Dynamic probabilistic constraints under continuous random distributions

The paper investigates analytical properties of dynamic probabilistic constraints (chance constraints). The underlying random distribution is supposed to be continuous. In the first part, a general multistage model with decision rules depending on past observations of the random process is analyzed. Basic properties like (weak sequential) (semi-) continuity of the probability function or existence of solutions are studied. It turns out that the results differ significantly according to whether decision rules are embedded into Lebesgue or Sobolev spaces. In the second part, the simplest meaningful two-stage model with decision rules from L2 is investigated. More specific properties like Lipschitz continuity and differentiability of the probability function are considered. Explicitly verifiable conditions for these properties are provided along with explicit gradient formulae in the Gaussian case. The application of such formulae in the context of necessary optimality conditions is discussed and a concrete identification of solutions presented. © 2020, The Author(s)

The Maristán stigma scale: a standardized international measure of the stigma of schizophrenia and other psychoses

Background: People with schizophrenia face prejudice and discrimination from a number of sources including professionals and families. The degree of stigma perceived and experienced varies across cultures and communities. We aimed to develop a cross-cultural measure of the stigma perceived by people with schizophrenia.Method: Items for the scale were developed from qualitative group interviews with people with schizophrenia in six countries. The scale was then applied in face-to-face interviews with 164 participants, 103 of which were repeated after 30 days. Principal Axis Factoring and Promax rotation evaluated the structure of the scale; Horn’s parallel combined with bootstrapping determined the number of factors; and intra-class correlation assessed test-retest reliability.Results: The final scale has 31 items and four factors: informal social networks, socio-institutional, health professionals and self-stigma. Cronbach’s alpha was 0.84 for the Factor 1; 0.81 for Factor 2; 0.74 for Factor 3, and 0.75 for Factor 4. Correlation matrix among factors revealed that most were in the moderate range [0.31-0.49], with the strongest occurring between perception of stigma in the informal network and self-stigma and there was also a weaker correlation between stigma from health professionals and self-stigma. Test-retest reliability was highest for informal networks [ICC 0.76 [0.67 -0.83]] and self-stigma [ICC 0.74 [0.64-0.81]]. There were no significant differences in the scoring due to sex or age. Service users in Argentina had the highest scores in almost all dimensions.Conclusions: The MARISTAN stigma scale is a reliable measure of the stigma of schizophrenia and related psychoses across several cultures. A confirmatory factor analysis is needed to assess the stability of its factor structure.We are also grateful for support from the Pan-American Health Office (PAHO), Camden and Islington NHS Foundation Trust and University College London (UCL)

Attitudes and burden in relatives of patients with schizophrenia in a middle income country

BACKGROUND: Most studies of family attitudes and burden have been conducted in developed countries. Thus it is important to test the generalizability of this research in other contexts where social conditions and extended family involvement may be different. The aim of this study was to assess the relationship between the attitudes of caregivers and the burden they experience in such a context, namely Arica, a town located in the northernmost region of Chile, close to the border with Peru and Bolivia. METHODS: We assessed attitudes towards schizophrenia (including affective, cognitive and behavioural components) and burden (including subjective distress, rejection and competence) in 41 main caregivers of patients with schizophrenia, all of whom were users of Public Mental Health Services in Arica. RESULTS: Attitude measures differed significantly according to socio-demographic variables, with parents (mainly mothers) exhibiting a more negative attitude towards the environment than the rest of the family (t = 4.04; p = 0.000).This was also the case for caregivers with a low educational level (t = 3.27; p < 0.003), for the oldest caregivers (r = 0.546; p = 0.000) and for those who had spent more time with the patient (r = 0.377; p = 0.015). Although attitudes had significant association with burden, their explanatory power was modest (R2 = .104, F = 4,55; p = .039). CONCLUSIONS: Similar to finding developed countries, the current study revealed a positive and significant relationship between the attitudes of caregivers and their burden. These findings emphasize the need to support the families of patients with schizophrenia in this social context