Abstract
Centrality measures are used in network science to assess the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of the most well-known centrality measures for weighted networks, degree centrality, closeness centrality and betweenness centrality have solely assumed the edge weights to be constants. This article proposes a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed intervals (interval-weighted networks, IWN). We apply our centrality measures approach to two real-world IWN. The first is a commuter network in mainland Portugal, between the 23 NUTS 3 Regions. The second focuses on annual merchandise trade between 28 European countries, from 2003 to 2015.

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Objectives: Social isolation and loneliness among older people are widespread, with an impact on physical and mental health. Cycling Without Age (CWA) is an international cycling programme developed to minimise social isolation and loneliness in older people. It involves trishaw (electric bicycle) rides in the open air, led by volunteer riders. This study aimed to analyse the effects of CWA intervention on loneliness and social isolation among older people living in Porto, Portugal. Methods: Older adults (aged 55 years or older) living in the community or a nursing home were included. The intervention comprised at least four bicycle rides, with a duration between 30 and 60 min. A research protocol was applied before and after the intervention, which included the UCLA Loneliness Scale and the Abbreviated Lubben Social Network Scale. Results: A total of 47 participants (median age = 85 years) completed the intervention. Participants were mostly female (81%), widowed (66%) and living in nursing homes (72%). A statistically significant decrease in loneliness was found after the intervention (Median [IQR]_after = 24.0 [16.0] vs. before = 17.0 [6.0]; p < 0.05). Discussion: This preliminary work highlights the positive effect the CWA intervention may have on loneliness among older adults, which is consistent with other CWA programme studies. However, future research is required to evaluate whether these effects persist over time.

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Increasing scientific evidence supports an association between alexithymia and psychoactive substance use. This study explores alexithymia´s expression in sample of long-term drug users, undergoing outpatient treatment in public health units in Oporto, Portugal, as well as its´ association with social demographic risk factors. Data was collected from a sample of 90 adults, participants, mainly men (n=90; 87%), considered to be old consumers (81% with a age>40 years), with a mean age of 46.1 years (SD=8.3; range=21–64).Two instruments were used: a sociodemographic questionnaire and the 20-item Toronto Alexithymia Scale (TAS-20). More than 51.1% of the individuals were alexithymic, indicating a high prevalence of deficits in emotional awareness. The treatment period varied from 0 to 15 years, included a medication in 55% of cases, mostly methadone (83%). This profile illustrates the gradual aging of the long-term users of illicit drugs and alcohol with a clear diagnosis of an emotional disorder. Therefore, clinicians who develop treatment strategies may want to take into account the likelihood that many of their patients may be alexithymic; in being so, they should integrate specific psychotherapeutic techniques that promote both the identification and the differentiation in emotionally dysfunctional patients.

Abstract
IntroductionWilson's disease (WD) is associated with a variety of movement disorders and progressive neurological dysfunction. The aim of this study was to correlate baseline brain magnetic resonance imaging (MRI) features with clinical phenotype and long-term outcomes in chronically treated WD patients.MethodsPatients were retrospectively selected from an institutional database. Two experienced neuroradiologists reviewed baseline brain MRI. Functional assessment was performed using the World Health Organization Disability Assessment Schedule 2.0 (WHODAS 2.0) scale, and disease severity was classified using the Global Assessment Scale for Wilson's Disease (GASWD).ResultsOf 27 patients selected, 14 were female (51.9%), with a mean (standard deviation [SD]) age at onset of 19.5 (7.1) years. Neurological symptoms developed in 22 patients (81.5%), with hyperkinetic symptoms being the most common (70.4%). Baseline brain MRI showed abnormal findings in 18 cases (66.7%), including T2 hyperintensities in 59.3% and atrophy in 29.6%. After a mean (SD) follow-up of 20.9 (11.0) years, WD patients had a mean score of 19.2 (10.2) on WHODAS 2.0 and 6.4 (5.7) on GASWD. The presence of hyperkinetic symptoms correlated with putaminal T2 hyperintensities (p = 0.003), putaminal T2 hypointensities (p = 0.009), and mesencephalic T2 hyperintensities (p = 0.009). Increased functional disability was associated with brain atrophy (p = 0.007), diffusion abnormalities (p = 0.013), and burden of T2 hyperintensities (p = 0.002). A stepwise regression model identified atrophy as a predictor of increased WHODAS 2.0 (p = 0.023) and GASWD (p = 0.007) scores.ConclusionsAtrophy and, to a lesser extent, deep T2 hyperintensity are associated with functional disability and disease severity in long-term follow-up of WD patients.