Complexity of equational theory of relational algebras with standard projection elements

The class $\mathsf{TPA}$ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $\mathsf{TPA}$ nor the first order theory of $\mathsf{TPA}$ are decidable. Moreover, we show that the set of all equations valid in $\mathsf{TPA}$ is exactly on the $\Pi ^1_1$ level. We consider the class $\mathsf{TPA}^-$ of the relation algebra reducts of $\mathsf{TPA}$’s, as well. We prove that the equational theory of $\mathsf{TPA}^-$ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work

Prevalence and predictors of complementary and alternative medicine use among people with coronary heart disease or at risk for this in the sixth Tromsø study: a comparative analysis using protection motivation theory

Background Engagement in healthy lifestyle behaviors, such as healthy diet and regular physical activity, are known to reduce the risk of developing coronary heart disease (CHD). Complementary and alternative medicine (CAM) is known to be associated with having a healthy lifestyle. The primary aim of this study was to examine the prevalence and predictors of CAM use in CHD patients, and in those without CHD but at risk for developing CHD, using Protection Motivation Theory (PMT) as a guiding conceptual framework. Method Questionnaire data were collected from 12,981 adult participants in the cross-sectional sixth Tromsø Study (2007–8). Eligible for analyses were 11,103 participants who reported whether they had used CAM or not. Of those, 830 participants reported to have or have had CHD (CHD group), 4830 reported to have parents, children or siblings with CHD (no CHD but family risk), while 5443 reported no CHD nor family risk of CHD. We first compared the patterns of CAM use in each group, and then examined the PMT predictors of CAM use. Health vulnerability from the threat appraisal process of PMT was assessed by self-rated health and expectations for future health. Response efficacy from the coping appraisal process of PMT was assessed as preventive health beliefs and health behavior frequency. Results Use of CAM was most commonly seen in people with no CHD themselves, but family risk of developing CHD (35.8%), compared to people already diagnosed with CHD (30.2%) and people with no CHD nor family risk (32.1%). All four of the PMT factors; self-rated health, expectations for future health, preventive health beliefs, and the health behavior index – were predictors for CAM use in the no CHD but family risk group. Conclusion These findings suggest that people use CAM in response to a perceived risk of developing CHD, and to prevent disease and to maintain health

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference