@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}
}
@article{BertzMolinnusSchoeningetal.2023,
  author    = {Bertz, Morten and Molinnus, Denise and Sch{\"o}ning, Michael Josef and Homma, Takayuki},
  title     = {Real-time monitoring of H₂O₂ sterilization on individual bacillus atrophaeus spores by optical sensing with trapping Raman spectroscopy},
  series = {Chemosensors},
  volume    = {8},
  journal   = {Chemosensors},
  number    = {11},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2227-9040},
  doi       = {10.3390/chemosensors11080445},
  pages     = {Artikel 445},
  year      = {2023},
  abstract  = {Hydrogen peroxide (H₂O₂), a strong oxidizer, is a commonly used sterilization agent employed during aseptic food processing and medical applications. To assess the sterilization efficiency with H₂O₂, bacterial spores are common microbial systems due to their remarkable robustness against a wide variety of decontamination strategies. Despite their widespread use, there is, however, only little information about the detailed time-resolved mechanism underlying the oxidative spore death by H₂O₂. In this work, we investigate chemical and morphological changes of individual Bacillus atrophaeus spores undergoing oxidative damage using optical sensing with trapping Raman microscopy in real-time. The time-resolved experiments reveal that spore death involves two distinct phases: (i) an initial phase dominated by the fast release of dipicolinic acid (DPA), a major spore biomarker, which indicates the rupture of the spore's core; and (ii) the oxidation of the remaining spore material resulting in the subsequent fragmentation of the spores' coat. Simultaneous observation of the spore morphology by optical microscopy corroborates these mechanisms. The dependence of the onset of DPA release and the time constant of spore fragmentation on H₂O₂ shows that the formation of reactive oxygen species from H₂O₂ is the rate-limiting factor of oxidative spore death.},
  language  = {en}
}
@article{ThiebesKleinZingsheimetal.2022,
  author    = {Thiebes, Anja Lena and Klein, Sarah and Zingsheim, Jonas and M{\"o}ller, Georg H. and G{\"u}rzing, Stefanie and Reddemann, Manuel A. and Behbahani, Mehdi and Cornelissen, Christian G.},
  title     = {Effervescent atomizer as novel cell spray technology to decrease the gas-to-liquid ratio},
  series = {pharmaceutics},
  volume    = {14},
  journal   = {pharmaceutics},
  number    = {11},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/pharmaceutics14112421},
  pages     = {Artikel 2421},
  year      = {2022},
  abstract  = {Cell spraying has become a feasible application method for cell therapy and tissue engineering approaches. Different devices have been used with varying success. Often, twin-fluid atomizers are used, which require a high gas velocity for optimal aerosolization characteristics. To decrease the amount and velocity of required air, a custom-made atomizer was designed based on the effervescent principle. Different designs were evaluated regarding spray characteristics and their influence on human adipose-derived mesenchymal stromal cells. The arithmetic mean diameters of the droplets were 15.4-33.5 µm with decreasing diameters for increasing gas-to-liquid ratios. The survival rate was >90\% of the control for the lowest gas-to-liquid ratio. For higher ratios, cell survival decreased to approximately 50\%. Further experiments were performed with the design, which had shown the highest survival rates. After seven days, no significant differences in metabolic activity were observed. The apoptosis rates were not influenced by aerosolization, while high gas-to-liquid ratios caused increased necrosis levels. Tri-lineage differentiation potential into adipocytes, chondrocytes, and osteoblasts was not negatively influenced by aerosolization. Thus, the effervescent aerosolization principle was proven suitable for cell applications requiring reduced amounts of supplied air. This is the first time an effervescent atomizer was used for cell processing.},
  language  = {en}
}
@article{BreussKleefeld2020,
  author    = {Breuß, Michael and Kleefeld, Andreas},
  title     = {Implicit monotone difference methods for scalar conservation laws with source terms},
  series = {Acta Mathematica Vietnamica},
  volume    = {45},
  journal   = {Acta Mathematica Vietnamica},
  publisher = {Springer Singapore},
  address   = {Singapore},
  issn      = {2315-4144},
  doi       = {10.1007/s40306-019-00354-1},
  pages     = {709 -- 738},
  year      = {2020},
  abstract  = {In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970-986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.},
  language  = {en}
}
@article{Gaigall2020,
  author    = {Gaigall, Daniel},
  title     = {Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic on partly not identically distributed data},
  series = {Communications in Statistics - Theory and Methods},
  volume    = {51},
  journal   = {Communications in Statistics - Theory and Methods},
  number    = {12},
  publisher = {Taylor \& Francis},
  address   = {London},
  issn      = {1532-415X},
  doi       = {10.1080/03610926.2020.1805767},
  pages     = {4006 -- 4028},
  year      = {2020},
  abstract  = {The established Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic is investigated for partly not identically distributed data. Surprisingly, it turns out that the statistic has the well-known distribution-free limiting null distribution of the classical criterion under standard regularity conditions. An application is testing goodness-of-fit for the regression function in a non parametric random effects meta-regression model, where the consistency is obtained as well. Simulations investigate size and power of the approach for small and moderate sample sizes. A real data example based on clinical trials illustrates how the test can be used in applications.},
  language  = {en}
}
@incollection{Kleefeld2020,
  author    = {Kleefeld, Andreas},
  title     = {Numerical calculation of interior transmission eigenvalues with mixed boundary conditions},
  series = {Computational and Analytic Methods in Science and Engineering},
  booktitle = {Computational and Analytic Methods in Science and Engineering},
  editor    = {Constanda, Christian},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-030-48185-8 (Hardcover)},
  doi       = {10.1007/978-3-030-48186-5_9},
  pages     = {173 -- 195},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@book{Laack2022,
  author    = {Laack, Walter van},
  title     = {Greater Than the Entire Universe},
  publisher = {van Laack GmbH},
  address   = {Aachen},
  isbn      = {978-3-936624-52-6},
  pages     = {120 Seiten},
  year      = {2022},
  language  = {en}
}
@inproceedings{Laack2016,
  author    = {Laack, Walter van},
  title     = {Schnittstelle Tod: Wo stehen wir nach 40 Jahren NTE-Forschung?},
  publisher = {van Laack GmbH},
  address   = {Aachen},
  isbn      = {978-3-936624-30-4 (Print-Ausgabe)},
  url       = {http://nbn-resolving.de/urn:nbn:de:101:1-201603132912},
  pages     = {92 Seiten},
  year      = {2016},
  language  = {de}
}
@article{BaringhausGaigall2019,
  author    = {Baringhaus, Ludwig and Gaigall, Daniel},
  title     = {On an asymptotic relative efficiency concept based on expected volumes of confidence regions},
  series = {Statistics - A Journal of Theoretical and Applied Statistic},
  volume    = {53},
  journal   = {Statistics - A Journal of Theoretical and Applied Statistic},
  number    = {6},
  publisher = {Taylor \& Francis},
  address   = {London},
  issn      = {1029-4910},
  doi       = {10.1080/02331888.2019.1683560},
  pages     = {1396 -- 1436},
  year      = {2019},
  abstract  = {The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.},
  language  = {en}
}
@article{BaringhausGaigall2015,
  author    = {Baringhaus, Ludwig and Gaigall, Daniel},
  title     = {On an independence test approach to the goodness-of-fit problem},
  series = {Journal of Multivariate Analysis},
  volume    = {2015},
  journal   = {Journal of Multivariate Analysis},
  number    = {140},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0047-259X},
  doi       = {10.1016/j.jmva.2015.05.013},
  pages     = {193 -- 208},
  year      = {2015},
  abstract  = {Let X₁,…,Xₙ be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R²→R and g:R²→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X₁,X₂),g(X₁,X₂) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xᵢ,Xⱼ),g(Xᵢ,Xⱼ)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov-Smirnov and Cram{\´e}r-von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions.},
  language  = {en}
}