@inproceedings{309, abstract = {We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding ' : G ! M of a graph G into a 2manifold M maps the vertices in V (G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to a common node or arc, due to data compression or low resolution. This raises the computational problem of deciding whether a given map ' : G ! M comes from an embedding. A map ' : G ! M is a weak embedding if it can be perturbed into an embedding ψ: G ! M with k' "k < " for every " > 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl [14], which reduces to solving a system of linear equations over Z2. It runs in O(n2!) O(n4:75) time, where 2:373 is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler than [14]: We perform a sequence of local operations that gradually "untangles" the image '(G) into an embedding (G), or reports that ' is not a weak embedding. It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon [1], and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.}, author = {Akitaya, Hugo and Fulek, Radoslav and Tóth, Csaba}, location = {New Orleans, LA, USA}, pages = {274 -- 292}, publisher = {ACM}, title = {{Recognizing weak embeddings of graphs}}, doi = {10.1137/1.9781611975031.20}, year = {2018}, } @article{5794, abstract = {We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as q-deformed Lie algebras. In particular, we show that, if the symmetry of a free quantum particle corresponds to a Lie group G, in the presence of a many-body environment this particle can be described by a deformed group, Gq. Crucially, the single deformation parameter, q, contains all the information about the many-particle interactions in the system. We exemplify our approach by considering a quantum rotor interacting with a bath of bosons, and demonstrate that extracting the value of q from closed-form solutions in the perturbative regime allows one to predict the behavior of the system for arbitrary values of the impurity-bath coupling strength, in good agreement with nonperturbative calculations. Furthermore, the value of the deformation parameter allows one to predict at which coupling strengths rotor-bath interactions result in a formation of a stable quasiparticle. The approach based on quantum groups does not only allow for a drastic simplification of impurity problems, but also provides valuable insights into hidden symmetries of interacting many-particle systems.}, author = {Yakaboylu, Enderalp and Shkolnikov, Mikhail and Lemeshko, Mikhail}, issn = {00319007}, journal = {Physical Review Letters}, number = {25}, publisher = {American Physical Society}, title = {{Quantum groups as hidden symmetries of quantum impurities}}, doi = {10.1103/PhysRevLett.121.255302}, volume = {121}, year = {2018}, } @article{87, abstract = {Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics.}, author = {Edelsbrunner, Herbert and Nikitenko, Anton}, journal = {Annals of Applied Probability}, number = {5}, pages = {3215 -- 3238}, publisher = {Institute of Mathematical Statistics}, title = {{Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics}}, doi = {10.1214/18-AAP1389}, volume = {28}, year = {2018}, } @article{192, abstract = {The phytohormone auxin is the information carrier in a plethora of developmental and physiological processes in plants(1). It has been firmly established that canonical, nuclear auxin signalling acts through regulation of gene transcription(2). Here, we combined microfluidics, live imaging, genetic engineering and computational modelling to reanalyse the classical case of root growth inhibition(3) by auxin. We show that Arabidopsis roots react to addition and removal of auxin by extremely rapid adaptation of growth rate. This process requires intracellular auxin perception but not transcriptional reprogramming. The formation of the canonical TIR1/AFB-Aux/IAA co-receptor complex is required for the growth regulation, hinting to a novel, non-transcriptional branch of this signalling pathway. Our results challenge the current understanding of root growth regulation by auxin and suggest another, presumably non-transcriptional, signalling output of the canonical auxin pathway.}, author = {Fendrych, Matyas and Akhmanova, Maria and Merrin, Jack and Glanc, Matous and Hagihara, Shinya and Takahashi, Koji and Uchida, Naoyuki and Torii, Keiko U and Friml, Jirí}, journal = {Nature Plants}, number = {7}, pages = {453 -- 459}, publisher = {Springer Nature}, title = {{Rapid and reversible root growth inhibition by TIR1 auxin signalling}}, doi = {10.1038/s41477-018-0190-1}, volume = {4}, year = {2018}, } @article{14, abstract = {The intercellular transport of auxin is driven by PIN-formed (PIN) auxin efflux carriers. PINs are localized at the plasma membrane (PM) and on constitutively recycling endomembrane vesicles. Therefore, PINs can mediate auxin transport either by direct translocation across the PM or by pumping auxin into secretory vesicles (SVs), leading to its secretory release upon fusion with the PM. Which of these two mechanisms dominates is a matter of debate. Here, we addressed the issue with a mathematical modeling approach. We demonstrate that the efficiency of secretory transport depends on SV size, half-life of PINs on the PM, pH, exocytosis frequency and PIN density. 3D structured illumination microscopy (SIM) was used to determine PIN density on the PM. Combining this data with published values of the other parameters, we show that the transport activity of PINs in SVs would have to be at least 1000× greater than on the PM in order to produce a comparable macroscopic auxin transport. If both transport mechanisms operated simultaneously and PINs were equally active on SVs and PM, the contribution of secretion to the total auxin flux would be negligible. In conclusion, while secretory vesicle-mediated transport of auxin is an intriguing and theoretically possible model, it is unlikely to be a major mechanism of auxin transport inplanta.}, author = {Hille, Sander and Akhmanova, Maria and Glanc, Matous and Johnson, Alexander J and Friml, Jirí}, issn = {1422-0067}, journal = {International Journal of Molecular Sciences}, number = {11}, publisher = {MDPI}, title = {{Relative contribution of PIN-containing secretory vesicles and plasma membrane PINs to the directed auxin transport: Theoretical estimation}}, doi = {10.3390/ijms19113566}, volume = {19}, year = {2018}, }