@article{22247, abstract = {A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, …, k such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO k-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the “linearly ordered chromatic number” of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).}, author = {Filakovský, Marek and Nakajima, Tamio Vesa and Opršal, Jakub and Tasinato, Gianluca and Wagner, Uli}, issn = {1942-3462}, journal = {ACM Transactions on Computation Theory}, keywords = {Constraint satisfaction problem, hypergraph colouring, promise problem, topological methods}, number = {2}, publisher = {Association for Computing Machinery}, title = {{Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs}}, doi = {10.1145/3779121}, volume = {18}, year = {2026}, } @article{19860, abstract = {An eight-partition of a finite set of points (respectively, of a continuous mass distribution) in R^3 consists of three planes that divide the space into 8 octants, such that each open octant contains at most 1/8 of the points (respectively, of the mass). In 1966, Hadwiger showed that any mass distribution in R^3 admits an eight-partition; moreover, one can prescribe the normal direction of one of the three planes. The analogous result for finite point sets follows by a standard limit argument. We prove the following variant of this result: any mass distribution (or point set) in R^3 admits an eight-partition for which the intersection of two of the planes is a line with a prescribed direction. Moreover, we present an efficient algorithm for calculating an eight-partition of a set of n points in R^3 (with prescribed normal direction of one of the planes) in time O(n^7/3). A preliminary version of this work appeared in SoCG’24 (Aronov et al., 40th International Symposium on Computational Geometry, 2024).}, author = {Aronov, Boris and Basit, Abdul and Ramesh, Indu and Tasinato, Gianluca and Wagner, Uli}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, pages = {1331--1355}, publisher = {Springer Nature}, title = {{Eight-partitioning points in 3D, and efficiently too}}, doi = {10.1007/s00454-025-00739-0}, volume = {75}, year = {2026}, } @article{21763, abstract = {Reactive oxygen species (ROS) have been implicated in multiple signaling processes in plants, but the underlying mechanisms and roles remain enigmatic. In this study, we developed a method of live imaging of apoplastic ROS at the root surface. Distinct signals, including auxin, extracellular adenosine triphosphate, and rapid alkalinization factor 1 peptide, induce cytosolic calcium transients and apoplastic ROS bursts. Genetic and optogenetic manipulations of Arabidopsis identified calcium transients as necessary and sufficient for ROS bursts through activation of reduced nicotinamide adenine dinucleotide phosphate (NADPH) oxidases RBOHC and RBOHF. Apoplastic ROS bursts are not required, but they do limit gravity-induced root bending. Root bending is sensed by the stretch-activated calcium channel MCA1, leading to NADPH oxidase activation. The resulting ROS production stiffens cell walls to facilitate soil penetration. Apoplastic ROS thus provides a means to balance tissue flexibility and stiffness to navigate soil.}, author = {Kulich, Ivan and Vladimirtsev, Dmitrii and Randuch, Marek and Gao, Shiqiang and Citterico, Matteo and Konrad, Kai R. and Nagel, Georg and Wrzaczek, Michael and Cascaro, Léa and Vinet, Pauline and Durand, Pauline and Asnacios, Atef and Verma, Lokesh and Bennett, Malcolm J. and Pandey, Bipin K. and Friml, Jiří}, issn = {1095-9203}, journal = {Science}, number = {6795}, pages = {296--300}, publisher = {AAAS}, title = {{Calcium-triggered apoplastic ROS bursts balance gravity and mechanical signals for soil navigation}}, doi = {10.1126/science.adu8197}, volume = {392}, year = {2026}, } @phdthesis{23145, author = {Randuch, Marek}, issn = {2663-337X}, pages = {289}, publisher = {Institute of Science and Technology Austria}, title = {{Fast growth responses in plants: Growth regulation and phospho-proteomic }}, doi = {10.15479/AT-ISTA-23145}, year = {2026}, } @unpublished{23175, abstract = {Plants must continually balance growth with arrest, especially under stress. Auxin signaling acts as a central regulatory hub in this process, yet the mechanisms that dynamically tune early auxin signalling in real time remain unknown. Here, we used the light-gated, Ca2+-permeable Channelrhodopsin 2 variant XXM2.0 to optogenetically impose defined Ca2+ signatures on Arabidopsis root cells. Repetitive light activation triggered cytosolic Ca2+ signals that in turn suppressed auxin-induced membrane depolarization and Ca2+ transients. Moreover, prolonged optogenetic Ca2+ stimulation affects auxin-responsive transcriptional reprogramming. As phenotypic output, reversible inhibition of root growth by suppressing cell division and elongation was observed. We further identify a candidate CaM7–CNGC14 module that likely mediates Ca2+-dependent gating of early auxin signalling. Our study thus introduces a synthetic biology approach to decompose calcium–auxin crosstalk in plant cells, and demonstrates that optogenetically imposed cytosolic Ca2+ signals act as dynamic regulators of auxin susceptibility in roots.}, author = {Song, Huifang and Baudon, Angel and Freund, Matthias and Randuch, Marek and Pěnčík, Aleš and Ondřej, Novák and He, Zhaohui and Kaufmann, Kerstin and Li, Nan and Gilliham, Matthew and Friml, Jiří and Hedrich, Rainer and Huang, Shouguang}, booktitle = {bioRxiv}, title = {{Ca2+ signature gates early auxin signaling in Arabidopsis roots}}, doi = {10.1101/2025.10.04.680446}, year = {2026}, } @article{18706, abstract = {We prove discrete-to-continuum convergence for dynamical optimal transport on Zd -periodic graphs with cost functional having linear growth at infinity. This result provides an answer to a problem left open by Gladbach, Kopfer, Maas, and Portinale (Calc Var Partial Differential Equations 62(5), 2023), where the convergence behaviour of discrete boundary-value dynamical transport problems is proved under the stronger assumption of superlinear growth. Our result extends the known literature to some important classes of examples, such as scaling limits of 1 -Wasserstein transport problems. Similarly to what happens in the quadratic case, the geometry of the graph plays a crucial role in the structure of the limit cost function, as we discuss in the final part of this work, which includes some visual representations.}, author = {Portinale, Lorenzo and Quattrocchi, Filippo}, issn = {1469-4425}, journal = {European Journal of Applied Mathematics}, keywords = {optimal transport, discrete-to-continuum, homogenisation, linear growth, gamma-convergence}, number = {3}, pages = {614--642}, publisher = {Cambridge University Press}, title = {{Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs}}, doi = {10.1017/s0956792524000810}, volume = {37}, year = {2026}, } @phdthesis{21423, abstract = {Biological systems, such as cytoskeletal filaments and multicellular collectives, exhibit rich self-organization driven by their intrinsic activity and physical constraints. Across scales, geometry plays a central role: the shape of active units and the structure of their environment strongly influence how order emerges in these far-from-equilibrium systems. In this thesis, we combine minimal active-matter models with bottom-up in vitro experiments to identify the principles by which geometry and activity shape collective behavior in biological matter. At the subcellular scale, we investigate how the physical properties of chiral FtsZ filaments govern their large-scale organization. Using a mesoscopic model validated by reconstituted filament assays, we show that filament shape, intrinsic curvature, and flexibility, together with activity-driven straightening, determine whether filaments form chiral rings, polar bands, or nematic-like states. Our model shows that small changes in filament mechanics produce large shifts in collective structures, revealing how the geometry of individual filaments amplifies through activity to control patterns relevant for bacterial cytokinesis. At the cellular scale, we examine how geometry of the external environment influences collective cancer cell migration. Experiments in controlled microfabricated obstacle environments demonstrate that geometric disorder alone can induce a transition from collective to single-cell invasion. A minimal model of active particles in disordered geometries reproduces these effects, demonstrating that cell dissemination results both from local geometrical constraints and a global integration of spatial disorder over time. Surprisingly, this transition is accompanied by a change in the universality class of interface dynamics, revealing that cell-environment interactions can shift the collective behavior of an invasive front purely through mechanics. In the last system, we study how cell-intrinsic geometry and chirality affect collective motion in confined and unconfined settings. Using a minimal model inspired by in vitro experiments, we analyze motile cells that exhibit persistent rotation due to intrinsic left-right asymmetry. In circular confinement, this simplified chiral model reproduces several experimentally observed features within specific parameter regimes. At high densities in unconfined environments, however, intrinsic chirality becomes masked even before the onset of the jamming transition. These results show that single-cell geometric asymmetry does not necessarily translate into large-scale chiral flows, offering new insight into how forces and symmetries shape collective motion in dense cellular systems. Overall, this work uncovers how geometric constraints – embedded in the intrinsic architecture of an active filament or encoded in the complexity of a microenvironment couple to active forces to generate different classes of complex behaviors. }, author = {Dunajova, Zuzana}, isbn = {978-3-99078-076-3}, issn = {2663-337X}, pages = {110}, publisher = {Institute of Science and Technology Austria}, title = {{Geometry-driven self-organization of migrating cells and chiral filaments}}, doi = {10.15479/AT-ISTA-21423}, year = {2026}, } @misc{21439, abstract = {These files contain supplementary movies accompanying the PhD thesis “Geometry-driven self-organization of migrating cells and chiral filaments” by Zuzana Dunajova (2026). The videos provide additional visual material supporting the experiments and results described in the thesis.}, author = {Dunajova, Zuzana}, publisher = {Institute of Science and Technology Austria}, title = {{Supplementary movies to PhD thesis “Geometry-driven self-organization of migrating cells and chiral filaments”}}, doi = {10.15479/AT-ISTA-21439}, year = {2026}, }