@article{9252, abstract = {This paper analyses the conditions for local adaptation in a metapopulation with infinitely many islands under a model of hard selection, where population size depends on local fitness. Each island belongs to one of two distinct ecological niches or habitats. Fitness is influenced by an additive trait which is under habitat‐dependent directional selection. Our analysis is based on the diffusion approximation and accounts for both genetic drift and demographic stochasticity. By neglecting linkage disequilibria, it yields the joint distribution of allele frequencies and population size on each island. We find that under hard selection, the conditions for local adaptation in a rare habitat are more restrictive for more polygenic traits: even moderate migration load per locus at very many loci is sufficient for population sizes to decline. This further reduces the efficacy of selection at individual loci due to increased drift and because smaller populations are more prone to swamping due to migration, causing a positive feedback between increasing maladaptation and declining population sizes. Our analysis also highlights the importance of demographic stochasticity, which exacerbates the decline in numbers of maladapted populations, leading to population collapse in the rare habitat at significantly lower migration than predicted by deterministic arguments.}, author = {Szep, Eniko and Sachdeva, Himani and Barton, Nicholas H}, issn = {1558-5646}, journal = {Evolution}, keywords = {Genetics, Ecology, Evolution, Behavior and Systematics, General Agricultural and Biological Sciences}, number = {5}, pages = {1030--1045}, publisher = {Wiley}, title = {{Polygenic local adaptation in metapopulations: A stochastic eco‐evolutionary model}}, doi = {10.1111/evo.14210}, volume = {75}, year = {2021}, } @inproceedings{9253, abstract = {In March 2020, the Austrian government introduced a widespread lock-down in response to the COVID-19 pandemic. Based on subjective impressions and anecdotal evidence, Austrian public and private life came to a sudden halt. Here we assess the effect of the lock-down quantitatively for all regions in Austria and present an analysis of daily changes of human mobility throughout Austria using near-real-time anonymized mobile phone data. We describe an efficient data aggregation pipeline and analyze the mobility by quantifying mobile-phone traffic at specific point of interests (POIs), analyzing individual trajectories and investigating the cluster structure of the origin-destination graph. We found a reduction of commuters at Viennese metro stations of over 80% and the number of devices with a radius of gyration of less than 500 m almost doubled. The results of studying crowd-movement behavior highlight considerable changes in the structure of mobility networks, revealed by a higher modularity and an increase from 12 to 20 detected communities. We demonstrate the relevance of mobility data for epidemiological studies by showing a significant correlation of the outflow from the town of Ischgl (an early COVID-19 hotspot) and the reported COVID-19 cases with an 8-day time lag. This research indicates that mobile phone usage data permits the moment-by-moment quantification of mobility behavior for a whole country. We emphasize the need to improve the availability of such data in anonymized form to empower rapid response to combat COVID-19 and future pandemics.}, author = {Heiler, Georg and Reisch, Tobias and Hurt, Jan and Forghani, Mohammad and Omani, Aida and Hanbury, Allan and Karimipour, Farid}, booktitle = {2020 IEEE International Conference on Big Data}, isbn = {9781728162515}, location = {Atlanta, GA, United States}, pages = {3123--3132}, publisher = {IEEE}, title = {{Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic}}, doi = {10.1109/bigdata50022.2020.9378374}, year = {2021}, } @article{9254, abstract = {Auxin is a key regulator of plant growth and development. Local auxin biosynthesis and intercellular transport generates regional gradients in the root that are instructive for processes such as specification of developmental zones that maintain root growth and tropic responses. Here we present a toolbox to study auxin-mediated root development that features: (i) the ability to control auxin synthesis with high spatio-temporal resolution and (ii) single-cell nucleus tracking and morphokinetic analysis infrastructure. Integration of these two features enables cutting-edge analysis of root development at single-cell resolution based on morphokinetic parameters under normal growth conditions and during cell-type-specific induction of auxin biosynthesis. We show directional auxin flow in the root and refine the contributions of key players in this process. In addition, we determine the quantitative kinetics of Arabidopsis root meristem skewing, which depends on local auxin gradients but does not require PIN2 and AUX1 auxin transporter activities. Beyond the mechanistic insights into root development, the tools developed here will enable biologists to study kinetics and morphology of various critical processes at the single cell-level in whole organisms.}, author = {Hu, Yangjie and Omary, Moutasem and Hu, Yun and Doron, Ohad and Hörmayer, Lukas and Chen, Qingguo and Megides, Or and Chekli, Ori and Ding, Zhaojun and Friml, Jiří and Zhao, Yunde and Tsarfaty, Ilan and Shani, Eilon}, issn = {20411723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Cell kinetics of auxin transport and activity in Arabidopsis root growth and skewing}}, doi = {10.1038/s41467-021-21802-3}, volume = {12}, year = {2021}, } @article{9255, abstract = {Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks—device-independent quantum random number generators (QRNGs) are highly impractical and standard semi-device-independent QRNGs are limited to a specific physical implementation and level of trust. Here we propose a framework for semi-device-independent randomness certification, using a source of trusted vacuum in the form of a signal shutter. It employs a flexible set of assumptions and levels of trust, allowing it to be applied in a wide range of physical scenarios involving both quantum and classical entropy sources. We experimentally demonstrate our protocol with a photonic setup and generate secure random bits under three different assumptions with varying degrees of security and resulting data rates.}, author = {Pivoluska, Matej and Plesch, Martin and Farkas, Máté and Ruzickova, Natalia and Flegel, Clara and Valencia, Natalia Herrera and Mccutcheon, Will and Malik, Mehul and Aguilar, Edgar A.}, issn = {2056-6387}, journal = {npj Quantum Information}, publisher = {Springer Nature}, title = {{Semi-device-independent random number generation with flexible assumptions}}, doi = {10.1038/s41534-021-00387-1}, volume = {7}, year = {2021}, } @article{9256, abstract = {We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin S≥1/2. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.}, author = {Napiórkowski, Marcin M and Seiringer, Robert}, issn = {15730530}, journal = {Letters in Mathematical Physics}, number = {2}, publisher = {Springer Nature}, title = {{Free energy asymptotics of the quantum Heisenberg spin chain}}, doi = {10.1007/s11005-021-01375-4}, volume = {111}, year = {2021}, } @article{9257, abstract = {The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems.}, author = {Goodrich, Carl Peter and King, Ella M. and Schoenholz, Samuel S. and Cubuk, Ekin D. and Brenner, Michael P.}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {10}, publisher = {National Academy of Sciences}, title = {{Designing self-assembling kinetics with differentiable statistical physics models}}, doi = {10.1073/pnas.2024083118}, volume = {118}, year = {2021}, } @article{9258, author = {Pinkard, Henry and Stuurman, Nico and Ivanov, Ivan E. and Anthony, Nicholas M. and Ouyang, Wei and Li, Bin and Yang, Bin and Tsuchida, Mark A. and Chhun, Bryant and Zhang, Grace and Mei, Ryan and Anderson, Michael and Shepherd, Douglas P. and Hunt-Isaak, Ian and Dunn, Raymond L. and Jahr, Wiebke and Kato, Saul and Royer, Loïc A. and Thiagarajah, Jay R. and Eliceiri, Kevin W. and Lundberg, Emma and Mehta, Shalin B. and Waller, Laura}, issn = {1548-7105}, journal = {Nature Methods}, number = {3}, pages = {226--228}, publisher = {Springer Nature}, title = {{Pycro-Manager: Open-source software for customized and reproducible microscope control}}, doi = {10.1038/s41592-021-01087-6}, volume = {18}, year = {2021}, } @article{9259, abstract = {Gradients of chemokines and growth factors guide migrating cells and morphogenetic processes. Migration of antigen-presenting dendritic cells from the interstitium into the lymphatic system is dependent on chemokine CCL21, which is secreted by endothelial cells of the lymphatic capillary, binds heparan sulfates and forms gradients decaying into the interstitium. Despite the importance of CCL21 gradients, and chemokine gradients in general, the mechanisms of gradient formation are unclear. Studies on fibroblast growth factors have shown that limited diffusion is crucial for gradient formation. Here, we used the mouse dermis as a model tissue to address the necessity of CCL21 anchoring to lymphatic capillary heparan sulfates in the formation of interstitial CCL21 gradients. Surprisingly, the absence of lymphatic endothelial heparan sulfates resulted only in a modest decrease of CCL21 levels at the lymphatic capillaries and did neither affect interstitial CCL21 gradient shape nor dendritic cell migration toward lymphatic capillaries. Thus, heparan sulfates at the level of the lymphatic endothelium are dispensable for the formation of a functional CCL21 gradient.}, author = {Vaahtomeri, Kari and Moussion, Christine and Hauschild, Robert and Sixt, Michael K}, issn = {1664-3224}, journal = {Frontiers in Immunology}, publisher = {Frontiers}, title = {{Shape and function of interstitial chemokine CCL21 gradients are independent of heparan sulfates produced by lymphatic endothelium}}, doi = {10.3389/fimmu.2021.630002}, volume = {12}, year = {2021}, } @article{9260, abstract = {We study the density of rational points on a higher-dimensional orbifold (Pn−1,Δ) when Δ is a Q-divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgain–Demeter–Guth and Wooley.}, author = {Browning, Timothy D and Yamagishi, Shuntaro}, issn = {1432-1823}, journal = {Mathematische Zeitschrift}, pages = {1071–1101}, publisher = {Springer Nature}, title = {{Arithmetic of higher-dimensional orbifolds and a mixed Waring problem}}, doi = {10.1007/s00209-021-02695-w}, volume = {299}, year = {2021}, } @unpublished{9281, abstract = {We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics.}, author = {Dubach, Guillaume and Mühlböck, Fabian}, booktitle = {arXiv}, title = {{Formal verification of Zagier's one-sentence proof}}, doi = {10.48550/arXiv.2103.11389}, year = {2021}, } @article{9282, abstract = {Several Ising-type magnetic van der Waals (vdW) materials exhibit stable magnetic ground states. Despite these clear experimental demonstrations, a complete theoretical and microscopic understanding of their magnetic anisotropy is still lacking. In particular, the validity limit of identifying their one-dimensional (1-D) Ising nature has remained uninvestigated in a quantitative way. Here we performed the complete mapping of magnetic anisotropy for a prototypical Ising vdW magnet FePS3 for the first time. Combining torque magnetometry measurements with their magnetostatic model analysis and the relativistic density functional total energy calculations, we successfully constructed the three-dimensional (3-D) mappings of the magnetic anisotropy in terms of magnetic torque and energy. The results not only quantitatively confirm that the easy axis is perpendicular to the ab plane, but also reveal the anisotropies within the ab, ac, and bc planes. Our approach can be applied to the detailed quantitative study of magnetism in vdW materials.}, author = {Nauman, Muhammad and Kiem, Do Hoon and Lee, Sungmin and Son, Suhan and Park, J-G and Kang, Woun and Han, Myung Joon and Jo, Youn Jung}, issn = {2053-1583}, journal = {2D Materials}, keywords = {Mechanical Engineering, General Materials Science, Mechanics of Materials, General Chemistry, Condensed Matter Physics}, number = {3}, publisher = {IOP Publishing}, title = {{Complete mapping of magnetic anisotropy for prototype Ising van der Waals FePS3}}, doi = {10.1088/2053-1583/abeed3}, volume = {8}, year = {2021}, } @article{9283, abstract = {Gene expression levels are influenced by multiple coexisting molecular mechanisms. Some of these interactions such as those of transcription factors and promoters have been studied extensively. However, predicting phenotypes of gene regulatory networks (GRNs) remains a major challenge. Here, we use a well-defined synthetic GRN to study in Escherichia coli how network phenotypes depend on local genetic context, i.e. the genetic neighborhood of a transcription factor and its relative position. We show that one GRN with fixed topology can display not only quantitatively but also qualitatively different phenotypes, depending solely on the local genetic context of its components. Transcriptional read-through is the main molecular mechanism that places one transcriptional unit (TU) within two separate regulons without the need for complex regulatory sequences. We propose that relative order of individual TUs, with its potential for combinatorial complexity, plays an important role in shaping phenotypes of GRNs.}, author = {Nagy-Staron, Anna A and Tomasek, Kathrin and Caruso Carter, Caroline and Sonnleitner, Elisabeth and Kavcic, Bor and Paixão, Tiago and Guet, Calin C}, issn = {2050-084X}, journal = {eLife}, keywords = {Genetics and Molecular Biology}, publisher = {eLife Sciences Publications}, title = {{Local genetic context shapes the function of a gene regulatory network}}, doi = {10.7554/elife.65993}, volume = {10}, year = {2021}, } @article{9287, abstract = {The phytohormone auxin and its directional transport through tissues are intensively studied. However, a mechanistic understanding of auxin-mediated feedback on endocytosis and polar distribution of PIN auxin transporters remains limited due to contradictory observations and interpretations. Here, we used state-of-the-art methods to reexamine the auxin effects on PIN endocytic trafficking. We used high auxin concentrations or longer treatments versus lower concentrations and shorter treatments of natural (IAA) and synthetic (NAA) auxins to distinguish between specific and nonspecific effects. Longer treatments of both auxins interfere with Brefeldin A-mediated intracellular PIN2 accumulation and also with general aggregation of endomembrane compartments. NAA treatment decreased the internalization of the endocytic tracer dye, FM4-64; however, NAA treatment also affected the number, distribution, and compartment identity of the early endosome/trans-Golgi network (EE/TGN), rendering the FM4-64 endocytic assays at high NAA concentrations unreliable. To circumvent these nonspecific effects of NAA and IAA affecting the endomembrane system, we opted for alternative approaches visualizing the endocytic events directly at the plasma membrane (PM). Using Total Internal Reflection Fluorescence (TIRF) microscopy, we saw no significant effects of IAA or NAA treatments on the incidence and dynamics of clathrin foci, implying that these treatments do not affect the overall endocytosis rate. However, both NAA and IAA at low concentrations rapidly and specifically promoted endocytosis of photo-converted PIN2 from the PM. These analyses identify a specific effect of NAA and IAA on PIN2 endocytosis, thus contributing to its polarity maintenance and furthermore illustrate that high auxin levels have nonspecific effects on trafficking and endomembrane compartments. }, author = {Narasimhan, Madhumitha and Gallei, Michelle C and Tan, Shutang and Johnson, Alexander J and Verstraeten, Inge and Li, Lanxin and Rodriguez Solovey, Lesia and Han, Huibin and Himschoot, E and Wang, R and Vanneste, S and Sánchez-Simarro, J and Aniento, F and Adamowski, Maciek and Friml, Jiří}, issn = {1532-2548}, journal = {Plant Physiology}, number = {2}, pages = {1122–1142}, publisher = {Oxford University Press}, title = {{Systematic analysis of specific and nonspecific auxin effects on endocytosis and trafficking}}, doi = {10.1093/plphys/kiab134}, volume = {186}, year = {2021}, } @article{9288, abstract = {• The phenylpropanoid pathway serves a central role in plant metabolism, providing numerous compounds involved in diverse physiological processes. Most carbon entering the pathway is incorporated into lignin. Although several phenylpropanoid pathway mutants show seedling growth arrest, the role for lignin in seedling growth and development is unexplored. • We use complementary pharmacological and genetic approaches to block CINNAMATE‐4‐HYDROXYLASE (C4H) functionality in Arabidopsis seedlings and a set of molecular and biochemical techniques to investigate the underlying phenotypes. • Blocking C4H resulted in reduced lateral rooting and increased adventitious rooting apically in the hypocotyl. These phenotypes coincided with an inhibition in auxin transport. The upstream accumulation in cis‐cinnamic acid was found to likely cause polar auxin transport inhibition. Conversely, a downstream depletion in lignin perturbed phloem‐mediated auxin transport. Restoring lignin deposition effectively reestablished phloem transport and, accordingly, auxin homeostasis. • Our results show that the accumulation of bioactive intermediates and depletion in lignin jointly cause the aberrant phenotypes upon blocking C4H, and demonstrate that proper deposition of lignin is essential for the establishment of auxin distribution in seedlings. Our data position the phenylpropanoid pathway and lignin in a new physiological framework, consolidating their importance in plant growth and development.}, author = {El Houari, I and Van Beirs, C and Arents, HE and Han, Huibin and Chanoca, A and Opdenacker, D and Pollier, J and Storme, V and Steenackers, W and Quareshy, M and Napier, R and Beeckman, T and Friml, Jiří and De Rybel, B and Boerjan, W and Vanholme, B}, issn = {1469-8137}, journal = {New Phytologist}, number = {6}, pages = {2275--2291}, publisher = {Wiley}, title = {{Seedling developmental defects upon blocking CINNAMATE-4-HYDROXYLASE are caused by perturbations in auxin transport}}, doi = {10.1111/nph.17349}, volume = {230}, year = {2021}, } @article{9290, abstract = {Polar subcellular localization of the PIN exporters of the phytohormone auxin is a key determinant of directional, intercellular auxin transport and thus a central topic of both plant cell and developmental biology. Arabidopsis mutants lacking PID, a kinase that phosphorylates PINs, or the MAB4/MEL proteins of unknown molecular function display PIN polarity defects and phenocopy pin mutants, but mechanistic insights into how these factors convey PIN polarity are missing. Here, by combining protein biochemistry with quantitative live-cell imaging, we demonstrate that PINs, MAB4/MELs, and AGC kinases interact in the same complex at the plasma membrane. MAB4/MELs are recruited to the plasma membrane by the PINs and in concert with the AGC kinases maintain PIN polarity through limiting lateral diffusion-based escape of PINs from the polar domain. The PIN-MAB4/MEL-PID protein complex has self-reinforcing properties thanks to positive feedback between AGC kinase-mediated PIN phosphorylation and MAB4/MEL recruitment. We thus uncover the molecular mechanism by which AGC kinases and MAB4/MEL proteins regulate PIN localization and plant development.}, author = {Glanc, Matous and Van Gelderen, K and Hörmayer, Lukas and Tan, Shutang and Naramoto, S and Zhang, Xixi and Domjan, David and Vcelarova, L and Hauschild, Robert and Johnson, Alexander J and de Koning, E and van Dop, M and Rademacher, E and Janson, S and Wei, X and Molnar, Gergely and Fendrych, Matyas and De Rybel, B and Offringa, R and Friml, Jiří}, issn = {1879-0445}, journal = {Current Biology}, number = {9}, pages = {1918--1930}, publisher = {Elsevier}, title = {{AGC kinases and MAB4/MEL proteins maintain PIN polarity by limiting lateral diffusion in plant cells}}, doi = {10.1016/j.cub.2021.02.028}, volume = {31}, year = {2021}, } @misc{9291, abstract = {This .zip File contains the transport data for figures presented in the main text and supplementary material of "Enhancement of Proximity Induced Superconductivity in Planar Germanium" by K. Aggarwal, et. al. The measurements were done using Labber Software and the data is stored in the hdf5 file format. The files can be opened using either the Labber Log Browser (https://labber.org/overview/) or Labber Python API (http://labber.org/online-doc/api/LogFile.html).}, author = {Katsaros, Georgios}, publisher = {Institute of Science and Technology Austria}, title = {{Raw transport data for: Enhancement of proximity induced superconductivity in planar germanium}}, doi = {10.15479/AT:ISTA:9291}, year = {2021}, } @article{9293, abstract = {We consider planning problems for graphs, Markov Decision Processes (MDPs), and games on graphs in an explicit state space. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems with k different target sets: (a) the coverage problem asks whether there is a plan for each individual target set; and (b) the sequential target reachability problem asks whether the targets can be reached in a given sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds, based on the boolean matrix multiplication (BMM) conjecture and strong exponential time hypothesis (SETH), establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs, and for the sequential reachability problem games on graphs are harder than MDPs and graphs; and (ii) problem-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.}, author = {Chatterjee, Krishnendu and Dvořák, Wolfgang and Henzinger, Monika H and Svozil, Alexander}, issn = {0004-3702}, journal = {Artificial Intelligence}, number = {8}, publisher = {Elsevier}, title = {{Algorithms and conditional lower bounds for planning problems}}, doi = {10.1016/j.artint.2021.103499}, volume = {297}, year = {2021}, } @article{9294, abstract = {In this issue of Developmental Cell, Doyle and colleagues identify periodic anterior contraction as a characteristic feature of fibroblasts and mesenchymal cancer cells embedded in 3D collagen gels. This contractile mechanism generates a matrix prestrain required for crawling in fibrous 3D environments.}, author = {Gärtner, Florian R and Sixt, Michael K}, issn = {18781551}, journal = {Developmental Cell}, number = {6}, pages = {723--725}, publisher = {Elsevier}, title = {{Engaging the front wheels to drive through fibrous terrain}}, doi = {10.1016/j.devcel.2021.03.002}, volume = {56}, year = {2021}, } @article{9295, abstract = {Hill's Conjecture states that the crossing number cr(𝐾𝑛) of the complete graph 𝐾𝑛 in the plane (equivalently, the sphere) is 14⌊𝑛2⌋⌊𝑛−12⌋⌊𝑛−22⌋⌊𝑛−32⌋=𝑛4/64+𝑂(𝑛3) . Moon proved that the expected number of crossings in a spherical drawing in which the points are randomly distributed and joined by geodesics is precisely 𝑛4/64+𝑂(𝑛3) , thus matching asymptotically the conjectured value of cr(𝐾𝑛) . Let cr𝑃(𝐺) denote the crossing number of a graph 𝐺 in the projective plane. Recently, Elkies proved that the expected number of crossings in a naturally defined random projective plane drawing of 𝐾𝑛 is (𝑛4/8𝜋2)+𝑂(𝑛3) . In analogy with the relation of Moon's result to Hill's conjecture, Elkies asked if lim𝑛→∞ cr𝑃(𝐾𝑛)/𝑛4=1/8𝜋2 . We construct drawings of 𝐾𝑛 in the projective plane that disprove this.}, author = {Arroyo Guevara, Alan M and Mcquillan, Dan and Richter, R. Bruce and Salazar, Gelasio and Sullivan, Matthew}, issn = {1097-0118}, journal = {Journal of Graph Theory}, number = {3}, pages = {426--440}, publisher = {Wiley}, title = {{Drawings of complete graphs in the projective plane}}, doi = {10.1002/jgt.22665}, volume = {97}, year = {2021}, } @inproceedings{9296, abstract = { matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.}, author = {Aichholzer, Oswin and Arroyo Guevara, Alan M and Masárová, Zuzana and Parada, Irene and Perz, Daniel and Pilz, Alexander and Tkadlec, Josef and Vogtenhuber, Birgit}, booktitle = {15th International Conference on Algorithms and Computation}, isbn = {9783030682101}, issn = {16113349}, location = {Yangon, Myanmar}, pages = {221--233}, publisher = {Springer Nature}, title = {{On compatible matchings}}, doi = {10.1007/978-3-030-68211-8_18}, volume = {12635}, year = {2021}, }