A QUBO formulation for top-τ eigencentrality nodes.

The efficient calculation of the centrality or "hierarchy" of nodes in a network has gained great relevance in recent years due to the generation of large amounts of data. The eigenvector centrality (aka eigencentrality) is quickly becoming a good metric for centrality due to both its simplicity and fidelity. In this work we lay the foundations for solving the eigencentrality problem of ranking the importance of the nodes of a network with scores from the eigenvector of the network, using quantum computational paradigms such as quantum annealing and gate-based quantum computing. The problem is reformulated as a quadratic unconstrained binary optimization (QUBO) that can be solved on both quantum architectures. The results focus on correctly identifying a given number of the most important nodes in numerous networks given by the sparse vector solution of our QUBO formulation of the problem of identifying the top-τ highest eigencentrality nodes in a network on both the D-Wave and IBM quantum computers.

Uncertainty, Anxiety and Isolation: Experiencing the COVID-19 Pandemic and Lockdown as a Woman with Polycystic Ovary Syndrome (PCOS).

Background: The COVID-19 pandemic and the related lockdown measures presented a significant risk to physical and mental wellbeing in affected populations. Women with polycystic ovary syndrome (PCOS) are predisposed to several cardio-metabolic risk factors which increase the susceptibility to severe COVID-19 and also exhibit increased likelihood of impaired mental health wellbeing. Therefore, these women who usually receive care from multiple primary and specialist healthcare services may be disproportionately impacted by this pandemic and the related restrictions. This study aimed to explore the lived experience of the first UK national lockdown as a woman with PCOS. Methods: As part of a larger cross-sectional study, 12 women with PCOS living in the UK during the first national COVID-19 lockdown were recruited to a qualitative study. Telephone interviews were conducted in June/July of 2020, and data collected were subjected to thematic analysis. Results: Five themes were identified. "My PCOS Journey" describes participants' experiences of diagnosis, treatment and ongoing management of their PCOS. "Living Through Lockdown" describes the overall experience and impact of the lockdown on all aspects of participants' lives. "Self-care and Managing Symptoms" describe multiple challenges to living well with PCOS during the lockdown, including lack of access to supplies and services, and disruption to weight management. "Healthcare on Hold" describes the uncertainty and anxiety associated with delays in accessing specialised healthcare for a range of PCOS aspects, including fertility treatment. "Exacerbating Existing Issues" captures the worsening of pre-existing mental health issues, and an increase in health anxiety and feelings of isolation. Conclusion: For the women with PCOS in this study, the COVID-19 pandemic and the first national lockdown was mostly experienced as adding to the pre-existing challenges of living with their condition. The mental health impact experienced by the study participants was increased due to lack of access to their normal support strategies, limitations on healthcare services and uncertainty about their risk of COVID-19.