[{"publication_identifier":{"issn":["01668641"]},"day":"01","doi":"10.1016/j.topol.2016.10.005","publist_id":"7299","oa":1,"abstract":[{"text":"Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.","lang":"eng"}],"year":"2017","citation":{"apa":"Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005","ama":"Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.","mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.","ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57."},"date_updated":"2021-01-12T08:01:21Z","type":"journal_article","date_published":"2017-01-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.03954v1"}],"volume":215,"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:46:56Z","oa_version":"Submitted Version","publication_status":"published","intvolume":" 215","month":"01","title":"Higson compactification and dimension raising","_id":"521","publication":"Topology and its Applications","author":[{"last_name":"Austin","first_name":"Kyle","full_name":"Austin, Kyle"},{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga"}],"publisher":"Elsevier","quality_controlled":"1","page":"45 - 57","language":[{"iso":"eng"}]},{"_id":"568","scopus_import":1,"author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Franek","full_name":"Franek, Peter"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál","full_name":"Krcál, Marek"}],"issue":"2","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_created":"2018-12-11T11:47:14Z","title":"Persistence of zero sets","intvolume":" 19","page":"313 - 342","ec_funded":1,"quality_controlled":"1","publisher":"International Press","date_updated":"2021-01-12T08:03:12Z","year":"2017","citation":{"ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.","short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16","apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16"},"doi":"10.4310/HHA.2017.v19.n2.a16","day":"01","abstract":[{"lang":"eng","text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C)."}],"volume":19,"publication":"Homology, Homotopy and Applications","oa_version":"Submitted Version","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"},{"call_identifier":"H2020","_id":"2590DB08-B435-11E9-9278-68D0E5697425","grant_number":"701309","name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)"}],"month":"01","language":[{"iso":"eng"}],"date_published":"2017-01-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["15320073"]},"publist_id":"7246","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.04310"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","status":"public"},{"title":"Construction of persistent Voronoi diagram on 3D digital plane","alternative_title":["LNCS"],"intvolume":" 10256","publication_status":"published","department":[{"_id":"HeEd"}],"date_created":"2019-01-08T20:42:56Z","article_processing_charge":"No","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"}],"_id":"5803","publisher":"Springer Nature","page":"93-104","quality_controlled":"1","abstract":[{"lang":"eng","text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept."}],"doi":"10.1007/978-3-319-59108-7_8","day":"17","date_updated":"2022-01-28T07:48:24Z","year":"2017","citation":{"short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.","ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:10.1007/978-3-319-59108-7_8","apa":"Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8","chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104."},"extern":"1","volume":10256,"month":"05","oa_version":"None","publication":"Combinatorial image analysis","conference":{"name":"IWCIA: International Workshop on Combinatorial Image Analysis","start_date":"2017-06-19","end_date":"2017-06-21","location":"Plovdiv, Bulgaria"},"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-3-319-59107-0","978-3-319-59108-7"],"issn":["0302-9743","1611-3349"]},"date_published":"2017-05-17T00:00:00Z","type":"book_chapter","status":"public","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","place":"Cham"},{"type":"dissertation","date_published":"2017-10-27T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"publication_identifier":{"issn":["2663-337X"]},"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"relation":"part_of_dissertation","id":"718","status":"public"},{"status":"public","id":"5678","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"87"}]},"file":[{"access_level":"open_access","relation":"main_file","file_id":"6289","creator":"dernst","date_created":"2019-04-09T14:54:51Z","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","file_size":2324870,"date_updated":"2020-07-14T12:47:26Z","file_name":"2017_Thesis_Nikitenko.pdf","content_type":"application/pdf"},{"file_size":2863219,"checksum":"99b7ad76e317efd447af60f91e29b49b","date_created":"2019-04-09T14:54:51Z","file_name":"2017_Thesis_Nikitenko_source.zip","content_type":"application/zip","date_updated":"2020-07-14T12:47:26Z","relation":"source_file","access_level":"closed","creator":"dernst","file_id":"6290"}],"has_accepted_license":"1","month":"10","oa_version":"Published Version","language":[{"iso":"eng"}],"citation":{"mla":"Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.","short":"A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017.","ista":"Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria.","ama":"Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873","apa":"Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873","chicago":"Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.","ieee":"A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017."},"year":"2017","date_updated":"2023-09-15T12:10:34Z","abstract":[{"text":"The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's.","lang":"eng"}],"day":"27","doi":"10.15479/AT:ISTA:th_873","degree_awarded":"PhD","ddc":["514","516","519"],"author":[{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","last_name":"Nikitenko","first_name":"Anton"}],"_id":"6287","title":"Discrete Morse theory for random complexes ","pubrep_id":"873","alternative_title":["ISTA Thesis"],"department":[{"_id":"HeEd"}],"article_processing_charge":"No","date_created":"2019-04-09T15:04:32Z","publication_status":"published","file_date_updated":"2020-07-14T12:47:26Z","page":"86","publisher":"Institute of Science and Technology Austria"},{"publication":"Journal of Symbolic Computation","month":"01","oa_version":"Published Version","project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493"}],"language":[{"iso":"eng"}],"date_published":"2017-01-01T00:00:00Z","type":"journal_article","oa":1,"publist_id":"5765","publication_identifier":{"issn":[" 07477171"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"status":"public","id":"10894","relation":"earlier_version"}]},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2016.03.008"}],"author":[{"first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"_id":"1433","scopus_import":"1","title":"Phat - Persistent homology algorithms toolbox","intvolume":" 78","publication_status":"published","date_created":"2018-12-11T11:51:59Z","department":[{"_id":"HeEd"}],"article_processing_charge":"No","page":"76 - 90","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Academic Press","isi":1,"external_id":{"isi":["000384396000005"]},"date_updated":"2023-09-20T09:42:40Z","citation":{"chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation. Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic Press, pp. 76–90, 2017.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90.","mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008."},"year":"2017","abstract":[{"text":"Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology.","lang":"eng"}],"doi":"10.1016/j.jsc.2016.03.008","day":"01","volume":78},{"page":"588 - 596","ec_funded":1,"quality_controlled":"1","publisher":"Mathematical Association of America","article_type":"original","_id":"909","scopus_import":"1","author":[{"last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Vysotsky, Vladislav","last_name":"Vysotsky","first_name":"Vladislav"}],"issue":"7","publication_status":"published","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:49:09Z","article_processing_charge":"No","title":"On the lengths of curves passing through boundary points of a planar convex shape","intvolume":" 124","volume":124,"date_updated":"2023-10-17T11:24:57Z","year":"2017","citation":{"mla":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:10.4169/amer.math.monthly.124.7.588.","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.","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.","apa":"Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588","ama":"Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596. doi:10.4169/amer.math.monthly.124.7.588","chicago":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588.","ieee":"A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” The American Mathematical Monthly, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017."},"isi":1,"external_id":{"isi":["000413947300002"],"arxiv":["1605.07997"]},"doi":"10.4169/amer.math.monthly.124.7.588","arxiv":1,"day":"01","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 &#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"}],"language":[{"iso":"eng"}],"publication":"The American Mathematical Monthly","oa_version":"Submitted Version","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.07997"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2017-01-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["00029890"]},"publist_id":"6534","oa":1},{"citation":{"short":"P. Pranav, H. Edelsbrunner, R. Van De Weygaert, G. Vegter, M. Kerber, B. Jones, M. Wintraecken, Monthly Notices of the Royal Astronomical Society 465 (2017) 4281–4310.","mla":"Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical Society, vol. 465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:10.1093/mnras/stw2862.","ista":"Pranav P, Edelsbrunner H, Van De Weygaert R, Vegter G, Kerber M, Jones B, Wintraecken M. 2017. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 465(4), 4281–4310.","ama":"Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862","apa":"Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M., Jones, B., & Wintraecken, M. (2017). The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. Oxford University Press. https://doi.org/10.1093/mnras/stw2862","chicago":"Pranav, Pratyush, Herbert Edelsbrunner, Rien Van De Weygaert, Gert Vegter, Michael Kerber, Bernard Jones, and Mathijs Wintraecken. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical Society. Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862.","ieee":"P. Pranav et al., “The topology of the cosmic web in terms of persistent Betti numbers,” Monthly Notices of the Royal Astronomical Society, vol. 465, no. 4. Oxford University Press, pp. 4281–4310, 2017."},"year":"2017","date_updated":"2023-09-22T09:40:55Z","external_id":{"isi":["000395170200039"]},"isi":1,"day":"01","doi":"10.1093/mnras/stw2862","abstract":[{"text":"We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different web-like morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of web-like configurations and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys.","lang":"eng"}],"acknowledgement":"Part of this work has been supported by the 7th Framework Programme for Research of the European Commission, under FETOpen grant number 255827 (CGL Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random Systems via Algebraic Topology) number 320422.","volume":465,"scopus_import":"1","_id":"1022","issue":"4","author":[{"last_name":"Pranav","first_name":"Pratyush","full_name":"Pranav, Pratyush"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Van De Weygaert, Rien","last_name":"Van De Weygaert","first_name":"Rien"},{"first_name":"Gert","last_name":"Vegter","full_name":"Vegter, Gert"},{"last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"},{"first_name":"Bernard","last_name":"Jones","full_name":"Jones, Bernard"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:49:44Z","article_processing_charge":"No","publication_status":"published","intvolume":" 465","title":"The topology of the cosmic web in terms of persistent Betti numbers","quality_controlled":"1","page":"4281 - 4310","publisher":"Oxford University Press","type":"journal_article","date_published":"2017-01-01T00:00:00Z","publication_identifier":{"issn":["00358711"]},"publist_id":"6373","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.04519"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","publication":"Monthly Notices of the Royal Astronomical Society","oa_version":"Submitted Version","month":"01","language":[{"iso":"eng"}]},{"month":"06","project":[{"_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"name":"Game Theory","grant_number":"S11407","call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425"}],"oa_version":"Submitted Version","has_accepted_license":"1","publication":"Information Processing Letters","language":[{"iso":"eng"}],"oa":1,"publist_id":"6323","publication_identifier":{"issn":["00200190"]},"type":"journal_article","date_published":"2017-06-01T00:00:00Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","file":[{"creator":"system","file_id":"4998","access_level":"open_access","relation":"main_file","file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","content_type":"application/pdf","date_updated":"2019-10-15T07:44:51Z","file_size":247657,"date_created":"2018-12-12T10:13:17Z"}],"intvolume":" 122","pubrep_id":"991","title":"Pushdown reachability with constant treewidth","date_created":"2018-12-11T11:49:57Z","article_processing_charge":"No","department":[{"_id":"KrCh"},{"_id":"HeEd"}],"publication_status":"published","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","last_name":"Chatterjee"},{"last_name":"Osang","first_name":"Georg F","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"1065","publisher":"Elsevier","file_date_updated":"2019-10-15T07:44:51Z","ec_funded":1,"quality_controlled":"1","page":"25 - 29","abstract":[{"text":"We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs.","lang":"eng"}],"day":"01","doi":"10.1016/j.ipl.2017.02.003","external_id":{"isi":["000399506600005"]},"isi":1,"year":"2017","citation":{"ieee":"K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.","chicago":"Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003.","apa":"Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003","ama":"Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003","ista":"Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29.","short":"K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.","mla":"Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp. 25–29, doi:10.1016/j.ipl.2017.02.003."},"date_updated":"2023-09-20T12:08:18Z","ddc":["000"],"volume":122},{"main_file_link":[{"url":"https://arxiv.org/abs/1508.07594","open_access":"1"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","publication_identifier":{"issn":["00018708"]},"publist_id":"6173","oa":1,"type":"journal_article","date_published":"2017-02-21T00:00:00Z","language":[{"iso":"eng"}],"project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"oa_version":"Submitted Version","month":"02","publication":"Advances in Mathematics","volume":308,"day":"21","doi":"10.1016/j.aim.2016.12.026","abstract":[{"text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform.","lang":"eng"}],"citation":{"ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.","chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.","apa":"Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026","ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026","ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644.","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.","mla":"Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026."},"year":"2017","date_updated":"2023-09-20T11:21:27Z","external_id":{"isi":["000409292900015"]},"isi":1,"publisher":"Academic Press","quality_controlled":"1","ec_funded":1,"page":"627 - 644","article_processing_charge":"No","date_created":"2018-12-11T11:50:34Z","department":[{"_id":"HeEd"}],"publication_status":"published","intvolume":" 308","title":"Algebraic vertices of non-convex polyhedra","scopus_import":"1","_id":"1180","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Bárány","first_name":"Imre","full_name":"Bárány, Imre"},{"full_name":"Robins, Sinai","last_name":"Robins","first_name":"Sinai"}]},{"author":[{"full_name":"Miyaji, Tomoyuki","last_name":"Miyaji","first_name":"Tomoyuki"},{"full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gameiro, Marcio","first_name":"Marcio","last_name":"Gameiro"},{"last_name":"Kokubu","first_name":"Hiroshi","full_name":"Kokubu, Hiroshi"},{"first_name":"Konstantin","last_name":"Mischaikow","full_name":"Mischaikow, Konstantin"}],"publication":"Applied Numerical Mathematics","_id":"1149","scopus_import":1,"title":"A study of rigorous ODE integrators for multi scale set oriented computations","month":"09","intvolume":" 107","oa_version":"None","publication_status":"published","date_created":"2018-12-11T11:50:25Z","project":[{"name":"Persistent Homology - Images, Data and Maps","grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"page":"34 - 47","quality_controlled":"1","ec_funded":1,"publisher":"Elsevier","date_published":"2016-09-01T00:00:00Z","type":"journal_article","date_updated":"2021-01-12T06:48:38Z","year":"2016","citation":{"ieee":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” Applied Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016.","chicago":"Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.apnum.2016.04.005.","ama":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005","apa":"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. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005","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.","mla":"Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier, 2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005.","short":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47."},"abstract":[{"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.","lang":"eng"}],"publist_id":"6209","doi":"10.1016/j.apnum.2016.04.005","day":"01","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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.","volume":107},{"publist_id":"5549","oa":1,"abstract":[{"text":"We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of equal measure and placing a random point inside each of the N=md cubes. We prove that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d, where the upper bound with an unspecified constant Cd was proven earlier by Beck. Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality and a suitably taylored Bernstein inequality; we have reasons to believe that the upper bound has the sharp scaling in N. Additional heuristics suggest that jittered sampling should be able to improve known bounds on the inverse of the star-discrepancy in the regime N≳dd. We also prove a partition principle showing that every partition of [0,1]d combined with a jittered sampling construction gives rise to a set whose expected squared L2-discrepancy is smaller than that of purely random points.","lang":"eng"}],"day":"01","doi":"10.1016/j.jco.2015.11.003","type":"journal_article","date_published":"2016-04-01T00:00:00Z","year":"2016","citation":{"mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216, doi:10.1016/j.jco.2015.11.003.","short":"F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.","ista":"Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216.","apa":"Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003","ama":"Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003","ieee":"F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,” Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016.","chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003."},"date_updated":"2021-01-12T06:52:02Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"url":"http://arxiv.org/abs/1510.00251","open_access":"1"}],"acknowledgement":"We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition.","volume":33,"intvolume":" 33","month":"04","title":"On the discrepancy of jittered sampling","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:53:03Z","publication_status":"published","oa_version":"Submitted Version","author":[{"full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Steinerberger","first_name":"Stefan","full_name":"Steinerberger, Stefan"}],"scopus_import":1,"_id":"1617","publication":"Journal of Complexity","publisher":"Academic Press","language":[{"iso":"eng"}],"quality_controlled":"1","page":"199 - 216"},{"volume":287,"acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014.","ddc":["004"],"day":"10","doi":"10.1016/j.aim.2015.10.004","abstract":[{"lang":"eng","text":"We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball."}],"year":"2016","citation":{"ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016.","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016. https://doi.org/10.1016/j.aim.2015.10.004.","apa":"Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004","ama":"Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004","ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703.","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press, 2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004."},"date_updated":"2023-09-07T11:41:25Z","publisher":"Academic Press","ec_funded":1,"quality_controlled":"1","page":"674 - 703","file_date_updated":"2020-07-14T12:45:10Z","date_created":"2018-12-11T11:53:20Z","department":[{"_id":"HeEd"}],"publication_status":"published","intvolume":" 287","title":"Approximation and convergence of the intrinsic volume","pubrep_id":"774","scopus_import":1,"_id":"1662","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Pausinger","first_name":"Florian","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"file":[{"file_id":"4928","creator":"system","relation":"main_file","access_level":"open_access","date_updated":"2020-07-14T12:45:10Z","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf","content_type":"application/pdf","date_created":"2018-12-12T10:12:10Z","checksum":"f8869ec110c35c852ef6a37425374af7","file_size":248985}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"1399"}]},"oa":1,"publist_id":"5488","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png"},"type":"journal_article","date_published":"2016-01-10T00:00:00Z","language":[{"iso":"eng"}],"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems"}],"oa_version":"Published Version","month":"01","has_accepted_license":"1","publication":"Advances in Mathematics"},{"conference":{"name":"CTIC: Computational Topology in Image Context","start_date":"2016-06-15","end_date":"2016-06-17","location":"Marseille, France"},"language":[{"iso":"eng"}],"oa_version":"None","month":"06","publication":"Computational Topology in Image Context","place":"Cham","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","publication_identifier":{"eisbn":["978-3-319-39441-1"],"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["978-3-319-39440-4"]},"type":"book_chapter","date_published":"2016-06-02T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","page":"253-264","article_processing_charge":"No","department":[{"_id":"HeEd"}],"date_created":"2019-01-08T20:44:24Z","publication_status":"published","intvolume":" 9667","title":"On some local topological properties of naive discrete sphere","alternative_title":["LNCS"],"_id":"5805","author":[{"last_name":"Sen","first_name":"Nabhasmita","full_name":"Sen, Nabhasmita"},{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"}],"volume":9667,"extern":"1","day":"02","doi":"10.1007/978-3-319-39441-1_23","abstract":[{"lang":"eng","text":"Discretization of sphere in the integer space follows a particular discretization scheme, which, in principle, conforms to some topological model. This eventually gives rise to interesting topological properties of a discrete spherical surface, which need to be investigated for its analytical characterization. This paper presents some novel results on the local topological properties of the naive model of discrete sphere. They follow from the bijection of each quadraginta octant of naive sphere with its projection map called f -map on the corresponding functional plane and from the characterization of certain jumps in the f-map. As an application, we have shown how these properties can be used in designing an efficient reconstruction algorithm for a naive spherical surface from an input voxel set when it is sparse or noisy."}],"year":"2016","citation":{"chicago":"Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological Properties of Naive Discrete Sphere.” In Computational Topology in Image Context, 9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.","ieee":"N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties of naive discrete sphere,” in Computational Topology in Image Context, vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.","apa":"Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological properties of naive discrete sphere. In Computational Topology in Image Context (Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23","ama":"Sen N, Biswas R, Bhowmick P. On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. Vol 9667. Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23","ista":"Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol. 9667, 253–264.","short":"N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 2016, pp. 253–264.","mla":"Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature, 2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23."},"date_updated":"2022-01-28T08:01:22Z"},{"extern":"1","volume":9647,"citation":{"short":"R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, pp. 256–267.","mla":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.","ista":"Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive sphere with application to circle drawing. Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 9647, 256–267.","apa":"Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants of naive sphere with application to circle drawing. In Discrete Geometry for Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20","ama":"Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere with application to circle drawing. In: Discrete Geometry for Computer Imagery. Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20","chicago":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.","ieee":"R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive sphere with application to circle drawing,” in Discrete Geometry for Computer Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267."},"year":"2016","date_updated":"2022-01-28T08:10:11Z","abstract":[{"lang":"eng","text":"Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane."}],"day":"09","doi":"10.1007/978-3-319-32360-2_20","quality_controlled":"1","page":"256-267","publisher":"Springer Nature","author":[{"last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Bhowmick, Partha","first_name":"Partha","last_name":"Bhowmick"}],"_id":"5806","intvolume":" 9647","title":"On functionality of quadraginta octants of naive sphere with application to circle drawing","alternative_title":["LNCS"],"department":[{"_id":"HeEd"}],"date_created":"2019-01-08T20:44:37Z","article_processing_charge":"No","publication_status":"published","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","place":"Cham","type":"conference","date_published":"2016-04-09T00:00:00Z","publication_identifier":{"isbn":["978-3-319-32359-6"],"issn":["0302-9743","1611-3349"],"eisbn":["978-3-319-32360-2"]},"language":[{"iso":"eng"}],"conference":{"start_date":"2016-04-18","name":"DGCI: International Conference on Discrete Geometry for Computer Imagery","end_date":"2016-04-20","location":"Nantes, France"},"publication":"Discrete Geometry for Computer Imagery","month":"04","oa_version":"None"},{"author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas","first_name":"Ranita"},{"full_name":"Bhowmick, Partha","first_name":"Partha","last_name":"Bhowmick"},{"full_name":"Brimkov, Valentin E.","last_name":"Brimkov","first_name":"Valentin E."}],"publication":"Combinatorial image analysis","_id":"5809","intvolume":" 9448","title":"On the connectivity and smoothness of discrete spherical circles","month":"01","department":[{"_id":"HeEd"}],"date_created":"2019-01-08T20:45:19Z","article_processing_charge":"No","oa_version":"None","publication_status":"published","language":[{"iso":"eng"}],"quality_controlled":"1","page":"86-100","conference":{"end_date":"2015-11-27","location":"Kolkata, India","name":"IWCIA: International Workshop on Combinatorial Image Analysis","start_date":"2015-11-24"},"publisher":"Springer Nature","type":"book_chapter","date_published":"2016-01-06T00:00:00Z","year":"2016","citation":{"short":"R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100.","mla":"Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016, pp. 86–100, doi:10.1007/978-3-319-26145-4_7.","ista":"Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.","apa":"Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity and smoothness of discrete spherical circles. In Combinatorial image analysis (Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7","ama":"Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7","ieee":"R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness of discrete spherical circles,” in Combinatorial image analysis, vol. 9448, Cham: Springer Nature, 2016, pp. 86–100.","chicago":"Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis, 9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7."},"date_updated":"2022-01-28T08:13:03Z","abstract":[{"text":"A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness.","lang":"eng"}],"publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"eisbn":["978-3-319-26145-4"],"isbn":["978-3-319-26144-7"]},"day":"06","doi":"10.1007/978-3-319-26145-4_7","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","extern":"1","place":"Cham","volume":9448},{"status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/1506.06014","open_access":"1"}],"date_published":"2016-10-15T00:00:00Z","type":"journal_article","oa":1,"publist_id":"5938","language":[{"iso":"eng"}],"publication":"Israel Journal of Mathematics","month":"10","oa_version":"Preprint","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"volume":216,"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.","date_updated":"2021-01-12T06:49:56Z","citation":{"ieee":"A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845, 2016.","chicago":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z.","apa":"Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z","ama":"Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z","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.","mla":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:10.1007/s11856-016-1429-z."},"year":"2016","abstract":[{"lang":"eng","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."}],"doi":"10.1007/s11856-016-1429-z","day":"15","page":"833 - 845","ec_funded":1,"quality_controlled":"1","publisher":"Springer","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Balitskiy, Alexey","first_name":"Alexey","last_name":"Balitskiy"}],"issue":"2","_id":"1330","scopus_import":1,"title":"Billiards in convex bodies with acute angles","intvolume":" 216","publication_status":"published","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:51:24Z"},{"month":"10","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"oa_version":"Preprint","publication":"Proceedings of the American Mathematical Society","language":[{"iso":"eng"}],"publist_id":"5885","oa":1,"type":"journal_article","date_published":"2016-10-01T00:00:00Z","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/1401.0442","open_access":"1"}],"intvolume":" 144","title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","date_created":"2018-12-11T11:51:34Z","department":[{"_id":"HeEd"}],"article_processing_charge":"No","publication_status":"published","issue":"10","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Balitskiy, Alexey","last_name":"Balitskiy","first_name":"Alexey"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"},{"full_name":"Sharipova, Anastasia","first_name":"Anastasia","last_name":"Sharipova"}],"scopus_import":1,"_id":"1360","publisher":"American Mathematical Society","ec_funded":1,"quality_controlled":"1","page":"4501 - 4513","abstract":[{"lang":"eng","text":"We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results. "}],"day":"01","doi":"10.1090/proc/13062","citation":{"short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513.","mla":"Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062.","ista":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513.","ama":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062","apa":"Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062","chicago":"Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/13062.","ieee":"A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” Proceedings of the American Mathematical Society, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016."},"year":"2016","date_updated":"2021-01-12T06:50:09Z","volume":144,"acknowledgement":"The first and third authors were supported by the Dynasty Foundation. The first, second and third authors were supported by the Russian Foundation for Basic Re- search grant 15-31-20403 (mol a ved)."},{"publisher":"Springer","file_date_updated":"2020-07-14T12:44:53Z","quality_controlled":"1","ec_funded":1,"page":"126 - 164","intvolume":" 56","pubrep_id":"614","title":"On computability and triviality of well groups","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2018-12-11T11:51:51Z","publication_status":"published","issue":"1","author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","full_name":"Franek, Peter","first_name":"Peter","last_name":"Franek"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek","first_name":"Marek","last_name":"Krcál"}],"scopus_import":1,"_id":"1408","ddc":["510"],"volume":56,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","abstract":[{"lang":"eng","text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status."}],"day":"01","doi":"10.1007/s00454-016-9794-2","year":"2016","citation":{"ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164, 2016.","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.","apa":"Franek, P., & Krcál, M. (2016). On computability and triviality of well groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2","ama":"Franek P, Krcál M. On computability and triviality of well groups. Discrete & Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2","ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete & Computational Geometry. 56(1), 126–164.","short":"P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.","mla":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:10.1007/s00454-016-9794-2."},"date_updated":"2023-02-23T10:02:11Z","language":[{"iso":"eng"}],"month":"07","project":[{"call_identifier":"FWF","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425","name":"Robust invariants of Nonlinear Systems","grant_number":"M01980"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Discrete & Computational Geometry","related_material":{"record":[{"relation":"earlier_version","id":"1510","status":"public"}]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"relation":"main_file","access_level":"open_access","creator":"system","file_id":"4846","file_size":905303,"checksum":"e0da023abf6b72abd8c6a8c76740d53c","date_created":"2018-12-12T10:10:55Z","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","content_type":"application/pdf","date_updated":"2020-07-14T12:44:53Z"}],"publist_id":"5799","oa":1,"type":"journal_article","date_published":"2016-07-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}},{"date_published":"2016-01-01T00:00:00Z","type":"journal_article","date_updated":"2021-01-12T06:49:09Z","citation":{"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.","mla":"Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing House, 2016, pp. 55–80.","short":"J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80.","ieee":"J. Kasten et al., “Acceleration feature points of unsteady shear flows,” Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing House, pp. 55–80, 2016.","chicago":"Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House, 2016.","apa":"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. Polish Academy of Sciences Publishing House.","ama":"Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 2016;68(1):55-80."},"year":"2016","abstract":[{"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.","lang":"eng"}],"oa":1,"publist_id":"6118","day":"01","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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","volume":68,"main_file_link":[{"url":"http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf","open_access":"1"}],"author":[{"first_name":"Jens","last_name":"Kasten","full_name":"Kasten, Jens"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus"},{"last_name":"Hotz","first_name":"Ingrid","full_name":"Hotz, Ingrid"},{"full_name":"Hege, Hans","last_name":"Hege","first_name":"Hans"},{"last_name":"Noack","first_name":"Bernd","full_name":"Noack, Bernd"},{"first_name":"Guillaume","last_name":"Daviller","full_name":"Daviller, Guillaume"},{"full_name":"Morzyński, Marek","first_name":"Marek","last_name":"Morzyński"}],"issue":"1","publication":"Archives of Mechanics","_id":"1216","scopus_import":1,"title":"Acceleration feature points of unsteady shear flows","month":"01","intvolume":" 68","publication_status":"published","oa_version":"Published Version","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:50:46Z","language":[{"iso":"eng"}],"page":"55 - 80","quality_controlled":"1","publisher":"Polish Academy of Sciences Publishing House"},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1212.0649"}],"oa":1,"publist_id":"6111","type":"journal_article","date_published":"2016-01-01T00:00:00Z","language":[{"iso":"eng"}],"month":"01","oa_version":"Preprint","publication":"Discrete & Computational Geometry","volume":55,"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.","abstract":[{"lang":"eng","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."}],"day":"01","doi":"10.1007/s00454-015-9742-6","citation":{"ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 55(1), 1–20.","short":"O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20.","mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.","ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer, pp. 1–20, 2016.","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-015-9742-6.","ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6","apa":"Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-015-9742-6"},"year":"2016","date_updated":"2021-01-12T06:49:11Z","publisher":"Springer","quality_controlled":"1","page":"1 - 20","intvolume":" 55","title":"Optimal packings of congruent circles on a square flat torus","date_created":"2018-12-11T11:50:48Z","department":[{"_id":"HeEd"}],"publication_status":"published","issue":"1","author":[{"full_name":"Musin, Oleg","last_name":"Musin","first_name":"Oleg"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","first_name":"Anton","last_name":"Nikitenko"}],"scopus_import":1,"_id":"1222"}]