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A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p.","ieee":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed. Cham: Springer Nature, 2014.","apa":"Edelsbrunner, H. (2014). A Short Course in Computational Geometry and Topology (1st ed.). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-05957-0"},"language":[{"iso":"eng"}],"date_published":"2014-01-01T00:00:00Z","doi":"10.1007/978-3-319-05957-0","alternative_title":["SpringerBriefs in Applied Sciences and Technology"],"place":"Cham","type":"book","abstract":[{"lang":"eng","text":"This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields."}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","title":"A Short Course in Computational Geometry and Topology","publication_status":"published","status":"public","year":"2014","_id":"6853","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","date_created":"2019-09-06T09:22:33Z","date_updated":"2022-03-04T07:47:54Z","related_material":{"link":[{"relation":"other","description":"available as eBook via catalog IST BookList","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106"},{"description":"available via catalog IST BookList","relation":"other","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842"}]},"edition":"1","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}]},{"alternative_title":["Mathematics and Visualization"],"type":"conference","abstract":[{"text":"We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set.","lang":"eng"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"status":"public","publication_status":"published","title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","_id":"10886","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","year":"2014","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","oa_version":"None","date_created":"2022-03-18T13:05:39Z","date_updated":"2023-09-05T14:13:16Z","author":[{"first_name":"Valentin","last_name":"Zobel","full_name":"Zobel, Valentin"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Hotz","first_name":"Ingrid","full_name":"Hotz, Ingrid"}],"scopus_import":"1","article_processing_charge":"No","publication_identifier":{"eissn":["2197-666X"],"isbn":["9783319040981"],"issn":["1612-3786"],"eisbn":["9783319040998"]},"day":"19","month":"03","page":"249-262","quality_controlled":"1","citation":{"ama":"Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In: Topological Methods in Data Analysis and Visualization III . Springer; 2014:249-262. doi:10.1007/978-3-319-04099-8_16","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature,” in Topological Methods in Data Analysis and Visualization III , 2014, pp. 249–262.","apa":"Zobel, V., Reininghaus, J., & Hotz, I. (2014). Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In Topological Methods in Data Analysis and Visualization III (pp. 249–262). Springer. https://doi.org/10.1007/978-3-319-04099-8_16","ista":"Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262.","mla":"Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–62, doi:10.1007/978-3-319-04099-8_16.","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In Topological Methods in Data Analysis and Visualization III , 249–62. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_16."},"publication":"Topological Methods in Data Analysis and Visualization III ","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-04099-8_16","date_published":"2014-03-19T00:00:00Z"},{"publication_identifier":{"eissn":["2197-666X"],"isbn":["9783319040981"],"issn":["1612-3786"],"eisbn":["9783319040998"]},"month":"03","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"quality_controlled":"1","doi":"10.1007/978-3-319-04099-8_9","language":[{"iso":"eng"}],"place":"Cham","ec_funded":1,"year":"2014","acknowledgement":"This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"editor":[{"full_name":"Bremer, Peer-Timo","last_name":"Bremer","first_name":"Peer-Timo"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"},{"last_name":"Peikert","first_name":"Ronald","full_name":"Peikert, Ronald"}],"publication_status":"published","author":[{"first_name":"David","last_name":"Günther","full_name":"Günther, David"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"},{"full_name":"Seidel, Hans-Peter","last_name":"Seidel","first_name":"Hans-Peter"},{"full_name":"Weinkauf, Tino","last_name":"Weinkauf","first_name":"Tino"}],"date_updated":"2023-09-05T15:33:45Z","date_created":"2022-03-04T08:33:57Z","scopus_import":"1","series_title":"Mathematics and Visualization","article_processing_charge":"No","day":"19","citation":{"mla":"Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.” Topological Methods in Data Analysis and Visualization III., edited by Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:10.1007/978-3-319-04099-8_9.","short":"D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.","chicago":"Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf. “Notes on the Simplification of the Morse-Smale Complex.” In Topological Methods in Data Analysis and Visualization III., edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-04099-8_9.","ama":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Cham: Springer Nature; 2014:135-150. doi:10.1007/978-3-319-04099-8_9","ista":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization III. , 135–150.","apa":"Günther, D., Reininghaus, J., Seidel, H.-P., & Weinkauf, T. (2014). Notes on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III. (pp. 135–150). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-04099-8_9","ieee":"D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the simplification of the Morse-Smale complex,” in Topological Methods in Data Analysis and Visualization III., P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150."},"publication":"Topological Methods in Data Analysis and Visualization III.","page":"135-150","date_published":"2014-03-19T00:00:00Z","type":"book_chapter","abstract":[{"lang":"eng","text":"The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption."}],"_id":"10817","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Notes on the simplification of the Morse-Smale complex","oa_version":"None"},{"type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm."}],"intvolume":" 50","title":"Stable length estimates of tube-like shapes","status":"public","ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2255","file":[{"file_id":"5204","relation":"main_file","date_updated":"2020-07-14T12:45:35Z","date_created":"2018-12-12T10:16:18Z","checksum":"2f93f3e63a38a85cd4404d7953913b14","file_name":"IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf","access_level":"open_access","creator":"system","content_type":"application/pdf","file_size":3941391}],"oa_version":"Submitted Version","pubrep_id":"549","scopus_import":1,"has_accepted_license":"1","day":"01","page":"164 - 177","citation":{"chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer, 2014. https://doi.org/10.1007/s10851-013-0468-x.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:10.1007/s10851-013-0468-x.","short":"H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177.","ista":"Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp. 164–177, 2014.","apa":"Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x","ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x"},"publication":"Journal of Mathematical Imaging and Vision","date_published":"2014-09-01T00:00:00Z","ec_funded":1,"publist_id":"4691","file_date_updated":"2020-07-14T12:45:35Z","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","year":"2014","volume":50,"date_created":"2018-12-11T11:56:36Z","date_updated":"2023-09-07T11:41:25Z","related_material":{"record":[{"id":"2843","relation":"earlier_version","status":"public"},{"id":"1399","status":"public","relation":"dissertation_contains"}]},"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger"}],"publication_identifier":{"issn":["09249907"]},"month":"09","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s10851-013-0468-x"},{"publication_identifier":{"eisbn":["9783662441992"],"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783662441985"]},"month":"09","language":[{"iso":"eng"}],"doi":"10.1007/978-3-662-44199-2_24","conference":{"name":"ICMS: International Congress on Mathematical Software","end_date":"2014-08-09","location":"Seoul, South Korea","start_date":"2014-08-05"},"quality_controlled":"1","place":"Berlin, Heidelberg","volume":8592,"date_updated":"2023-09-20T09:42:40Z","date_created":"2022-03-21T07:12:16Z","related_material":{"record":[{"relation":"later_version","status":"public","id":"1433"}]},"author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Wagner, Hubert","first_name":"Hubert","last_name":"Wagner"}],"publisher":"Springer Berlin Heidelberg","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2014","article_processing_charge":"No","day":"01","series_title":"LNCS","scopus_import":"1","date_published":"2014-09-01T00:00:00Z","page":"137-143","citation":{"ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology Algorithms Toolbox,” in ICMS 2014: International Congress on Mathematical Software, Seoul, South Korea, 2014, vol. 8592, pp. 137–143.","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In ICMS 2014: International Congress on Mathematical Software (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_24","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software. ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms Toolbox. In: ICMS 2014: International Congress on Mathematical Software. Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143. doi:10.1007/978-3-662-44199-2_24","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT – Persistent Homology Algorithms Toolbox.” In ICMS 2014: International Congress on Mathematical Software, 8592:137–43. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. https://doi.org/10.1007/978-3-662-44199-2_24.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 137–143.","mla":"Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” ICMS 2014: International Congress on Mathematical Software, vol. 8592, Springer Berlin Heidelberg, 2014, pp. 137–43, doi:10.1007/978-3-662-44199-2_24."},"publication":"ICMS 2014: International Congress on Mathematical Software","abstract":[{"text":"PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations.","lang":"eng"}],"type":"conference","oa_version":"None","intvolume":" 8592","status":"public","title":"PHAT – Persistent Homology Algorithms Toolbox","_id":"10894","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"day":"01","month":"01","article_processing_charge":"No","publication":"arXiv","citation":{"ista":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv, 1401.0468.","apa":"Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468","ieee":"M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” arXiv. .","ama":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. doi:10.48550/arXiv.1401.0468","chicago":"Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468.","mla":"Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, doi:10.48550/arXiv.1401.0468.","short":"M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.)."},"external_id":{"arxiv":["1401.0468"]},"main_file_link":[{"open_access":"1","url":"http://cccg.ca/proceedings/2014/papers/paper23.pdf"}],"oa":1,"language":[{"iso":"eng"}],"date_published":"2014-01-01T00:00:00Z","doi":"10.48550/arXiv.1401.0468","article_number":"1401.0468","type":"preprint","abstract":[{"lang":"eng","text":"The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of overlap with other balls. We study two natural choices of overlap measures and obtain the optimal lattice packings in a parameterized family of lattices which contains the FCC, BCC, and integer lattice."}],"publist_id":"5064","status":"public","publication_status":"submitted","title":"Sphere packing with limited overlap","department":[{"_id":"HeEd"},{"_id":"CaUh"}],"_id":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"We thank Herbert Edelsbrunner for his valuable discussions and ideas on the topic of this paper. The second author has been supported by the Max Planck Center for Visual Computing and Communication","year":"2014","date_created":"2018-12-11T11:55:12Z","date_updated":"2023-10-18T08:06:45Z","oa_version":"Submitted Version","author":[{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299"},{"id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216","first_name":"Caroline","last_name":"Uhler","full_name":"Uhler, Caroline"}]},{"publication_status":"published","status":"public","title":"Recognizing straight skeletons and Voronoi diagrams and reconstructing their input","department":[{"_id":"HeEd"}],"publisher":"IEEE","_id":"2209","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2013","date_created":"2018-12-11T11:56:20Z","date_updated":"2021-01-12T06:56:00Z","oa_version":"None","author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"last_name":"Huber","first_name":"Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","full_name":"Huber, Stefan"}],"alternative_title":["2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) "],"type":"conference","abstract":[{"text":"A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straight-line graph for which this was the straight skeleton? We show how to reduce this problem to the problem of finding a line that intersects a set of convex polygons. We can find these convex polygons and all such lines in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number of edges of the input graph. We also explain how our approach can be used for recognizing Voronoi diagrams of points, thereby completing a partial solution provided by Ash and Bolker in 1985.\r\n","lang":"eng"}],"publist_id":"4763","quality_controlled":"1","page":"37 - 46","citation":{"mla":"Biedl, Therese, et al. Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input. IEEE, 2013, pp. 37–46, doi:10.1109/ISVD.2013.11.","short":"T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46.","chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. https://doi.org/10.1109/ISVD.2013.11.","ama":"Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: IEEE; 2013:37-46. doi:10.1109/ISVD.2013.11","ista":"Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) , , 37–46.","ieee":"T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.","apa":"Biedl, T., Held, M., & Huber, S. (2013). Recognizing straight skeletons and Voronoi diagrams and reconstructing their input (pp. 37–46). Presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia: IEEE. https://doi.org/10.1109/ISVD.2013.11"},"language":[{"iso":"eng"}],"conference":{"name":"ISVD: Voronoi Diagrams in Science and Engineering","start_date":"2013-07-08","location":"St. Petersburg, Russia","end_date":"2013-07-10"},"doi":"10.1109/ISVD.2013.11","date_published":"2013-12-01T00:00:00Z","scopus_import":1,"day":"01","month":"12","publication_identifier":{"eisbn":["978-0-7695-5037-4 "]}},{"publist_id":"4762","abstract":[{"lang":"eng","text":"A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon. In this paper, we ask the reverse question: Given the straight skeleton (in form of a tree with a drawing in the plane, but with the exact position of the leaves unspecified), can we reconstruct the polygon? We show that in most cases there exists at most one polygon; in the remaining case there is an infinite number of polygons determined by one angle that can range in an interval. We can find this (set of) polygon(s) in linear time in the Real RAM computer model."}],"type":"conference","oa_version":"Submitted Version","date_updated":"2021-01-12T06:56:00Z","date_created":"2018-12-11T11:56:21Z","author":[{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber","full_name":"Huber, Stefan"}],"publisher":"TU Braunschweig","department":[{"_id":"HeEd"}],"status":"public","title":"Reconstructing polygons from embedded straight skeletons","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2210","year":"2013","month":"03","day":"01","language":[{"iso":"eng"}],"date_published":"2013-03-01T00:00:00Z","conference":{"end_date":"2013-03-20","start_date":"2013-03-17","location":"Braunschweig, Germany","name":"EuroCG: European Workshop on Computational Geometry"},"page":"95 - 98","citation":{"ama":"Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons. In: 29th European Workshop on Computational Geometry. TU Braunschweig; 2013:95-98.","apa":"Biedl, T., Held, M., & Huber, S. (2013). Reconstructing polygons from embedded straight skeletons. In 29th European Workshop on Computational Geometry (pp. 95–98). Braunschweig, Germany: TU Braunschweig.","ieee":"T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight skeletons,” in 29th European Workshop on Computational Geometry, Braunschweig, Germany, 2013, pp. 95–98.","ista":"Biedl T, Held M, Huber S. 2013. Reconstructing polygons from embedded straight skeletons. 29th European Workshop on Computational Geometry. EuroCG: European Workshop on Computational Geometry, 95–98.","short":"T. Biedl, M. Held, S. Huber, in:, 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98.","mla":"Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.” 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98.","chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons from Embedded Straight Skeletons.” In 29th European Workshop on Computational Geometry, 95–98. TU Braunschweig, 2013."},"oa":1,"main_file_link":[{"open_access":"1","url":"http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf"}],"publication":"29th European Workshop on Computational Geometry"},{"scopus_import":1,"day":"05","month":"09","citation":{"ama":"Pausinger F. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 2013;43:43-50. doi:10.1016/j.endm.2013.07.008","apa":"Pausinger, F. (2013). Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2013.07.008","ieee":"F. Pausinger, “Van der Corput sequences and linear permutations,” Electronic Notes in Discrete Mathematics, vol. 43. Elsevier, pp. 43–50, 2013.","ista":"Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 43, 43–50.","short":"F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50.","mla":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics, vol. 43, Elsevier, 2013, pp. 43–50, doi:10.1016/j.endm.2013.07.008.","chicago":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics. Elsevier, 2013. https://doi.org/10.1016/j.endm.2013.07.008."},"publication":"Electronic Notes in Discrete Mathematics","page":"43 - 50","quality_controlled":"1","date_published":"2013-09-05T00:00:00Z","doi":"10.1016/j.endm.2013.07.008","language":[{"iso":"eng"}],"type":"journal_article","publist_id":"4623","abstract":[{"text":"This extended abstract is concerned with the irregularities of distribution of one-dimensional permuted van der Corput sequences that are generated from linear permutations. We show how to obtain upper bounds for the discrepancy and diaphony of these sequences, by relating them to Kronecker sequences and applying earlier results of Faure and Niederreiter.","lang":"eng"}],"year":"2013","_id":"2304","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria).","intvolume":" 43","publisher":"Elsevier","department":[{"_id":"HeEd"}],"title":"Van der Corput sequences and linear permutations","publication_status":"published","status":"public","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger","full_name":"Pausinger, Florian"}],"volume":43,"oa_version":"None","date_updated":"2021-01-12T06:56:39Z","date_created":"2018-12-11T11:56:53Z"},{"scopus_import":1,"has_accepted_license":"1","day":"01","page":"595 - 604","citation":{"ama":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps: Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683","apa":"Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013). Extending continuous maps: Polynomiality and undecidability. In 45th Annual ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United States: ACM. https://doi.org/10.1145/2488608.2488683","ieee":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory of computing, Palo Alto, CA, United States, 2013, pp. 595–604.","ista":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of computing. STOC: Symposium on the Theory of Computing, 595–604.","short":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604.","mla":"Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.” 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604, doi:10.1145/2488608.2488683.","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner. “Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683."},"publication":"45th Annual ACM Symposium on theory of computing","date_published":"2013-06-01T00:00:00Z","type":"conference","abstract":[{"text":"We consider several basic problems of algebraic topology, with connections to combinatorial and geometric questions, from the point of view of computational complexity. The extension problem asks, given topological spaces X; Y , a subspace A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X → Y . For computational purposes, we assume that X and Y are represented as finite simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map. In this generality the problem is undecidable, as follows from Novikov's result from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected; informally, this means that Y has \\no holes up to dimension k-1" (a basic example of such a Y is the sphere Sk). We prove that, on the one hand, this problem is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2, we obtain an algorithm that solves the extension problem in polynomial time assuming Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides a classification of all extensions up to homotopy (continuous deformation). This relies on results of our SODA 2012 paper, and the main new ingredient is a machinery of objects with polynomial-time homology, which is a polynomial-time analog of objects with effective homology developed earlier by Sergeraert et al. We also consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected Y . Their computability was established by Brown in 1957; we show that πk(Y ) can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where Y is a cell complex with certain rather compact encoding. We strengthen his result to #P-hardness for Y given as a simplicial complex. ","lang":"eng"}],"ddc":["510"],"title":"Extending continuous maps: Polynomiality and undecidability","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2807","file":[{"access_level":"open_access","file_name":"IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf","content_type":"application/pdf","file_size":447945,"creator":"system","relation":"main_file","file_id":"5081","checksum":"06c2ce5c1135fbc1f71ca15eeb242dcf","date_updated":"2020-07-14T12:45:48Z","date_created":"2018-12-12T10:14:29Z"}],"oa_version":"Submitted Version","pubrep_id":"533","month":"06","quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"doi":"10.1145/2488608.2488683","conference":{"name":"STOC: Symposium on the Theory of Computing","end_date":"2013-06-04","location":"Palo Alto, CA, United States","start_date":"2013-06-01"},"publist_id":"4078","file_date_updated":"2020-07-14T12:45:48Z","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"ACM","publication_status":"published","year":"2013","date_created":"2018-12-11T11:59:42Z","date_updated":"2021-01-12T06:59:51Z","author":[{"full_name":"Čadek, Martin","first_name":"Martin","last_name":"Čadek"},{"full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Matoušek, Jiří","last_name":"Matoušek","first_name":"Jiří"},{"full_name":"Vokřínek, Lukáš","first_name":"Lukáš","last_name":"Vokřínek"},{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}]},{"type":"conference","abstract":[{"lang":"eng","text":"We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H* (X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard."}],"publist_id":"4072","title":"Homological reconstruction and simplification in R3","publication_status":"published","status":"public","department":[{"_id":"HeEd"}],"publisher":"ACM","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2812","acknowledgement":"Some of the authors were partially supported by the GIGA ANR grant (contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827).","year":"2013","date_created":"2018-12-11T11:59:44Z","date_updated":"2023-02-23T10:15:15Z","oa_version":"Submitted Version","author":[{"last_name":"Attali","first_name":"Dominique","full_name":"Attali, Dominique"},{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich"},{"full_name":"Devillers, Olivier","last_name":"Devillers","first_name":"Olivier"},{"first_name":"Marc","last_name":"Glisse","full_name":"Glisse, Marc"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"}],"related_material":{"record":[{"id":"1805","relation":"later_version","status":"public"}]},"scopus_import":1,"month":"06","day":"01","quality_controlled":"1","page":"117 - 125","publication":"Proceedings of the 29th annual symposium on Computational Geometry","oa":1,"citation":{"ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. In: Proceedings of the 29th Annual Symposium on Computational Geometry. ACM; 2013:117-125. doi:10.1145/2462356.2462373","ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” in Proceedings of the 29th annual symposium on Computational Geometry, Rio de Janeiro, Brazil, 2013, pp. 117–125.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2013). Homological reconstruction and simplification in R3. In Proceedings of the 29th annual symposium on Computational Geometry (pp. 117–125). Rio de Janeiro, Brazil: ACM. https://doi.org/10.1145/2462356.2462373","ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction and simplification in R3. Proceedings of the 29th annual symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 117–125.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125.","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–25, doi:10.1145/2462356.2462373.","chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” In Proceedings of the 29th Annual Symposium on Computational Geometry, 117–25. ACM, 2013. https://doi.org/10.1145/2462356.2462373."},"main_file_link":[{"open_access":"1","url":"http://hal.archives-ouvertes.fr/hal-00833791/"}],"language":[{"iso":"eng"}],"conference":{"end_date":"2013-06-20","location":"Rio de Janeiro, Brazil","start_date":"2013-06-17","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.1145/2462356.2462373","date_published":"2013-06-01T00:00:00Z"},{"date_published":"2013-04-30T00:00:00Z","citation":{"chicago":"Topp, Christopher, Anjali Iyer Pascuzzi, Jill Anderson, Cheng Lee, Paul Zurek, Olga Symonova, Ying Zheng, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1304354110.","short":"C. Topp, A. Iyer Pascuzzi, J. Anderson, C. Lee, P. Zurek, O. Symonova, Y. Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. Moore, J. Harer, H. Edelsbrunner, T. Mitchell Olds, J. Weitz, P. Benfey, PNAS 110 (2013) E1695–E1704.","mla":"Topp, Christopher, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS, vol. 110, no. 18, National Academy of Sciences, 2013, pp. E1695–704, doi:10.1073/pnas.1304354110.","apa":"Topp, C., Iyer Pascuzzi, A., Anderson, J., Lee, C., Zurek, P., Symonova, O., … Benfey, P. (2013). 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1304354110","ieee":"C. Topp et al., “3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture,” PNAS, vol. 110, no. 18. National Academy of Sciences, pp. E1695–E1704, 2013.","ista":"Topp C, Iyer Pascuzzi A, Anderson J, Lee C, Zurek P, Symonova O, Zheng Y, Bucksch A, Mileyko Y, Galkovskyi T, Moore B, Harer J, Edelsbrunner H, Mitchell Olds T, Weitz J, Benfey P. 2013. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 110(18), E1695–E1704.","ama":"Topp C, Iyer Pascuzzi A, Anderson J, et al. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 2013;110(18):E1695-E1704. doi:10.1073/pnas.1304354110"},"publication":"PNAS","page":"E1695 - E1704","day":"30","scopus_import":1,"oa_version":"Submitted Version","_id":"2822","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 110","status":"public","title":"3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture","issue":"18","abstract":[{"lang":"eng","text":"Identification of genes that control root system architecture in crop plants requires innovations that enable high-throughput and accurate measurements of root system architecture through time. We demonstrate the ability of a semiautomated 3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative genetic basis of root system growth in a rice biparental mapping population, Bala x Azucena. We phenotyped >1,400 3D root models and >57,000 2D images for a suite of 25 traits that quantified the distribution, shape, extent of exploration, and the intrinsic size of root networks at days 12, 14, and 16 of growth in a gellan gum medium. From these data we identified 89 quantitative trait loci, some of which correspond to those found previously in soil-grown plants, and provide evidence for genetic tradeoffs in root growth allocations, such as between the extent and thoroughness of exploration. We also developed a multivariate method for generating and mapping central root architecture phenotypes and used it to identify five major quantitative trait loci (r2 = 24-37%), two of which were not identified by our univariate analysis. Our imaging and analytical platform provides a means to identify genes with high potential for improving root traits and agronomic qualities of crops."}],"type":"journal_article","doi":"10.1073/pnas.1304354110","language":[{"iso":"eng"}],"main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/","open_access":"1"}],"external_id":{"pmid":["25673779"]},"oa":1,"quality_controlled":"1","month":"04","author":[{"last_name":"Topp","first_name":"Christopher","full_name":"Topp, Christopher"},{"full_name":"Iyer Pascuzzi, Anjali","last_name":"Iyer Pascuzzi","first_name":"Anjali"},{"full_name":"Anderson, Jill","last_name":"Anderson","first_name":"Jill"},{"last_name":"Lee","first_name":"Cheng","full_name":"Lee, Cheng"},{"first_name":"Paul","last_name":"Zurek","full_name":"Zurek, Paul"},{"full_name":"Symonova, Olga","last_name":"Symonova","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Zheng, Ying","first_name":"Ying","last_name":"Zheng"},{"full_name":"Bucksch, Alexander","last_name":"Bucksch","first_name":"Alexander"},{"full_name":"Mileyko, Yuriy","last_name":"Mileyko","first_name":"Yuriy"},{"full_name":"Galkovskyi, Taras","first_name":"Taras","last_name":"Galkovskyi"},{"first_name":"Brad","last_name":"Moore","full_name":"Moore, Brad"},{"full_name":"Harer, John","last_name":"Harer","first_name":"John"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Thomas","last_name":"Mitchell Olds","full_name":"Mitchell Olds, Thomas"},{"full_name":"Weitz, Joshua","first_name":"Joshua","last_name":"Weitz"},{"last_name":"Benfey","first_name":"Philip","full_name":"Benfey, Philip"}],"volume":110,"date_created":"2018-12-11T11:59:47Z","date_updated":"2021-01-12T06:59:58Z","pmid":1,"year":"2013","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"publisher":"National Academy of Sciences","publication_status":"published","publist_id":"3979"},{"quality_controlled":"1","page":"XV - XIX","publication":"17th IAPR International Conference on Discrete Geometry for Computer Imagery","citation":{"chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” In 17th IAPR International Conference on Discrete Geometry for Computer Imagery, 7749:XV–XIX. Springer, 2013. https://doi.org/10.1007/978-3-642-37067-0.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” 17th IAPR International Conference on Discrete Geometry for Computer Imagery, vol. 7749, Springer, 2013, pp. XV–XIX, doi:10.1007/978-3-642-37067-0.","short":"H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX.","ista":"Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes. 17th IAPR International Conference on Discrete Geometry for Computer Imagery. DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.","apa":"Edelsbrunner, H., & Pausinger, F. (2013). Stable length estimates of tube-like shapes. In 17th IAPR International Conference on Discrete Geometry for Computer Imagery (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. https://doi.org/10.1007/978-3-642-37067-0","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” in 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Seville, Spain, 2013, vol. 7749, pp. XV–XIX.","ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. In: 17th IAPR International Conference on Discrete Geometry for Computer Imagery. Vol 7749. Springer; 2013:XV-XIX. doi:10.1007/978-3-642-37067-0"},"language":[{"iso":"eng"}],"conference":{"end_date":"2013-03-22","start_date":"2013-03-20","location":"Seville, Spain","name":"DGCI: Discrete Geometry for Computer Imagery"},"doi":"10.1007/978-3-642-37067-0","date_published":"2013-02-21T00:00:00Z","scopus_import":1,"month":"02","day":"21","status":"public","publication_status":"published","title":"Stable length estimates of tube-like shapes","intvolume":" 7749","department":[{"_id":"HeEd"}],"publisher":"Springer","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2843","year":"2013","date_updated":"2023-02-23T10:35:00Z","date_created":"2018-12-11T11:59:53Z","volume":7749,"oa_version":"None","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger","first_name":"Florian","full_name":"Pausinger, Florian"}],"related_material":{"record":[{"id":"2255","status":"public","relation":"later_version"}]},"alternative_title":["LNCS"],"type":"conference","abstract":[{"lang":"eng","text":"Mathematical objects can be measured unambiguously, but not so objects from our physical world. Even the total length of tubelike shapes has its difficulties. We introduce a combination of geometric, probabilistic, and topological methods to design a stable length estimate for tube-like shapes; that is: one that is insensitive to small shape changes."}],"publist_id":"3952"},{"page":"51 - 72","citation":{"chicago":"Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “Homology and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications. International Press, 2013. https://doi.org/10.4310/HHA.2013.v15.n1.a3.","mla":"Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications, vol. 15, no. 1, International Press, 2013, pp. 51–72, doi:10.4310/HHA.2013.v15.n1.a3.","short":"P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and Applications 15 (2013) 51–72.","ista":"Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72.","ieee":"P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness of level and interlevel sets,” Homology, Homotopy and Applications, vol. 15, no. 1. International Press, pp. 51–72, 2013.","apa":"Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2013). Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2013.v15.n1.a3","ama":"Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 2013;15(1):51-72. doi:10.4310/HHA.2013.v15.n1.a3"},"publication":"Homology, Homotopy and Applications","date_published":"2013-05-01T00:00:00Z","scopus_import":1,"day":"01","intvolume":" 15","title":"Homology and robustness of level and interlevel sets","status":"public","_id":"2859","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"journal_article","issue":"1","abstract":[{"text":"Given a continuous function f:X-R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization.","lang":"eng"}],"quality_controlled":"1","external_id":{"arxiv":["1102.3389"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1102.3389v1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.4310/HHA.2013.v15.n1.a3","month":"05","department":[{"_id":"HeEd"}],"publisher":"International Press","publication_status":"published","year":"2013","volume":15,"date_created":"2018-12-11T11:59:58Z","date_updated":"2021-01-12T07:00:18Z","author":[{"id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","last_name":"Bendich","first_name":"Paul","full_name":"Bendich, Paul"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Dmitriy","last_name":"Morozov","full_name":"Morozov, Dmitriy"},{"id":"34A254A0-F248-11E8-B48F-1D18A9856A87","last_name":"Patel","first_name":"Amit","full_name":"Patel, Amit"}],"publist_id":"3930"},{"scopus_import":1,"article_processing_charge":"No","day":"12","citation":{"short":"S. Fang, R. Clark, Y. Zheng, A. Iyer Pascuzzi, J. Weitz, L. Kochian, H. Edelsbrunner, H. Liao, P. Benfey, PNAS 110 (2013) 2670–2675.","mla":"Fang, Suqin, et al. “Genotypic Recognition and Spatial Responses by Rice Roots.” PNAS, vol. 110, no. 7, National Academy of Sciences, 2013, pp. 2670–75, doi:10.1073/pnas.1222821110.","chicago":"Fang, Suqin, Randy Clark, Ying Zheng, Anjali Iyer Pascuzzi, Joshua Weitz, Leon Kochian, Herbert Edelsbrunner, Hong Liao, and Philip Benfey. “Genotypic Recognition and Spatial Responses by Rice Roots.” PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1222821110.","ama":"Fang S, Clark R, Zheng Y, et al. Genotypic recognition and spatial responses by rice roots. PNAS. 2013;110(7):2670-2675. doi:10.1073/pnas.1222821110","apa":"Fang, S., Clark, R., Zheng, Y., Iyer Pascuzzi, A., Weitz, J., Kochian, L., … Benfey, P. (2013). Genotypic recognition and spatial responses by rice roots. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1222821110","ieee":"S. Fang et al., “Genotypic recognition and spatial responses by rice roots,” PNAS, vol. 110, no. 7. National Academy of Sciences, pp. 2670–2675, 2013.","ista":"Fang S, Clark R, Zheng Y, Iyer Pascuzzi A, Weitz J, Kochian L, Edelsbrunner H, Liao H, Benfey P. 2013. Genotypic recognition and spatial responses by rice roots. PNAS. 110(7), 2670–2675."},"publication":"PNAS","page":"2670 - 2675","article_type":"original","date_published":"2013-02-12T00:00:00Z","type":"journal_article","issue":"7","abstract":[{"text":"Root system growth and development is highly plastic and is influenced by the surrounding environment. Roots frequently grow in heterogeneous environments that include interactions from neighboring plants and physical impediments in the rhizosphere. To investigate how planting density and physical objects affect root system growth, we grew rice in a transparent gel system in close proximity with another plant or a physical object. Root systems were imaged and reconstructed in three dimensions. Root-root interaction strength was calculated using quantitative metrics that characterize the extent towhich the reconstructed root systems overlap each other. Surprisingly, we found the overlap of root systems of the same genotype was significantly higher than that of root systems of different genotypes. Root systems of the same genotype tended to grow toward each other but those of different genotypes appeared to avoid each other. Shoot separation experiments excluded the possibility of aerial interactions, suggesting root communication. Staggered plantings indicated that interactions likely occur at root tips in close proximity. Recognition of obstacles also occurred through root tips, but through physical contact in a size-dependent manner. These results indicate that root systems use two different forms of communication to recognize objects and alter root architecture: root-root recognition, possibly mediated through root exudates, and root-object recognition mediated by physical contact at the root tips. This finding suggests that root tips act as local sensors that integrate rhizosphere information into global root architectural changes.","lang":"eng"}],"_id":"2887","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 110","title":"Genotypic recognition and spatial responses by rice roots","status":"public","oa_version":"Published Version","month":"02","external_id":{"pmid":["23362379"]},"main_file_link":[{"open_access":"1","url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/"}],"oa":1,"quality_controlled":"1","doi":"10.1073/pnas.1222821110","language":[{"iso":"eng"}],"publist_id":"3872","pmid":1,"year":"2013","publisher":"National Academy of Sciences","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"last_name":"Fang","first_name":"Suqin","full_name":"Fang, Suqin"},{"full_name":"Clark, Randy","first_name":"Randy","last_name":"Clark"},{"first_name":"Ying","last_name":"Zheng","full_name":"Zheng, Ying"},{"last_name":"Iyer Pascuzzi","first_name":"Anjali","full_name":"Iyer Pascuzzi, Anjali"},{"full_name":"Weitz, Joshua","last_name":"Weitz","first_name":"Joshua"},{"full_name":"Kochian, Leon","last_name":"Kochian","first_name":"Leon"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Liao, Hong","last_name":"Liao","first_name":"Hong"},{"full_name":"Benfey, Philip","first_name":"Philip","last_name":"Benfey"}],"volume":110,"date_updated":"2021-01-12T07:00:29Z","date_created":"2018-12-11T12:00:09Z"},{"scopus_import":1,"day":"01","month":"01","oa":1,"main_file_link":[{"open_access":"1","url":"http://jmlr.org/proceedings/papers/v31/chen13a.html"}],"citation":{"ista":"Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. 2013. Computing the M most probable modes of a graphical model. AISTATS: Conference on Uncertainty in Artificial Intelligence, JMLR: W&CP, vol. 31, 161–169.","ieee":"C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, and C. Lampert, “Computing the M most probable modes of a graphical model,” presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States, 2013, vol. 31, pp. 161–169.","apa":"Chen, C., Kolmogorov, V., Yan, Z., Metaxas, D., & Lampert, C. (2013). Computing the M most probable modes of a graphical model (Vol. 31, pp. 161–169). Presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States: JMLR.","ama":"Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. Computing the M most probable modes of a graphical model. In: Vol 31. JMLR; 2013:161-169.","chicago":"Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph Lampert. “Computing the M Most Probable Modes of a Graphical Model,” 31:161–69. JMLR, 2013.","mla":"Chen, Chao, et al. Computing the M Most Probable Modes of a Graphical Model. Vol. 31, JMLR, 2013, pp. 161–69.","short":"C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, JMLR, 2013, pp. 161–169."},"quality_controlled":"1","page":"161 - 169","conference":{"name":" AISTATS: Conference on Uncertainty in Artificial Intelligence","end_date":"2013-05-01","start_date":"2013-04-29","location":"Scottsdale, AZ, United States"},"date_published":"2013-01-01T00:00:00Z","language":[{"iso":"eng"}],"type":"conference","alternative_title":[" JMLR: W&CP"],"abstract":[{"lang":"eng","text":" We introduce the M-modes problem for graphical models: predicting the M label configurations of highest probability that are at the same time local maxima of the probability landscape. M-modes have multiple possible applications: because they are intrinsically diverse, they provide a principled alternative to non-maximum suppression techniques for structured prediction, they can act as codebook vectors for quantizing the configuration space, or they can form component centers for mixture model approximation. We present two algorithms for solving the M-modes problem. The first algorithm solves the problem in polynomial time when the underlying graphical model is a simple chain. The second algorithm solves the problem for junction chains. In synthetic and real dataset, we demonstrate how M-modes can improve the performance of prediction. We also use the generated modes as a tool to understand the topography of the probability distribution of configurations, for example with relation to the training set size and amount of noise in the data. "}],"publist_id":"3846","_id":"2901","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Computing the M most probable modes of a graphical model","status":"public","publication_status":"published","intvolume":" 31","department":[{"_id":"HeEd"},{"_id":"VlKo"},{"_id":"ChLa"}],"publisher":"JMLR","author":[{"last_name":"Chen","first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao"},{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Yan, Zhu","first_name":"Zhu","last_name":"Yan"},{"full_name":"Metaxas, Dimitris","last_name":"Metaxas","first_name":"Dimitris"},{"orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","last_name":"Lampert","first_name":"Christoph","full_name":"Lampert, Christoph"}],"date_created":"2018-12-11T12:00:14Z","date_updated":"2021-01-12T07:00:35Z","volume":31,"oa_version":"None"},{"date_published":"2013-01-01T00:00:00Z","page":"70 - 77","citation":{"ama":"Kerber M, Edelsbrunner H. 3D kinetic alpha complexes and their implementation. In: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments. Society of Industrial and Applied Mathematics; 2013:70-77. doi:10.1137/1.9781611972931.6","apa":"Kerber, M., & Edelsbrunner, H. (2013). 3D kinetic alpha complexes and their implementation. In 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments (pp. 70–77). New Orleans, LA, United States: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611972931.6","ieee":"M. Kerber and H. Edelsbrunner, “3D kinetic alpha complexes and their implementation,” in 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, New Orleans, LA, United States, 2013, pp. 70–77.","ista":"Kerber M, Edelsbrunner H. 2013. 3D kinetic alpha complexes and their implementation. 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, ALENEX, , 70–77.","short":"M. Kerber, H. Edelsbrunner, in:, 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2013, pp. 70–77.","mla":"Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and Their Implementation.” 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2013, pp. 70–77, doi:10.1137/1.9781611972931.6.","chicago":"Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and Their Implementation.” In 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, 70–77. Society of Industrial and Applied Mathematics, 2013. https://doi.org/10.1137/1.9781611972931.6."},"publication":"2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments","has_accepted_license":"1","day":"01","scopus_import":1,"file":[{"relation":"main_file","file_id":"4720","checksum":"a15a3ba22df9445731507f3e06c9fcee","date_updated":"2020-07-14T12:45:52Z","date_created":"2018-12-12T10:08:57Z","access_level":"open_access","file_name":"IST-2016-547-v1+1_2013-P-08-MedusaII.pdf","content_type":"application/pdf","file_size":403013,"creator":"system"}],"oa_version":"Submitted Version","pubrep_id":"547","title":"3D kinetic alpha complexes and their implementation","ddc":["500"],"status":"public","_id":"2906","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"Motivated by an application in cell biology, we describe an extension of the kinetic data structures framework from Delaunay triangulations to fixed-radius alpha complexes. Our algorithm is implemented\r\nusing CGAL, following the exact geometric computation paradigm. We report on several\r\ntechniques to accelerate the computation that turn our implementation applicable to the underlying biological\r\nproblem."}],"alternative_title":["ALENEX"],"type":"conference","language":[{"iso":"eng"}],"doi":"10.1137/1.9781611972931.6","conference":{"name":"ALENEX: Algorithm Engineering and Experiments","start_date":"2013-01-07","location":"New Orleans, LA, United States","end_date":"2013-01-07"},"quality_controlled":"1","oa":1,"month":"01","date_updated":"2021-01-12T07:00:36Z","date_created":"2018-12-11T12:00:16Z","author":[{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"publisher":"Society of Industrial and Applied Mathematics","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2013","publist_id":"3841","file_date_updated":"2020-07-14T12:45:52Z"},{"publist_id":"3991","volume":49,"date_created":"2018-12-11T11:59:44Z","date_updated":"2023-02-23T11:13:49Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"3134"}]},"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Fasy, Brittany Terese","id":"F65D502E-E68D-11E9-9252-C644099818F6","last_name":"Fasy","first_name":"Brittany Terese"},{"first_name":"Günter","last_name":"Rote","full_name":"Rote, Günter"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2013","acknowledgement":"This research is partially supported by the National Science Foundation (NSF) under Grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.1007/s00454-013-9517-x","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.1007/s00454-013-9517-x","open_access":"1"}],"oa":1,"issue":"4","abstract":[{"lang":"eng","text":"The fact that a sum of isotropic Gaussian kernels can have more modes than kernels is surprising. Extra (ghost) modes do not exist in ℝ1 and are generally not well studied in higher dimensions. We study a configuration of n+1 Gaussian kernels for which there are exactly n+2 modes. We show that all modes lie on a finite set of lines, which we call axes, and study the restriction of the Gaussian mixture to these axes in order to discover that there are an exponential number of critical points in this configuration. Although the existence of ghost modes remained unknown due to the difficulty of finding examples in ℝ2, we show that the resilience of ghost modes grows like the square root of the dimension. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes."}],"type":"journal_article","oa_version":"Published Version","intvolume":" 49","status":"public","title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","_id":"2815","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2013-06-01T00:00:00Z","page":"797 - 822","article_type":"original","citation":{"mla":"Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Discrete & Computational Geometry, vol. 49, no. 4, Springer, 2013, pp. 797–822, doi:10.1007/s00454-013-9517-x.","short":"H. Edelsbrunner, B.T. Fasy, G. Rote, Discrete & Computational Geometry 49 (2013) 797–822.","chicago":"Edelsbrunner, Herbert, Brittany Terese Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Discrete & Computational Geometry. Springer, 2013. https://doi.org/10.1007/s00454-013-9517-x.","ama":"Edelsbrunner H, Fasy BT, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. 2013;49(4):797-822. doi:10.1007/s00454-013-9517-x","ista":"Edelsbrunner H, Fasy BT, Rote G. 2013. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. 49(4), 797–822.","apa":"Edelsbrunner, H., Fasy, B. T., & Rote, G. (2013). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-013-9517-x","ieee":"H. Edelsbrunner, B. T. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” Discrete & Computational Geometry, vol. 49, no. 4. Springer, pp. 797–822, 2013."},"publication":"Discrete & Computational Geometry"},{"scopus_import":1,"month":"05","day":"01","page":"435 - 447","quality_controlled":"1","citation":{"short":"C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013) 435–447.","mla":"Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” Computational Geometry: Theory and Applications, vol. 46, no. 4, Elsevier, 2013, pp. 435–47, doi:10.1016/j.comgeo.2012.02.010.","chicago":"Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” Computational Geometry: Theory and Applications. Elsevier, 2013. https://doi.org/10.1016/j.comgeo.2012.02.010.","ama":"Chen C, Kerber M. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 2013;46(4):435-447. doi:10.1016/j.comgeo.2012.02.010","ieee":"C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,” Computational Geometry: Theory and Applications, vol. 46, no. 4. Elsevier, pp. 435–447, 2013.","apa":"Chen, C., & Kerber, M. (2013). An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2012.02.010","ista":"Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 46(4), 435–447."},"publication":"Computational Geometry: Theory and Applications","language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2012.02.010","date_published":"2013-05-01T00:00:00Z","type":"journal_article","issue":"4","publist_id":"3796","abstract":[{"text":"In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ > 0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0, 1), the running time is O (C (1 - δ) Γ R d (n) log n), where C (1 - δ) Γ is the number of homology classes with persistence at least (1 - δ) Γ, n is the total number of simplices in the complex, d its dimension, and R d (n) is the complexity of computing the rank of an n × n matrix with O (d n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O (C (1 - δ) Γ n 2.376) algorithm, an O (C (1 - δ) Γ n 2.28) Las-Vegas algorithm, or an O (C (1 - δ) Γ n 2 + ε{lunate}) Monte-Carlo algorithm for an arbitrary ε{lunate} > 0. The space complexity of the Monte-Carlo version is bounded by O (d n) = O (n log n).","lang":"eng"}],"publisher":"Elsevier","intvolume":" 46","department":[{"_id":"HeEd"}],"publication_status":"published","title":"An output sensitive algorithm for persistent homology","status":"public","_id":"2939","acknowledgement":"The authors thank Herbert Edelsbrunner for many helpful discussions and suggestions. Moreover, they are grateful for the careful reviews that helped to improve the quality of the paper.","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","volume":46,"date_created":"2018-12-11T12:00:27Z","date_updated":"2023-02-23T11:24:10Z","related_material":{"record":[{"id":"3367","status":"public","relation":"earlier_version"}]},"author":[{"full_name":"Chen, Chao","first_name":"Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"}]},{"month":"06","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783642382208"],"eisbn":["9783642382215"],"issn":["0302-9743"]},"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"conference":{"name":"GbRPR: Graph-based Representations in Pattern Recognition","location":"Vienna, Austria","start_date":"2013-05-15","end_date":"2013-05-17"},"doi":"10.1007/978-3-642-38221-5_19","place":"Berlin, Heidelberg","ec_funded":1,"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","year":"2013","acknowledgement":"This research is partially supported by the European Science Foundation (ESF) under the Research Network Programme, the European Union under the Toposys Project FP7-ICT-318493-STREP, the Russian Government under the Mega Project 11.G34.31.0053.","date_updated":"2023-09-05T15:10:20Z","date_created":"2022-03-21T07:30:33Z","volume":7877,"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"series_title":"LNCS","scopus_import":"1","day":"01","article_processing_charge":"No","page":"182-183","publication":"Graph-Based Representations in Pattern Recognition","citation":{"short":"H. Edelsbrunner, in:, Graph-Based Representations in Pattern Recognition, Springer Nature, Berlin, Heidelberg, 2013, pp. 182–183.","mla":"Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” Graph-Based Representations in Pattern Recognition, vol. 7877, Springer Nature, 2013, pp. 182–83, doi:10.1007/978-3-642-38221-5_19.","chicago":"Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” In Graph-Based Representations in Pattern Recognition, 7877:182–83. LNCS. Berlin, Heidelberg: Springer Nature, 2013. https://doi.org/10.1007/978-3-642-38221-5_19.","ama":"Edelsbrunner H. Persistent homology in image processing. In: Graph-Based Representations in Pattern Recognition. Vol 7877. LNCS. Berlin, Heidelberg: Springer Nature; 2013:182-183. doi:10.1007/978-3-642-38221-5_19","apa":"Edelsbrunner, H. (2013). Persistent homology in image processing. In Graph-Based Representations in Pattern Recognition (Vol. 7877, pp. 182–183). Berlin, Heidelberg: Springer Nature. https://doi.org/10.1007/978-3-642-38221-5_19","ieee":"H. Edelsbrunner, “Persistent homology in image processing,” in Graph-Based Representations in Pattern Recognition, Vienna, Austria, 2013, vol. 7877, pp. 182–183.","ista":"Edelsbrunner H. 2013. Persistent homology in image processing. Graph-Based Representations in Pattern Recognition. GbRPR: Graph-based Representations in Pattern RecognitionLNCS vol. 7877, 182–183."},"date_published":"2013-06-01T00:00:00Z","type":"conference","abstract":[{"lang":"eng","text":"Taking images is an efficient way to collect data about the physical world. It can be done fast and in exquisite detail. By definition, image processing is the field that concerns itself with the computation aimed at harnessing the information contained in images [10]. This talk is concerned with topological information. Our main thesis is that persistent homology [5] is a useful method to quantify and summarize topological information, building a bridge that connects algebraic topology with applications. We provide supporting evidence for this thesis by touching upon four technical developments in the overlap between persistent homology and image processing."}],"title":"Persistent homology in image processing","status":"public","intvolume":" 7877","_id":"10897","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"None"},{"type":"journal_article","issue":"6","_id":"2849","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 67","title":"On the configuration space of Steiner minimal trees","ddc":["000"],"status":"public","pubrep_id":"546","file":[{"file_id":"5078","relation":"main_file","checksum":"44ee8d173487e8ed41a51136816bbeb4","date_created":"2018-12-12T10:14:26Z","date_updated":"2020-07-14T12:45:51Z","access_level":"open_access","file_name":"IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf","creator":"system","content_type":"application/pdf","file_size":392021}],"oa_version":"Submitted Version","scopus_import":1,"has_accepted_license":"1","day":"01","citation":{"ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 67(6), 1167–1168.","apa":"Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. IOP Publishing Ltd. https://doi.org/10.1070/RM2012v067n06ABEH004820","ieee":"H. Edelsbrunner and N. Strelkova, “On the configuration space of Steiner minimal trees,” Russian Mathematical Surveys, vol. 67, no. 6. IOP Publishing Ltd., pp. 1167–1168, 2012.","ama":"Edelsbrunner H, Strelkova N. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 2012;67(6):1167-1168. doi:10.1070/RM2012v067n06ABEH004820","chicago":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space of Steiner Minimal Trees.” Russian Mathematical Surveys. IOP Publishing Ltd., 2012. https://doi.org/10.1070/RM2012v067n06ABEH004820.","mla":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space of Steiner Minimal Trees.” Russian Mathematical Surveys, vol. 67, no. 6, IOP Publishing Ltd., 2012, pp. 1167–68, doi:10.1070/RM2012v067n06ABEH004820.","short":"H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168."},"publication":"Russian Mathematical Surveys","page":"1167 - 1168","date_published":"2012-01-01T00:00:00Z","publist_id":"3943","file_date_updated":"2020-07-14T12:45:51Z","year":"2012","department":[{"_id":"HeEd"}],"publisher":"IOP Publishing Ltd.","publication_status":"published","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Strelkova, Nataliya","first_name":"Nataliya","last_name":"Strelkova"}],"volume":67,"date_updated":"2021-01-12T07:00:13Z","date_created":"2018-12-11T11:59:55Z","month":"01","oa":1,"quality_controlled":"1","doi":"10.1070/RM2012v067n06ABEH004820","language":[{"iso":"eng"}]},{"date_published":"2012-08-06T00:00:00Z","page":"41 - 48","citation":{"ama":"Edelsbrunner H, Symonova O. The adaptive topology of a digital image. In: IEEE; 2012:41-48. doi:10.1109/ISVD.2012.11","ieee":"H. Edelsbrunner and O. Symonova, “The adaptive topology of a digital image,” presented at the ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, New Brunswick, NJ, USA , 2012, pp. 41–48.","apa":"Edelsbrunner, H., & Symonova, O. (2012). The adaptive topology of a digital image (pp. 41–48). Presented at the ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, New Brunswick, NJ, USA : IEEE. https://doi.org/10.1109/ISVD.2012.11","ista":"Edelsbrunner H, Symonova O. 2012. The adaptive topology of a digital image. ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, 41–48.","short":"H. Edelsbrunner, O. Symonova, in:, IEEE, 2012, pp. 41–48.","mla":"Edelsbrunner, Herbert, and Olga Symonova. The Adaptive Topology of a Digital Image. 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In this paper, we introduce a single topology that enjoys this theorem for all thresholds decomposing a real-valued image into foreground and background. This topology is easy to construct and it generalizes to n-dimensional images."}],"type":"conference","language":[{"iso":"eng"}],"doi":"10.1109/ISVD.2012.11","conference":{"end_date":"2012-06-29","location":"New Brunswick, NJ, USA ","start_date":"2012-06-27","name":"ISVD: International Symposium on Voronoi Diagrams in Science and Engineering"},"quality_controlled":"1","oa":1,"month":"08","date_created":"2018-12-11T12:00:15Z","date_updated":"2021-01-12T07:00:35Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Olga","last_name":"Symonova","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","full_name":"Symonova, Olga"}],"publisher":"IEEE","department":[{"_id":"HeEd"},{"_id":"MaJö"}],"publication_status":"published","year":"2012","publist_id":"3844","file_date_updated":"2020-07-14T12:45:52Z"},{"month":"11","quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"doi":"10.1070/RM2012v067n04ABEH004807","file_date_updated":"2020-07-14T12:45:55Z","publist_id":"3792","publication_status":"published","publisher":"IOP Publishing","department":[{"_id":"HeEd"}],"year":"2012","date_updated":"2021-01-12T07:39:55Z","date_created":"2018-12-11T12:00:28Z","volume":67,"author":[{"first_name":"Nikolai","last_name":"Dolbilin","full_name":"Dolbilin, Nikolai"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Musin, Oleg","first_name":"Oleg","last_name":"Musin"}],"scopus_import":1,"day":"01","has_accepted_license":"1","page":"781 - 783","publication":"Russian Mathematical Surveys","citation":{"apa":"Dolbilin, N., Edelsbrunner, H., & Musin, O. (2012). On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. IOP Publishing. https://doi.org/10.1070/RM2012v067n04ABEH004807","ieee":"N. Dolbilin, H. Edelsbrunner, and O. Musin, “On the optimality of functionals over triangulations of Delaunay sets,” Russian Mathematical Surveys, vol. 67, no. 4. IOP Publishing, pp. 781–783, 2012.","ista":"Dolbilin N, Edelsbrunner H, Musin O. 2012. On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. 67(4), 781–783.","ama":"Dolbilin N, Edelsbrunner H, Musin O. On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. 2012;67(4):781-783. doi:10.1070/RM2012v067n04ABEH004807","chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, and Oleg Musin. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” Russian Mathematical Surveys. IOP Publishing, 2012. https://doi.org/10.1070/RM2012v067n04ABEH004807.","short":"N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012) 781–783.","mla":"Dolbilin, Nikolai, et al. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” Russian Mathematical Surveys, vol. 67, no. 4, IOP Publishing, 2012, pp. 781–83, doi:10.1070/RM2012v067n04ABEH004807."},"date_published":"2012-11-01T00:00:00Z","type":"journal_article","issue":"4","status":"public","ddc":["510"],"title":"On the optimality of functionals over triangulations of Delaunay sets","intvolume":" 67","_id":"2941","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","file":[{"content_type":"application/pdf","file_size":253816,"creator":"system","access_level":"open_access","file_name":"IST-2013-132-v1+1_2012-J-04-Functional-E.pdf","checksum":"389a5ae53d6347de36c3468034f2821d","date_created":"2018-12-12T10:16:49Z","date_updated":"2020-07-14T12:45:55Z","relation":"main_file","file_id":"5239"}],"oa_version":"Submitted Version","pubrep_id":"132"},{"citation":{"short":"G. Zankl, Y. Haxhimusa, A. Ion, in:, Springer, 2012, pp. 11–20.","mla":"Zankl, Georg, et al. Interactive Labeling of Image Segmentation Hierarchies. Vol. 7476, Springer, 2012, pp. 11–20, doi:10.1007/978-3-642-32717-9_2.","chicago":"Zankl, Georg, Yll Haxhimusa, and Adrian Ion. “Interactive Labeling of Image Segmentation Hierarchies,” 7476:11–20. Springer, 2012. https://doi.org/10.1007/978-3-642-32717-9_2.","ama":"Zankl G, Haxhimusa Y, Ion A. Interactive labeling of image segmentation hierarchies. In: Vol 7476. Springer; 2012:11-20. doi:10.1007/978-3-642-32717-9_2","apa":"Zankl, G., Haxhimusa, Y., & Ion, A. (2012). Interactive labeling of image segmentation hierarchies (Vol. 7476, pp. 11–20). Presented at the Pattern Recognition, Graz, Austria: Springer. https://doi.org/10.1007/978-3-642-32717-9_2","ieee":"G. Zankl, Y. Haxhimusa, and A. Ion, “Interactive labeling of image segmentation hierarchies,” presented at the Pattern Recognition, Graz, Austria, 2012, vol. 7476, pp. 11–20.","ista":"Zankl G, Haxhimusa Y, Ion A. 2012. Interactive labeling of image segmentation hierarchies. Pattern Recognition vol. 7476, 11–20."},"quality_controlled":"1","page":"11 - 20","conference":{"name":"Pattern Recognition","end_date":"2012-08-31","start_date":"2012-08-28","location":"Graz, Austria"},"date_published":"2012-01-01T00:00:00Z","doi":"10.1007/978-3-642-32717-9_2","language":[{"iso":"eng"}],"scopus_import":1,"month":"01","day":"01","year":"2012","_id":"2971","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication_status":"published","status":"public","title":"Interactive labeling of image segmentation hierarchies","publisher":"Springer","department":[{"_id":"HeEd"}],"intvolume":" 7476","author":[{"first_name":"Georg","last_name":"Zankl","full_name":"Zankl, Georg"},{"full_name":"Haxhimusa, Yll","last_name":"Haxhimusa","first_name":"Yll"},{"id":"29F89302-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian","last_name":"Ion","full_name":"Ion, Adrian"}],"date_created":"2018-12-11T12:00:37Z","date_updated":"2021-01-12T07:40:10Z","volume":7476,"oa_version":"None","type":"conference","abstract":[{"lang":"eng","text":"We study the task of interactive semantic labeling of a segmentation hierarchy. To this end we propose a framework interleaving two components: an automatic labeling step, based on a Conditional Random Field whose dependencies are defined by the inclusion tree of the segmentation hierarchy, and an interaction step that integrates incremental input from a human user. Evaluated on two distinct datasets, the proposed interactive approach efficiently integrates human interventions and illustrates the advantages of structured prediction in an interactive framework. "}],"publist_id":"3737"},{"publisher":"Cambridge University Press","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.","year":"2012","volume":148,"date_created":"2018-12-11T12:01:30Z","date_updated":"2021-01-12T07:41:12Z","author":[{"full_name":"Brown, Gavin","first_name":"Gavin","last_name":"Brown"},{"first_name":"Michael","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael"},{"full_name":"Reid, Miles","first_name":"Miles","last_name":"Reid"}],"publist_id":"3579","quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1009.4313"}],"language":[{"iso":"eng"}],"doi":"10.1112/S0010437X11007226","month":"07","intvolume":" 148","status":"public","title":"Fano 3 folds in codimension 4 Tom and Jerry Part I","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"3120","oa_version":"Preprint","type":"journal_article","issue":"4","abstract":[{"text":"We introduce a strategy based on Kustin-Miller unprojection that allows us to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions (that is, nine equations and sixteen first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology. © 2012 Copyright Foundation Compositio Mathematica.","lang":"eng"}],"page":"1171 - 1194","citation":{"chicago":"Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” Compositio Mathematica. Cambridge University Press, 2012. https://doi.org/10.1112/S0010437X11007226.","short":"G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194.","mla":"Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” Compositio Mathematica, vol. 148, no. 4, Cambridge University Press, 2012, pp. 1171–94, doi:10.1112/S0010437X11007226.","ieee":"G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry Part I,” Compositio Mathematica, vol. 148, no. 4. Cambridge University Press, pp. 1171–1194, 2012.","apa":"Brown, G., Kerber, M., & Reid, M. (2012). Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. Cambridge University Press. https://doi.org/10.1112/S0010437X11007226","ista":"Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 148(4), 1171–1194.","ama":"Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 2012;148(4):1171-1194. doi:10.1112/S0010437X11007226"},"publication":"Compositio Mathematica","date_published":"2012-07-01T00:00:00Z","scopus_import":1,"day":"01"},{"publist_id":"3564","abstract":[{"text":"This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions. Given a perfect Morse function f: S n+1 →[0, 1 and a decomposition S n+1 = U ∪ V into two (n + 1)-manifolds with common boundary M, we prove elementary relationships between the persistence diagrams of f restricted to U, to V, and to M. ","lang":"eng"}],"type":"conference","oa_version":"Preprint","date_updated":"2021-01-12T07:41:17Z","date_created":"2018-12-11T12:01:35Z","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"HeEd"}],"publisher":"ACM","status":"public","publication_status":"published","title":"Alexander duality for functions: The persistent behavior of land and water and shore","_id":"3133","acknowledgement":"his research is partially supported by the National Science Foundation (NSF) under grant DBI-0820624, the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.\r\nThe authors thank an anonymous referee for suggesting the simplified proof of the Contravariant PE Theorem given in this paper. They also thank Frederick Cohen, Yuriy Mileyko and Amit Patel for helpful discussions.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2012","day":"20","month":"06","scopus_import":1,"language":[{"iso":"eng"}],"doi":"10.1145/2261250.2261287","date_published":"2012-06-20T00:00:00Z","conference":{"name":"SCG: Symposium on Computational Geometry","end_date":"2012-06-20","start_date":"2012-06-17","location":"Chapel Hill, NC, USA"},"page":"249 - 258","quality_controlled":"1","citation":{"apa":"Edelsbrunner, H., & Kerber, M. (2012). Alexander duality for functions: The persistent behavior of land and water and shore. In Proceedings of the twenty-eighth annual symposium on Computational geometry (pp. 249–258). Chapel Hill, NC, USA: ACM. https://doi.org/10.1145/2261250.2261287","ieee":"H. Edelsbrunner and M. Kerber, “Alexander duality for functions: The persistent behavior of land and water and shore,” in Proceedings of the twenty-eighth annual symposium on Computational geometry , Chapel Hill, NC, USA, 2012, pp. 249–258.","ista":"Edelsbrunner H, Kerber M. 2012. Alexander duality for functions: The persistent behavior of land and water and shore. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 249–258.","ama":"Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry . ACM; 2012:249-258. doi:10.1145/2261250.2261287","chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” In Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , 249–58. ACM, 2012. https://doi.org/10.1145/2261250.2261287.","short":"H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–258.","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–58, doi:10.1145/2261250.2261287."},"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1109.5052","open_access":"1"}],"publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry "},{"citation":{"chicago":"Edelsbrunner, Herbert, Brittany Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” In Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , 91–100. ACM, 2012. https://doi.org/10.1145/2261250.2261265.","short":"H. Edelsbrunner, B. Fasy, G. Rote, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100.","mla":"Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100, doi:10.1145/2261250.2261265.","apa":"Edelsbrunner, H., Fasy, B., & Rote, G. (2012). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In Proceedings of the twenty-eighth annual symposium on Computational geometry (pp. 91–100). Chapel Hill, NC, USA: ACM. https://doi.org/10.1145/2261250.2261265","ieee":"H. Edelsbrunner, B. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” in Proceedings of the twenty-eighth annual symposium on Computational geometry , Chapel Hill, NC, USA, 2012, pp. 91–100.","ista":"Edelsbrunner H, Fasy B, Rote G. 2012. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 91–100.","ama":"Edelsbrunner H, Fasy B, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In: Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry . ACM; 2012:91-100. doi:10.1145/2261250.2261265"},"publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","page":"91 - 100","quality_controlled":"1","doi":"10.1145/2261250.2261265","date_published":"2012-06-20T00:00:00Z","conference":{"name":"SCG: Symposium on Computational Geometry","location":"Chapel Hill, NC, USA","start_date":"2012-06-17","end_date":"2012-06-20"},"language":[{"iso":"eng"}],"scopus_import":1,"day":"20","month":"06","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"3134","acknowledgement":"This research is partially supported by the National Science Foun- dation (NSF) under grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.","year":"2012","department":[{"_id":"HeEd"}],"publisher":"ACM","title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","publication_status":"published","status":"public","related_material":{"record":[{"id":"2815","status":"public","relation":"later_version"}]},"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Fasy, Brittany","last_name":"Fasy","first_name":"Brittany"},{"full_name":"Rote, Günter","last_name":"Rote","first_name":"Günter"}],"oa_version":"None","date_updated":"2023-02-23T10:59:27Z","date_created":"2018-12-11T12:01:35Z","type":"conference","publist_id":"3563","abstract":[{"text":"It has been an open question whether the sum of finitely many isotropic Gaussian kernels in n ≥ 2 dimensions can have more modes than kernels, until in 2003 Carreira-Perpiñán and Williams exhibited n +1 isotropic Gaussian kernels in ℝ n with n + 2 modes. We give a detailed analysis of this example, showing that it has exponentially many critical points and that the resilience of the extra mode grows like √n. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes. ","lang":"eng"}]},{"pubrep_id":"543","file":[{"access_level":"open_access","file_name":"IST-2016-543-v1+1_2012-J-08-HierarchyCubeComplex.pdf","creator":"system","file_size":203636,"content_type":"application/pdf","file_id":"4675","relation":"main_file","checksum":"76486f3b2c9e7fd81342f3832ca387e7","date_created":"2018-12-12T10:08:15Z","date_updated":"2020-07-14T12:46:05Z"}],"oa_version":"Submitted Version","_id":"3256","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"title":"Dual complexes of cubical subdivisions of ℝn","status":"public","intvolume":" 47","abstract":[{"lang":"eng","text":"We use a distortion to define the dual complex of a cubical subdivision of ℝ n as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ n."}],"issue":"2","type":"journal_article","date_published":"2012-03-01T00:00:00Z","publication":"Discrete & Computational Geometry","citation":{"ama":"Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 2012;47(2):393-414. doi:10.1007/s00454-011-9382-4","ieee":"H. Edelsbrunner and M. Kerber, “Dual complexes of cubical subdivisions of ℝn,” Discrete & Computational Geometry, vol. 47, no. 2. Springer, pp. 393–414, 2012.","apa":"Edelsbrunner, H., & Kerber, M. (2012). Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-011-9382-4","ista":"Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 47(2), 393–414.","short":"H. Edelsbrunner, M. Kerber, Discrete & Computational Geometry 47 (2012) 393–414.","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry, vol. 47, no. 2, Springer, 2012, pp. 393–414, doi:10.1007/s00454-011-9382-4.","chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry. Springer, 2012. https://doi.org/10.1007/s00454-011-9382-4."},"page":"393 - 414","day":"01","has_accepted_license":"1","scopus_import":1,"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","first_name":"Michael"}],"date_updated":"2021-01-12T07:42:10Z","date_created":"2018-12-11T12:02:17Z","volume":47,"year":"2012","acknowledgement":"This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0057 and HR0011-09-0065 as well as the National Science Foundation (NSF) under grant DBI-0820624.","publication_status":"published","publisher":"Springer","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:05Z","publist_id":"3398","doi":"10.1007/s00454-011-9382-4","language":[{"iso":"eng"}],"oa":1,"quality_controlled":"1","month":"03"},{"abstract":[{"text":"We propose a mid-level statistical model for image segmentation that composes multiple figure-ground hypotheses (FG) obtained by applying constraints at different locations and scales, into larger interpretations (tilings) of the entire image. Inference is cast as optimization over sets of maximal cliques sampled from a graph connecting all non-overlapping figure-ground segment hypotheses. Potential functions over cliques combine unary, Gestalt-based figure qualities, and pairwise compatibilities among spatially neighboring segments, constrained by T-junctions and the boundary interface statistics of real scenes. Learning the model parameters is based on maximum likelihood, alternating between sampling image tilings and optimizing their potential function parameters. State of the art results are reported on the Berkeley and Stanford segmentation datasets, as well as VOC2009, where a 28% improvement was achieved.","lang":"eng"}],"publist_id":"3382","article_number":"6126486","type":"conference","date_updated":"2021-01-12T07:42:15Z","date_created":"2018-12-11T12:02:21Z","oa_version":"None","author":[{"full_name":"Ion, Adrian","id":"29F89302-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian","last_name":"Ion"},{"full_name":"Carreira, Joao","last_name":"Carreira","first_name":"Joao"},{"last_name":"Sminchisescu","first_name":"Cristian","full_name":"Sminchisescu, Cristian"}],"publication_status":"published","status":"public","title":"Image segmentation by figure-ground composition into maximal cliques","department":[{"_id":"HeEd"}],"publisher":"IEEE","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"3265","year":"2012","day":"12","month":"01","language":[{"iso":"eng"}],"conference":{"name":"ICCV: International Conference on Computer Vision","end_date":"2011-11-13","location":"Barcelona, Spain","start_date":"2011-11-06"},"date_published":"2012-01-12T00:00:00Z","doi":"10.1109/ICCV.2011.6126486","quality_controlled":"1","citation":{"apa":"Ion, A., Carreira, J., & Sminchisescu, C. (2012). Image segmentation by figure-ground composition into maximal cliques. Presented at the ICCV: International Conference on Computer Vision, Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126486","ieee":"A. Ion, J. Carreira, and C. Sminchisescu, “Image segmentation by figure-ground composition into maximal cliques,” presented at the ICCV: International Conference on Computer Vision, Barcelona, Spain, 2012.","ista":"Ion A, Carreira J, Sminchisescu C. 2012. Image segmentation by figure-ground composition into maximal cliques. ICCV: International Conference on Computer Vision, 6126486.","ama":"Ion A, Carreira J, Sminchisescu C. Image segmentation by figure-ground composition into maximal cliques. In: IEEE; 2012. doi:10.1109/ICCV.2011.6126486","chicago":"Ion, Adrian, Joao Carreira, and Cristian Sminchisescu. “Image Segmentation by Figure-Ground Composition into Maximal Cliques.” IEEE, 2012. https://doi.org/10.1109/ICCV.2011.6126486.","short":"A. Ion, J. Carreira, C. Sminchisescu, in:, IEEE, 2012.","mla":"Ion, Adrian, et al. Image Segmentation by Figure-Ground Composition into Maximal Cliques. 6126486, IEEE, 2012, doi:10.1109/ICCV.2011.6126486."}},{"type":"journal_article","abstract":[{"text":"We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(nlogn)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using the cgal library, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter δ its running time additionally depends on δ. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.","lang":"eng"}],"issue":"4","title":"Deconstructing approximate offsets","status":"public","intvolume":" 48","_id":"3115","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","scopus_import":1,"day":"01","page":"964 - 989","publication":"Discrete & Computational Geometry","citation":{"mla":"Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Discrete & Computational Geometry, vol. 48, no. 4, Springer, 2012, pp. 964–89, doi:10.1007/s00454-012-9441-5.","short":"E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete & Computational Geometry 48 (2012) 964–989.","chicago":"Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” Discrete & Computational Geometry. Springer, 2012. https://doi.org/10.1007/s00454-012-9441-5.","ama":"Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. Discrete & Computational Geometry. 2012;48(4):964-989. doi:10.1007/s00454-012-9441-5","ista":"Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate offsets. Discrete & Computational Geometry. 48(4), 964–989.","apa":"Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2012). Deconstructing approximate offsets. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-012-9441-5","ieee":"E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” Discrete & Computational Geometry, vol. 48, no. 4. Springer, pp. 964–989, 2012."},"date_published":"2012-12-01T00:00:00Z","publist_id":"3584","publication_status":"published","publisher":"Springer","department":[{"_id":"HeEd"}],"year":"2012","acknowledgement":"We thank Eyal Flato (Plataine Ltd.) for raising the offset-deconstruction problem in connection with wood cutting. We also thank Tim Bretl (UIUC) for suggesting the digital-pen offset-deconstruction problem. This work has been supported in part by the Israel Science Foundation (grant no. 1102/11), by the German–Israeli Foundation (grant no. 969/07), by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University, and by the EU Project under Contract No. 255827 (CGL—Computational Geometry Learning).\r\n","date_updated":"2023-02-23T11:22:30Z","date_created":"2018-12-11T12:01:28Z","volume":48,"author":[{"full_name":"Berberich, Eric","first_name":"Eric","last_name":"Berberich"},{"full_name":"Halperin, Dan","last_name":"Halperin","first_name":"Dan"},{"full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","first_name":"Michael"},{"last_name":"Pogalnikova","first_name":"Roza","full_name":"Pogalnikova, Roza"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"3329"}]},"month":"12","quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1109.2158","open_access":"1"}],"external_id":{"arxiv":["1109.2158"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00454-012-9441-5"},{"day":"01","month":"03","scopus_import":1,"date_published":"2012-03-01T00:00:00Z","doi":"10.1016/j.jsc.2011.11.001","language":[{"iso":"eng"}],"publication":" Journal of Symbolic Computation","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1104.1510","open_access":"1"}],"citation":{"mla":"Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” Journal of Symbolic Computation, vol. 47, no. 3, Elsevier, 2012, pp. 239–58, doi:10.1016/j.jsc.2011.11.001.","short":"M. Kerber, M. Sagraloff, Journal of Symbolic Computation 47 (2012) 239–258.","chicago":"Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” Journal of Symbolic Computation. Elsevier, 2012. https://doi.org/10.1016/j.jsc.2011.11.001.","ama":"Kerber M, Sagraloff M. A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation. 2012;47(3):239-258. doi:10.1016/j.jsc.2011.11.001","ista":"Kerber M, Sagraloff M. 2012. A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation. 47(3), 239–258.","apa":"Kerber, M., & Sagraloff, M. (2012). A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/j.jsc.2011.11.001","ieee":"M. Kerber and M. Sagraloff, “A worst case bound for topology computation of algebraic curves,” Journal of Symbolic Computation, vol. 47, no. 3. Elsevier, pp. 239–258, 2012."},"quality_controlled":"1","page":"239 - 258","abstract":[{"text":"Computing the topology of an algebraic plane curve C means computing a combinatorial graph that is isotopic to C and thus represents its topology in R2. We prove that, for a polynomial of degree n with integer coefficients bounded by 2ρ, the topology of the induced curve can be computed with bit operations ( indicates that we omit logarithmic factors). Our analysis improves the previous best known complexity bounds by a factor of n2. The improvement is based on new techniques to compute and refine isolating intervals for the real roots of polynomials, and on the consequent amortized analysis of the critical fibers of the algebraic curve.","lang":"eng"}],"issue":"3","publist_id":"3303","type":"journal_article","author":[{"orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"},{"full_name":"Sagraloff, Michael","first_name":"Michael","last_name":"Sagraloff"}],"date_updated":"2021-01-12T07:42:43Z","date_created":"2018-12-11T12:02:43Z","volume":47,"oa_version":"Preprint","_id":"3331","year":"2012","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","title":"A worst case bound for topology computation of algebraic curves","publication_status":"published","publisher":"Elsevier","intvolume":" 47","department":[{"_id":"HeEd"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"3129","intvolume":" 7357","status":"public","title":"Annotating simplices with a homology basis and its applications","oa_version":"Preprint","type":"conference","alternative_title":["LNCS"],"abstract":[{"lang":"eng","text":"Let K be a simplicial complex and g the rank of its p-th homology group Hp(K) defined with ℤ2 coefficients. We show that we can compute a basis H of Hp(K) and annotate each p-simplex of K with a binary vector of length g with the following property: the annotations, summed over all p-simplices in any p-cycle z, provide the coordinate vector of the homology class [z] in the basis H. The basis and the annotations for all simplices can be computed in O(n ω ) time, where n is the size of K and ω < 2.376 is a quantity so that two n×n matrices can be multiplied in O(n ω ) time. The precomputed annotations permit answering queries about the independence or the triviality of p-cycles efficiently.\r\n\r\nUsing annotations of edges in 2-complexes, we derive better algorithms for computing optimal basis and optimal homologous cycles in 1 - dimensional homology. Specifically, for computing an optimal basis of H1(K) , we improve the previously known time complexity from O(n 4) to O(n ω + n 2 g ω − 1). Here n denotes the size of the 2-skeleton of K and g the rank of H1(K) . Computing an optimal cycle homologous to a given 1-cycle is NP-hard even for surfaces and an algorithm taking 2 O(g) nlogn time is known for surfaces. We extend this algorithm to work with arbitrary 2-complexes in O(n ω ) + 2 O(g) n 2logn time using annotations.\r\n"}],"citation":{"mla":"Busaryev, Oleksiy, et al. Annotating Simplices with a Homology Basis and Its Applications. Vol. 7357, Springer, 2012, pp. 189–200, doi:10.1007/978-3-642-31155-0_17.","short":"O. Busaryev, S. Cabello, C. Chen, T. Dey, Y. Wang, in:, Springer, 2012, pp. 189–200.","chicago":"Busaryev, Oleksiy, Sergio Cabello, Chao Chen, Tamal Dey, and Yusu Wang. “Annotating Simplices with a Homology Basis and Its Applications,” 7357:189–200. Springer, 2012. https://doi.org/10.1007/978-3-642-31155-0_17.","ama":"Busaryev O, Cabello S, Chen C, Dey T, Wang Y. Annotating simplices with a homology basis and its applications. In: Vol 7357. Springer; 2012:189-200. doi:10.1007/978-3-642-31155-0_17","ista":"Busaryev O, Cabello S, Chen C, Dey T, Wang Y. 2012. Annotating simplices with a homology basis and its applications. SWAT: Symposium and Workshops on Algorithm Theory, LNCS, vol. 7357, 189–200.","apa":"Busaryev, O., Cabello, S., Chen, C., Dey, T., & Wang, Y. (2012). Annotating simplices with a homology basis and its applications (Vol. 7357, pp. 189–200). Presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki, Finland: Springer. https://doi.org/10.1007/978-3-642-31155-0_17","ieee":"O. Busaryev, S. Cabello, C. Chen, T. Dey, and Y. Wang, “Annotating simplices with a homology basis and its applications,” presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki, Finland, 2012, vol. 7357, pp. 189–200."},"page":"189 - 200","date_published":"2012-06-19T00:00:00Z","scopus_import":1,"day":"19","year":"2012","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Busaryev, Oleksiy","last_name":"Busaryev","first_name":"Oleksiy"},{"full_name":"Cabello, Sergio","last_name":"Cabello","first_name":"Sergio"},{"first_name":"Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao"},{"full_name":"Dey, Tamal","first_name":"Tamal","last_name":"Dey"},{"full_name":"Wang, Yusu","first_name":"Yusu","last_name":"Wang"}],"volume":7357,"date_updated":"2021-01-12T07:41:15Z","date_created":"2018-12-11T12:01:33Z","publist_id":"3569","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1107.3793"}],"external_id":{"arxiv":["1107.3793"]},"quality_controlled":"1","doi":"10.1007/978-3-642-31155-0_17","conference":{"name":"SWAT: Symposium and Workshops on Algorithm Theory","end_date":"2012-07-06","start_date":"2012-07-04","location":"Helsinki, Finland"},"language":[{"iso":"eng"}],"month":"06"},{"author":[{"full_name":"Mileyko, Yuriy","last_name":"Mileyko","first_name":"Yuriy"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Price","first_name":"Charles","full_name":"Price, Charles"},{"full_name":"Weitz, Joshua","first_name":"Joshua","last_name":"Weitz"}],"volume":7,"date_updated":"2021-01-12T07:41:28Z","date_created":"2018-12-11T12:01:44Z","year":"2012","acknowledgement":"his work was supported by the National Science Foundation Plant Genome Research Program (grant 0820624 to H.E. and J.S.W.), the Defense Advanced Projects Research Agency (grant HR0011-09-1-0055 to H.E. and J.S.W.), and the European Science Foundation (under the Research Networking Programme on “Applied and Computational Algebraic Topology” run by H.E.). Joshua S. Weitz, Ph.D., holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund.\r\n\r\n\r\n\r\nDuring preparation of this manuscript the authors became aware of a related work by Katifori and Magnasco (arXiv:1110.1412v1), concurrently submitted and accepted for publication in PLoS ONE.","publisher":"Public Library of Science","department":[{"_id":"HeEd"}],"publication_status":"published","publist_id":"3530","file_date_updated":"2020-07-14T12:46:01Z","article_number":"e36715","doi":"10.1371/journal.pone.0036715","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","month":"06","pubrep_id":"385","file":[{"checksum":"515a98ad72e470752f03f13663dcaff8","date_created":"2019-02-05T12:38:43Z","date_updated":"2020-07-14T12:46:01Z","file_id":"5922","relation":"main_file","creator":"kschuh","file_size":541583,"content_type":"application/pdf","access_level":"open_access","file_name":"2012_PLoS_Mileyko.PDF"}],"oa_version":"Published Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"3159","intvolume":" 7","status":"public","title":"Hierarchical ordering of reticular networks","ddc":["510"],"issue":"6","abstract":[{"text":"The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the "root" of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. In doing so, we show that the ordering of the reticular edges is more robust to noise in weight estimation than is the ordering of the tree edges. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks.","lang":"eng"}],"type":"journal_article","date_published":"2012-06-06T00:00:00Z","citation":{"ama":"Mileyko Y, Edelsbrunner H, Price C, Weitz J. Hierarchical ordering of reticular networks. PLoS One. 2012;7(6). doi:10.1371/journal.pone.0036715","ieee":"Y. Mileyko, H. Edelsbrunner, C. Price, and J. Weitz, “Hierarchical ordering of reticular networks,” PLoS One, vol. 7, no. 6. Public Library of Science, 2012.","apa":"Mileyko, Y., Edelsbrunner, H., Price, C., & Weitz, J. (2012). Hierarchical ordering of reticular networks. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0036715","ista":"Mileyko Y, Edelsbrunner H, Price C, Weitz J. 2012. Hierarchical ordering of reticular networks. PLoS One. 7(6), e36715.","short":"Y. Mileyko, H. Edelsbrunner, C. Price, J. Weitz, PLoS One 7 (2012).","mla":"Mileyko, Yuriy, et al. “Hierarchical Ordering of Reticular Networks.” PLoS One, vol. 7, no. 6, e36715, Public Library of Science, 2012, doi:10.1371/journal.pone.0036715.","chicago":"Mileyko, Yuriy, Herbert Edelsbrunner, Charles Price, and Joshua Weitz. “Hierarchical Ordering of Reticular Networks.” PLoS One. Public Library of Science, 2012. https://doi.org/10.1371/journal.pone.0036715."},"publication":"PLoS One","has_accepted_license":"1","day":"06","scopus_import":1},{"page":"1436 - 1444","publication":"Pattern Recognition Letters","citation":{"chicago":"Bendich, Paul, Sergio Cabello, and Herbert Edelsbrunner. “A Point Calculus for Interlevel Set Homology.” Pattern Recognition Letters. Elsevier, 2012. https://doi.org/10.1016/j.patrec.2011.10.007.","short":"P. Bendich, S. Cabello, H. Edelsbrunner, Pattern Recognition Letters 33 (2012) 1436–1444.","mla":"Bendich, Paul, et al. “A Point Calculus for Interlevel Set Homology.” Pattern Recognition Letters, vol. 33, no. 11, Elsevier, 2012, pp. 1436–44, doi:10.1016/j.patrec.2011.10.007.","apa":"Bendich, P., Cabello, S., & Edelsbrunner, H. (2012). A point calculus for interlevel set homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2011.10.007","ieee":"P. Bendich, S. Cabello, and H. Edelsbrunner, “A point calculus for interlevel set homology,” Pattern Recognition Letters, vol. 33, no. 11. Elsevier, pp. 1436–1444, 2012.","ista":"Bendich P, Cabello S, Edelsbrunner H. 2012. A point calculus for interlevel set homology. Pattern Recognition Letters. 33(11), 1436–1444.","ama":"Bendich P, Cabello S, Edelsbrunner H. A point calculus for interlevel set homology. Pattern Recognition Letters. 2012;33(11):1436-1444. doi:10.1016/j.patrec.2011.10.007"},"date_published":"2012-08-01T00:00:00Z","scopus_import":1,"day":"01","has_accepted_license":"1","status":"public","ddc":["000"],"title":"A point calculus for interlevel set homology","intvolume":" 33","_id":"3310","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","file":[{"file_size":280280,"content_type":"application/pdf","creator":"system","access_level":"open_access","file_name":"IST-2016-542-v1+1_2012-J-01-Poinculus.pdf","checksum":"d65f79775b51258a604ca5ec741297cc","date_created":"2018-12-12T10:15:00Z","date_updated":"2020-07-14T12:46:06Z","relation":"main_file","file_id":"5116"}],"pubrep_id":"542","type":"journal_article","abstract":[{"lang":"eng","text":"The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs, and written for non-experts in algebraic topology."}],"issue":"11","quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.patrec.2011.10.007","month":"08","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","year":"2012","acknowledgement":"Research by the third author is partially supported by the National Science Foundation (NSF) under grant DBI-0820624.","date_updated":"2021-01-12T07:42:34Z","date_created":"2018-12-11T12:02:36Z","volume":33,"author":[{"id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","last_name":"Bendich","first_name":"Paul","full_name":"Bendich, Paul"},{"first_name":"Sergio","last_name":"Cabello","full_name":"Cabello, Sergio"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"file_date_updated":"2020-07-14T12:46:06Z","publist_id":"3330"},{"oa_version":"Published Version","intvolume":" 8","status":"public","title":"Elementary solutions of the Bernstein problem on two intervals","_id":"6588","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","abstract":[{"lang":"eng","text":"First we note that the best polynomial approximation to vertical bar x vertical bar on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev polynomials. Then we explore the cases when a solution of the related problem on two intervals can be given in elementary functions."}],"type":"journal_article","date_published":"2012-01-01T00:00:00Z","page":"63-78","article_type":"original","citation":{"mla":"Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” Journal of Mathematical Physics, Analysis, Geometry, vol. 8, no. 1, B. Verkin Institute for Low Temperature Physics and Engineering, 2012, pp. 63–78.","short":"F. Pausinger, Journal of Mathematical Physics, Analysis, Geometry 8 (2012) 63–78.","chicago":"Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” Journal of Mathematical Physics, Analysis, Geometry. B. Verkin Institute for Low Temperature Physics and Engineering, 2012.","ama":"Pausinger F. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 2012;8(1):63-78.","ista":"Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78.","apa":"Pausinger, F. (2012). Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. B. Verkin Institute for Low Temperature Physics and Engineering.","ieee":"F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals,” Journal of Mathematical Physics, Analysis, Geometry, vol. 8, no. 1. B. Verkin Institute for Low Temperature Physics and Engineering, pp. 63–78, 2012."},"publication":"Journal of Mathematical Physics, Analysis, Geometry","article_processing_charge":"No","day":"01","scopus_import":"1","volume":8,"date_created":"2019-06-27T08:16:56Z","date_updated":"2023-10-16T09:41:31Z","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger","full_name":"Pausinger, Florian"}],"department":[{"_id":"HeEd"}],"publisher":"B. Verkin Institute for Low Temperature Physics and Engineering","publication_status":"published","acknowledgement":"This work is supported by the Austrian Science Fund (FWF), Project P22025-N18.\r\n","year":"2012","language":[{"iso":"eng"}],"isi":1,"quality_controlled":"1","main_file_link":[{"url":"http://mi.mathnet.ru/eng/jmag525","open_access":"1"}],"oa":1,"external_id":{"isi":["000301173600004"]},"publication_identifier":{"issn":["1812-9471"]},"month":"01"},{"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Nataliya","last_name":"Strelkova","full_name":"Strelkova, Nataliya"}],"oa_version":"None","volume":67,"date_created":"2018-12-11T12:00:18Z","date_updated":"2023-10-17T11:40:39Z","_id":"2912","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2012","intvolume":" 67","publisher":"Russian Academy of Sciences","department":[{"_id":"HeEd"}],"title":"On the configuration space for the shortest networks","publication_status":"published","status":"public","publist_id":"3831","issue":"6","type":"journal_article","doi":"10.4213/rm9503","date_published":"2012-10-01T00:00:00Z","language":[{"iso":"eng"}],"citation":{"short":"H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168.","mla":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space for the Shortest Networks.” Russian Mathematical Surveys, vol. 67, no. 6, Russian Academy of Sciences, 2012, pp. 1167–1168, doi:10.4213/rm9503.","chicago":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space for the Shortest Networks.” Russian Mathematical Surveys. Russian Academy of Sciences, 2012. https://doi.org/10.4213/rm9503.","ama":"Edelsbrunner H, Strelkova N. On the configuration space for the shortest networks. Russian Mathematical Surveys. 2012;67(6):1167–1168. doi:10.4213/rm9503","ieee":"H. Edelsbrunner and N. Strelkova, “On the configuration space for the shortest networks,” Russian Mathematical Surveys, vol. 67, no. 6. Russian Academy of Sciences, pp. 1167–1168, 2012.","apa":"Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space for the shortest networks. Russian Mathematical Surveys. Russian Academy of Sciences. https://doi.org/10.4213/rm9503","ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space for the shortest networks. Russian Mathematical Surveys. 67(6), 1167–1168."},"publication":"Russian Mathematical Surveys","page":"1167–1168","quality_controlled":"1","article_processing_charge":"No","day":"01","month":"10"},{"scopus_import":"1","article_processing_charge":"No","month":"06","day":"01","page":"211-218","quality_controlled":"1","oa":1,"citation":{"ista":"Quadrianto N, Lampert C, Chen C. 2012. The most persistent soft-clique in a set of sampled graphs. Proceedings of the 29th International Conference on Machine Learning. ICML: International Conference on Machine Learning, 211–218.","apa":"Quadrianto, N., Lampert, C., & Chen, C. (2012). The most persistent soft-clique in a set of sampled graphs. In Proceedings of the 29th International Conference on Machine Learning (pp. 211–218). Edinburgh, United Kingdom: ML Research Press.","ieee":"N. Quadrianto, C. Lampert, and C. Chen, “The most persistent soft-clique in a set of sampled graphs,” in Proceedings of the 29th International Conference on Machine Learning, Edinburgh, United Kingdom, 2012, pp. 211–218.","ama":"Quadrianto N, Lampert C, Chen C. The most persistent soft-clique in a set of sampled graphs. In: Proceedings of the 29th International Conference on Machine Learning. ML Research Press; 2012:211-218.","chicago":"Quadrianto, Novi, Christoph Lampert, and Chao Chen. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” In Proceedings of the 29th International Conference on Machine Learning, 211–18. ML Research Press, 2012.","mla":"Quadrianto, Novi, et al. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 211–18.","short":"N. Quadrianto, C. Lampert, C. Chen, in:, Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 211–218."},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1206.4652"}],"publication":"Proceedings of the 29th International Conference on Machine Learning","language":[{"iso":"eng"}],"date_published":"2012-06-01T00:00:00Z","conference":{"start_date":"2012-06-26","location":"Edinburgh, United Kingdom","end_date":"2012-07-01","name":"ICML: International Conference on Machine Learning"},"type":"conference","publist_id":"3572","abstract":[{"lang":"eng","text":"When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques.\r\n We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data, we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations."}],"department":[{"_id":"ChLa"},{"_id":"HeEd"}],"publisher":"ML Research Press","title":"The most persistent soft-clique in a set of sampled graphs","publication_status":"published","status":"public","_id":"3127","year":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","date_created":"2018-12-11T12:01:33Z","date_updated":"2023-10-17T11:55:06Z","author":[{"full_name":"Quadrianto, Novi","first_name":"Novi","last_name":"Quadrianto"},{"full_name":"Lampert, Christoph","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","last_name":"Lampert","first_name":"Christoph"},{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","first_name":"Chao","full_name":"Chen, Chao"}]},{"date_published":"2012-01-01T00:00:00Z","article_type":"original","page":"729 - 749","publication":"Journal de Theorie des Nombres des Bordeaux","citation":{"chicago":"Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux, 2012. https://doi.org/10.5802/jtnb.819.","short":"F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749.","mla":"Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” Journal de Theorie Des Nombres Des Bordeaux, vol. 24, no. 3, Université de Bordeaux, 2012, pp. 729–49, doi:10.5802/jtnb.819.","ieee":"F. Pausinger, “Weak multipliers for generalized van der Corput sequences,” Journal de Theorie des Nombres des Bordeaux, vol. 24, no. 3. Université de Bordeaux, pp. 729–749, 2012.","apa":"Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences. Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.819","ista":"Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.","ama":"Pausinger F. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 2012;24(3):729-749. doi:10.5802/jtnb.819"},"day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","oa_version":"Published Version","file":[{"date_created":"2020-05-11T12:40:39Z","date_updated":"2020-07-14T12:45:52Z","checksum":"6954bfe9d7f4119fbdda7a11cf0f5c67","file_id":"7819","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":819275,"file_name":"JTNB_2012__24_3_729_0.pdf","access_level":"open_access"}],"ddc":["510"],"title":"Weak multipliers for generalized van der Corput sequences","status":"public","intvolume":" 24","_id":"2904","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences."},{"text":"Les suites de Van der Corput généralisées sont dessuites unidimensionnelles et infinies dans l’intervalle de l’unité.Elles sont générées par permutations des entiers de la basebetsont les éléments constitutifs des suites multi-dimensionnelles deHalton. Suites aux progrès récents d’Atanassov concernant le com-portement de distribution uniforme des suites de Halton nous nousintéressons aux permutations de la formuleP(i) =ai(modb)pour les entiers premiers entre euxaetb. Dans cet article nousidentifions des multiplicateursagénérant des suites de Van derCorput ayant une mauvaise distribution. Nous donnons les bornesinférieures explicites pour cette distribution asymptotique asso-ciée à ces suites et relions ces dernières aux suites générées parpermutation d’identité, qui sont, selon Faure, les moins bien dis-tribuées des suites généralisées de Van der Corput dans une basedonnée.","lang":"fre"}],"issue":"3","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.5802/jtnb.819","quality_controlled":"1","oa":1,"month":"01","publication_identifier":{"issn":["1246-7405"],"eissn":["2118-8572"]},"date_updated":"2023-10-18T07:53:47Z","date_created":"2018-12-11T12:00:15Z","volume":24,"author":[{"full_name":"Pausinger, Florian","first_name":"Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Université de Bordeaux","year":"2012","file_date_updated":"2020-07-14T12:45:52Z","publist_id":"3843"},{"date_created":"2018-12-11T12:00:15Z","date_updated":"2023-10-18T07:34:45Z","oa_version":"Published Version","volume":19,"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"first_name":"Oleg","last_name":"Musin","full_name":"Musin, Oleg"},{"first_name":"Alexey","last_name":"Ukhalov","full_name":"Ukhalov, Alexey"},{"full_name":"Yakimova, Olga","first_name":"Olga","last_name":"Yakimova"},{"full_name":"Alexeev, Vladislav","first_name":"Vladislav","last_name":"Alexeev"},{"last_name":"Bogaevskaya","first_name":"Victoriya","full_name":"Bogaevskaya, Victoriya"},{"full_name":"Gorohov, Andrey","first_name":"Andrey","last_name":"Gorohov"},{"last_name":"Preobrazhenskaya","first_name":"Margarita","full_name":"Preobrazhenskaya, Margarita"}],"publication_status":"published","status":"public","title":"Fractal and computational geometry for generalizing cartographic objects","publisher":"Russian Academy of Sciences","department":[{"_id":"HeEd"}],"intvolume":" 19","_id":"2902","year":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"We present an algorithm for simplifying linear cartographic objects and results obtained with a computer program implementing this algorithm. "}],"publist_id":"3845","issue":"6","type":"journal_article","language":[{"iso":"rus"}],"date_published":"2012-12-01T00:00:00Z","quality_controlled":"1","article_type":"original","page":"152 - 160","publication":"Modeling and Analysis of Information Systems","main_file_link":[{"url":"http://mi.mathnet.ru/eng/mais280","open_access":"1"}],"citation":{"chicago":"Edelsbrunner, Herbert, Oleg Musin, Alexey Ukhalov, Olga Yakimova, Vladislav Alexeev, Victoriya Bogaevskaya, Andrey Gorohov, and Margarita Preobrazhenskaya. “Fractal and computational geometry for generalizing cartographic objects.” Modeling and Analysis of Information Systems. Russian Academy of Sciences, 2012.","short":"H. Edelsbrunner, O. Musin, A. Ukhalov, O. Yakimova, V. Alexeev, V. Bogaevskaya, A. Gorohov, M. Preobrazhenskaya, Modeling and Analysis of Information Systems 19 (2012) 152–160.","mla":"Edelsbrunner, Herbert, et al. “Fractal and computational geometry for generalizing cartographic objects.” Modeling and Analysis of Information Systems, vol. 19, no. 6, Russian Academy of Sciences, 2012, pp. 152–60.","apa":"Edelsbrunner, H., Musin, O., Ukhalov, A., Yakimova, O., Alexeev, V., Bogaevskaya, V., … Preobrazhenskaya, M. (2012). Fractal and computational geometry for generalizing cartographic objects. Modeling and Analysis of Information Systems. Russian Academy of Sciences.","ieee":"H. Edelsbrunner et al., “Fractal and computational geometry for generalizing cartographic objects,” Modeling and Analysis of Information Systems, vol. 19, no. 6. Russian Academy of Sciences, pp. 152–160, 2012.","ista":"Edelsbrunner H, Musin O, Ukhalov A, Yakimova O, Alexeev V, Bogaevskaya V, Gorohov A, Preobrazhenskaya M. 2012. Fractal and computational geometry for generalizing cartographic objects. Modeling and Analysis of Information Systems. 19(6), 152–160.","ama":"Edelsbrunner H, Musin O, Ukhalov A, et al. Fractal and computational geometry for generalizing cartographic objects. Modeling and Analysis of Information Systems. 2012;19(6):152-160."},"oa":1,"month":"12","day":"01","article_processing_charge":"No"},{"intvolume":" 24","publisher":"Neural Information Processing Systems Foundation","department":[{"_id":"HeEd"}],"status":"public","publication_status":"published","title":"Probabilistic joint image segmentation and labeling","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"3266","year":"2011","volume":24,"oa_version":"None","date_updated":"2021-01-12T07:42:15Z","date_created":"2018-12-11T12:02:21Z","author":[{"full_name":"Ion, Adrian","id":"29F89302-F248-11E8-B48F-1D18A9856A87","last_name":"Ion","first_name":"Adrian"},{"full_name":"Carreira, Joao","first_name":"Joao","last_name":"Carreira"},{"full_name":"Sminchisescu, Cristian","last_name":"Sminchisescu","first_name":"Cristian"}],"type":"conference","publist_id":"3381","abstract":[{"lang":"eng","text":"We present a joint image segmentation and labeling model (JSL) which, given a bag of figure-ground segment hypotheses extracted at multiple image locations and scales, constructs a joint probability distribution over both the compatible image interpretations (tilings or image segmentations) composed from those segments, and over their labeling into categories. The process of drawing samples from the joint distribution can be interpreted as first sampling tilings, modeled as maximal cliques, from a graph connecting spatially non-overlapping segments in the bag [1], followed by sampling labels for those segments, conditioned on the choice of a particular tiling. We learn the segmentation and labeling parameters jointly, based on Maximum Likelihood with a novel Incremental Saddle Point estimation procedure. The partition function over tilings and labelings is increasingly more accurately approximated by including incorrect configurations that a not-yet-competent model rates probable during learning. We show that the proposed methodologymatches the current state of the art in the Stanford dataset [2], as well as in VOC2010, where 41.7% accuracy on the test set is achieved."}],"page":"1827 - 1835","quality_controlled":"1","citation":{"ieee":"A. Ion, J. Carreira, and C. Sminchisescu, “Probabilistic joint image segmentation and labeling,” in NIPS Proceedings, Granada, Spain, 2011, vol. 24, pp. 1827–1835.","apa":"Ion, A., Carreira, J., & Sminchisescu, C. (2011). Probabilistic joint image segmentation and labeling. In NIPS Proceedings (Vol. 24, pp. 1827–1835). Granada, Spain: Neural Information Processing Systems Foundation.","ista":"Ion A, Carreira J, Sminchisescu C. 2011. Probabilistic joint image segmentation and labeling. NIPS Proceedings. NIPS: Neural Information Processing Systems vol. 24, 1827–1835.","ama":"Ion A, Carreira J, Sminchisescu C. Probabilistic joint image segmentation and labeling. In: NIPS Proceedings. Vol 24. Neural Information Processing Systems Foundation; 2011:1827-1835.","chicago":"Ion, Adrian, Joao Carreira, and Cristian Sminchisescu. “Probabilistic Joint Image Segmentation and Labeling.” In NIPS Proceedings, 24:1827–35. Neural Information Processing Systems Foundation, 2011.","short":"A. Ion, J. Carreira, C. Sminchisescu, in:, NIPS Proceedings, Neural Information Processing Systems Foundation, 2011, pp. 1827–1835.","mla":"Ion, Adrian, et al. “Probabilistic Joint Image Segmentation and Labeling.” NIPS Proceedings, vol. 24, Neural Information Processing Systems Foundation, 2011, pp. 1827–35."},"publication":"NIPS Proceedings","language":[{"iso":"eng"}],"date_published":"2011-12-01T00:00:00Z","conference":{"name":"NIPS: Neural Information Processing Systems","start_date":"2011-12-12","location":"Granada, Spain","end_date":"2011-12-14"},"scopus_import":1,"day":"01","month":"12"},{"publication_status":"published","publisher":"Wiley-Blackwell","department":[{"_id":"HeEd"}],"year":"2011","date_updated":"2021-01-12T07:42:16Z","date_created":"2018-12-11T12:02:22Z","volume":30,"author":[{"last_name":"Sheng","first_name":"Yu","full_name":"Sheng, Yu"},{"full_name":"Cutler, Barbara","last_name":"Cutler","first_name":"Barbara"},{"full_name":"Chen, Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","first_name":"Chao"},{"full_name":"Nasman, Joshua","last_name":"Nasman","first_name":"Joshua"}],"publist_id":"3377","quality_controlled":"1","main_file_link":[{"url":"http://www.cs.cmu.edu/%7Eshengyu/download/egsr2011_paper.pdf","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1111/j.1467-8659.2011.01985.x","month":"07","title":"Perceptual global illumination cancellation in complex projection environments","status":"public","intvolume":" 30","_id":"3269","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","type":"journal_article","abstract":[{"text":"The unintentional scattering of light between neighboring surfaces in complex projection environments increases the brightness and decreases the contrast, disrupting the appearance of the desired imagery. To achieve satisfactory projection results, the inverse problem of global illumination must be solved to cancel this secondary scattering. In this paper, we propose a global illumination cancellation method that minimizes the perceptual difference between the desired imagery and the actual total illumination in the resulting physical environment. Using Gauss-Newton and active set methods, we design a fast solver for the bound constrained nonlinear least squares problem raised by the perceptual error metrics. Our solver is further accelerated with a CUDA implementation and multi-resolution method to achieve 1–2 fps for problems with approximately 3000 variables. We demonstrate the global illumination cancellation algorithm with our multi-projector system. Results show that our method preserves the color fidelity of the desired imagery significantly better than previous methods.","lang":"eng"}],"issue":"4","article_type":"original","page":"1261 - 1268","publication":"Computer Graphics Forum","citation":{"ista":"Sheng Y, Cutler B, Chen C, Nasman J. 2011. Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. 30(4), 1261–1268.","apa":"Sheng, Y., Cutler, B., Chen, C., & Nasman, J. (2011). Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. Wiley-Blackwell. https://doi.org/10.1111/j.1467-8659.2011.01985.x","ieee":"Y. Sheng, B. Cutler, C. Chen, and J. Nasman, “Perceptual global illumination cancellation in complex projection environments,” Computer Graphics Forum, vol. 30, no. 4. Wiley-Blackwell, pp. 1261–1268, 2011.","ama":"Sheng Y, Cutler B, Chen C, Nasman J. Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. 2011;30(4):1261-1268. doi:10.1111/j.1467-8659.2011.01985.x","chicago":"Sheng, Yu, Barbara Cutler, Chao Chen, and Joshua Nasman. “Perceptual Global Illumination Cancellation in Complex Projection Environments.” Computer Graphics Forum. Wiley-Blackwell, 2011. https://doi.org/10.1111/j.1467-8659.2011.01985.x.","mla":"Sheng, Yu, et al. “Perceptual Global Illumination Cancellation in Complex Projection Environments.” Computer Graphics Forum, vol. 30, no. 4, Wiley-Blackwell, 2011, pp. 1261–68, doi:10.1111/j.1467-8659.2011.01985.x.","short":"Y. Sheng, B. Cutler, C. Chen, J. Nasman, Computer Graphics Forum 30 (2011) 1261–1268."},"date_published":"2011-07-19T00:00:00Z","scopus_import":1,"day":"19","article_processing_charge":"No"},{"language":[{"iso":"eng"}],"doi":"10.1007/s00454-010-9322-8","date_published":"2011-01-14T00:00:00Z","page":"425 - 448","quality_controlled":"1","citation":{"ama":"Chen C, Freedman D. Hardness results for homology localization. Discrete & Computational Geometry. 2011;45(3):425-448. doi:10.1007/s00454-010-9322-8","ieee":"C. Chen and D. Freedman, “Hardness results for homology localization,” Discrete & Computational Geometry, vol. 45, no. 3. Springer, pp. 425–448, 2011.","apa":"Chen, C., & Freedman, D. (2011). Hardness results for homology localization. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-010-9322-8","ista":"Chen C, Freedman D. 2011. Hardness results for homology localization. Discrete & Computational Geometry. 45(3), 425–448.","short":"C. Chen, D. Freedman, Discrete & Computational Geometry 45 (2011) 425–448.","mla":"Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” Discrete & Computational Geometry, vol. 45, no. 3, Springer, 2011, pp. 425–48, doi:10.1007/s00454-010-9322-8.","chicago":"Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” Discrete & Computational Geometry. Springer, 2011. https://doi.org/10.1007/s00454-010-9322-8."},"publication":"Discrete & Computational Geometry","day":"14","month":"01","scopus_import":1,"oa_version":"None","volume":45,"date_created":"2018-12-11T12:02:21Z","date_updated":"2023-02-21T16:07:10Z","related_material":{"record":[{"id":"10909","relation":"earlier_version","status":"public"}]},"author":[{"full_name":"Chen, Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao","last_name":"Chen"},{"full_name":"Freedman, Daniel","first_name":"Daniel","last_name":"Freedman"}],"department":[{"_id":"HeEd"}],"publisher":"Springer","intvolume":" 45","status":"public","title":"Hardness results for homology localization","publication_status":"published","_id":"3267","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2011","issue":"3","publist_id":"3379","abstract":[{"lang":"eng","text":"We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We study the problem with different measures: volume, diameter and radius. For volume, that is, the 1-norm of a cycle, two main results are presented. First, we prove that the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). The latter result leads to the inapproximability of the problem of computing the nonbounding cycle with the smallest volume and computing cycles representing a homology basis with the minimal total volume. As for the other two measures defined by pairwise geodesic distance, diameter and radius, we show that the localization problem is NP-hard for diameter but is polynomial for radius. Our work is restricted to homology over the ℤ2 field."}],"type":"journal_article"},{"day":"09","scopus_import":1,"series_title":"Special Issue on Voronoi Diagrams and Delaunay Triangulation","date_published":"2011-11-09T00:00:00Z","publication":"Transactions on Computational Science XIV","citation":{"ama":"Van De Weygaert R, Vegter G, Edelsbrunner H, et al. Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web. In: Gavrilova M, Tan K, Mostafavi M, eds. Transactions on Computational Science XIV. Vol 6970. Special Issue on Voronoi Diagrams and Delaunay Triangulation. Springer; 2011:60-101. doi:10.1007/978-3-642-25249-5_3","apa":"Van De Weygaert, R., Vegter, G., Edelsbrunner, H., Jones, B., Pranav, P., Park, C., … Teillaud, M. (2011). Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web. In M. Gavrilova, K. Tan, & M. Mostafavi (Eds.), Transactions on Computational Science XIV (Vol. 6970, pp. 60–101). Springer. https://doi.org/10.1007/978-3-642-25249-5_3","ieee":"R. Van De Weygaert et al., “Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web,” in Transactions on Computational Science XIV, vol. 6970, M. Gavrilova, K. Tan, and M. Mostafavi, Eds. Springer, 2011, pp. 60–101.","ista":"Van De Weygaert R, Vegter G, Edelsbrunner H, Jones B, Pranav P, Park C, Hellwing W, Eldering B, Kruithof N, Bos P, Hidding J, Feldbrugge J, Ten Have E, Van Engelen M, Caroli M, Teillaud M. 2011.Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web. In: Transactions on Computational Science XIV. LNCS, vol. 6970, 60–101.","short":"R. Van De Weygaert, G. Vegter, H. Edelsbrunner, B. Jones, P. Pranav, C. Park, W. Hellwing, B. Eldering, N. Kruithof, P. Bos, J. Hidding, J. Feldbrugge, E. Ten Have, M. Van Engelen, M. Caroli, M. Teillaud, in:, M. Gavrilova, K. Tan, M. Mostafavi (Eds.), Transactions on Computational Science XIV, Springer, 2011, pp. 60–101.","mla":"Van De Weygaert, Rien, et al. “Alpha, Betti and the Megaparsec Universe: On the Topology of the Cosmic Web.” Transactions on Computational Science XIV, edited by Marina Gavrilova et al., vol. 6970, Springer, 2011, pp. 60–101, doi:10.1007/978-3-642-25249-5_3.","chicago":"Van De Weygaert, Rien, Gert Vegter, Herbert Edelsbrunner, Bernard Jones, Pratyush Pranav, Changbom Park, Wojciech Hellwing, et al. “Alpha, Betti and the Megaparsec Universe: On the Topology of the Cosmic Web.” In Transactions on Computational Science XIV, edited by Marina Gavrilova, Kenneth Tan, and Mir Mostafavi, 6970:60–101. Special Issue on Voronoi Diagrams and Delaunay Triangulation. Springer, 2011. https://doi.org/10.1007/978-3-642-25249-5_3."},"page":"60 - 101","abstract":[{"lang":"eng","text":"We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, α. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of α, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. These can be tuned to consist of specific morphological elements of the Cosmic Web, i.e. clusters, filaments, or sheets. To elucidate the relative prominence of the various Betti numbers in different stages of morphological evolution, we introduce the concept of alpha tracks. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web. We also demonstrate that the scale-dependence of the Betti numbers yields a promising measure of cosmological parameters, with a potential to help in determining the nature of dark energy and to probe primordial non-Gaussianities. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field. Finally, we introduce the concept of persistent homology. It measures scale levels of the mass distribution and allows us to separate small from large scale features. Within the context of the hierarchical cosmic structure formation, persistence provides a natural formalism for a multiscale topology study of the Cosmic Web."}],"type":"book_chapter","alternative_title":["LNCS"],"oa_version":"Preprint","_id":"3335","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web","intvolume":" 6970","month":"11","doi":"10.1007/978-3-642-25249-5_3","language":[{"iso":"eng"}],"external_id":{"arxiv":["1306.3640"]},"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1306.3640"}],"quality_controlled":"1","publist_id":"3295","author":[{"first_name":"Rien","last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien"},{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Jones","first_name":"Bernard","full_name":"Jones, Bernard"},{"full_name":"Pranav, Pratyush","last_name":"Pranav","first_name":"Pratyush"},{"last_name":"Park","first_name":"Changbom","full_name":"Park, Changbom"},{"full_name":"Hellwing, Wojciech","first_name":"Wojciech","last_name":"Hellwing"},{"first_name":"Bob","last_name":"Eldering","full_name":"Eldering, Bob"},{"full_name":"Kruithof, Nico","last_name":"Kruithof","first_name":"Nico"},{"full_name":"Bos, Patrick","first_name":"Patrick","last_name":"Bos"},{"full_name":"Hidding, Johan","last_name":"Hidding","first_name":"Johan"},{"full_name":"Feldbrugge, Job","last_name":"Feldbrugge","first_name":"Job"},{"last_name":"Ten Have","first_name":"Eline","full_name":"Ten Have, Eline"},{"full_name":"Van Engelen, Matti","first_name":"Matti","last_name":"Van Engelen"},{"full_name":"Caroli, Manuel","last_name":"Caroli","first_name":"Manuel"},{"full_name":"Teillaud, Monique","last_name":"Teillaud","first_name":"Monique"}],"date_updated":"2021-01-12T07:42:44Z","date_created":"2018-12-11T12:02:44Z","volume":6970,"year":"2011","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","editor":[{"last_name":"Gavrilova","first_name":"Marina","full_name":"Gavrilova, Marina"},{"first_name":"Kenneth","last_name":"Tan","full_name":"Tan, Kenneth"},{"full_name":"Mostafavi, Mir","first_name":"Mir","last_name":"Mostafavi"}]},{"conference":{"name":"SCG: Symposium on Computational Geometry","start_date":"2011-06-13","location":"Paris, France","end_date":"2011-06-15"},"date_published":"2011-06-13T00:00:00Z","doi":"10.1145/1998196.1998225","language":[{"iso":"eng"}],"publication":"Proceedings of the twenty-seventh annual symposium on Computational geometry","main_file_link":[{"url":"http://arxiv.org/abs/1109.2158","open_access":"1"}],"oa":1,"citation":{"chicago":"Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” In Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, 187–96. ACM, 2011. https://doi.org/10.1145/1998196.1998225.","mla":"Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, ACM, 2011, pp. 187–96, doi:10.1145/1998196.1998225.","short":"E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, in:, Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, ACM, 2011, pp. 187–196.","ista":"Berberich E, Halperin D, Kerber M, Pogalnikova R. 2011. Deconstructing approximate offsets. Proceedings of the twenty-seventh annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 187–196.","ieee":"E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” in Proceedings of the twenty-seventh annual symposium on Computational geometry, Paris, France, 2011, pp. 187–196.","apa":"Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2011). Deconstructing approximate offsets. In Proceedings of the twenty-seventh annual symposium on Computational geometry (pp. 187–196). Paris, France: ACM. https://doi.org/10.1145/1998196.1998225","ama":"Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. In: Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry. ACM; 2011:187-196. doi:10.1145/1998196.1998225"},"quality_controlled":"1","page":"187 - 196","month":"06","day":"13","scopus_import":1,"author":[{"full_name":"Berberich, Eric","last_name":"Berberich","first_name":"Eric"},{"full_name":"Halperin, Dan","last_name":"Halperin","first_name":"Dan"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pogalnikova, Roza","first_name":"Roza","last_name":"Pogalnikova"}],"related_material":{"record":[{"id":"3115","status":"public","relation":"later_version"}]},"date_created":"2018-12-11T12:02:42Z","date_updated":"2023-02-23T11:12:57Z","oa_version":"Preprint","_id":"3329","year":"2011","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication_status":"published","status":"public","title":"Deconstructing approximate offsets","department":[{"_id":"HeEd"}],"publisher":"ACM","abstract":[{"text":"We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance µ in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution shape P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. An alternative algorithm, based purely on rational arithmetic, answers the same deconstruction problem, up to an uncertainty parameter, and its running time depends on the parameter δ (in addition to the other input parameters: n, δ and the radius of the disk). If the input shape is found to be approximable, the rational-arithmetic algorithm also computes an approximate solution shape for the problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution shape P with at most one more vertex than a vertex-minimal one. Our study is motivated by applications from two different domains. However, since the offset operation has numerous uses, we anticipate that the reverse question that we study here will be still more broadly applicable. We present results obtained with our implementation of the rational-arithmetic algorithm.","lang":"eng"}],"publist_id":"3306","type":"conference"},{"_id":"3332","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 27","title":"A note on the complexity of real algebraic hypersurfaces","status":"public","ddc":["500"],"oa_version":"Submitted Version","file":[{"date_created":"2020-05-19T16:11:36Z","date_updated":"2020-07-14T12:46:08Z","checksum":"a63a1e3e885dcc68f1e3dea68dfbe213","file_id":"7869","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":143976,"file_name":"2011_GraphsCombi_Kerber.pdf","access_level":"open_access"}],"type":"journal_article","issue":"3","abstract":[{"lang":"eng","text":"Given an algebraic hypersurface O in ℝd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d ≥ 3."}],"citation":{"chicago":"Kerber, Michael, and Michael Sagraloff. “A Note on the Complexity of Real Algebraic Hypersurfaces.” Graphs and Combinatorics. Springer, 2011. https://doi.org/10.1007/s00373-011-1020-7.","mla":"Kerber, Michael, and Michael Sagraloff. “A Note on the Complexity of Real Algebraic Hypersurfaces.” Graphs and Combinatorics, vol. 27, no. 3, Springer, 2011, pp. 419–30, doi:10.1007/s00373-011-1020-7.","short":"M. Kerber, M. Sagraloff, Graphs and Combinatorics 27 (2011) 419–430.","ista":"Kerber M, Sagraloff M. 2011. A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. 27(3), 419–430.","ieee":"M. Kerber and M. Sagraloff, “A note on the complexity of real algebraic hypersurfaces,” Graphs and Combinatorics, vol. 27, no. 3. Springer, pp. 419–430, 2011.","apa":"Kerber, M., & Sagraloff, M. (2011). A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. Springer. https://doi.org/10.1007/s00373-011-1020-7","ama":"Kerber M, Sagraloff M. A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. 2011;27(3):419-430. doi:10.1007/s00373-011-1020-7"},"publication":"Graphs and Combinatorics","page":"419 - 430","article_type":"original","date_published":"2011-03-17T00:00:00Z","scopus_import":1,"has_accepted_license":"1","article_processing_charge":"No","day":"17","year":"2011","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","author":[{"orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"},{"last_name":"Sagraloff","first_name":"Michael","full_name":"Sagraloff, Michael"}],"volume":27,"date_updated":"2021-01-12T07:42:43Z","date_created":"2018-12-11T12:02:43Z","publist_id":"3301","file_date_updated":"2020-07-14T12:46:08Z","oa":1,"quality_controlled":"1","doi":"10.1007/s00373-011-1020-7","language":[{"iso":"eng"}],"month":"03"},{"quality_controlled":"1","page":"209 - 216","oa":1,"citation":{"ama":"Kerber M, Sagraloff M. Root refinement for real polynomials. In: Springer; 2011:209-216. doi:10.1145/1993886.1993920","ieee":"M. Kerber and M. Sagraloff, “Root refinement for real polynomials,” presented at the ISSAC: International Symposium on Symbolic and Algebraic Computation, California, USA, 2011, pp. 209–216.","apa":"Kerber, M., & Sagraloff, M. (2011). Root refinement for real polynomials (pp. 209–216). Presented at the ISSAC: International Symposium on Symbolic and Algebraic Computation, California, USA: Springer. https://doi.org/10.1145/1993886.1993920","ista":"Kerber M, Sagraloff M. 2011. Root refinement for real polynomials. ISSAC: International Symposium on Symbolic and Algebraic Computation, 209–216.","short":"M. Kerber, M. Sagraloff, in:, Springer, 2011, pp. 209–216.","mla":"Kerber, Michael, and Michael Sagraloff. Root Refinement for Real Polynomials. Springer, 2011, pp. 209–16, doi:10.1145/1993886.1993920.","chicago":"Kerber, Michael, and Michael Sagraloff. “Root Refinement for Real Polynomials,” 209–16. Springer, 2011. https://doi.org/10.1145/1993886.1993920."},"external_id":{"arxiv":["1104.1362"]},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1104.1362"}],"language":[{"iso":"eng"}],"conference":{"name":"ISSAC: International Symposium on Symbolic and Algebraic Computation","location":"California, USA","start_date":"2011-06-08","end_date":"2011-06-11"},"date_published":"2011-06-08T00:00:00Z","doi":"10.1145/1993886.1993920","scopus_import":1,"month":"06","day":"08","article_processing_charge":"No","status":"public","publication_status":"published","title":"Root refinement for real polynomials","department":[{"_id":"HeEd"}],"publisher":"Springer","_id":"3330","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2011","date_updated":"2021-01-12T07:42:42Z","date_created":"2018-12-11T12:02:43Z","oa_version":"Preprint","author":[{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Sagraloff, Michael","first_name":"Michael","last_name":"Sagraloff"}],"type":"conference","abstract":[{"lang":"eng","text":"We consider the problem of approximating all real roots of a square-free polynomial f. Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary point. Our method provides a certified answer for arbitrary real polynomials, only requiring finite approximations of the polynomial coefficient and choosing a suitable working precision adaptively. In this way, we get a correct algorithm that is simple to implement and practically efficient. Our algorithm uses the quadratic interval refinement method; we adapt that method to be able to cope with inaccuracies when evaluating f, without sacrificing its quadratic convergence behavior. We prove a bound on the bit complexity of our algorithm in terms of degree, coefficient size and discriminant. Our bound improves previous work on integer polynomials by a factor of deg f and essentially matches best known theoretical bounds on root approximation which are obtained by very sophisticated algorithms."}],"publist_id":"3304"},{"date_published":"2011-06-13T00:00:00Z","doi":"10.1145/1998196.1998224","conference":{"location":"Paris, France","start_date":"2011-06-13","end_date":"2011-06-15","name":"SCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"citation":{"ama":"Berberich E, Hemmer M, Kerber M. A generic algebraic kernel for non linear geometric applications. In: ACM; 2011:179-186. doi:10.1145/1998196.1998224","ista":"Berberich E, Hemmer M, Kerber M. 2011. A generic algebraic kernel for non linear geometric applications. SCG: Symposium on Computational Geometry, 179–186.","ieee":"E. Berberich, M. Hemmer, and M. Kerber, “A generic algebraic kernel for non linear geometric applications,” presented at the SCG: Symposium on Computational Geometry, Paris, France, 2011, pp. 179–186.","apa":"Berberich, E., Hemmer, M., & Kerber, M. (2011). A generic algebraic kernel for non linear geometric applications (pp. 179–186). Presented at the SCG: Symposium on Computational Geometry, Paris, France: ACM. https://doi.org/10.1145/1998196.1998224","mla":"Berberich, Eric, et al. A Generic Algebraic Kernel for Non Linear Geometric Applications. ACM, 2011, pp. 179–86, doi:10.1145/1998196.1998224.","short":"E. Berberich, M. Hemmer, M. Kerber, in:, ACM, 2011, pp. 179–186.","chicago":"Berberich, Eric, Michael Hemmer, and Michael Kerber. “A Generic Algebraic Kernel for Non Linear Geometric Applications,” 179–86. ACM, 2011. https://doi.org/10.1145/1998196.1998224."},"oa":1,"main_file_link":[{"url":"https://hal.inria.fr/inria-00480031/file/RR-7274.pdf","open_access":"1"}],"page":"179 - 186","quality_controlled":"1","article_processing_charge":"No","day":"13","month":"06","scopus_import":1,"author":[{"full_name":"Berberich, Eric","first_name":"Eric","last_name":"Berberich"},{"full_name":"Hemmer, Michael","first_name":"Michael","last_name":"Hemmer"},{"orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"}],"oa_version":"Published Version","date_updated":"2021-01-12T07:42:41Z","date_created":"2018-12-11T12:02:42Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"3328","year":"2011","publisher":"ACM","department":[{"_id":"HeEd"}],"status":"public","publication_status":"published","title":"A generic algebraic kernel for non linear geometric applications","publist_id":"3307","abstract":[{"lang":"eng","text":"We report on a generic uni- and bivariate algebraic kernel that is publicly available with CGAL 3.7. It comprises complete, correct, though efficient state-of-the-art implementations on polynomials, roots of polynomial systems, and the support to analyze algebraic curves defined by bivariate polynomials. The kernel design is generic, that is, various number types and substeps can be exchanged. It is accompanied with a ready-to-use interface to enable arrangements induced by algebraic curves, that have already been used as basis for various geometric applications, as arrangements on Dupin cyclides or the triangulation of algebraic surfaces. We present two novel applications: arrangements of rotated algebraic curves and Boolean set operations on polygons bounded by segments of algebraic curves. We also provide experiments showing that our general implementation is competitive and even often clearly outperforms existing implementations that are explicitly tailored for specific types of non-linear curves that are available in CGAL."}],"type":"conference"},{"issue":"1","publist_id":"3297","type":"journal_article","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Pach, János","last_name":"Pach","first_name":"János"},{"last_name":"Ziegler","first_name":"Günter","full_name":"Ziegler, Günter"}],"volume":45,"oa_version":"None","date_created":"2018-12-11T12:02:44Z","date_updated":"2021-01-12T07:42:44Z","_id":"3334","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2011","department":[{"_id":"HeEd"}],"publisher":"Springer","intvolume":" 45","publication_status":"published","status":"public","title":"Letter from the new editors-in-chief","day":"01","month":"01","scopus_import":1,"doi":"10.1007/s00454-010-9313-9","date_published":"2011-01-01T00:00:00Z","language":[{"iso":"eng"}],"citation":{"apa":"Edelsbrunner, H., Pach, J., & Ziegler, G. (2011). Letter from the new editors-in-chief. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-010-9313-9","ieee":"H. Edelsbrunner, J. Pach, and G. Ziegler, “Letter from the new editors-in-chief,” Discrete & Computational Geometry, vol. 45, no. 1. Springer, pp. 1–2, 2011.","ista":"Edelsbrunner H, Pach J, Ziegler G. 2011. Letter from the new editors-in-chief. Discrete & Computational Geometry. 45(1), 1–2.","ama":"Edelsbrunner H, Pach J, Ziegler G. Letter from the new editors-in-chief. Discrete & Computational Geometry. 2011;45(1):1-2. doi:10.1007/s00454-010-9313-9","chicago":"Edelsbrunner, Herbert, János Pach, and Günter Ziegler. “Letter from the New Editors-in-Chief.” Discrete & Computational Geometry. Springer, 2011. https://doi.org/10.1007/s00454-010-9313-9.","short":"H. Edelsbrunner, J. Pach, G. Ziegler, Discrete & Computational Geometry 45 (2011) 1–2.","mla":"Edelsbrunner, Herbert, et al. “Letter from the New Editors-in-Chief.” Discrete & Computational Geometry, vol. 45, no. 1, Springer, 2011, pp. 1–2, doi:10.1007/s00454-010-9313-9."},"publication":"Discrete & Computational Geometry","page":"1 - 2","quality_controlled":"1","article_type":"letter_note"},{"type":"conference","abstract":[{"lang":"eng","text":"In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ>0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0,1), the running time is O(C(1-δ)ΓR(n)log n), where C(1-δ)Γ is the number of homology classes with persistence at least (1-δ)Γ, n is the total number of simplices, and R(n) is the complexity of computing the rank of an n x n matrix with O(n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O(C(1-δ)Γn2.376) algorithm, a O(C(1-δ)Γn2.28) Las-Vegas algorithm, or a O(C(1-δ)Γn2+ε) Monte-Carlo algorithm for an arbitrary ε>0."}],"publist_id":"3245","_id":"3367","year":"2011","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","title":"An output sensitive algorithm for persistent homology","status":"public","department":[{"_id":"HeEd"}],"publisher":"ACM","author":[{"last_name":"Chen","first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"2939"}]},"date_updated":"2023-02-23T11:05:04Z","date_created":"2018-12-11T12:02:56Z","oa_version":"None","scopus_import":1,"day":"13","month":"06","article_processing_charge":"No","citation":{"ama":"Chen C, Kerber M. An output sensitive algorithm for persistent homology. In: ACM; 2011:207-216. doi:10.1145/1998196.1998228","ista":"Chen C, Kerber M. 2011. An output sensitive algorithm for persistent homology. SoCG: Symposium on Computational Geometry, 207–216.","apa":"Chen, C., & Kerber, M. (2011). An output sensitive algorithm for persistent homology (pp. 207–216). Presented at the SoCG: Symposium on Computational Geometry, Paris, France: ACM. https://doi.org/10.1145/1998196.1998228","ieee":"C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,” presented at the SoCG: Symposium on Computational Geometry, Paris, France, 2011, pp. 207–216.","mla":"Chen, Chao, and Michael Kerber. An Output Sensitive Algorithm for Persistent Homology. ACM, 2011, pp. 207–16, doi:10.1145/1998196.1998228.","short":"C. Chen, M. Kerber, in:, ACM, 2011, pp. 207–216.","chicago":"Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology,” 207–16. ACM, 2011. https://doi.org/10.1145/1998196.1998228."},"quality_controlled":"1","page":"207 - 216","conference":{"location":"Paris, France","start_date":"2011-06-13","end_date":"2011-06-15","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.1145/1998196.1998228","date_published":"2011-06-13T00:00:00Z","language":[{"iso":"eng"}]},{"publisher":"Szegedi Tudományegyetem","department":[{"_id":"HeEd"}],"intvolume":" 77","title":"The difference in length of curves in R^n","status":"public","publication_status":"published","acknowledgement":"Funded by Graduate Aid in Areas of National Need (GAANN) Fellowship.","_id":"3781","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2011","oa_version":"None","volume":77,"date_updated":"2021-01-12T07:52:09Z","date_created":"2018-12-11T12:05:08Z","author":[{"full_name":"Fasy, Brittany Terese","last_name":"Fasy","first_name":"Brittany Terese","id":"F65D502E-E68D-11E9-9252-C644099818F6"}],"type":"journal_article","issue":"1-2","publist_id":"2446","abstract":[{"text":"We bound the difference in length of two curves in terms of their total curvatures and the Fréchet distance. The bound is independent of the dimension of the ambient Euclidean space, it improves upon a bound by Cohen-Steiner and Edelsbrunner, and it generalizes a result by Fáry and Chakerian.","lang":"eng"}],"page":"359 - 367","quality_controlled":"1","citation":{"mla":"Fasy, Brittany Terese. “The Difference in Length of Curves in R^n.” Acta Sci. Math. (Szeged), vol. 77, no. 1–2, Szegedi Tudományegyetem, 2011, pp. 359–67.","short":"B.T. Fasy, Acta Sci. Math. (Szeged) 77 (2011) 359–367.","chicago":"Fasy, Brittany Terese. “The Difference in Length of Curves in R^n.” Acta Sci. Math. (Szeged). Szegedi Tudományegyetem, 2011.","ama":"Fasy BT. The difference in length of curves in R^n. Acta Sci Math (Szeged). 2011;77(1-2):359-367.","ista":"Fasy BT. 2011. The difference in length of curves in R^n. Acta Sci. Math. (Szeged). 77(1–2), 359–367.","apa":"Fasy, B. T. (2011). The difference in length of curves in R^n. Acta Sci. Math. (Szeged). Szegedi Tudományegyetem.","ieee":"B. T. Fasy, “The difference in length of curves in R^n,” Acta Sci. Math. (Szeged), vol. 77, no. 1–2. Szegedi Tudományegyetem, pp. 359–367, 2011."},"publication":"Acta Sci. Math. (Szeged)","language":[{"iso":"eng"}],"date_published":"2011-01-01T00:00:00Z","day":"01","month":"01"}]