ALGEBRA
The work developed sits within various areas of Algebra, intrinsically related, namely groups,
semigroups, languages and universal algebra. Computational algebra was also considered in two aspects:
using computational tools to prove new theorems and producing new software packages. More specifically,
we have considered:
 Synchronizing groups and primitive permutation groups applied to the study of transformation semigroups;
 Commuting graphs of semigroups;
 Non regular semigroups, namely onesided adequate, Ehresmann and restriction;
 Tiling semigroups;
 Classes of regular languages and profinite identities; decidability problems on regular languages;
 Entailment in duality theory;
 Canonical extensions of lattices and semilattices; profinite completions of semilattices;
 Applications of automated reasoning to various areas of algebra including: quasigroups/loops, semigroups, noncommutative lattices, combinatorics.
The team will continue to deepen the interaction between the theory of semigroups and
universal algebra with other areas of mathematics, namely groups, logic and theoretical computer science.
This includes, for example, the study of classes of regular languages, Heyting algebras, decibility problems,
and the interplay between semigroups of transformations and groups of permutations. We also aim at
developing applications of automated reasoning to areas of algebra linked to theoretical computer science;
this includes the production of new software packages for GAP and automated reasoning, and for the interplay of both these systems.
APPLIED AND NUMERICAL ANALYSIS
We developed work in several areas of applied and numerical analysis, including computational fluid dynamics, inverse problems, numerical methods for differential and
integral equations, and computational geometry. More specifically, we were successful in obtaining results:
 Existence and uniqueness of timeperiodic solutions with finite kinetic energy for the NavierStokes equations
 Fluidstructure interaction: new results on the motion of a rigid body with a cavity filled with viscous liquid
 Computational fluid dynamics implementation with meshless methods (2D and 3D).
 Meshless connection between the method of fundamental solutions (MFS) and RBF, and application to inverse source and obstacle problems.
 Determination of bilaplacian eigenvalues using the MFS.
 Multifrequency uniqueness for the reconstruction of a source.
 Analysis of the asymptotic behaviour of a singular boundary value problem, involving the degenerate pLaplacian: new numerical methods, application to the propagation of nerve impulses.
 Convergence results of piecewise collocation methods for weakly singular Cordial Volterra Integral Equations (VIEs) and nonlinear VIEs;
development and analysis of mathematical model for a homogenous immunoassay, the Fluorescent CapillaryFill Device.
 Advanced numerical schemes for ODEs with automatic global error control, able to produce numerical solutions with accuracy requested by the user (eg. Nordsiek methods).
 Exact computational geometry algorithms based on the idea of the method of orienting curves (in optimal control), for solving convex hull problem in 2D and in 3D.
Work will be developed in several areas of applied and
numerical analysis, including computational fluid dynamics, inverse problems, numerical methods for
differential and integral equations, and computational geometry. The main priority will be on research
problems with relevant engineering applications and challenging from the mathematical point of view.
MATHEMATICAL MODELING AND SIMULATIONS IN BIOMEDICINE
The research activity in this interdisciplinary area aimed at developing appropriate mathematical and numerical models for largescale
computational simulations of the human cardiovascular system. The main goal was to setup patientspecific
models built for virtual realistic geometries reconstructed from in vivo medical images, and to use highly
integrated and efficient numerical algorithms for their simulation at acceptable computational costs. This
required a close collaboration between mathematical and computational scientists, bioengineers, medical
researchers and clinicians. Research was centered on the following main topics:
 Multiscale modeling of the integrated circulatory system: analysis and simulation of FSI problems to model
blood flow in compliant vessels using nonNewtonian models for the blood and hyperelastic models for the
vessel wall mechanics; development of mathematical and numerical coupling strategies for the integration
3D models with a hierarchy of reduced FSI models associated to the multiscale approach of the
cardiovascular system.
 Morphology and flow in the cerebral vasculature based on patientspecific data: medical images acquisition
of patientspecific cerebral aneurysms using in vivo rotational Computed Tomography Angiography (CTA)
and 3T Magnetic Resonance Imaging (MRI); development of robust and efficient methodologies for medical
image processing of cerebral aneurysms; computational hemodynamics in idealized and patientspecific
cerebral aneurysms using High Performance Computing (HPC) inhouse software tools for the simulation of
FSI appropriate models; study of blood coagulation models combining biochemical and mechanical actions
in view of a better understanding of the occurrence of thrombosis in unruptured cerebral aneurysms;
sensitivity analysis of the numerical solutions to the computational domain, and rheological model choice.
The main goal will be the
development and analysis of mathematical models and algorithms for the computational simulation of
problems closely connected to vascular diseases, of clinical relevance, including: interpretation, processing
and 3D reconstruction from medical images, progression of cerebral aneurysms, inflammation and
thrombosis processes, and electromechanical activity of the heart. These activities will reinforce the
longstanding collaboration with bioengineers and medical doctors and will contribute to develop new ones.
STATISTICS AND STOCHASTIC PROCESSES
In broad terms, the research carried out in this area focused mainly on stochastic and
telecommunication networks, statistical inference on Internet networks,
multivariate analysis, robust statistics, biostatistics, and quality control. In particular, we have investigated:
 Queues with correlated input traffic and correlated services of interest in communication networks;
 Stochastic networks where different classes of individuals move according to some routing policy, showing
in particular that under some conditions on the parameters, in the limit, several stable equilibrium points;
 Analysis of multihop path reliability in Mobile Adhoc Networks (MANETs);
 Modeling of Internet traffic and estimation of Internet traffic from sampling traffic;
 Robust estimation and hypothesis testing in common principal components, and detection of influential
observations in principal components and common principal components;
 Robust linear regression methods, with a Rpackage code, in genomic association studies;
 Robust feature selection and robust principal component for Internet traffic anomaly detection;
 Stochastic ordering of the performance of quality control charts for simultaneous schemes for the mean and
covariance matrix of bivariate processes and misleading signals in simultaneous residual schemes for the
 Development of the new efficient applied methods and codes for maximum (or quasimaximum) likelihood
estimation of linear dynamic stochastic systems by using numerically stable Kalman filtering algorithms;
 New efficient applied methods and codes for the quasimaximum likelihood estimation of
financial timeseries model estimation (GARCH and stochastic volatility models).
The research will focus on several areas of applied statistics and stochastic processes, including: multivariate analysis, quality control, robust statistics,
mathematical finance, and stochastic and telecommunication networks. The research will be carried out in
close connection with engineers and economists, and there will be emphasis in producing codes
implementing the methods resulting from the research in widely used software packages like the R statistical
package.
In 20082012, CEMAT had 24 integrated members (on average), and CEMAT's publication record included:
 more than 200 papers published in about 100 international peer reviewed journals
 4 international research monographs
 132 papers in books and proceedings of international conferences
 edition of 8 books and journal special issues
 supervision of 17 PhD theses
Ten illustrative publications (20082012)
 C.J.S. Alves,
A.L. Silvestre, T. Takahashi, M. Tucsnak (2009)
Solving Inverse Source Problems Using Observability; applications to the EulerBernoulli Plate Equation.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION 48(3), 16321659.
 N. Antunes, Ch. Fricker, Ph. Robert, J. Roberts (2008)
Stochastic networks with multiple stable points.
ANNALS OF PROBABILITY 36(1), 255278.
 J. Araújo,
M. Kinyon, J. Konieczny (2011)
Minimal paths in the commuting graphs of semigroups.
EUROPEAN JOURNAL OF COMBINATORICS 32(2), 178197.

T. Bodnár, K. R. Rajagopal, A. Sequeira (2011)
Simulation of the threedimensional flow of blood using a shearthinning viscoelastic fluid model.
MATHEMATICAL MODELING OF NATURAL PHENOMENA 6(5), 124.

T. Bodnar, A. Sequeira, M. Prosi (2011)
On the shearthinning and viscoelastic effects of blood flow under various flow rates.
APPLIED MATHEMATICS AND COMPUTATION 217 (11), 50555067.

T.Diogo,
P. Lima (2008)
Superconvergence of collocation methods for a class of weakly singular Volterra integral equations.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 218(2), 307316.

F. Ferreira, A. Pacheco (2008)
Analysis of GI(X)/M(n)/N systems with stochastic customer acceptance policy.
QUEUEING SYSTEMS 58(1), 2955.

G. M. S. Gomes, V. Gould, (2011)
Left adequate and left Ehresmann monoids II.
JOURNAL OF ALGEBRA 348(1), 171195.

V. M. Lourenço, A. M. Pires, M. Kirst (2011)
Robust linear regression methods in association studies.
BIOINFORMATICS 27(6), 815821.

E. J. Sellountos, A. Sequeira (2008)
An advanced meshless LBIE/RBF method for solving twodimensional incompressible fluid flows.
COMPUTATIONAL MECHANICS 41(5), 617631.