Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Loneliness in Middle and Old Age

Purpose of the research: (a) To identify the degree of much loneliness reported in the Portuguese population over 50 years of age and (b) test whether loneliness can be predicted by socio-demographic, health related or social characteristic of the sample other than age. Materials and methods: 1174 late middle age and older adults were interviewed face to face by different interviewers across the country; after the informed consent was signed, we asked the participants several socio-demographic and health-related questions; finally we asked ‘‘How often do you feel lonely?’’ and participants responded according to a five point Likert scale. Principal results: The results showed that 12% of participants reporting feeling lonely often or always, whereas 40% reporting never feeling lonely. The remaining 48% self-reported they felt lonely seldom or sometimes. Additionally, results show that, when taken together, variables such as marital status, type of housing, residence settings, health conditions, social satisfaction, social isolation, lack of interest, transportation, and age were predictors of loneliness. Major conclusions: (1) The association of loneliness with advanced age has been greatly exaggerated by mass media and common sense; (2) But although our findings did not confirm the most alarmist views, the 12% of older adults reporting that they are feeling lonely always or often should be cause for attention and concern. It is necessary to understand the meaning, reasons and level of suffering implied on those feelings of loneliness. (3) Our findings suggest that it makes no sense to construe age as a singular feature or cause for feelings of loneliness. Instead, age and also a number of other features combine to predict feelings of loneliness. But even with our predictor variables there was a substantial of variance left unexplained. Therefore it is necessary to continue exploring how feelings of loneliness arise from the experience of living and how they can be changed.

O skate como estímulo para a criação artística

O presente trabalho de projecto pretende, em primeira instância, a análise da cultura do Skate enquanto estímulo de novas atitudes ou movimentos num contexto artístico que engloba diversas disciplinas. Esta escolha possibilitou um estudo singular a par da produção criativa bem como pela dinamização e exploração de novos conceitos. É relevante a apresentação deste percurso, reflectindo o que foi concebido pela ambição de evidenciar este projecto enquanto tributo a uma cultura que está em contínua expressão. Deste trabalho de projecto faz parte um segundo volume que documenta conteúdos desenvolvidos no âmbito do projecto Deka.