised by the five research groups of CMAT
in accordance with each group’s objectives, includes:
• Seminars and short courses presented in CMAT;
• Participation of CMAT members in scientific meetings;
• Visits of CMAT members to other research centres;
• Visits of external researchers to CMAT;
• Organisation of scientific meetings;
• Supervision of under-graduate and post-graduate students and of post-doctoral researchers;
• Development of projects with external funding.
Interactions between some groups have given rise to activities that involve members of
different groups. This is the case of the joint organisation, by GATHA and MathPhys, of
the seminar programme on Analysis, Geometry and Mathematical Physics and of research
projects involving members from different groups (eg, SAAP and GATHA, MathPhys and
GATHA). These activities are expected to contribute to the unity of CMAT.
In the Unit’s application to FCT 2007-10 programme, some of the activities to be planned
are considered to be strategic for the Unit. Examples of such activities are the organisation of
conferences, the support for long-term visits to the Unit and the acquisition of bibliographic
resources. As a consequence, a percentage of the total budget of the Unit should be spent
on strategic activities. Apart from these expenses, CMAT has general expenses and group
expenses. General expenses are presented in section II. In principal, the general expenses
together with the strategic expenses should correspond approximately to 40% of the total
budget of the Unit. The remaining 60% of the total budget will support the group expenses
which are described in sections 4 to 8.
As stated in the Annual Report for 2008, at the beginning of 2009 CMAT had a balance of
92.320,36e, of which 80.436,75e were allocated, in 2008, to group expenses. The remaining
11.883,61e are allocated to the general expenses of the Unit. Authorization to spend this
funding until 30/June of 2009 has been given by FCT.
Taking into account the rating awarded to the Unit and the number of FTE members
of the Unit in December of 2008, it is expected that FCT financial support for 2009 will be
185.625 e (= 4.125 × 45). The Unit has received no indication of when and how (number of
payments) transfer will occur.
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In January of 2009, CMAT received, from FCT, the amount of 70.962,49e. This refers to
a payment, due in 2006, which was withheld by FCT.
The two tables below, summarize the budget of CMAT for 2009.
Summary of the Unit Budget
General and Strategic Expenses
60.295 (32.900+27.395) e
Group Expenses
178.144,25 e
Total
238.439,25 e
Unit Budget - distribution by categories
Visits of members to other research centres
Visits of external researchers to CMAT
Participation of members in meetings
53.834,8 e
54.200 e
75.694,45 e
Organisation of seminars
6.000 e
Organisation of short courses
5.750 e
Organisation of conferences
3.600 e
Organisation of one-day meetings
3.500 e
Bibliographic resources
23.960 e
Other expenses
11.900 e
Total
238.439,25 e
On the basis of a decision of the Coordinating Committee of the Unit, the amount of
60.295e will be allocated to general and strategic expenses. This corresponds approximately
to 32% of the total budget of the Unit. The remaining 68% of the total budget will be
distributed between the five research groups.
The contribution of the externally financed projects to the expenses indicated in the previous table is expected to be 19.400e.
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General Activities
Among the general activities, in 2009 CMAT will organise monthly colloquia, a seminar
programme and the visit of the Advisory Committee.
1. Colloquia: The objective is to invite well known portuguese and foreign scientists
working in mathematical sciences to give public talks for a broad university audience.
Two colloquia are already scheduled for 2009:
• “Conjuntos parcialmente ordenados, polinómios cromáticos e Sudoku”, by Domingos Moreira Cardoso (Univ. Aveiro), 19/January;
• “Em busca do teorema perdido”, by Jorge Buescu (Univ. Lisboa), 9/March;
• “Quinhentos anos do ”Liber de Triplici Motu” (Paris, 1509) de lvaro Toms”, by
Henrique Leitão (Univ. Lisboa), 27/April.
2. Seminars: Based on scientific affinity of the five research groups, CMAT has a seminar
programme structured in the following three groups:
• Algebra and Logic;
• Analysis, Geometry and Mathematical Physics;
• Computational Mathematics;
• Probability and Statistics.
The Unit feels that this programme stimulates the exchange of ideas within each group
and between members of different groups and should, therefore, be encouraged and increased.
The seminars scheduled for January and February are included below.
Seminars on Algebra and Logic
- Christian Lomp (Dep. Matemática Pura, Univ. Porto), Módulos uniformes e ocos,
6/January
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- Ralph Matthes, IRIT (CNRS and Univ. Toulouse III, France), Category theory on
a computer - the example of the Coq system, 5/February
- Luı́s Antunes (Dep. Ciências de Computação, Univ. Porto), Cryptographic Security of Individual Instances, 17/February
Seminars on Analysis, Geometry and Mathematical Physics
- Patrı́cia Gonçalves (CMAT), Hydrodynamic limit and equilibrium fluctuations for
the simplenexclusion process, 8/January
- Maria do Carmo Martins, (Univ. Açores), Functional analysis, 21/January
- Delfim Torres (U. Aveiro), Calculus of variations on time scales, 22/January
- Gilberto Kremer (Univ. Paraná, Brazil), Interacting dark fluids in Cosmology,
23/January
- Frank Speck, IST, Functional analysis, 28/January
- V.A Solonnikov (POMI, Academia Russa de Ciências, St. Petersburg, Russia),
On the linearization principle for the evolution problem governed by the system of
equations of a mixed type, 29/January
- Atle Hahn (Univ. Lisboa), The unreasonable effectiveness of heuristic path integrals, 5/February
- José Garcia, (CNRS, France), General relativity, 9/February
- Assis Azevedo (CMAT), Um problema de difusão com restrição do gradiente dependente da temperatura, 26/February
Seminars on Computational Mathematics
- Sofia Lopes, (CMAT), Non degenerate forms of the necessary conditions of optimality for dynamic problems, 13/February
- Rui Ralha, (CMAT), A mixed precision bisection algorithm, 27/February
Seminars on Probability and Statistics
- Giovani Silva, (Depto Matemática, IST, Lisboa), Análise bayesiana de modelos
sobredispersos espaciais e especı́ficos segundo a idade, 18/February
- Inês Sousa (CMAT), Joint modelling for repeated measurements and time-to-event
in observational clinical studies, 27/February
3. Visit of the Advisory Committee - The Advisory Committee of CMAT is composed of 4 mathematicians of international reputation, invited to visit the Unit anually,
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during a period of approximately 3 years. The constitution of an Advisory Committee
is a requirement imposed by FCT on all the research centres funded. The committee
was created at the beginning of 2009 and the first visit is expected to take place in ???
of 2009. The objective of this visit is to meet the members of the Unit, analyse and
comment on the annual report 2008 and plan 2009 and provide suggestions to improve
the performance of the Unit.
The members of this committee are:
• Kresimir Veselic, Fernuniversitaet, Hagen, Germany;
• Marcelo Viana, Instituto Nacional de Matemtica Pura e Aplicada, Brasil;
• Norman Reilly, Simon Fraser University, Canada;
• Peter Diggle, University of Lancaster, U.K..
Expenses associated to the organisation of seminars are supported by the groups. Expenses
to be supported centrally include the costs of Colloquia, bibliographic resources, the visit of
the Advisory Committee and the daily running of CMAT. This is summarised in the next
table.
Budget for General Expenses
Colloquia
Journal subscription
1.500 e
17.500 e
MathSciNet subscription
3.500 e
AMS and CIM membership fees
1.800 e
Visit of the Advisory Committee
3.600 e
Other expenses
5.000 e
Total
32.900 e
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Strategic Activities
As described in Section I, strategic funding can be allocated to a variety of activities. The
groups of the Unit apply for this funding justifying the importance of the proposed activities.
The activities submitted in 2009 for strategic funding are described below. They include the
organisation of conferences and of one-day meetings, long term visits, a group of short term
visits and subscription of electronic journals.
1 Algebra, Logic and Computation (ALC)
Most of the papers published by members of this group were written in collaboration with
non-members of the group. For this to continue, substantial financial support is needed to
allow collaborators to visit the group and for members to visit their co-workers. During the
past 5 years, a significant portion of the financial support attributed to the group was used to
finance both medium and long-duration visits (4 visits of 1 month each, 1 visit of 2 months
and 4 visits of 3 months each). This proved to be a successful strategy and the members of
the group feel that it should be re-applied and extended.
Increase of internationalization, improvement of the scientific environment throughout the
Unit and increase of the research productivity of the Unit are among the objectives of the
Unit for the future, clearly presented in the application for FCT Pluriannual Funding Programme. The three medium/long-duration visits planned by the group for 2009 are important
contributions to these objectives. In this section we describe, briefly, the expected impact of
each of these visits.
Visit of R. P. Sullivan (Univ.
weeks)
Western Australia, Australia)(duration: 6
In 1970, Schein posed the problem of describing all maximal inverse subsemigroups of the
full transformation semigroup on an arbitrary set. Several authors contributed to progress
on the problem but it is as yet partially unsolved. In 1974, Sneperman considered a linear
version of Schein’s problem and he described the maximal inverse subsemigroups of the semigroup of all linear transformations on a finite-dimensional vector space. It is the aim of this
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visit to characterize all maximal inverse subsemigroups for the infinite-dimensional case. A
long-duration visit will allow to complete the answer for the linear version of Schein’s problem, thus contributing to a relevant advance in the theory of linear transformation semigroups.
Required funding: 4.275 e (3.975 + 300 (Frankfurt-Porto airfare)) The visitor will support
travel expenses from Perth (Australia) to Frankfurt.
Visit of R. E. Hartwig (North Caroline State Univ., USA) (duration: 1 month)
The visit of R. E. Hartwig would make possible the continuation of the research work in
the following topics:
- block Drazin inverses via recurrence relations (as a sequel of a submitted paper; partial
results were obtained in 2008, and further work is important);
- the study of relationships between polynomial multiplication, Toeplitz matrix multiplication, and their application to the study of convolutional coding; this topic is part of
the ALC plan for research and international expertise is important;
- further study of non-negative matrices, and their link to graph theory (as a sequel of a
jointly submitted paper).
Other members of the group will most likely profit of this visit, as the area of Algebraic
Generalized Inverses has new interested parties. The scientific interests of R. E. Hartwig are
spread through a wide scope of areas, and his knowledge on several topics will, for sure, be
profitable for the CMAT as a whole.
Required funding: 3.050 e (2.650 + 400 (airfare))
Visit of B. Billhardt ( Univ. Kassel, Germany) (duration: 1 month)
In 2006 a project in the area of algebraic theory of semigroups was begun in collaboration
with B. Billhardt and E. Giraldes (CM-UTAD). The concept of associate inverse subsemigroup
of a regular semigroup was introduced and the structure of regular semigroups containing such
subsemigroups was determined. As a particular application, the structure of a well known
class of semigroups was obtained [1]. The research proceeded with the investigation of some
subclasses of these semigroups such as the orthodox semigroups [2]. We now intend to continue
this algebraic study by describing homomorphisms and congruences on semigroups containing
an associate inverse subsemigroup. A short visit to CMAT will take place in March and a
1 month visit is planned for September/October. We feel that this long-duration visit will
allow the research group to achieve the objectives planned for this stage of the project.
[1] Billhardt, B., Giraldes, E., Marques-Smith, P., Mendes Martins, P. “Associate inverse
subsemigroups of regular semigroups”, accepted for publication in Semigroup Forum
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[2] Billhardt, B., Giraldes, E., Marques-Smith, P., Mendes Martins, P. “Some orthodox
semigroups with associate inverse subsemigroups”, pre-print
Required funding: 3.000 e (2.650 + 350 (Frankfurt-Porto airfare))
Total required: 10.325 e
2 Computational Mathematics (COMAPP)
An important general goal of the group is to establish and further develop lines of research
with colleagues from applied areas.
Short term visits (duration: 4 to 5 days)
Within the framework of the project “Dynamic Field Theory and its applications”, in
2009 we plan to invite, for short term visits, three outstanding researchers in their respective
fields. Since we want to cover various areas and applications, inviting several researchers for
stays up to one week seems to be more beneficial for the group compared to one long term
visitors. The work of the colleagues is directly related to problems we are currently trying
to solve so that a limited number of intensive working days will be sufficient to guarantee a
direct impact on our work. Researchers to be invited are Yannis Demiris (Imperial College,
UK), Dirk Jancke (Ruhr-University of Bochum, Germany), Leo Fogassi (Univ. Parma).
Estimated costs: 2.100 e (3 × 700)
Visit of Liu ZhongYun (duration: 2 months)
Within the framework of the project “Algorithms for structured matrices arising on digital
image processing”, we plan to invite Liu ZhongYun for a two months visit to CMAT. This
project is the continuation of previous collaboration. We have published one paper on Applied
Mathematics and Computation, 186 (2007) 715-726, and another paper entitled “On inverse
eigenvalue problems for block Toeplitz matrices with Toeplitz blocks” is about to be finished.
We are currently working on a method for the computation of the square root of Hamilton
and skew-Hamilton matrices. We are also planning to attack the following problem which
arises in image restoration applications. Let U(x,y)=H*(x,y)F(x,y)+N(x,y), where U is the
derogatory image, F is the original image, N is additive noise and H is a point spread function
of the linear system. Our purpose is the get a good approximation of F. The discretization
of the equation produces a structured linear system. Our goal is to design an efficient solver
that exploits such structure.
Estimated costs: 4.000 e (3.000+1.000 (airfare)
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Visit of Wang Shuanghu (duration: 1 month)
In October 2008, Yulin Zhang started a collaboration with Wang Shuanghu (Institute of
Applied Physics and Computational Mathematics, Beijing, China) in matrix problems which
do occur in computational physics, more precisely, in isospectral flows. She is currently studying the following: given a matrix M, find a matrix function Y(t) that satisfies the equation
Y’(t)=MY-YM. The visit of Wang Shuanghu to CMAT in 2009 will be an opportunity for
other members of the group to get involved in this starting project.
Estimated costs: 2.500 e (1.500+1.000 (airfare)
3 Geometry and Analysis - Theory, History and Applications
(GATHA)
International workshop on Didactics of Mathematics as a Mathematics Discipline)
International workshop to be held in Funchal (Univ. Madeira), Portugal, 1-4/October.
Organising Committee: M. Elfrida Ralha (Univ. Minho), J. Carvalho e Silva (Univ. Coimbra), José Francisco Rodrigues and M. Suzana Nápoles (Univ. Lisboa), J. M. Castanheira
(Univ. Madeira).
A century ago Felix Klein’s lectures on mathematics for secondary teachers were first published: “Elementarmathematik vom höheren Standpunkte aus” (1908). This comprehensive
view challenged both teachers and mathematicians to consider the relationship between mathematics as a school subject, and mathematics as a scientific discipline. This last 100 years
have witnessed many changes in mathematics that provoked major changes and challenges for
school mathematics. The role of mathematics in the education of scientists, economists and
engineers seems to have achieved unprecedented societal unanimity. While Klein’s writing
remains a valuable source insight, it seems timely to revisit this theme by linking the topics
and approaches of upper secondary with the field of mathematics. A portuguese group of
researchers from different universities and with different mathematical scientific interests are
planning to organise an international workshop where we aim at analysing the new challenges
for mathematics in the XXI century.
Funding asked: 2.500 e
Equations Day
One day of lectures on ODE’s and PDE’s at Univ. Minho, gathering researchers from
Portugal and Galiza, trying to use the geographic proximity to establish new scientific contacts. organising Committee: Assis Azevedo, Fernando Miranda, Lisa Santos.
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Funding asked: 1000 e
Journal subscriptions
The quality of the research conditions at the Centre can at least partially be measured
by the number of available mathematical journals. It should therefore be a general strategic
goal of the Centre to increase this number. This can be achieved both through new journal
subscriptions and through the subscription to older volumes of already accessible journals.
In the scientific areas of the group we propose the subscription to the following important
journals:
- Algebraic and Geometric Topology (electronic) ca. 150 e;
- Geometry and Topology (electronic) ca. 220 e;
- Journal of Homotopy and Related Structures (electronic) ca. 30 e.
4 Mathematical Physics (MathPhys)
One day Meeting on Mathematical Physics
Univ. Minho, 20 participants, organisation: Filipe Mena and Ana Jacinta Soares (main
organisers).
The objective is to interact with researchers of geographically closed research centers in
Portugal and Spain such as in Porto, Lisbon, Salamanca and Santiago de Compostela. This
will be also important to the training of our PhD students.
Costs: 1.500 e
Visit of Gilberto Kremer (Univ. Paraná, Curitiba, Brazil) (duration: 2 weeks)
The objective is to proceed with the research activity within the group, in particular with
Ana Jacinta Soares. The joint work has been very fruitful in the past. Other researchers
in the group can also benefit from this visit. For this, the external researcher supports an
amount of 1400 e approximately for the travel.
Costs to be supported by CMAT: 420 e (accommodation)
Visit of Jacek Polewczak (California State Univ., USA): (duration: 2 weeks)
The objective is to study the global well-posedness of the initial-boundary value problem
for the spatially homogeneous Boltzmann equation extended to chemically reacting gases in
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the case of hard or soft potentials, with or without cutoff. For this visit, the external researcher supports an amount of 400 e approximately.
Costs to be supported by CMAT 1.750 e (travel 1300 e, Accom. 450 e)
International Conference on Mathematical Relativity
International Conference to be held in Lisbon, in honour of Aureliano Mira Fernandes
(www.math.ist.utl/ jnatar/Mira). 18-19/Junho, IST, Lisboa. The support of CMAT to this
conference contributes to CMAT’s visibility at a national and international level. There are
only two groups in Portugal on Mathematical Relativity (IST and Minho). The logo of CMAT
would be on the conference webpage and posters. Filipe Mena is on the scientific committee.
Costs: 350 e (to pay the travel expenses of an invited speaker)
Journals online
We wish to extend the access to past editions of some journals which are already available
online such as “Communications in Mathematical Physics”, “Journal of Mathematical Physics”, “Classical and Quantum Gravity” and “General Relativity and Gravitation”. These
are key journals for the research within the group and their full access would be particularly
important for the PhD students.
Costs: 550 e
5 Statistics and Applied probability (SAAP)
Workshop in Branching Processes and Applications
University of Minho, 15- 17 April
Organizer: Conceição Serra
The main purpose of this meetingis to strengthen the already existing research in the
area of branching processes and to to give the possibility to the other researchers of CMAT
to interact with some of the experts in this field. Given the huge range of applications of
branching processes in other sciences such usmedicine, biology and physics, we expect that
researchers from these areas will also attend this meeting. (25 participants expected)
Requested funding: 1.500 e
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Short course in longitudinal data analysis
University of Minho, two-days in June
Organizer: Inês Sousa
This course will consider the main statistical issues in the analysis of longitudinal data.
The course will focus on models for longitudinal data, motivated by medical problems. We
are interested in developing an understanding of the assumptions behind these models. A
computer practical session will provide participants with the opportunity to undertake the
analyses discussed. We will be using the software for statistical analysis R (http://cran.rproject.org/).
Target Audience: Clinical reseachers, applied statisticians and other data analysts faced
with the need to analyse longitudinal data. Some priory knowledge of R will be assumed. (25
participants expected)
Bibliography: Peter Diggle, Patrick Heagerty, Kung-Yee Liang and Scott Zeger (2002),
Analysis of Longitudinal Data, second edition, Oxford University Press
Requested funding: 1.500 e
The Coordinating Committee decided to apply the following financial distribution:
• ALC: 10.325 e
• COMAPP: 8.600 e
• GATHA: 3.900 e
• MathPhys: 4.570 e
• SAAP: 3.000 e
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Algebra, Logic and Computation
Group members description
PhD FTE members
Name
General area of research
Carla Mendes
Semigroup Theory
Cláudia Mendes Araújo
Linear Algebra
José Carlos Costa (group leader)
Semigroup Theory
José Espı́rito Santo
Logic
Luı́s Pinto
Logic
Paula Marques Smith
Semigroup Theory
Paula Mendes Martins
Semigroup Theory
Pedro Patrı́cio
Linear Algebra
Suzana Mendes Gonçalves
Semigroup Theory
PhD collaborators
Name
António Veloso
Linear Algebra
Lurdes Teixeira
Semigroup Theory
Members without PhD
Name
Conceição Nogueira
Semigroup Theory
General research description
The investigation of this group is carried out in the domain of Algebra, Logic and Computation, with research topics in the areas of matrix theory, semigroup theory, proof and type
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systems, and automata theory. The group expects to develop these areas by exploring specific
new models and applications. Some particular research topics to be pursued include algebraic
generalized invertibility, sign pattern of classes of matrices, the meta-theory of proof and type
systems, the tameness of pseudovarieties of semigroups and the study of both algebraic and
transformation semigroups. Some of this research has potential applications in Computer
Science (functional programming and formal verification of programs, automata and formal
languages) and in Information Theory (algebraic theory of convolutional codes). Collaboration within the group is encouraged, for instance, with the organisation of a regular seminar,
and involves many members of the group. This group also maintains a strong level of international collaboration, with members involved in different joint work with research staff from
7 countries. The group has some level of participation in multidisciplinary research, with
members taking part in external research projects, like RESCUE (on the formal verification
of embedded systems) and ASA (on automata, semigroups and applications), in collaboration with other mathematicians and computer scientists. A joint project, with Universidad
Politécnica de Madrid, on generalized invertibility in C*-algebras has been submitted to FCT,
with the purpose of obtaining external funding. This will strengthen the joint work within
the group, continuing with the research work undertaken in 2008.
Research projects
Matrix theory (Cláudia Mendes Araújo and Pedro Patrı́cio)
We aim to continue the study of properties of the class of matrices whose inverses are nonnegative. In recent papers, N. Castro-González et. al. have computed the Drazin inverse of
a class of two by two block matrix with zero (2,2) block. Their main tool was the use of the
recurrence relations satisfied by the Catalan numbers. We will study an alternative approach.
We plan to continue to apply algebraic matrix theory to convolutional coding, enduring the
work in the scope of “Integration into research grant, Programa Ciência 2008, FCT”.
Collaborators: J. R. Torregrosa (Univ. Politécnica de Valencia); R. E. Hartwig (North Caroline State Univ.).
Decidability problems on finite semigroups (José Carlos Costa, Lurdes Teixeira
and Conceição Nogueira)
Decision problems involving finite semigroups arise frequently in various areas of mathematics.
With particular interest is the decidability (of the membership) problem of pseudovarieties
by its applications in formal languages and automata theory. In this project we intend to
continue the investigation of algorithmic properties of semigroups, with particular attention
devoted to the notion of tameness and its applications. Tameness is a strong property which is
expected to play a crucial role in establishing decidability of pseudovarieties defined by some
important operators. Having the (open problem of the) calculation of the Krohn-Rhodes
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complexity of a finite semigroup in mind, the semidirect product operator should deserve a
special attention.
Collaborators: Jorge Almeida (CMUP, Univ. Porto); Alfredo Costa (CMUC, Univ. Coimbra); Marc Zeitoun (LaBRi, Bordeaux 1).
Structure and order properties of semigroups (Carla Mendes, Paula Marques
Smith, Paula Mendes Martins and Suzana Mendes Gonçalves)
The research interests of these members lie in the algebraic theory of semigroups and in the
study of semigroups of transformations. The latter is related to a partially solved problem
posed by Schein in 1970, concerning the description of all maximal inverse subsemigroups
of full transformation semigroups. A linear version of this problem was first considered by
Sneperman in 1974, for the semigroup of all linear transformations on a finite-dimensional vector space. The description of the maximal inverse subsemigroups for the infinite-dimensional
case is expected to be achieved. The research in the algebraic theory of semigroups planned
for 2009 is concerned with the study of two classes of regular semigroups: (i) the class of
semigroups containing an associate subgroup - major results, obtained by a member of the
group, published in 2008, justify this research; (ii) the class of semigroups containing an associate inverse subsemigroup – having classified some subclasses of these semigroups, we intend
to continue the algebraic study by describing the homomorphisms and the congruences on
such semigroups.
Collaborators: B. Bilhardt (Univ. Kassel, Germany); E. Giraldes (CM-UTAD, Portugal); M.
Petrich (Croatia); R. Sullivan (Univ. Western Australia, Australia).
Proof systems and programming (José Espı́rito Santo and Luı́s Pinto)
Proof and type systems are a central tool in foundations of programming, with applications in
functional programming and formal verification of computer systems and programs. On the
one hand, we intend to continue the study of the meta-theory and applications of proof and
type systems in the sequent calculus format, with emphasis in the corresponding lambdacalculi. Special attention should be devoted to the study of normal forms, continuation
passing-style translations and delayed substitutions. On the other hand, we intend to explore
and develop logics for formal verification of real-time embedded systems.
Collaborators: Jorge Sousa Pinto and Maria João Frade (Department of Informatics, Univ.
Minho); Silvia Ghilezan (Univ. Novi Sad, Serbia); Ralph Matthes (CNRS and Univ. Toulouse
III, France); Tarmo Uustalu (Institute of Cybernetics, Estonia).
Advanced training
1 Members in training
In this section the member, the degree, the area of the thesis, the title of the thesis, the
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supervisor and the university that awards the degree are identified. A summary of the project
is also included.
Conceição Nogueira, PhD, Finite Semigroup Theory; Title of thesis: Algorithmic properties of pseudovarieties of semigroups; José Carlos Costa, Univ. Minho.
Summary: The objective of this work is to investigate several algorithmic properties
of pseudovarieties, studying connections between them and exploring their applications to
decidability. With the goal of better understand the important pseudovariety of aperiodic
semigroups, some simpler pseudovarieties, such as LSl and DA, will receive special attention.
2 Supervision of students
2.1 Supervision of PhD students
- José Carlos Costa
Student: Conceição Nogueira, Univ. Minho
2.2 Supervision of MSc students
- José Carlos Costa
Student: Rita Bezerra, Univ. Minho
- José Espı́rito Santo and Luı́s Pinto
Student: Jorge Correia, Univ. Minho
- Paula Mendes Martins and Suzana Mendes Gonçalves
Student: Rosário Freitas, Univ. Minho
2.3 Supervision of undergraduate students
- Pedro Patrı́cio
Integration into research grant, Programa Ciência 2008, FCT
Student: Rui Barbosa, Computer Science, Univ. Minho
Scientific exchange
1 Visits of members to other research centres
- Cláudia Mendes Araújo, Univ. Politecnica de Valencia, 5 days
- José Carlos Costa, CMUP, Porto, 10 visits of one day each one
- José Carlos Costa, LaBRI, Bordeaux 1, 20-27/June
18
- José Espı́rito Santo, Department of Computer Science, Carnegie-Mellon University,
USA, 2 weeks
- Lurdes Teixeira, CMUP, Porto, 10 visits of one day each one
2 Visits of external researchers
- B. Billhardt, Univ. Kassel, Germany, 15/March-4/April and 1 month (September)
(Paula Marques Smith and Paula Mendes Martins)
- R. E. Hartwig (NCSU, USA), 1 month (Pedro Patrı́cio)
- Ralph Matthes, CNRS and Univ. Toulouse III, France, 31/January-7/February, (José
Espı́rito Santo and Luı́s Pinto)
- M. Petrich (Croatia), 1 month in October/November (Paula Mendes Martins)
- R. P. Sullivan (Univ.
Gonçalves)
Western Australia), 30/August-10/October (Suzana Mendes
- Tarmo Uustalu, Institute of Cybernetics, Estonia, 8 days, (José Espı́rito Santo and
Luı́s Pinto)
3 Participation in Meetings
- José Carlos Costa, International Conference on Semigroups and related topics, 6-11/July,
Porto, Portugal
- José Carlos Costa, Workshop on Equational Theory of Regular Languages, 5-6/March,
Brno, Czech Republic
- José Espı́rito Santo, CSL’09, 7-11/September, Coimbra, Portugal
- Luı́s Pinto, CSL’09, 7-11/September, Coimbra, Portugal
- Luı́s Pinto, Tableaux’09, 6-10/July, Oslo, Norway
- Lurdes Teixeira, International Conference on Semigroups and related topics, 6-11/July,
Porto, Portugal
- Paula Marques Smith, International Conference on Semigroups and related topics, 611/July, Porto, Portugal
- Paula Mendes Martins, International Conference on Semigroups and related topics, 611/July, Porto, Portugal
- Pedro Patrı́cio, 2009 Haifa Matrix Theory Conference, 18-21/May, Haifa, Israel
- Suzana Mendes Gonçalves, International Conference on Semigroups and related topics,
6-11/July, Porto, Portugal
19
Organisation of events
1 Seminars
The group organises regular seminars. A list of scheduled seminars for January and February
is shown in section II.
2 Conferences and other scientific meetings
“18th EACSL Annual Conference on Computer Science Logic”, Coimbra, Portugal, 7-11/September,
100 participants, José Espı́rito Santo (member of the organising Committee)
External funding
1 Projects
Some members of CMAT are involved in research projects that receive financial support
from various sources. In this section, the name of the project, the financial source, the
members involved and the principal researcher are indicated. The budget for CMAT members
is also indicated.
- ASA (Automata, Semigroups and Applications), project PTDC/MAT/65481/2006 from
FCT, José Carlos Costa, Lurdes Teixeira, António Veloso and Conceição Nogueira (principal researcher: Manuel Delgado, FCUP), 52.000 e of global budget
- AutoMathA (Automata: from Mathematics to Applications), from the European Science Foundation (FCT is a Contributing Member Organisation), José Carlos Costa and
Lurdes Teixeira
- RESCUE, project PTDC/EIA/65862/2006 from FCT, José Espı́rito Santo and Luı́s
Pinto, (principal researcher: Simão Sousa, Univ. Beira Interior, Portugal), 25.000 e for
the Minho site (which includes other 4 researchers from the Department of Informatics)
2 Individual Grants
- Conceição Nogueira PhD grant from FCT, “Algorithmic properties of pseudovarieties
of semigroups”, 2.750e (registration or tuition) and 250e/month
Other activities
Members of the group will be involved in various outreach activities:
- Visits to schools and presentation of lectures on the importance of mathematics in day
to day life;
- Lectures of short courses which provide support for school teachers in selected topics of
the national secondary science curriculum.
20
Budget
Budget
Visits of external researchers
4.903 e
18.200 e
Participation in meetings
7.682,45 e
1.000 e
0e
750 e
Organisation of one-day events
0e
Bibliograpyh
0e
TOTAL
32.535,45 e
It is expected that the amount of 1.200 e will be supported by external funding.
5 Computational Mathematics
and Applications
PhD FTE members
Name
Gaspar Machado
Modelling, Differential Equations
M. Antónia Forjaz
Numerical Analysis
M. Fernanda Costa
Numerical Analysis
Rui Pereira
Rui Ralha (group leader)
Matrix Computations
Wolfram Erlhagen
Robotics, Dynamical Systems
YuLin Zhang
Matrix Computations
PhD collaborators
Name
Carla Ferreira
Matrix Computations
Jorge Figueiredo
Members without PhD
Name
Carolina Ribeiro
Eliana Silva
Emanuel Sousa
Fabian Chersi
Flora Ferreira
21
22
Florbela Fernandes
Numerical Analysis
Luı́s Louro
M. Rosário Fernandes
Numerical Analysis
Miguel Vaz
Nzoji Hipólito
Paulo Pereira
Numerical Analysis
Sofia Lopes
Numerical Analysis
Vitor Mariano Sousa
Numerical Analysis
Group research description
The group aims at developing new techniques of mathematical modelling, mathematical analysis, and numerical algorithms for solving problems in applied areas. Currently, group members lead or are involved in multidisciplinary research projects and proposals in the domains
of Robotics, (Bio-)Mechanics and (Neuro-)Biology. The mathematical analysis not only becomes the basis for defining the mathematical model, but is also essential to understand
the properties of the model itself (e.g., the sensitivity to input data). Carefully analysed
numerical tests are an indispensable tool to compare the predictions of the model with behaviours actually observed in nature or in the laboratory. Within the framework of existing
research projects, we will continue developing the dynamic field (DF) approach to Robotics
and Cognitive Neurocience. The main challenge is to perform a more rigorous mathematical
analysis of the dynamics of the coupled systems of nonlinear DFs that we have introduced
in our previous work. Of particular interest are stability issues and the sensitivity on initial
conditions and external perturbations. The convergence of the proposed learning dynamics
will be studied. In the domain of optimization we plan to test the filter line search globalization procedure for solving nonlinear programming problems proposed in our previous work.
The tests will include real optimal control problems. A global convergence analysis of the algorithm will be carried out. We will continue our collaboration with colleagues from the Dep.
of Mechanics (UM) on computational and analytical techniques for mechanical systems. The
concrete projects are: 1) the development of a general computational methodology for the
modelling of journal bearings subjected to dynamic loads, and 2) the modelling of the dynamics of multi-body systems. As an application of great practical importance, the movements
of parts of the human body will be simulated.
Most applications in science and engineering do require the efficient numerical solution
of linear algebra problems. We will continue previous work on the design and analysis of
algorithms for large structured matrices. Furthermore, we are also interested in the design of
algorithms that adapt well to the emerging paradigm of mixed-precision arithmetic.
Also, we will pursue our research on new methods for the discretization of integral equations. The corresponding spectral problem will be also considered. We envisage the develop-
23
ment of parallel codes on clusters of processors. This work will be done in collaboration with
the Numerical Analysis, Probability and Statistics group of “Centro de Matemática da Universidade do Porto” and the “Laboratoire de Mathématiques de l’Université de Saint-étienne”,
France.
Research projects
Dynamic field theory and its applications (Wolfram Erlhagen and PhD students)
In close cooperation with researchers from other national and international institutions we
will continue our work on the mathematical foundations of Dynamic Field Theory and its
applications. We have a number of projects in this area:
• Analysis of pattern formation and learning in dynamic fields. (Wolfram Erlhagen and PhD students Flora Ferreira and Emanuel Sousa) On the mathematical level we want to focus on the learning dynamics proposed to establish a coupling
between different dynamic fields. In addition, we are interested to apply recent “Evens
functions techniques” to show the existence and stability of multi-peak solutions with
a local threshold adaptation mechanism.
Collaborators: Gregor Schöner (Ruhr-Univ. Bochum, Germany).
• Learning to time: a dynamic field model (Wolfram Erlhagen and PhD students Flora Ferreira and Emanuel Sousa) We want to continue our modelling work
started in 2008 on a dynamic field model of learning to time.
Collaborators: Teresa Malheiro (CMAT), Armando Machado (Centre for Psychology,
UM), Estela Bicho (Algoritmi Centre, Univ. Minho).
• Neuro-cognitive mechanimes underlying action understanding (Wolfram Erlhagen and PhD student Emanuel Sousa) Within the context of the European JAST
project we will continue our collaborative work on the theoretical foundations of cognitive capacities like goal inference in humans and other primates.The project is financed
by the Science Foundation of the The Netherlands.
Collaborators: Harold Bekkering and Ivan Toni (Radbould Univ. Nijnegen, The Netherlands).
• Dynamic field account for visual perception (Wolfram Erlhagen) We will continue
the work on the development of dynamic field models for neural population data in visual
cortex. We will also continue the research on the application of the field models in the
domain of visual psychophysics.
Collaborators: Dirk Jancke and Christian Igel (Ruhr-Univ. Bochum, Germany) and the
group of Jochen Müsseler (Technical Univ. Aachen, Germany).
24
• Learning by Imitation (Wolfram Erlhagen and PhD student Fabio Chersi) The PhD
project on modelling neural population dynamics in the mirror circuit of monkey will
finish in 2009.
Collaborators: Leo Fogassi (Univ. Parma, Italy).
• Human-robot interaction (Wolfram Erlhagen, Emanuel Sousa, Eliana Silva and
Flora Ferreira) Within the context of the European project JAST we will further elaborate and test the dynamic field model of joint action. The final evaluation of the
integrated project will be in June.
Collaborators: Estela Bicho (Algoritmi, Univ. Minho); Alois Knoll (Technical Univ.
Munich, Germany); Günter Westphal (Ruhr-Univ. Bochum, Germany).
Algorithms for structured matrices arising on digital image processing (YuLin
Zhang, Rui Ralha, Carla Ferreira)
Although fast algorithms are known for some structured matrices, this is not the case for
centrosymmetric, generalized centro-symmetric and centro-Hermitian, which do occur when
wavelet techniques are used in image processing. We will continue our previous efforts in
designing efficient and robust pre-conditioners for Ax=b which do preserve at least some of
the initial structure of the problem. The size of the matrices may be extremely large, making
the problem very demanding both in terms of storage and computing. We will try to use
a “divide-and-conquer” approach by decomposing the original matrix into several blocks of
smaller size. These blocks are also structured and may be used to build up the global solution.
Collaborators: Liu ZhongYun (Changsha Univ. Science and Technology, China).
A mixed precision algorithm for the tridiagonal eigenvalue problem (Rui Ralha)
We have done significant progress in the design of methods that can be adapted to the emerging paradigm of scientific computing which is that of mixed precision arithmetic. This is
motivated by the appearance in the market of processors that are much faster in simple precision than they are in double precision. The goal of these algorithms is to compute the
eigenvalues to full accuracy while using faster single precision in the first k iterations. The
key issue is a correct estimate of the number k because this depends critically on the entries
of the matrix and on the particular eigenvalue being computed. This is clearly an application
of (classical and new) perturbation theory results and we will continue this line of research.
Field value of division and product of two matrices (YuLin Zhang)
This is a theoretical linear algebra project. Let A, B ∈ Mn . We will study the properties
of the following two sets: (i) R(A, B) = {(x ∗ Bx)/(x ∗ Ax) : 0 6= x ∈ C}; (ii) P (A, B) =
{(x ∗ Ax(x ∗ Bx) : x ∈ C, x ∗ x = 1}. It is an extension of the usual field value.
Collaborators: Charles Johnson (Dep. of Mathematics, College of William and Mary, USA).
25
Indicators in water management (Gaspar Machado, Rui Pereira)
The (IPCC, 2007) (international panel on climate change), recently awarded the Nobel Peace
Prize, released recently its fourth assessment report. There we can read among other important conclusions that with very high confidence the conditions (drought and high temperatures)
in Southern Europe will worsen. This region that includes Portugal, already very vulnerable,
will experience a reduction in water availability, hydropower potential and crop yield. In this
context it is necessary to be able to measure the efficiency of the water used in each of the
main consumers (PNUEA, 2001) (Agriculture, Urban areas and Industry). Our group will try
to develop a method to calculate these indicators for some regions of the Iberian Peninsula.
Collaborators: Naim Haie (Civil Engineering Center, UM), Manuela Gonçalves (CMAT).
Kinematics of the roller motion and cam size optimization of disc cam follower
mechanisms with translating roller followers (Gaspar Machado, Rui Pereira)
This project deals with the kinematic analysis and design optimization of disc cam mechanisms
with eccentric translating roller followers. The objective function considered in this project
takes into account the three major parameters that influence the final cam size, namely
the base circle radius of the cam, the radius of the roller and the offset of the follower.
Furthermore, geometric constraints related to the maximum pressure angle and minimum
radius of curvature are included to ensure good working conditions of the system.
Collaborators: Paulo Flores and J. C. Pimenta Claro (Mechanical Engineering Center, UM).
Study of transonic flows (Rui Pereira) Modern airplane carriers fly at transonic speeds,
that is, speeds close to the speed of sound. In this study, a numerical method will be presented,
that will allow us to study how a transonic flow passes an airfoil. We will focus our study in
the inviscid part of the flow, where the transonic small disturbance equation was considered.
The numerical method we use differentiates with respect to x using finite differences and
different types of computational stars. For the y derivatives we used Chebyshev collocation.
Part of this study was developed in my PhD thesis (2005) for the case where the airfoil is
symmetric and we will add the study for the case where the airfoil in non-symmetric. Another
issue related with transonic flows where collaboration with Prof Gajjar is also pertinent is to
try to solve the so far unsolved problem of shock oscillation in transonic flows. It is observed
experimentally that the presence of separated flow cause a low frequency oscillation of the
shock.
Collaborators: Jitesh Gajjar (Univ. Manchester, UK).
A 3D material optimization model to approximate energy bounds for cellular
materials (Gaspar Machado) Inverse homogenization and topology design can be used
to approximate the energy bounds for two-phase composites under multiple load cases. The
aim of this project is to compare the computational results with the globally optimal bounds
26
given via rank-N layered composites for different basic unit cells and different load conditions
for the 3D case.
Collaborators: J. M. Guedes and H. C. Rodrigues (IDMEC, IST, Lisbon)
Evaluation of an interior point filter line search method for solving nonlinear
optimization problems (M. Fernanda Costa, Florbela Fernandes) Past research work
is mainly concerned with the implementation of a 3-dimensional filter line search method in
an interior point method for solving nonlinear programming problems. The algorithm has
been tested with academic as well as with some engineering design problems. However, tests
with large scale problems is now required. Future research will involve the integration of our
3-dimensional filter strategy into the interior point code of a well-known solver – available in
the NEOS server - so that we can explore the capacities of the code, concerning numerical
linear algebraic computations. Comparisons, using a set of benchmark problems, with the
original solver will then be carried out. The global convergence analysis of the algorithm
is under investigation. A branch-and-bound type method will also be incorporated in the
algorithm so that mixed-integer nonlinear programming problems could also be solved.
Collaborators: Edite Fernandes (Algoritmi Center, UM).
Hybrid methodologies for improving the performance of Multi-Objective Evolutionary Algorithms (MOEA) (M. Fernanda Costa, Vı́tor Mariano Sousa) In this
project a hybridization of a local search algorithm with an MOEA will be implemented. This
strategy enables the possibility of using the advantages of each one of the algorithms used.
In this case the local search algorithm will allow searching locally for new improved solutions
using some of the solutions belonging to the Pareto set in each generation, obtained using the
MOEA. The main aim is to reduce the computation time required by the MOEA. Different
type of local search algorithms can be applied. In the present project the Filter Method (FM)
has been selected for that purpose.
Collaborators: António Gaspar Cunha (I3N, Associate Laboratory, UM).
Piezoelectric problems for beams: approximate solutions (Jorge Figueiredo, Carolina Ribeiro) The piezoelectric effect has many important industrial applications and is
receiving increasing attention. Our contribution in this field is to derive and justify in a mathematical rigorous way asymptotical models for piezoelectric beams. Furthermore, we want
to study a numerical approximation method to solve the reduced model resulting from the
asymptotic analysis. This work involves the use of asymptotic and finite element methods.
Collaborators: Juan Viaño Rey (Department of Applied Mathematics, Univ. Santiago de
Compostela).
27
Advanced training
is also included.
Carolina Ribeiro, PhD, Asymptotic Analysis, Partial Differential Equations, Piezoelectric problems; Title of thesis: Reduced mathematical models for piezoelectric problems; Juan
Viaño Rey (Department of Applied Mathematics, Univ. Santiago de Compostela) and Jorge
Figueiredo, Univ. Minho.
Summary: The main objective of the thesis consists in the development of mathematical models that are able to describe in a precise way the coupling between the mechanical
deformation and the electric potential for a piezoelectric material in a linear homogenous
anisotropic beam that avoids the typical ill-conditioning of the numerical problem resulting
from the three-dimensional classic equations.
Eliana Silva, PhD, Dynamical Systems, Control and Optimization; Title of thesis: Reaching, grasping and manipulation in anthropomorphic robot systems; Wolfram Erlhagen, Estela
Bicho (Algoritmi Centre, Univ. Minho) and Ruud Meulenbroek (Institute for Informatics
and Communication, Univ. Nijmegen, The Netherlands), Univ. Minho
Summary: The PhD work aims at using dynamical systems theory and optimization principles derived form human arm movement to control a 7 degrees-of-freedom robot arm for
human-robot interactions.
Emanuel Sousa, PhD, Robotics; Title of thesis: On learning and generalizing representations for personal service robots; Wolfram Erlhagen, Estela Bicho (Algoritmi Centre, Univ.
Minho), Univ. Minho
Summary: one important condition for a successful service robot is its ability to interact
with a human user in a natural manner. Most importunately, the robot should understand
observed actions in terms of their goals or end-states to anticipate an appropriate complementary action. The focus of the PhD proposal is on the development or emergence of
a sophisticated intention understanding capacity. On the technical level, the work will be
based on learning in a dynamic neural field architecture that is inspired by neuro-cognitive
principles underlying joint action in humans. Based on previous work of the group at the University of Minho, the PhD project focuses on the autonomous development and generalization
of representations that allow the robot to understand why a particular action is performed.
The learning capacity will be validated in robot-human tasks that involve the manipulation
of objects in domestic environments.
28
Fabian Chersi, PhD, Computational Neurocience and Applications in Robotics; Title of
thesis: Learning by imitation: a biologically inspired approach; Wolfram Erlhagen, Leonardo
Fogassi (Institute for Neurobiology, Univ. Parma, Italy), Univ. Minho
Summary: The goal of the thesis is to develop a dynamic model for explaining neural
data obtained in experiments with monkeys and apply this model to endow robots with the
capacity to learn through imitation. The theoretical framework is learning in networks of
spiking neurons.
Flora Ferreira, PhD, Dynamic Field Theory; Title of thesis: Mathematical learning;
Wolfram Erlhagen, Univ. Minho
Summary: The goal of the PhD thesis is to mathematically analyse different correlation
based learning rules formalized as dynamical systems. A better understanding of the learning
dynamics is important to advance toward more complex models consisting of various coupled
dynamic fields.
Florbela Fernandes, PhD, Mixed-Integer Nonlinear Programming; Title of thesis: An
interior point filter method for nonlinear mixed-integer programming; M. Fernanda Costa,
Edite Fernandes (Algoritmi Centre, Univ. Minho), Univ. Minho
Summary: The PhD work is motivated by the fact that mixed-integer nonlinear programming is an important and difficult area for which there is a need for developing new methods
and software for solving large scale problems. Moreover, both fundamental building blocks,
namely mixed-integer linear programming and nonlinear programming, have had considerable
and steady progress in recent years. So, with this work we intend to exploit expertise in these
areas and to adapt the existing algorithms to solve mixed- integer large scale problems.
Luı́s Louro, PhD, Robotics; Title of thesis: Control and representations for joint action
in autonomous systems; Estela Bicho (Algoritmi Centre, Univ. Minho), Wolfram Erlhagen,
Univ. Minho
Summary: The goal of the PhD work is to develop and evaluate a dynamic robot control
architecture for joint action. It integrates the dynamic approach for motion control (stability
and bifurcation analysis of non-linear dynamical systems) with the dynamic field approach
(pattern formation in dynamic fields) for endowing the robot cognitive skills like memory,
prediction and decision making. The work is closely linked to the European project “JAST”.
Miguel Vaz, PhD, Robotics; Title of thesis: Language imitation learning for autonomous
robots; Estela Bicho (Algoritmi Centre, Univ. Minho), Wolfram Erlhagen, Frank Joublin
(Honda Research Institute Europe, Germany), Univ. Minho
Summary: The objective of the PhD project is to design a dynamic model which allows
29
implementing and testing the imitation hypothesis for the development of communicative
gestures and, in particular, language abilities in a humanoid robot. The model architecture
is grounded on our current neurobiological and psychological knowledge about the processing
principles underlying imitation learning. This project in the area of cognitive robotics builds
on a strong cooperation with the Honda Research Institute Europe in Germany. Honda has
developed over the last couple of years one of the most advanced humanoid robot that exist
in the world.
M. Rosário Fernandes, PhD, Numerical Analysis; Title of thesis: Weakly singular
integral equations and applications to a radiative transfer problem; Filomena Dias d’Almeida
(Univ. Porto) and Mario Ahues (Univ. St. Etienne), Univ. Porto
Summary: The main purpose of this work is the development of iterative refinement methods from initial approximations to integral equations of the second kind, defined in a Banach
space. In particular, we are interested in Fredholm equations with weakly singular kernel
which occur, for instance, in Astrophysics, related to radiative transfer phenomena.
Nzoji Hipólito, PhD, Robotics; Title of thesis: Action understanding and anticipation
in multi-robot systems: a dynamical systems approach; Estela Bicho (Algoritmi Centre, Univ.
Minho), Wolfram Erlhagen, Univ. Minho
Summary: The project aims at endowing autonomous robots with the capacity to understand the actions and intentions of partners (humans or robots) in cooperative task. The
implementation is based on dynamical field theory, and more specifically, on the analysis of
self-stabilized stationary and travelling pulse solutions in dynamic fields of Amari-type. The
work is closely linked to the European project “JAST”.
Paulo Pereira, PhD, Optimization; Title of thesis: A decision support system to plan the
best assignment of the weekly self-promotion space for a TV station; Fernando Fontes (Univ.
Minho), Univ. Minho
Summary: TV stations typically reserve a promotion space (broadcasting time) for selfpromotion (future programs, etc.). Each product to promote has a given target audience that
is best reached at specific time periods during the week. The optimizer, based on a genetic
algorithm, aims to maximize the total number of contacts for each product within its target
audience while fulfilling a set of constraints defined by the user.
Sofia Lopes, PhD, Optimization; Title of thesis: Fortify necessary conditions of optimality for dynamic problems; Fernando Fontes (Univ. Minho), M. Rosário de Pinho (Univ.
Porto)
Summary: The Necessary Conditions of Optimality (NCO) typically identify a small set
of candidates where the minimizer belongs. However, there are some cases where certain
30
multipliers, existing in the NCO, take forms that do not allow the NCO to supply useful information to determine the solution. When this happens we say that degeneracy phenomenon
occurs. So, we study fortified forms of NCO that do not admit multipliers leading to degeneracy.
Vitor Mariano Sousa, PhD, Optimazation; Title of thesis: Hybrid methodology for
multi-objective optimization using evolutionary algorithms and filter methods: application to
polymer extrusion; M. Fernanda Costa, António Gaspar Cunha (DP, Univ. Minho), Univ.
Minho
Summary: The main objective of the PhD work is to develop a hybrid optimization
methodology by incorporating a local search algorithm in global multi-objective optimization
algorithm (MOEA). The aim will be to accelerate the global search of a MOEA through the
use of a local search algorithm. The Filter Method (FM) was been selected for that purpose.
The filter technique has been extended successfully to other areas of optimization. During the
successive generations of the MOEA, some of the solutions belonging to the Pareto optimal
frontier will be selected to perform a local search using the FM. The new improved solutions
created by the FM will be incorporated in the current population of the MOEA. It is expected
that the improvements given by the FM will accelerate the global search of the MOEA.
- Jorge Figueiredo (co-supervision with Juan Viaño Rey (Department of Applied Mathematics, Univ. de Santiago de Compostela))
Student: Carolina Ribeiro, Univ.Minho
- M. Fernanda Costa (co-supervison with Edite Fernandes (Algoritmi Center, UM))
Student: Florbela Fernandes, Univ. Minho
- M. Fernanda Costa (co-supervision with A. G. Cunha (I3N, Associate Laboratory, UM))
Student: Vı́tor Mariano Sousa, Univ. Minho
- Rui Ralha (co-supervision with Vicente Hernandez (Univ. Politecnica de Valencia))
Student: Carlos Campos, Univ. Politecnica de Valência
- Wolfram Erlhagen (co-supervision with Estela Bicho (DEI, Univ. Minho) and Ruud
Meulenbroek (Institute for Informatics and Communication, Univ. of Nijmegen, The
Netherlands)
Student: Eliana Silva, Univ. Minho
31
- Wolfram Erlhagen (co-supervision with Leonardo Fogassi (Institute for Neurobiology,
Univ. of Parma, Italy))
Student: Fabian Chersi, Univ. Minho
- Wolfram Erlhagen,
Student: Flora Ferreira, Univ. Minho
- Wolfram Erlhagen (co-supervision with Estela Bicho (DEI, Univ. Minho))
Student: Nzoji Hipólito, Univ. Minho
- Wolfram Erlhagen (co-supervision with Estela Bicho (DEI, Univ. Minho))
Student: Luı́s Louro, Univ. Minho
- Wolfram Erlhagen (co-supervision with Estela Bicho (DEI, Univ. Minho) and Frank
Joublin (Honda Research Institute Europe, Germany))
Student: Miguel Vaz, Univ. Minho
Scientific exchange
- Carla Ferreira, Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences, Beijing, and Changsha Univ. of Science and
Technology, China, three weeks in August and September
- Carolina Ribeiro, Department of Applied Mathematics, Univ. Santiago de Compostela,
Spain, one week in February
- Gaspar Machado, several visits to IST, Lisbon
- M. Rosário Fernandes, LaMUSE (Laboratoire de Mathématiques de l’Univ. Saintétienne), 2 weeks
- Rui Pereira, Univ. Manchester, UK, two weeks
- Wolfram Erlhagen, Technical Univ. Munich, Germany, 17-22/January
- Wolfram Erlhagen, review meeting of the European project JAST, Technical Univ.
Munich, Germany, 16-18/June
- C. Johnson, College of William and Mary, 10 days (YuLin Zhang)
32
- D. Jancke, Ruhr-Univ. Bochum, Germany, 5 days (Wolfram Erlhagen)
- J. V. Rey, Department of Applied Mathematics, Univ. Santiago de Compostela, Spain,
two days (Carolina Ribeiro)
- L. Fogassi, Univ. Parma, Italy, 4 days (Wolfram Erlhagen)
- L. ZhongYun, Changsha Univ. of Science and Technology, China, 2 months (YuLin
Zhang, Rui Ralha, Carla Ferreira)
- W. Shuanghu, Institute of Applied Physics and Computational Mathematics, Beijing,
China, one month (YuLin Zhang)
- Y. Demiris, Imperial College, UK, 5 days (Wolfram Erlhagen)
- Carla Ferreira, 7th International Conference on Numerical Optimization and Numerical
Linear Algebra (ICNONLA2009), Lijiang, China, 16-19/August
- Carolina Ribeiro, 11th International Conference on Mathematical Methods and Computational Tecniques in Electrical Engineering (MMACTEE’09), Athens, Greece, 2830/September
- Emanuel Sousa or Wolfram Erlhagen, 8th IEEE International Conference on Development and Learning, Shanghai, China, 5-7/June
- Flora Ferreira, Summer School on Dynamic Field Theory, Iowa, USA, 8-12/June
- Gaspar Machado, ASME 2009 Int. Design Engineering Technical Conferences and
Computers and Information in Engineering Conference, San Diego, USA, 30/August4/September
- M. Fernanda Costa, 8th World Congress on Structural and Multidisciplinary Optimization, Lisbon, Portugal, 1-5/June
- M. Fernanda Costa, 7th EUROPT Workshop Advances in Continuous Optimization,
Remagen, Germany, 3-4/July
- M. Fernanda Costa, 6th International Conference on Computational Management Science, Geneve, Switzerland, 1-3/May
- M. Fernanda Costa, 7th International Conference of Numerical Analysis and Applied
Mathematics, Crete, Greece, 18-22/September
33
- Nzoji Hipólito/Luı́s Louro, Emanuel Sousa/ Wolfram Erlhagen (one group member
only), 2009 IEEE/RSJ Conference on Intelligent Robotics and Systems (IROS 2009),
St. Louis, USA, 11-15/October
- Rui Pereira, ASME 2009 Int. Design Engineering Technical Conferences and Computers
and Information in Engineering Conference, San Diego, USA, 30/August-4/September
- Rui Ralha, Congresso de Métodos Numéricos en Ingenieria (METNUM 2009), Barcelona, Spain, 29/June- 2/July
- Rui Ralha, GAMM Workshop on Applied and Numerical Linear Algebra (and Lectures
on Numerical Linear Algebra in CSE), ETH Zurich, Switzerland, 9-11/September
- Sofia Lopes, Workshop on Control, Nonsmooth Analysis and Optimization, Porto, Portugal, 4-8/May
- Sofia Lopes, 48th IEEE Conference on Decision and Control, Shangai, China, 1618/December
- Wolfram Erlhagen (member of the Program Committee), New Frontiers in HumanRobot Interaction, Symposium at the conference “Adaptive, Emergent Behaviour and
Complex Systems (ASIB 2009)”, Edinburgh, U.K., 6-9/April
- Wolfram Erlhagen, Third Joint Action Meeting (JAM 2009), Amsterdam, The Netherlands, 27-29/July
- Wolfram Erlhagen, Donders Centre for Cognition, Univ. Nijmegen, The Netherlands,
10/February
- Wolfram Erlhagen, RIKEN Brain Science Institute (BSI) Summer Program 2009, Tokyo,
Japan, 13-25/July
- Wolfram Erlhagen, reviewer for the European Commission, Brussels, Belgium, 2-6/June
Seminars
The group organises seminars (two per month) on Computational Mathematics. A list of
scheduled seminars for January and February is shown in Section 2.
External funding
1 Projects
34
is also indicated.
- AST-Joint Action Science and Technology, European project IST-2-003747-IP, members
involved: Wolfram Erlhagen, Eliana Silva (PhD student), Luis Louro (PhD student),
Nzoji Hipólito (PhD student), total funding for UM 560000 Euro, 10/2004-05/2009.
2 Individual Grants
- Eliana Silva PhD grant from FCT, 980 e/month
- Emanuel Sousa PhD grant from FCT, 980 e/month
- Flora Ferreira PhD grant from FCT, 980 e/month
- M. Rosário Fernandes PhD grant from FCT, 250 e/month
Other activities
Members of the group will keep collaborating in projects for the promotion of science in
general, and mathematics in particular, for the general public. This includes talks and other
activities with high school students, aiming to raise their interest for applied mathematics.
Budget
Budget
6.900 e
10.400 e
23.922 e
1.000 e
0e
0e
0e
Bibliography
0e
TOTAL
42.222 e
It is expected that the amount of 3.000e will be supported by external funding.
6 Geometry and Analysis Theory, History and Applications
PhD FTE members
Name
Alberto Adrego Pinto
Dynamical Systems
Assis Azevedo
Analysis and Differential Equations
Fernando Miranda
João Caramalho Domingues
History of Mathematics
José Joaquim Oliveira
Lisa Santos (group leader)
Lucı́a Fernández-Suárez
Algebraic Topology
Lucile Vandembroucq
Algebraic Topology
M. Elfrida Ralha
Mahendra Panthee
M. Isabel Caiado
M. Joana Torres
Dynamical Systems
Patrı́cia Gonçalves
Dynamical Systems
Pawel Pilarczyk
Algebraic Topology
Thomas Kahl
Algebraic Topology
PhD collaborators
Name
Ana Pereira do Vale
Geometry and Topology
Carlos Vilar
José Francisco Rodrigues
35
36
M. Fernanda Estrada
Salvatore Cosentino
Dynamical Systems
Members without PhD
Name
Ana Cristina Ferreira
Differential Geometry
Helena Ferreira
Dynamical Systems
João Paulo Almeida
Dynamical Systems
José Manuel Oliveira
Geometry and Topology
José Martins
Dynamical Systems
Luı́s Miguel Ferreira
Dynamical Systems
General research Description
The main research interests of this group are Algebraic Topology, Analysis, Dynamical Systems and their interdisciplinary applications, History and Epistemology of Mathematics. The
group has three post-doctoral researchers and six doctoral students. Senior members of the
group are currently supervising Master, Doctoral and Postdoctoral research.
The work in Algebraic Topology deals with homotopy theory, computational homology
and applications. It is studied H-spaces, homotopy and homology of manifolds, numerical
homotopy invariants, rational homotopy theory, and homology computation algorithms. Applications of algebraic topology in other research areas such as Dynamical Systems (Conley
index), Robotics (topological complexity) and Computer Science (persistent homology, concurrency theory) are also studied.
The research in Analysis is developed essentially on ODEs and PDEs. The topics studied
are to find sufficient conditions for global stability related to a n-dimensional Lotka-Volterra
system with infinity delays; generalize some classical results from calculus of variations to
calculus of variations on time scales; to prove existence, regularity and asymptotic behaviour
of solutions of nonlinear evolutive systems of equations or variational and quasivariational
inequalities involving operators of type p-laplacian, p-curl or other nonlinear operators.
The research in Differential Geometry includes a project on generalized and riemannian
geometry aiming to classify metric connections with totally skew-symmetric torsion which
have vanishing Riemann/Ricci tensor.
In Dynamical Systems it will be studied:
- the spectral stability of semigroups of stochastic dynamical systems and the quantization
of disordered dynamical systems;
- the geometry of infinitely renormalizable Henon maps, to develop a theory of pseudo-
37
diffeomorphisms in C r new flat structures;
- links between dynamical systems and hydrodynamic limit theory for particles.
It will pursue interdisciplinary applications to epidemiology, neurology, immunology, financial mathematics and industrial organisation.
On History and Epistemology of Mathematics, we are planning to continue the research
focused mainly on the 18th century European Mathematics (Analysis and Geometry) as well
as on the history of teaching and learning of mathematics on the Portuguese educational
systems. Research work conducted during the past three years with colleagues from the
Departments of Mathematics of Porto, Coimbra and Lisboa will be also an objective to
pursue.
Research projects
Variational and quasivariational inequalities (Assis Azevedo, Fernando Miranda,
Lisa Santos)
We intend to study several topics:
- A nonlinear evolutive electromagnetic and thermal coupled system - We consider an evolutionary system coupling the electromagnetic and thermal fields associated with power type
laws both in the electromagnetic induction and Joule heat. Existence of solution and asymptotic behaviour in time will be treated;
- A problem with gradient constraint depending on the temperature - We study the existence
of solution of a coupled problem consisting of a parabolic variational inequality with a gradient constraint depending on the temperature, being the temperature the solution of the heat
equation where the heat source depends on the diffusion process;
- Evolutive problems involving the p-curl operator - We study an evolutive equation modelling an electromagnetic problem obtained by considering a general operator with structural
properties similar to the p-curl operator. We also study the variational inequality defined by
the same general operator and the convex set obtained by imposing a curl constraint. The
asymptotic behaviour, when time tends to infinity, will also be treated;
- Reaction-diffusion systems related to multiphase problems - The problem of proving existence and regularity of solution to constrained reaction-diffusion systems of multiphase problems, considering general convex constraints, will also be studied, generalizing a result already
proved for the Gibbs N-triangles;
- The evolutive nonlinear N-membranes problem with time-dependent data - We study the
N-membranes evolutive problem with non-homogeneous Dirichlet boundary condition, with
special emphasis to the asymptotic behaviour in time and to the stability of the coincidence
sets.
Collaborators: J. M. Urbano (CMUP, Univ. Coimbra); José Francisco Rodrigues (CMAF,
38
Univ. Lisboa).
A hyperbolic system modelling an antennas problem (Fernando Miranda, Lisa
Santos, Mahendra Panthee)
We intend to consider a modification of an antennas model with constitutive laws of power
type. It consists of a new nonlinear hyperbolic system that extends a Duvaut-Lions model.
The goal is to find solutions with some regularity using hyperbolic systems tools.
Collaborators: José Francisco Rodrigues (CMAF, Univ. Lisboa).
Reception and developments of logarithms in Portugal in the 17th and 18th centuries (João Caramalho Domingues)
Logarithms appeared for the first time in [Napier 1614]. A study of their introduction and
development in Spain has been published recently [Navarro-Loidi & Llombart 2008]. That
study begs the question of the portuguese parallel situation, which may be particularly interesting both because of an early introduction, in Ignace Stafford’s classes at the Colégio
de Sto Antão, Lisbon (c.1635), and because of the innovative treatment given to them by
José Anastácio da Cunha in the 1780’s (defining them through power series). We hope to
understand the context of their reception and the development of the approaches used in
addressing them.
Collaborators: Samuel Gessner (Centro de História das Ciências, Univ. Lisboa); Carlos Correia de Sá (Centro de Matemática, Univ. Porto).
Global stability for functional differential equations (José Joaquim Oliveira)
We expect to find sufficient conditions for global stability related to a n-dimensional LotkaVolterra system with infinity delays. We also expect to obtain sufficient conditions for the
existence and global attractivity of an equilibrium point of Neural Network Models with
infinite delays.
Collaborators: Teresa Faria (CMAF, Univ. Lisboa); I. Gyori (Univ. Veszprém, Hungary).
Classical and rational homotopy theory (Lucı́a Fernández-Suárez, Lucile Vandembroucq)
We plan to continue our work on the homotopy theory of H-spaces, more specifically, on the
homotopy classification of p-local-H-spaces of low rank, using homological and homotopical
techniques. On the other hand, as established in Y. Félix, J. Oprea, and D. Tanré. Algebraic
Models in Geometry, Oxford GTM (2008), the techniques of Rational Homotopy Theory can
be successfully used in the study of numerous geometrical objects. In this context, we plan
to pursue our work on embeddings of spaces into euclidean space and also to initiate a study
of the rational homotopy type of the space of connections of a principal G-bundle.
Collaborators: J. Harper (Univ. Rochester, USA); P. Lambrechts (Univ. Louvain-la-Neuve,
39
Belgium); D. Tanré (Univ. Lille, France).
Applications of algebraic topology (Lucı́a Fernández-Suárez, Lucile Vandembroucq,
Pawel Pilarczyk, Thomas Kahl)
The theory of persistent homology developed within the time period of the recent two decades
provides new methodology for topological analysis of data coming from various sources. The
basic idea of persistence is to keep track of topological features as they are born and die during
the growth of a cellular complex, and to classify these features based on their lifespan. The
purpose of our project is to get acquainted with the subject of persistent homology and work
together on some new results in this area. Besides this we plan to pursue our work on the
topological complexity which is a numerical homotopy invariant measuring the complexity of
motion planning problems in Robotics. We also plan to continue our work on applications of
Algebraic Topology in Concurrency Theory.
Collaborators: J. M. Garcı́a Calcines (Univ. La Laguna, Spain).
Nonlinear evolution equations of dispersive type (Mahendra Panthee)
We would like to study the nonlinear evolution equations of dispersive type. Our interest
is to address the low regularity well-posedness issues for some bi-dimensional versions of the
KdV equations like KP-II in cylinders and the stabilization of the solution with localized
damping mechanism. Our next interest is to study the unique continuation property for the
Benny system and Hirota equation which are the mixed system of nonlinear Schrodinger and
Korteweg-de Vries equations. Also we plan to work on Boltzmann equation to find solutions
with some regularity using hyperbolic systems. The works of Kenig, Ponce Vega (2006),
Bourgain (1993), T. Tao (2003), Zuazua (2002), M. Panthee, J. Silva, A. Grunrock (2007),
D. Serre (2004) and references therein are some base and motivation for our project.
Collaborators: Jorge Silva and Diogo Gomes (IST, Lisbon); Axel Grunrock (Univ. Bonn,
Germany); F. Linares (IMPA, Brazil); X. Carvajal (UFRJ, Brazil); M. Scialom (UNICAMP,
Brazil); A. J. Soares (CMat).
History and Epistemology of Mathematics (M. Elfrida Ralha)
We aim at continuing the work on:
- life and work of José Anastácio da Cunha (1744–1783);
- a historical-didactical program which involves divulgation (through talks at secondary
schools, communications for general public, organisation of posters, etc.) of the life and works
of portuguese mathematicians;
- the history and teaching of mathematical concepts
Collaborators: José Francisco Rodrigues (Univ. Lisboa); J. Carvalho e Silva and A. L. Duarte
(Univ. Coimbra); C. Sá (Univ. Porto); M. Fernanda Estrada and Carlos Vilar (CMAT); A.
Gomes (UM).
40
Calculus of variations on time scales (M. Isabel Caiado)
We intend to generalize some classical results from calculus of variations to calculus of variations on time scales.
Collaborators: Delfim Torres (Univ. Aveiro).
Extension of functions with bounded finite differences (M. Joana Torres)
We plan to prove that functions defined on a lattice in the torus Td with bounded finite
differences can be smoothly extended to the whole torus, and to relate the bounds on the
extension’s derivatives with bounds on the original function’s finite differences. This result
should also hold for some class of domains which are proper subsets of lattices in the torus
Td. We plan to characterize this class of subsets.
Collaborators: P. M. Duarte (CMAF, Univ. Lisboa).
Stability and Morse decompositions of non-deterministic systems (M. Joana Torres
and Pawel Pilarczyk)
We plan to introduce some regularity concept (smoothness) for non-deterministic systems,
prove a version of Smale’ Spectral Decomposition Theorem for them, and analyze their stability. The aimed non-deterministic systems will be Markov like but with no probabilities.
The approach is also intended to give theoretical support to computational methods in smooth
(deterministic) dynamics.
Collaborators: P. M. Duarte (CMAF, Univ. Lisboa).
Hydrodynamic limit of particle systems (Patrı́cia Gonçalves)
In this project we want to study interacting particle systems with hydrodynamic behaviour.
These systems are continuous time Markov processes with a conserved quantity and one wants
to characterize the temporal evolution of this quantity, as well as the global qualitative study
of the system. Here three different types of models are considered, the asymmetric exclusion
process, particle systems with degenerate rates (kinetically constrained lattice gases) and
particle systems on random environments. Related to these processes, I am interested on
analyzing multiclass processes, convergence to local equilibrium and asymptotic behaviour
for a second class particle or a discrepancy. The idea is to develop the results of P. Ferrari,
P. Gonçalves, J. Martin (2008), P. Ferrari.; C. Kipnis. (1995) and P. Gonçalves.; C. Landim,
C. Toninelli. (2007).
Collaborators: C. Landim (IMPA, Brazil); P. Ferrari (Univ. S. Paulo, Brazil); J. Martin (Univ.
Oxford, UK); S. Assing (Univ. Warwick, UK); M. Jara (Univ. Paris – Dauphine, France);
Beltran (Ecole Polytechnique Fédérale de Lausanne, Switzerland); C. Toninelli (Univ. Paris,
France).
41
Computational algebraic topology and applied dynamical systems (Pawel Pilarczyk)
This is a multi-threaded and multi-disciplinary research project with many collaboration lines.
Together with a group in Seville, we are going to work on the extension of the computation
of cohomology operations from the context of simplicial complexes to cubical ones. In collaboration with S. Luzzatto, we develop a theory of finite resolution dynamics and apply it
to sample maps, like the Hénon map. With a group in Kyoto, we work on applying graph
algorithms to the automatic analysis of discrete dynamical systems on a bounded area in
the Euclidean space in order to determine the global dynamical picture. Together with G.
Graff and his group, we are going to study topological questions that can be reduced to
combinatorial problems and we plan to develop algorithms for solving these problems.
Collaborators: P. Real (Univ. Seville, Spain); S. Luzzatto (Imperial College, U. K.); H.
Kokubu and M. Gameiro (Univ. Kyoto, Japan); G. Graff (Gdansk University of Technology,
Poland).
Advanced training
is also included.
Ana Cristina Ferreira, PhD, Differential geometry; Title of thesis: Skew torsion and
generalized geometry; Nigel Hitchin (Univ. Oxford, UK).
Summary: This project focuses on different aspects of metric connections with skew torsion on the tangent bundle of a Riemannian manifold. Past research has involved Dirac
operators, some index theory and the study of curvature. Recently, a generalization of the
Hitchin-Thorpe inequality has been obtained and manifolds for which equality occurs have
been classified in terms of their universal cover.
Helena Ferreira, PhD, Dynamical Systems; Title of thesis:Sistemas dinâmicos naturais
e complexos; Alberto Adrego Pinto, Univ. Minho
Summary: We characterize the dynamic of river flows in specific regimes, using the BHP
and gaussian distributions, proceeding to the identification and understanding of the differences and resemblances between different rivers. We will extend our results to other natural
and complex dynamical systems.
João Paulo Almeida, PhD, Dynamical Systems; Title of thesis: Medidas geométricas e
aplicações pseudo-Anosov; Alberto Adrego Pinto, Univ. Minho
42
Summary: We develop a theory on flexibility and rigidity of smooth conjugacy classes for
pseudo-Anosov diffeomorphism in new ”pseudo-smooth” structures on surfaces according to
the existing theory of Pinto-Rand. We study the links between tilings and hyperbolic diffeomorphism according to the results of Pinto-Sullivan.
José Manuel Oliveira, PhD, Geometry and Topology; Title of thesis: Some homological
properties of topology of manifolds; Alexandr Mishchenko (Moscow State Univ.) and Anton
Alekseev (Univ. Geneve), Univ. Geneve
Summary: The de Rham complex homology of differential forms on a smooth manifold
can be considered as a differential graded algebra of all polylinear functionals on the Lie algebra of vector fields on the manifold. This construction is generalized to the Lie algebroids
in which we define the Poincaré duality and piecewise smooth cohomology. We construct a
theory similar to the Lie algebroid in the case of triangulated smooth manifolds.
José Martins, PhD, Dynamical Systems; Title of thesis: Modelos dinâmicos para propagação de epidemias e BH; Alberto Adrego Pinto and N. Stollenwerk (Fundação Calouste
Gulbenkian), Univ. Minho
Summary: We characterize analytically the critical thresholds of epidemiological outbreaks, using the ”master equation” to establish, recursively, the dynamics of the moments
corresponding to the number of infected in the population. We study the influence of the
higher moment dynamics in the critical threshold region. The distributions of infected associated with epidemiological models will also be studied.
Luı́s Miguel Ferreira, PhD, Dynamical Systems; Title of thesis: Modelos microeconómicos; Alberto Adrego Pinto, Univ. Minho.
Summary: We model different economical problems (the Cournot models with R&D programs) and we prove the existence of Nash equilibria. For auction models, we compare the
revenue between the different kinds of auctions in different settings. For general equilibrium
models, we study price convergence and stability.
- Alberto Adrego Pinto
Student: Abdelrahim Mousa, Univ. Minho
Student: Gabriela Muller Goes, Univ. Minho
43
Student: Joaquim Baião, Univ. Minho
Student: João Paulo Almeida, Univ. Minho
Student: José Martins, Univ. Minho
Student: Luı́s Miguel Ferreira, Univ. Minho
- M. Elfrida Ralha
Student: Ana Cláudia Amaral, Univ. Minho (co-supervision with M. A. Gomes (Univ.
Minho))
- M. Elfrida Ralha
Student: Margarida Cristina Oliveira, Univ.Minho (co-supervision with José Francisco
Rodrigues and M. Suzana Nápoles (Univ. Lisboa))
Student: Joana Pinto, Univ. Minho
Student: Joaquim Baião, Univ. Minho
Student: Sofia Cerqueira, Univ. Minho
- Lucı́a Fernández-Suárez
Student: Carla Ramalho, Univ. Minho
- M. Elfrida Ralha
Student: Susana Maria da Costa Ribeiro, Univ. Minho (co-supervision with M. Fernanda
Estrada)
- Thomas Kahl
Student: Ivone Vieira, Univ. Minho
2.3 Supervision of undergraduate students
44
- M. Joana Torres and Salvatore Cosentino
Integration into research grant, Programa Ciência 2008, FCT
Student: Ana Alexandra Costa, Licenciatura em Ciências da Computação, Univ. Minho
- Thomas Kahl
Novos Talentos em Matemática (Fundação Calouste Gulbenkian)
Student: Rui Barbosa, Licenciatura em Ciẽncias da Computação, Univ. Minho
2.4 Supervision of postdoctoral researchers
Researcher: Patrı́cia Gonçalves, Univ. Minho
Scientific exchange
- Assis Azevedo, CMAF, Univ. Lisboa, several one or two days visits
- Fernando Miranda, CMAF, Univ. Lisboa, several one or two days visits
- João Caramalho Domingues, Centro de História das Ciências, Univ. Lisboa, several 1
or 2 days visits
- José Joaquim Oliveira, Regional Centre of the Hungarian Academy of Sciences, Veszprém,
Hungary, July
- José Joaquim Oliveira, CMAF, Univ. Lisboa, once a month
- José Manuel Oliveira, Banach Center, Poland, 16-31/January
- José Manuel Oliveira, Chern Institute of Mathematics, China, 1-5/June
- Lisa Santos, CMAF, Univ. Lisboa, several one or two days visits
- Lisa Santos, CMUC, Univ. Coimbra, several one day visits
- Lucı́a Fernández-Suárez, Univ. Rochester, US, 1-15/July
- Lucı́a Fernández-Suérez, Univ. New Brunswick, Canada, 15/July-15/August
- Mahendra Panthee, IMPA, Brazil, 3-18/January
- Mahendra Panthee, IST, Lisboa, 26/January-6/February
45
- M. Elfrida Ralha, CMUP (Porto), CMUC (Coimbra) and CMAF (Lisbon), short term
visits (1 or 2 days), throughout the year
- M. Isabel Caiado, Univ. Aveiro, several 1 or 2 days visits
- M. Joana Torres, CMAF, Lisboa, Portugal, 10 visits of one day
- Patrı́cia Gonçalves, EPFL, Switzerland, 21-28/February
- Patrı́cia Gonçalves, Univ. Paris - Dauphine, France, 7/September-18/December
- Pawel Pilarczyk, Univ. Kyoto, Japan, 1 month
- Pawel Pilarczyk, Gdansk University of Technology, Poland, 2 weeks
- Pawel Pilarczyk, Univ. of Seville, Spain, 1 week
- Pawel Pilarczyk, Imperial College, United Kingdom, 1 week
- Pawel Pilarczyk, Univ. Lisboa, Portugal, 2 one day visits
- Aleksandr Mishchenko, Moscow State University, Russia, 21-31/March (José Manuel
Oliveira)
- Doug Ravenel, Univ. Rochester, US, 19-25/April (Lucı́a Fernández-Suárez)
- Grzegorz Graff, Gdansk University of Technology, Poland, 2 weeks (Pawel Pilarczyk)
- Johel Beltran, EPFL, Switzerland, 2 weeks (Patrı́cia Gonçalves)
- John Harper, Univ. Rochester, US, 1-21/October (Lucı́a Fernández-Suárez)
- José Manuel Garcı́a Calcines, Universidad de La Laguna, Spain, 1 week (Lucile Vandembroucq)
- Milton Jara, University Paris - Dauphine, France, 2 weeks (Patrı́cia Gonçalves)
- Pascal Lambrechts, Université Catholique de Louvain-la-Neuve, Belgium, 2 weeks (Lucile Vandembroucq)
- Xavier Carvajal, Federal Univ. of Rio de Janeiro, Brazil, March (Mahendra Panthee)
- Assis Azevedo, 6th European Conference on Elliptic and Parabolic Problems, Gaeta,
Italy, 25-29/May
46
- Ana Cristina Ferreira, Geometry and Physics: Atiyah80, Edinburgh, UK, 20-22/April
- Fernando Miranda,6th European Conference on Elliptic and Parabolic Problems, Gaeta,
Italy, 25-29/May
- João Caramalho Domingues, Annual Meeting of the Seminário Nacional de História da
Matemática, location to be announced (Portugal), dates to be announced (2 days)
- José Manuel Oliveira, International Conference on C*-algebras and Elliptic Theory III,
Bedlewo, Poland, 26-31/January
- José Manuel Oliveira, International Conference on K-Theory, C*-algebras and Topology
of Manifolds, Tianjin, China, 1-5/June
- Lisa Santos, 6th European Conference on Elliptic and Parabolic Problems, Gaeta, Italy,
25-29/May
- Mahendra Panthee, Nonlinear Waves and Dispersion, April Workshop, Center Emı́le
Borel, Paris, France, 27-30/April
- Mahendra Panthee, Nonlinear Waves and Dispersion, June Workshop, Center Emı́le
Borel, Paris, France, 22-26/June
- Mahendra Panthee, 27 Colóquio Brasileiro de Matemática, IMPA, Rio de Janeiro,
Brazil, 27-31/July
- M. Elfrida Ralha, Didactics of Mathematics as a Mathematics Discipline (a XXIst
century Felix Klein’s follow up), Funchal, Portugal, 1-4/October
- M. Isabel Caiado, Workshop in Control, Nonsmooth Analysis and Optimization, Porto,
Portugal, 4-8/May
- Patrı́cia Gonçalves, 5th International Institute of Forecasters’ Workshop on the Predictability of Financial Markets, Lisbon, Portugal, 16-17/January
- Patrı́cia Gonçalves, Workshop on Interacting Particle Systems, Beijing, China, 1519/June
- Patrı́cia Gonçalves, 33rd Conference on Stochastic Processes and Their Applications,
Berlin, Germany, 27-31/July
- Patrı́cia Gonçalves, Statistical Physics, Combinatorics and Probability: from discrete
to continuous models, a thematic trimester at the Centre Emile Borel, Institut Henri
Poincaré, Paris, France, from 7/September-18/December
- Pawel Pilarczyk, Progress on Difference Equations 2009, Bedlewo, Poland, 25-29/May
47
- Pawel Pilarczyk, Dynamics, Topology and Computations, Bedlewo, Poland, 31/May6/June
1 Seminars
The group organises seminars on “Analysis, Geometry and Mathematical Physics” together
with the group MathPhys. A list of scheduled seminars for January and February is in Section
2.
- “Didactics of Mathematics as a Mathematics Discipline (a XXIst century Felix Klein’s
follow up)”. International workshop to be held in Funchal (Univ. Madeira), Portugal,
1-4/October.
Organising Committee: M. Elfrida Ralha (Univ. Minho), J. Carvalho e Silva (Univ.
Coimbra), José Francisco Rodrigues and M. Suzana Nápoles (Univ. Lisboa), J.M.
Castanheira (Univ. Madeira).
- One day of lectures on ODE’s and PDE’s at Univ. Minho, gathering researchers from
Portugal and Galiza, trying to use the geographic proximity to establish new scientific
contacts. Organising Committee: Assis Azevedo, Fernando Miranda, Lisa Santos.
External funding
1 Projects
is also indicated.
- Analysis of Nonlinear Partial Differential Equations, project FCT,
UTAustin/MAT/0035/2008, Fernando Miranda, Ana Jacinta Soares, Lisa Santos, J.M.
Urbano (principal researcher, CMUC, Univ. Coimbra), Budget: not yet known
2 Individual Grants
- Ana Cristina Ferreira PhD Grant from FCT, “Skew torsion and generalized geometry”,
app 8 000 e (registration) and 750 e/month
- José Martins PhD Grant from FCT, “Modelos dinmicos para propagao de epidemias e
BH”, 2 750 e (registration) and 250 e/ month
48
- Luı́s Miguel Ferreira PhD Grant from FCT ,“Modelos microeconmicos”, 2750 e (registration) and 250 e/ month
- Patrı́cia Gonçalves Pos-doc Grant from FCT, ”Interacting Particle Systems”, 1 500
e/month
Other activities
- Patrı́cia Gonçalves - Professora Auxiliar Convidada - Invited lecturer at Universidade
Nova de Lisboa, from 01/February of 2009 to 31/August of 2009, Lisboa, Portugal
- Patrı́cia Gonçalves - “Research Position” at the “Centro de Matemática da Universidade
do Minho, from 01/September of 2009, Braga, Portugal
Budget
Budget
25 331,80 e
13 730,00 e
Participation in scientific meetings
18 360,00 e
2 000,00 e
1 250,00 e
2 500,00 e
2 000,00 e
Bibliography
1 410,00 e
TOTAL
65 581,80 e
7 Mathematical Physics and
Modelling
PhD FTE members
Name
Ana Jacinta Soares
Kinetic Theory, Modelling
Estelita Vaz
General Relativity
Filipe Mena (group leader)
General Relativity, Modelling
Filipe Moura
General Relativity, String Theory
Irene Brito
General Relativity
M. Piedade Ramos
General Relativity
Teresa Malheiro
Functional Analysis, Modelling
Members without PhD
Name
Artur Alho
General Relativity
Cristina Diogo
Functional Analysis, Modelling
Filipe Carvalho
Kinetic Theory
João Nunes
General Relativity
General research description
The members of this group mainly study mathematical problems of physics. Our main goal
is to develop new techniques and obtain new mathematical results which are motivated from
physical phenomena. Our research topics concern the modelling, consistency and stability
properties of some nonlinear problems in the context of functional analysis, partial differen49
50
tial equations, general relativity and kinetic theory. In particular, the group intends to exploit
the interplay between kinetic theory and relativity with emphasis on the study of the existence, stability and asymptotic behaviour of solutions to partial differential equations arising
in those theories. Besides the internal collaborations associated to the PhD students, some
senior group members collaborate on common projects. The group maintains a high level of
internationalisation with a rather vast set of external collaborators, both mathematicians and
theoretical physicists.
Research projects
Invariant classification of exact solutions of Einstein’s equations (M. Piedade
Ramos)
We intend to continue our research on classification of metrics and determining the isometry
group structure, the subclasses with additional isometries and the explicit form of the Killing
vectors both within the original spacetime, and within its subclasses. The method developed
by Edgar and Ramos simplifies the difficult equivalence problem in General Relativity.
Collaborators: Brian Edgar (Univ. Linkoping, Sweden).
Kinetic theory of chemically reacting gases (Ana Jacinta Soares)
Kinetic theory of chemically reacting gases constitutes a widely investigated topic in Mathematical Physics that studies some mathematical problems with applications to engineering,
combustion, chemical technologies and other physical fields. In particular we intend to face:
a) the global well-posedness of the initial-boundary value problem for the spatially homogeneous Boltzmann equation extended to chemically reacting gases in the case of hard or soft
potentials, with or without cutoff; b) the extension of the Boltzmann equation to a chemically reacting mixture modelling chemical reactions without barriers and study of consistency
properties of the model.
Collaborators: Filipe Oliveira (Univ. Nova de Lisboa, Portugal), Gilberto Kremer (Univ.
Paraná, Brazil); Giuliana Lauro (Univ. Naples); Jacek Polewczak (California State Univ.,
USA); Miriam Pandolfi Bianchi and Roberto Monaco (Politecnico di Torino, Italy).
Mathematical problems of spacetime matching (Filipe Mena)
There are very few analytical results about the matching problem in general relativity. The
main reason for this is the difficulty to treat the initial boundary value problem (IBVP) for
the Einstein equations (Elhers and Kundt, 1998), which are non-linear partial differential
equations. In this project we shall take a given (say interior) family of spacetimes and conditions at a matching boundary to prove existence and uniqueness of a (say exterior) spacetime.
Following Mena and Tod (2004), we shall start by considering highly symmetric cases such as
51
stationary, spherical and cylindrical. This sheds light into the IBVP for the Einstein equations
and is useful, for example, for modelling isolated bodies in general relativity.
Collaborators: Paul Tod (Oxford, U.K.); Jose Natario (IST, Lisbon); Marc Mars (Salamanca,
Spain); Raul Vera (Univ. Basque Country, Spain); Simone Calogero (Granada, Spain).
Relativistic elasticity (Estelita Vaz, Irene Brito)
We intend to pursue the study of space-times corresponding to solutions of the Einstein equations of General Relativity, when the matter is modelled by a material body in elasticity
theory. Such matter models are of primary importance in astrophysics, where they are used
for instance to model the solid crust of neutron stars or for developing techniques (for example the Weber antenna) for detecting gravitational waves. Estelita Vaz and Irene Brito
have already some results in this area: one publication in 2008, two publications in an international conference and some results concerning spherically symmetric spacetimes which
are being written to submit to an international journal. We intend to carry out studying
space-times possessing cylindrical symmetry, associated with a nonflat material space. Interpretation of exact solutions from the point of view of elastic properties and relationship
between symmetries in the spacetime and in the material space will be investigated. Moreover,
we intend to carry out results associated with conformally related material metrics.
Collaborators: Jaume Carot (Univ. Illes Balears, Spain).
Toeplitz operators, Riemann-Hilbert problems and matrix factorization (Teresa
Malheiro)
To study the invertibility and Fredholm properties of various operators of Toeplitz type,
in particular those suggested by applications in Physics and Engineering, to develop new
methods to solve the Riemann-Hilbert problem, namely by defining appropriate new types
of factorization and to determine conditions for invertibility and expressions for the inverse
operator. Câmara, M. C., Malheiro, M. T,Complex Analysis and Operator Theory, 2008
Birkhauser Verlag. verificar
Collaborators: Maria Cristina Câmara (IST, Lisbon).
Stability of stringy dilatonic black holes (Filipe Moura)
We generalize our study of black holes in heterotic string theory in d spacetime dimensions
(with higher-derivative corrections) to solutions with dilatonic charge, by consideryng the
dynamics of the internal metric of the (10-d)-dimensional compactification manifold. We
check how this charge affects our previous results (perturbative stability and absorption crosssection).
Collaborators: R. Schiappa (IST, Lisbon).
Stability and scattering of superstringy black holes (Filipe Moura, Filipe Mena)
52
We extend the study of black holes in heterotic string theory in d spacetime dimensions (with
corrections of second order in the Riemann tensor) to the corresponding solutions in type II
superstring theory, which because of supersymmetry only have corrections of fourth order in
the Riemann tensor. We compare the results from superstring theory to the corresponding
ones in heterotic string theory (perturbative stability and absorption cross-section).
Advanced training
is also included.
Artur Alho, PhD, General Relativity; Title of thesis: Non-linear evolution and stability
problems in general relativity; Filipe Mena and José Natário (IST, Lisboa), Univ. Minho.
Summary: The project concerns nonlinear aspects of the Einstein field equations with
emphasis on stability problems: (i) Theory and applications of non-linear perturbations of
homogeneous and isotropic space-times. (ii) Stability analysis of space-time matching solutions.
Cristina Diogo, PhD, Functional Analysis; Title of thesis: Fredholm properties of Toeplitz operators and generalized corona problems; Estelita Vaz and Cristina Câmara (IST, Lisboa), Univ. Minho.
Summary: The invertibility and Fredholm properties of Toeplitz operators with 2x2 matrix
symbol G is studied in connection with the corona theorem and the solutions to a RiemannHilbert problem associated with G. A method to verify the corona conditions for such solutions is developed and used to obtain invertibility criteria for new classes of Toeplitz operators.
Filipe Carvalho, PhD, Kinetic Theory; Title of thesis: Mathematical methods to solve
the Boltzmann equation extended to chemically reacting gases; Ana Jacinta Soares and Filipe
Oliveira (UNL, Lisboa), Univ. Minho.
Summary: The existence, asymptotic behaviour and stability of shock wave solutions to
the hyperbolic model equations proposed in [Kremer, Pandolfi Bianchi, Soares, Phys Fluids,
2006] are investigated.
João Nunes, PhD, General Relativity; Title of thesis: Elasticity in general relativity as
a perturbative theory; M. Piedade Ramos, Univ. Minho.
Summary: In this project the student should translate the model for relativistic elasticity
53
in terms of perturbative theory. It seems useful to use the tool of the 1+3 formalism to try
and describe the elastic model in General Relativity. Some simple examples should be tested.
- Ana Jacinta Soares
Student: Filipe Carvalho, Univ. Minho, (co-supervision with Filipe Oliveira (UNL,
Lisboa))
- Estelita Vaz
Student: Cristina Diogo, Univ. Minho, (co-supervision with Cristina Câmara (IST,
Lisboa))
- Filipe Mena
Student: Artur Alho, Univ. Minho, (co-supervision with José Natário (IST, Lisboa))
- M. Piedade Ramos
Student: João Nunes, Univ. Minho
- Filipe Mena
Student: António Correia, Univ. Minho (co-supervision with Ana Jacinta Soares)
Scientific Exchange
- Ana Jacinta Soares, Dep. Mathematics, Univ. Naples, (Italy), 1 week in February
- Ana Jacinta Soares, Dep. Physics, Univ. Paraná, Curitiba (Brazil), 2 weeks in AprilMay
- Estelita Vaz, Univ. Aberdeen, UK, 1 week
- Estelita Vaz, Univ. Illes Balears, Mallorca, Spain, 2 visits of 5 days each
- Filipe Mena, Mathematical Institute, Univ. Oxford and Queen Mary, Univ. London, 2
weeks in February/March
- Filipe Mena, Univ. Granada, 1 week in June
54
- Filipe Mena, Dep. Matemática, IST, Lisbon, 3 months
- Irene Brito, Univ. Aberdeen, UK, 1 week
- Irene Brito, Univ. Illes Balears, Mallorca, Spain, 2 visits of 5 days each
- M. Piedade Ramos, Department of Mathematics, Univ. Linköping, Sweden, 15 days
- Teresa Malheiro, CEAF, IST, several times for the period of 2 or 3 days
- Brian Edgar, Univ. Linköping, Sweden 15 days (M. Piedade Ramos)
- C. Uggla, Univ. Stockholm, Sweeden, 5 days (Estelita Vaz, Irene Brito)
- Gilberto Kremer, Univ. Paraná, Curitiba, Brazil, 11-25/January (Ana Jacinta Soares)
- G.S. Hall, Univ. Aberdeen, UK, 1 visit of 5 days (Estelita Vaz, Irene Brito)
- Jacek Polewczak, California State Univ., USA, 2 weeks in May-June (Ana Jacinta
Soares)
- J. Carot, Univ. Illes Balears, Spain, 2 visits of 5 days (Estelita Vaz, Irene Brito)
- Maria Cristina Câmara (IST, Portugal), 2-3 days in January (Teresa Malheiro)
- Maria do Carmo Martins (Univ. Açores, Portugal), 2 days in January (Teresa Malheiro)
- Miriam Pandolfi Bianchi, Politecnico di Torino, Turin, Italy, 7 days (Ana Jacinta Soares)
- José Maria Martin, LUTH, CNRS, France, 14 days (M. Piedade Ramos)
- S. Calogero, Univ. Granada, Spain, 1 week (Estelita Vaz, Irene Brito)
- Ana Jacinta Soares, XXI International Conference on Transport Theory, Turin, Italy,
12-17/July
- Artur Alho, 12th Marcel Grossmann Meeting, Paris, France, 12-18/July
- Artur Alho, Mathematical Relativity in Lisbon, Lisboa, Portugal, 18-19/June
- Artur Alho, Spanish Relativity Meeting - ERE 2009, Bilbao, Spain, September
- Cristina Diogo, 7th International ISAAC Congress, London, UK, 13-18/July
- Cristina Diogo, 3rd International Workshop on Elementary Operators and their Applications, Belfast, Ireland, 14-17/April
55
- Estelita Vaz, Mathematical Relativity in Lisbon, Lisboa, Portugal, 18-19/June
- Estelita Vaz, Spanish Relativity Meeting - ERE 2009, Bilbao, Spain, September
- Filipe Mena, 12th Marcel Grossmann Meeting, Paris, France, 12-18/July
- Filipe Mena, Mathematical Relativity in Lisbon, Lisboa, Portugal, 18-19/June
- Filipe Mena, Spanish Relativity Meeting - ERE 2009, Bilbao, Spain, September
- Filipe Carvalho, XXI International Conference on Transport Theory, Turin, Italy, 1217/July
- Filipe Moura, Frontiers in Black Hole Physics at Dubna, Dubna, Russia, 25-30/May
- Filipe Moura, 12th Marcel Grossmann Meeting, Paris, France, 12-18/July
- Irene Brito, Mathematical Relativity in Lisbon, Lisboa, Portugal, 18-19/June
- Irene Brito, Spanish Relativity Meeting - ERE 2009, Bilbao, Spain, September
- Irene Brito, 12th Marcel Grossmann Meeting, Paris, France, 12-18/July
- Irene Brito, Mathematical Aspects of General Relativity, Oberwolfbach, Germany, 1117/October
- M. Piedade Ramos, Spanish Relativity Meeting - ERE 2009, Bilbao, Spain, September
- Teresa Malheiro, 7th International ISAAC Congress, London, UK, 13/July-18/July
1 Seminars
The group organises seminars on “Analysis, Geometry and Mathematical Physics” together
with the Geometry and Analysis group. A list of scheduled seminars for January and February
is in Section 2.
2 Short courses
- Quantum field theory in curved space and black holes, Filipe Moura (CMAT- Univ.
Minho), March-May (dates to be confirmed)
- “XTensor”, José Maria Martin (LUTH, CNRS, France), 10 hours, 8-14/February
• One day Meeting on Mathematical Physics, Univ. Minho, 20 participants, organisation:
Filipe Mena and Ana Jacinta Soares (main organisers)
56
External Funding
1 Projects Some members of CMAT are involved in research projects that receive financial
support from various sources. In this section, the name of the project, the financial source,
the members involved and the principal researcher are indicated. The budget for CMAT
members is also indicated.
- Kinetic Models and Applications, FCT project PTDC/MAT/68615/2006; Ana Jacinta
Soares (principal researcher Filipe Oliveira (UNL, Lisboa)); 2000 e for the visit of Ana
Jacinta Soares to the Univ. Paraná, Brazil
- Mathematical Problems of spacetime matching, CRUP/British Council, project B29/08, Filipe Mena (principal researcher), 3000 e
- Toeplitz operators, factorization and corona problems, FCT-MCTES project
(PTDC/MAT/81385/2006,) Teresa Malheiro and Cristina Diogo, principal researcher
Maria Cristina Câmara (CEAF, IST), from July 2007 for a period of 36 months
- Analysis of Nonlinear Partial Differential Equations, project FCT,
UTAustin/MAT/0035/2008, Ana Jacinta Soares, Fernando Miranda, Lisa Santos, J.M.
Urbano (principal researcher, CMUC, Univ. Coimbra), Budget: not yet known
2 Individual Grants
- Artur Alho, PhD grant from FCT, “Non-linear evolution and stability problems in
General Relativity”, 2750e (registration or tuition) and 980e/month
- Cristina Diogo, PhD grant from FCT, “Fredholm properties of Toeplitz operators and
generalized corona problems”, 2750e (registration or tuition) and 250e/month
- Filipe Carvalho, PhD grant from FCT, “Mathematical methods to solve the Boltzmann
equation extended to chemically reacting gases”, 2750e (registration or tuition) and
250e/month
Other Activities
Group members often give public talks at high schools and are regularly involved in administration at Univ. Minho.
57
Budget
Budget
9.700 e
8.370 e
16.730 e
500 e
1.500 e
350 e
1.500 e
Bibliography
1.550 e
TOTAL
40.200 e
8 Statistics and Applied
Probability
PhD FTE members
Name
Cecı́lia Azevedo (group leader)
Statistics and Applied Probability
Conceição Serra
Inês Sousa
Luı́s Machado
Marta Ferreira
Raquel Menezes
Susana Faria
PhD collaborators
Name
Manuela Gonçalves
Members without PhD
Name
Ana Paula Amorim
General Research Description
The group is interested in a number of areas of probability and statistics. Probability is mainly
used to model physical and biological phenomena. In statistics, the focus lies on modelling
phenomena using statistical models to explain available data. The aim is to explain data
58
59
using statistical models, thereby learning about the underlying processes that have produced
these data sets.
The research areas in which staff members are actively involved are:
• extreme value theory;
• branching processes;
• survival analysis;
• biostatistics;
• longitudinal data analysis;
• spatial and temporal statistics;
• nonparametric inference;
• generalized additive models and mixture models.
All the members of the group are involved in the research topic “Statistics in Medicine”
(for details see plan of activities of CMAT-FCT 2008).
This project involves also CINTESIS - Center for Research in Health Information Systems and Technologies and CI-IPOP - Research Center of the Portuguese Oncology Institute
- Porto.
Strong points:
Collaborations with other scientific research groups within the Univ. Minho, and outside,
such as, groups from the Univ. Santiago de Compostela (Spain), the Univ. Vigo (Spain),
the Univ. Lisboa (Portugal), the Univ. Nova de Lisboa (Portugal), the Univ. Coimbra (Portugal), the Lancaster Univ. (UK), the Univ. Copenhagen (Denmark), the Univ. Catholique
de Louvain (Belgium), Chalmers Univ. of Technology (Sweden) and Institute of Theoretical
Biology of Leiden Univ. (The Netherlands), Aalborg Univ. (Denmark), Univ. Federal Salvador da Baia (Brazil), Univ. Federal de Curitiba (Brazil), Liverpool Univ. (UK), Newcastle
upon Tyne (UK), Escola Nacional de Saúde Pública do Instituto FIOCRUZ (Rio de Janeiro,
Brazil), Univ. Valencia (Spain).
Research projects
Biomedical applications (Luı́s Machado)
In many medical studies, patients can experience several events through a follow-up period. If
the events are of the same nature this are usually referred as recurrent event, whereas if they
60
represent different states (i.e. multi-state models) they are usually modeled thought their
intensity functions. In our previous work we have developed new non-parametric estimation
methods for the estimation of several functions in a multi-state framework. Our aim is to
develop new nonparametric estimators in a progressive three-state model. Another issue
of interest is the development of new methods in ROC (Receiver Operating Characteristic)
analysis. In fact, some of the methods developed for the progressive three-state model (for
example, the bivariate distribution function) can be used in this context.
Collaborators: Carmen Cadarso (Univ. Santiago de Compustela, Spain), Jacobo de UñaAlvarez (Univ. Vigo, Spain), Javirr Roca (Univ. Vigo, Spain) snd Bruno Sousa (Instituto de
Higiene e Medicina Tropical, UNL)
Max-autoregressive processes in the modelling of extreme values (Marta Ferreira)
Max-autoregressive models have revealed very useful in the analysis of rare events based
on time series data, mainly in areas like hydrology, geophysics and finances. The maxautoregressive moving average processes (MARMA) introduced by Davis and Resnick (1989)
present similar paths to the heavy tailed ARMA, typically used in modelling stationary data
which exhibit sudden large peaks, like telephone signals and stock market prices. A satisfactory fit can be achieved with a MARMA for which deriving extremal features is easier than
for heavy tailed ARMA. The same happens with the Power Max-autoregressive processes
(pRARMAX) presented in Ferreira and Canto e Castro (2007, 2008), which are also interesting alternatives for modelling such data. A general approach based on minimizing the Bayes
risk in classification theory to fit a max-autoregressive model to a series of observed data, as
well as an analysis of it through simulation will be the subject of our study.
Collaborators: Luı́sa Canto e Castro, (DEIO-CEAUL, Univ. Lisboa).
Multitype branching processes escaping extinction (Conceição Serra)
Multitype branching processes have been used to study the probability that a virus placed
in a hostile environment escapes extinction via a chain of mutations. To escape extinction,
the virus tries to find a new form better adapted to the new environment and this is usually
achieved by mutations at certain positions of the genome. So far only discrete time processes,
the so called Galton-Watson processes, have been used to model the evolution of such populations and to describe the random path to escape, i.e., the chain of mutations leading to
an escape form of the virus (Sagitov and Serra, 2008). In the future we want to extend these
results to markovian continuous time and to age-dependent branching processes.
Collaborators: Patsy Haccou (Leiden, The Nederlands)) and Serik Sagitov (Gothenburg,
Sweden).
GLMs and environmental spatio - temporal applications (Manuela Gonçalves,
61
Raquel Menezes, Susana Faria)
In environmental monitoring networks, preferential sampling happens if there is a natural
inclination to place more monitors in areas classified as high risk for pollution. We plan
to submit for publication a new geostatistical model with the application to “Heavy-metal
biomonitoring in Galicia”. Moreover, we aim to study the performance of two proposed
non-parametric predictors, when considering data generated from a Poisson log-linear model
or a binomial logistic-linear model. We will also proceed with trend analysis methods for
environmental data using (Generalized) Linear Models.
Collaborators: P.Diggle and Ting-Li Su (Lancaster Univ.), P. Garcia-Soidán (Univ. Vigo), G.
Soromenho (Univ. Lisboa).
Monitoring and modelling environmental data (Manuela Gonçalves)
The aim of this project is to apply the state-space models and to develop new methods of
Multivariate Statistics Analysis to identify homogeneous groups of quality water monitoring
sites, based on comparison of temporal dynamics of the concentration of pollutants in the
surface water of a river basin. This comparison is performed using by considering the Kullback
information, like adopted in Bengtsson and Cavanaugh (2007). The purpose of our study is
to identify spatial and temporal patterns.
Collaborators: Teresa Alpuim and Marco Costa (CMAF, Univ. Lisboa).
On multiclass particles in TASEP (Cecı́lia Azevedo)
Consider the one dimensional Totally Asymmetric Simple Exclusion Process (TASEP) with
drift to the right start the configuration “all one” to the left and “all zero” to the right.
1. The site 1 is occupied by a second class particle. It was shown by Ferrari and Kipnis
that a Law of Large Numbers holds for this particle and the limiting distribution is a
Uniform. For this process we want to find the limit distribution for more general initial
conditions and even if a partial asymmetry is considered the same result should hold.
2. The origin of the process is occupied by a second class particle, site 1 is filled with a
third class particle and site 2 is filled with a fourth class particle. Based on the results
of our simulations studies, we intend to prove that the asymptotic probability of the
second class particle jumping over the fourth class particle is 7/12.
3. Also we want to establish lower and a upper bounds for the asymptotic probability of
the second class particle jumping over the particle of order m (m > 4) when the origin
of the process is occupied by a second class particle, site 1 is filled with a third class
particle, site 2 is filled with a fourth class particle, site 3 is filled with a fifth class
particle and so on.
62
Collaborators: Patrı́cia Gonçalves (CMAT-GATHA).
Real-time monitoring of progression towards renal failure: predict decline in
renal function in people with diabetes (Inês Sousa) We consider the problem of using
routinely collected primary care data to monitor the progression of undiagnosed incipient renal
failure in a large sample of people in primary care. Progression is characterised by a sustained
rise in serum creatinine, as determined from blood samples. We develop a dynamic model
to the longitudinal data, incorporating variability within and between patients, considering
repeated measurements from same subjects. The models described are non-stationary, but
we are focusing on two diagnostics for model checking when fitting the model. We use a
Kalman Filter algorithm which allows to calculate the conditional distribution of the random
processes at each time point, iteratively depending only on the previous observation, without
having to compute the marginal mean and variance at each time. The aim of this study was
to assess progression of CKD in people with diabetes according to their eGFR and presence
of albuminuria, in line with NICE,ADA and K/DOQI guidelines. We apply the methodology
to data sets available from Kent (UK) and Manchester (Hope Hospital, UK).
Collaborators: Peter J. Diggle (Lancaster Univ.), John New and Richard Hoefield (Vascular
Research Group, Salford Royal Hospital Foundation Trust, UK).
Advanced training
is also included.
Ana Paula Amorim, PhD, Probability and Statistics, Multivariate Survival Analysis;
New contributions in multivariate survival analysis; Jacobo Ua Alvarez, Univ. Vigo.
Summary: In this work, we consider the statistical analysis of gap times which are observed
under right-censoring. Specifically, we concentrate in the problem of estimating nonparametrically the bivariate distribution function of the gap times, as well as other functionals. To
improve the efficiency in the estimation, we use some presmoothing of the conditional probability of uncensoring given the observed information. Applications include correlation analysis
and regression.
- Luı́s Machado
Student: Ilı́dio Miguel de Sousa Andrade Pereira, Univ. Minho
63
- Luı́s Machado (co-supervision with Bruno Sousa)
Student: Ana Cristina T. Costa Pereira Silva, Univ. Minho
- Luı́s Machado and Raquel Menezes
Student: Alda Marisa Ribeiro Fernandes, Univ. Minho
- Manuela Gonçalves
Student: Sı́lvia Gabriela Machado Pontes, Lusı́ada Univ.
- Manuela Gonçalves
Student: Susana Luı́sa Vaz da Silva Lameiras, Univ. Minho
- Raquel Menezes
Student: Ana Cristina Fernandes da Silva, Univ. Minho
- Susana Faria
Student: Fátima Isabel Rodrigues Gonçalves, Univ. Minho
Scientific exchange
- Ana Paula Amorim, Univ. Vigo, 14 one-day visits
- Cecı́lia Azevedo, Univ. Vigo, 7 two days visits
- Conceição Serra, Department of Mathematical Sciences of Chalmers Univ. of Technology (Sweden), 3 months
- Conceição Serra, Leiden Univ. (The Netherlands), 3 months
- Inês Sousa, Lancaster Univ., UK, 3 ten days visits
- Luı́s Machado, Univ. Vigo, Spain, 7-one day visits
- Luı́s Machado, Univ. Santiago de Compostela, Spain, 7 one-day visits
- Manuela Gonçalves, Univ. Aveiro, Portugal, 7 one-day visits
- Manuela Gonçalves, Univ. Lisboa, Portugal, 5 one-day visits
- Marta Ferreira, Department of Statistics and Operations Research, Univ. Lisboa, 6
one-day visits
- Raquel Menezes, Univ. Vigo, 6 one-day visits
64
- Raquel Menezes, Univ. Santiago de Compostela, 3 one-day visits
- Susana Faria, Univ. Lisboa, 6 one-day visits.
- Ana Paula Amorim, Inês Sousa, EMS 2009 European Meeting of Statisticians, Toulose,
20-24/July
- Ana Paula Amorim, Raquel Menezes, IX Congresso Galego de Estadı́stica e Investigación Operativa, Ourense, October
- Ana Paula Amorim, Cecı́lia Azevedo, Conceição Serra, Inês Sousa, Luı́s Machado, Marta
Ferreira, Susana Faria, Raquel Menezes, XVII Congresso Sociedade Portuguesa Estatı́stica, Sesimbra, 30/September - 3/October
- Inês Sousa, Luı́s Machado, ISCB2009 International Society for Clinical Biostatistics,
Prague, Czech Republic, 23-27/August
- Inês Sousa, Raquel Menezes, IASC-ERS Summer School on Computational Aspects in
Environmental Statistics, Bulgária, 7-11/September
- Luı́s Machado, Int. Conf. on Simulation, Modelling and Optimization SMO’09, Budapest, Hungary, 3-5/September
- Luı́s Machado, Manuela Gonçalves, Applied Statistics 2009 - AS2009, Slovenia, 2023/September
- Manuela Gonçalves, Cecı́lia Azevedo, Raquel Menezes, The International Environmetrics Society-TIES 2009, Bologna, Italy, 5-9/July
- Manuela Gonçalves, Susana Faria, Amostragem Indirecta, Univ. Católica, Porto, Portugal, 16/January
- Manuela Gonçalves, Cecı́lia Azevedo, Missing Categorical Data Analysis, CEAUL, Lisboa, Portugal, January
- Marta Ferreira, 6th Conference on Extreme Value Analysis (EVA 2009), Colorado –
USA, 22-26/June
- Susana Faria, ASMDA 2009-Applied Stochastic Models and Data Analysis, Lithuania,
30/June-3/July
65
1 Seminars
The group organises seminars on “Computational Mathematics, Probability and Statistics”
together with the group COMAPP. A list of scheduled seminars for January and February is
shown in Section 2.
- “Branching processes and applications”, Univ. Minho, 15-17/April, 20 participants
expected, Conceição Serra
- “A short course in longitudinal data analysis”, Univ. Minho, 2-days workshop, June,
25 participants expected, Inês Sousa
External Funding
1 Projects
is also indicated.
- “Modelos aditivos generalizados en estudios de asociacion, prediccion y clasificacion.
Aplicaciones en medicina y biologia”. Ministerio de Educación y Ciencia (Espanha).
Fondos FEDER (Conv. Publica). Member involved: Luı́s Machado. Total budget:
88.300 e
- “Inferencia estadı́stica flexible: avances metodológicos y nuevas aplicaciones a la ingenieria, la economia, y las ciencias biomédicas” - MTM2008/2011-Spanish Ministry of
Education and Science. Member involved: Ana Paula Amorim. Total budget: 51600 e
2 Individual Grants
- Conceição Serra, Postdoc scholarship from FCT, “Branching Processes escaping extinction and its applications in Biology”, 6.250 e
Other activities
Group members often give public talks at high schools and are regularly involved in administration at University of Minho.
66
Budget
Budget
7.000 e
3.500 e
9.000 e
1.500 e
3.000 e
0e
0e
Bibliography
0e
TOTAL
24.000 e
9 List of members of the Research
Unit on December 31st
PhD FTE members
Name
General area of research - Research Group
Alberto Adrego Pinto
Dynamical Systems - GATHA
Ana Jacinta Soares
Kinetic Theory, Modelling - MathPhys
Assis Azevedo
Analysis and Differential Equations - GATHA
Carla Mendes
Semigroup Theory - ALC
Cecı́lia Azevedo
Statistics and Applied Probability - SAAP
Cláudia Mendes Araújo
Linear Algebra - ALC
Conceição Serra
Estelita Vaz
General Relativity - MathPhys
Fernando Miranda
Filipe Mena
General Relativity, Modelling - MathPhys
Filipe Moura
General Relativity, String Theory - MathPhys
Gaspar Machado
Modelling, Differential Equations - COMAPP
Inês Sousa
Irene Brito
João Caramalho Domingues
History of Mathematics - GATHA
José Carlos Costa
José Espı́rito Santo
Logic - ALC
José Joaquim Oliveira
Lisa Santos
Lucı́a Férnandez-Suárez
Algebraic Topology - GATHA
Lucile Vandembroucq
Luı́s Machado
Luı́s Pinto
Logic - ALC
Mahendra Panthee
67
68
M. Antónia Forjaz
Numerical Analysis - COMAPP
M. Elfrida Ralha
M. Fernanda Costa
M. Isabel Caiado
M. Joana Torres
M. Piedade Ramos
General Relativity - MAthPhys
Marta Ferreira
Patrı́cia Gonçalves
Paula Marques Smith
Semigroup Theory - SAAP
Paula Mendes Martins
Pawel Pilarczyk
Pedro Patrı́cio
Raquel Menezes
Rui Pereira
Rui Ralha
Matrix Computations - COMAPP
Susana Faria
Suzana Mendes Gonçalves
Thomas Kahl
Teresa Malheiro
Functional Analysis, Modelling - MathPhys
Wolfram Erlhagen
Robotics, Dynamical Systems - COMAPP
YuLin Zhang
PhD collaborators
Name
Ana Pereira do Vale
Geometry and Topology - GATHA
António Veloso
Carla Ferreira
Carlos Vilar
Jorge Figueiredo
José Francisco Rodrigues
Lurdes Teixeira
Manuela Gonçalves
M. Fernanda Estrada
Salvatore Cosentino
69
Members without PhD
Name
Ana Cristina Ferreira
Differential Geometry - GATHA
Ana Paula Amorim
Artur Alho
Carolina Ribeiro
Conceição Nogueira
Cristina Diogo
Functional Analysis, Modelling - MathPhys
Eliana Silva
Emanuel Sousa
Fabian Chersi
Filipe Carvalho
Kinetic Theory - MathPhys
Flora Ferreira
Florbela Fernandes
Helena Ferreira
João Nunes
João Paulo Almeida
José Manuel Oliveira
Geometry and Topology - GATHA
José Martins
Luı́s Louro
Robotics, Dynamical Systems - GATHA
Luı́s Miguel Ferreira
Dynamical Systems -GATHA
M. Rosário Fernandes
Miguel Vaz
Nzoji Hipólito
Paulo Pereira
Sofia Lopes
Vitor Mariano Sousa

Plan of Activities - CMat

Transcrição

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