@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{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{SchmitzMoldt2018,
author = {Schmitz, Dennis and Moldt, Daniel},
title = {Ein Lehr- und Lernkonzept f{\"u}r die Softwareentwicklung im Team},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {12},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416324},
pages = {63 -- 78},
year = {2018},
abstract = {Um beim Berufseinstieg erfolgreich als Informatiker wirken zu k{\"o}nnen, reicht es oft nicht aus nur separierte Kenntnisse {\"u}ber technische und theoretische Grundlagen, Programmiersprachen, Werkzeuge und Selbst- und Zeitmanagement zu besitzen. Vielmehr sollten Absolventen diese Kenntnisse praktisch miteinander verzahnt einsetzen k{\"o}nnen. An der Universit{\"a}t wird Studierenden leider selten die M{\"o}glichkeit geboten, diese verschiedenen Bereiche der Informatik miteinander integriert auszu{\"u}ben. Daf{\"u}r entwickeln wir seit {\"u}ber zwei Dekaden ein Lehr- und Lernkonzept zur Unterst{\"u}tzung praktischer Softwareentwicklungsveranstaltungen und setzen dieses um. Dadurch bieten wir angehenden SoftwareentwicklerInnen und ProjektmanagerInnen eine Umgebung, in der sie neues, praktisch relevantes Wissen erwerben k{\"o}nnen, sich selbst praktisch erproben und ihr Wissen konkret einsetzen k{\"o}nnen. Hier legen wir einen Schwerpunkt auf das Arbeiten im Team. Das hier vorgestellte Konzept kann auf {\"a}hnliche Lehrveranstaltungen {\"u}bertragen und aufgrund seiner Modularisierung ver{\"a}ndert und erweitert werden.},
language = {de}
}
@article{RoepkeLarischSchroeder2018,
author = {R{\"o}pke, Ren{\´e} and Larisch, Kathrin and Schroeder, Ulrik},
title = {F{\"o}rderung {\"u}berfachlicher Kompetenzen in praktischen Software- Engineering-Veranstaltungen der RWTH Aachen},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {12},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416334},
pages = {79 -- 89},
year = {2018},
abstract = {Im Rahmen eines Informatikstudiums wird neben theoretischen Grundlagen und Programmierf{\"a}higkeiten auch gezielt vermittelt, wie moderne Software in der Praxis entwickelt wird. Dabei wird oftmals eine Form der Projektarbeit gew{\"a}hlt, um Studierenden m{\"o}glichst realit{\"a}tsnahe Erfahrungen zu erm{\"o}glichen. Die Studierenden entwickeln einzeln oder in kleineren Teams Softwareprodukte f{\"u}r ausgew{\"a}hlte Problemstellungen. Neben fachlichen Inhalte stehen durch gruppendynamische Prozesse auch {\"u}berfachliche Kompetenzen im Fokus. Dieser Beitrag pr{\"a}sentiert eine Interviewstudie mit Dozierenden von Softwareprojektpraktika an der RWTH Aachen und konzentriert sich auf die Ausgestaltung der Veranstaltungen sowie F{\"o}rderung von {\"u}berfachlichen Kompetenzen nach einem Kompetenzprofil f{\"u}r Softwareingenieure.},
language = {de}
}
@article{StrieweKramer2018,
author = {Striewe, Michael and Kramer, Matthias},
title = {Empirische Untersuchungen von L{\"u}ckentext-Items zur Beherrschung der Syntax einer Programmiersprache},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {12},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416353},
pages = {101 -- 115},
year = {2018},
abstract = {L{\"u}ckentext-Items auf der Basis von Programmcode k{\"o}nnen eingesetzt werden, um Kenntnisse in der Syntax einer Programmiersprache zu pr{\"u}fen, ohne dazu komplexe Programmieraufgaben zu stellen, deren Bearbeitung weitere Kompetenzen erfordert. Der vorliegende Beitrag dokumentiert den Einsatz von insgesamt zehn derartigen Items in einer universit{\"a}ren Erstsemestervorlesung zur Programmierung mit Java. Es werden sowohl Erfahrungen mit der Konstruktion der Items als auch empirische Daten aus dem Einsatz diskutiert. Der Beitrag zeigt dadurch insbesondere die Herausforderungen bei der Konstruktion valider Instrumente zur Kompetenzmessung in der Programmierausbildung auf. Die begrenzten und teilweise vorl{\"a}ufigen Ergebnisse zur Qualit{\"a}t der erzeugten Items legen trotzdem nahe, dass Erstellung und Einsatz entsprechender Items m{\"o}glich ist und einen Beitrag zur Kompetenzmessung leisten kann.},
language = {de}
}
@article{GrillenbergerRomeike2018,
author = {Grillenberger, Andreas and Romeike, Ralf},
title = {Was ist Data Science?},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {10},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416369},
pages = {119 -- 134},
year = {2018},
abstract = {In Zusammenhang mit den Entwicklungen der vergangenen Jahre, insbesondere in den Bereichen Big Data, Datenmanagement und Maschinenlernen, hat sich der Umgang mit Daten und deren Analyse wesentlich weiterentwickelt. Mittlerweile wird die Datenwissenschaft als eigene Disziplin angesehen, die auch immer st{\"a}rker durch entsprechende Studieng{\"a}nge an Hochschulen repr{\"a}sentiert wird. Trotz dieser zunehmenden Bedeutung ist jedoch oft unklar, welche konkreten Inhalte mit ihr in Verbindung stehen, da sie in verschiedensten Auspr{\"a}gungen auftritt. In diesem Beitrag werden daher die hinter der Data Science stehenden informatischen Inhalte durch eine qualitative Analyse der Modulhandb{\"u}cher etablierter Studieng{\"a}nge aus diesem Bereich ermittelt und so ein Beitrag zur Charakterisierung dieser Disziplin geleistet. Am Beispiel der Entwicklung eines Data-Literacy-Kompetenzmodells, die als Ausblick skizziert wird, wird die Bedeutung dieser Charakterisierung f{\"u}r die weitere Forschung expliziert.},
language = {de}
}
@article{FredeKnobelsdorf2018,
author = {Frede, Christiane and Knobelsdorf, Maria},
title = {Explorative Datenanalyse der Studierendenperformance in der Theoretischen Informatik},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {10},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416378},
pages = {135 -- 149},
year = {2018},
abstract = {In diesem Artikel werden die Ergebnisse einer explorativen Datenanalyse {\"u}ber die Studierendenperformance in Klausur- und Hausaufgaben eines Einf{\"u}hrungskurses der Theoretischen Informatik vorgestellt. Da bisher empirisch wenig untersucht ist, welche Probleme Studierenden in den Einf{\"u}hrungskursen haben und die Durchfallquoten in diesen Kursen sehr hoch sind, soll auf diesem Weg ein {\"U}berblick gegeben werden. Die Ergebnisse zeigen, dass alle Studierenden unabh{\"a}ngig von ihrer Klausurnote die niedrigste Performance in den Klausur- und Hausaufgaben aufweisen, in denen formale Beweise gefordert sind. Dieses Ergebnis st{\"a}rkt die Vermutung, dass didaktische Ans{\"a}tze und Maßnahmen sich insbesondere auf das Erlernen formaler Beweismethoden fokussieren sollten, um Informatik-Studierende nachhaltiger dabei zu unterst{\"u}tzen, in Theoretischer Informatik erfolgreich zu sein.},
language = {de}
}
@article{GrevenSchroeder2018,
author = {Greven, Christoph and Schroeder, Ulrik},
title = {Wissenschaftliches Arbeiten lernen},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {10},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416380},
pages = {151 -- 161},
year = {2018},
abstract = {Die Lehre von wissenschaftlichem Arbeiten stellt einen zentralen Aspekt in forschungsorientierten Studieng{\"a}ngen wie der Informatik dar. Trotz diverser Angebote werden mittel- und langfristig M{\"a}ngel in der Arbeitsqualit{\"a}t von Studierenden sichtbar. Dieses Paper analysiert daher das Profil der Studierenden, deren Anwendung des wissenschaftlichen Arbeitens, und das Angebot von Proseminaren zum Thema „Einf{\"u}hrung in das wissenschaftliche Arbeiten" einer deutschen Universit{\"a}t. Die Ergebnisse mehrerer Erhebungen zeigen dabei diverse Probleme bei Studierenden auf, u. a. bei dem Prozessverst{\"a}ndnis, dem Zeitmanagement und der Kommunikation.},
language = {de}
}
@article{SeegererRomeike2018,
author = {Seegerer, Stefan and Romeike, Ralf},
title = {Was jeder {\"u}ber Informatik lernen sollte},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {12},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416298},
pages = {13 -- 28},
year = {2018},
abstract = {Um f{\"u}r ein Leben in der digitalen Gesellschaft vorbereitet zu sein, braucht jeder heute in verschiedenen Situationen umfangreiche informatische Grundlagen. Die Bedeutung von Informatik nimmt nicht nur in immer mehr Bereichen unseres t{\"a}glichen Lebens zu, sondern auch in immer mehr Ausbildungsrichtungen. Um junge Menschen auf ihr zuk{\"u}nftiges Leben und/oder ihre zuk{\"u}nftige berufliche T{\"a}tigkeit vorzubereiten, bieten verschiedene Hochschulen Informatikmodule f{\"u}r Studierende anderer Fachrichtungen an. Die Materialien jener Kurse bilden einen umfangreichen Datenpool, um die f{\"u}r Studierende anderer F{\"a}cher bedeutenden Aspekte der Informatik mithilfe eines empirischen Ansatzes zu identifizieren. Im Folgenden werden 70 Module zu informatischer Bildung f{\"u}r Studierende anderer Fachrichtungen analysiert. Die Materialien - Publikationen, Syllabi und Stundentafeln - werden zun{\"a}chst mit einer qualitativen Inhaltsanalyse nach Mayring untersucht und anschließend quantitativ ausgewertet. Basierend auf der Analyse werden Ziele, zentrale Themen und Typen eingesetzter Werkzeuge identifiziert.},
language = {de}
}
@article{TillmannKroemkerHornetal.2018,
author = {Tillmann, Alexander and Kr{\"o}mker, Detlef and Horn, Florian and Gattinger, Thorsten},
title = {Analysing \& Predicting Students Performance in an Introductory Computer Science Course},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {12},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416307},
pages = {29 -- 45},
year = {2018},
abstract = {Students of computer science studies enter university education with very different competencies, experience and knowledge. 145 datasets collected of freshmen computer science students by learning management systems in relation to exam outcomes and learning dispositions data (e. g. student dispositions, previous experiences and attitudes measured through self-reported surveys) has been exploited to identify indicators as predictors of academic success and hence make effective interventions to deal with an extremely heterogeneous group of students.},
language = {en}
}
@article{Weicker2018,
author = {Weicker, Karsten},
title = {Vorlesungs-Pflege},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {12},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416315},
pages = {47 -- 59},
year = {2018},
abstract = {{\"A}hnlich zu Alterungsprozessen bei Software degenerieren auch Vorlesungen, wenn sie nicht hinreichend gepflegt werden. Die Gr{\"u}nde hierf{\"u}r werden ebenso beleuchtet wie m{\"o}gliche Indikatoren und Maßnahmen - der Blick ist dabei immer der eines Informatikers. An drei Vorlesungen wird erl{\"a}utert, wie der Degeneration von Lehrveranstaltungen gegengewirkt werden kann. Mangels hinreichend großer empirischer Daten liefert das Paper keine unumst{\"o}ßlichen Wahrheiten. Ein Ziel ist es vielmehr Kollegen, die {\"a}hnliche Ph{\"a}nomene beobachten, einen ersten Anker f{\"u}r einen inneren Diskurs zu bieten. Ein langfristiges Ziel ist die Sammlung eines Katalogs an Maßnahmen zur Pflege von Informatikvorlesungen.},
language = {de}
}
@article{KeverpuetzKueppers2018,
author = {Keverp{\"u}tz, Claudia and K{\"u}ppers, Bastian},
title = {Konsistente Lehr-Lern-Prozesse in der dualen IT-Ausbildung},
series = {Commentarii informaticae didacticae},
journal = {Commentarii informaticae didacticae},
number = {12},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416341},
pages = {91 -- 100},
year = {2018},
abstract = {In der dualen IT-Ausbildung als Verbindung von beruflicher und akademischer Qualifikation werden die berufstypischen Werkzeuge, wie z. B. Laptops, ebenso in den Lehr-Lern-Prozessen der akademischen Unterrichtseinheiten eingesetzt. Im Pr{\"u}fungswesen wird oft auf klassische Papierklausuren zur{\"u}ckgegriffen. Unterrichtseinheiten mit hohem Blended-Learning-Anteil ohne E-Pr{\"u}fung werden dabei als „nicht konsistent" wahrgenommen. In diesem Artikel wird eine empirische Studie dargelegt, die untersucht, welche Einfl{\"u}sse aus der pers{\"o}nlichen Lernbiografie bei den Lehrenden in einer dualen IT-Ausbildung dazu f{\"u}hren k{\"o}nnen, die M{\"o}glichkeiten eines E-Assessments als summative Modulpr{\"u}fung anzunehmen oder abzulehnen. Beispielhaft wurden in der dargelegten Studie Interviews mit Dozenten gef{\"u}hrt und diese hinsichtlich der Verbindung zwischen Lernbiografie, Gestaltung der Didaktik der Lehr-Lern-Prozesse, Zufriedenheit und Ver{\"a}nderungsbereitschaft untersucht.},
language = {de}
}
@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
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.
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{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}
}
@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.
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{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}
}