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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.
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.
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.