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12. Axis-Parallel Right Angle Crossing Graphs

Author

Patrizio Angelini and Michael A. Bekos and Julia Katheder and Michael Kaufmann and Maximilian Pfister and Torsten Ueckerdt, Angelini, Patrizio, Bekos, Michael A., Katheder, Julia, Kaufmann, Michael, Pfister, Maximilian, Ueckerdt, Torsten, Patrizio Angelini and Michael A. Bekos and Julia Katheder and Michael Kaufmann and Maximilian Pfister and Torsten Ueckerdt, Angelini, Patrizio, Bekos, Michael A., Katheder, Julia, Kaufmann, Michael, Pfister, Maximilian, and Ueckerdt, Torsten

Abstract

A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent graph classes in beyond planarity. In this work, we study a subclass of RAC graphs, called axis-parallel RAC (or apRAC, for short), that restricts the crossings to pairs of axis-parallel edge-segments. apRAC drawings combine the readability of planar drawings with the clarity of (non-planar) orthogonal drawings. We consider these graphs both with and without bends. Our contribution is as follows: (i) We study inclusion relationships between apRAC and traditional RAC graphs. (ii) We establish bounds on the edge density of apRAC graphs. (iii) We show that every graph with maximum degree 8 is 2-bend apRAC and give a linear time drawing algorithm. Some of our results on apRAC graphs also improve the state of the art for general RAC graphs. We conclude our work with a list of open questions and a discussion of a natural generalization of the apRAC model.

Published
2023
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14. RAC Drawings of Graphs with Low Degree

Author

Patrizio Angelini and Michael A. Bekos and Julia Katheder and Michael Kaufmann and Maximilian Pfister, Angelini, Patrizio, Bekos, Michael A., Katheder, Julia, Kaufmann, Michael, Pfister, Maximilian, Patrizio Angelini and Michael A. Bekos and Julia Katheder and Michael Kaufmann and Maximilian Pfister, Angelini, Patrizio, Bekos, Michael A., Katheder, Julia, Kaufmann, Michael, and Pfister, Maximilian

Abstract

Motivated by cognitive experiments providing evidence that large crossing-angles do not impair the readability of a graph drawing, RAC (Right Angle Crossing) drawings were introduced to address the problem of producing readable representations of non-planar graphs by supporting the optimal case in which all crossings form 90° angles. In this work, we make progress on the problem of finding RAC drawings of graphs of low degree. In this context, a long-standing open question asks whether all degree-3 graphs admit straight-line RAC drawings. This question has been positively answered for the Hamiltonian degree-3 graphs. We improve on this result by extending to the class of 3-edge-colorable degree-3 graphs. When each edge is allowed to have one bend, we prove that degree-4 graphs admit such RAC drawings, a result which was previously known only for degree-3 graphs. Finally, we show that 7-edge-colorable degree-7 graphs admit RAC drawings with two bends per edge. This improves over the previous result on degree-6 graphs.

Published
2022
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15. Drawing Shortest Paths in Geodetic Graphs

Author

Michael Hoffmann, Maximilian Pfister, Thomas Schneck, Stephen G. Kobourov, Henry Förster, Sabine Cornelsen, Martin Gronemann, Auber, David, and Valtr, Pavel

Subjects
Computational Geometry (cs.CG), FOS: Computer and information sciences, 050101 languages & linguistics, Class (set theory), General Computer Science, Discrete Mathematics (cs.DM), Computer science, 05 social sciences, Geodetic datum, 02 engineering and technology, Space (mathematics), Graph, Computer Science Applications, Theoretical Computer Science, Combinatorics, Computational Theory and Mathematics, Shortest path problem, 0202 electrical engineering, electronic engineering, information engineering, Computer Science - Computational Geometry, 020201 artificial intelligence & image processing, 0501 psychology and cognitive sciences, Geometry and Topology, Edge crossings, Unique shortest paths, Geodetic graphs, Computer Science - Discrete Mathematics
Abstract

Motivated by the fact that in a space where shortest paths are unique, no two shortest paths meet twice, we study a question posed by Greg Bodwin: Given a geodetic graph G, i.e., an unweighted graph in which the shortest path between any pair of vertices is unique, is there a philogeodetic drawing of G, i.e., a drawing of G in which the curves of any two shortest paths meet at most once? We answer this question in the negative by showing the existence of geodetic graphs that require some pair of shortest paths to cross at least four times. The bound on the number of crossings is tight for the class of graphs we construct. Furthermore, we exhibit geodetic graphs of diameter two that do not admit a philogeodetic drawing. On the positive side we show that geodetic graphs admit a philogeodetic drawing if both the diameter and the density are very low., Journal of Graph Algorithms and Applications, 26 (3), ISSN:1526-1719

Published
2022

16. The Aurora B-controlled PP1/RepoMan complex determines the spatial and temporal distribution of mitotic H2B S6 phosphorylation

Author

Maximilian Pfisterer, Roman Robert, Vera V. Saul, Amelie Pritz, Markus Seibert, Regina Feederle, and M. Lienhard Schmitz

Subjects
mitosis, histone phosphorylation, phosphatase scaffold, centromere, Biology (General), QH301-705.5
Abstract

The precise spatial and temporal control of histone phosphorylations is important for the ordered progression through the different phases of mitosis. The phosphorylation of H2B at S6 (H2B S6ph), which is crucial for chromosome segregation, reaches its maximum level during metaphase and is limited to the inner centromere. We discovered that the temporal and spatial regulation of this modification, as well as its intensity, are governed by the scaffold protein RepoMan and its associated catalytically active phosphatases, PP1α and PP1γ. Phosphatase activity is inhibited at the area of maximal H2B S6 phosphorylation at the inner centromere by site-specific Aurora B-mediated inactivation of the PP1/RepoMan complex. The motor protein Mklp2 contributes to the relocalization of Aurora B from chromatin to the mitotic spindle during anaphase, thus alleviating Aurora B-dependent repression of the PP1/RepoMan complex and enabling dephosphorylation of H2B S6. Accordingly, dysregulation of Mklp2 levels, as commonly observed in tumour cells, leads to the lack of H2B S6 dephosphorylation during early anaphase, which might contribute to chromosomal instability.

Published
2024
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17. A transient increase of HIF-1α during the G1 phase (G1-HIF) ensures cell survival under nutritional stress

Author

Ratnal Belapurkar, Maximilian Pfisterer, Jan Dreute, Sebastian Werner, Sven Zukunft, Ingrid Fleming, Michael Kracht, and M. Lienhard SCHMITZ

Subjects
Cytology, QH573-671
Abstract

Abstract The family of hypoxia-inducible transcription factors (HIF) is activated to adapt cells to low oxygen conditions, but is also known to regulate some biological processes under normoxic conditions. Here we show that HIF-1α protein levels transiently increase during the G1 phase of the cell cycle (designated as G1-HIF) in an AMP-activated protein kinase (AMPK)-dependent manner. The transient elimination of G1-HIF by a degron system revealed its contribution to cell survival under unfavorable metabolic conditions. Indeed, G1-HIF plays a key role in the cell cycle-dependent expression of genes encoding metabolic regulators and the maintenance of mTOR activity under conditions of nutrient deprivation. Accordingly, transient elimination of G1-HIF led to a significant reduction in the concentration of key proteinogenic amino acids and carbohydrates. These data indicate that G1-HIF acts as a cell cycle-dependent surveillance factor that prevents the onset of starvation-induced apoptosis.

Published
2023
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18. Beyond-Planarity: Turán-Type Results for Non-Planar Bipartite Graphs

Author

Patrizio Angelini and Michael A. Bekos and Michael Kaufmann and Maximilian Pfister and Torsten Ueckerdt, Angelini, Patrizio, Bekos, Michael A., Kaufmann, Michael, Pfister, Maximilian, Ueckerdt, Torsten, Patrizio Angelini and Michael A. Bekos and Michael Kaufmann and Maximilian Pfister and Torsten Ueckerdt, Angelini, Patrizio, Bekos, Michael A., Kaufmann, Michael, Pfister, Maximilian, and Ueckerdt, Torsten

Abstract

Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations. Early research dates back to the 1960s (e.g., Avital and Hanani 1966) for extremal problems on geometric graphs, but is also related to graph drawing problems where visual clutter due to edge crossings should be minimized (e.g., Huang et al. 2018). Most of the literature focuses on Turán-type problems, which ask for the maximum number of edges a beyond-planar graph can have. Here, we study this problem for bipartite topological graphs, considering several types of beyond-planar graphs, i.e. 1-planar, 2-planar, fan-planar, and RAC graphs. We prove bounds on the number of edges that are tight up to additive constants; some of them are surprising and not along the lines of the known results for non-bipartite graphs. Our findings lead to an improvement of the leading constant of the well-known Crossing Lemma for bipartite graphs, as well as to a number of interesting questions on topological graphs.

Published
2018
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19. Sensor and Actuator Placement for Linear Systems Based on <tex-math notation='TeX'>$H_{2}$</tex-math> and <tex-math notation='TeX'>$H_{\infty}$</tex-math> Optimization

Author

Maximilian Pfister, Philipp Wolfrum, and Ulrich Münz

Subjects
Discrete mathematics, Control and Systems Engineering, Control theory, Norm (mathematics), Convex optimization, Linear system, Full state feedback, Algorithm design, Power grid, Electrical and Electronic Engineering, Actuator, Computer Science Applications, Mathematics
Abstract

Sensor and actuator placement algorithms are developed for linear discrete-time systems based on $H_{2}$ and $H_{\infty}$ optimization. For sensor placement, we design an observer that minimizes the $H_{2}$ norm of the error dynamics and the number of sensors at the same time. For actuator placement, we design a state feedback controller that minimizes the $H_{\infty}$ norm of the closed-loop system and the number of actuators at the same time. Any other combination of actuator placement for state-feedback design or sensor placement for observer design for continuous-time or discrete-time linear systems based on $H_{2}$ or $H_{\infty}$ optimization can be derived from these results. In both presented cases, the number of sensors or actuators is formulated as the $\ell_{0}$ norm of the observer or controller gain matrix. This $\ell_{0}$ norm is then relaxed to a weighted $\ell_{1}$ norm in order to obtain an iterative convex optimization problem. As an application example, we use the sensor placement algorithm to place phase measurement units with maximal impact on the $H_{2}$ performance in a power grid.

Published
2014

20. Dibutylsilylene Derivatives of Tartaric Acid

Author

Peter Klüfers, Sarah Illi, Maximilian Pfister, and Johanna Schulten

Subjects
Inorganic Chemistry, chemistry.chemical_compound, Crystallography, Silicon, chemistry, Tartaric acid, Silylene, chemistry.chemical_element, Chelation, Nuclear magnetic resonance spectroscopy, Trifluoromethanesulfonate
Abstract

Crystals of the bis(tert-butyl)silylene (DTBS) derivatives of the tartaric acids were synthesized from D-, L-, rac-, and meso-tartaric acid and DTBS bis(trifluoromethanesulfonate): two polymorphs of Si2tBu4(L-Tart1,2;3,4H–4) (L-1a and L-1b), the mirror image of the denser modification (D-1b) as well as the racemate (2), and the meso analogue Si2tBu4(meso-Tart1,3;2,4H–4) (3). The structures were determined by single-crystal X-ray diffraction. The threo-configured D- and L- (and rac-) tartrates were coordinated by two tBu2Si units forming five-membered chelate rings, whereas the erythro-configured meso-tartrate formed six-membered chelate rings. The new compounds were analyzed by NMR techniques, including 29Si NMR spectroscopy, and single-crystal X-ray crystallography.

Published
2013

21. Tetramethoxy-λ4-tellane and Tetrakis(2,2,2-trifluoroethoxy)-λ4-tellane

Author

Maximilian Pfister, Felix Roeßner, Moritz M. Reichvilser, Martin Stapel, Richard Betz, and Peter Klüfers

Subjects
Inorganic Chemistry, Diffraction, Crystallography, chemistry.chemical_compound, Bond theory, chemistry, Tetrachloride, Intermolecular force, chemistry.chemical_element, Methanol, Tellurium, Natural bond orbital, Sodium salt
Abstract

Two tetraalkoxy-λ 4 -telluranes were prepared from tel- lurium tetrachloride and the sodium salts of methanol and 2,2,2- trifluoroethanol, respectively. Their molecular structures which were determined by single-crystal X-ray diffraction show dipolar intermolecular contacts. NBO analyses for the title compounds

Published
2008

22. SIAH ubiquitin E3 ligases as modulators of inflammatory gene expression

Author

M. Lienhard Schmitz, Jan Dreute, Maximilian Pfisterer, Stefan Günther, Michael Kracht, and Shashipavan Chillappagari

Subjects
SIAH1, SIAH2, Ubiquitin E3 ligase, NF-κB, Inflammatory gene expression, Science (General), Q1-390, Social sciences (General), H1-99
Abstract

The functionally redundant ubiquitin E3 ligases SIAH1 and SIAH2 have been implicated in the regulation of metabolism and the hypoxic response, while their role in other signal-mediated processes such inflammatory gene expression remains to be defined. Here we have downregulated the expression of both SIAH proteins with specific siRNAs and investigated the functional consequences for IL-1α-induced gene expression. The knockdown of SIAH1/2 modulated the expression of approximately one third of IL-1α-regulated genes. These effects were not due to changes in the NF-κB and MAPK signaling pathways and rather employed further processes including those mediated by the coactivator p300. Most of the proteins encoded by SIAH1/2-regulated genes form a regulatory network of proinflammatory factors. Thus SIAH1/2 proteins function as variable rheostats that control the amplitude rather than the principal activation of the inflammatory gene response.

Published
2022
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25. Brief aus China

Author

Maximilian Pfister

Subjects
General Medicine
Published
1928

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