Topological entropy and blocking cost for geodesics in riemannian manifolds

For a pair of points $x,y$ in a compact, riemannian manifold $M$ let $n_t(x,y)$ (resp. $s_t(x,y)$) be the number of geodesic segments with length $\leq t$ joining these points (resp. the minimal number of point obstacles needed to block them). We study relationships between the growth rates of $n_t(x,y)$ and $s_t(x,y)$ as $t\to\infty$. We derive lower bounds on $s_t(x,y)$ in terms of the topological entropy $h(M)$ and its fundamental group. This strengthens the results of Burns-Gutkin \cite{BG06} and Lafont-Schmidt \cite{LS}. For instance, by \cite{BG06,LS}, $h(M)>0$ implies that $s$ is unbounded; we show that $s$ grows exponentially, with the rate at least $h(M)/2$.Comment: 13 page

Time, institutional support and quality of decision making in child protection:A cross-country analysis

This paper examines perceptions of time and institutional support for decision making and staff confidence in child welfare staffs ultimate decisions – examining differences and similarities between and within the service-oriented Nordic countries (Norway and Finland) and the risk-oriented Anglo-American countries (England and California). The study identifies a high degree of work pressure across all the countries, lines of predominantly vertical institutional support and relatively high confidence in decisions. Finland stands out with higher perceived work pressure and with a horizontal support line, whereas England stands out with workers having a lower degree of confidence in their own and others’ decisions

Integral constraints on the monodromy group of the hyperkahler resolution of a symmetric product of a K3 surface

Let M be a 2n-dimensional Kahler manifold deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface S. Let Mon be the group of automorphisms of the cohomology ring of M, which are induced by monodromy operators. The second integral cohomology of M is endowed with the Beauville-Bogomolov bilinear form. We prove that the restriction homomorphism from Mon to the isometry group O[H^2(M)] is injective, for infinitely many n, and its kernel has order at most 2, in the remaining cases. For all n, the image of Mon in O[H^2(M)] is the subgroup generated by reflections with respect to +2 and -2 classes. As a consequence, we get counter examples to a version of the weight 2 Torelli question, when n-1 is not a prime power.Comment: Version 3: Latex, 54 pages. Expository change

Wellness and coping of physicians who worked in ICUs during the pandemic: A multicenter cross-sectional North American survey

OBJECTIVES: Few surveys have focused on physician moral distress, burnout, and professional fulfilment. We assessed physician wellness and coping during the COVID-19 pandemic. DESIGN: Cross-sectional survey using four validated instruments. SETTING: Sixty-two sites in Canada and the United States. SUBJECTS: Attending physicians (adult, pediatric; intensivist, nonintensivist) who worked in North American ICUs. INTERVENTION: None. MEASUREMENTS AND MAIN RESULTS: We analysed 431 questionnaires (43.3% response rate) from 25 states and eight provinces. Respondents were predominantly male (229 [55.6%]) and in practice for 11.8 ± 9.8 years. Compared with prepandemic, respondents reported significant intrapandemic increases in days worked/mo, ICU bed occupancy, and self-reported moral distress (240 [56.9%]) and burnout (259 [63.8%]). Of the 10 top-ranked items that incited moral distress, most pertained to regulatory/organizational ( n = 6) or local/institutional ( n = 2) issues or both ( n = 2). Average moral distress (95.6 ± 66.9), professional fulfilment (6.5 ± 2.1), and burnout scores (3.6 ± 2.0) were moderate with 227 physicians (54.6%) meeting burnout criteria. A significant dose-response existed between COVID-19 patient volume and moral distress scores. Physicians who worked more days/mo and more scheduled in-house nightshifts, especially combined with more unscheduled in-house nightshifts, experienced significantly more moral distress. One in five physicians used at least one maladaptive coping strategy. We identified four coping profiles (active/social, avoidant, mixed/ambivalent, infrequent) that were associated with significant differences across all wellness measures. CONCLUSIONS: Despite moderate intrapandemic moral distress and burnout, physicians experienced moderate professional fulfilment. However, one in five physicians used at least one maladaptive coping strategy. We highlight potentially modifiable factors at individual, institutional, and regulatory levels to enhance physician wellness

Nowhere minimal CR submanifolds and Levi-flat hypersurfaces

A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces.Comment: 21 pages; conjecture 2.8 was removed in proof; to appear in J. Geom. Ana

Is There a Peccei-Quinn Phase Transition?

The nature of axion cosmology is usually said to depend on whether the Peccei-Quinn (PQ) symmetry breaks before or after inflation. The PQ symmetry itself is believed to be an accident, so there is not necessarily a symmetry during inflation at all. We explore these issues in some simple models, which provide examples of symmetry breaking before and after inflation, or in which there is no symmetry during inflation and no phase transition at all. One effect of these observations is to relax the constraints from isocurvature fluctuations due to the axion during inflation. We also observe new possibilities for evading the constraints due to cosmic strings and domain walls, but they seem less generic.Comment: 14 pages. Several references adde

Drivers of European bat population change: a review reveals evidence gaps

Bat populations are thought to have suffered significant declines in the past century throughout Europe. Fortunately, there are some signs of recovery; for instance, of the 11 species monitored in the UK, population trends of five are increasing. The drivers of past losses and recent trends are unclear; identifying them will enable targeted conservation strategies to support further recovery. We review the evidence linking proposed drivers to impacts on bat populations in Europe, using the results of a previous cross‐taxa semi‐quantitative assessment as a framework. Broadly, the drivers reviewed relate to land‐use practices, climate change, pollution, development and infrastructure, and human disturbance. We highlight where evidence gaps or conflicts present barriers to successful conservation and review emerging opportunities to address these gaps. We find that the relative importance or impacts of the potential drivers of bat population change are not well understood or quantified, with conflicting evidence in many cases. To close key gaps in the evidence for responses of bat populations to environmental change, future studies should focus on the impacts of climate change, urbanisation, offshore wind turbines, and water pollution, as well as on mitigation measures and the synergistic effects of putative drivers. To increase available evidence of drivers of bat population change, we propose utilising advances in monitoring tools and statistical methods, together with robust quantitative assessment of conservation interventions to mitigate threats and enable the effective conservation of these protected species

Optically bound microscopic particles in one dimension

Counter-propagating light fields have the ability to create self-organized one-dimensional optically bound arrays of microscopic particles, where the light fields adapt to the particle locations and vice versa. We develop a theoretical model to describe this situation and show good agreement with recent experimental data (Phys. Rev. Lett. 89, 128301 (2002)) for two and three particles, if the scattering force is assumed to dominate the axial trapping of the particles. The extension of these ideas to two and three dimensional optically bound states is also discussed.Comment: 12 pages, incl. 5 figures, accepted by Phys. Rev.