Pseudo-Compact Semi-Topological Groups

Митрофан М. Чобан, Петър Ст. Кендеров, Уорън Б. Муурс - Полу-топологична група (съответно, топологична група) е група, снабдена с топология, относно която груповата оперция произведение е частично непрекъсната по всяка от променливите (съответно, непрекъсната по съвкупност от променливите и обратната операция е също непрекъсната). В настоящата работа ние даваме условия, от топологичен характер, една полу-топологична група да е всъщност топологична група. Например, ние показваме, че всяка сепарабелна псевдокомпактна полу-топологична група е топологична група. Показваме също, че всяка локално псевдокомпактна полу-топологична група, чиято групова операция е непрекъсната по съвкупност от променливите е топологична група.

Absolutely Continuous Spectrum for Parabolic Flows/Maps

This work is devoted to creating an abstract framework for the study of certain spectral properties of parabolic systems. Specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spectral results for twisted horocycle flows and to rederive spectral results for skew products over translations and Furstenberg transformations.

Statistically modelling the relationships between Type D personality and social support, health behaviors and symptom severity in chronic illness groups

OBJECTIVE: The study aimed to develop a predictive model of how Type D personality influences health behaviours, social support and symptom severity and assess its generalisability to a range of chronic illnesses.

DESIGN: Participants were classified as either healthy (n = 182) or having a chronic illness (n = 207). Participants completed an online survey measuring Type D and a range of health-related variables. Chronic illness participants were classified as having either a functional somatic syndrome (i.e. chronic fatigue syndrome or fibromyalgia), where the underlying pathological processes were unclear, or illnesses such as type 2 diabetes, osteoarthritis or rheumatoid arthritis, where the causes are well understood.

MAIN OUTCOME MEASURES: Outcome measures were health behaviours, social support and both physical and psychological symptoms.

RESULTS: The rate of Type D was higher in chronic illness participants (53%) than in healthy controls (39%). Negative affectivity (NA) and social inhibition (SI) both correlated with outcome measures, although NA was generally the stronger predictor. Using NA and SI as independent subscales led to superior prediction of health outcomes than using categorical or continuous representations.

CONCLUSION: Findings suggest that the relationship between Type D and health outcomes may generalise across different chronic illnesses.

Continuous validation for data analytics systems

From a future history of 2025: Continuous development is common for build/test (continuous integration) and operations (devOps). This trend continues through the lifecycle, into what we call `devUsage': continuous usage validation. In addition to ensuring systems meet user needs, organisations continuously validate their legal and ethical use. The rise of end-user programming and multi-sided platforms exacerbate validation challenges. A separate trend isthe specialisation of software engineering for technical domains, including data analytics. This domain has specific validation challenges. We must validate the accuracy of sta-tistical models, but also whether they have illegal or unethical biases. Usage needs addressed by machine learning are sometimes not speci able in the traditional sense, and statistical models are often `black boxes'. We describe future research to investigate solutions to these devUsage challenges for data analytics systems. We will adapt risk management and governance frameworks previously used for soft-ware product qualities, use social network communities for input from aligned stakeholder groups, and perform cross-validation using autonomic experimentation, cyber-physical data streams, and online discursive feedback.