@inproceedings{DroszezSannoGoldmannetal.2016, author = {Droszez, Anna and Sanno, Maximilian and Goldmann, Jan-Peter and Albracht, Kirsten and Br{\"u}ggemann, Gerd-Peter and Braunstein, Bjoern}, title = {Differences between take-off behavior during vertical jumps and two artistic elements}, series = {34th International Conference of Biomechanics in Sport, Tsukuba, Japan, July 18-22, 2016}, booktitle = {34th International Conference of Biomechanics in Sport, Tsukuba, Japan, July 18-22, 2016}, issn = {1999-4168}, pages = {577 -- 580}, year = {2016}, language = {en} } @inproceedings{AbelBoninAlbrachtetal.2010, author = {Abel, Thomas and Bonin, Dominik and Albracht, Kirsten and Zeller, Sebastian and Br{\"u}ggemann, Gert-Peter and Burkett, Brendan and Str{\"u}der, Heiko K.}, title = {Kinematic profile of the elite handcyclist}, series = {28th International Conference on Biomechanics in Sports, Marquette, Michigan, USA, July 19 - 23, 2010}, booktitle = {28th International Conference on Biomechanics in Sports, Marquette, Michigan, USA, July 19 - 23, 2010}, issn = {1999-4168}, pages = {140 -- 141}, year = {2010}, language = {en} } @inproceedings{BraunsteinGoldmannAlbrachtetal.2013, author = {Braunstein, Bjoern and Goldmann, Jan-Peter and Albracht, Kirsten and Sanno, Maximilian and Willwacher, Steffen and Heinrich, Kai and Herrmann, Volker and Br{\"u}ggemann, Gert-Peter}, title = {Joint specific contribution of mechanical power and work during acceleration and top speed in elite sprinters}, series = {31 International Conference on Biomechanics in Sports, Taipei, Taiwan, July 07 - July 22, 2013}, booktitle = {31 International Conference on Biomechanics in Sports, Taipei, Taiwan, July 07 - July 22, 2013}, issn = {1999-4168}, year = {2013}, language = {en} } @inproceedings{KolditzAlbrachtFasseetal.2015, author = {Kolditz, Melanie and Albracht, Kirsten and Fasse, Alessandro and Albin, Thivaharan and Br{\"u}ggemann, Gert-Peter and Abel, Dirk}, title = {Evaluation of an industrial robot as a leg press training device}, series = {XV International Symposium on Computer Simulation in Biomechanics July 9th - 11th 2015, Edinburgh, UK}, booktitle = {XV International Symposium on Computer Simulation in Biomechanics July 9th - 11th 2015, Edinburgh, UK}, pages = {41 -- 42}, year = {2015}, language = {en} } @inproceedings{KolditzAlbinFasseetal.2015, author = {Kolditz, Melanie and Albin, Thivaharan and Fasse, Alessandro and Br{\"u}ggemann, Gert-Peter and Abel, Dirk and Albracht, Kirsten}, title = {Simulative Analysis of Joint Loading During Leg Press Exercise for Control Applications}, series = {IFAC-PapersOnLine}, volume = {48}, booktitle = {IFAC-PapersOnLine}, number = {20}, doi = {10.1016/j.ifacol.2015.10.179}, pages = {435 -- 440}, year = {2015}, language = {en} } @inproceedings{RichterBraunsteinStaeudleetal.2018, author = {Richter, Charlotte and Braunstein, Bjoern and St{\"a}udle, Benjamin and Attias, Julia and Suess, Alexander and Weber, T. and Rittweger, Joern and Green, David A. and Albracht, Kirsten}, title = {In vivo fascicle length of the gastrocnemius muscle during walking in simulated martian gravity using two different body weight support devices}, series = {23rd Annual Congress of the European College of Sport Science, Dublin, Irland}, booktitle = {23rd Annual Congress of the European College of Sport Science, Dublin, Irland}, year = {2018}, language = {en} } @inproceedings{BehbahaniRibleMoulinecetal.2015, author = {Behbahani, Mehdi and Rible, Sebastian and Moulinec, Charles and Fournier, Yvan and Nicolai, Mike and Crosetto, Paolo}, title = {Simulation of the FDA Centrifugal Blood Pump Using High Performance Computing}, series = {World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering}, volume = {9}, booktitle = {World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering}, number = {5}, year = {2015}, language = {en} } @inproceedings{WeldenSeverinsPoghossianetal.2022, author = {Welden, Melanie and Severins, Robin and Poghossian, Arshak and Wege, Christina and Siegert, Petra and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Studying the immobilization of acetoin reductase with Tobacco mosaic virus particles on capacitive field-effect sensors}, series = {2022 IEEE International Symposium on Olfaction and Electronic Nose (ISOEN)}, booktitle = {2022 IEEE International Symposium on Olfaction and Electronic Nose (ISOEN)}, publisher = {IEEE}, isbn = {978-1-6654-5860-3 (Online)}, doi = {10.1109/ISOEN54820.2022.9789657}, pages = {4 Seiten}, year = {2022}, abstract = {A capacitive electrolyte-insulator-semiconductor (EISCAP) biosensor modified with Tobacco mosaic virus (TMV) particles for the detection of acetoin is presented. The enzyme acetoin reductase (AR) was immobilized on the surface of the EISCAP using TMV particles as nanoscaffolds. The study focused on the optimization of the TMV-assisted AR immobilization on the Ta 2 O 5 -gate EISCAP surface. The TMV-assisted acetoin EISCAPs were electrochemically characterized by means of leakage-current, capacitance-voltage, and constant-capacitance measurements. The TMV-modified transducer surface was studied via scanning electron microscopy.}, language = {en} } @inproceedings{Gaigall2022, author = {Gaigall, Daniel}, title = {On Consistent Hypothesis Testing In General Hilbert Spaces}, series = {Proceedings of the 4th International Conference on Statistics: Theory and Applications (ICSTA'22)}, booktitle = {Proceedings of the 4th International Conference on Statistics: Theory and Applications (ICSTA'22)}, publisher = {Avestia Publishing}, address = {Orl{\´e}ans, Kanada}, doi = {10.11159/icsta22.157}, pages = {Paper No. 157}, year = {2022}, abstract = {Inference on the basis of high-dimensional and functional data are two topics which are discussed frequently in the current statistical literature. A possibility to include both topics in a single approach is working on a very general space for the underlying observations, such as a separable Hilbert space. We propose a general method for consistently hypothesis testing on the basis of random variables with values in separable Hilbert spaces. We avoid concerns with the curse of dimensionality due to a projection idea. We apply well-known test statistics from nonparametric inference to the projected data and integrate over all projections from a specific set and with respect to suitable probability measures. In contrast to classical methods, which are applicable for real-valued random variables or random vectors of dimensions lower than the sample size, the tests can be applied to random vectors of dimensions larger than the sample size or even to functional and high-dimensional data. In general, resampling procedures such as bootstrap or permutation are suitable to determine critical values. The idea can be extended to the case of incomplete observations. Moreover, we develop an efficient algorithm for implementing the method. Examples are given for testing goodness-of-fit in a one-sample situation in [1] or for testing marginal homogeneity on the basis of a paired sample in [2]. Here, the test statistics in use can be seen as generalizations of the well-known Cram{\´e}rvon-Mises test statistics in the one-sample and two-samples case. The treatment of other testing problems is possible as well. By using the theory of U-statistics, for instance, asymptotic null distributions of the test statistics are obtained as the sample size tends to infinity. Standard continuity assumptions ensure the asymptotic exactness of the tests under the null hypothesis and that the tests detect any alternative in the limit. Simulation studies demonstrate size and power of the tests in the finite sample case, confirm the theoretical findings, and are used for the comparison with concurring procedures. A possible application of the general approach is inference for stock market returns, also in high data frequencies. In the field of empirical finance, statistical inference of stock market prices usually takes place on the basis of related log-returns as data. In the classical models for stock prices, i.e., the exponential L{\´e}vy model, Black-Scholes model, and Merton model, properties such as independence and stationarity of the increments ensure an independent and identically structure of the data. Specific trends during certain periods of the stock price processes can cause complications in this regard. In fact, our approach can compensate those effects by the treatment of the log-returns as random vectors or even as functional data.}, language = {en} } @inproceedings{TranTrinhDaoetal.2022, author = {Tran, Ngoc Trinh and Trinh, Tu Luc and Dao, Ngoc Tien and Giap, Van Tan and Truong, Manh Khuyen and Dinh, Thuy Ha and Staat, Manfred}, title = {Limit and shakedown analysis of structures under random strength}, series = {Proceedings of (NACOME2022) The 11th National Conference on Mechanics, Vol. 1. Solid Mechanics, Rock Mechanics, Artificial Intelligence, Teaching and Training}, booktitle = {Proceedings of (NACOME2022) The 11th National Conference on Mechanics, Vol. 1. Solid Mechanics, Rock Mechanics, Artificial Intelligence, Teaching and Training}, publisher = {Nha xuat ban Khoa hoc tu nhien va Cong nghe (Verlag Naturwissenschaft und Technik)}, address = {Hanoi}, isbn = {978-604-357-084-7}, pages = {510 -- 518}, year = {2022}, abstract = {Direct methods comprising limit and shakedown analysis is a branch of computational mechanics. It plays a significant role in mechanical and civil engineering design. The concept of direct method aims to determinate the ultimate load bearing capacity of structures beyond the elastic range. For practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and onstraints. If strength and loading are random quantities, the problem of shakedown analysis is considered as stochastic programming. This paper presents a method so called chance constrained programming, an effective method of stochastic programming, to solve shakedown analysis problem under random condition of strength. In this our investigation, the loading is deterministic, the strength is distributed as normal or lognormal variables.}, language = {en} } @inproceedings{Maurer2022, author = {Maurer, Florian}, title = {Framework to provide a simulative comparison of different energy market designs}, series = {Energy Informatics}, volume = {5}, booktitle = {Energy Informatics}, number = {2, Article number: 12}, publisher = {Springer Nature}, issn = {2520-8942}, doi = {10.1186/s42162-022-00215-6}, pages = {18 -- 20}, year = {2022}, abstract = {Useful market simulations are key to the evaluation of diferent market designs existing of multiple market mechanisms or rules. Yet a simulation framework which has a comparison of diferent market mechanisms in mind was not found. The need to create an objective view on different sets of market rules while investigating meaningful agent strategies concludes that such a simulation framework is needed to advance the research on this subject. An overview of diferent existing market simulation models is given which also shows the research gap and the missing capabilities of those systems. Finally, a methodology is outlined how a novel market simulation which can answer the research questions can be developed.}, language = {en} } @inproceedings{BuesgenKloeserKohletal.2023, author = {B{\"u}sgen, Andr{\´e} and Kl{\"o}ser, Lars and Kohl, Philipp and Schmidts, Oliver and Kraft, Bodo and Z{\"u}ndorf, Albert}, title = {From cracked accounts to fake IDs: user profiling on German telegram black market channels}, series = {Data Management Technologies and Applications}, booktitle = {Data Management Technologies and Applications}, editor = {Cuzzocrea, Alfredo and Gusikhin, Oleg and Hammoudi, Slimane and Quix, Christoph}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-37889-8 (Print)}, doi = {10.1007/978-3-031-37890-4_9}, pages = {176 -- 202}, year = {2023}, abstract = {Messenger apps like WhatsApp and Telegram are frequently used for everyday communication, but they can also be utilized as a platform for illegal activity. Telegram allows public groups with up to 200.000 participants. Criminals use these public groups for trading illegal commodities and services, which becomes a concern for law enforcement agencies, who manually monitor suspicious activity in these chat rooms. This research demonstrates how natural language processing (NLP) can assist in analyzing these chat rooms, providing an explorative overview of the domain and facilitating purposeful analyses of user behavior. We provide a publicly available corpus of annotated text messages with entities and relations from four self-proclaimed black market chat rooms. Our pipeline approach aggregates the extracted product attributes from user messages to profiles and uses these with their sold products as features for clustering. The extracted structured information is the foundation for further data exploration, such as identifying the top vendors or fine-granular price analyses. Our evaluation shows that pretrained word vectors perform better for unsupervised clustering than state-of-the-art transformer models, while the latter is still superior for sequence labeling.}, language = {en} } @inproceedings{KohlFreyerKraemeretal.2023, author = {Kohl, Philipp and Freyer, Nils and Kr{\"a}mer, Yoka and Werth, Henri and Wolf, Steffen and Kraft, Bodo and Meinecke, Matthias and Z{\"u}ndorf, Albert}, title = {ALE: a simulation-based active learning evaluation framework for the parameter-driven comparison of query strategies for NLP}, series = {Deep Learning Theory and Applications}, booktitle = {Deep Learning Theory and Applications}, editor = {Conte, Donatello and Fred, Ana and Gusikhin, Oleg and Sansone, Carlo}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-39058-6 (Print)}, doi = {10.1007/978-3-031-39059-3_16}, pages = {235 -- 253}, year = {2023}, abstract = {Supervised machine learning and deep learning require a large amount of labeled data, which data scientists obtain in a manual, and time-consuming annotation process. To mitigate this challenge, Active Learning (AL) proposes promising data points to annotators they annotate next instead of a subsequent or random sample. This method is supposed to save annotation effort while maintaining model performance. However, practitioners face many AL strategies for different tasks and need an empirical basis to choose between them. Surveys categorize AL strategies into taxonomies without performance indications. Presentations of novel AL strategies compare the performance to a small subset of strategies. Our contribution addresses the empirical basis by introducing a reproducible active learning evaluation (ALE) framework for the comparative evaluation of AL strategies in NLP. The framework allows the implementation of AL strategies with low effort and a fair data-driven comparison through defining and tracking experiment parameters (e.g., initial dataset size, number of data points per query step, and the budget). ALE helps practitioners to make more informed decisions, and researchers can focus on developing new, effective AL strategies and deriving best practices for specific use cases. With best practices, practitioners can lower their annotation costs. We present a case study to illustrate how to use the framework.}, language = {en} } @inproceedings{KloeserBuesgenKohletal.2023, author = {Kl{\"o}ser, Lars and B{\"u}sgen, Andr{\´e} and Kohl, Philipp and Kraft, Bodo and Z{\"u}ndorf, Albert}, title = {Explaining relation classification models with semantic extents}, series = {Deep Learning Theory and Applications}, booktitle = {Deep Learning Theory and Applications}, editor = {Conte, Donatello and Fred, Ana and Gusikhin, Oleg and Sansone, Carlo}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-39058-6 (Print)}, doi = {10.1007/978-3-031-39059-3_13}, pages = {189 -- 208}, year = {2023}, abstract = {In recent years, the development of large pretrained language models, such as BERT and GPT, significantly improved information extraction systems on various tasks, including relation classification. State-of-the-art systems are highly accurate on scientific benchmarks. A lack of explainability is currently a complicating factor in many real-world applications. Comprehensible systems are necessary to prevent biased, counterintuitive, or harmful decisions. We introduce semantic extents, a concept to analyze decision patterns for the relation classification task. Semantic extents are the most influential parts of texts concerning classification decisions. Our definition allows similar procedures to determine semantic extents for humans and models. We provide an annotation tool and a software framework to determine semantic extents for humans and models conveniently and reproducibly. Comparing both reveals that models tend to learn shortcut patterns from data. These patterns are hard to detect with current interpretability methods, such as input reductions. Our approach can help detect and eliminate spurious decision patterns during model development. Semantic extents can increase the reliability and security of natural language processing systems. Semantic extents are an essential step in enabling applications in critical areas like healthcare or finance. Moreover, our work opens new research directions for developing methods to explain deep learning models.}, language = {en} } @inproceedings{KetelhutGoellBraunsteinetal.2019, author = {Ketelhut, Maike and G{\"o}ll, Fabian and Braunstein, Bjoern and Albracht, Kirsten and Abel, Dirk}, title = {Iterative learning control of an industrial robot for neuromuscular training}, series = {2019 IEEE Conference on Control Technology and Applications}, booktitle = {2019 IEEE Conference on Control Technology and Applications}, publisher = {IEEE}, address = {New York}, isbn = {978-1-7281-2767-5 (ePub)}, doi = {10.1109/CCTA.2019.8920659}, pages = {7 Seiten}, year = {2019}, abstract = {Effective training requires high muscle forces potentially leading to training-induced injuries. Thus, continuous monitoring and controlling of the loadings applied to the musculoskeletal system along the motion trajectory is required. In this paper, a norm-optimal iterative learning control algorithm for the robot-assisted training is developed. The algorithm aims at minimizing the external knee joint moment, which is commonly used to quantify the loading of the medial compartment. To estimate the external knee joint moment, a musculoskeletal lower extremity model is implemented in OpenSim and coupled with a model of an industrial robot and a force plate mounted at its end-effector. The algorithm is tested in simulation for patients with varus, normal and valgus alignment of the knee. The results show that the algorithm is able to minimize the external knee joint moment in all three cases and converges after less than seven iterations.}, language = {en} } @inproceedings{SimsekKrauseEngelmann2024, author = {Simsek, Beril and Krause, Hans-Joachim and Engelmann, Ulrich M.}, title = {Magnetic biosensing with magnetic nanoparticles: Simulative approach to predict signal intensity in frequency mixing magnetic detection}, series = {YRA MedTech Symposium (2024)}, booktitle = {YRA MedTech Symposium (2024)}, editor = {Digel, Ilya and Staat, Manfred and Trzewik, J{\"u}rgen and Sielemann, Stefanie and Erni, Daniel and Zylka, Waldemar}, publisher = {Universit{\"a}t Duisburg-Essen}, address = {Duisburg}, organization = {MedTech Symposium}, isbn = {978-3-940402-65-3}, doi = {10.17185/duepublico/81475}, pages = {27 -- 28}, year = {2024}, abstract = {Magnetic nanoparticles (MNP) are investigated with great interest for biomedical applications in diagnostics (e.g. imaging: magnetic particle imaging (MPI)), therapeutics (e.g. hyperthermia: magnetic fluid hyperthermia (MFH)) and multi-purpose biosensing (e.g. magnetic immunoassays (MIA)). What all of these applications have in common is that they are based on the unique magnetic relaxation mechanisms of MNP in an alternating magnetic field (AMF). While MFH and MPI are currently the most prominent examples of biomedical applications, here we present results on the relatively new biosensing application of frequency mixing magnetic detection (FMMD) from a simulation perspective. In general, we ask how the key parameters of MNP (core size and magnetic anisotropy) affect the FMMD signal: by varying the core size, we investigate the effect of the magnetic volume per MNP; and by changing the effective magnetic anisotropy, we study the MNPs' flexibility to leave its preferred magnetization direction. From this, we predict the most effective combination of MNP core size and magnetic anisotropy for maximum signal generation.}, language = {en} } @inproceedings{SchmitzApandiSpillneretal.2024, author = {Schmitz, Annika and Apandi, Shah Eiman Amzar Shah and Spillner, Jan and Hima, Flutura and Behbahani, Mehdi}, title = {Effect of different cannula positions in the pulmonary artery on blood flow and gas exchange using computational fluid dynamics analysis}, series = {YRA MedTech Symposium (2024)}, booktitle = {YRA MedTech Symposium (2024)}, editor = {Digel, Ilya and Staat, Manfred and Trzewik, J{\"u}rgen and Sielemann, Stefanie and Erni, Daniel and Zylka, Waldemar}, publisher = {Universit{\"a}t Duisburg-Essen}, address = {Duisburg}, organization = {MedTech Symposium}, isbn = {978-3-940402-65-3}, doi = {10.17185/duepublico/81475}, pages = {29 -- 30}, year = {2024}, abstract = {Pulmonary arterial cannulation is a common and effective method for percutaneous mechanical circulatory support for concurrent right heart and respiratory failure [1]. However, limited data exists to what effect the positioning of the cannula has on the oxygen perfusion throughout the pulmonary artery (PA). This study aims to evaluate, using computational fluid dynamics (CFD), the effect of different cannula positions in the PA with respect to the oxygenation of the different branching vessels in order for an optimal cannula position to be determined. The four chosen different positions (see Fig. 1) of the cannulas are, in the lower part of the main pulmonary artery (MPA), in the MPA at the junction between the right pulmonary artery (RPA) and the left pulmonary artery (LPA), in the RPA at the first branch of the RPA and in the LPA at the first branch of the LPA.}, language = {en} } @inproceedings{MaurerMiskiwAcostaetal.2023, author = {Maurer, Florian and Miskiw, Kim K. and Acosta, Rebeca Ramirez and Harder, Nick and Sander, Volker and Lehnhoff, Sebastian}, title = {Market abstraction of energy markets and policies - application in an agent-based modeling toolbox}, series = {EI.A 2023: Energy Informatics}, booktitle = {EI.A 2023: Energy Informatics}, editor = {Jorgensen, Bo Norregaard and Pereira da Silva, Luiz Carlos and Ma, Zheng}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-48651-7 (Print)}, doi = {10.1007/978-3-031-48652-4_10}, pages = {139 -- 157}, year = {2023}, abstract = {In light of emerging challenges in energy systems, markets are prone to changing dynamics and market design. Simulation models are commonly used to understand the changing dynamics of future electricity markets. However, existing market models were often created with specific use cases in mind, which limits their flexibility and usability. This can impose challenges for using a single model to compare different market designs. This paper introduces a new method of defining market designs for energy market simulations. The proposed concept makes it easy to incorporate different market designs into electricity market models by using relevant parameters derived from analyzing existing simulation tools, morphological categorization and ontologies. These parameters are then used to derive a market abstraction and integrate it into an agent-based simulation framework, allowing for a unified analysis of diverse market designs. Furthermore, we showcase the usability of integrating new types of long-term contracts and over-the-counter trading. To validate this approach, two case studies are demonstrated: a pay-as-clear market and a pay-as-bid long-term market. These examples demonstrate the capabilities of the proposed framework.}, language = {en} } @inproceedings{BurgethKleefeldZhangetal.2022, author = {Burgeth, Bernhard and Kleefeld, Andreas and Zhang, Eugene and Zhang, Yue}, title = {Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification}, series = {Discrete Geometry and Mathematical Morphology}, booktitle = {Discrete Geometry and Mathematical Morphology}, editor = {Baudrier, {\´E}tienne and Naegel, Beno{\^i}t and Kr{\"a}henb{\"u}hl, Adrien and Tajine, Mohamed}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-19897-7}, doi = {10.1007/978-3-031-19897-7_5}, pages = {48 -- 59}, year = {2022}, abstract = {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.}, language = {en} } @inproceedings{KahraBreussKleefeldetal.2024, author = {Kahra, Marvin and Breuß, Michael and Kleefeld, Andreas and Welk, Martin}, title = {An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation}, series = {Discrete Geometry and Mathematical Morphology}, booktitle = {Discrete Geometry and Mathematical Morphology}, editor = {Brunetti, Sara and Frosini, Andrea and Rinaldi, Simone}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-57793-2}, doi = {10.1007/978-3-031-57793-2_25}, pages = {325 -- 337}, year = {2024}, abstract = {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.}, language = {en} }