@article{MaesPetračekBurgeretal.2013, author = {Maes, Bjorn and Petr{\´a}ček, Jiř{\´i} and Burger, Sven and Kwiecien, Pavel and Luksch, Jaroslav and Richter, Ivan}, title = {Simulations of high-Q optical nanocavities with a gradual 1D bandgap}, volume = {21}, journal = {Opt. Express}, publisher = {OSA}, doi = {10.1364/OE.21.006794}, pages = {6794 -- 6806}, year = {2013}, language = {en} } @article{GoetschelWeiserMaierhoferetal.2013, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina and R{\"o}llig, Mathias}, title = {Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography}, volume = {6}, journal = {Nondestructive Testing of Materials and Structures}, pages = {83 -- 89}, year = {2013}, language = {en} } @article{HartmannRichterSchuetteetal.2017, author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: theory and algorithms}, volume = {19}, journal = {Entropy}, number = {11}, doi = {10.3390/e19110626}, pages = {626}, year = {2017}, language = {en} } @article{EgeFothBaumetal.2020, author = {Ege, Yannic and Foth, Christian and Baum, Daniel and Wirkner, Christian S. and Richter, Stefan}, title = {Making spherical-harmonics-based Geometric Morphometrics (SPHARM) approachable for 3D images containing large cavity openings using Ambient Occlusion - a study using hermit crab claw shape variability}, volume = {139}, journal = {Zoomorphology}, doi = {10.1007/s00435-020-00488-z}, pages = {421 -- 432}, year = {2020}, abstract = {An advantageous property of mesh-based geometric morphometrics (GM) towards landmark-based approaches, is the possibility of precisely examining highly irregular shapes and highly topographic surfaces. In case of spherical-harmonics-based GM the main requirement is a completely closed mesh surface, which often is not given, especially when dealing with natural objects. Here we present a methodological workflow to prepare 3D segmentations containing large cavity openings for the conduction of spherical-harmonics-based GM. This will be exemplified with a case study on claws of hermit crabs (Paguroidea, Decapoda, Crustacea), whereby joint openings - between manus and "movable finger" - typify the large-cavity-opening problem. We found a methodology including an ambient-occlusion-based segmentation algorithm leading to results precise and suitable to study the inter- and intraspecific differences in shape of hermit crab claws. Statistical analyses showed a significant separation between all examined diogenid and pagurid claws, whereas the separation between all left and right claws did not show significance. Additionally, the procedure offers other benefits. It is easy to reproduce and creates sparse variance in the data, closures integrate smoothly into the total structures and the algorithm saves a significant amount of time.}, language = {en} } @misc{EgeFothBaumetal.2020, author = {Ege, Yannic and Foth, Christian and Baum, Daniel and Wirkner, Christian S. and Richter, Stefan}, title = {Making spherical-harmonics-based Geometric Morphometrics (SPHARM) approachable for 3D images containing large cavity openings using Ambient Occlusion - a study using hermit crab claw shape variability}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77744}, year = {2020}, abstract = {An advantageous property of mesh-based geometric morphometrics (GM) towards landmark-based approaches, is the possibility of precisely examining highly irregular shapes and highly topographic surfaces. In case of spherical-harmonics-based GM the main requirement is a completely closed mesh surface, which often is not given, especially when dealing with natural objects. Here we present a methodological workflow to prepare 3D segmentations containing large cavity openings for the conduction of spherical-harmonics-based GM. This will be exemplified with a case study on claws of hermit crabs (Paguroidea, Decapoda, Crustacea), whereby joint openings - between manus and "movable finger" - typify the large-cavity-opening problem. We found a methodology including an ambient-occlusion-based segmentation algorithm leading to results precise and suitable to study the inter- and intraspecific differences in shape of hermit crab claws. Statistical analyses showed a significant separation between all examined diogenid and pagurid claws, whereas the separation between all left and right claws did not show significance. Additionally, the procedure offers other benefits. It is easy to reproduce and creates sparse variance in the data, closures integrate smoothly into the total structures and the algorithm saves a significant amount of time.}, language = {en} } @misc{RichterGebertZiegler1993, author = {Richter-Gebert, J{\"u}rgen and Ziegler, G{\"u}nter M.}, title = {Zonotopal Tilings and the Bohne-Dress Theorem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1212}, number = {SC-93-25}, year = {1993}, abstract = {We prove a natural bijection between the polytopal tilings of a zonotope \$Z\$ by zonotopes, and the one-element-liftings of the oriented matroid \${\cal M}(Z)\$ associated with \$Z\$. This yields a simple proof and a strengthening of the Bohne-Dress Theorem on zonotopal tilings.}, language = {en} } @misc{RichterGebert1993, author = {Richter-Gebert, J{\"u}rgen}, title = {Mechanical Theorem Proving in Projective Geometry.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1013}, number = {SC-93-05}, year = {1993}, abstract = {We present an algorithm that is able to confirm projective incidence statements by carrying out calculations in the ring of all formal determinants (brackets) of a configuration. We will describe an implementation of this power and present a series of examples treated by the prover, including {\it Pappos' and Desargues' Theorems,} the {\it Sixteen Point Theorem, Saam's Theorem, }the {\it Bundle Condition,} the uniqueness of a harmonic Point and {\it Pascal's Theorem.}}, language = {en} } @article{KoschekDurmazKrylovaetal.2015, author = {Koschek, and Durmaz, Vedat and Krylova, and Wieczorek, and Gupta, Pooja and Richter, and Bujotzek, Alexander and Fischer, and Haag, Rainer and Freund, and Weber, Marcus and Rademann,}, title = {Peptide polymer ligands for a tandem WW-domain, a soft multivalent protein-protein interaction: lessons on the thermodynamic fitness of flexible ligands}, volume = {11}, journal = {Beilstein J. Org. Chem.}, pages = {837 -- 847}, year = {2015}, language = {en} } @misc{GoetschelWeiserMaierhoferetal.2012, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina}, title = {Data Enhancement for Active Thermography}, journal = {E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples}, editor = {Cardone, Gennaro}, year = {2012}, abstract = {Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise.}, language = {en} } @article{BirkRaharinirinaFackeldeyetal.2021, author = {Birk, Ralph and Raharinirina, N. Alexia and Fackeldey, Konstantin and Richter, Tonio Sebastian and Weber, Marcus}, title = {Inferring cultural and social processes based on patterns of statistical relationships between Synodal texts}, year = {2021}, abstract = {In this paper, we explore the relationship patterns between Ancient Egyptian texts of the corpus ``Synodal decrees'', which are originating between 243 and 185 BCE, during the Ptolemaic period. Particularly, we are interested in analyzing the grammatical features of the different texts. Conventional data analysis methods such as correspondence Analysis are very useful to explore the patterns of statistical interdependence between categories of variables. However, it is based on a PCA-like dimension-reduction method and turned out to be unsuitable for our dataset due to the high dimensionality of our data representations. Additionally, the similarity between pairs of texts and pairs of grammatical features is observed through the distance between their representation, but the degree of association between a particular grammatical feature and a text is not. Here, we applied a qualitative Euclidean embedding method that provides a new Euclidean representation of the categories of variables. This new representation of the categories is constructed in such a way that all the patterns of statistical interdependence, similarity, and association, are seen through the Euclidean distance between them. Nevertheless, the PCA-like dimension-reduction method also performed poorly on our new representation. Therefore, we obtained a two-dimensional visualization using non-linear methods such UMAP or t-SNE. Although these dimension-reduction methods reduced the interpretability of interpoint distances, we were still able to identify important similarity patterns between the Synodal text as well as their association patterns with the grammatical features.}, language = {en} }