@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{StaatTran2022,
  author    = {Staat, Manfred and Tran, Ngoc Trinh},
  title     = {Strain based brittle failure criteria for rocks},
  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     = {500 -- 509},
  year      = {2022},
  abstract  = {When confining pressure is low or absent, extensional fractures are typical, with fractures occurring on unloaded planes in rock. These "paradox" fractures can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. But this criterion makes unrealistic strength predictions in biaxial compression and tension. A new extension strain criterion overcomes this limitation by adding a weighted principal shear component. The weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr-Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting failure modes, which are unexpected in the understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak P. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.},
  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}
}
@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{KirchnerHenkelNaetheretal.2008,
  author    = {Kirchner, Patrick and Henkel, H. and N{\"a}ther, Niko and Spelthahn, H. and Schneider, A. and Berger, J{\"o}rg and Kolstad, J. and Friedrich, P. and Sch{\"o}ning, Michael Josef},
  title     = {RFID-basiertes Sensorsystem zur Realisierung intelligenter Verpackungen f{\"u}r die Nahrungsmittelindustrie},
  series = {KMU - innovativ: IKT 2008. CD-ROM : BMBF-Statustagung KMU - innovativ: IKT, Darmstadt, 17. - 18. Nov. 2008},
  booktitle = {KMU - innovativ: IKT 2008. CD-ROM : BMBF-Statustagung KMU - innovativ: IKT, Darmstadt, 17. - 18. Nov. 2008},
  number    = {CD-ROM-Ausg.},
  publisher = {BMBF},
  address   = {Berlin},
  pages     = {9 S.},
  year      = {2008},
  language  = {de}
}
@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{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{DroszezSannoGoldmannetal.2016,
  author    = {Droszez, Anna and Sanno, Maximilian and Goldmann, Jan-Peter and Albracht, Kirsten and Br{\"u}ggemann, Gert-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}
}