The Liouville property and random walks on topological groups

We study harmonic functions and Poisson boundaries for Borel probability measures on general (i.e., not necessarily locally compact) topological groups, and we prove that a second-countable topological group is amenable if and only if it admits a fully supported, regular Borel probability measure with trivial Poisson boundary. This generalizes work of Kaimanovich--Vershik and Rosenblatt, confirms a general topological version of Furstenberg's conjecture, and entails a characterization of the amenability of isometry groups in terms of the Liouville property for induced actions. Moreover, our result has non-trivial consequences concerning Liouville actions of discrete groups on countable setsComment: 24 pages, no figures; v2: referee report taken into account, Proposition 4.2 generalized, minor error in the statement of Lemma 4.5 corrected, some references and background material added, 26 pages, final version to appear in Commentarii Mathematici Helvetic

Stable isotope fractionation during ultraviolet photolysis of N_2O

The biogeochemical cycling of nitrous oxide plays an important role in greenhouse forcing and ozone regulation. Laboratory studies of N_2O:N_2 mixtures irradiated between 193–207 nm reveal a significant enrichment of the residual heavy nitrous oxide isotopomers. The isotopic signatures resulting from photolysis are well modeled by an irreversible Rayleigh distillation process, with large enrichment factors of ε_(15,18)(193 nm) = −18.4,‐14.5 per mil and ε_(15,18)(207 nm) = −48.7,‐46.0 per mil. These results, when combined with diffusive mixing processes, have the potential to explain the stratospheric enrichments previously observed

Student Preferences for Reference Services at a Remote Biological Station Library

During the 2020 and 2021 summer semesters, the University of Michigan Biological Station (UMBS) transitioned to hybrid classes that were primarily distance learning with two-week inperson sections. The library offered both synchronous and asynchronous reference assistance over the summer term. An analysis showed that students favored using the UMBS LibGuide over synchronous virtual reference help via Zoom. Students further preferred face-to-face interactions over virtual formats, and their preference for LibGuide assistance may carry into the post- COVID-19 classroom. This finding suggests that students prioritize convenience and immediacy over personalized assistance in the Zoom platform. Thus, in providing reference assistance to student populations in the field sciences, balancing face-to-face interactions with convenience and immediacy should be a priority. Recommendations based on the success of the 2020 and 2021 field seasons were suggested for reference interactions in future field courses

Cost-effectiveness of initial stress cardiovascular MR, stress SPECT or stress echocardiography as a gate-keeper test, compared with upfront invasive coronary angiography in the investigation and management of patients with stable chest pain: Mid-term outcomes from the CECaT randomised controlled trial

Objectives: To compare outcomes and cost-effectiveness of various initial imaging strategies in the management of stable chest pain in a long-term prospective randomised trial. Setting: Regional cardiothoracic referral centre in the east of England. Participants: 898 patients (69% man) entered the study with 869 alive at 2 years of follow-up. Patients were included if they presented for assessment of stable chest pain with a positive exercise test and no prior history of ischaemic heart disease. Exclusion criteria were recent infarction, unstable symptoms or any contraindication to stress MRI. Primary outcome measures: The primary outcomes of this follow-up study were survival up to a minimum of 2 years post-treatment, quality-adjusted survival and cost-utility of each strategy. Results: 898 patients were randomised. Compared with angiography, mortality was marginally higher in the groups randomised to cardiac MR (HR 2.6, 95% CI 1.1 to 6.2), but similar in the single photon emission CT-methoxyisobutylisonitrile (SPECT-MIBI; HR 1.0, 95% CI 0.4 to 2.9) and ECHO groups (HR 1.6, 95% CI 0.6 to 4.0). Although SPECT-MIBI was marginally superior to other non-invasive tests there were no other significant differences between the groups in mortality, quality-adjusted survival or costs. Conclusions: Non-invasive cardiac imaging can be used safely as the initial diagnostic test to diagnose coronary artery disease without adverse effects on patient outcomes or increased costs, relative to angiography. These results should be interpreted in the context of recent advances in imaging technology. Trial registration: ISRCTN 47108462, UKCRN 3696

A qualitative content analysis of online public mental health resources for COVID-19

The COVID-19 pandemic has far reaching potential public mental health impacts and is linked to higher levels of depression and anxiety. To address these in part, online information resources acted as mass interventions. It is vital to explore the content of these interventions, to consider the framing of the pandemic and to examine the extent to which their content is relevant. In March 2020, a qualitative content analysis was undertaken of 39 easily accessible online resources that offered advice, tips or guidance relating to mental health or mental wellbeing and COVID-19. Their content was compared to subsequent reports of the mental health impact of the pandemic. Resources frequently focused on anxiety. The content of intervention was typically of a cognitive-behavioral nature, with a significant focus on maintaining social contact. Typically, distress related to the situation was normalized and stigmatizing language was not seen. Data revealed a significant impact of the pandemic on depression as well as anxiety measures in the general UK population. A key recommendation is to ensure both depression and anxiety are addressed in these public mental health resources

Short Plane Supports for Spatial Hypergraphs

A graph $G=(V,E)$ is a support of a hypergraph $H=(V,S)$ if every hyperedge induces a connected subgraph in $G$. Supports are used for certain types of hypergraph visualizations. In this paper we consider visualizing spatial hypergraphs, where each vertex has a fixed location in the plane. This is the case, e.g., when modeling set systems of geospatial locations as hypergraphs. By applying established aesthetic quality criteria we are interested in finding supports that yield plane straight-line drawings with minimum total edge length on the input point set $V$. We first show, from a theoretical point of view, that the problem is NP-hard already under rather mild conditions as well as a negative approximability results. Therefore, the main focus of the paper lies on practical heuristic algorithms as well as an exact, ILP-based approach for computing short plane supports. We report results from computational experiments that investigate the effect of requiring planarity and acyclicity on the resulting support length. Further, we evaluate the performance and trade-offs between solution quality and speed of several heuristics relative to each other and compared to optimal solutions.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018