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In the research domain of energy informatics, the importance of open datais rising rapidly. This can be seen as various new public datasets are created andpublished. Unfortunately, in many cases, the data is not available under a permissivelicense corresponding to the FAIR principles, often lacking accessibility or reusability.Furthermore, the source format often differs from the desired data format or does notmeet the demands to be queried in an efficient way. To solve this on a small scale atoolbox for ETL-processes is provided to create a local energy data server with openaccess data from different valuable sources in a structured format. So while the sourcesitself do not fully comply with the FAIR principles, the provided unique toolbox allows foran efficient processing of the data as if the FAIR principles would be met. The energydata server currently includes information of power systems, weather data, networkfrequency data, European energy and gas data for demand and generation and more.However, a solution to the core problem - missing alignment to the FAIR principles - isstill needed for the National Research Data Infrastructure.
Due to the transition to renewable energies, electricity markets need to be made fit for purpose. To enable the comparison of different energy market designs, modeling tools covering market actors and their heterogeneous behavior are needed. Agent-based models are ideally suited for this task. Such models can be used to simulate and analyze changes to market design or market mechanisms and their impact on market dynamics. In this paper, we conduct an evaluation and comparison of two actively developed open-source energy market simulation models. The two models, namely AMIRIS and ASSUME, are both designed to simulate future energy markets using an agent-based approach. The assessment encompasses modelling features and techniques, model performance, as well as a comparison of model results, which can serve as a blueprint for future comparative studies of simulation models. The main comparison dataset includes data of Germany in 2019 and simulates the Day-Ahead market and participating actors as individual agents. Both models are comparable close to the benchmark dataset with a MAE between 5.6 and 6.4 €/MWh while also modeling the actual dispatch realistically.
We conducted a scoping review for active learning in the domain of natural language processing (NLP), which we summarize in accordance with the PRISMA-ScR guidelines as follows:
Objective: Identify active learning strategies that were proposed for entity recognition and their evaluation environments (datasets, metrics, hardware, execution time).
Design: We used Scopus and ACM as our search engines. We compared the results with two literature surveys to assess the search quality. We included peer-reviewed English publications introducing or comparing active learning strategies for entity recognition.
Results: We analyzed 62 relevant papers and identified 106 active learning strategies. We grouped them into three categories: exploitation-based (60x), exploration-based (14x), and hybrid strategies (32x). We found that all studies used the F1-score as an evaluation metric. Information about hardware (6x) and execution time (13x) was only occasionally included. The 62 papers used 57 different datasets to evaluate their respective strategies. Most datasets contained newspaper articles or biomedical/medical data. Our analysis revealed that 26 out of 57 datasets are publicly accessible.
Conclusion: Numerous active learning strategies have been identified, along with significant open questions that still need to be addressed. Researchers and practitioners face difficulties when making data-driven decisions about which active learning strategy to adopt. Conducting comprehensive empirical comparisons using the evaluation environment proposed in this study could help establish best practices in the domain.
Subglacial environments on Earth offer important analogs to Ocean World targets in our solar system. These unique microbial ecosystems remain understudied due to the challenges of access through thick glacial ice (tens to hundreds of meters). Additionally, sub-ice collections must be conducted in a clean manner to ensure sample integrity for downstream microbiological and geochemical analyses. We describe the field-based cleaning of a melt probe that was used to collect brine samples from within a glacier conduit at Blood Falls, Antarctica, for geomicrobiological studies. We used a thermoelectric melting probe called the IceMole that was designed to be minimally invasive in that the logistical requirements in support of drilling operations were small and the probe could be cleaned, even in a remote field setting, so as to minimize potential contamination. In our study, the exterior bioburden on the IceMole was reduced to levels measured in most clean rooms, and below that of the ice surrounding our sampling target. Potential microbial contaminants were identified during the cleaning process; however, very few were detected in the final englacial sample collected with the IceMole and were present in extremely low abundances (∼0.063% of 16S rRNA gene amplicon sequences). This cleaning protocol can help minimize contamination when working in remote field locations, support microbiological sampling of terrestrial subglacial environments using melting probes, and help inform planetary protection challenges for Ocean World analog mission concepts.
Methane is a valuable energy source helping to mitigate the growing energy demand worldwide. However, as a potent greenhouse gas, it has also gained additional attention due to its environmental impacts. The biological production of methane is performed primarily hydrogenotrophically from H2 and CO2 by methanogenic archaea. Hydrogenotrophic methanogenesis also represents a great interest with respect to carbon re-cycling and H2 storage. The most significant carbon source, extremely rich in complex organic matter for microbial degradation and biogenic methane production, is coal. Although interest in enhanced microbial coalbed methane production is continuously increasing globally, limited knowledge exists regarding the exact origins of the coalbed methane and the associated microbial communities, including hydrogenotrophic methanogens. Here, we give an overview of hydrogenotrophic methanogens in coal beds and related environments in terms of their energy production mechanisms, unique metabolic pathways, and associated ecological functions.
Elastic transmission eigenvalues and their computation via the method of fundamental solutions
(2020)
A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach.
We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues.
The method of fundamental solutions is applied to the approximate computation of interior transmission eigenvalues for a special class of inhomogeneous media in two dimensions. We give a short approximation analysis accompanied with numerical results that clearly prove practical convenience of our alternative approach.
Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations.
In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric 2x2 matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach.
Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary
(2024)
In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we study a new direct sampling indicator based on the Landweber iteration and the factorization method. Therefore, we prove the connection between these reconstruction methods. The method studied here falls under the category of qualitative reconstruction methods where an imaging function is used to recover the absorbing scatterer. We prove stability of our new imaging function as well as derive a discrepancy principle for recovering the regularization parameter. The theoretical results are verified with numerical examples to show how the reconstruction performs by the new Landweber direct sampling method.
We consider the numerical approximation of second-order semi-linear parabolic stochastic partial differential equations interpreted in the mild sense which we solve on general two-dimensional domains with a C² boundary with homogeneous Dirichlet boundary conditions. The equations are driven by Gaussian additive noise, and several Lipschitz-like conditions are imposed on the nonlinear function. We discretize in space with a spectral Galerkin method and in time using an explicit Euler-like scheme. For irregular shapes, the necessary Dirichlet eigenvalues and eigenfunctions are obtained from a boundary integral equation method. This yields a nonlinear eigenvalue problem, which is discretized using a boundary element collocation method and is solved with the Beyn contour integral algorithm. We present an error analysis as well as numerical results on an exemplary asymmetric shape, and point out limitations of the approach.
Analysis and computation of the transmission eigenvalues with a conductive boundary condition
(2022)
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber–Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.
Fields of asymmetric tensors play an important role in many applications such as medical imaging (diffusion tensor magnetic resonance imaging), physics, and civil engineering (for example Cauchy-Green-deformation tensor, strain tensor with local rotations, etc.). However, such asymmetric tensors are usually symmetrized and then further processed. Using this procedure results in a loss of information. A new method for the processing of asymmetric tensor fields is proposed restricting our attention to tensors of second-order given by a 2x2 array or matrix with real entries. This is achieved by a transformation resulting in Hermitian matrices that have an eigendecomposition similar to symmetric matrices. With this new idea numerical results for real-world data arising from a deformation of an object by external forces are given. It is shown that the asymmetric part indeed contains valuable information.
An alternative method is presented to numerically compute interior elastic transmission eigenvalues for various domains in two dimensions. This is achieved by discretizing the resulting system of boundary integral equations in combination with a nonlinear eigenvalue solver. Numerical results are given to show that this new approach can provide better results than the finite element method when dealing with general domains.
The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10− 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.
There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost.
Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.
Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme.
A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.