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We prove a functional version of the additive kinematic formula as an application of the Hadwiger theorem on convex functions together with a Kubota-type formula for mixed Monge–Ampère measures. As an application, we give a new explanation for the equivalence of the representations of functional intrinsic volumes as singular Hessian valuations and as integrals with respect to mixed Monge–Ampère measures. In addition, we obtain a new integral geometric formula for mixed area measures of convex bodies, where integration on $\operatorname {SO}(n-1)\times \operatorname {O}(1)$ is considered.
Recent work demonstrated that detection of SARS-CoV-2 on the floor of long-term care facilities is associated with impending COVID-19 outbreaks. It is unknown if similar results will be observed in hospitals.
Methods:
Floor swabs were prospectively collected weekly from healthcare worker-only areas (eg, staff locker rooms) at two hospitals in Ontario, Canada for 39 weeks. Floor swabs were processed for SARS-CoV-2 using quantitative reverse-transcriptase polymerase chain reaction. Results were reported as percentage of positive floor swabs and viral copy number. Grouped fivefold cross-validation was used to evaluate model outbreak discrimination.
Results:
SARS-CoV-2 RNA was detected on 537 of 760 floor swabs (71%). At Hospital A, overall positivity was 90% (95% CI: 85%–93%; N = 280); at Hospital B, overall positivity was 60% (95% CI: 55%–64%; N = 480). There were four COVID-19 outbreaks at Hospital A and seven at Hospital B during the study period. The outbreaks consisted of primarily patient cases (ie, 140 patient cases and 4 staff cases). For every 10-fold increase in viral copies, there was a 22-fold higher odds of a COVID-19 outbreak (OR = 22.0, 95% CI 7.3, 91.8). The cross-validated area under the receiver operating curve for SARS-CoV-2 viral copies for predicting a contemporaneous outbreak was 0.86 (95% CI 0.82–0.90).
Conclusion:
Viral burden of SARS-CoV-2 on floors, even in healthcare worker-only areas, was strongly associated with COVID-19 outbreaks in those hospital wards. Built environment sampling may support hospital COVID-19 outbreak identification, fill gaps in traditional surveillance, and guide infection prevention and control measures.
The distribution and chemical state of Si in a synthetic 2-line ferrihydrite with a Si/(Si + Fe) molar ratio of 0.11 was studied. Heat treatment under oxidizing conditions shows that Si-rich ferrihydrite is stable to 400°C. The transformation to hematite and the formation of a polymerized amorphous-silica phase occur at 850°C. At this temperature, the specific surface area decreases greatly and the average pore diameter increases, which is indicative of sintering. Heating under severe reducing conditions causes a segregation of Si from Fe and results in a mixture of elemental Fe and SiO2. Surface and structural data suggest that Si is located near the particle surface where it limits the rearrangement of Fe octahedra to form hematite.
This article analyses a domestic litigation matter seeking to establish accountability for air pollution-related human rights violations. It examines how the judiciary applied national and international law to dismiss the case on procedural grounds. It argues that the domestic case deserves careful reading for a number of reasons that can be distilled into two premises. Firstly, the national legal framework and its respective judicial interpretation impede access to justice for victims of state and/or corporate human rights violations. Secondly, it is essential that the state develops laws and policies in line with the United Nations Guiding Principles on Business and Human Rights, which would allow claimants to focus their argumentation on material, rather than procedural issues relevant to proving the merits of the case.
Most of the textual sources concerning the imperial court are relatively short; many recount anecdotes illuminating a single moment, a memorable saying, or a specific practice. The surviving works of history and biography do, however, contain a few longer narratives of connected sequences of events at court. Such narratives most commonly occur when historians and biographers describe crises, when events at court had wider implications for the political history of the Principate. Prompted by this observation, this chapter presents a selection of the richest crisis narratives. The narratives presented relate to: the fall of Claudius’ wife, Messalina; the loss of position at court suffered by Nero’s mother, Agrippina the Younger, and her ensuing murder by her son; and the assassinations of the emperors Domitian and Commodus.