On manifolds with nonhomogeneous factors

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

The effect of intolerance of uncertainty on anxiety and depression, and their symptom networks, during the COVID-19 pandemic

Individuals vary in their ability to tolerate uncertainty. High intolerance of uncertainty (the tendency to react nega‑ tively to uncertain situations) is a known risk factor for mental health problems. In the current study we examined the degree to which intolerance of uncertainty predicted depression and anxiety symptoms and their interrelations across the frst year of the COVID-19 pandemic. We examined these associations across three time points (May 2020 – April 2021) in an international sample of adults (N=2087, Mean age=41.13) from three countries (UK, USA, Australia) with varying degrees of COVID-19 risk. We found that individuals with high and moderate levels of intolerance of uncertainty reported reductions in depression and anxiety symptoms over time. However, symptom levels remained signifcantly elevated compared to individuals with low intolerance of uncertainty. Individuals with low intolerance of uncertainty had low and stable levels of depression and anxiety across the course of the study. Network analyses further revealed that the relationships between depression and anxiety symptoms became stronger over time among individuals with high intolerance of uncertainty and identified that feeling afraid showed the strongest association with intolerance of uncertainty. Our findings are consistent with previous work identifying intolerance of uncertainty as an important risk factor for mental health problems, especially in times marked by actual health, economic and social uncertainty. The results highlight the need to explore ways to foster resilience among individuals who struggle to tolerate uncertainty, as ongoing and future geopolitical, climate and health threats will likely lead to continued exposure to significant uncertainty.Jack L. Andrews, Meiwei Li, Savannah Minihan, Annabel Songco, Elaine Fox, Cecile D. Ladouceur, Louise Mewton, Michelle Moulds, Jennifer H. Pfeifer, Anne, Laura Van Harmelen, and Susanne Schweize

Monitoring Charge Exchange in P3HT-Nanotube Composites Using Optical and Electrical Characterisation

Charge exchange at the bulk heterojunctions of composites made by mixing single wall nanotubes (SWNTs) and polymers show potential for use in optoelectronic devices such as solar cells and optical sensors. The density/total area of these heterojunctions is expected to increase with increasing SWNT concentration but the efficiency of solar cell peaks at low SWNT concentrations. Most researchers use current–voltage measurements to determine the evolution of the SWNT percolation network and optical absorption measurements to monitor the spectral response of the composites. However, these methods do not provide a detailed account of carrier transport at the concentrations of interest; i.e., near or below the percolation threshold. In this article, we show that capacitance–voltage (C–V) response of (metal)-(oxide)-(semiconducting composite) devices can be used to fill this gap in studying bulk heterojunctions. In an approach where we combine optical absorption methods withC–Vmeasurements we can acquire a unified optoelectronic response from P3HT-SWNT composites. This methodology can become an important tool for optoelectronic device optimization

A simplified (modified) Duke Activity Status Index (M-DASI) to characterise functional capacity: A secondary analysis of the Measurement of Exercise Tolerance before Surgery (METS) study

Background Accurate assessment of functional capacity, a predictor of postoperative morbidity and mortality, is essential to improving surgical planning and outcomes. We assessed if all 12 items of the Duke Activity Status Index (DASI) were equally important in reflecting exercise capacity. Methods In this secondary cross-sectional analysis of the international, multicentre Measurement of Exercise Tolerance before Surgery (METS) study, we assessed cardiopulmonary exercise testing and DASI data from 1455 participants. Multivariable regression analyses were used to revise the DASI model in predicting an anaerobic threshold (AT) >11 ml kg −1 min −1 and peak oxygen consumption (VO 2 peak) >16 ml kg −1 min −1, cut-points that represent a reduced risk of postoperative complications. Results Five questions were identified to have dominance in predicting AT>11 ml kg −1 min −1 and VO 2 peak>16 ml.kg −1min −1. These items were included in the M-DASI-5Q and retained utility in predicting AT>11 ml.kg −1.min −1 (area under the receiver-operating-characteristic [AUROC]-AT: M-DASI-5Q=0.67 vs original 12-question DASI=0.66) and VO 2 peak (AUROC-VO2 peak: M-DASI-5Q 0.73 vs original 12-question DASI 0.71). Conversely, in a sensitivity analysis we removed one potentially sensitive question related to the ability to have sexual relations, and the ability of the remaining four questions (M-DASI-4Q) to predict an adequate functional threshold remained no worse than the original 12-question DASI model. Adding a dynamic component to the M-DASI-4Q by assessing the chronotropic response to exercise improved its ability to discriminate between those with VO 2 peak>16 ml.kg −1.min −1 and VO 2 peak<16 ml.kg −1.min −1. Conclusions The M-DASI provides a simple screening tool for further preoperative evaluation, including with cardiopulmonary exercise testing, to guide perioperative management