@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},
publisher = {IEEE},
title = {{Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic}},
doi = {10.1109/bigdata50022.2020.9378374},
year = {2021},
}
@inproceedings{9605,
abstract = {Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness. },
author = {Corbet, René and Kerber, Michael and Lesnick, Michael and Osang, Georg F},
booktitle = {Leibniz International Proceedings in Informatics},
isbn = {9783959771849},
issn = {18688969},
location = {Online},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Computing the multicover bifiltration}},
doi = {10.4230/LIPIcs.SoCG.2021.27},
volume = {189},
year = {2021},
}
@article{7962,
abstract = {A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.},
author = {Pach, János and Reed, Bruce and Yuditsky, Yelena},
issn = {14320444},
journal = {Discrete and Computational Geometry},
number = {4},
pages = {888--917},
publisher = {Springer Nature},
title = {{Almost all string graphs are intersection graphs of plane convex sets}},
doi = {10.1007/s00454-020-00213-z},
volume = {63},
year = {2020},
}
@inproceedings{8135,
abstract = {Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics.},
author = {Edelsbrunner, Herbert and Nikitenko, Anton and Ölsböck, Katharina and Synak, Peter},
booktitle = {Topological Data Analysis},
isbn = {9783030434076},
issn = {21978549},
pages = {181--218},
publisher = {Springer Nature},
title = {{Radius functions on Poisson–Delaunay mosaics and related complexes experimentally}},
doi = {10.1007/978-3-030-43408-3_8},
volume = {15},
year = {2020},
}
@article{8163,
abstract = {Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces.},
author = {Vegter, Gert and Wintraecken, Mathijs},
issn = {1588-2896},
journal = {Studia Scientiarum Mathematicarum Hungarica},
number = {2},
pages = {193--199},
publisher = {AKJournals},
title = {{Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes}},
doi = {10.1556/012.2020.57.2.1454},
volume = {57},
year = {2020},
}