Summary n‐dimensional hypervolumes are commonly applied in ecology and evolutionary studies to describe and compare niches, trait spaces characterizing phenotypes or the functional composition of communities. Classical ecological surveys, modern analytical tools and the establishment of online data bases will produce large multivariate data sets, which demands robust statistical tools to analyse and interpret hypervolumes. Existing approaches often have weaknesses; for example, they rely on multivariate normally or elliptically distributed data, perform poorly in higher dimensions, or their outputs vary arbitrarily with parameter choice. Here we introduce dynamic range boxes as a robust nonparametric approach to quantify size and overlap of n‐dimensional hypervolumes. Dynamic range boxes (implemented in the r package dynRB) improve the concept of multivariate range boxes by accounting for the distribution of the data within their range, while still no assumptions on the underlying distributions are needed. In addition to calculating the whole n‐dimensional hypervolume, the package dynRB also provides functions for a coordinate‐wise analysis and interpretation of the data. The concept of dynamic range boxes reliably computes sizes and overlaps of n‐dimensional hypervolumes, which makes dynamic range boxes readily applicable for a broad range of data sets to answer questions related to various disciplines.

Global navigation satellite systems such as the Global Positioning System (GPS) is one of the most important sensors for movement analysis. GPS is widely used to record the trajectories of vehicles, animals and human beings. However, all GPS movement data are affected by both measurement and interpolation errors. In this article we show that measurement error causes a systematic bias in distances recorded with a GPS; the distance between two points recorded with a GPS is – on average – bigger than the true distance between these points. This systematic ‘overestimation of distance’ becomes relevant if the influence of interpolation error can be neglected, which in practice is the case for movement sampled at high frequencies. We provide a mathematical explanation of this phenomenon and illustrate that it functionally depends on the autocorrelation of GPS measurement error (C). We argue that C can be interpreted as a quality measure for movement data recorded with a GPS. If there is a strong autocorrelation between any two consecutive position estimates, they have very similar error. This error cancels out when average speed, distance or direction is calculated along the trajectory. Based on our theoretical findings we introduce a novel approach to determine C in real-world GPS movement data sampled at high frequencies. We apply our approach to pedestrian trajectories and car trajectories. We found that the measurement error in the data was strongly spatially and temporally autocorrelated and give a quality estimate of the data. Most importantly, our findings are not limited to GPS alone. The systematic bias and its implications are bound to occur in any movement data collected with absolute positioning if interpolation error can be neglected.

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PURPOSE To analyze the prevalence of SARS-CoV-2 infection in patients with cancer in hospital care after implementation of institutional and governmental safety measurements. METHODS Patients with cancer routinely tested for SARS-CoV-2 RNA by nasal swab and real-time polymerase chain reaction between March 21 and May 4, 2020, were included. The results of this cancer cohort were statistically compared with the SARS-CoV-2 prevalence in the Austrian population as determined by a representative nationwide random sample study (control cohort 1) and a cohort of patients without cancer presenting to our hospital (control cohort 2). RESULTS A total of 1,688 SARS-CoV-2 tests in 1,016 consecutive patients with cancer were performed. A total of 270 of 1,016 (26.6%) of the patients were undergoing active anticancer treatment in a neoadjuvant/adjuvant and 560 of 1,016 (55.1%) in a palliative setting. A total of 53 of 1,016 (5.2%) patients self-reported symptoms potentially associated with COVID-19. In 4 of 1,016 (0.4%) patients, SARS-CoV-2 was detected. At the time of testing at our department, all four SARS-CoV-2–positive patients were asymptomatic, and two of them had recovered from symptomatic COVID-19. Viral clearance was achieved in three of the four patients 14-56 days after testing positive. The estimated odds ratio of SARS-CoV-2 prevalence between the cancer cohort and control cohort 1 was 1.013 (95% CI, 0.209 to 4.272; P = 1), and between control cohort 2 and the cancer cohort it was 18.333 (95% CI, 6.056 to 74.157). CONCLUSION Our data indicate that continuation of active anticancer therapy and follow-up visits in a large tertiary care hospital are feasible and safe after implementation of strict population-wide and institutional safety measures during the current COVID-19 pandemic. Routine SARS-CoV-2 testing of patients with cancer seems advisable to detect asymptomatic virus carriers and avoid uncontrolled viral spread.