Non-liftable Calabi-Yau spaces

We construct many new non-liftable three-dimensional Calabi-Yau spaces in positive characteristic. The technique relies on lifting a nodal model to a smooth rigid Calabi-Yau space over some number field as introduced by the first author and D. van Straten.Comment: 16 pages, 5 tables; v2: minor corrections and addition

Magnetoresistance of compensated semimetals in confined geometries

Two-component conductors -- e.g., semi-metals and narrow band semiconductors -- often exhibit unusually strong magnetoresistance in a wide temperature range. Suppression of the Hall voltage near charge neutrality in such systems gives rise to a strong quasiparticle drift in the direction perpendicular to the electric current and magnetic field. This drift is responsible for a strong geometrical increase of resistance even in weak magnetic fields. Combining the Boltzmann kinetic equation with sample electrostatics, we develop a microscopic theory of magnetotransport in two and three spatial dimensions. The compensated Hall effect in confined geometry is always accompanied by electron-hole recombination near the sample edges and at large-scale inhomogeneities. As the result, classical edge currents may dominate the resistance in the vicinity of charge compensation. The effect leads to linear magnetoresistance in two dimensions in a broad range of parameters. In three dimensions, the magnetoresistance is normally quadratic in the field, with the linear regime restricted to rectangular samples with magnetic field directed perpendicular to the sample surface. Finally, we discuss the effects of heat flow and temperature inhomogeneities on the magnetoresistance.Comment: 22 pages, 7 figures, published versio

Assessment of the impacts of clear-cutting on soil loss by water erosion in Italian forests: First comprehensive monitoring and modelling approach

Abstract As a member of the European Union, Italy has committed to the maintenance and protection of its forests based on sustainable forest development and management practices. According to Eurostat, Italy has the seventh largest forest surface available for wood supply in the EU-28, which is equal to 8.086 million hectares. For 2012, the Italian National Institute of Statistics estimated the total roundwood production of Italy to be 7.7 million m3, from a harvested forest surface of 61,038 ha. Large parts of the country's forests, mainly located in vulnerable mountainous landscapes that are highly sensitive to environmental changes, are subject to anthropogenic disturbance driven by wood supply interests. Despite the extensive logging activities and the well-known impacts that such management practices have on the soil-related forest ecosystems, there is a lack of spatially and temporally explicit information about the removal of trees. Hence, this study aims to: i) assess the soil loss by water erosion in Italian forest areas, ii) map forest harvests and iii) evaluate the effects of logging activities in terms of soil loss by means of comprehensive remote sensing and GIS modelling techniques. The study area covers about 785.6 × 104 ha, which corresponds to the main forest units of the CORINE land cover 2006 database (i.e. broad-leaved forests, coniferous forests and mixed forests). Annual forest logging activities were mapped using Landsat imagery. Validation procedures were applied. A revised version of the Universal Soil Loss Equation (USLE) was used to predict the soil loss potential due to rill and inter-rill processes. To ensure a thorough modelling approach, the input parameters were calculated using the original methods reported in the USDA handbooks. The derived high-resolution data regarding forest cover change shows that 317,535 ha (4.04% of the total forest area in Italy) were harvested during the period under review. The predicted long-term annual average soil loss rate was 0.54 Mg ha− 1 yr− 1. The average rate of soil loss in forests that remained undisturbed during the modelled period is equal to 0.33 Mg ha− 1 yr− 1. Notably, about half of the soil loss (45.3%) was predicted for the logged areas, even though these cover only about 10.6% of the Italian forests. The identified erosion hotspots may represent a serious threat for the soil-related forest ecosystems, and are in contrast to the EC Thematic Strategy for Soil Protection and Water Framework Directive

Quantum-chemical insights from deep tensor neural networks

Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding quantum many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into quantum-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep tensor neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol−1) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the model reveals a classification of aromatic rings with respect to their stability. Further applications of our model for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies, and molecules with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex quantum-chemical systems

Generation of Relativistic Electron Bunches with Arbitrary Current Distribution via Transverse-to-Longitudinal Phase Space Exchange

We propose a general method for tailoring the current distribution of relativistic electron bunches. The technique relies on a recently proposed method to exchange the longitudinal phase space emittance with one of the transverse emittances. The method consists of transversely shaping the bunch and then converting its transverse profile into a current profile via a transverse-to-longitudinal phase-space-exchange beamline. We show that it is possible to tailor the current profile to follow, in principle, any desired distributions. We demonstrate, via computer simulations, the application of the method to generate trains of microbunches with tunable spacing and linearly-ramped current profiles. We also briefly explore potential applications of the technique.Comment: 13 pages, 17 figure

SchNetPack 2.0: A neural network toolbox for atomistic machine learning

SchNetPack is a versatile neural networks toolbox that addresses both the requirements of method development and application of atomistic machine learning. Version 2.0 comes with an improved data pipeline, modules for equivariant neural networks as well as a PyTorch implementation of molecular dynamics. An optional integration with PyTorch Lightning and the Hydra configuration framework powers a flexible command-line interface. This makes SchNetPack 2.0 easily extendable with custom code and ready for complex training task such as generation of 3d molecular structures

Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte