@article{KayaFreitag2022,
  author    = {Kaya, Adem and Freitag, Melina A.},
  title     = {Conditioning analysis for discrete Helmholtz problems},
  series = {Computers and mathematics with applications : an international journal},
  volume    = {118},
  journal   = {Computers and mathematics with applications : an international journal},
  publisher = {Elsevier Science},
  address   = {Amsterdam},
  issn      = {0898-1221},
  doi       = {10.1016/j.camwa.2022.05.016},
  pages     = {171 -- 182},
  year      = {2022},
  abstract  = {In this paper, we examine conditioning of the discretization of the Helmholtz problem. Although the discrete Helmholtz problem has been studied from different perspectives, to the best of our knowledge, there is no conditioning analysis for it. We aim to fill this gap in the literature. We propose a novel method in 1D to observe the near-zero eigenvalues of a symmetric indefinite matrix. Standard classification of ill-conditioning based on the matrix condition number is not true for the discrete Helmholtz problem. We relate the ill-conditioning of the discretization of the Helmholtz problem with the condition number of the matrix. We carry out analytical conditioning analysis in 1D and extend our observations to 2D with numerical observations. We examine several discretizations. We find different regions in which the condition number of the problem shows different characteristics. We also explain the general behavior of the solutions in these regions.},
  language  = {en}
}
@article{Kind2014,
  author    = {Kind, Josephine},
  title     = {Creation of topographic maps},
  series = {Process design for natural scientists: an agile model-driven approach},
  journal   = {Process design for natural scientists: an agile model-driven approach},
  number    = {500},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-662-45005-5},
  pages     = {229 -- 238},
  year      = {2014},
  abstract  = {Location analyses are among the most common tasks while working with spatial data and geographic information systems. Automating the most frequently used procedures is therefore an important aspect of improving their usability. In this context, this project aims to design and implement a workflow, providing some basic tools for a location analysis. For the implementation with jABC, the workflow was applied to the problem of finding a suitable location for placing an artificial reef. For this analysis three parameters (bathymetry, slope and grain size of the ground material) were taken into account, processed, and visualized with the The Generic Mapping Tools (GMT), which were integrated into the workflow as jETI-SIBs. The implemented workflow thereby showed that the approach to combine jABC with GMT resulted in an user-centric yet user-friendly tool with high-quality cartographic outputs.},
  language  = {en}
}
@article{HartungBorghardt2020,
  author    = {Hartung, Niklas and Borghardt, Jens Markus},
  title     = {A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs},
  series = {PLoS Computational Biology : a new community journal},
  volume    = {16},
  journal   = {PLoS Computational Biology : a new community journal},
  number    = {12},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1553-734X},
  doi       = {10.1371/journal.pcbi.1008466},
  pages     = {24},
  year      = {2020},
  abstract  = {Author summary <br /> The use of orally inhaled drugs for treating lung diseases is appealing since they have the potential for lung selectivity, i.e. high exposure at the site of action -the lung- without excessive side effects. However, the degree of lung selectivity depends on a large number of factors, including physiochemical properties of drug molecules, patient disease state, and inhalation devices. To predict the impact of these factors on drug exposure and thereby to understand the characteristics of an optimal drug for inhalation, we develop a predictive mathematical framework (a "pharmacokinetic model"). In contrast to previous approaches, our model allows combining knowledge from different sources appropriately and its predictions were able to adequately predict different sets of clinical data. Finally, we compare the impact of different factors and find that the most important factors are the size of the inhaled particles, the affinity of the drug to the lung tissue, as well as the rate of drug dissolution in the lung. In contrast to the common belief, the solubility of a drug in the lining fluids is not found to be relevant. These findings are important to understand how inhaled drugs should be designed to achieve best treatment results in patients. <br /> The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.},
  language  = {en}
}
@article{DereudreMazzonettoRoelly2017,
  author    = {Dereudre, David and Mazzonetto, Sara and Roelly, Sylvie},
  title     = {Exact simulation of Brownian diffusions with drift admitting jumps},
  series = {SIAM journal on scientific computing},
  volume    = {39},
  journal   = {SIAM journal on scientific computing},
  number    = {3},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/16M107699X},
  pages     = {A711 -- A740},
  year      = {2017},
  abstract  = {In this paper, using an algorithm based on the retrospective rejection sampling scheme introduced in [A. Beskos, O. Papaspiliopoulos, and G. O. Roberts,Methodol. Comput. Appl. Probab., 10 (2008), pp. 85-104] and [P. Etore and M. Martinez, ESAIM Probab.Stat., 18 (2014), pp. 686-702], we propose an exact simulation of a Brownian di ff usion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical di ffi culty due to the presence of t w o jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.},
  language  = {en}
}
@article{SchindlerMoldenhawerStangeetal.2021,
  author    = {Schindler, Daniel and Moldenhawer, Ted and Stange, Maike and Lepro, Valentino and Beta, Carsten and Holschneider, Matthias and Huisinga, Wilhelm},
  title     = {Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows},
  series = {PLoS Computational Biology : a new community journal},
  volume    = {17},
  journal   = {PLoS Computational Biology : a new community journal},
  number    = {8},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1553-734X},
  doi       = {10.1371/journal.pcbi.1009268},
  pages     = {33},
  year      = {2021},
  abstract  = {Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach. <br /> Author summary Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum.},
  language  = {en}
}
@article{deWiljesPathirajaReich2020,
  author    = {de Wiljes, Jana and Pathiraja, Sahani Darschika and Reich, Sebastian},
  title     = {Ensemble transform algorithms for nonlinear smoothing problems},
  series = {SIAM journal on scientific computing},
  volume    = {42},
  journal   = {SIAM journal on scientific computing},
  number    = {1},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/19M1239544},
  pages     = {A87 -- A114},
  year      = {2020},
  abstract  = {Several numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.},
  language  = {en}
}