The Geometry of Neural Nets' Parameter Spaces Under Reparametrization

Model reparametrization -- transforming the parameter space via a bijective differentiable map -- is a popular way to improve the training of neural networks. But reparametrizations have also been problematic since they induce inconsistencies in, e.g., Hessian-based flatness measures, optimization trajectories, and modes of probability density functions. This complicates downstream analyses, e.g. one cannot make a definitive statement about the connection between flatness and generalization. In this work, we study the invariance quantities of neural nets under reparametrization from the perspective of Riemannian geometry. We show that this notion of invariance is an inherent property of any neural net, as long as one acknowledges the assumptions about the metric that is always present, albeit often implicitly, and uses the correct transformation rules under reparametrization. We present discussions on measuring the flatness of minima, in optimization, and in probability-density maximization, along with applications in studying the biases of optimizers and in Bayesian inference

Detailed analysis of metagenome datasets obtained from biogas-producing microbial communities residing in biogas reactors does not indicate the presence of putative pathogenic microorganisms

Background: In recent years biogas plants in Germany have been supposed to be involved in amplification and dissemination of pathogenic bacteria causing severe infections in humans and animals. In particular, biogas plants are discussed to contribute to the spreading of Escherichia coli infections in humans or chronic botulism in cattle caused by Clostridium botulinum. Metagenome datasets of microbial communities from an agricultural biogas plant as well as from anaerobic lab-scale digesters operating at different temperatures and conditions were analyzed for the presence of putative pathogenic bacteria and virulence determinants by various bioinformatic approaches. Results: All datasets featured a low abundance of reads that were taxonomically assigned to the genus Escherichia or further selected genera comprising pathogenic species. Higher numbers of reads were taxonomically assigned to the genus Clostridium. However, only very few sequences were predicted to originate from pathogenic clostridial species. Moreover, mapping of metagenome reads to complete genome sequences of selected pathogenic bacteria revealed that not the pathogenic species itself, but only species that are more or less related to pathogenic ones are present in the fermentation samples analyzed. Likewise, known virulence determinants could hardly be detected. Only a marginal number of reads showed similarity to sequences described in the Microbial Virulence Database MvirDB such as those encoding protein toxins, virulence proteins or antibiotic resistance determinants. Conclusions: Findings of this first study of metagenomic sequence reads of biogas producing microbial communities suggest that the risk of dissemination of pathogenic bacteria by application of digestates from biogas fermentations as fertilizers is low, because obtained results do not indicate the presence of putative pathogenic microorganisms in the samples analyzed

Annexes 1-5: Urban Sprawl in Europe. Joint EEA-FOEN report. No 11/2016.

See main report "Urban Sprawl in Europe. Joint EEA-FOEN report"

Urban Sprawl in Europe. Joint EEA-FOEN report. No 11/2016.

Executive summary Urban sprawl is associated with a number of ecological, economic and social effects. Some of these relate to people's desires, for example, to live in single-family homes with gardens. However, urban sprawl has detrimental and long-lasting effects. For example, urban sprawl contributes significantly to the loss of fertile farmland, to soil sealing and to the loss of ecological soil functions. The increase in built-up areas reduces the size of wildlife habitats and increases landscape fragmentation and the spread of invasive species. Urban sprawl leads to higher greenhouse gas emissions, higher infrastructure costs for transport, water and electrical power, the loss of open landscapes, and the degradation of various ecosystem services. Despite various efforts to address this problem, urban sprawl has increased rapidly in Europe in recent decades. Thus, urban sprawl presents a major challenge with regard to sustainable land use, as the International Year of Soils 2015 highlighted. Sprawl is a result not only of population growth but also of lifestyles that take up more space. Accordingly, urban sprawl has increased even in regions with a declining human population. Many more urban development and transport infrastructure projects are planned for the future, in particular in the European Union (EU) Member States which joined after 2004. Consequently, further increases in urban sprawl in the future will be significant. Therefore, consistent data on the degree of urban sprawl are needed, particularly data that are suitable for the comparison of regions across Europe. This report investigates the degree of urban sprawl in 32 countries in Europe by considering two points in time (2006 and 2009) at three levels. The three levels include the country level, the NUTS-2 region level (based on the Nomenclature of Territorial Units for Statistics (NUTS)) and the 1-km2 cell level (based on the Land and Ecosystem Accounting (LEAC) grid). The comparison of two points in time allowed an assessment of temporal changes in urban sprawl. This report applies the method of 'weighted urban proliferation' (WUP), which quantifies the degree of urban sprawl for any given landscape through a combination of three components: (1) the size of the built-up areas; (2) the spatial configuration (dispersion) of the built-up areas in the landscape; and (3) the uptake of built-up area per inhabitant or job. The report provides, for the first time, an assessment of urban sprawl in all EU and European Free Trade Association (EFTA) countries using the WUP method. The urban sprawl values obtained cover a large range, from low values for large parts of Scandinavia ( 4 UPU/m2) and very high values for large parts of western and central Europe (> 6 UPU/m2). The two largest clusters of high-sprawl values in Europe are located in (1) north-eastern France, Belgium, the Netherlands and part of western Germany; and (2) in the United Kingdom between London and the Midlands. The analysis of sprawl at the 1-km2-grid level shows that sprawl is most pronounced in wide rings around city centres, along large transport corridors, and along many coastlines (particularly in the Mediterranean countries). The lowest levels of sprawl are mainly associated with mountain ranges or remote areas. The level of sprawl, as measured by WUP, increased in all European countries between 2006 and 2009. The overall WUP value for Europe (all 32 countries combined) increased from 1.56 urban permeation units (UPU)/m2 in 2006 to 1.64 UPU/m2 in 2009, that is by 5 % in 3 years or by 1.7 % per year. In most countries, the increase was higher than 1 % per year, and in many countries WUP increased by more than 2 % per year. This was also the case for most NUTS-2 regions. Future studies using additional time-points will allow more detailed temporal comparisons. Base data for 2012 will be available in 2016 and these could be analysed in a follow-up project. Driving forces and predictive models of urban sprawl The level of urban sprawl is largely a function of socio-economic and demographic drivers, and the geophysical context. Current levels of urban sprawl need to be interpreted within the context of regional socio-economic and geophysical conditions. Therefore, the second part of this study investigated the potential factors that may contribute to an increase or decrease in the degree of urban sprawl, and determined their relative importance. The report applied a set of statistical models to determine which of these factors drive the process of urban sprawl in Europe. We analysed the statistical relationships between urban sprawl and a range of explanatory variables (14 variables at the country level and 12 at the NUTS-2 level). We also applied these relationships to predict the expected sprawl values for all regions in our study area and compared actual values with predicted values. Most of our hypotheses about the likely driving forces of urban sprawl were confirmed by the statistical analyses. The relevant variables identified as affecting urban sprawl are population density, road density, railway density, household size, governmental effectiveness, the number of cars per 1 000 inhabitants and two environmental factors (i.e. net primary production and relief energy). This result was consistent for both of the years (2006 and 2009) considered in the analysis. The results indicate that economic development has, largely, not been decoupled from increases in urban sprawl. A high amount of variation in the level of urban sprawl, as measured by WUP, was explained by the predictor variables: 72–80 % at the country level and 80–81 % at the NUTS-2 level. The variation explained for the three components of WUP ranged between 67 % and 94 % at the NUTS-2 level. Efforts to control urban sprawl should take these driving forces into account. Relevance for monitoring and policymaking The results provided by this study are intended to contribute to more sustainable political decision- making and planning throughout Europe. In the last 15 years (2000–2015), several projects and programmes at the European level have proposed a suite of concepts and measures to address urban sprawl and promote more sustainable land use. The most recent (2014), and perhaps most important, of these is the Seventh Environment Action Programme (7EAP), which calls for indicators of resource efficiency to be established in order to guide public and private decision-makers. Although the urgent challenge presented by urban sprawl has been recognised, there is still no monitoring in place for European urban sprawl. This report aims to help close this gap. The results confirm the conclusion of earlier reports (e.g. EEA, 2006a; EEA, 2006b) namely that there is an increasingly urgent need for action. Large discrepancies between the predicted and observed levels of urban sprawl provide a basis for identifying areas for prioritising management action. Our data also provide a basis for scenarios regarding the future development of urban sprawl in Europe. There is an increasing need and interest in including indicators of urban sprawl in systems for monitoring sustainable development, the state of the environment, biodiversity and landscape quality. The results presented in this report are intended for this purpose and can be updated on a regular basis in order to detect trends in urban sprawl. This report also demonstrates the usefulness of the WUP method as a tool for urban and regional planning and for performance review based on benchmarks, targets and limits. This study provides a comparable measurement of urban sprawl for most of the European continent using a consistent data set across Europe. The results will support managers and policymakers with the allocation of resources for the better protection of agricultural soils and landscape quality, and more sustainable political decision-making related to land use. The report also identifies the most immediate priorities and future research needs

Zersiedelung in Europa: Ländervergleich und treibende Kräfte. (Urban sprawl in Europe: Comparison of countries and driving forces.)

Steigende Zersiedelung steht im Widerspruch zu den Prinzipien und dem Geist von Nachhaltigkeit. Daten zur Zersiedelung werden benötigt, um die Wirksamkeit von Maßnahmen und Verordnungen zu überprüfen, welche die Zersiedelung begrenzen sollen. Die Autoren haben die Methode der „gewichteten Zersiedelung“ (Weighted Urban Proliferation, WUP) auf 32 Länder in Europa angewendet, um die Zersiedelung zu messen. Dazu wurden die europäischen HRL-Imperviousness-Daten von 2006 und 2009 verwendet. Die Ergebnisse zeigen, dass große Teile Europas von Zersiedelung betroffen sind. Der Gesamtwert von WUP für Europa beträgt 1,64 Durchsiedlungseinheiten/m2 (2009). Er ist zwischen 2006 und 2009 deutlich angestiegen, aber die Werte der einzel- nen Länder unterscheiden sich stark voneinander. Außerdem wurde der Zusammenhang mit zwölf potenziellen Treibern der Zersiedelung statistisch untersucht. Dieses Projekt ist die erste Analyse der Zersiedelung und ihrer zeitlichen Veränderung für einen gesamten Kontinent mit WUP. Der Beitrag stellt erste Ergebnisse vor und weist auf die Veröffentlichungen hin, die derzeit in Vorbereitung sind

Viscosity and Diffusion: Crowding and Salt Effects in Protein Solutions

We report on a joint experimental-theoretical study of collective diffusion in, and static shear viscosity of solutions of bovine serum albumin (BSA) proteins, focusing on the dependence on protein and salt concentration. Data obtained from dynamic light scattering and rheometric measurements are compared to theoretical calculations based on an analytically treatable spheroid model of BSA with isotropic screened Coulomb plus hard-sphere interactions. The only input to the dynamics calculations is the static structure factor obtained from a consistent theoretical fit to a concentration series of small-angle X-ray scattering (SAXS) data. This fit is based on an integral equation scheme that combines high accuracy with low computational cost. All experimentally probed dynamic and static properties are reproduced theoretically with an at least semi-quantitative accuracy. For lower protein concentration and low salinity, both theory and experiment show a maximum in the reduced viscosity, caused by the electrostatic repulsion of proteins. The validity range of a generalized Stokes-Einstein (GSE) relation connecting viscosity, collective diffusion coefficient, and osmotic compressibility, proposed by Kholodenko and Douglas [PRE 51, 1081 (1995)] is examined. Significant violation of the GSE relation is found, both in experimental data and in theoretical models, in semi-dilute systems at physiological salinity, and under low-salt conditions for arbitrary protein concentrations