The divider set of explicit parametric geometry

In this paper we describe a novel concept for classification of complex parametric geometry based on the concept of the Divider Set. The Divider Set is an alternative concept to maximal disks, Voronoi sets and cut loci. The Divider Set is based on a formal definition relating to topology and differential geometry. In this paper firstly we discuss the formal definition of the Divider Set for complex 3-dimensional geometry. This is then followed by the introduction of a computationally feasible algorithm for computing the Divider Set for geometry which can be defined in explicit parametric form. Thus, an explicit solution form taking advantage of the special form of the parametric geometry is presented. We also show how the Divider Set can be computed for various complex parametric geometry by means of illustrating our concept through a number of example

Correction to: Two years later: Is the SARS-CoV-2 pandemic still having an impact on emergency surgery? An international cross-sectional survey among WSES members

Background: The SARS-CoV-2 pandemic is still ongoing and a major challenge for health care services worldwide. In the first WSES COVID-19 emergency surgery survey, a strong negative impact on emergency surgery (ES) had been described already early in the pandemic situation. However, the knowledge is limited about current effects of the pandemic on patient flow through emergency rooms, daily routine and decision making in ES as well as their changes over time during the last two pandemic years. This second WSES COVID-19 emergency surgery survey investigates the impact of the SARS-CoV-2 pandemic on ES during the course of the pandemic. Methods: A web survey had been distributed to medical specialists in ES during a four-week period from January 2022, investigating the impact of the pandemic on patients and septic diseases both requiring ES, structural problems due to the pandemic and time-to-intervention in ES routine. Results: 367 collaborators from 59 countries responded to the survey. The majority indicated that the pandemic still significantly impacts on treatment and outcome of surgical emergency patients (83.1% and 78.5%, respectively). As reasons, the collaborators reported decreased case load in ES (44.7%), but patients presenting with more prolonged and severe diseases, especially concerning perforated appendicitis (62.1%) and diverticulitis (57.5%). Otherwise, approximately 50% of the participants still observe a delay in time-to-intervention in ES compared with the situation before the pandemic. Relevant causes leading to enlarged time-to-intervention in ES during the pandemic are persistent problems with in-hospital logistics, lacks in medical staff as well as operating room and intensive care capacities during the pandemic. This leads not only to the need for triage or transferring of ES patients to other hospitals, reported by 64.0% and 48.8% of the collaborators, respectively, but also to paradigm shifts in treatment modalities to non-operative approaches reported by 67.3% of the participants, especially in uncomplicated appendicitis, cholecystitis and multiple-recurrent diverticulitis. Conclusions: The SARS-CoV-2 pandemic still significantly impacts on care and outcome of patients in ES. Well-known problems with in-hospital logistics are not sufficiently resolved by now; however, medical staff shortages and reduced capacities have been dramatically aggravated over last two pandemic years