Spatio-temporal modelling of environmental data

Programa Doutoral em Matemática e Aplicações.

Spatial-temporal modellization of the NO2 concentration data through geostatistical tools

The nitrogen dioxide is a primary pollutant, regarded for the estimation of the air quality index, whose excessive presence may cause significant environmental and health problems. In the current work, we suggest characterizing the evolution of NO2 levels, by using geostatisti- cal approaches that deal with both the space and time coordinates. To develop our proposal, a first exploratory analysis was carried out on daily values of the target variable, daily measured in Portugal from 2004 to 2012, which led to identify three influential covariates (type of site, environment and month of measurement). In a second step, appropriate geostatistical tools were applied to model the trend and the space-time variability, thus enabling us to use the kriging techniques for prediction, without requiring data from a dense monitoring network. This method- ology has valuable applications, as it can provide accurate assessment of the nitrogen dioxide concentrations at sites where either data have been lost or there is no monitoring station nearby.

Finite integration methods for isospectral flows

In this paper we consider the approximate computation of isospectral flows based on finite integration methods( FIM) with radial basis functions( RBF) interpolation,a new algorithm is developed. Our method ensures the symmetry of the solutions. Numerical experiments demonstrate that the solutions have higher accuracy by our algorithm than by the second order Runge- Kutta( RK2) method.

Development of procedures for the design, optimization and manufacturing of customized orthopaedic and trauma implants: Geometrical/anatomical modelling from 3D medical imaging

Tese de Doutoramento (Programa Doutoral em Engenharia Biomédica)