@inproceedings{7989,
abstract = {We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.},
author = {Patakova, Zuzana},
booktitle = {36th International Symposium on Computational Geometry},
isbn = {9783959771436},
issn = {18688969},
location = {Zürich, Switzerland},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Bounding radon number via Betti numbers}},
doi = {10.4230/LIPIcs.SoCG.2020.61},
volume = {164},
year = {2020},
}
@inproceedings{7990,
abstract = {Given a finite point set P in general position in the plane, a full triangulation is a maximal straight-line embedded plane graph on P. A partial triangulation on P is a full triangulation of some subset P' of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge, removes a non-extreme point of degree 3, or adds a point in P ⧵ P' as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The goal of this paper is to investigate the structure of this graph, with emphasis on its connectivity. For sets P of n points in general position, we show that the bistellar flip graph is (n-3)-connected, thereby answering, for sets in general position, an open questions raised in a book (by De Loera, Rambau, and Santos) and a survey (by Lee and Santos) on triangulations. This matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points and projecting the lower convex hull), where (n-3)-connectivity has been known since the late 1980s through the secondary polytope (Gelfand, Kapranov, Zelevinsky) and Balinski’s Theorem. Our methods also yield the following results (see the full version [Wagner and Welzl, 2020]): (i) The bistellar flip graph can be covered by graphs of polytopes of dimension n-3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n-3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations are regular iff the trivial subdivision has height n-3 in the partial order of partial subdivisions. (iv) There are arbitrarily large sets P with non-regular partial triangulations, while every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular partial triangulations (answering a question by F. Santos in the unexpected direction).},
author = {Wagner, Uli and Welzl, Emo},
booktitle = {36th International Symposium on Computational Geometry},
isbn = {9783959771436},
issn = {18688969},
location = {Zürich, Switzerland},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips)}},
doi = {10.4230/LIPIcs.SoCG.2020.67},
volume = {164},
year = {2020},
}
@inproceedings{7991,
abstract = {We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes the link between "grid peeling" and the ACSF observed by Eppstein et al. (2017), which applied only to convex curves, and which was studied only for regular grids. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase.},
author = {Avvakumov, Sergey and Nivasch, Gabriel},
booktitle = {36th International Symposium on Computational Geometry},
isbn = {9783959771436},
issn = {18688969},
location = {Zürich, Switzerland},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Homotopic curve shortening and the affine curve-shortening flow}},
doi = {10.4230/LIPIcs.SoCG.2020.12},
volume = {164},
year = {2020},
}
@inproceedings{7992,
abstract = {Let K be a convex body in ℝⁿ (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K ∩ h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p₀ is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n ≥ 2, there are always at least three distinct barycentric cuts through the point p₀ ∈ K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p₀ are guaranteed if n ≥ 3.},
author = {Patakova, Zuzana and Tancer, Martin and Wagner, Uli},
booktitle = {36th International Symposium on Computational Geometry},
isbn = {9783959771436},
issn = {18688969},
location = {Zürich, Switzerland},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Barycentric cuts through a convex body}},
doi = {10.4230/LIPIcs.SoCG.2020.62},
volume = {164},
year = {2020},
}
@inproceedings{7994,
abstract = {In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line) drawings. A characterization of the pseudolinear drawings of K_n was found recently. We extend this characterization to all graphs, by describing the set of minimal forbidden subdrawings for pseudolinear drawings. Our characterization also leads to a polynomial-time algorithm to recognize pseudolinear drawings and construct the pseudolines when it is possible.},
author = {Arroyo Guevara, Alan M and Bensmail, Julien and Bruce Richter, R.},
booktitle = {36th International Symposium on Computational Geometry},
isbn = {9783959771436},
issn = {18688969},
location = {Zürich, Switzerland},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Extending drawings of graphs to arrangements of pseudolines}},
doi = {10.4230/LIPIcs.SoCG.2020.9},
volume = {164},
year = {2020},
}
@article{7940,
abstract = {We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay, Regelskis, and Wendlandt [GRW18].},
author = {Yang, Yaping and Zhao, Gufang},
issn = {1531586X},
journal = {Transformation Groups},
pages = {1371--1385},
publisher = {Springer Nature},
title = {{The PBW theorem for affine Yangians}},
doi = {10.1007/s00031-020-09572-6},
volume = {25},
year = {2020},
}
@inbook{7941,
abstract = {Expansion microscopy is a recently developed super-resolution imaging technique, which provides an alternative to optics-based methods such as deterministic approaches (e.g. STED) or stochastic approaches (e.g. PALM/STORM). The idea behind expansion microscopy is to embed the biological sample in a swellable gel, and then to expand it isotropically, thereby increasing the distance between the fluorophores. This approach breaks the diffraction barrier by simply separating the emission point-spread-functions of the fluorophores. The resolution attainable in expansion microscopy is thus directly dependent on the separation that can be achieved, i.e. on the expansion factor. The original implementation of the technique achieved an expansion factor of fourfold, for a resolution of 70–80 nm. The subsequently developed X10 method achieves an expansion factor of 10-fold, for a resolution of 25–30 nm. This technique can be implemented with minimal technical requirements on any standard fluorescence microscope, and is more easily applied for multi-color imaging than either deterministic or stochastic super-resolution approaches. This renders X10 expansion microscopy a highly promising tool for new biological discoveries, as discussed here, and as demonstrated by several recent applications.},
author = {Truckenbrodt, Sven M and Rizzoli, Silvio O.},
booktitle = {Methods in Cell Biology},
issn = {0091679X},
publisher = {Elsevier},
title = {{Simple multi-color super-resolution by X10 microscopy}},
doi = {10.1016/bs.mcb.2020.04.016},
year = {2020},
}
@article{7942,
abstract = {An understanding of the missing antinodal electronic excitations in the pseudogap state is essential for uncovering the physics of the underdoped cuprate high-temperature superconductors1,2,3,4,5,6. The majority of high-temperature experiments performed thus far, however, have been unable to discern whether the antinodal states are rendered unobservable due to their damping or whether they vanish due to their gapping7,8,9,10,11,12,13,14,15,16,17,18. Here, we distinguish between these two scenarios by using quantum oscillations to examine whether the small Fermi surface pocket, found to occupy only 2% of the Brillouin zone in the underdoped cuprates19,20,21,22,23,24, exists in isolation against a majority of completely gapped density of states spanning the antinodes, or whether it is thermodynamically coupled to a background of ungapped antinodal states. We find that quantum oscillations associated with the small Fermi surface pocket exhibit a signature sawtooth waveform characteristic of an isolated two-dimensional Fermi surface pocket25,26,27,28,29,30,31,32. This finding reveals that the antinodal states are destroyed by a hard gap that extends over the majority of the Brillouin zone, placing strong constraints on a drastic underlying origin of quasiparticle disappearance over almost the entire Brillouin zone in the pseudogap regime7,8,9,10,11,12,13,14,15,16,17,18.},
author = {Hartstein, Máté and Hsu, Yu Te and Modic, Kimberly A and Porras, Juan and Loew, Toshinao and Tacon, Matthieu Le and Zuo, Huakun and Wang, Jinhua and Zhu, Zengwei and Chan, Mun K. and Mcdonald, Ross D. and Lonzarich, Gilbert G. and Keimer, Bernhard and Sebastian, Suchitra E. and Harrison, Neil},
issn = {17452481},
journal = {Nature Physics},
pages = {841--847},
publisher = {Springer Nature},
title = {{Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-Tc superconductors}},
doi = {10.1038/s41567-020-0910-0},
volume = {16},
year = {2020},
}
@article{7948,
abstract = {In agricultural systems, nitrate is the main source of nitrogen available for plants. Besides its role as a nutrient, nitrate has been shown to act as a signal molecule for plant growth, development and stress responses. In Arabidopsis, the NRT1.1 nitrate transceptor represses lateral root (LR) development at low nitrate availability by promoting auxin basipetal transport out of the LR primordia (LRPs). In addition, our present study shows that NRT1.1 acts as a negative regulator of the TAR2 auxin biosynthetic gene expression in the root stele. This is expected to repress local auxin biosynthesis and thus to reduce acropetal auxin supply to the LRPs. Moreover, NRT1.1 also negatively affects expression of the LAX3 auxin influx carrier, thus preventing cell wall remodeling required for overlying tissues separation during LRP emergence. Both NRT1.1-mediated repression of TAR2 and LAX3 are suppressed at high nitrate availability, resulting in the nitrate induction of TAR2 and LAX3 expression that is required for optimal stimulation of LR development by nitrate. Altogether, our results indicate that the NRT1.1 transceptor coordinately controls several crucial auxin-associated processes required for LRP development, and as a consequence that NRT1.1 plays a much more integrated role than previously anticipated in regulating the nitrate response of root system architecture.},
author = {Maghiaoui, A and Bouguyon, E and Cuesta, Candela and Perrine-Walker, F and Alcon, C and Krouk, G and Benková, Eva and Nacry, P and Gojon, A and Bach, L},
issn = {0022-0957},
journal = {Journal of Experimental Botany},
number = {15},
pages = {4480--4494},
publisher = {Oxford University Press},
title = {{The Arabidopsis NRT1.1 transceptor coordinately controls auxin biosynthesis and transport to regulate root branching in response to nitrate}},
doi = {10.1093/jxb/eraa242},
volume = {71},
year = {2020},
}
@article{7949,
abstract = {Peptides derived from non-functional precursors play important roles in various developmental processes, but also in (a)biotic stress signaling. Our (phospho)proteome-wide analyses of C-terminally encoded peptide 5 (CEP5)-mediated changes revealed an impact on abiotic stress-related processes. Drought has a dramatic impact on plant growth, development and reproduction, and the plant hormone auxin plays a role in drought responses. Our genetic, physiological, biochemical and pharmacological results demonstrated that CEP5-mediated signaling is relevant for osmotic and drought stress tolerance in Arabidopsis, and that CEP5 specifically counteracts auxin effects. Specifically, we found that CEP5 signaling stabilizes AUX/IAA transcriptional repressors, suggesting the existence of a novel peptide-dependent control mechanism that tunes auxin signaling. These observations align with the recently described role of AUX/IAAs in stress tolerance and provide a novel role for CEP5 in osmotic and drought stress tolerance.},
author = {Smith, S and Zhu, S and Joos, L and Roberts, I and Nikonorova, N and Vu, LD and Stes, E and Cho, H and Larrieu, A and Xuan, W and Goodall, B and van de Cotte, B and Waite, JM and Rigal, A and R Harborough, SR and Persiau, G and Vanneste, S and Kirschner, GK and Vandermarliere, E and Martens, L and Stahl, Y and Audenaert, D and Friml, Jiří and Felix, G and Simon, R and Bennett, M and Bishopp, A and De Jaeger, G and Ljung, K and Kepinski, S and Robert, S and Nemhauser, J and Hwang, I and Gevaert, K and Beeckman, T and De Smet, I},
issn = {1535-9476},
journal = {Molecular & Cellular Proteomics},
number = {8},
pages = {1248--1262},
publisher = {American Society for Biochemistry and Molecular Biology},
title = {{The CEP5 peptide promotes abiotic stress tolerance, as revealed by quantitative proteomics, and attenuates the AUX/IAA equilibrium in Arabidopsis}},
doi = {10.1074/mcp.ra119.001826},
volume = {19},
year = {2020},
}