The geometry in Plato's Meno

In this paper, we analyze the two geometrical passages in Plato's Meno, (81c -- 85c) and (86e4 -- 87b2), from the points of view of a geometer in Plato's time and today. We give, in our opinion, a complete explanation of the difficult second geometrical passage. Our explanation solves an ingenious geometry puzzle that has baffled readers of Plato's Meno for over 2,400 years.Comment: 50 pages, 21 figure

Identifiers in e-Science platforms for the ecological sciences

In the emerging Web of Data, publishing stable and unique identifiers promises great potential in using the web as common platform to discover and enrich data in the ecologic sciences. With our collaborative e-Science platform “BEFdata”, we generated and published unique identifiers for the data repository of the Biodiversity – Ecosystem Functioning Research Unit of the German Research Foundation (BEF-China; DFG: FOR 891). We linked part of the identifiers to two external data providers, thus creating a virtual common platform including several ecological repositories. We used the Global Biodiversity Facility (GBIF) as well the International Plant Name Index (IPNI) to enrich the data from our own field observations. We conclude in discussing other potential providers for identifiers for the ecological research domain. We demonstrate the ease of making use of existing decentralized and unsupervised identifiers for a data repository, which opens new avenues to collaborative data discovery for learning, teaching, and research in ecology

Complementarity effects on tree growth are contingent on tree size and climatic conditions across Europe

Although sustainable development was defined in the Brundtland Report almost 30 years ago, the current usage of the concepts of sustainability and sustainable development remain highly equivocal. In the context of rural communities, multiple interpretations and weak definitions lead to confusion in understanding what comprises a sustainable rural community. Building on existing definitions (e.g. Baker's, 2006, ‘Ladder of Sustainable Development'), models (principally, The Egan Review's, 2004, ‘Components of Sustainable Communities') and findings of this study, a sustainable community is defined and a holistic model of a sustainable place-based rural community is presented. This model, the sustainable community design (SCD) is used as the basis for analysing community sustainability, which is measured using mixed methods and scorecard assessment. Sensitivity of the method is demonstrated with inter- and intra-community variations in sustainability across three diverse Scottish rural communities. Intra-community variations illustrate heterogeneity in community sustainability, explain ambiguity in characterisations of an individual community's sustainability, and highlight the importance of an interdisciplinary and holistic approach to community development. The SCD framework is presented as a useful tool for meso-level sustainability assessment and to facilitate the sustainable development of rural communities

Tree identity rather than tree diversity drives earthworm communities in European forests

Given the key role of belowground biota on forest ecosystem functioning, it is important to identify the factors that influence their abundance and composition. However, the understanding of the ecological linkage between tree diversity and belowground biota is still insufficient. Here we investigated the influence of tree diversity (richness, True Shannon diversity index, functional diversity) and identity (proportion of evergreen leaf litter and leaf litter quality) on earthworm species richness and biomass at a continental and regional scale, using data from a Europe-wide forest research platform (FunDivEUROPE) spanning six major forest types. We found a marked tree identity effect at the continental scale, with proportion of evergreen leaf litter negatively affecting total earthworm biomass and species richness, as well as their biomass per functional group. Furthermore, there were clear litter quality effects with a latitudinal variation in trait-specific responses. In north and central Europe, earthworm biomass and species richness clearly increased with increasing litter nutrient concentrations (decreasing C:N ratio and increasing calcium concentration), whereas this influence of litter nutrients was absent or even reversed in southern Europe. In addition, although earthworms were unaffected by the number of tree species, tree diversity positively affected earthworm biomass at the continental scale through functional diversity of the leaf litter. By focusing on tree leaf litter traits, this study advanced our understanding of the mechanisms driving tree identity effects and supported previous findings that litter quality, as a proxy of tree identity, was a stronger driver of earthworm species richness and biomass than tree diversit

Available and missing data to model impact of climate change on European forests

Climate change is expected to cause major changes in forest ecosystems during the 21st century and beyond. To assess forest impacts from climate change, the existing empirical information must be structured, harmonised and assimilated into a form suitable to develop and test state-of-the-art forest and ecosystem models. The combination of empirical data collected at large spatial and long temporal scales with suitable modelling approaches is key to understand forest dynamics under climate change. To facilitate data and model integration, we identified major climate change impacts observed on European forest functioning and summarised the data available for monitoring and predicting such impacts. Our analysis of c. 120 forest-related databases (including information from remote sensing, vegetation inventories, dendroecology, palaeoecology, eddy-flux sites, common garden experiments and genetic techniques) and 50 databases of environmental drivers highlights a substantial degree of data availability and accessibility. However, some critical variables relevant to predicting European forest responses to climate change are only available at relatively short time frames (up to 10-20 years), including intra-specific trait variability, defoliation patterns, tree mortality and recruitment. Moreover, we identified data gaps or lack of data integration particularly in variables related to local adaptation and phenotypic plasticity, dispersal capabilities and physiological responses. Overall, we conclude that forest data availability across Europe is improving, but further efforts are needed to integrate, harmonise and interpret this data (i.e. making data useable for non-experts). Continuation of existing monitoring and networks schemes together with the establishments of new networks to address data gaps is crucial to rigorously predict climate change impacts on European forests. © 2019 The Author(s

Available and missing data to model impact of climate change on European forests

Climate change is expected to cause major changes in forest ecosystems during the 21st century and beyond. To assess forest impacts from climate change, the existing empirical information must be structured, harmonised and assimilated into a form suitable to develop and test state-of-the-art forest and ecosystem models. The combination of empirical data collected at large spatial and long temporal scales with suitable modelling approaches is key to understand forest dynamics under climate change. To facilitate data and model integration, we identified major climate change impacts observed on European forest functioning and summarised the data available for monitoring and predicting such impacts. Our analysis of c. 120 forest-related databases (including information from remote sensing, vegetation inventories, dendroecology, palaeoecology, eddy-flux sites, common garden experiments and genetic techniques) and 50 databases of environmental drivers highlights a substantial degree of data availability and accessibility. However, some critical variables relevant to predicting European forest responses to climate change are only available at relatively short time frames (up to 10-20 years), including intra-specific trait variability, defoliation patterns, tree mortality and recruitment. Moreover, we identified data gaps or lack of data integration particularly in variables related to local adaptation and phenotypic plasticity, dispersal capabilities and physiological responses. Overall, we conclude that forest data availability across Europe is improving, but further efforts are needed to integrate, harmonise and interpret this data (i.e. making data useable for non-experts). Continuation of existing monitoring and networks schemes together with the establishments of new networks to address data gaps is crucial to rigorously predict climate change impacts on European forests.Peer reviewe

Biotic homogenization can decrease landscape-scale forest multifunctionality.

Many experiments have shown that local biodiversity loss impairs the ability of ecosystems to maintain multiple ecosystem functions at high levels (multifunctionality). In contrast, the role of biodiversity in driving ecosystem multifunctionality at landscape scales remains unresolved. We used a comprehensive pan-European dataset, including 16 ecosystem functions measured in 209 forest plots across six European countries, and performed simulations to investigate how local plot-scale richness of tree species (α-diversity) and their turnover between plots (β-diversity) are related to landscape-scale multifunctionality. After accounting for variation in environmental conditions, we found that relationships between α-diversity and landscape-scale multifunctionality varied from positive to negative depending on the multifunctionality metric used. In contrast, when significant, relationships between β-diversity and landscape-scale multifunctionality were always positive, because a high spatial turnover in species composition was closely related to a high spatial turnover in functions that were supported at high levels. Our findings have major implications for forest management and indicate that biotic homogenization can have previously unrecognized and negative consequences for large-scale ecosystem multifunctionality.We thank the Hainich National Park administration as well as Felix Berthold and Carsten Beinhoff for support of this study and Gerald Kaendler and the Johann Heinrich von Thünen-Institut for providing access to the German National Forest Inventory data. The research leading to these results received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under Grant Agreement 265171.This is the final version of the article. It first appeared from the National Academy of Sciences via https://doi.org//10.1073/pnas.151790311

Author Correction: Scalable and robust SARS-CoV-2 testing in an academic center.

An amendment to this paper has been published and can be accessed via a link at the top of the paper

Exponential growth, high prevalence of SARS-CoV-2, and vaccine effectiveness associated with the Delta variant

SARS-CoV-2 infections were rising during early summer 2021 in many countries associated with the Delta variant. We assessed RT-PCR swab-positivity in the REal-time Assessment of Community Transmission-1 (REACT-1) study in England. We observed sustained exponential growth with average doubling time (June-July 2021) of 25 days driven by complete replacement of Alpha variant by Delta, and by high prevalence at younger less-vaccinated ages. Unvaccinated people were three times more likely than double-vaccinated people to test positive. However, after adjusting for age and other variables, vaccine effectiveness for double-vaccinated people was estimated at between ~50% and ~60% during this period in England. Increased social mixing in the presence of Delta had the potential to generate sustained growth in infections, even at high levels of vaccination