Constructions of free commutative integro-differential algebras

In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras by mixable shuffles. The first is by evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004

Estimates of protection levels against SARS-CoV-2 infection and severe COVID-19 in Germany before the 2022/2023 winter season: the IMMUNEBRIDGE project

PURPOSE: Despite the need to generate valid and reliable estimates of protection levels against SARS-CoV-2 infection and severe course of COVID-19 for the German population in summer 2022, there was a lack of systematically collected population-based data allowing for the assessment of the protection level in real time. METHODS: In the IMMUNEBRIDGE project, we harmonised data and biosamples for nine population-/hospital-based studies (total number of participants n = 33,637) to provide estimates for protection levels against SARS-CoV-2 infection and severe COVID-19 between June and November 2022. Based on evidence synthesis, we formed a combined endpoint of protection levels based on the number of self-reported infections/vaccinations in combination with nucleocapsid/spike antibody responses ("confirmed exposures"). Four confirmed exposures represented the highest protection level, and no exposure represented the lowest. RESULTS: Most participants were seropositive against the spike antigen; 37% of the participants ≥ 79 years had less than four confirmed exposures (highest level of protection) and 5% less than three. In the subgroup of participants with comorbidities, 46-56% had less than four confirmed exposures. We found major heterogeneity across federal states, with 4-28% of participants having less than three confirmed exposures. CONCLUSION: Using serological analyses, literature synthesis and infection dynamics during the survey period, we observed moderate to high levels of protection against severe COVID-19, whereas the protection against SARS-CoV-2 infection was low across all age groups. We found relevant protection gaps in the oldest age group and amongst individuals with comorbidities, indicating a need for additional protective measures in these groups

Simulation-based training and learning: A review on technology-enhanced education for the minerals industry

There is a lack of skilled operators for mineral processing plants in the mining sector, which might be related to the challenge of creating trainings that addresses the operator's daily work problems. In recent years, the use of simulator-based trainings as a tool to build competence has grown in many different fields. With the help of technologies like virtual reality, these tools have been demonstrated to increase awareness and the capability of workers when compared to traditional learning methods. In this paper, a review is presented on the development and application of such technologies in simulation-based training for the training of operators of the minerals industry in the last 20 years. Proposed next steps and new technologies with the potential of improving these applications are also discussed. © 202

Visual function resists early neurodegeneration in the visual system in primary progressive multiple sclerosis

BACKGROUND: Neurodegeneration in multiple sclerosis (MS) affects the visual system but dynamics and pathomechanisms over several years especially in primary progressive MS (PPMS) are not fully understood. METHODS: We assessed longitudinal changes in visual function, retinal neurodegeneration using optical coherence tomography, MRI and serum NfL (sNfL) levels in a prospective PPMS cohort and matched healthy controls. We investigated the changes over time, correlations between outcomes and with loss of visual function. RESULTS: We followed 81 patients with PPMS (mean disease duration 5.9 years) over 2.7 years on average. Retinal nerve fibre layer thickness (RNFL) was reduced in comparison with controls (90.1 vs 97.8 µm; p<0.001). Visual function quantified by the area under the log contrast sensitivity function (AULCSF) remained stable over a continuous loss of RNFL (0.46 µm/year, 95% CI 0.10 to 0.82; p=0.015) up until a mean turning point of 91 µm from which the AULCSF deteriorated. Intereye RNFL asymmetry above 6 µm, suggestive of subclinical optic neuritis, occurred in 15 patients and was related to lower AULCSF but occurred also in 5 out of 44 controls. Patients with an AULCSF progression had a faster increase in Expanded Disability Status Scale (beta=0.17/year, p=0.043). sNfL levels were elevated in patients (12.2 pg/mL vs 8.0 pg/mL, p<0.001), but remained stable during follow-up (beta=-0.14 pg/mL/year, p=0.291) and were not associated with other outcomes. CONCLUSION: Whereas neurodegeneration in the anterior visual system is already present at onset, visual function is not impaired until a certain turning point. sNfL is not correlated with structural or functional impairment in the visual system