@article{8248,
abstract = {We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic.},
author = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit and Lieutier, Andre and Wintraecken, Mathijs},
issn = {0179-5376},
journal = {Discrete and Computational Geometry},
publisher = {Springer Nature},
title = {{Local conditions for triangulating submanifolds of Euclidean space}},
doi = {10.1007/s00454-020-00233-9},
year = {2020},
}
@article{8317,
abstract = {When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.},
author = {Aichholzer, Oswin and Akitaya, Hugo A. and Cheung, Kenneth C. and Demaine, Erik D. and Demaine, Martin L. and Fekete, Sándor P. and Kleist, Linda and Kostitsyna, Irina and Löffler, Maarten and Masárová, Zuzana and Mundilova, Klara and Schmidt, Christiane},
issn = {09257721},
journal = {Computational Geometry: Theory and Applications},
publisher = {Elsevier},
title = {{Folding polyominoes with holes into a cube}},
doi = {10.1016/j.comgeo.2020.101700},
volume = {93},
year = {2020},
}
@article{8538,
abstract = {We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.},
author = {Akopyan, Arseniy and Schwartz, Richard and Tabachnikov, Serge},
issn = {21996768},
journal = {European Journal of Mathematics},
publisher = {Springer Nature},
title = {{Billiards in ellipses revisited}},
doi = {10.1007/s40879-020-00426-9},
year = {2020},
}
@inproceedings{8580,
abstract = {We evaluate the usefulness of persistent homology in the analysis of heart rate variability. In our approach we extract several topological descriptors characterising datasets of RR-intervals, which are later used in classical machine learning algorithms. By this method we are able to differentiate the group of patients with the history of transient ischemic attack and the group of hypertensive patients.},
author = {Graff, Grzegorz and Graff, Beata and Jablonski, Grzegorz and Narkiewicz, Krzysztof},
booktitle = {11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, },
isbn = {9781728157511},
location = {Pisa, Italy},
publisher = {IEEE},
title = {{The application of persistent homology in the analysis of heart rate variability}},
doi = {10.1109/ESGCO49734.2020.9158054},
year = {2020},
}
@article{8773,
abstract = {Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.},
author = {Brown, Adam and Romanov, Anna},
issn = {1088-6826},
journal = {Proceedings of the American Mathematical Society},
keywords = {Applied Mathematics, General Mathematics},
pages = {37--52},
publisher = {American Mathematical Society},
title = {{Contravariant forms on Whittaker modules}},
doi = {10.1090/proc/15205},
volume = {149},
year = {2020},
}