[{"oa_version":"Preprint","article_type":"original","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1312.1231","open_access":"1"}],"acknowledgement":"This research has been supported by the EU project Toposys(FP7-ICT-318493-STREP), by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”.","date_updated":"2025-04-15T08:37:54Z","month":"05","ec_funded":1,"article_processing_charge":"No","abstract":[{"lang":"eng","text":"Given a finite set of points in Rn and a radius parameter, we study the Čech, Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which are explicitly described by a single discrete gradient field."}],"doi":"10.1090/tran/6991","publisher":"American Mathematical Society","_id":"1072","author":[{"last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","first_name":"Ulrich"},{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"}],"external_id":{"isi":["000398030400024"],"arxiv":["1312.1231"]},"publication_status":"published","day":"01","project":[{"call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems"}],"department":[{"_id":"HeEd"}],"isi":1,"page":"3741 - 3762","arxiv":1,"date_published":"2017-05-01T00:00:00Z","publist_id":"6311","intvolume":"       369","language":[{"iso":"eng"}],"title":"The Morse theory of Čech and delaunay complexes","publication":"Transactions of the American Mathematical Society","type":"journal_article","issue":"5","year":"2017","citation":{"mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” <i>Transactions of the American Mathematical Society</i>, vol. 369, no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:<a href=\"https://doi.org/10.1090/tran/6991\">10.1090/tran/6991</a>.","ama":"Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. <i>Transactions of the American Mathematical Society</i>. 2017;369(5):3741-3762. doi:<a href=\"https://doi.org/10.1090/tran/6991\">10.1090/tran/6991</a>","short":"U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society 369 (2017) 3741–3762.","ista":"Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 369(5), 3741–3762.","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2017. <a href=\"https://doi.org/10.1090/tran/6991\">https://doi.org/10.1090/tran/6991</a>.","apa":"Bauer, U., &#38; Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay complexes. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/6991\">https://doi.org/10.1090/tran/6991</a>","ieee":"U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,” <i>Transactions of the American Mathematical Society</i>, vol. 369, no. 5. American Mathematical Society, pp. 3741–3762, 2017."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","volume":369,"status":"public","date_created":"2018-12-11T11:49:59Z","quality_controlled":"1","scopus_import":"1"},{"main_file_link":[{"url":"https://arxiv.org/abs/1705.02045","open_access":"1"}],"month":"07","date_updated":"2025-06-04T09:54:22Z","editor":[{"last_name":"Felsberg","full_name":"Felsberg, Michael","first_name":"Michael"},{"first_name":"Anders","full_name":"Heyden, Anders","last_name":"Heyden"},{"last_name":"Krüger","first_name":"Norbert","full_name":"Krüger, Norbert"}],"oa_version":"Submitted Version","oa":1,"article_processing_charge":"No","abstract":[{"lang":"eng","text":"We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams."}],"doi":"10.1007/978-3-319-64689-3_32","day":"28","conference":{"end_date":"2017-08-24","name":"CAIP: Computer Analysis of Images and Patterns","start_date":"2017-08-22","location":"Ystad, Sweden"},"author":[{"first_name":"Teresa","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss"},{"first_name":"Hubert","full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"}],"_id":"833","publication_status":"published","external_id":{"isi":["000432085900032"],"arxiv":["1705.02045"]},"publisher":"Springer","date_published":"2017-07-28T00:00:00Z","alternative_title":["LNCS"],"page":"397 - 409","arxiv":1,"intvolume":"     10424","publist_id":"6815","department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["0302-9743"]},"isi":1,"volume":10424,"status":"public","citation":{"mla":"Heiss, Teresa, and Hubert Wagner. <i>Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images</i>. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:<a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">10.1007/978-3-319-64689-3_32</a>.","ama":"Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:<a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">10.1007/978-3-319-64689-3_32</a>","short":"T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409.","ista":"Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409.","chicago":"Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">https://doi.org/10.1007/978-3-319-64689-3_32</a>.","apa":"Heiss, T., &#38; Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, &#38; N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. <a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">https://doi.org/10.1007/978-3-319-64689-3_32</a>","ieee":"T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:48:45Z","title":"Streaming algorithm for Euler characteristic curves of multidimensional images","corr_author":"1","language":[{"iso":"eng"}],"type":"conference","year":"2017"},{"publication_identifier":{"isbn":["978-331956930-7"]},"department":[{"_id":"HeEd"}],"isi":1,"publist_id":"6812","intvolume":"       198","page":"119 - 136","date_published":"2017-07-27T00:00:00Z","alternative_title":["PROMS"],"type":"conference","year":"2017","language":[{"iso":"eng"}],"title":"Finding eigenvalues of self-maps with the Kronecker canonical form","publication":"Special Sessions in Applications of Computer Algebra","date_created":"2018-12-11T11:48:46Z","quality_controlled":"1","scopus_import":"1","citation":{"ieee":"M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps with the Kronecker canonical form,” in <i>Special Sessions in Applications of Computer Algebra</i>, Kalamata, Greece, 2017, vol. 198, pp. 119–136.","apa":"Ethier, M., Jablonski, G., &#38; Mrozek, M. (2017). Finding eigenvalues of self-maps with the Kronecker canonical form. In <i>Special Sessions in Applications of Computer Algebra</i> (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. <a href=\"https://doi.org/10.1007/978-3-319-56932-1_8\">https://doi.org/10.1007/978-3-319-56932-1_8</a>","chicago":"Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” In <i>Special Sessions in Applications of Computer Algebra</i>, 198:119–36. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-56932-1_8\">https://doi.org/10.1007/978-3-319-56932-1_8</a>.","short":"M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications of Computer Algebra, Springer, 2017, pp. 119–136.","ista":"Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with the Kronecker canonical form. Special Sessions in Applications of Computer Algebra. ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.","ama":"Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the Kronecker canonical form. In: <i>Special Sessions in Applications of Computer Algebra</i>. Vol 198. Springer; 2017:119-136. doi:<a href=\"https://doi.org/10.1007/978-3-319-56932-1_8\">10.1007/978-3-319-56932-1_8</a>","mla":"Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” <i>Special Sessions in Applications of Computer Algebra</i>, vol. 198, Springer, 2017, pp. 119–36, doi:<a href=\"https://doi.org/10.1007/978-3-319-56932-1_8\">10.1007/978-3-319-56932-1_8</a>."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","volume":198,"status":"public","oa_version":"None","date_updated":"2025-04-15T08:37:55Z","month":"07","ec_funded":1,"_id":"836","external_id":{"isi":["000434088200008"]},"author":[{"last_name":"Ethier","first_name":"Marc","full_name":"Ethier, Marc"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","first_name":"Grzegorz","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"full_name":"Mrozek, Marian","first_name":"Marian","last_name":"Mrozek"}],"publisher":"Springer","publication_status":"published","conference":{"location":"Kalamata, Greece","start_date":"2015-07-20","name":"ACA: Applications of Computer Algebra","end_date":"2015-07-23"},"day":"27","project":[{"grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"abstract":[{"lang":"eng","text":"Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces."}],"article_processing_charge":"No","doi":"10.1007/978-3-319-56932-1_8"},{"month":"11","publist_id":"7970","date_updated":"2023-10-16T11:15:22Z","date_published":"2017-11-09T00:00:00Z","page":"1709 - 1735","department":[{"_id":"HeEd"}],"publication_identifier":{"eisbn":["9781498711425"]},"editor":[{"last_name":"Toth","first_name":"Csaba","full_name":"Toth, Csaba"},{"first_name":"Joseph","full_name":"O'Rourke, Joseph","last_name":"O'Rourke"},{"full_name":"Goodman, Jacob","first_name":"Jacob","last_name":"Goodman"}],"oa_version":"None","scopus_import":"1","quality_controlled":"1","series_title":"Handbook of Discrete and Computational Geometry","day":"09","publication_status":"published","_id":"84","publisher":"Taylor & Francis","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Koehl","first_name":"Patrice","full_name":"Koehl, Patrice"}],"date_created":"2018-12-11T11:44:32Z","status":"public","doi":"10.1201/9781315119601","abstract":[{"text":"The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed into genomes, from the many genes that encode for the proteins that are responsible for most if not all cellular functions, to the noncoding regions that are now known to provide regulatory functions. Proteomics initiatives help to decipher the role of post-translation modifications on the protein structures and provide maps of protein-protein interactions, while functional genomics is the field that attempts to make use of the data produced by these projects to understand protein functions. The biggest challenge today is to assimilate the wealth of information provided by these initiatives into a conceptual framework that will help us decipher life. For example, the current views of the relationship between protein structure and function remain fragmented. We know of their sequences, more and more about their structures, we have information on their biological activities, but we have difficulties connecting this dotted line into an informed whole. We lack the experimental and computational tools for directly studying protein structure, function, and dynamics at the molecular and supra-molecular levels. In this chapter, we review some of the current developments in building the computational tools that are needed, focusing on the role that geometry and topology play in these efforts. One of our goals is to raise the general awareness about the importance of geometric methods in elucidating the mysterious foundations of our very existence. Another goal is the broadening of what we consider a geometric algorithm. There is plenty of valuable no-man’s-land between combinatorial and numerical algorithms, and it seems opportune to explore this land with a computational-geometric frame of mind.","lang":"eng"}],"article_processing_charge":"No","citation":{"ista":"Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular biology. In: Handbook of Discrete and Computational Geometry, Third Edition. , 1709–1735.","short":"H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition, Taylor &#38; Francis, 2017, pp. 1709–1735.","mla":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” <i>Handbook of Discrete and Computational Geometry, Third Edition</i>, edited by Csaba Toth et al., Taylor &#38; Francis, 2017, pp. 1709–35, doi:<a href=\"https://doi.org/10.1201/9781315119601\">10.1201/9781315119601</a>.","ama":"Edelsbrunner H, Koehl P. Computational topology for structural molecular biology. In: Toth C, O’Rourke J, Goodman J, eds. <i>Handbook of Discrete and Computational Geometry, Third Edition</i>. Handbook of Discrete and Computational Geometry. Taylor &#38; Francis; 2017:1709-1735. doi:<a href=\"https://doi.org/10.1201/9781315119601\">10.1201/9781315119601</a>","apa":"Edelsbrunner, H., &#38; Koehl, P. (2017). Computational topology for structural molecular biology. In C. Toth, J. O’Rourke, &#38; J. Goodman (Eds.), <i>Handbook of Discrete and Computational Geometry, Third Edition</i> (pp. 1709–1735). Taylor &#38; Francis. <a href=\"https://doi.org/10.1201/9781315119601\">https://doi.org/10.1201/9781315119601</a>","ieee":"H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular biology,” in <i>Handbook of Discrete and Computational Geometry, Third Edition</i>, C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor &#38; Francis, 2017, pp. 1709–1735.","chicago":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” In <i>Handbook of Discrete and Computational Geometry, Third Edition</i>, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35. Handbook of Discrete and Computational Geometry. Taylor &#38; Francis, 2017. <a href=\"https://doi.org/10.1201/9781315119601\">https://doi.org/10.1201/9781315119601</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2017","type":"book_chapter","publication":"Handbook of Discrete and Computational Geometry, Third Edition","title":"Computational topology for structural molecular biology","language":[{"iso":"eng"}]},{"publist_id":"6534","intvolume":"       124","arxiv":1,"page":"588 - 596","date_published":"2017-01-01T00:00:00Z","isi":1,"publication_identifier":{"issn":["0002-9890"]},"department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:49:09Z","quality_controlled":"1","scopus_import":"1","citation":{"ista":"Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.","ama":"Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. <i>The American Mathematical Monthly</i>. 2017;124(7):588-596. doi:<a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">10.4169/amer.math.monthly.124.7.588</a>","mla":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” <i>The American Mathematical Monthly</i>, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:<a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">10.4169/amer.math.monthly.124.7.588</a>.","ieee":"A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” <i>The American Mathematical Monthly</i>, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017.","apa":"Akopyan, A., &#38; Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. <i>The American Mathematical Monthly</i>. Mathematical Association of America. <a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">https://doi.org/10.4169/amer.math.monthly.124.7.588</a>","chicago":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” <i>The American Mathematical Monthly</i>. Mathematical Association of America, 2017. <a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">https://doi.org/10.4169/amer.math.monthly.124.7.588</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","volume":124,"year":"2017","type":"journal_article","issue":"7","language":[{"iso":"eng"}],"publication":"The American Mathematical Monthly","title":"On the lengths of curves passing through boundary points of a planar convex shape","date_updated":"2025-07-10T12:01:35Z","month":"01","main_file_link":[{"url":"https://arxiv.org/abs/1605.07997","open_access":"1"}],"oa":1,"article_type":"original","oa_version":"Submitted Version","_id":"909","publication_status":"published","author":[{"last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"full_name":"Vysotsky, Vladislav","first_name":"Vladislav","last_name":"Vysotsky"}],"publisher":"Mathematical Association of America","external_id":{"isi":["000413947300002"],"arxiv":["1605.07997"]},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734"}],"day":"01","doi":"10.4169/amer.math.monthly.124.7.588","article_processing_charge":"No","abstract":[{"text":"We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor &amp;#xbd; cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.","lang":"eng"}],"ec_funded":1},{"publist_id":"7021","intvolume":"        77","page":"391-3916","date_published":"2017-06-01T00:00:00Z","alternative_title":["LIPIcs"],"department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publication_identifier":{"issn":["1868-8969"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2018-12-11T11:47:56Z","scopus_import":"1","quality_controlled":"1","citation":{"ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2017.39\">10.4230/LIPIcs.SoCG.2017.39</a>","mla":"Edelsbrunner, Herbert, and Hubert Wagner. <i>Topological Data Analysis with Bregman Divergences</i>. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2017.39\">10.4230/LIPIcs.SoCG.2017.39</a>.","short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2017.39\">https://doi.org/10.4230/LIPIcs.SoCG.2017.39</a>.","ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","apa":"Edelsbrunner, H., &#38; Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2017.39\">https://doi.org/10.4230/LIPIcs.SoCG.2017.39</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":77,"status":"public","year":"2017","type":"conference","language":[{"iso":"eng"}],"file":[{"creator":"system","file_id":"4856","access_level":"open_access","date_updated":"2020-07-14T12:47:42Z","date_created":"2018-12-12T10:11:03Z","content_type":"application/pdf","file_size":990546,"relation":"main_file","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf"}],"title":"Topological data analysis with Bregman divergences","corr_author":"1","date_updated":"2025-07-10T11:53:56Z","has_accepted_license":"1","month":"06","oa":1,"file_date_updated":"2020-07-14T12:47:42Z","oa_version":"Published Version","pubrep_id":"895","_id":"688","publication_status":"published","author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Wagner, Hubert","first_name":"Hubert"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","conference":{"start_date":"2017-07-04","location":"Brisbane, Australia","name":"Symposium on Computational Geometry, SoCG","end_date":"2017-07-07"},"day":"01","abstract":[{"text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. ","lang":"eng"}],"article_processing_charge":"No","doi":"10.4230/LIPIcs.SoCG.2017.39","ddc":["514","516"]},{"citation":{"apa":"Akopyan, A., &#38; Karasev, R. (2017). A tight estimate for the waist of the ball . <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12062\">https://doi.org/10.1112/blms.12062</a>","ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” <i>Bulletin of the London Mathematical Society</i>, vol. 49, no. 4. Wiley, pp. 690–693, 2017.","chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2017. <a href=\"https://doi.org/10.1112/blms.12062\">https://doi.org/10.1112/blms.12062</a>.","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693.","mla":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” <i>Bulletin of the London Mathematical Society</i>, vol. 49, no. 4, Wiley, 2017, pp. 690–93, doi:<a href=\"https://doi.org/10.1112/blms.12062\">10.1112/blms.12062</a>.","ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . <i>Bulletin of the London Mathematical Society</i>. 2017;49(4):690-693. doi:<a href=\"https://doi.org/10.1112/blms.12062\">10.1112/blms.12062</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","volume":49,"date_created":"2018-12-11T11:48:02Z","quality_controlled":"1","scopus_import":"1","language":[{"iso":"eng"}],"corr_author":"1","publication":"Bulletin of the London Mathematical Society","title":"A tight estimate for the waist of the ball ","type":"journal_article","year":"2017","issue":"4","page":"690 - 693","arxiv":1,"date_published":"2017-08-01T00:00:00Z","publist_id":"6982","intvolume":"        49","isi":1,"department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["0024-6093"]},"doi":"10.1112/blms.12062","article_processing_charge":"No","abstract":[{"text":"We answer a question of M. Gromov on the waist of the unit ball.","lang":"eng"}],"_id":"707","publication_status":"published","publisher":"Wiley","author":[{"last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"external_id":{"isi":["000407045900012"],"arxiv":["1608.06279"]},"project":[{"grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"day":"01","ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.06279"}],"date_updated":"2025-09-10T11:04:43Z","month":"08","oa_version":"Preprint","oa":1},{"status":"public","volume":49,"citation":{"mla":"Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” <i>Advances in Applied Probability</i>, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:<a href=\"https://doi.org/10.1017/apr.2017.20\">10.1017/apr.2017.20</a>.","ama":"Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. <i>Advances in Applied Probability</i>. 2017;49(3):745-767. doi:<a href=\"https://doi.org/10.1017/apr.2017.20\">10.1017/apr.2017.20</a>","ista":"Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767.","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” <i>Advances in Applied Probability</i>. Cambridge University Press, 2017. <a href=\"https://doi.org/10.1017/apr.2017.20\">https://doi.org/10.1017/apr.2017.20</a>.","apa":"Edelsbrunner, H., Nikitenko, A., &#38; Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. <i>Advances in Applied Probability</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/apr.2017.20\">https://doi.org/10.1017/apr.2017.20</a>","ieee":"H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson Delaunay mosaics and their discrete Morse functions,” <i>Advances in Applied Probability</i>, vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","quality_controlled":"1","scopus_import":"1","related_material":{"record":[{"relation":"dissertation_contains","id":"6287","status":"public"}]},"date_created":"2018-12-11T11:48:07Z","publication":"Advances in Applied Probability","title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions","language":[{"iso":"eng"}],"issue":"3","type":"journal_article","year":"2017","date_published":"2017-09-01T00:00:00Z","page":"745 - 767","arxiv":1,"intvolume":"        49","publist_id":"6962","isi":1,"publication_identifier":{"issn":["0001-8678"]},"department":[{"_id":"HeEd"}],"doi":"10.1017/apr.2017.20","article_processing_charge":"No","abstract":[{"lang":"eng","text":"Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4."}],"project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF"}],"day":"01","external_id":{"arxiv":["1607.05915"],"isi":["000416417500004"]},"_id":"718","publisher":"Cambridge University Press","publication_status":"published","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","first_name":"Anton"},{"last_name":"Reitzner","full_name":"Reitzner, Matthias","first_name":"Matthias"}],"ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1607.05915"}],"month":"09","date_updated":"2026-04-08T14:19:30Z","oa_version":"Preprint","oa":1},{"doi":"10.1016/j.topol.2017.09.015","article_processing_charge":"No","abstract":[{"text":"We generalize Brazas’ topology on the fundamental group to the whole universal path space X˜ i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action.","lang":"eng"}],"day":"01","_id":"737","external_id":{"isi":["000413889100012"]},"author":[{"first_name":"Ziga","full_name":"Virk, Ziga","last_name":"Virk","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Zastrow, Andreas","first_name":"Andreas","last_name":"Zastrow"}],"publication_status":"published","publisher":"Elsevier","oa_version":"None","month":"11","date_updated":"2026-04-16T10:04:39Z","publication":"Topology and its Applications","corr_author":"1","title":"A new topology on the universal path space","language":[{"iso":"eng"}],"year":"2017","type":"journal_article","status":"public","volume":231,"citation":{"chicago":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” <i>Topology and Its Applications</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.topol.2017.09.015\">https://doi.org/10.1016/j.topol.2017.09.015</a>.","apa":"Virk, Z., &#38; Zastrow, A. (2017). A new topology on the universal path space. <i>Topology and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.topol.2017.09.015\">https://doi.org/10.1016/j.topol.2017.09.015</a>","ieee":"Z. Virk and A. Zastrow, “A new topology on the universal path space,” <i>Topology and its Applications</i>, vol. 231. Elsevier, pp. 186–196, 2017.","mla":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” <i>Topology and Its Applications</i>, vol. 231, Elsevier, 2017, pp. 186–96, doi:<a href=\"https://doi.org/10.1016/j.topol.2017.09.015\">10.1016/j.topol.2017.09.015</a>.","ama":"Virk Z, Zastrow A. A new topology on the universal path space. <i>Topology and its Applications</i>. 2017;231:186-196. doi:<a href=\"https://doi.org/10.1016/j.topol.2017.09.015\">10.1016/j.topol.2017.09.015</a>","short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196."},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","quality_controlled":"1","scopus_import":"1","date_created":"2018-12-11T11:48:14Z","isi":1,"department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["0166-8641"]},"date_published":"2017-11-01T00:00:00Z","page":"186 - 196","intvolume":"       231","publist_id":"6930"},{"ec_funded":1,"project":[{"name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"622033"}],"day":"01","_id":"1149","author":[{"first_name":"Tomoyuki","full_name":"Miyaji, Tomoyuki","last_name":"Miyaji"},{"full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk"},{"last_name":"Gameiro","first_name":"Marcio","full_name":"Gameiro, Marcio"},{"full_name":"Kokubu, Hiroshi","first_name":"Hiroshi","last_name":"Kokubu"},{"first_name":"Konstantin","full_name":"Mischaikow, Konstantin","last_name":"Mischaikow"}],"publisher":"Elsevier","external_id":{"isi":["000378447000003"]},"publication_status":"published","doi":"10.1016/j.apnum.2016.04.005","article_processing_charge":"No","abstract":[{"lang":"eng","text":"We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved."}],"oa_version":"None","month":"09","date_updated":"2025-09-22T09:58:16Z","acknowledgement":"MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9, and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry of Education, Science, Technology, Culture and Sports, Japan. KM was supported by NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE – Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (Ref. FCT PTDC/MAT/098871/2008); from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department of Mathematics of Kyoto University for making their server available for conducting the computations described in the paper, and to the reviewers for helpful comments that contributed towards increasing the quality of the paper.","year":"2016","type":"journal_article","publication":"Applied Numerical Mathematics","title":"A study of rigorous ODE integrators for multi scale set oriented computations","language":[{"iso":"eng"}],"scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:50:25Z","status":"public","volume":107,"citation":{"chicago":"Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” <i>Applied Numerical Mathematics</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.apnum.2016.04.005\">https://doi.org/10.1016/j.apnum.2016.04.005</a>.","apa":"Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., &#38; Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. <i>Applied Numerical Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.apnum.2016.04.005\">https://doi.org/10.1016/j.apnum.2016.04.005</a>","ieee":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” <i>Applied Numerical Mathematics</i>, vol. 107. Elsevier, pp. 34–47, 2016.","mla":"Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” <i>Applied Numerical Mathematics</i>, vol. 107, Elsevier, 2016, pp. 34–47, doi:<a href=\"https://doi.org/10.1016/j.apnum.2016.04.005\">10.1016/j.apnum.2016.04.005</a>.","ama":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. <i>Applied Numerical Mathematics</i>. 2016;107:34-47. doi:<a href=\"https://doi.org/10.1016/j.apnum.2016.04.005\">10.1016/j.apnum.2016.04.005</a>","short":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47.","ista":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 107, 34–47."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"department":[{"_id":"HeEd"}],"intvolume":"       107","publist_id":"6209","date_published":"2016-09-01T00:00:00Z","page":"34 - 47"},{"oa_version":"Published Version","oa":1,"acknowledgement":"The authors acknowledge funding of the German Re-\r\nsearch  Foundation  (DFG)  via  the  Collaborative  Re-\r\nsearch  Center  (SFB  557)  \\Control  of  Complex  Turbu-\r\nlent  Shear  Flows\"  and  the  Emmy  Noether  Program.\r\nFurther  funding  was  provided  by  the  Zuse  Institute\r\nBerlin  (ZIB),  the  DFG-CNRS  research  group  \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence 'Closed-loop control of turbulent shear  ows\r\nusing reduced-order models' (TUCOROM) of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean  Social  Fund  (ESF  App.   No.   100098251).   We\r\nthank  the  Ambrosys  Ltd.  Society  for  Complex  Sys-\r\ntems  Management  and  the  Bernd  R.  Noack  Cybernet-\r\nics  Foundation  for  additional  support.   A  part  of  this\r\nwork was performed using HPC resources from GENCI-[CCRT/CINES/IDRIS]  supported  by  the  Grant  2011-\r\n[x2011020912","main_file_link":[{"url":"http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf","open_access":"1"}],"month":"01","date_updated":"2026-06-18T17:23:52Z","ddc":["500"],"abstract":[{"lang":"eng","text":"A framework fo r extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance is proposed in this paper. The minima of the acceleration magnitude (a superset of acceleration zeros) are extracted and discriminated into vortices and saddle points, based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These feature points are tracked in time with a robust algorithm for tracking features. Thus, a space-time hierarchy of the minima is built and vortex merging events are detected. We apply the acceleration feature extraction strategy to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure field and minima of λ2."}],"article_processing_charge":"No","day":"01","publisher":"Polish Academy of Sciences Publishing House","_id":"1216","author":[{"full_name":"Kasten, Jens","first_name":"Jens","last_name":"Kasten"},{"full_name":"Reininghaus, Jan","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"},{"full_name":"Hege, Hans","first_name":"Hans","last_name":"Hege"},{"last_name":"Noack","first_name":"Bernd","full_name":"Noack, Bernd"},{"last_name":"Daviller","full_name":"Daviller, Guillaume","first_name":"Guillaume"},{"first_name":"Marek","full_name":"Morzyński, Marek","last_name":"Morzyński"}],"publication_status":"published","department":[{"_id":"HeEd"}],"date_published":"2016-01-01T00:00:00Z","page":"55 - 80","intvolume":"        68","publist_id":"6118","title":"Acceleration feature points of unsteady shear flows","publication":"Archives of Mechanics","language":[{"iso":"eng"}],"type":"journal_article","year":"2016","issue":"1","volume":68,"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady shear flows. <i>Archives of Mechanics</i>. 2016;68(1):55-80.","mla":"Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.” <i>Archives of Mechanics</i>, vol. 68, no. 1, Polish Academy of Sciences Publishing House, 2016, pp. 55–80.","ista":"Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M. 2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 68(1), 55–80.","short":"J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80.","chicago":"Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear Flows.” <i>Archives of Mechanics</i>. Polish Academy of Sciences Publishing House, 2016.","ieee":"J. Kasten <i>et al.</i>, “Acceleration feature points of unsteady shear flows,” <i>Archives of Mechanics</i>, vol. 68, no. 1. Polish Academy of Sciences Publishing House, pp. 55–80, 2016.","apa":"Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., &#38; Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. <i>Archives of Mechanics</i>. Polish Academy of Sciences Publishing House."},"scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:50:46Z"},{"isi":1,"department":[{"_id":"HeEd"}],"page":"1 - 20","arxiv":1,"date_published":"2016-01-01T00:00:00Z","publist_id":"6111","intvolume":"        55","language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","title":"Optimal packings of congruent circles on a square flat torus","type":"journal_article","year":"2016","issue":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"short":"O. Musin, A. Nikitenko, Discrete &#38; Computational Geometry 55 (2016) 1–20.","ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete &#38; Computational Geometry. 55(1), 1–20.","ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. <i>Discrete &#38; Computational Geometry</i>. 2016;55(1):1-20. doi:<a href=\"https://doi.org/10.1007/s00454-015-9742-6\">10.1007/s00454-015-9742-6</a>","mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” <i>Discrete &#38; Computational Geometry</i>, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:<a href=\"https://doi.org/10.1007/s00454-015-9742-6\">10.1007/s00454-015-9742-6</a>.","ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” <i>Discrete &#38; Computational Geometry</i>, vol. 55, no. 1. Springer, pp. 1–20, 2016.","apa":"Musin, O., &#38; Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-015-9742-6\">https://doi.org/10.1007/s00454-015-9742-6</a>","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00454-015-9742-6\">https://doi.org/10.1007/s00454-015-9742-6</a>."},"status":"public","volume":55,"date_created":"2018-12-11T11:50:48Z","quality_controlled":"1","scopus_import":"1","oa_version":"Preprint","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1212.0649"}],"acknowledgement":"We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy for some useful comments and remarks, and especially Thom Sulanke for modifying surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government Grant 11.G34.31.0026.","date_updated":"2025-09-22T09:32:23Z","month":"01","doi":"10.1007/s00454-015-9742-6","article_processing_charge":"No","abstract":[{"text":"We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason—the problem of “super resolution of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs.","lang":"eng"}],"external_id":{"isi":["000367625500001"],"arxiv":["1212.0649"]},"_id":"1222","author":[{"full_name":"Musin, Oleg","first_name":"Oleg","last_name":"Musin"},{"last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","first_name":"Anton"}],"publisher":"Springer","publication_status":"published","day":"01"},{"intvolume":"      9667","publist_id":"6096","alternative_title":["LNCS"],"date_published":"2016-06-02T00:00:00Z","page":"140 - 151","isi":1,"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"quality_controlled":"1","scopus_import":"1","date_created":"2018-12-11T11:50:52Z","status":"public","volume":9667,"citation":{"ieee":"M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented at the CTIC: Computational Topology in Image Context, Marseille, France, 2016, vol. 9667, pp. 140–151.","apa":"Krcál, M., &#38; Pilarczyk, P. (2016). Computation of cubical Steenrod squares (Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image Context, Marseille, France: Springer. <a href=\"https://doi.org/10.1007/978-3-319-39441-1_13\">https://doi.org/10.1007/978-3-319-39441-1_13</a>","chicago":"Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,” 9667:140–51. Springer, 2016. <a href=\"https://doi.org/10.1007/978-3-319-39441-1_13\">https://doi.org/10.1007/978-3-319-39441-1_13</a>.","ista":"Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151.","short":"M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.","ama":"Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667. Springer; 2016:140-151. doi:<a href=\"https://doi.org/10.1007/978-3-319-39441-1_13\">10.1007/978-3-319-39441-1_13</a>","mla":"Krcál, Marek, and Pawel Pilarczyk. <i>Computation of Cubical Steenrod Squares</i>. Vol. 9667, Springer, 2016, pp. 140–51, doi:<a href=\"https://doi.org/10.1007/978-3-319-39441-1_13\">10.1007/978-3-319-39441-1_13</a>."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2016","type":"conference","title":"Computation of cubical Steenrod squares","language":[{"iso":"eng"}],"month":"06","date_updated":"2025-09-22T09:19:17Z","acknowledgement":"The research conducted by both authors has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and no. 622033 (for P. P.).","oa_version":"None","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734"},{"grant_number":"622033","call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425"}],"conference":{"location":"Marseille, France","start_date":"2016-06-15","name":"CTIC: Computational Topology in Image Context","end_date":"2016-06-17"},"day":"02","_id":"1237","author":[{"full_name":"Krcál, Marek","first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Pawel","full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000389805800013"]},"publisher":"Springer","publication_status":"published","doi":"10.1007/978-3-319-39441-1_13","abstract":[{"lang":"eng","text":"Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher than 3. If such an operation is determined at the level of simplicial chains [see e.g. González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively computable. However, decomposing a cubical complex into a simplicial one deleteriously affects the efficiency of such an approach. In order to avoid this overhead, a direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015, 253-275] for the cup product in cohomology, and implemented in the ChainCon software package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series, 1947, 290-320] directly at the level of cubical chains, and we prove the correctness of this formula. An implementation of this formula is programmed in C++ within the ChainCon software framework. We provide a few examples and discuss the effectiveness of this approach. One specific application follows from the fact that Steenrod squares yield tests for the topological extension problem: Can a given map A → Sd to a sphere Sd be extended to a given super-complex X of A? In particular, the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value r &gt; 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the extension problem."}],"article_processing_charge":"No","ec_funded":1},{"acknowledgement":"The authors gratefully acknowledge the support of the Lorenz Center which\r\nprovided an opportunity for us to discuss in depth the work of this paper. Research leading to these results has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033 (supporting PP). The work of the first and third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019, 1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029), Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan.","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1411.7563"}],"month":"04","date_updated":"2025-09-22T09:09:31Z","oa_version":"Preprint","article_type":"original","oa":1,"doi":"10.1090/proc/12812","abstract":[{"lang":"eng","text":"We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points."}],"article_processing_charge":"No","project":[{"call_identifier":"FP7","grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","name":"Persistent Homology - Images, Data and Maps"}],"day":"01","_id":"1252","external_id":{"isi":["000369298400038"],"arxiv":["1411.7563"]},"publication_status":"published","author":[{"first_name":"Shaun","full_name":"Harker, Shaun","last_name":"Harker"},{"first_name":"Hiroshi","full_name":"Kokubu, Hiroshi","last_name":"Kokubu"},{"full_name":"Mischaikow, Konstantin","first_name":"Konstantin","last_name":"Mischaikow"},{"full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk"}],"publisher":"American Mathematical Society","ec_funded":1,"date_published":"2016-04-01T00:00:00Z","page":"1787 - 1801","arxiv":1,"intvolume":"       144","publist_id":"6075","isi":1,"department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["1088-6826"]},"status":"public","volume":144,"citation":{"apa":"Harker, S., Kokubu, H., Mischaikow, K., &#38; Pilarczyk, P. (2016). Inducing a map on homology from a correspondence. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/12812\">https://doi.org/10.1090/proc/12812</a>","ieee":"S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on homology from a correspondence,” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.","chicago":"Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk. “Inducing a Map on Homology from a Correspondence.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2016. <a href=\"https://doi.org/10.1090/proc/12812\">https://doi.org/10.1090/proc/12812</a>.","ista":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 144(4), 1787–1801.","short":"S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American Mathematical Society 144 (2016) 1787–1801.","mla":"Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1787–801, doi:<a href=\"https://doi.org/10.1090/proc/12812\">10.1090/proc/12812</a>.","ama":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from a correspondence. <i>Proceedings of the American Mathematical Society</i>. 2016;144(4):1787-1801. doi:<a href=\"https://doi.org/10.1090/proc/12812\">10.1090/proc/12812</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:50:57Z","publication":"Proceedings of the American Mathematical Society","corr_author":"1","title":"Inducing a map on homology from a correspondence","language":[{"iso":"eng"}],"issue":"4","type":"journal_article","year":"2016"},{"title":"Uniform expansivity outside a critical neighborhood in the quadratic family","corr_author":"1","publication":"Experimental Mathematics","language":[{"iso":"eng"}],"issue":"2","type":"journal_article","year":"2016","volume":25,"status":"public","citation":{"mla":"Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” <i>Experimental Mathematics</i>, vol. 25, no. 2, Taylor and Francis, 2016, pp. 116–24, doi:<a href=\"https://doi.org/10.1080/10586458.2015.1048011\">10.1080/10586458.2015.1048011</a>.","ama":"Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical neighborhood in the quadratic family. <i>Experimental Mathematics</i>. 2016;25(2):116-124. doi:<a href=\"https://doi.org/10.1080/10586458.2015.1048011\">10.1080/10586458.2015.1048011</a>","short":"A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016) 116–124.","ista":"Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 25(2), 116–124.","chicago":"Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” <i>Experimental Mathematics</i>. Taylor and Francis, 2016. <a href=\"https://doi.org/10.1080/10586458.2015.1048011\">https://doi.org/10.1080/10586458.2015.1048011</a>.","apa":"Golmakani, A., Luzzatto, S., &#38; Pilarczyk, P. (2016). Uniform expansivity outside a critical neighborhood in the quadratic family. <i>Experimental Mathematics</i>. Taylor and Francis. <a href=\"https://doi.org/10.1080/10586458.2015.1048011\">https://doi.org/10.1080/10586458.2015.1048011</a>","ieee":"A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside a critical neighborhood in the quadratic family,” <i>Experimental Mathematics</i>, vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:50:58Z","department":[{"_id":"HeEd"}],"isi":1,"date_published":"2016-04-02T00:00:00Z","arxiv":1,"page":"116 - 124","intvolume":"        25","publist_id":"6071","ec_funded":1,"abstract":[{"text":"We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We first compute a radius of the critical neighborhood outside which the map is uniformly expanding. This radius is taken as small as possible, yet large enough for our numerical procedure to succeed in proving that the expansivity exponent outside this neighborhood is positive. Then, for each of the intervals, we compute a lower bound for this expansivity exponent, valid for all the parameters in that interval. We illustrate and study the distribution of the radii and the expansivity exponents. The results of our computations are mathematically rigorous. The source code of the software and the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/.","lang":"eng"}],"article_processing_charge":"No","doi":"10.1080/10586458.2015.1048011","day":"02","project":[{"_id":"255F06BE-B435-11E9-9278-68D0E5697425","name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7","grant_number":"622033"}],"publication_status":"published","_id":"1254","publisher":"Taylor and Francis","external_id":{"isi":["000372490500002"],"arxiv":["1504.00116"]},"author":[{"last_name":"Golmakani","full_name":"Golmakani, Ali","first_name":"Ali"},{"last_name":"Luzzatto","full_name":"Luzzatto, Stefano","first_name":"Stefano"},{"first_name":"Pawel","full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Preprint","oa":1,"acknowledgement":"AG and PP were partially supported by Abdus Salam International Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS, and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033. The  authors  gratefully  acknowledge  the  Department  of\r\nMathematics  of  Kyoto  University  for  providing  access\r\nto  their  server  for  conducting  computations  for  this\r\nproject.","main_file_link":[{"url":"https://arxiv.org/abs/1504.00116","open_access":"1"}],"month":"04","date_updated":"2025-09-22T09:07:52Z"},{"has_accepted_license":"1","date_updated":"2021-01-12T06:49:32Z","month":"09","acknowledgement":"This work was supported by Austrian Science Fund (FWF): P25816-N15.","oa":1,"oa_version":"Published Version","file_date_updated":"2020-07-14T12:44:42Z","pubrep_id":"694","publication_status":"published","_id":"1272","publisher":"Taylor and Francis","author":[{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"day":"02","doi":"10.1080/16864360.2016.1150718","abstract":[{"text":"We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams.","lang":"eng"}],"ddc":["004","516"],"publist_id":"6048","intvolume":"        13","page":"712 - 721","date_published":"2016-09-02T00:00:00Z","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:51:04Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"scopus_import":1,"quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” <i>Computer-Aided Design and Applications</i>. Taylor and Francis, 2016. <a href=\"https://doi.org/10.1080/16864360.2016.1150718\">https://doi.org/10.1080/16864360.2016.1150718</a>.","ieee":"M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” <i>Computer-Aided Design and Applications</i>, vol. 13, no. 5. Taylor and Francis, pp. 712–721, 2016.","apa":"Held, M., Huber, S., &#38; Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. <i>Computer-Aided Design and Applications</i>. Taylor and Francis. <a href=\"https://doi.org/10.1080/16864360.2016.1150718\">https://doi.org/10.1080/16864360.2016.1150718</a>","ama":"Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using skeletons. <i>Computer-Aided Design and Applications</i>. 2016;13(5):712-721. doi:<a href=\"https://doi.org/10.1080/16864360.2016.1150718\">10.1080/16864360.2016.1150718</a>","mla":"Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” <i>Computer-Aided Design and Applications</i>, vol. 13, no. 5, Taylor and Francis, 2016, pp. 712–21, doi:<a href=\"https://doi.org/10.1080/16864360.2016.1150718\">10.1080/16864360.2016.1150718</a>.","short":"M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721.","ista":"Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721."},"status":"public","volume":13,"year":"2016","type":"journal_article","issue":"5","file":[{"access_level":"open_access","file_id":"5206","creator":"system","file_size":1678369,"relation":"main_file","file_name":"IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf","checksum":"c746f3a48edb62b588d92ea5d0fd2c0e","date_created":"2018-12-12T10:16:20Z","date_updated":"2020-07-14T12:44:42Z","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication":"Computer-Aided Design and Applications","title":"Generalized offsetting of planar structures using skeletons"},{"oa":1,"oa_version":"Submitted Version","file_date_updated":"2020-07-14T12:44:42Z","pubrep_id":"975","has_accepted_license":"1","date_updated":"2025-09-23T13:44:16Z","month":"11","ddc":["004","514"],"author":[{"last_name":"Dunaeva","first_name":"Olga","full_name":"Dunaeva, Olga"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Lukyanov","first_name":"Anton","full_name":"Lukyanov, Anton"},{"first_name":"Michael","full_name":"Machin, Michael","last_name":"Machin"},{"first_name":"Daria","full_name":"Malkova, Daria","last_name":"Malkova"},{"first_name":"Roman","full_name":"Kuvaev, Roman","last_name":"Kuvaev"},{"last_name":"Kashin","full_name":"Kashin, Sergey","first_name":"Sergey"}],"_id":"1289","publisher":"Elsevier","publication_status":"published","external_id":{"isi":["000386874700003"]},"day":"01","doi":"10.1016/j.patrec.2015.12.012","article_processing_charge":"No","abstract":[{"lang":"eng","text":"Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI) magnifying endoscopic (ME) images of the stomach, we combine methods from image processing, topology, geometry, and machine learning to classify patterns into three classes: oval, tubular and irregular. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions."}],"isi":1,"department":[{"_id":"HeEd"}],"publist_id":"6027","intvolume":"        83","page":"13 - 22","date_published":"2016-11-01T00:00:00Z","type":"journal_article","year":"2016","issue":"1","file":[{"checksum":"33458bbb8c32a339e1adeca6d5a1112d","file_name":"2016-Edelsbrunner_The_classification.pdf","relation":"main_file","file_size":1921113,"content_type":"application/pdf","date_updated":"2020-07-14T12:44:42Z","date_created":"2019-04-17T07:55:51Z","file_id":"6334","access_level":"open_access","creator":"dernst"}],"language":[{"iso":"eng"}],"publication":"Pattern Recognition Letters","title":"The classification of endoscopy images with persistent homology","date_created":"2018-12-11T11:51:10Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"scopus_import":"1","quality_controlled":"1","related_material":{"record":[{"id":"1568","status":"public","relation":"earlier_version"}]},"citation":{"chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria Malkova, Roman Kuvaev, and Sergey Kashin. “The Classification of Endoscopy Images with Persistent Homology.” <i>Pattern Recognition Letters</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.patrec.2015.12.012\">https://doi.org/10.1016/j.patrec.2015.12.012</a>.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., Malkova, D., Kuvaev, R., &#38; Kashin, S. (2016). The classification of endoscopy images with persistent homology. <i>Pattern Recognition Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.patrec.2015.12.012\">https://doi.org/10.1016/j.patrec.2015.12.012</a>","ieee":"O. Dunaeva <i>et al.</i>, “The classification of endoscopy images with persistent homology,” <i>Pattern Recognition Letters</i>, vol. 83, no. 1. Elsevier, pp. 13–22, 2016.","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” <i>Pattern Recognition Letters</i>, vol. 83, no. 1, Elsevier, 2016, pp. 13–22, doi:<a href=\"https://doi.org/10.1016/j.patrec.2015.12.012\">10.1016/j.patrec.2015.12.012</a>.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, et al. The classification of endoscopy images with persistent homology. <i>Pattern Recognition Letters</i>. 2016;83(1):13-22. doi:<a href=\"https://doi.org/10.1016/j.patrec.2015.12.012\">10.1016/j.patrec.2015.12.012</a>","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev, S. Kashin, Pattern Recognition Letters 83 (2016) 13–22.","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin S. 2016. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 83(1), 13–22."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","volume":83},{"page":"441 - 455","arxiv":1,"date_published":"2016-12-01T00:00:00Z","publist_id":"6023","intvolume":"       150","isi":1,"department":[{"_id":"HeEd"}],"citation":{"ieee":"S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant in open books,” <i>Acta Mathematica Hungarica</i>, vol. 150, no. 2. Springer, pp. 441–455, 2016.","apa":"Durst, S., Kegel, M., &#38; Klukas, M. D. (2016). Computing the Thurston–Bennequin invariant in open books. <i>Acta Mathematica Hungarica</i>. Springer. <a href=\"https://doi.org/10.1007/s10474-016-0648-4\">https://doi.org/10.1007/s10474-016-0648-4</a>","chicago":"Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin Invariant in Open Books.” <i>Acta Mathematica Hungarica</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s10474-016-0648-4\">https://doi.org/10.1007/s10474-016-0648-4</a>.","short":"S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455.","ista":"Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455.","ama":"Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in open books. <i>Acta Mathematica Hungarica</i>. 2016;150(2):441-455. doi:<a href=\"https://doi.org/10.1007/s10474-016-0648-4\">10.1007/s10474-016-0648-4</a>","mla":"Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open Books.” <i>Acta Mathematica Hungarica</i>, vol. 150, no. 2, Springer, 2016, pp. 441–55, doi:<a href=\"https://doi.org/10.1007/s10474-016-0648-4\">10.1007/s10474-016-0648-4</a>."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","volume":150,"date_created":"2018-12-11T11:51:11Z","scopus_import":"1","quality_controlled":"1","language":[{"iso":"eng"}],"publication":"Acta Mathematica Hungarica","corr_author":"1","title":"Computing the Thurston–Bennequin invariant in open books","issue":"2","year":"2016","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.00794"}],"acknowledgement":"The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful discussions and advice and Christian Evers for helpful remarks on a draft version.","date_updated":"2025-09-22T08:29:12Z","month":"12","oa_version":"Preprint","oa":1,"doi":"10.1007/s10474-016-0648-4","abstract":[{"lang":"eng","text":"We give explicit formulas and algorithms for the computation of the Thurston–Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on Heegaard surfaces in convex position. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds."}],"article_processing_charge":"No","_id":"1292","publication_status":"published","external_id":{"arxiv":["1605.00794"],"isi":["000387471100014"]},"publisher":"Springer","author":[{"last_name":"Durst","first_name":"Sebastian","full_name":"Durst, Sebastian"},{"last_name":"Kegel","full_name":"Kegel, Marc","first_name":"Marc"},{"first_name":"Mirko D","full_name":"Klukas, Mirko D","id":"34927512-F248-11E8-B48F-1D18A9856A87","last_name":"Klukas"}],"day":"01"},{"type":"journal_article","year":"2016","language":[{"iso":"eng"}],"title":"Multiple covers with balls II: Weighted averages","publication":"Electronic Notes in Discrete Mathematics","corr_author":"1","date_created":"2018-12-11T11:51:12Z","scopus_import":1,"quality_controlled":"1","citation":{"ista":"Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174.","short":"H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. <i>Electronic Notes in Discrete Mathematics</i>. 2016;54:169-174. doi:<a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">10.1016/j.endm.2016.09.030</a>","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” <i>Electronic Notes in Discrete Mathematics</i>, vol. 54, Elsevier, 2016, pp. 169–74, doi:<a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">10.1016/j.endm.2016.09.030</a>.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” <i>Electronic Notes in Discrete Mathematics</i>, vol. 54. Elsevier, pp. 169–174, 2016.","apa":"Edelsbrunner, H., &#38; Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. <i>Electronic Notes in Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">https://doi.org/10.1016/j.endm.2016.09.030</a>","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” <i>Electronic Notes in Discrete Mathematics</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">https://doi.org/10.1016/j.endm.2016.09.030</a>."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","volume":54,"status":"public","department":[{"_id":"HeEd"}],"publist_id":"5976","intvolume":"        54","page":"169 - 174","date_published":"2016-10-01T00:00:00Z","ec_funded":1,"_id":"1295","publisher":"Elsevier","publication_status":"published","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"first_name":"Mabel","full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"day":"01","project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493"}],"abstract":[{"lang":"eng","text":"Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls."}],"doi":"10.1016/j.endm.2016.09.030","oa_version":"None","date_updated":"2024-10-09T20:57:05Z","month":"10","acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme."},{"doi":"10.1007/s11856-016-1429-z","article_processing_charge":"No","abstract":[{"text":"In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K.","lang":"eng"}],"project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7"}],"day":"15","external_id":{"isi":["000386356400012"],"arxiv":["1506.06014"]},"_id":"1330","publisher":"Springer","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan"},{"last_name":"Balitskiy","full_name":"Balitskiy, Alexey","first_name":"Alexey"}],"publication_status":"published","ec_funded":1,"acknowledgement":"Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734]. Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation.","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1506.06014"}],"month":"10","date_updated":"2025-09-22T08:23:27Z","oa_version":"Preprint","oa":1,"status":"public","volume":216,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” <i>Israel Journal of Mathematics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11856-016-1429-z\">https://doi.org/10.1007/s11856-016-1429-z</a>.","apa":"Akopyan, A., &#38; Balitskiy, A. (2016). Billiards in convex bodies with acute angles. <i>Israel Journal of Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s11856-016-1429-z\">https://doi.org/10.1007/s11856-016-1429-z</a>","ieee":"A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” <i>Israel Journal of Mathematics</i>, vol. 216, no. 2. Springer, pp. 833–845, 2016.","mla":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” <i>Israel Journal of Mathematics</i>, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:<a href=\"https://doi.org/10.1007/s11856-016-1429-z\">10.1007/s11856-016-1429-z</a>.","ama":"Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. <i>Israel Journal of Mathematics</i>. 2016;216(2):833-845. doi:<a href=\"https://doi.org/10.1007/s11856-016-1429-z\">10.1007/s11856-016-1429-z</a>","ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845.","short":"A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845."},"scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:51:24Z","corr_author":"1","publication":"Israel Journal of Mathematics","title":"Billiards in convex bodies with acute angles","language":[{"iso":"eng"}],"year":"2016","issue":"2","type":"journal_article","date_published":"2016-10-15T00:00:00Z","arxiv":1,"page":"833 - 845","intvolume":"       216","publist_id":"5938","isi":1,"department":[{"_id":"HeEd"}]}]