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2. Majority Edge-Colorings of Graphs

Author

Bock, Felix, Kalinowski, Rafał, Pardey, Johannes, Pilśniak, Monika, Rautenbach, Dieter, and Woźniak, Mariusz

Subjects
Mathematics - Combinatorics
Abstract

We propose the notion of a majority $k$-edge-coloring of a graph $G$, which is an edge-coloring of $G$ with $k$ colors such that, for every vertex $u$ of $G$, at most half the edges of $G$ incident with $u$ have the same color. We show the best possible results that every graph of minimum degree at least $2$ has a majority $4$-edge-coloring, and that every graph of minimum degree at least $4$ has a majority $3$-edge-coloring. Furthermore, we discuss a natural variation of majority edge-colorings and some related open problems.

Published
2022

3. Relating the independence number and the dissociation number

Author

Bock, Felix, Pardey, Johannes, Penso, Lucia D., and Rautenbach, Dieter

Subjects
Mathematics - Combinatorics
Abstract

The independence number $\alpha(G)$ and the dissociation number ${\rm diss}(G)$ of a graph $G$ are the largest orders of induced subgraphs of $G$ of maximum degree at most $0$ and at most $1$, respectively. We consider possible improvements of the obvious inequality $2\alpha(G)\geq {\rm diss}(G)$. For connected cubic graphs $G$ distinct from $K_4$, we show $5\alpha(G)\geq 3{\rm diss}(G)$, and describe the rich and interesting structure of the extremal graphs in detail. For bipartite graphs, and, more generally, triangle-free graphs, we also obtain improvements. For subcubic graphs though, the inequality cannot be improved in general, and we characterize all extremal subcubic graphs.

Published
2022

4. A bound on the dissociation number

Author

Bock, Felix, Pardey, Johannes, Penso, Lucia D., and Rautenbach, Dieter

Subjects
Mathematics - Combinatorics
Abstract

The dissociation number ${\rm diss}(G)$ of a graph $G$ is the maximum order of a set of vertices of $G$ inducing a subgraph that is of maximum degree at most $1$. Computing the dissociation number of a given graph is algorithmically hard even when restricted to subcubic bipartite graphs. For a graph $G$ with $n$ vertices, $m$ edges, $k$ components, and $c_1$ induced cycles of length $1$ modulo $3$, we show ${\rm diss}(G)\geq n-\frac{1}{3}\Big(m+k+c_1\Big)$. Furthermore, we characterize the extremal graphs in which every two cycles are vertex-disjoint.

Published
2022

5. Relating dissociation, independence, and matchings

Author

Bock, Felix, Pardey, Johannes, Penso, Lucia D., and Rautenbach, Dieter

Subjects
Mathematics - Combinatorics
Abstract

A dissociation set in a graph is a set of vertices inducing a subgraph of maximum degree at most $1$. Computing the dissociation number ${\rm diss}(G)$ of a given graph $G$, defined as the order of a maximum dissociation set in $G$, is algorithmically hard even when $G$ is restricted to be bipartite. Recently, Hosseinian and Butenko proposed a simple $\frac{4}{3}$-approximation algorithm for the dissociation number problem in bipartite graphs. Their result relies on the inequality ${\rm diss}(G)\leq\frac{4}{3}\alpha(G-M)$ implicit in their work, where $G$ is a bipartite graph, $M$ is a maximum matching in $G$, and $\alpha(G-M)$ denotes the independence number of $G-M$. We show that the pairs $(G,M)$ for which this inequality holds with equality can be recognized efficiently, and that a maximum dissociation set can be determined for them efficiently. The dissociation number of a graph $G$ satisfies $\max\{ \alpha(G),2\nu_s(G)\} \leq {\rm diss}(G)\leq \alpha(G)+\nu_s(G)\leq 2\alpha(G)$, where $\nu_s(G)$ denotes the induced matching number of $G$. We show that deciding whether ${\rm diss}(G)$ equals any of the four terms lower and upper bounding ${\rm diss}(G)$ is NP-hard.

Published
2022

7. Case study on scheduling cyclic conveyor belts

Author

Bock, Felix and Bruhn, Henning

Subjects
Mathematics - Optimization and Control
Abstract

We optimise the production line of a manufacturing company in southern Germany in order to improve throughput. While the optimisation problem is NP-hard in general, analysing production data we find that in practice the problem can be solved very efficiently by aggressive generation of random machine schedules.

Published
2019

8. The novel role of lymphatic vessels in the pathogenesis of ocular diseases

Author

Clahsen, Thomas, Hadrian, Karina, Notara, Maria, Schlereth, Simona L., Howaldt, Antonia, Prokosch, Verena, Volatier, Thomas, Hos, Deniz, Schroedl, Falk, Kaser-Eichberger, Alexandra, Heindl, Ludwig M., Steven, Philipp, Bosch, Jacobus J., Steinkasserer, Alexander, Rokohl, Alexander C., Liu, Hanhan, Mestanoglu, Mert, Kashkar, Hamid, Schumacher, Björn, Kiefer, Friedemann, Schulte-Merker, Stefan, Matthaei, Mario, Hou, Yanhong, Fassbender, Sonja, Jantsch, Jonathan, Zhang, Wei, Enders, Philip, Bachmann, Björn, Bock, Felix, and Cursiefen, Claus

Published
2023
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13. Selective, Temporary Postoperative Inhibition of Lymphangiogenesis by Integrin α5β1 Blockade Improves Allograft Survival in a Murine Model of High-Risk Corneal Transplantation.

Author

Dietrich-Ntoukas, Tina, Bock, Felix, Onderka, Jasmine, Hos, Deniz, Bachmann, Bjoern O., Zahn, Grit, and Cursiefen, Claus

Subjects
*GRAFT survival, *GRAFT rejection, *IMMUNOLOGICAL tolerance, *SMALL molecules, *POSTOPERATIVE period, *CORNEAL transplantation, *HOMOGRAFTS
Abstract

Background: Corneal inflammatory hem- and lymphangiogenesis significantly increase the risk for immune rejection after subsequent allogeneic corneal transplantation. The purpose of this study was to analyze the impact of temporary selective inhibition of lymphangiogenesis after transplantation on graft survival. Methods: Allogeneic transplantation from C57BL/6 mice to BalbC mice was performed as "high-risk" keratoplasty in a prevascularized corneal host bed (suture-induced inflammatory corneal neovascularization). The treatment group received integrin α5β1-blocking small molecules (JSM6427) at the time of transplantation and for two weeks afterwards. Control mice received a vehicle solution. Grafts were evaluated weekly for graft rejection using an opacity score. At the end of the follow-up, immunohistochemical staining of corneal wholemounts for lymphatic vessels as well as CD11b+ immune cells was performed. Results: Temporary postoperative inhibition of lymphangiogenesis by JSM6427 improved the corneal graft survival significantly. At the end of the follow-up, no significant reduction in CD11b+ immunoreactive cells within the graft compared to controls was found. Conclusions: The significant improvement of corneal graft survival by the selective, temporary postoperative inhibition of lymphangiogenesis after keratoplasty using integrin antagonists shows the impact of lymphatic vessels in the early postoperative phase. Retarding lymphatic vessel ingrowth into the graft might be sufficient for the shift to immunological tolerance in the postoperative period, even after high-risk keratoplasty. [ABSTRACT FROM AUTHOR]

Published
2024
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24. The unique ORF8 protein from SARS-CoV-2 binds to human dendritic cells and induces a hyper-inflammatory cytokine storm

Author

Hamdorf, Matthias, primary, Imhof, Thomas, additional, Bailey-Elkin, Ben, additional, Betz, Janina, additional, Theobald, Sebastian J, additional, Simonis, Alexander, additional, Di Cristanziano, Veronica, additional, Gieselmann, Lutz, additional, Dewald, Felix, additional, Lehmann, Clara, additional, Augustin, Max, additional, Klein, Florian, additional, Alcazar, Miguel A Alejandre, additional, Rongisch, Robert, additional, Fabri, Mario, additional, Rybniker, Jan, additional, Goebel, Heike, additional, Stetefeld, Jörg, additional, Brachvogel, Bent, additional, Cursiefen, Claus, additional, Koch, Manuel, additional, and Bock, Felix, additional

Published
2023
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33. Majority Edge-Colorings of Graphs

Author

Bock, Felix, primary, Kalinowski, Rafał, additional, Pardey, Johannes, additional, Pilśniak, Monika, additional, Rautenbach, Dieter, additional, and Woźniak, Mariusz, additional

Published
2023
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41. Mathematical optimisation : theory and application

Author

Bock, Felix, Bruhn-Fujimoto, Henning, and Rautenbach, Dieter

Subjects
Dissociation sets, Scheduling, Reihenfolgeproblem, Mathematical optimization, DDC 510 / Mathematics, ddc:510, Lineare Optimierung, Cluster-Analyse, High resolution imaging, Super resolution
Abstract

In mathematical optimisation there is a rich interaction between theory and application. Theory provides tools to solve real life problems, which in return motivate further theoretical research. This doctoral thesis presents results of the different aspects of mathematical optimisation. In the first part we investigate the dissociation set problem, a theoretical problem on graphs. We prove several bounds and show structural properties. In the next part we consider clusterings. We provide approximation guarantees for the clustering volume and analyse the consequences of hierarchical clusterings. In the third part we apply mathematical optimisation to improve the quality of micro X-ray fluorescence measurements. Finally, in the last part we consider two real life optimisation problems that occur in the production of a medium-sized company.

Published
2023
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47. The unique ORF8 protein from SARS-CoV-2 binds to human dendritic cells and induces a hyper-inflammatory cytokine storm

Author

Hamdorf, Matthias, primary, Imhof, Thomas, additional, Bailey-Elkin, Ben Allan, additional, Betz, Janina, additional, Theobald, Sebastian J, additional, Simonis, Alexander, additional, Di Cristanziano, Veronica, additional, Gieselmann, Lutz, additional, Dewald, Felix, additional, Lehmann, Clara, additional, Augustin, Max, additional, Klein, Florian, additional, Alcazar, Miguel Alejandre, additional, Rogisch, Robert, additional, Fabri, Mario, additional, Rybniker, Jan, additional, Goebel, Heike, additional, Stetefeld, Jörg, additional, Brachvogel, Bent, additional, Cursiefen, Claus, additional, Koch, Manuel, additional, and Bock, Felix, additional

Published
2022
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50. New Therapeutic Approaches for Conjunctival Melanoma-What We Know So Far and Where Therapy Is Potentially Heading: Focus on Lymphatic Vessels and Dendritic Cells

Author

Peil, Jennifer, Bock, Felix, Kiefer, Friedemann, Schmidt, Rebecca, Heindl, Ludwig M., Cursiefen, Claus, Schlereth, Simona L., Peil, Jennifer, Bock, Felix, Kiefer, Friedemann, Schmidt, Rebecca, Heindl, Ludwig M., Cursiefen, Claus, and Schlereth, Simona L.

Abstract

Conjunctival melanoma (CM) accounts for 5% of all ocular melanomas and arises from malignantly transformed melanocytes in the conjunctival epithelium. Current therapies using surgical excision in combination with chemo- or cryotherapy still have high rates for recurrences and metastatic disease. Lately, novel signal transduction-targeted and immune checkpoint inhibitors like cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) inhibitors, programmed cell death protein-1 (PD-1) receptor inhibitors, BRAF- or MEK-inhibitors for systemic treatment of melanoma have improved the outcome even for unresectable cutaneous melanoma, improving patient survival dramatically. The use of these therapies is now also recommended for CM; however, the immunological background of CM is barely known, underlining the need for research to better understand the immunological basics when treating CM patients with immunomodulatory therapies. Immune checkpoint inhibitors activate tumor defense by interrupting inhibitory interactions between tumor cells and T lymphocytes at the so-called checkpoints. The tumor cells exploit these inhibitory targets on T-cells that are usually used by dendritic cells (DCs). DCs are antigen-presenting cells at the forefront of immune response induction. They contribute to immune tolerance and immune defense but in the case of tumor development, immune tolerance is often prevalent. Enhancing the immune response via DCs, interfering with the lymphatic pathways during immune cell migration and tumor development and specifically targeting tumor cells is a major therapeutic opportunity for many tumor entities including CM. This review summarizes the current knowledge on the function of lymphatic vessels in tumor growth and immune cell transport and continues to compare DC subsets in CM with related melanomas, such as cutaneous melanoma and mucosal melanoma.

Published
2022

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