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Name of the Research Unit: Centro de Matemática - CMAT uI D:13 | (L700013)

Coordinator: Luís Filipe Ribeiro Pinto

Main Scientific Domain: Mathematics

Other subdomains: Biomedics, Computer Science, Physics, Robotics

The Research Unit resulted from a merge of: Officina Mathematica

Host institutions

Leading Host Institution Universidade do Minho

Other Institutions n/a

Objectives and Achievements

Unit Description

CMAT is a research unit of the University of Minho that aims at promoting the development of scientific research in Mathematics and that is now applying for pluriannual funding from FCT. This Unit is a merger of two previous research units of Mathematics integrated in the Pluriannual Funding Programme for portuguese research units: CMAT and Officina Mathematica.

As a consequence of this new organisation and in accordance with indications from FCT, internal regulations were approved in order to organise the management of the Unit.

This research team has 68 members who, following a criteria defined in the regulations referred to above, are classified as PhD-qualified integrated members (FTE), PhD-qualified collaborators (C) and members who are not PhD-qualified (S). In accordance with scientific interests and affinities, the members of the Unit are organised in 5 Research Groups in the following areas: Algebra and Logic (10FTE, 1C, 1S); Analysis and Geometry (10FTE, 3C, 4S); Statistics and Probabilities (5FTE, 1C, 3S); Computational Mathematics (7FTE, 3C, 10S); Mathematical Physics (5FTE, 1C, 4S). The Unit is managed by 3 bodies: the Scientific Coordinator SCo, the Scientific Council SC (composed of all PhD-qualified members) and the Coordinating Committee CC (composed of the SCo, 3 members indicated by the SCo and the principal investigators of the groups). The CC directs and coordinates the research policy and plans the activities of the Unit. This committee is also responsible for the day-to-day management of the Unit. The annual and pluriannual plan of activities, the annual report and the annual budget are prepared by the CC for approval by the SC. Part of the funding awarded will meet general and strategic expenses of the Unit. These include the acquisition of bibliographic resources, the organisation of conferences and support for long-term visitors. The residual funding (about 60%) will be distributed to the 5 research

groups to support their activity. Within each group, the principal investigator is responsible for the budget in accordance with the plan of activities previously prepared and approved by the group. In the future the Unit will be accompanied by an Advisory Committee which will be composed of internationally recognised specialists from various fields of Mathematics.

General Objectives

The consolidation of scientifically coherent research groups with appropriate critical mass was a fundamental strategic goal of the merger with Officina Mathematica. This merger permitted an aggregation of researchers in the areas of Computational Mathematics, Mathematical Physics and Statistics and Probability. The Unit expects that the new organization of research groups will contribute to intensify the 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 intends to devote more attention to applications of Mathematics in other scientific and technological domains. All research groups have some of their objectives orientated towards applications, in some cases involving multidisciplinary teams. Having enforced the condition for continuing integrated-membership to be the publication of at least one refereed publication in the last three years, the Unit expects to improve the quality of its research, as well as its productivity. In order to guarantee this quality, it is important that the Unit maintains its international collaborations and invests in the creation and participation in other international networks. Another priority is the improvement of the scientific environment throughout the Unit. The following aspects are expected to be key contributions to this objective: -- the admission in 2007 of three doctors, on five year contracts, through the FCT national programme “Compromisso com a Ciência”; -- the increase of the number of long term visitors; in 2006 the overall expenditure across the Unit with this kind of activity represented 17% of the FCT funding; as this activity has already been fruitful, the aim is to increase this figure over the next four years; to this end a fixed percentage of the Unit’s annual budget will be devoted to the support of this activity; -- the consolidation of thematic seminars in the various areas of research; these seminars have had a great impact in 2006, and the increased number of researchers in the Unit is expected to facilitate this consolidation; -- a more regular organization of short courses and scientific events of national and international impact, such as specialised one day meetings or conferences; part of the Unit budget will be attributed to this activity. A further objective of the Unit is to increase the number of externally-financed projects with colleagues from national and international research institutions. The allocation of part of the budget to strategic investments, for example organization of conferences or the support of long-term visits, will diminish the number of individual actions which can be supported by the Unit and encourage more of its members to create or participate in externally-financed projects. The Unit expects to increase the number of graduate and post-graduate students engaged in its research projects. The two main contributions to this goal are: -- the new Doctoral (Ph.D.) Programme in Mathematics and Applications, set up in collaboration with the University of Aveiro; the first edition of this programme will start in October 2007; -- the award of short-term research grants (BIC’s and BI ’s) to undergraduate and graduate students in key areas (subject to project evaluation); a fixed percentage of the Unit’s annual budget should be reserved for these grants.

Main Achievements

During the period under evaluation, the members of the Unit have published 86 papers in international journals and 85 papers in refereed proceedings of international conferences. Training of graduates within the Unit has resulted in the qualification of 17 PhD and 42 MSc students .

These indicators represent a significative improvement in relation to the previous pluriannual period (1999-2002). The average number of publications in international journals per year and per integrated doctor increased about 20%, from 0,54 to 0,65. The average number of publications in proceedings of international conferences increased about 30%, from 0,49 to 0,64. The results for postgraduate training also improved with a significant increase of about 60% and 30% for PhD and MSc degrees respectively. In the following text, a list of selected research results obtained during the period under evaluation, illustrating the variety of the research carried out within the Unit, is presented. 1. In the context of the Singular Value Decomposition, a new algorithm for the reduction of a dense matrix to bidiagonal form was proposed (Linear Algebra and its Applications 358, 2003). This triggered further research by other specialists (two more papers have already been published). The algorithm is better suited to parallel computing (another two papers on this subject are already accepted by the SIAM J. of Matrix Analysis and Applications). 2. The concept of F-inverse semigroup was introduced by Wagner in 1961 and involves the well known natural partial order in inverse semigroups. The extension of this order to any semigroup (Mitsch, 1986) made the generalization to non-inverse semigroups possible. Members of the Unit introduced the concept of F-semigroup and developed a new theory. This opened a new field of research. Part of their work is published in J. Algebra 274 (2004). 3. Global existence and uniqueness of classical solutions for the Nordström-Vlasov system in 3 dimensions for large data was proved. The latter is a non-linear system of hyperbolic equations describing the motion of particles in a relativistic scalar theory of gravity. The result was obtained in 2 steps published in J. Differential Equations 204 (2004) and Communications in Mathematical Physics 260 (2006). 4. The H lder regularity of the invariant distributions for horocycle flows described by Flaminio and Forni (Duke Mathematical J. 2003) has been studied (Nonlinearity 18, 2005). Observations of this work were used by Anantharaman and Zelditch (Annales Henri Poincaré 2007) to understand the semiclassical quantization of geodesic flows and the Quantum Unique Ergodicity problem. 5. Three members of the Unit and P. Ghienne (Université d’Artois, France) have developed a method to compute a homotopy invariant measuring the topological complexity of robot motion planning problems. Their work has been published in Algebraic & Geometric Topology 6 (2006) and has been presented in an invited talk at the interdisciplinary conference Topology and Robotics 2006 held at ETH Zürich. 6. A dynamical system based control architecture for autonomous robots that takes into account experimental data from Cognitive Neuroscience (Brain Research 1083, 2006) has been developed and validated within the context of several multi-disciplinary projects. The architecture builds on the existence and stability analysis of specific solutions of Dynamic Fields formalized by nonlinear integro-differential equations (J. Neural Engineering 3, 2006).

Activities

I ntegrative/ multidisciplinary activities in the 2003-2006 period

The projects undertaken by members of the Unit include various collaborations with research centres in areas other than Mathematics, both at the internal level, with other centres of the University of Minho UM, and at the external level, with research centres of other national and foreign institutions. A description of the main multidisciplinary research activity by area is presented below. -- Probability and Statistics: The members in this area carry out research typically focused at the interface between methodology and applications such as Biostatistics, Geostatistics, Point Processes, Branching Processes, Extreme Value Theory, Nonparametric Estimation and Trend Analysis Methods for Environmental Data. This research promotes strong interdisciplinary connections. The members in this area are collaborating with other groups within the UM like GESTAP (Grupo de Estatística Aplicada) and outside with researchers from Universities in various countries (Santiago de Compostela, Vigo, Copenhagen, Louvain-la-Neuve, Leiden and Chalmers Technology).

-- Robotics: Within the context of multidisciplinary European projects, mathematical models based on dynamical systems theory have been developed. These models allowed to link two completely distinct areas of research: Cognitive Neuroscience and Robotics. The mathematical models were used to explain data obtained in experiments with humans and other primates. At the same time they were

validated as part of the control architecture of autonomous robots with the ultimate goal to advance towards physical machines with near human levels of perception, cognition and action capacities. The projects bring together researchers from various Universities (Parma, T-Munich, Nijmegen, Edinburgh) and Max-Planck Institutes (Tübingen, Nijmegen).

-- Logic: The work in Proof Systems and Programming is multidisciplinary in nature, aiming at obtaining application to programming of the study of proof systems. Specifically, the task is concerned with fundamental issues in reasoning about (the implementation of) functional programs, like types, termination, continuations, and explicit substitution. These concerns have led to collaborative work with computer scientists, for example at the Informatics Department of UM or INRIA Sophia Antipolis, resulting in published papers and participation in European networks like TYPES and APPSEM II . -- Computational Mechanics: The members in this research area focused most of their activity on subjects that are multidisciplinary, the emphasis being on topics such as piezoelectric materials, bio and solid mechanics, transonic flows and molecular dynamics in polymers. Researchers of the Universities of Santiago de Compostela, Manchester, and UM (Mechanics and Polymer Departments) collaborate in this work. --Numerical Linear Algebra: Some of the research on efficient algorithms for the computation of eigensystems of large matrices has been motivated by mathematical models of problems studied by colleagues from Centro de Física of UM. Examples of these problems are the calculation of energy transfer in certain media, electronic spectra and the vibration of nanoparticles. --Topology: Joint work of three members of the Geometry and Topology group and P. Ghienne (Université d’Artois) have led to results concerning the motion planning problem in robotics, which have been presented at the interdisciplinary conference Topology and Robotics 2006, ETH Zürich.

Outreach activities in the 2003-2006 period

The Unit has organized various outreach activities whose main objective was to foster a closer relationship with the local population, particularly school teachers and young students. Most of the activities were intended to underline the relevance and impact of Mathematics in daily life. Among them: -- Public lectures and exhibitions at UM: The activities included open lectures of broad interest for a general public at UM, for example: a) Unit members participated in the “Fascinating World of Science 2004” (initiative of the UM School of Sciences), by organizing an exhibition and giving a series of talks intended to raise public awareness of Mathematics. b) Open day: Every year, there is an open day at UM, when schools are invited to visit its departments, attend talks and see exhibitions. -- Short courses at UM: During the academic year 2006, several members organized short courses for secondary school teachers, for example: a) Dynamical Systems for Mathematics teachers; b) Initial data analysis and data modulation with software R.

As a result of the interest expressed by attendees, further courses are planned for 2007. Furthermore, the following course was organized for medical doctors in 2003: “Statistical Methods in Health: an introduction to SPSS.”

--Colloquia at UM: In 2006 the Unit has started to organize monthly colloquia by renowned national and foreign mathematicians for a wide university public.

Apart from these activities, which took place within the facilities of the Unit, many of its members were also involved in: -- Activities for school students: several members visited schools located within the region of Minho to present more than 30 talks to students of ages from 12 to 18; Unit members organized, together with the Department of Electronics of UM, the ROBOTICA06 initiative, oriented to 10 to 18 year old students, which included public talks and robot competitions;

-- Activities in other public institutions: Unit members gave public talks and workshops outside schools and universities, for example: “Teaching Geometry and Applications”, which took place at the Cultural Centre of Paredes de Coura. They have also been engaged in activities of national organizations such as the Portuguese Mathematical Society and the “Ciência Viva” programme.

-- Press contacts: the public events were publicized prior to occurrence and most of them were subsequently reported in local and regional papers; members of the Unit have given interviews/demonstrations to the national, local and university press (newspapers, tv and radio) about general activities going on at the Unit; the press has taken a special interest in applied areas such as the mathematical modelling of brain functions and robotics, which, from our experience, are topics suited to communicate the importance of Mathematics for modern societies.

In view of the success of those events, a series of similar and extended activities will be implemented during 2007-2010. Examples of new strategies include: hosting the national competition of Mathematical Games for school students; participating in the project “Sentidos da Ciência” (financed 90,000 Euros) of the UM School of Sciences to promote science to the general public; developing the national programme “Census Vivo” (financed 25,000 Euros) directed to high schools and whose objective is to introduce a series of activities raising awareness of the importance of statistics in daily life.

Future vision of the Unit’s activities for the period 2007-2010

The opportunity created by the merger of the teams of CMAT and Officina Mathematica should play a central role in the future development of the Unit. The reinforcement of the areas of Computational Mathematics, Mathematical Physics and Statistics and Probability, and the relevance of these areas for applications, is expected to lead to an increased visibility of the research produced in the Unit.

An increased impact of the research carried out in the areas of Differential Equations and Dynamical Systems, due to the recent integration of new senior members in each of these areas, is also expected.

The admission of three doctors under the FCT programme “Compromisso com a Ciência” in the areas of Analysis, Mathematical Physics and Semigroup Theory will have a major impact in the future activity in these areas. In all cases, the contracted researchers should help in establishing connections between different topics of research in the Unit. In the subsequent two editions of this Programme, the Unit intends to submit new applications in selected areas. The number of FTE's will increase during the period 2007-2010. At least 3 members should complete their PhD's until the end of 2007. The new PhD program in Mathematics and Applications, set up in collaboration with the University of Aveiro, should also play an important role in future development of the Unit, since a significant increase in PhD thesis supervision is expected. A significant part of the research carried out in the Unit will be oriented at applications in Science and Engineering. Indeed, three of the five research groups (Mathematical Physics, Statistics and Probability and Computational Mathematics) are essentially concerned with Applied Mathematics. The two groups covering areas of Pure Mathematics also pursue some research activities relevant to applications. The work in Logic and Semigroup Theory, for instance, has important applications in Computer Science. I t should also be mentioned that the members working in Algebraic Topology intend to continue their work on applications of Topology in Robotics and Computer Science and that members working in Dynamical Systems have already significant work in Game Theory and applications in Financial Mathematics, Industrial Organization and Medical Sciences. Some of the Unit’s research will be carried out within multidisciplinary projects. Examples are the joint project of the group on Statistics and Probability with the Portuguese Institute of Oncology and the project in Robotics which involves different mathematical and non-mathematical disciplines.

The increment in size of the Unit will contribute to the consolidation of the seminars in different research areas, which in turn should help to increase the scientific coherence of the research groups. I t is also hoped that the seminars stimulate scientific exchange between members of different groups. Such an exchange could even lead to new interdisciplinary collaborations in subjects such as Robotics or Biology in which various mathematical disciplines are relevant. The members of the Unit believe that the increase in the research indicators, observed in the period 2003-2006, will continue in 2007-2010. In 2007, members have already published 18 papers in international journals and 15 papers in proceedings of international meetings and 10 papers have been accepted for publication in international journals. The Unit will maintain its engagement in outreach activities as illustrated at the end of the previous section.

Future Networking activities in the 2007-2010

Resource and equipment sharing: In the framework of the project SeARCH (Services and Advanced Research Computing with HTC/HPC clusters – FCT) the Unit shares a computational infrastructure with the Computer Science and Physics research units of UM. There is also a consortium involving the Mathematical Research Centres of the Universities of Minho, Évora and Madeira for the subscription of the MathSciNet database. Joint Doctoral Programme: The new Doctoral program in Mathematics and Applications starting in 2007-08 was set up in collaboration with the Department of Mathematics of the University of Aveiro and is expected to contribute to increase research interchange with CEOC and UIMA (Aveiro). Scientific networking: Several research groups will be involved in projects with members of other portuguese research units. Among them: -- Probability and Statistics: The group will work with the Portuguese Oncology Institute (IPO) and the Research Centre of Technology and Information Systems in Health (CINTESIS), by using and developing statistical methods to investigate trends in incidence, mortality, and survival rates of several cancers in the North of Portugal. -- Robotics: Within the multidisciplinary FCT project “Anthropomorphic robotic systems: control based on the processing principles of the human and other primates’ motor system and potential applications in service robotics and biomedical engineering” robotics hardware was bought. The robotics platform is the base for current and future projects which involve researchers from three UM units: Mathematics, Algoritmi and Psychology. Group members will also participate in the Portuguese Network of Computational Biology headed by the Gulbenkian Institute for Science. -- Numerical Linear Algebra: In the field of eigenvalues computation, we interact with colleagues from the University of Porto; in particular, we collaborate in the organization of the Workshop and Advanced School EPSA2007 (Eigenvalue Problems: Software and Applications). Also, some of our research on efficient algorithms is motivated by mathematical models studied at the UM Physics Centre. -- Dynamical Systems: A Unit member leads the 2004-07 FCT project “Dynamical Systems and Applications” and the 2007-08 Spanish-Portuguese Integrated Action project “Game theory”. The projects involve collaborations with researchers of the Polytechnic Institute as well as of the Faculties of Nutrition, Engineering and Science of the University of Porto. -- Algebra: Group members participate with researchers from the Universities of Porto, Aveiro and Coimbra, in various projects including: the 2007-10 FCT project “Automata, Semigroups and Applications”; the French-Portuguese Integrated Action “Automata, profinite semigroups and symbolic dynamics” of the PESSOA Program; the ESF programme “AutoMathA (Automata: from Mathematics to Applications)”, a multidisciplinary programme at the crossroads of Mathematics, theoretical computer science and applications, financed by 16 organizations from 14 countries. -- History of Mathematics: Manuscripts of José Anastácio da Cunha (1744-1787) have been found at the Public Library of Braga by a group member, and a network of portuguese researchers on History of Mathematics from the Universities of Minho, Porto, Coimbra, Lisboa and Évora has been set up in order to study them. A conference on this subject has recently been organized at UM and future networking activities are planned.

General I ndicators

2003 2004 2005 2006

Nº of Researchers (FTE)* 29 31 33 40

Masters Completed in the Period 13 6 8 15

PhDs Completed in the Period 3 4 6 4

Research Groups

Group Title Principal Investigator

1(2003-2010)

Algebra, Logic and ComputationMaria Paula Beirão de Oliveira Marques Smith

2(2007-2010)

Statistics and Applied Probability (SAAP)Cecília Maria Vasconcelos Costa e Castro de Azevedo

5(2007-2010)

Mathematical Physics and Modelling (MathPhys). ana jacinta pereira da costa soares

6(2003-2007)

Computational Mathematics and Applications (COMAPP) Rui Manuel Silva Ralha

7(2003-2007)

History and Epistemology of Mathematics and Calculus Education (HISEPCALC)

Maria Elfrida Ramos de Matos Ralha

8(2003-2007)

Non-linear evolution, Modelling and Stability problems in Mathematical Physics (MathPhys)

ana jacinta pereira da costa soares

9(2003-2007)

Probability and Dynamical Systems (DYNPRO)Cecília Maria Vasconcelos Costa e Castro de Azevedo

9(2007-2010)

Computational Mathematics and Applications (COMAPP) Rui Manuel Silva Ralha

10(2003-2007)

Geometry and Topology (GEOTOP) Lucia Fernandez-Suarez

11(2003-2007)

Statistics in the North (SIN) Bruno Cecílio de Sousa

12(2003-2007)

Exact solutions of Einstein's equations in General Relativity (GR Solutions) Estelita da Graça Lopes Rodrigues Vaz

13(2003-2007)

Computational and Theoretical Mechanics (Mechanics) Jorge Manuel da Silva Figueiredo

14(2003-2007)

Project Optimization and Control (POpCon) Fernando Armenio da Costa Castro e Fontes

15(2003-2007)

The Dynamical Field Approach to Cognition (DyFACo) Wolfram Erlhagen

16(2007-2010)

Geometry and Analysis: Theory, History and Applications (GATHA) Lisa Maria de Freitas Santos

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Group Description

Research Unit: Centro de Matemática - CMAT uID:13 | (L700013)

Group Name/Designation: Algebra, Logic and Computation Principal Investigador: Maria Paula Beirão de Oliveira Marques Smith Time Interval: (2003-2010) Location of Group (Host Institution): Universidade do Minho Keywords: Matrix theory; Semigroup structures; Semigroups and automata; Structural proof theory Funding, source, dates: - FCT (Pluriannual base + progammatic); 115 458,44 (2003/2006)

- Spanish DGI (Grant number BFM2001-0081-C03-02); 1 500 ¼�� - FCT (POCTI/32817/MAT/2000); 6 337,60 ¼�� - European Union (TYPES, Coord. Action 6th FP 510996); 5 250 ¼�� - European Union (APPSEM-II, IST 38957); 3 000 ¼��) - European Union (TYPES, IST 29001); 2 000 ¼�� - FLAD (Proj.L-V-685/2005); 600 ¼��

- FCT (FACC 05/1/820); 850 ¼�� - FLAD (Proj.L-V-318/2003); 1 180,48 ¼��

PI and Researchers Researchers in the Group (Ph.D. Only) (CV) Carla Albertina Carvalhinho da Silva Mendes (CV) José Carlos Cruz da Costa (CV) José Carlos Soares do Espírito Santo (CV) José Pedro Miranda Mourão Patrício (CV) Luís Filipe Ribeiro Pinto (CV) Maria Cláudia Freitas de Sousa Mendes Araújo (CV) Maria de Lurdes Azevedo Teixeira (CV) Maria Paula Beirão de Oliveira Marques Smith (CV) Maria Paula Freitas de Sousa Mendes Martins (CV) Maria Suzana Freitas de Sousa Mendes Gonçalves Other Researchers in the Group (Ph.D. Only) (CV) António Augusto Veloso da Costa Other Researchers in the Group (non Ph.D.) (CV) Conceição Veloso Nogueira Objectives and Achievements General Objectives Characterisation and decidability problems in algebraic and logic structures were studied. The objectives of these studies were proposed in accordance with the four tasks identified below. Further information can be found in http://www.cmat.uminho.pt/algebralogica Matrix completion problems We aimed to determine whether there exists a completion of a given partial matrix lying in some classes of partial matrices, involving positive definiteness and signed principal minors. We also aimed to characterize the pseudo-equivalence of a block triangular matrix

over a regular ring, and its block diagonal matrix, in terms of suitable Roth conditions and to express the latter in terms of the solvability of matrix equations. Decidability problems on finite semigroups One of the most promising ideas to prove decidability results is the notion of tameness of a pseudovariety. The main objective of this task was to study this important notion and various degrees of it and to explore its applications to decidability problems. We intended to prove tameness of various pseudovarieties, namely pseudovarieties defined by common operators such as semidirect product and join. Structure and order properties of semigroups In the semigroup literature, regular semigroups have attracted more attention than any other class of semigroups. The main objective of this task was to study specific classes of regular semigroups, namely, unary semigroups with an associate subgroup, semigroups having an homomorphic group image and transformation semigroups. We aimed to show that their structural and order-properties deserve a thorough treatment. Proof systems and programming The main goals set for the task were: the definition of extensions of the lambda-calculus in Curry-Howard correspondence to sequent calculi; the study of some fundamental properties of these extensions, namely confluence and termination of the normalisation procedure; the investigation of these systems in connection to foundational aspects of functional programming such as substitution and sharing, continuations, and pattern-matching. In the area of type systems with constructor subtyping mechanisms, the goal was to study decidability of type checking and type inference. Main Achievements In 2003-2006, this group published 23 papers in peer review journals and 3 papers in proceedings of international conferences and presented 18 talks at international conferences. During this period, the following results were achieved. Matrix completion problems In this task, members - characterized the lower triangular matrices, with a regular diagonal over a ring, which are equivalent to its diagonal - proved the existence of an N-matrix completion of partial N-matrices whose associated graphs are 1-chordal, undirected or directed cycles and acyclic - characterized the partial DN-matrices with associated p-chordal graphs that admit a DN-matrix completion Decidability problems on finite semigroups It was proved that

- the pseudovariety R of finite R-trivial semigroups is completely tame and has decidable pointlike sets - the pseudovariety LSl of finite local semilattices is tame - various joins involving R, or the pseudovariety J of finite J-trivial semigroups, or some locally trivial pseudovarieties are tame or completely tame - the join RvG is decidable, where G is the pseudovariety of groups Structure and order properties of semigroups Members described - unary semigroups with an associate subgroup and all homomorphisms and congruences on such semigroups - a new class of semigroups with a special homomorphic group image - all congruences on semigroups generated by partial (injective) nilpotent transformations - two natural orders on a partial transformation semigroup and their meet and join - Green’s relations and maximal subsemigroups of some linear transformation semigroups, as well as isomorphisms between these semigroups Studies on Ockham algebras and on double Ockham algebras, leading to a Ph.D. degree, were also completed. Proof systems and programming Members defined - extensions of the lambda-calculus giving a Curry-Howard interpretation of sequent calculus for intuitionistic implicational logic together with results on confluence and strong normalisation for reduction, permutative conversions and the characterisation of several classes of normal forms (some of them new) - a mechanism for ensuring termination of recursive functions, based on a simple size annotation of types, explored by various authors for termination of type theories with inductive types Productivity Publications in peer review Journals (3000 ca.) (Up to a max of 10. Always indicate at the end of the citation, impact factor of the journal (IF=) and number of citations (nº C=). Give title and full citation in original language. DO NOT translate) For each of the following publications we indicate the impact factor IP from ISI 2006 and the Mathematical Citation Quotient MCQ from MathSciNet 2005. The number of citations, NC, refer to citations by authors of papers that are referred in those two data bases. [P1] C. Mendes Araújo, Juan R. Torregrosa and Ana M. Urbano, “The N-matrix completion problem under digraph assumptions”, Linear Algebra and its Applications, 380 (2004), 213-225 (IP=0,585; MCQ=0,478; NC=1)

[P2] C. Mendes Araújo, Juan R. Torregrosa and Ana M. Urbano, “N-matrix completion problem”, Linear Algebra and its Applications, 372 (2003), 111-125 (IP=0,585; MCQ=0,478; NC=3) [P3] C. Mendes, “Complemented congruences on Ockham algebras”, Algebra Universalis, 54 (2006), 279-290 (IP=0,230, MCQ=0,304; NC=1) [P4] E. Giraldes, Paula Marques-Smith, H. Mitsch, F-Regular Semigroups, J. Algebra 274 (2004), 491-510 (IP=0,568, MCQ=0,498; NC=2) [P5] G. Barthe, M. J. Frade, E. Giménez, L. Pinto, T. Uustalu: “Type-based termination of recursive definitions”, Mathematical Structures in Computer Science, nº 14(2004), 97-141 (IP=1,102, MCQ=0,189; NC=18) [P6] José Carlos Costa, “Biinfinite words with maximal recurrent unbordered factors”, Theoretical Computer Science, nº 290 (2003), 2053-2061 (IP=0,843, MCQ=0,237; NC=2) [P7] José Carlos Costa and Lurdes Teixeira, “Tameness of the pseudovariety LSl”, International Journal of Algebra and Computation, nº 14 (2004), 627-654 (IP=0,357, MCQ=0,474; NC=2) [P8] M. Paula Marques-Smith, R.P. Sullivan, Congruences on semigroups generated by injective nilpotent transformations, Bull. Austral. Math. Soc. 74 (2006), 393-409 (IP=0,266, MCQ=0,293; NC=0) [P9] P. Patricio, R.E. Hartwig and R. Puystjens, “Diagonalizing matrices via orthogonal Pierce decompositions”, Linear Algebra and Its Applications, 401 (2005), 381-391 (IP=0,585 MCQ=0,478; NC=0) [P10] S. Mendes-Gonçalves and R. P. Sullivan, Baer-Levi semigroups of linear transformations, Proc. Royal Soc. Edinburgh, 134A (2004), 477-499 (IP=0,684, MCQ=0,556; NC=2) Other publications (3000 ca.) (Include only Books, chapters or full papers published in conference proceedings up to max of 10. Give title and full citation in original language) [O1] C. Mendes Araújo, S. Mendes-Gonçalves, P. Mendes Martins and P. Patrício, "Actas do Encontro de Algebristas Portugueses 2005", CMAT (2006), ISBN: 989-95122-0-6

[O2] J. Espírito Santo and L. Pinto, “ Permutative conversions in intuitionistic multiary sequent calculus with cuts” , M. Hoffman (ed.), Proc. of 6th Int. Conf. on Typed Lambda Calculi and Applications (TLCA 2003), Lecture Notes in Computer Science vol. 2701, Springer (2003), 286-300, ISBN 3-540-40332-9 [O3] J. Espírito Santo and L. Pinto, “ Confluence and strong normalization of the generalised multiary lambda-calculus” , S. Berardi, M. Coppo, F. Damiani (eds.), Revised selected papers from the Int. Workshop TYPES 2003, Lecture Notes in Computer Science vol. 3085, Springer (2004), 194-209, ISBN: 3-540-22164-6 [O4] J. Espírito Santo, M. J. Frade, and L. Pinto, “ Structural proof theory as rewriting” , F. Pfenning (ed.), Proc. of 17th Int. Conf. on Rewriting Techniques and Applications (RTA 2006), Lecture Notes in Computer Science vol. 4098, Springer (2006), 197-211, ISBN: 3-540-36834-5 [O5] M. Paula Marques-Smith, “ Ordens parciais em semigrupos de transformações” , Actas do Encontro de Algebristas Portugueses 2004, Departamento de Matemática da Universidade de Trás-os-Montes e Alto Douro (2005), 105-117, ISBN: 972-669-669-0 [O6] P. Patrício, “ Matrizes EP: de Schwerdtfeger aos dias de hoje” , Actas do Encontro de Algebristas Portugueses 2004, Departamento de Matemática da Universidade de Trás-os-Montes e Alto Douro (2005), 73-88, ISBN: 972-669-669-0 Master and Ph.D. thesis completed (3000 ca.) During 2003-2006, the following members of this research group completed their doctorate. The member, the title of the thesis, the date of completion and the university that awarded the degree are identified. - António Veloso, PhD Mathematics, “ G-produtos de monóides e semigrupos” , February 2003, Universidade do Porto - Carla Mendes, PhD Mathematics, “ Estudos em álgebras de Ockham e em álgebras de Ockham duplas” , December 2005, Universidade do Minho - Cláudia Mendes Araújo, PhD Mathematics, “ Uma contribuição para o estudo de problemas de completamento de matrizes” , November 2004, Universidade do Minho The members of the group involved in supervision of post-graduate students during 2003-2006 are identified below. The name of the student, the degree, the title of the thesis, the university that awarded the degree and the date of completion are also indicated. - Ana Margarida da Gama Correia Martins, supervised by Pedro Patrício, MSc Mathematics, “ Elementos de Criptologia: uma aplicação da Álgebra” , Universidade do Minho, March 2006 - Ana Sofia Figueiredo, supervised by Luís Pinto, MSc in Mathematics, “ Construção de contra-modelos em Lógica Porposicional Intuicionista” , Universidade do Minho” , March 2003 - Carla Bernardete Delgado Josefino, supervised by Paula Mendes Martins, MSc Mathematics, “ Semigrupos Regulares Principalmente Ordenados” , Universidade do Minho, May 2006

- Carlos Monteiro, supervised by Luís Pinto, MSc in Mathematics, “ Caracterizações semânticas e dedutivas da Lógica Proposicional Bi-intuicionista", Universidade de Trás-os-Montes e Alto Douro, December 2006 - Conceição Veloso Nogueira, supervised by José Carlos Costa, MSc Mathematics, “ O problema da palavra-omega para pseudovariedades de semigrupos” , Universidade do Minho, July 2006 - Cristina da Silva Alves, supervised by Paula Mendes Martins, MSc Mathematics, “ Sobre o semigrupo de endomorfismos de um conjunto ordenado” , Universidade do Minho, June 2004 - Márcia Lopes Eiras, supervised by Emília Giraldes, MSc Mathematics, “ Semigrupos com Inversos Máximos” , Universidade de Trás-os-Montes e Alto Douro, 2003 - Maria Paula Montenegro Vieira Cardoso, supervised by Emília Giraldes, MSc Mathematics, “ Semigrupos Regulares Naturalmente Ordenados com Idempotente Máximo” , Universidade de Trás-os-Montes e Alto Douro, 2006 - Nuno Paulo Sousa Costa Patrício, co-supervised by Emília Giraldes, MSc Mathematics, “ Monoides Finitamente Gerados” , Universidade dos Açores, 2006 - Paulo Jorge Ferreira de Medeiros, co-supervised by Emília Giraldes, PhD Mathematics, “ Relações de ordem compatíveis em semigrupos ?-regulares” , Universidade dos Açores, 2006 - Paulo José Martins Vasco, supervised by Emília Giraldes, MSc Mathematics, “ Semigrupos Regulares e E-unitários” , Universidade de Trás-os-Montes e Alto Douro, 2004 - Sílvia Araújo Pereira, supervised by Emília Giraldes, MSc Mathematics, “ Semigrupos de Dubreil-Jacotin e Semigrupos de Dubreil-Jacotin Generalizados” , Universidade de Trás-os-Montes e Alto Douro, 2005 - Sílvia Filipa Carvalho, supervised by José Carlos Costa, MSc Mathematics, “ Um estudo do operador supremo sobre pseudovariedades de semigrupos” , Universidade do Minho, July 2005 Patents/propotypes (2000 ca.) n/a Organization of conferences (2000 ca.) Reflecting the research interests of the members of this project, a regular seminar, four conferences and three short courses were organised. Seminars In addition to 10 seminars by members of the group, the following seminars by visiting researchers were presented. - Substitution - surprising challenges with inductive families, R. Matthes (CNRS and Université de Tolouse III) - On the importance of normalization for typed rewrite systems, R. Matthes (CNRS and Université de Tolouse III)

- A sequent calculus with derivations isomorphic to those in Gentzen’s natural deduction, Jan von Plato (University of Helsínquia) - Fundamental Order Relations on Semigroups, B. Schein (University of Arkansas) - Monóides Solúveis, V. H. Fernandes (Universidade Nova de Lisboa) - Recursive coalgebras from comonads, T. Uustalu (Institute of Cybernetics, Tallinn) - Skew pairs of idempotents in regular semigroup, T. S. Blyth (University of St. Andrews) - Power bounded matrices, R. Hartwig (NCSU, USA) - Proof theoretic methods in linear lattice theory, R. Dyckhoff (University of St Andrews) - Generalised Transformation Semigroups, B. Sullivan (UWA, Australia) - Inclusion-Exclusion (All you should know!), R. Hartwig (NCSU, USA) Conferences - C. Mendes Araújo, S. Mendes Gonçalves, P. Mendes Martins and P. Patrício, organising committee, “ Encontro de Algebristas Portugueses 2005” , Univ. Minho, 22nd-24th September 2005 http://w3.math.uminho.pt/~eap2005/ - J. C. Costa and L. Teixeira, organising committee, “ International Meeting on Semigroup Theory and Related Topics” , Univ. Minho, 25th-28th June 2003 http://w3.math.uminho.pt/imapst/imapst.html - J. C. Espírito Santo, member of the organising committee, “ Jornada de Ciências da Computação” , Univ. Porto, 14th June 2006 http://wiki.di.uminho.pt/twiki/bin/view/Events/JCC/2006 L. Pinto, member of the organising committee, “ Days in Logic 04” , Univ. Minho, 22nd-24th January 2004 http://w3.math.uminho.pt/~dil2004/ Short courses - Lectures on Proof Analysis, S. Negri, Univ. of Helsinky, 18th-29th September, (2006); duration: 9 hours - Uma Introdução ao GAP, M. Delgado, Univ. of Porto, 31st October, 7th and 14th November (2006); duration: 6 hours - Cycle of Lectures on Algebra, T. Laffey, Univ. College Dublin, Ireland, 4th-16th December (2006); duration: 9 hours Industry contract research (2000 ca.) n/a Internationalization (2000 ca.) (Collaborative publication, Research, Graduate Training Networks or other forms of participation of the Research Group at the international level) Between 2003 and 2006, 23 papers were published in international journals by the 11 members of the Algebra and Logic research group. Almost 75% of these publications were co-authored by collaborators from other countries. This level of international

collaboration and projection of scientific results brings considerable benefit to members of the research group. At the present time one researcher from the group participate in a bilateral project funded by Program PESSOA, “ Automata, profinite semigroups and symbolic dynamics” , and 5 researchers participate in two european netwoks: - TYPES, on type theory, where University of Minho is a sub-site coordinated by a member of the group (2 members); - AutoMathA, in automata theory (3 members). Members are also involved in different joint work with research staff from 7 countries (Australia, Germany, , Belgium, Spain, Estonia, France, USA) Future Research Objectives This group carries out research in the domain of Algebra and Logic, with projects involving matrix theory, semigroup theory, structural proof theory and applications to: Computer Science, in the fields of functional programming, automata and formal languages, and information theory, in the algebraic theory of convolutional codes. Since the beginning of 2007, 13 papers have been published or accepted for publication in international journals or refereed proceedings of international conferences. Proposals for future research have been prepared on the basis of previous achievements and exploratory studies. Matrix completion problems 1. To develop research concerning Drazin invertibility of a sum of ring elements with certain properties and its connection to the (Dedekind) finiteness of the ring, using the same reasoning as in [P8] 2. To characterise complex matrices which are power-bounded via Frobenius Normal Form and (1,1)-Focal matrices 3. To study recent applications of algebra to information theory 4. To study the class of partial N0 -matrices and the related matrix completion problem, based on the use of combinatorial methodology, extending the work [P2] 5. To characterise the admissible sign pattern matrices of special classes of real matrices as P-matrices, M-matrices, inverse M-matrices an N-matrices Decidability problems on finite semigroups To continue the research on algorithmic properties of semigroups and its applications to computation. Some specific problems to explore are - tameness or complete tameness (two notions stronger than decidability) of the pseudovarieties of groups, p-groups, aperiodic semigroups and semigroups in which regular elements are idempotents

- preservation of (complete) tameness under various operators ([F1] contains foundational work in this direction). For instance, if tameness were preserved by semidirect product and the pseudovariety of aperiodic semigroups were tame, then the Krohn-Rhodes complexity problem would be solved Structure and order properties of semigroups 1. To study properties of transformations semigroups: - to pursue the algebraic study of all total transformations of a set X that preserve a reflexive and symmetric binary relation on X - to investigate maximal inverse subsemigroups of linear transformation semigroups defined over an infinite-dimensional vector space and related ideas - to describe meets and joins and upper and lower covers of partial transformations under various partial orders ([F3]) 2. To continue the work developed in [F4], in order to characterise the (free) monogenic unary semigroups with an associate subgroup which identity element is a medial idempotent of S 3. To initiate the study of semigroups containing an associate inverse subsemigroup, investigating a possible connection with inverse transversals ([P4]) Proof systems and programming To study the meta-theory and applications to functional programming of proof and type systems in the sequent calculus format, together with the corresponding lambda-calculi; three sub-goals are - to extend the work [O4] on normal forms for sequent calculus, to cover all forms of cuts - to extend to classical logic and dependent types the recent work [F2] on continuation passing-style translations and strong normalisation of intuitionistic sequent calculi - to develop the theory and applications of “ delayed substitutions” , moving from the recent applications in proof theory to applications in reasoning about functional programs Funding, source, dates In order to meet the goals indicated for 2007-2010, this group has received financial support from FCT, through Programa de Financiamento Plurianual. The research of some members of the group will also be partially supported by other sources, through external projects. In relation to the financial support provided by FCT for 2007, this research group received 17.365,10¼��FRUUHVSRQGLQJ�WR��RI�WKH�total funding for 2007). It is expected that the remaining amount will be paid in July. In addition to these funds, the amount of 10.267,46¼��FRUUHVSRQGLQJ�WR��RI the total funding for 2006 and paid by FCT in the end of 2006, was also available. So, the funding already available is 27.632,56¼��WKH�SHQGLQJ�IXQGLQJ�EHLQJ��¼�

In relation to external funding, the following projects also provide financial support for the research of 5 members of the group: - FCT: This funding is provided for the project ASA, PTDC/MAT/65481/2006, and involves group members J. C. Costa, L. Teixeira, A. Veloso and C. Nogueira. The project was started in April 2007 and will terminate in March 2010. It involves 17 researchers from the Universities of Minho, Porto, Aveiro and Coimbra. The support attributed to the whole project for the period 2007-2010 is 52 000,00 Euros; - European Union: This funding is provided via the project TYPES - Coordination Action 510996 of the 6th Framework Programme and involves group members J. Espírito Santo and L. Pinto. University of Minho is a sub-site of the Project, coordinated by L. Pinto. The sub-site involves also M.J. Frade, a member of the Informatics Department of Univ. Minho. Previous publications in the area To achieve the objectives proposed for the period 2007-2010, in addition to [P2], [P4], [P5], [P8], [P9] and [O4], the following publications are also relevant. [F1] Jorge Almeida, José Carlos Costa, Marc Zeitoun, “ Tameness of pseudovariety joins involving R” , Monatshefte für Mathematik, nº146 (2005), 89-111. (IP=0,439, MCQ=0,396; NC=1) [F2] J. Espírito Santo, R. Matthes, L. Pinto, Continuation-passing style and strong normalisation for intuitionistic sequent calculi, in S. Ronchi Della Rocha (ed.), Proc. of 8th Int. Conf. on Typed Lambda Calculi and Applications (TLCA 2007), Lecture Notes in Computer Science vol. 4583, Springer, (2007), 133-147, ISBN 978-3-540-73227-3 (IP=0,402 (ISI2005); NC=0) [F3] M. Paula Marques-Smith, R.P. Sullivan, Partial orders on transformation semigroups. Monatsh. Math. 140 (2003), 103-118 (IP=0,439, MCQ=0,396; NC=1) [F4] Paula Mendes Martins, Petrich, Mario, Unary semigroups with an associate subgroup, accepted for publication in Communications in Algebra (2006) (IP=0,268, MCQ=0,298) [F5] Pedro Patrício, R.E. Hartwig, “ On Roth's pseudo equivalence over rings” , Electronic Linear Algebra, 16 (2007), 111-124 (MCQ=0,221) Special Requirements Most of the papers published by members 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 4 years, a significant portion of the financial support attributed to the project was used to finance both medium and long-duration visits (3 visits of 1 month each, 1 visit of 2 months and 4 visits of 3 months each). This proved to be a successful strategy which the members of the group feel should be re-applied and extended. In 2006, the group organized 3 short courses on areas of interest to the members, providing an opportunity to diversify the panel of invited visitors and broaden the research experience of the group. In order to continue with this strategy, additional support for the delivery of (or attendance at) short courses on topics related to members’ activities would also constitute a useful contribution to the development of the group. A major improvement in the research performance of the group would be achieved by a reduction in the annual teaching and administration load of active researchers.


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Group Description

Research Unit: Centro de Matemática - CMAT uI D:13 | (L700013)

Group Name/Designation: Computational Mathematics and Applications (COMAPP)

Principal Investigador: Rui Manuel Silva Ralha

Time Interval: (2007-2010)

Location of Group (Host Institution): Universidade do Minho

Keywords: Mathematical modelling ; Bio-mechanics; Robotics; Matrix computations

Funding, source, dates: n/a

PI and Researchers

Researchers in the Group (Ph.D. Only)

(CV) Anwar Hussein

(CV) Gaspar Jose Brandao Queiroz Azevedo Machado

(CV) Maria Fernanda Pires da Costa

(CV) Rui Manuel Silva Ralha

(CV) Rui Miguel Soares Pereira

(CV) Wolfram Erlhagen

(CV) zhang yulin

Other Researchers in the Group (Ph.D. Only)

(CV) Carla Maria Alves Ferreira

(CV) Jorge Manuel da Silva Figueiredo

(CV) Maria Antónia PAulo Dias Pereira Forjaz

Other Researchers in the Group (non Ph.D.)

(CV) Carolina Paula Baptista Ribeiro

(CV) Chersi Fabian Nestore

(CV) Eliana Oliveira da Costa e Silva

(CV) Florbela Alexandre Pires Fernandes

(CV) Luís Filipe de Castro e Freitas Louro

(CV) Maria do Rosario Ribeiro Fernandes

(CV) Miguel José Lopes Rodrigues Martins Vaz

(CV) NZOJI EUSTÁQUIO AGOSTINHO HIPÓLITO

(CV) Paulo Alexandre da Silva Pereira

(CV) Sofia Oliveira Lopes


General Objectives

n/a

Main Achievements

n/a

Productivity

n/a

Future Research

Objectives

The mission of the group is to develop new techniques of mathematical modelling, mathematical analysis, and numerical algorithms for solving problems in applied areas. This includes the study of mathematically well formulated problems known from the literature. However, we also want to bring the communication between Mathematics, Engineering and Science to a new level by actively participating in collaborative projects which first require the development of an adequate mathematical model. 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 constitute 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 Neuroscience. 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.

Many of the above mentioned 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 the computation of eigenvalues and singular values of large matrices, very much in the spirit of the LAPACK and ScALAPACK libraries. 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 development 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. Together with colleagues from the Civil Engineering Dep., we recently submitted to the European Commission another multidisciplinary project: Climate Change Impacts Assessment in Agriculture (CCIAA). Group members will develop a large scale computational model of the Douro basin river for the prediction of water and energy fluxes.

Funding, source, dates

European project “JAST-Joint Action Science and Technology”, Ref. IST-2-003747-IP, Responsible Wolfram Erlhagen and Estela Bicho (Dep. of Industrial Electronics), total funding for UM 560 000 Euro, 10/2004-12/2008. FCT project “Learning to read the motor intention of others: towards socially intelligent robots”, POCI/V.5/A0119/2005, 65 000 Euro, 08/2007-12/2008. The partners are Estela Bicho (DEI) and Leonardo Fogassi (Neurobiology, University of Parma, Italy) Travel grant “Modeling the dynamics of activity patterns in primary visual cortex”, Acções Integradas Luso-Alemãs, Ref. Acção N. A-12/06,

5 000 Euro, 2006-2007. Project partners are Dirk Jancke and Christian Igel at the University of Bochum, Germany. From FCT (Programa Plurianual) 25 500 Euro for 2007.

Previous publications in the area

W. Erlhagen and E. Bicho, The dynamic neural field approach to cognitive robotics, Journal of Neural Engineering 3:R36-R54, 2006 (published by the Institute of Physics since 2004, thus far more than 500 full paper downloads from the European Network of Excellence “euCognition” webpage http:/ /www.eucognition.org/ ). W. Erlhagen and G. Schöner, Dynamic field theory of motor preparation, Psychological Review, 109 (2002), 545-572. (IP ISI06= 8.825, citations= 39). G. Machado and L. Trabucho, Some Results in Topology Optimization applied to Biomechanics, International Journal of Computers and Structures, 82, 17 – 19 (2004), 1389 – 1397. ( IP ISI06= 0.846, citations= 0). R. Ralha, One-sided reduction to bidiagonal form, Special issue on accurate solution of eigenvalue problems, Linear Algebra and its Applications, 358 (2003), 219-238. (IP ISI06= 0.585, MCQ MSN05= 0.223, citations= 4). C. Campos, D. Guerrero, V. Hernandez, R. Ralha, Parallel Bidiagonalization of a Dense Matrix, accepted for publication in SIAM Journal of Matrix Analysis and Applications (to appear in 2007).

Special Requirements

The group wants to develop mathematical models and new mathematical techniques for solving applied problems, in close cooperation with colleagues from Engineering and Science. We plan to organize a workshop with high-level researchers (or either to invite high-level researchers) with experience in multi-disciplinary projects.



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Group Description


Group Name/Designation: Geometry and Analysis: Theory, History and Applications (GATHA)

Principal Investigador: Lisa Maria de Freitas Santos



Keywords: Differential Equations; Dynamical Systems; Geometry and Topology; History of Mathematics


PI and Researchers


(CV) Alberto Adrego Pinto

(CV) Ana Maria Almeida Santos Pereira do Vale

(CV) João Manuel Caramalho de Melo Domingues

(CV) Lisa Maria de Freitas Santos

(CV) Lucia Fernandez-Suarez

(CV) Lucile Vandembroucq

(CV) Maria Elfrida Ramos de Matos Ralha

(CV) Maria Joana da Costa Cruz de Oliveira Torres Ramos

(CV) Salvatore Cosentino

(CV) Thomas Walter Kahl


(CV) Carlos Alberto da Silva Vilar

(CV) José Francisco Silva Costa Rodrigues

(CV) Maria Fernanda de Oliveira Gonçalves Estrada


(CV) Ana Cristina Castro Ferreira

(CV) José Joaquim Martins Oliveira

(CV) José Manuel Ribeiro Oliveira

(CV) Maria Isabel Rocha Ferreira Caiado


General Objectives

n/a

Main Achievements

n/a

Productivity

n/a

Future Research

Objectives

The main research interests of this group are Analysis, Dynamical Systems and their interdisciplinary applications, Differential Geometry, Algebraic Topology, History and Epistemology of Mathematics. Among the members of the group, there are four doctoral students: one has already submitted her thesis, one is in an advanced stage, and two are in an intermediate stage. One vacancy has been advertised for a research position in Analysis within the FCT program "Compromisso com a Ciência''.

Senior members of the group are currently supervising Master, Doctoral and Postdoctoral research. The research in Analysis is developed essentially on ODE's and PDE's. We emphasize the following topics: to find conditions for the global asymptotic stability of an equilibrium point of a n-dimensional system of delay differential equations; to study forced elastic systems (described by a hyperbolic partial differential equation), extending tools of chronological calculus to derive Floquet theory for time-periodic hyperbolic PDE's; to study existence, regularity and asymptotic behavior of solutions of nonlinear evolutive systems of equations or variational inequalities involving operators of type p-Laplacian and p-Rot. The research in Dynamical Systems extends from pure mathematics to interdisciplinary applications. We plan to understand the spectral stability of semigroups of stochastic dynamical systems and the quantization of disordered dynamical systems, to study the geometry of infinitely renormalizable Henon maps, to develop a theory of pseudo-diffeomorphisms in C r new flat structures and to finish a book on Fine Structures of Hyperbolic Diffeomorphisms already accepted to be a Springer Monograph. We pursue interdisciplinary applications to epidemiology, neurology, immunology, financial mathematics and industrial organization. We also plan to produce interactive material for general public and schools in dynamical systems and applied mathematics. The research in Differential Geometry includes the continuation of a project with IST and the University of Évora on Quaternionic Kahler manifolds and a project in Generalized Geometry aiming to reformulate the results of Bismut on the index theorem. The work in Algebraic Topology deals with Homotopy Theory, and more precisely with H-spaces, homotopy and homology of manifolds, numerical homotopy invariants and rational homotopy theory. Applications of Algebraic Topology in other research areas such as Robotics or Concurrency Theory are also studied.

The research on History and Epistemology of Mathematics is focused mainly on the 18th century European Mathematics (Analysis and Geometry) and on the reform conducted, at that time, on the Portuguese educational system. Research work conducted during the past two years with colleagues from the Departments of Mathematics of Porto, Coimbra and Lisboa will also be pursued.


32.200 euros of FCT Pluriannual Funding of 2007. 10000 euros, Sistemas Dinâmicos e Aplicações, FCT POCTI/MAT/55954/2004-2007.

3000 euros, Integrated Action Luso-Espanhola in Game Theory, 2007-2008.


A. Azevedo, J.-F. Rodrigues and L. Santos, The N-membranes problem for quasilinear degenerate systems, Interfaces Free Bound, 7 (2005), no. 3, 319-337. ISI06-IP= 1.091 MSN05-MCQ= 0.580 nº C= 1 S. Cosentino, A note on Holder regularity of invariant distributions for horocycle flows, Nonlinearity 18 (2005), no.6, 2715-2726.

ISI06-IP= 1.288 MSN05-MCQ= 0.548 nº C= 1 E. de Faria, W. de Melo and A. Pinto, Global hyperbolicity of renormalization for C r unimodal mappings, Annals of Mathematics (2) 164 (2006), no. 3, 731-824. ISI06-IP= 2.426 MSN05-MCQ= 1.992 nº C= 0 T. Faria, E. Liz, J.J. Oliveira and S. Trofimchuk, On a generalized Yorke condition for scalar delayed population models, Discrete Cont. Dyn. Sys. 12 (2005), no.3, 481-500. ISI06-IP= 1.087 MSN05-MCQ= 0.406 nº C= 6 L. Fernández-Suárez, P. Ghienne, T. Kahl and L. Vandembroucq, Joins of DGA modules and sectional category, Algebr. Geom. Topol. 6 (2006), 119-144. ISI06-IP= n.a. MSN05-MCQ= 0.708 nº C= 1


In the last year, some of us started a project aiming to introduce students and teachers to modern topics in mathematics, such as dynamical systems. We developed interactive computational material to be used in the classroom and also suited for general public. I t would be important, in order for the project to grow, to set up a small team working for the project. The team should include a full time system manager and programmer, and should be equipped with a server.



Visão Global

Group Description


Group Name/Designation: Mathematical Physics and Modelling (MathPhys).

Principal Investigador: ana jacinta pereira da costa soares



Keywords: Differential Equations.; General Relativity.; Kinetic Theory.; Modelling.


PI and Researchers


(CV) ana jacinta pereira da costa soares

(CV) Estelita da Graça Lopes Rodrigues Vaz

(CV) Filipe Artur Pacheco Neves Carteado Mena

(CV) Maria da Piedade Machado Ramos

(CV) Simone Carmelo Calogero


(CV) Maria Teresa Mesquita da Cunha Machado Malheiro


(CV) Cristina Isabel Correia Diogo

(CV) Filipe Manuel Sampaio Carvalho

(CV) Irene Vitória Ribeiro de Brito

(CV) João Carlos Oliveira Nunes


General Objectives

n/a

Main Achievements

n/a

Productivity

n/a

Future Research

Objectives

This group intends to study different topics concerning the mathematical modeling, consistency and stability properties of some nonlinear problems in leading areas of Mathematical Physics, namely general relativity and kinetic theory. All the considered problems are motivated by physical phenomena and have therefore important applications, from both theoretical and practical points of view.

The group also intends to exploit the interplay between kinetic theory and relativity and study some problems involving the non-linear differential equations of Einstein-Boltzmann. In order to do that, a postdoctoral research fellow will be hired in September 2007 on a 5 year contract within a FCT national Programme. The group is engaged in collaborations with members of the geometry and analysis group maintaining a joint seminar. We also intend to continue our strategy of inviting long term visitors, integrate young researchers and keep a high level of internationalisation. In 2007-08 we intend to host a small workshop on mathematical physics and in 2009-10 an international conference. Some details are described bellow. General relativity:

a) to investigate elasticity properties for several classes of space-time metrics , in particular for warped and double warped spacetimes; to apply the 1+ 3 formalism to elasticity theory in General Relativity;

b) to obtain existence, uniqueness and stability results for some spacetime matching solutions; c) to study the (linear and non-linear) stability of steady states for the Vlasov-Einstein system and the global regularity of solutions in three dimensions and the future null asymptotics of isolated solutions for the Vlasov-Maxwell system; d) to study invariant properties of pure radiation metrics with a cosmological constant; to develop a simple method for determining the isometry group structure and the explicit form of the Killing vectors for spacetimes previously obtained via application of a special formalism.

Kinetic theory: e) to obtain existence and stability results for BGK equations for chemically reacting gases; to study the influence of the chemical reaction on the solution to the Boltzmann equation; to study linear stability of the steady detonation.


(2007-2008) Project Relativistic Elasticity, external founding (including approximately 11000 Euros from Acções integradas luso-espanholas). Universidade do Minho and Universitat de les I lles Balears (Spain). FCT plurannual funding for 2007: 12885 Euros. Total: 23885 Euros.


1) E Vaz, M P Machado Ramos and J Carot, Double-warped space-times, J Math Phys, V 44 (2003) pp 4839-4865. Citations 3

IP ISI06 = 1.018 MCQ MSN05= 0.311 2) S B Edgar and M P Machado Ramos, Obtaining a class of type N pure radiation metrics using invariant operators, Classical Quantum Gravity, V 22 (2005) 791-802. Citations 4 IP ISI06 2.773 MCQ MSN05= 0.093 3) G Kremer, M Pandolfi Bianchi and A J Soares, A relaxation kinetic model for transport phenomena in reactive flow, Phys. Fluids, V 18 (2006) 037104 (15 pages). Citations 0

IP ISI06= 1.697 MCQ MSN05= 0.044 4) P Tod and F C Mena, Matching of spatially homogeneous non-stationary space-times to vaccum in cylindrical symmetry, Physical Review D, V 70 (2004) 104028 (9 pages). Citations 2. IP ISI06= 4.896 MCQ MSN05= 0.055 5) S Calogero, Global Small Solutions of the Vlasov-Maxwell System in the Absence of Incoming Radiation. Indiana Univ Math Journal 53, 1331-1364 (2004) Citations 5 (2 MS + 3 ISI) IP ISI06= 1.029 MCQ MSN05= 0.908


Funding for updating software such as Maple. This software is used by three members of the group.



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Group Description


Group Name/Designation: Statistics and Applied Probability (SAAP)

Principal Investigador: Cecília Maria Vasconcelos Costa e Castro de Azevedo



Keywords: biostatistics; geostatistics; branching processes; nonparametric estimation


PI and Researchers


(CV) Bruno Cecílio de Sousa

(CV) Cecília Maria Vasconcelos Costa e Castro de Azevedo

(CV) Luis Filipe Meira Machado

(CV) Raquel Menezes da Mota Leite

(CV) Susana Margarida Ferreira De Sá Faria


(CV) ARMINDA MANUELA ANDRADE PEREIRA GONCALVES


(CV) Ana Paula Costa da Conceição Amorim

(CV) Maria da Conceição Soares Serra

(CV) Marta Susana Ribeiro Ferreira


General Objectives

n/a

Main Achievements

n/a

Productivity

n/a

Future Research

Objectives

In longitudinal studies of disease the sequentially ordered events (gap times) are often of interest. Our aim is to develop a new nonparametric estimator for the bivariate distribution function of the gap times. Some related problems as estimation of the marginal distribution of the second gap time will be discussed. Another issue of interest is the development of new techniques in the multi-state framework. The Markov assumption is typically assumed for the inference in multi-state models. This may be checked by including covariates in the modelling process. Our main interest is to develop new methods for testing this assumption. Working together with the Portuguese Oncology Institute (IPO) we propose to investigate trends in incidence, mortality, and survival rates of childhood cancers in the North of Portugal. Considering different statistical methods we hope to be able to predict the evolution of some type of these cancers and what are the regions of major incidence for the next 5 to 10 years. Cancers in the esophagus, stomach, colon, liver, and pancreas causes billions of deaths all over the world. The increased incidence of this type of cancers in the North of Portugal, is well known . Our goal is to investigate the environmental causes. In this task the group will be involved together with members from other research groups such as the Centro de Investigação do IPO-Porto and the Centro de Investigação em Tecnologias e Sistemas de Informação em Saúde – CINTESIS.

It is common knowledge that breast cancer risk increases with a multitude of reproductive factors. In this cohort study with approximately 260,000 women registered in the North of Portugal, we intend to perform an exploratory data analysis to check for any possible patterns in this population. After this, and with the help of different statistical tools, such as Cox Regression Analysis, we will study the different risk factors in breast cancer disease. This study will involve the collaboration of the School of Medicine at the University of Coimbra and has also the potential to promote new contacts with similar studies being done in Spain and therefore increasing the relevance and scope for the Iberian Peninsula.

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 apply a proposed geostatistical model to two real data sets. 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. The theory of extreme values under the evidence of temporal dependence in the majority of the variables of interest, is promoting results in contexts of dependence. Our aim is to study max-autoregressive series and to apply the results to estimation of probabilities of rare events and return periods. Evolution of populations, may they be cells, pieces of DNA, organisms, etc, is suitably modelled with branching processes. We use these stochastic processes to study populations that, due to a small reproductive ratio, are doomed to extinction but where mutations occurring during the reproduction allow them to escape extinction. We obtained results for simple reproduction and mutation schemes, and will generalize to more complex situations.


This research group is an union of some elements of DynPro (3/5 of total) and all the elements of SIN. The research group DynPro, in relation to the financial support provided by FCT for 2007, received 7.456,68

�

(corresponding to 50% of the total funding for 2007). It is expected that the remaining amount will be paid in July. In addition to these funds, the amount of 3.876,80

�

, corresponding to 30% of the total funding for 2006 and paid by FCT in the end of 2006, was also available. So, for DynPro, the funding already available is 11.333,58

�

and the pending funding is 7.456,78

�

. In what concerns to SIN , in relation to the financial support provided by FCT for 2007, received 5.400

�

, corresponding to 50% of the total funding for 2007. This new group SAAP, has (from DynPro and SIN) already available 12.200,147

�

and pending 9.874,068

�

.


Faria, S., Melfi, G.; “LAD Regression and Non parametric Methods for Detecting Outliers and Leverage Points”, Student, 5, p. 265-272, 200

Meira-Machado, L., Cadarso-Suárez, C., de Uña-Àlvarez, J.; “An R library for the analysis multi-state survival data”, Computer Methods and Programs in Biomedicine, 86:131-140, 2007

IP ISI06= 0.624, MCQ MSN05= NA, citations= 0 Menezes, R., Garcia-Soidán, P., Febrero-Bande, M.; “A kernel variogram estimator for clustered data”, Scandinavian Journal of Statistics (in press), 2007 IP ISI06= 0.903, MCQ MSN05= 0.291, citations= 0 Serra, M.C., Haccou, P.; "Dynamics of escape mutants", Theoretical Population Biology, 72(1):167-178, 2007 IP ISI06= 2.491, MCQ MSN05= NA, citations= 0.

Sousa, B., Michailidis, G.; “A Diagnostic Plot for Estimating the Tail Index of a Distributions”, Journal of Computational and Graphical Statistics, vol. 13, no. 4, pp. 974-1001(28),2004.

IP ISI06= 1, MCQ MSN05= 0.142, citations= 3.


To carry out this future research program we need symbolic and numerical software, computers and, at least, one PhD Student.


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