Geometry of the set of quantum correlations

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.Comment: 11 + 8 pages, 6 figures, v2: added an argument relating self-testing and extremality, v3: typos corrected, results unchanged, published versio

Distinct hyperuricemia trajectories are associated with different risks of incident diabetes: A prospective cohort study

Background and aim: Conflicting results suggest a link between serum uric acid and diabetes and previous studies ignored the effect of continuous exposure of serum uric acid on diabetes risk. This study aims to characterize hyperuricemia trajectories in middle-aged adults and to examine its potential impact on diabetes risk, considering the role of obesity, dyslipidemia, and hypertension. Methods and results: The cohort included 9192 participants who were free of diabetes before 2013. The hyperuricemia trajectories during 2009–2013 were identified by latent class growth models. Incident diabetes during 2014–2018 was used as the outcome. Modified Poisson regression models were used to assess the association of trajectories with diabetes. Furthermore, marginal structural models were used to estimate the mediating effects of the relationship between hyperuricemia trajectories and diabetes. We identified three discrete hyperuricemia trajectories: high-increasing (n = 5794), moderate-stable (n = 2049), and low-stable (n = 1349). During 5 years of follow-up, we documented 379 incident diabetes cases. Compared with the low-stable pattern, the high-increasing pattern had a higher risk of developing diabetes (RR, 1.42; 95% CI: 1.09–1.84). In addition, the percentages of total effect between the high-increasing hyperuricemia pattern and diabetes mediated by obesity, dyslipidemia, and hypertension were 24.41%, 18.26%, and 6.29%. However, the moderate-stable pattern was not associated with an increased risk of diabetes. Conclusions: These results indicate that the high-increasing hyperuricemia trajectory is significantly associated with an increased risk of diabetes. Furthermore, obesity, dyslipidemia, and hypertension play mediating roles in the relationship between the high-increasing hyperuricemia pattern and increased diabetes risk

A Parametric Investigation on Energy-Saving Effect of Solar Building Based on Double Phase Change Material Layer Wallboard

In order to further understand the thermal performance of the double phase change material (PCM) layer wallboard, the wallboard model was established and a comprehensively numerical parametric investigation was carried out. The variation laws of inner wall temperature rise and the heat flux transferred under different phase transition temperatures and thermal conductivities are presented in detail. The main results show that the temperature of the inside wall for case 2 can be reduced by about 1.5 K further compared to that for case 1. About 83% of the heat transferred from the outside is absorbed by the PCM layer in case 2. Reducing the phase transition temperature of the PCM layer can decrease the inside wall temperature to a certain extent in the period of high temperature. The utilization of double PCM layers shows much more performance compared to that of the single PCM layer case, and the temperature of the inside wall can be reduced by 2 K further