@article{BertzSchoeningMolinnusetal.2024,
  author    = {Bertz, Morten and Sch{\"o}ning, Michael Josef and Molinnus, Denise and Homma, Takayuki},
  title     = {Influence of temperature, light, and H₂O₂ concentration on microbial spore inactivation: in-situ Raman spectroscopy combined with optical trapping},
  series = {Physica status solidi (a) applications and materials science},
  journal   = {Physica status solidi (a) applications and materials science},
  number    = {Early View},
  publisher = {Wiley-VCH},
  address   = {Berlin},
  issn      = {1862-6319 (Online)},
  doi       = {10.1002/pssa.202300866},
  pages     = {8 Seiten},
  year      = {2024},
  abstract  = {To gain insight on chemical sterilization processes, the influence of temperature (up to 70 °C), intense green light, and hydrogen peroxide (H₂O₂) concentration (up to 30\% in aqueous solution) on microbial spore inactivation is evaluated by in-situ Raman spectroscopy with an optical trap. Bacillus atrophaeus is utilized as a model organism. Individual spores are isolated and their chemical makeup is monitored under dynamically changing conditions (temperature, light, and H₂O₂ concentration) to mimic industrially relevant process parameters for sterilization in the field of aseptic food processing. While isolated spores in water are highly stable, even at elevated temperatures of 70 °C, exposure to H₂O₂ leads to a loss of spore integrity characterized by the release of the key spore biomarker dipicolinic acid (DPA) in a concentration-dependent manner, which indicates damage to the inner membrane of the spore. Intensive light or heat, both of which accelerate the decomposition of H₂O₂ into reactive oxygen species (ROS), drastically shorten the spore lifetime, suggesting the formation of ROS as a rate-limiting step during sterilization. It is concluded that Raman spectroscopy can deliver mechanistic insight into the mode of action of H₂O₂-based sterilization and reveal the individual contributions of different sterilization methods acting in tandem.},
  language  = {en}
}
@article{PogorelovaRogachevAkimbekovetal.2024,
  author    = {Pogorelova, Natalia and Rogachev, Evgeniy and Akimbekov, Nuraly S. and Digel, Ilya},
  title     = {Effect of dehydration method on the micro- and nanomorphological properties of bacterial cellulose produced by Medusomyces gisevii on different substrates},
  series = {Journal of materials science},
  volume    = {2024},
  journal   = {Journal of materials science},
  publisher = {Springer Science + Business Media},
  address   = {Dordrecht},
  issn      = {1573-4803 (Online)},
  doi       = {10.1007/s10853-024-09596-3},
  pages     = {13 Seiten},
  year      = {2024},
  abstract  = {Many important properties of bacterial cellulose (BC), such as moisture absorption capacity, elasticity and tensile strength, largely depend on its structure. This paper presents a study on the effect of the drying method on BC films produced by Medusomyces gisevii using two different procedures: room temperature drying (RT, (24 ± 2 °C, humidity 65 ± 1\%, dried until a constant weight was reached) and freeze-drying (FD, treated at - 75 °C for 48 h). BC was synthesized using one of two different carbon sources—either glucose or sucrose. Structural differences in the obtained BC films were evaluated using atomic force microscopy (AFM), scanning electron microscopy (SEM), and X-ray diffraction. Macroscopically, the RT samples appeared semi-transparent and smooth, whereas the FD group exhibited an opaque white color and sponge-like structure. SEM examination showed denser packing of fibrils in FD samples while RT-samples displayed smaller average fiber diameter, lower surface roughness and less porosity. AFM confirmed the SEM observations and showed that the FD material exhibited a more branched structure and a higher surface roughness. The samples cultivated in a glucose-containing nutrient medium, generally displayed a straight and ordered shape of fibrils compared to the sucrose-derived BC, characterized by a rougher and wavier structure. The BC films dried under different conditions showed distinctly different crystallinity degrees, whereas the carbon source in the culture medium was found to have a relatively small effect on the BC crystallinity.},
  language  = {en}
}
@article{KarschuckPoghossianSeretal.2024,
  author    = {Karschuck, Tobias and Poghossian, Arshak and Ser, Joey and Tsokolakyan, Astghik and Achtsnicht, Stefan and Wagner, Patrick and Sch{\"o}ning, Michael Josef},
  title     = {Capacitive model of enzyme-modified field-effect biosensors: Impact of enzyme coverage},
  series = {Sensors and Actuators B: Chemical},
  volume    = {408},
  journal   = {Sensors and Actuators B: Chemical},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0925-4005 (Print)},
  doi       = {10.1016/j.snb.2024.135530},
  pages     = {12 Seiten},
  year      = {2024},
  abstract  = {Electrolyte-insulator-semiconductor capacitors (EISCAP) belong to field-effect sensors having an attractive transducer architecture for constructing various biochemical sensors. In this study, a capacitive model of enzyme-modified EISCAPs has been developed and the impact of the surface coverage of immobilized enzymes on its capacitance-voltage and constant-capacitance characteristics was studied theoretically and experimentally. The used multicell arrangement enables a multiplexed electrochemical characterization of up to sixteen EISCAPs. Different enzyme coverages have been achieved by means of parallel electrical connection of bare and enzyme-covered single EISCAPs in diverse combinations. As predicted by the model, with increasing the enzyme coverage, both the shift of capacitance-voltage curves and the amplitude of the constant-capacitance signal increase, resulting in an enhancement of analyte sensitivity of the EISCAP biosensor. In addition, the capability of the multicell arrangement with multi-enzyme covered EISCAPs for sequentially detecting multianalytes (penicillin and urea) utilizing the enzymes penicillinase and urease has been experimentally demonstrated and discussed.},
  language  = {en}
}
@article{BornheimGriegerBlanecketal.2024,
  author    = {Bornheim, Tobias and Grieger, Niklas and Blaneck, Patrick Gustav and Bialonski, Stephan},
  title     = {Speaker Attribution in German Parliamentary Debates with QLoRA-adapted Large Language Models},
  series = {Journal for language technology and computational linguistics : JLCL},
  volume    = {37},
  journal   = {Journal for language technology and computational linguistics : JLCL},
  number    = {1},
  publisher = {Gesellschaft f{\"u}r Sprachtechnologie und Computerlinguistik},
  address   = {Regensburg},
  issn      = {2190-6858},
  doi       = {10.21248/jlcl.37.2024.244},
  pages     = {13 Seiten},
  year      = {2024},
  abstract  = {The growing body of political texts opens up new opportunities for rich insights into political dynamics and ideologies but also increases the workload for manual analysis. Automated speaker attribution, which detects who said what to whom in a speech event and is closely related to semantic role labeling, is an important processing step for computational text analysis. We study the potential of the large language model family Llama 2 to automate speaker attribution in German parliamentary debates from 2017-2021. We fine-tune Llama 2 with QLoRA, an efficient training strategy, and observe our approach to achieve competitive performance in the GermEval 2023 Shared Task On Speaker Attribution in German News Articles and Parliamentary Debates. Our results shed light on the capabilities of large language models in automating speaker attribution, revealing a promising avenue for computational analysis of political discourse and the development of semantic role labeling systems.},
  language  = {en}
}
@article{SchoenrockMuckeltHastermannetal.2024,
  author    = {Schoenrock, Britt and Muckelt, Paul E. and Hastermann, Maria and Albracht, Kirsten and MacGregor, Robert and Martin, David and Gunga, Hans-Christian and Salanova, Michele and Stokes, Maria J. and Warner, Martin B. and Blottner, Dieter},
  title     = {Muscle stiffness indicating mission crew health in space},
  series = {Scientific Reports},
  volume    = {14},
  journal   = {Scientific Reports},
  number    = {Article number: 4196},
  publisher = {Springer Nature},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/s41598-024-54759-6},
  pages     = {13 Seiten},
  year      = {2024},
  abstract  = {Muscle function is compromised by gravitational unloading in space affecting overall musculoskeletal health. Astronauts perform daily exercise programmes to mitigate these effects but knowing which muscles to target would optimise effectiveness. Accurate inflight assessment to inform exercise programmes is critical due to lack of technologies suitable for spaceflight. Changes in mechanical properties indicate muscle health status and can be measured rapidly and non-invasively using novel technology. A hand-held MyotonPRO device enabled monitoring of muscle health for the first time in spaceflight (> 180 days). Greater/maintained stiffness indicated countermeasures were effective. Tissue stiffness was preserved in the majority of muscles (neck, shoulder, back, thigh) but Tibialis Anterior (foot lever muscle) stiffness decreased inflight vs. preflight (p < 0.0001; mean difference 149 N/m) in all 12 crewmembers. The calf muscles showed opposing effects, Gastrocnemius increasing in stiffness Soleus decreasing. Selective stiffness decrements indicate lack of preservation despite daily inflight countermeasures. This calls for more targeted exercises for lower leg muscles with vital roles as ankle joint stabilizers and in gait. Muscle stiffness is a digital biomarker for risk monitoring during future planetary explorations (Moon, Mars), for healthcare management in challenging environments or clinical disorders in people on Earth, to enable effective tailored exercise programmes.},
  language  = {en}
}
@article{EngelmannSimsekShalabyetal.2024,
  author    = {Engelmann, Ulrich M. and Simsek, Beril and Shalaby, Ahmed and Krause, Hans-Joachim},
  title     = {Key contributors to signal generation in frequency mixing magnetic detection (FMMD): an in silico study},
  series = {Sensors},
  volume    = {24},
  journal   = {Sensors},
  number    = {6},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {1424-8220},
  doi       = {10.3390/s24061945},
  pages     = {Artikel 1945},
  year      = {2024},
  abstract  = {Frequency mixing magnetic detection (FMMD) is a sensitive and selective technique to detect magnetic nanoparticles (MNPs) serving as probes for binding biological targets. Its principle relies on the nonlinear magnetic relaxation dynamics of a particle ensemble interacting with a dual frequency external magnetic field. In order to increase its sensitivity, lower its limit of detection and overall improve its applicability in biosensing, matching combinations of external field parameters and internal particle properties are being sought to advance FMMD. In this study, we systematically probe the aforementioned interaction with coupled N{\´e}el-Brownian dynamic relaxation simulations to examine how key MNP properties as well as applied field parameters affect the frequency mixing signal generation. It is found that the core size of MNPs dominates their nonlinear magnetic response, with the strongest contributions from the largest particles. The drive field amplitude dominates the shape of the field-dependent response, whereas effective anisotropy and hydrodynamic size of the particles only weakly influence the signal generation in FMMD. For tailoring the MNP properties and parameters of the setup towards optimal FMMD signal generation, our findings suggest choosing large particles of core sizes dc > 25 nm nm with narrow size distributions (σ < 0.1) to minimize the required drive field amplitude. This allows potential improvements of FMMD as a stand-alone application, as well as advances in magnetic particle imaging, hyperthermia and magnetic immunoassays.},
  language  = {en}
}
@article{ZhenLiangStaatetal.2024,
  author    = {Zhen, Manghao and Liang, Yunpei and Staat, Manfred and Li, Quanqui and Li, Jianbo},
  title     = {Discontinuous fracture behaviors and constitutive model of sandstone specimens containing non-parallel prefabricated fissures under uniaxial compression},
  series = {Theoretical and Applied Fracture Mechanics},
  volume    = {131},
  journal   = {Theoretical and Applied Fracture Mechanics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-8442},
  doi       = {10.1016/j.tafmec.2024.104373},
  pages     = {Artikel 104373},
  year      = {2024},
  abstract  = {The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress-strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress-strain curves of the fissured sandstone specimens.},
  language  = {en}
}
@unpublished{GriegerMehrkanoonBialonski2024,
  author    = {Grieger, Niklas and Mehrkanoon, Siamak and Bialonski, Stephan},
  title     = {Preprint: Data-efficient sleep staging with synthetic time series pretraining},
  series = {arXiv},
  journal   = {arXiv},
  pages     = {10 Seiten},
  year      = {2024},
  abstract  = {Analyzing electroencephalographic (EEG) time series can be challenging, especially with deep neural networks, due to the large variability among human subjects and often small datasets. To address these challenges, various strategies, such as self-supervised learning, have been suggested, but they typically rely on extensive empirical datasets. Inspired by recent advances in computer vision, we propose a pretraining task termed "frequency pretraining" to pretrain a neural network for sleep staging by predicting the frequency content of randomly generated synthetic time series. Our experiments demonstrate that our method surpasses fully supervised learning in scenarios with limited data and few subjects, and matches its performance in regimes with many subjects. Furthermore, our results underline the relevance of frequency information for sleep stage scoring, while also demonstrating that deep neural networks utilize information beyond frequencies to enhance sleep staging performance, which is consistent with previous research. We anticipate that our approach will be advantageous across a broad spectrum of applications where EEG data is limited or derived from a small number of subjects, including the domain of brain-computer interfaces.},
  language  = {en}
}
@article{PieronekKleefeld2024,
  author    = {Pieronek, Lukas and Kleefeld, Andreas},
  title     = {On trajectories of complex-valued interior transmission eigenvalues},
  series = {Inverse problems and imaging : IPI},
  volume    = {18},
  journal   = {Inverse problems and imaging : IPI},
  number    = {2},
  publisher = {AIMS},
  address   = {Springfield, Mo},
  issn      = {1930-8337 (Print)},
  doi       = {10.3934/ipi.2023041},
  pages     = {480 -- 516},
  year      = {2024},
  abstract  = {This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.},
  language  = {en}
}
@article{AliaziziOezsoyluBakhshiSichanietal.2024,
  author    = {Aliazizi, Fereshteh and {\"O}zsoylu, Dua and Bakhshi Sichani, Soroush and Khorshid, Mehran and Glorieux, Christ and Robbens, Johan and Sch{\"o}ning, Michael J. and Wagner, Patrick},
  title     = {Development and Calibration of a Microfluidic, Chip-Based Sensor System for Monitoring the Physical Properties of Water Samples in Aquacultures},
  series = {Micromachines},
  volume    = {15},
  journal   = {Micromachines},
  number    = {6},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2072-666X},
  doi       = {10.3390/mi15060755},
  year      = {2024},
  abstract  = {In this work, we present a compact, bifunctional chip-based sensor setup that measures the temperature and electrical conductivity of water samples, including specimens from rivers and channels, aquaculture, and the Atlantic Ocean. For conductivity measurements, we utilize the impedance amplitude recorded via interdigitated electrode structures at a single triggering frequency. The results are well in line with data obtained using a calibrated reference instrument. The new setup holds for conductivity values spanning almost two orders of magnitude (river versus ocean water) without the need for equivalent circuit modelling. Temperature measurements were performed in four-point geometry with an on-chip platinum RTD (resistance temperature detector) in the temperature range between 2 °C and 40 °C, showing no hysteresis effects between warming and cooling cycles. Although the meander was not shielded against the liquid, the temperature calibration provided equivalent results to low conductive Milli-Q and highly conductive ocean water. The sensor is therefore suitable for inline and online monitoring purposes in recirculating aquaculture systems.},
  language  = {en}
}
@article{HarrisKleefeld2018,
  author    = {Harris, Isaac and Kleefeld, Andreas},
  title     = {The inverse scattering problem for a conductive boundary condition and transmission eigenvalues},
  series = {Applicable Analysis},
  volume    = {99},
  journal   = {Applicable Analysis},
  number    = {3},
  publisher = {Taylor \& Francis},
  address   = {London},
  issn      = {1563-504X},
  doi       = {10.1080/00036811.2018.1504028},
  pages     = {508 -- 529},
  year      = {2018},
  abstract  = {In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside-outside duality method can be used to reconstruct the interior conductive eigenvalues.},
  language  = {en}
}
@article{KleefeldPieronek2020,
  author    = {Kleefeld, Andreas and Pieronek, J.},
  title     = {Elastic transmission eigenvalues and their computation via the method of fundamental solutions},
  series = {Applicable Analysis},
  volume    = {100},
  journal   = {Applicable Analysis},
  number    = {16},
  publisher = {Taylore \& Francis},
  address   = {London},
  issn      = {1563-504X},
  doi       = {10.1080/00036811.2020.1721473},
  pages     = {3445 -- 3462},
  year      = {2020},
  abstract  = {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.},
  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{AsanteAsamaniKleefeldWade2020,
  author    = {Asante-Asamani, E.O. and Kleefeld, Andreas and Wade, B.A.},
  title     = {A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting},
  series = {Journal of Computational Physics},
  volume    = {415},
  journal   = {Journal of Computational Physics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2020.109490},
  year      = {2020},
  abstract  = {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.},
  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}
}
@article{MartinVaqueroKleefeld2020,
  author    = {Mart{\´i}n-Vaquero, J. and Kleefeld, Andreas},
  title     = {Solving nonlinear parabolic PDEs in several dimensions: Parallelized ESERK codes},
  series = {Journal of Computational Physics},
  journal   = {Journal of Computational Physics},
  number    = {423},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2020.109771},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@article{Kleefeld2021,
  author    = {Kleefeld, Andreas},
  title     = {The hot spots conjecture can be false: some numerical examples},
  series = {Advances in Computational Mathematics},
  volume    = {47},
  journal   = {Advances in Computational Mathematics},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1019-7168},
  doi       = {10.1007/s10444-021-09911-5},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@misc{BurgethKleefeldNaegeletal.2020,
  author    = {Burgeth, Bernhard and Kleefeld, Andreas and Naegel, Beno{\^i}t and Perret, Benjamin},
  title     = {Editorial — Special Issue: ISMM 2019},
  series = {Mathematical Morphology - Theory and Applications},
  volume    = {4},
  journal   = {Mathematical Morphology - Theory and Applications},
  number    = {1},
  publisher = {De Gruyter},
  address   = {Warschau},
  issn      = {2353-3390},
  doi       = {10.1515/mathm-2020-0200},
  pages     = {159 -- 161},
  year      = {2020},
  abstract  = {This editorial presents the Special Issue dedicated to the conference ISMM 2019 and summarizes the articles published in this Special Issue.},
  language  = {en}
}
@article{KleefeldZimmermann2022,
  author    = {Kleefeld, Andreas and Zimmermann, M.},
  title     = {Computing Elastic Interior Transmission Eigenvalues},
  series = {Integral Methods in Science and Engineering},
  journal   = {Integral Methods in Science and Engineering},
  editor    = {Constanda, Christian and Bodmann, Bardo E.J. and Harris, Paul J.},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-031-07171-3},
  doi       = {10.1007/978-3-031-07171-3_10},
  pages     = {139 -- 155},
  year      = {2022},
  abstract  = {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.},
  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}
}
@article{HarrisKleefeld2022,
  author    = {Harris, Isaac and Kleefeld, Andreas},
  title     = {Analysis and computation of the transmission eigenvalues with a conductive boundary condition},
  series = {Applicable Analysis},
  volume    = {101},
  journal   = {Applicable Analysis},
  number    = {6},
  publisher = {Taylor \& Francis},
  address   = {London},
  issn      = {1563-504X},
  doi       = {10.1080/00036811.2020.1789598},
  pages     = {1880 -- 1895},
  year      = {2022},
  abstract  = {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.},
  language  = {en}
}
@article{ClausnitzerKleefeld2024,
  author    = {Clausnitzer, Julian and Kleefeld, Andreas},
  title     = {A spectral Galerkin exponential Euler time-stepping scheme for parabolic SPDEs on two-dimensional domains with a C² boundary},
  series = {Discrete and Continuous Dynamical Systems - Series B},
  volume    = {29},
  journal   = {Discrete and Continuous Dynamical Systems - Series B},
  number    = {4},
  publisher = {AIMS},
  address   = {Springfield},
  issn      = {1531-3492},
  doi       = {10.3934/dcdsb.2023148},
  pages     = {1624 -- 1651},
  year      = {2024},
  abstract  = {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.},
  language  = {en}
}
@article{AyalaHarrisKleefeld2024,
  author    = {Ayala, Rafael Ceja and Harris, Isaac and Kleefeld, Andreas},
  title     = {Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary},
  series = {Inverse Problems and Imaging},
  volume    = {18},
  journal   = {Inverse Problems and Imaging},
  number    = {3},
  publisher = {AIMS},
  address   = {Springfield},
  issn      = {1930-8337},
  doi       = {10.3934/ipi.2023051},
  pages     = {708 -- 729},
  year      = {2024},
  abstract  = {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.},
  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}
}
@incollection{PieronekKleefeld2019,
  author    = {Pieronek, Lukas and Kleefeld, Andreas},
  title     = {The Method of Fundamental Solutions for Computing Interior Transmission Eigenvalues of Inhomogeneous Media},
  series = {Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations},
  booktitle = {Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations},
  editor    = {Constanda, Christian and Harris, Paul},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-030-16077-7},
  doi       = {10.1007/978-3-030-16077-7_28},
  pages     = {353 -- 365},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@incollection{AbeleKleefeld2020,
  author    = {Abele, Daniel and Kleefeld, Andreas},
  title     = {New Numerical Results for the Optimization of Neumann Eigenvalues},
  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 (Print)},
  doi       = {10.1007/978-3-030-48186-5_1},
  pages     = {1 -- 20},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}