[{"file_date_updated":"2020-07-14T12:45:10Z","ec_funded":1,"publist_id":"5488","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","year":"2016","acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014.","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Academic Press","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","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":"1399","relation":"dissertation_contains","status":"public"}]},"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:53:20Z","volume":287,"month":"01","oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"quality_controlled":"1","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"doi":"10.1016/j.aim.2015.10.004","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"text":"We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball.","lang":"eng"}],"_id":"1662","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["004"],"title":"Approximation and convergence of the intrinsic volume","intvolume":" 287","pubrep_id":"774","file":[{"creator":"system","file_size":248985,"content_type":"application/pdf","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:10Z","date_created":"2018-12-12T10:12:10Z","checksum":"f8869ec110c35c852ef6a37425374af7","file_id":"4928","relation":"main_file"}],"oa_version":"Published Version","scopus_import":1,"day":"10","has_accepted_license":"1","publication":"Advances in Mathematics","citation":{"ama":"Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004","ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703.","ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016.","apa":"Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press, 2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004.","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016. https://doi.org/10.1016/j.aim.2015.10.004."},"page":"674 - 703","date_published":"2016-01-10T00:00:00Z"},{"quality_controlled":"1","page":"3070 - 3078","oa":1,"main_file_link":[{"open_access":"1","url":"https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective"}],"citation":{"apa":"Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information Processing Systems.","ieee":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological data analysis-A kernel perspective,” presented at the NIPS: Neural Information Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.","ista":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological data analysis-A kernel perspective. NIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 28, 3070–3078.","ama":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems; 2015:3070-3078.","chicago":"Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer. “Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural Information Processing Systems, 2015.","short":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information Processing Systems, 2015, pp. 3070–3078.","mla":"Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective. Vol. 28, Neural Information Processing Systems, 2015, pp. 3070–78."},"language":[{"iso":"eng"}],"conference":{"name":"NIPS: Neural Information Processing Systems","end_date":"2015-12-12","location":"Montreal, Canada","start_date":"2015-12-07"},"date_published":"2015-12-01T00:00:00Z","month":"12","day":"01","status":"public","publication_status":"published","title":"Statistical topological data analysis-A kernel perspective","publisher":"Neural Information Processing Systems","department":[{"_id":"HeEd"}],"intvolume":" 28","_id":"1424","acknowledgement":"This work was partially supported by the Austrian Science FUnd, project no. KLI 00012.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","date_updated":"2021-01-12T06:50:38Z","date_created":"2018-12-11T11:51:56Z","volume":28,"oa_version":"Submitted Version","author":[{"last_name":"Kwitt","first_name":"Roland","full_name":"Kwitt, Roland"},{"full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber"},{"first_name":"Marc","last_name":"Niethammer","full_name":"Niethammer, Marc"},{"full_name":"Lin, Weili","first_name":"Weili","last_name":"Lin"},{"full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"}],"alternative_title":["Advances in Neural Information Processing Systems"],"type":"conference","abstract":[{"text":"We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data.","lang":"eng"}],"publist_id":"5782"},{"author":[{"last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan"},{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich"},{"first_name":"Roland","last_name":"Kwitt","full_name":"Kwitt, Roland"}],"date_created":"2018-12-11T11:52:17Z","date_updated":"2021-01-12T06:51:03Z","oa_version":"Preprint","_id":"1483","year":"2015","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"A stable multi-scale kernel for topological machine learning","publication_status":"published","status":"public","publisher":"IEEE","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes."}],"publist_id":"5709","type":"conference","conference":{"location":"Boston, MA, USA","start_date":"2015-06-07","end_date":"2015-06-12","name":"CVPR: Computer Vision and Pattern Recognition"},"doi":"10.1109/CVPR.2015.7299106","date_published":"2015-10-14T00:00:00Z","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1412.6821"}],"citation":{"chicago":"Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106.","mla":"Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106.","short":"J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.","ista":"Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.","apa":"Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106","ieee":"J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.","ama":"Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106"},"page":"4741 - 4748","day":"14","month":"10","publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"scopus_import":1},{"scopus_import":1,"month":"08","day":"01","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"page":"128-135","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1505.03402"}],"oa":1,"citation":{"mla":"Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” Proceedings of the 27th Canadian Conference on Computational Geometry, vol. 2015–August, Queen’s University, 2015, pp. 128–35.","short":"H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.","chicago":"Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed Disk Packing.” In Proceedings of the 27th Canadian Conference on Computational Geometry, 2015–August:128–35. Queen’s University, 2015.","ama":"Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: Proceedings of the 27th Canadian Conference on Computational Geometry. Vol 2015-August. Queen’s University; 2015:128-135.","ista":"Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry vol. 2015–August, 128–135.","ieee":"H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in Proceedings of the 27th Canadian Conference on Computational Geometry, Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.","apa":"Edelsbrunner, H., Iglesias Ham, M., & Kurlin, V. (2015). Relaxed disk packing. In Proceedings of the 27th Canadian Conference on Computational Geometry (Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University."},"publication":"Proceedings of the 27th Canadian Conference on Computational Geometry","language":[{"iso":"eng"}],"date_published":"2015-08-01T00:00:00Z","conference":{"name":"CCCG: Canadian Conference on Computational Geometry","end_date":"2015-08-12","location":"Ontario, Canada","start_date":"2015-08-10"},"type":"conference","publist_id":"5684","ec_funded":1,"abstract":[{"lang":"eng","text":"Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations. "}],"publisher":"Queen's University","department":[{"_id":"HeEd"}],"publication_status":"published","status":"public","title":"Relaxed disk packing","_id":"1495","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2015","volume":"2015-August","oa_version":"Submitted Version","date_updated":"2021-01-12T06:51:09Z","date_created":"2018-12-11T11:52:21Z","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel"},{"last_name":"Kurlin","first_name":"Vitaliy","full_name":"Kurlin, Vitaliy"}]},{"scopus_import":1,"has_accepted_license":"1","day":"11","page":"842 - 856","citation":{"ista":"Franek P, Krcál M. 2015. On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands, 2015, vol. 34, pp. 842–856.","apa":"Franek, P., & Krcál, M. (2015). On computability and triviality of well groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SOCG.2015.842","ama":"Franek P, Krcál M. On computability and triviality of well groups. In: Vol 34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:10.4230/LIPIcs.SOCG.2015.842","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. https://doi.org/10.4230/LIPIcs.SOCG.2015.842.","mla":"Franek, Peter, and Marek Krcál. On Computability and Triviality of Well Groups. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:10.4230/LIPIcs.SOCG.2015.842.","short":"P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–856."},"date_published":"2015-06-11T00:00:00Z","alternative_title":["LIPIcs"],"type":"conference","abstract":[{"lang":"eng","text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f from K to R^n on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within L_infty distance r from f for a given r > 0. The main drawback of the approach is that the computability of well groups was shown only when dim K = n or n = 1. Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f, f' from K to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status. "}],"intvolume":" 34","title":"On computability and triviality of well groups","status":"public","ddc":["510"],"_id":"1510","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"creator":"system","file_size":623563,"content_type":"application/pdf","access_level":"open_access","file_name":"IST-2016-503-v1+1_32.pdf","checksum":"49eb5021caafaabe5356c65b9c5f8c9c","date_updated":"2020-07-14T12:44:59Z","date_created":"2018-12-12T10:13:19Z","file_id":"5001","relation":"main_file"}],"pubrep_id":"503","month":"06","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"quality_controlled":"1","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"},"language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SOCG.2015.842","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2015-06-25","start_date":"2015-06-22","location":"Eindhoven, Netherlands"},"ec_funded":1,"publist_id":"5667","file_date_updated":"2020-07-14T12:44:59Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publication_status":"published","year":"2015","volume":34,"date_updated":"2023-02-21T17:02:57Z","date_created":"2018-12-11T11:52:26Z","related_material":{"record":[{"id":"1408","status":"public","relation":"later_version"}]},"author":[{"full_name":"Franek, Peter","last_name":"Franek","first_name":"Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek","full_name":"Krcál, Marek"}]},{"publist_id":"5640","edition":"1","author":[{"last_name":"Zobel","first_name":"Valentin","full_name":"Zobel, Valentin"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan"},{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"}],"volume":40,"date_created":"2018-12-11T11:52:33Z","date_updated":"2022-06-10T09:50:14Z","year":"2015","department":[{"_id":"HeEd"}],"publisher":"Springer","editor":[{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"full_name":"Schultz, Thomas","first_name":"Thomas","last_name":"Schultz"}],"publication_status":"published","publication_identifier":{"isbn":["978-3-319-15089-5"]},"month":"01","doi":"10.1007/978-3-319-15090-1_13","language":[{"iso":"eng"}],"quality_controlled":"1","abstract":[{"lang":"eng","text":"The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece."}],"type":"book_chapter","alternative_title":["Mathematics and Visualization"],"oa_version":"None","_id":"1531","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 40","title":"Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature","status":"public","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2015-01-01T00:00:00Z","citation":{"ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267.","apa":"Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13","ista":"Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization, vol. 40, 257–267.","ama":"Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40. 1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer, 2015, pp. 257–267.","mla":"Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13."},"publication":"Visualization and Processing of Higher Order Descriptors for Multi-Valued Data","page":"257 - 267"},{"scopus_import":1,"article_processing_charge":"No","day":"01","citation":{"chicago":"Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934.","mla":"Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934.","short":"D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems 14 (2015) 980–1017.","ista":"Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017.","ieee":"D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.","apa":"Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934","ama":"Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017. doi:10.1137/140993934"},"publication":"SIAM Journal on Applied Dynamical Systems","page":"980 - 1017","article_type":"original","date_published":"2015-01-01T00:00:00Z","type":"journal_article","issue":"2","abstract":[{"lang":"eng","text":"We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each subpopulation, both forward and backward bifurcations can occur. This implies that for disconnected regions the two-patch system may admit several steady states. We consider traveling between the regions and investigate the impact of spatial dispersal of individuals on the model dynamics. We establish conditions for the existence of multiple nontrivial steady states in the system, and we study the structure of the equilibria. The mathematical analysis reveals an unusually rich dynamical behavior, not normally found in the simple epidemic models. In addition to the disease-free equilibrium, eight endemic equilibria emerge from backward transcritical and saddle-node bifurcation points, forming an interesting bifurcation diagram. Stability of steady states, their bifurcations, and the global dynamics are investigated with analytical tools, numerical simulations, and rigorous set-oriented numerical computations."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1555","intvolume":" 14","title":"Rich bifurcation structure in a two patch vaccination model","status":"public","ddc":["510"],"oa_version":"Published Version","publication_identifier":{"eissn":["1536-0040"]},"month":"01","main_file_link":[{"open_access":"1","url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf"}],"oa":1,"project":[{"name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7","grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","doi":"10.1137/140993934","language":[{"iso":"eng"}],"publist_id":"5616","ec_funded":1,"year":"2015","acknowledgement":"Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559 in the framework of the EPIDELAY project.","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Knipl, Diána","first_name":"Diána","last_name":"Knipl"},{"first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"},{"first_name":"Gergely","last_name":"Röst","full_name":"Röst, Gergely"}],"volume":14,"date_created":"2018-12-11T11:52:42Z","date_updated":"2021-01-12T06:51:34Z"},{"day":"05","month":"02","scopus_import":1,"language":[{"iso":"eng"}],"conference":{"name":"SYNASC: Symbolic and Numeric Algorithms for Scientific Computing","end_date":"2014-09-25","location":"Timisoara, Romania","start_date":"2014-09-22"},"doi":"10.1109/SYNASC.2014.81","date_published":"2015-02-05T00:00:00Z","quality_controlled":"1","page":"7034731","publication":"Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","citation":{"ieee":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 2015, p. 7034731.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D. (2015). The classification of endoscopy images with persistent homology. In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification of endoscopy images with persistent homology. Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, 7034731.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification of endoscopy images with persistent homology. In: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE; 2015:7034731. doi:10.1109/SYNASC.2014.81","chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731.","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81."},"abstract":[{"lang":"eng","text":"Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI) magnifying endoscopy (ME) images of the stomach, we combine methods from image processing, computational topology, and machine learning to classify patterns into normal, tubular, vessel. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions."}],"publist_id":"5603","type":"conference","date_updated":"2023-02-21T16:57:29Z","date_created":"2018-12-11T11:52:46Z","oa_version":"None","author":[{"full_name":"Dunaeva, Olga","last_name":"Dunaeva","first_name":"Olga"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Lukyanov","first_name":"Anton","full_name":"Lukyanov, Anton"},{"first_name":"Michael","last_name":"Machin","full_name":"Machin, Michael"},{"first_name":"Daria","last_name":"Malkova","full_name":"Malkova, Daria"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"1289"}]},"status":"public","publication_status":"published","title":"The classification of endoscopy images with persistent homology","department":[{"_id":"HeEd"}],"publisher":"IEEE","year":"2015","_id":"1568","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","acknowledgement":"This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research."},{"_id":"1567","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","year":"2015","intvolume":" 9411","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"status":"public","publication_status":"published","title":"Shape, homology, persistence, and stability","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"volume":9411,"oa_version":"None","date_updated":"2022-01-28T08:25:00Z","date_created":"2018-12-11T11:52:46Z","type":"conference","alternative_title":["LNCS"],"publist_id":"5604","abstract":[{"lang":"eng","text":"My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations."}],"citation":{"apa":"Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer Nature.","ieee":"H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd International Symposium, Los Angeles, CA, United States, 2015, vol. 9411.","ista":"Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.","ama":"Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International Symposium. Vol 9411. Springer Nature; 2015.","chicago":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In 23rd International Symposium, Vol. 9411. Springer Nature, 2015.","short":"H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015.","mla":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd International Symposium, vol. 9411, Springer Nature, 2015."},"publication":"23rd International Symposium","quality_controlled":"1","date_published":"2015-01-01T00:00:00Z","conference":{"start_date":"2015-09-24","location":"Los Angeles, CA, United States","end_date":"2015-09-26","name":"GD: Graph Drawing and Network Visualization"},"language":[{"iso":"eng"}],"scopus_import":"1","article_processing_charge":"No","day":"01","month":"01"},{"type":"journal_article","abstract":[{"text":"For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\\tt http://www.pawelpilarczyk.com/combtop/}.","lang":"eng"}],"issue":"1","publist_id":"5608","publication_status":"published","title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","status":"public","department":[{"_id":"HeEd"}],"intvolume":" 45","publisher":"Juliusz Schauder Center for Nonlinear Studies","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1563","year":"2015","date_created":"2018-12-11T11:52:44Z","date_updated":"2021-01-12T06:51:37Z","volume":45,"oa_version":"None","author":[{"first_name":"Grzegorz","last_name":"Graff","full_name":"Graff, Grzegorz"},{"first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"}],"scopus_import":1,"month":"03","day":"01","quality_controlled":"1","page":"273 - 286","publication":"Topological Methods in Nonlinear Analysis","citation":{"short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286.","mla":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014.","chicago":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014.","ama":"Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014","apa":"Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014","ieee":"G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015.","ista":"Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286."},"language":[{"iso":"eng"}],"doi":"10.12775/TMNA.2015.014","date_published":"2015-03-01T00:00:00Z"},{"scopus_import":1,"month":"08","day":"01","page":"507 - 519","quality_controlled":"1","citation":{"mla":"Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:10.1016/j.comgeo.2015.04.001.","short":"T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.","chicago":"Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001.","ama":"Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001","ista":"Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.","ieee":"T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier, pp. 507–519, 2015.","apa":"Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001"},"publication":"Computational Geometry","language":[{"iso":"eng"}],"date_published":"2015-08-01T00:00:00Z","doi":"10.1016/j.comgeo.2015.04.001","type":"journal_article","issue":"7","publist_id":"5593","abstract":[{"text":"We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations.","lang":"eng"}],"publisher":"Elsevier","intvolume":" 48","department":[{"_id":"HeEd"}],"publication_status":"published","title":"Triangulations from topologically correct digital Voronoi diagrams","status":"public","acknowledgement":"The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n","_id":"1578","year":"2015","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","volume":48,"date_created":"2018-12-11T11:52:49Z","date_updated":"2021-01-12T06:51:43Z","author":[{"first_name":"Thanhtung","last_name":"Cao","full_name":"Cao, Thanhtung"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Tan","first_name":"Tiowseng","full_name":"Tan, Tiowseng"}]},{"has_accepted_license":"1","day":"01","scopus_import":1,"date_published":"2015-07-01T00:00:00Z","citation":{"chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.","mla":"Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004"},"publication":"Computational Geometry: Theory and Applications","page":"429 - 442","issue":"5","abstract":[{"lang":"eng","text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights."}],"type":"journal_article","pubrep_id":"475","file":[{"creator":"system","file_size":508379,"content_type":"application/pdf","access_level":"open_access","file_name":"IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf","checksum":"5b33719a86f7f4c8e5dc62c1b6893f49","date_created":"2018-12-12T10:17:36Z","date_updated":"2020-07-14T12:45:03Z","file_id":"5292","relation":"main_file"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1584","intvolume":" 48","status":"public","title":"Reprint of: Weighted straight skeletons in the plane","ddc":["000"],"month":"07","doi":"10.1016/j.comgeo.2015.01.004","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","publist_id":"5587","file_date_updated":"2020-07-14T12:45:03Z","related_material":{"record":[{"id":"1582","relation":"other","status":"public"}]},"author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"last_name":"Huber","first_name":"Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","full_name":"Huber, Stefan"},{"full_name":"Kaaser, Dominik","first_name":"Dominik","last_name":"Kaaser"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"volume":48,"date_created":"2018-12-11T11:52:51Z","date_updated":"2023-02-23T10:05:22Z","year":"2015","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published"},{"has_accepted_license":"1","day":"01","scopus_import":1,"date_published":"2015-02-01T00:00:00Z","citation":{"short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.","mla":"Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:10.1016/j.comgeo.2014.08.006.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133. doi:10.1016/j.comgeo.2014.08.006","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133."},"publication":"Computational Geometry: Theory and Applications","page":"120 - 133","issue":"2","abstract":[{"text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.","lang":"eng"}],"type":"journal_article","pubrep_id":"474","file":[{"file_id":"5215","relation":"main_file","checksum":"c1ef67f6ec925e12f73a96b8fe285ab4","date_updated":"2020-07-14T12:45:02Z","date_created":"2018-12-12T10:16:28Z","access_level":"open_access","file_name":"IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf","creator":"system","content_type":"application/pdf","file_size":505987}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1582","intvolume":" 48","status":"public","title":"Weighted straight skeletons in the plane","ddc":["000"],"month":"02","doi":"10.1016/j.comgeo.2014.08.006","language":[{"iso":"eng"}],"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"},"oa":1,"quality_controlled":"1","publist_id":"5589","file_date_updated":"2020-07-14T12:45:02Z","related_material":{"record":[{"id":"1584","status":"public","relation":"other"}]},"author":[{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"last_name":"Kaaser","first_name":"Dominik","full_name":"Kaaser, Dominik"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"volume":48,"date_created":"2018-12-11T11:52:51Z","date_updated":"2023-02-23T10:05:27Z","year":"2015","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published"},{"page":"243 - 247","publication":"Information Processing Letters","citation":{"ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” Information Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015.","mla":"Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021."},"date_published":"2015-02-01T00:00:00Z","scopus_import":1,"day":"01","has_accepted_license":"1","status":"public","ddc":["000"],"title":"A simple algorithm for computing positively weighted straight skeletons of monotone polygons","intvolume":" 115","_id":"1583","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"file_size":270137,"content_type":"application/pdf","creator":"system","file_name":"IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf","access_level":"open_access","date_created":"2018-12-12T10:18:45Z","date_updated":"2020-07-14T12:45:03Z","checksum":"2779a648610c9b5c86d0b51a62816d23","relation":"main_file","file_id":"5367"}],"pubrep_id":"473","type":"journal_article","abstract":[{"lang":"eng","text":"We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon."}],"issue":"2","quality_controlled":"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"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.ipl.2014.09.021","month":"02","publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"year":"2015","date_updated":"2021-01-12T06:51:45Z","date_created":"2018-12-11T11:52:51Z","volume":115,"author":[{"full_name":"Biedl, Therese","last_name":"Biedl","first_name":"Therese"},{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"last_name":"Kaaser","first_name":"Dominik","full_name":"Kaaser, Dominik"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"file_date_updated":"2020-07-14T12:45:03Z","publist_id":"5588"},{"type":"book_chapter","alternative_title":["LNCS"],"abstract":[{"lang":"eng","text":"The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed."}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"1590","status":"public","title":"Representing directed trees as straight skeletons","intvolume":" 9411","oa_version":"Preprint","scopus_import":"1","day":"27","article_processing_charge":"No","publication":"Graph Drawing and Network Visualization","citation":{"mla":"Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:10.1007/978-3-319-27261-0_28.","short":"O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.","chicago":"Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28.","ama":"Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28","ista":"Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.","ieee":"O. Aichholzer et al., “Representing directed trees as straight skeletons,” in Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–347.","apa":"Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., & Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28"},"page":"335 - 347","date_published":"2015-11-27T00:00:00Z","publist_id":"5581","year":"2015","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"full_name":"Hackl, Thomas","first_name":"Thomas","last_name":"Hackl"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"date_created":"2018-12-11T11:52:54Z","date_updated":"2022-01-28T09:10:37Z","volume":9411,"month":"11","publication_identifier":{"isbn":["978-3-319-27260-3"],"eisbn":["978-3-319-27261-0"]},"main_file_link":[{"url":"http://arxiv.org/abs/1508.01076","open_access":"1"}],"oa":1,"quality_controlled":"1","conference":{"location":"Los Angeles, CA, United States","start_date":"2015-09-24","end_date":"2015-09-26","name":"GD: International Symposium on Graph Drawing"},"doi":"10.1007/978-3-319-27261-0_28","language":[{"iso":"eng"}]},{"abstract":[{"text":"We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α > 0, it holds that each function g: K → ℝn such that ||g - f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K > 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings.","lang":"eng"}],"publist_id":"5466","issue":"4","article_number":"26","type":"journal_article","author":[{"first_name":"Peter","last_name":"Franek","full_name":"Franek, Peter"},{"last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek"}],"date_updated":"2021-01-12T06:52:30Z","date_created":"2018-12-11T11:53:27Z","volume":62,"oa_version":"Preprint","_id":"1682","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","title":"Robust satisfiability of systems of equations","status":"public","publication_status":"published","intvolume":" 62","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"ACM","month":"08","day":"01","scopus_import":1,"doi":"10.1145/2751524","date_published":"2015-08-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"Journal of the ACM","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.0858"}],"citation":{"ista":"Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26.","apa":"Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations. Journal of the ACM. ACM. https://doi.org/10.1145/2751524","ieee":"P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal of the ACM, vol. 62, no. 4. ACM, 2015.","ama":"Franek P, Krcál M. Robust satisfiability of systems of equations. Journal of the ACM. 2015;62(4). doi:10.1145/2751524","chicago":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524.","mla":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM, vol. 62, no. 4, 26, ACM, 2015, doi:10.1145/2751524.","short":"P. Franek, M. Krcál, Journal of the ACM 62 (2015)."},"quality_controlled":"1"},{"type":"journal_article","abstract":[{"text":"We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞.","lang":"eng"}],"issue":"4","_id":"1710","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Minimal resistance of curves under the single impact assumption","status":"public","intvolume":" 47","oa_version":"Preprint","scopus_import":1,"day":"14","publication":"Society for Industrial and Applied Mathematics","citation":{"short":"A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47 (2015) 2754–2769.","mla":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics, vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843.","chicago":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics. SIAM, 2015. https://doi.org/10.1137/140993843.","ama":"Akopyan A, Plakhov A. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769. doi:10.1137/140993843","apa":"Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. SIAM. https://doi.org/10.1137/140993843","ieee":"A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single impact assumption,” Society for Industrial and Applied Mathematics, vol. 47, no. 4. SIAM, pp. 2754–2769, 2015.","ista":"Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769."},"page":"2754 - 2769","date_published":"2015-07-14T00:00:00Z","publist_id":"5423","ec_funded":1,"year":"2015","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"SIAM","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"first_name":"Alexander","last_name":"Plakhov","full_name":"Plakhov, Alexander"}],"date_created":"2018-12-11T11:53:36Z","date_updated":"2021-01-12T06:52:41Z","volume":47,"month":"07","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1410.3736"}],"oa":1,"quality_controlled":"1","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"doi":"10.1137/140993843","language":[{"iso":"eng"}]},{"article_processing_charge":"No","day":"01","scopus_import":1,"date_published":"2015-07-01T00:00:00Z","page":"163 - 167","citation":{"mla":"Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics, vol. 160, no. 1, Springer, 2015, pp. 163–67, doi:10.1007/s10955-015-1238-5.","short":"A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167.","chicago":"Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics. Springer, 2015. https://doi.org/10.1007/s10955-015-1238-5.","ama":"Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination process. Journal of Statistical Physics. 2015;160(1):163-167. doi:10.1007/s10955-015-1238-5","ista":"Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination process. Journal of Statistical Physics. 160(1), 163–167.","ieee":"A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination process,” Journal of Statistical Physics, vol. 160, no. 1. Springer, pp. 163–167, 2015.","apa":"Akopyan, A., Pirogov, S., & Rybko, A. (2015). Invariant measures of genetic recombination process. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-015-1238-5"},"publication":"Journal of Statistical Physics","issue":"1","abstract":[{"lang":"eng","text":"We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory."}],"type":"journal_article","oa_version":"Preprint","intvolume":" 160","status":"public","title":"Invariant measures of genetic recombination process","_id":"1828","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"07","language":[{"iso":"eng"}],"doi":"10.1007/s10955-015-1238-5","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"quality_controlled":"1","main_file_link":[{"url":"arxiv.org/abs/1406.5313","open_access":"1"}],"oa":1,"ec_funded":1,"publist_id":"5276","volume":160,"date_updated":"2021-01-12T06:53:28Z","date_created":"2018-12-11T11:54:14Z","author":[{"last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"last_name":"Pirogov","first_name":"Sergey","full_name":"Pirogov, Sergey"},{"full_name":"Rybko, Aleksandr","first_name":"Aleksandr","last_name":"Rybko"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2015"},{"quality_controlled":"1","page":"535 - 541","publication":"Physics Letters, Section A","citation":{"chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A. Elsevier, 2015. https://doi.org/10.1016/j.physleta.2014.12.010.","short":"F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A, vol. 379, no. 6, Elsevier, 2015, pp. 535–41, doi:10.1016/j.physleta.2014.12.010.","ieee":"F. Pausinger and S. Steinerberger, “On the distribution of local extrema in quantum chaos,” Physics Letters, Section A, vol. 379, no. 6. Elsevier, pp. 535–541, 2015.","apa":"Pausinger, F., & Steinerberger, S. (2015). On the distribution of local extrema in quantum chaos. Physics Letters, Section A. Elsevier. https://doi.org/10.1016/j.physleta.2014.12.010","ista":"Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541.","ama":"Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 2015;379(6):535-541. doi:10.1016/j.physleta.2014.12.010"},"language":[{"iso":"eng"}],"doi":"10.1016/j.physleta.2014.12.010","date_published":"2015-03-06T00:00:00Z","scopus_import":1,"day":"06","month":"03","status":"public","publication_status":"published","title":"On the distribution of local extrema in quantum chaos","intvolume":" 379","publisher":"Elsevier","department":[{"_id":"HeEd"}],"year":"2015","_id":"1938","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"F.P. was supported by the Graduate School of IST Austria. S.S. was partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm. ","date_updated":"2021-01-12T06:54:12Z","date_created":"2018-12-11T11:54:49Z","volume":379,"oa_version":"None","author":[{"last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian"},{"full_name":"Steinerberger, Stefan","last_name":"Steinerberger","first_name":"Stefan"}],"type":"journal_article","abstract":[{"lang":"eng","text":"We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2."}],"publist_id":"5152","issue":"6"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2035","title":"The persistent homology of a self-map","status":"public","ddc":["000"],"intvolume":" 15","pubrep_id":"486","oa_version":"Published Version","file":[{"file_size":1317546,"content_type":"application/pdf","creator":"system","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","access_level":"open_access","date_created":"2018-12-12T10:08:10Z","date_updated":"2020-07-14T12:45:26Z","checksum":"3566f3a8b0c1bc550e62914a88c584ff","relation":"main_file","file_id":"4670"}],"type":"journal_article","abstract":[{"text":"Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.\r\n","lang":"eng"}],"issue":"5","publication":"Foundations of Computational Mathematics","citation":{"short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:10.1007/s10208-014-9223-y.","chicago":"Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics. Springer, 2015. https://doi.org/10.1007/s10208-014-9223-y.","ama":"Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y","ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5. Springer, pp. 1213–1244, 2015.","apa":"Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244."},"page":"1213 - 1244","date_published":"2015-10-01T00:00:00Z","scopus_import":1,"day":"01","has_accepted_license":"1","year":"2015","acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the Polish National Science Center under Grant No. N201 419639.","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","first_name":"Grzegorz"},{"full_name":"Mrozek, Marian","first_name":"Marian","last_name":"Mrozek"}],"date_updated":"2021-01-12T06:54:53Z","date_created":"2018-12-11T11:55:20Z","volume":15,"file_date_updated":"2020-07-14T12:45:26Z","ec_funded":1,"publist_id":"5022","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"},"oa":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"doi":"10.1007/s10208-014-9223-y","language":[{"iso":"eng"}],"month":"10"},{"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"quality_controlled":"1","doi":"10.1016/j.comgeo.2014.08.010","language":[{"iso":"eng"}],"month":"06","year":"2015","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","related_material":{"record":[{"id":"2812","status":"public","relation":"earlier_version"}]},"author":[{"last_name":"Attali","first_name":"Dominique","full_name":"Attali, Dominique"},{"first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich"},{"full_name":"Devillers, Olivier","first_name":"Olivier","last_name":"Devillers"},{"first_name":"Marc","last_name":"Glisse","full_name":"Glisse, Marc"},{"full_name":"Lieutier, André","first_name":"André","last_name":"Lieutier"}],"volume":48,"date_created":"2018-12-11T11:54:06Z","date_updated":"2023-02-23T10:59:19Z","publist_id":"5305","ec_funded":1,"citation":{"ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” Computational Geometry: Theory and Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015). Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010","ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 48(8), 606–621.","ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010","chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier, 2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010."},"publication":"Computational Geometry: Theory and Applications","page":"606 - 621","date_published":"2015-06-03T00:00:00Z","scopus_import":1,"day":"03","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1805","intvolume":" 48","title":"Homological reconstruction and simplification in R3","status":"public","oa_version":"None","type":"journal_article","issue":"8","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 double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck 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."}]},{"volume":10,"date_updated":"2023-02-23T14:06:33Z","date_created":"2018-12-11T11:54:02Z","related_material":{"record":[{"status":"public","relation":"research_data","id":"9737"}]},"author":[{"full_name":"Symonova, Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","first_name":"Olga","last_name":"Symonova"},{"first_name":"Christopher","last_name":"Topp","full_name":"Topp, Christopher"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"department":[{"_id":"MaJö"},{"_id":"HeEd"}],"publisher":"Public Library of Science","publication_status":"published","year":"2015","publist_id":"5318","file_date_updated":"2020-07-14T12:45:16Z","article_number":"e0127657","language":[{"iso":"eng"}],"doi":"10.1371/journal.pone.0127657","quality_controlled":"1","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"},"month":"06","oa_version":"Published Version","file":[{"file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf","access_level":"open_access","creator":"system","content_type":"application/pdf","file_size":1850825,"file_id":"5150","relation":"main_file","date_created":"2018-12-12T10:15:30Z","date_updated":"2020-07-14T12:45:16Z","checksum":"d20f26461ca575276ad3ed9ce4bfc787"}],"pubrep_id":"454","intvolume":" 10","status":"public","title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1793","issue":"6","abstract":[{"lang":"eng","text":"We present a software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes. It aligns the shapes with each other, constructs a geometric graph representation together with the function that records the time of growth, and organizes the branches into a hierarchy that reflects the order of creation. The software includes the automatic computation of structural and dynamic traits for each root in the system enabling the quantification of growth on fine-scale. These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth."}],"type":"journal_article","date_published":"2015-06-01T00:00:00Z","citation":{"chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.","short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","mla":"Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657, Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.","apa":"Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots,” PLoS One, vol. 10, no. 6. Public Library of Science, 2015.","ista":"Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.","ama":"Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6). doi:10.1371/journal.pone.0127657"},"publication":"PLoS One","has_accepted_license":"1","day":"01","scopus_import":1},{"article_processing_charge":"No","month":"06","day":"01","citation":{"chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.s001.","short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","mla":"Symonova, Olga, et al. Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2. Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.s001.","apa":"Symonova, O., Topp, C., & Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657.s001","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots for the maize root shown in fig 2.” Public Library of Science, 2015.","ista":"Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots for the maize root shown in fig 2, Public Library of Science, 10.1371/journal.pone.0127657.s001.","ama":"Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001"},"doi":"10.1371/journal.pone.0127657.s001","date_published":"2015-06-01T00:00:00Z","type":"research_data_reference","_id":"9737","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","year":"2015","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"publisher":"Public Library of Science","status":"public","title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","related_material":{"record":[{"status":"public","relation":"used_in_publication","id":"1793"}]},"author":[{"id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","last_name":"Symonova","first_name":"Olga","full_name":"Symonova, Olga"},{"last_name":"Topp","first_name":"Christopher","full_name":"Topp, Christopher"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"oa_version":"Published Version","date_updated":"2023-02-23T10:14:42Z","date_created":"2021-07-28T06:20:13Z"},{"publication":"Journal of Complexity","citation":{"ama":"Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002","apa":"Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002","ieee":"F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797, 2015.","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.","mla":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002.","chicago":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002."},"quality_controlled":"1","page":"773 - 797","date_published":"2015-12-01T00:00:00Z","doi":"10.1016/j.jco.2015.06.002","language":[{"iso":"eng"}],"scopus_import":1,"day":"01","month":"12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1792","year":"2015","acknowledgement":"F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation.","title":"A Koksma-Hlawka inequality for general discrepancy systems","publication_status":"published","status":"public","intvolume":" 31","department":[{"_id":"HeEd"}],"publisher":"Academic Press","author":[{"full_name":"Pausinger, Florian","last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Svane, Anne","first_name":"Anne","last_name":"Svane"}],"related_material":{"record":[{"id":"1399","relation":"dissertation_contains","status":"public"}]},"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:54:02Z","oa_version":"None","volume":31,"type":"journal_article","abstract":[{"lang":"eng","text":"Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology."}],"issue":"6","publist_id":"5320"},{"type":"dissertation","alternative_title":["ISTA Thesis"],"abstract":[{"text":"This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold.","lang":"eng"}],"publist_id":"5808","year":"2015","_id":"1399","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_status":"published","status":"public","title":"On the approximation of intrinsic volumes","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"}],"author":[{"full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"1662"},{"status":"public","relation":"part_of_dissertation","id":"1792"},{"relation":"part_of_dissertation","status":"public","id":"2255"}]},"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:51:48Z","oa_version":"None","day":"01","month":"06","publication_identifier":{"issn":["2663-337X"]},"article_processing_charge":"No","citation":{"ama":"Pausinger F. On the approximation of intrinsic volumes. 2015.","ista":"Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","ieee":"F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015.","apa":"Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","mla":"Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute of Science and Technology Austria, 2015.","short":"F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015.","chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015."},"page":"144","date_published":"2015-06-01T00:00:00Z","supervisor":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"degree_awarded":"PhD","language":[{"iso":"eng"}]},{"publication_status":"published","publisher":"Springer","editor":[{"last_name":"Bremer","first_name":"Peer-Timo","full_name":"Bremer, Peer-Timo"},{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"},{"first_name":"Ronald","last_name":"Peikert","full_name":"Peikert, Ronald"}],"department":[{"_id":"HeEd"}],"acknowledgement":"First, we thank the reviewers of this paper for their ideas and critical comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions. This research is supported by the European Commission under the TOPOSYS project FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the European Science Foundation under the ACAT Research Network Program.","year":"2014","date_created":"2022-03-21T07:11:23Z","date_updated":"2022-06-21T12:01:47Z","volume":1,"author":[{"last_name":"Kasten","first_name":"Jens","full_name":"Kasten, Jens"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"},{"first_name":"Wieland","last_name":"Reich","full_name":"Reich, Wieland"},{"full_name":"Scheuermann, Gerik","first_name":"Gerik","last_name":"Scheuermann"}],"place":"Cham","ec_funded":1,"quality_controlled":"1","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-04099-8_4","month":"03","publication_identifier":{"isbn":["9783319040981"],"eissn":["2197-666X"],"issn":["1612-3786"],"eisbn":["9783319040998"]},"status":"public","title":"Toward the extraction of saddle periodic orbits","intvolume":" 1","_id":"10893","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","type":"book_chapter","abstract":[{"lang":"eng","text":"Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data."}],"page":"55-69","publication":"Topological Methods in Data Analysis and Visualization III ","citation":{"chicago":"Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward the Extraction of Saddle Periodic Orbits.” In Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_4.","short":"J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III , Springer, Cham, 2014, pp. 55–69.","mla":"Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4.","ieee":"J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization III , vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer, 2014, pp. 55–69.","apa":"Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4","ista":"Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III . vol. 1, 55–69.","ama":"Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4"},"date_published":"2014-03-19T00:00:00Z","series_title":"Mathematics and Visualization","scopus_import":"1","day":"19","article_processing_charge":"No"},{"type":"journal_article","abstract":[{"lang":"eng","text":"Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques."}],"issue":"1","title":"Topology-preserving watermarking of vector graphics","ddc":["000"],"status":"public","intvolume":" 24","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1816","oa_version":"Published Version","file":[{"creator":"system","content_type":"application/pdf","file_size":991734,"file_name":"IST-2016-443-v1+1_S0218195914500034.pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:17Z","date_created":"2018-12-12T10:08:43Z","checksum":"be45c133ab4d43351260e21beaa8f4b1","file_id":"4704","relation":"main_file"}],"pubrep_id":"443","scopus_import":1,"day":"16","has_accepted_license":"1","page":"61 - 86","publication":"International Journal of Computational Geometry and Applications","citation":{"chicago":"Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2014. https://doi.org/10.1142/S0218195914500034.","mla":"Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications, vol. 24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:10.1142/S0218195914500034.","short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86.","ista":"Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 24(1), 61–86.","apa":"Huber, S., Held, M., Meerwald, P., & Kwitt, R. (2014). Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195914500034","ieee":"S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking of vector graphics,” International Journal of Computational Geometry and Applications, vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.","ama":"Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 2014;24(1):61-86. doi:10.1142/S0218195914500034"},"date_published":"2014-03-16T00:00:00Z","file_date_updated":"2020-07-14T12:45:17Z","publist_id":"5290","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"World Scientific Publishing","year":"2014","acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","date_updated":"2021-01-12T06:53:23Z","date_created":"2018-12-11T11:54:10Z","volume":24,"author":[{"full_name":"Huber, Stefan","last_name":"Huber","first_name":"Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"last_name":"Meerwald","first_name":"Peter","full_name":"Meerwald, Peter"},{"last_name":"Kwitt","first_name":"Roland","full_name":"Kwitt, Roland"}],"month":"03","quality_controlled":"1","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"},"language":[{"iso":"eng"}],"doi":"10.1142/S0218195914500034"},{"type":"journal_article","abstract":[{"lang":"eng","text":"We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an (Formula presented.) upper bound on the Ramsey number of a path with n ordered vertices."}],"publist_id":"5260","issue":"1","publication_status":"published","status":"public","title":"On the geometric ramsey number of outerplanar graphs","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"intvolume":" 53","publisher":"Springer","acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","_id":"1842","year":"2014","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:54:18Z","date_updated":"2021-01-12T06:53:33Z","volume":53,"oa_version":"Submitted Version","author":[{"full_name":"Cibulka, Josef","last_name":"Cibulka","first_name":"Josef"},{"last_name":"Gao","first_name":"Pu","full_name":"Gao, Pu"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek","full_name":"Krcál, Marek"},{"full_name":"Valla, Tomáš","first_name":"Tomáš","last_name":"Valla"},{"full_name":"Valtr, Pavel","first_name":"Pavel","last_name":"Valtr"}],"scopus_import":1,"day":"14","month":"11","page":"64 - 79","publication":"Discrete & Computational Geometry","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.7004"}],"citation":{"mla":"Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational Geometry, vol. 53, no. 1, Springer, 2014, pp. 64–79, doi:10.1007/s00454-014-9646-x.","short":"J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational Geometry 53 (2014) 64–79.","chicago":"Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational Geometry. Springer, 2014. https://doi.org/10.1007/s00454-014-9646-x.","ama":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79. doi:10.1007/s00454-014-9646-x","ista":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 53(1), 64–79.","ieee":"J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey number of outerplanar graphs,” Discrete & Computational Geometry, vol. 53, no. 1. Springer, pp. 64–79, 2014.","apa":"Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x"},"oa":1,"language":[{"iso":"eng"}],"date_published":"2014-11-14T00:00:00Z","doi":"10.1007/s00454-014-9646-x"},{"citation":{"chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin. “Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal. Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-3-491-504.","short":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 491–504.","mla":"Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal, vol. 14, no. 3, Independent University of Moscow, 2014, pp. 491–504, doi:10.17323/1609-4514-2014-14-3-491-504.","ieee":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations of delaunay sets,” Moscow Mathematical Journal, vol. 14, no. 3. Independent University of Moscow, pp. 491–504, 2014.","apa":"Dolbilin, N., Edelsbrunner, H., Glazyrin, A., & Musin, O. (2014). Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. Independent University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-3-491-504","ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.","ama":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 2014;14(3):491-504. doi:10.17323/1609-4514-2014-14-3-491-504"},"publication":"Moscow Mathematical Journal","page":"491 - 504","article_type":"original","date_published":"2014-07-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","_id":"1876","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 14","title":"Functionals on triangulations of delaunay sets","status":"public","oa_version":"Submitted Version","type":"journal_article","issue":"3","abstract":[{"text":"We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.","lang":"eng"}],"external_id":{"arxiv":["1211.7053"]},"main_file_link":[{"url":"http://arxiv.org/abs/1211.7053","open_access":"1"}],"oa":1,"quality_controlled":"1","doi":"10.17323/1609-4514-2014-14-3-491-504","language":[{"iso":"eng"}],"publication_identifier":{"issn":["16093321"]},"month":"07","year":"2014","publisher":"Independent University of Moscow","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"last_name":"Dolbilin","first_name":"Nikolai","full_name":"Dolbilin, Nikolai"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Glazyrin","first_name":"Alexey","full_name":"Glazyrin, Alexey"},{"full_name":"Musin, Oleg","first_name":"Oleg","last_name":"Musin"}],"volume":14,"date_created":"2018-12-11T11:54:29Z","date_updated":"2022-03-03T11:47:09Z","publist_id":"5220"},{"date_published":"2014-11-16T00:00:00Z","article_type":"original","page":"754 - 760","publication":"Journal of Mathematical Sciences","citation":{"chicago":"Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” Journal of Mathematical Sciences. Springer, 2014. https://doi.org/10.1007/s10958-014-2165-8.","short":"V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner, O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.","mla":"Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” Journal of Mathematical Sciences, vol. 203, no. 6, Springer, 2014, pp. 754–60, doi:10.1007/s10958-014-2165-8.","apa":"Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y., Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. Springer. https://doi.org/10.1007/s10958-014-2165-8","ieee":"V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H. Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that preserves global topology,” Journal of Mathematical Sciences, vol. 203, no. 6. Springer, pp. 754–760, 2014.","ista":"Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 203(6), 754–760.","ama":"Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 2014;203(6):754-760. doi:10.1007/s10958-014-2165-8"},"day":"16","article_processing_charge":"No","scopus_import":"1","oa_version":"None","status":"public","title":"An algorithm for cartographic generalization that preserves global topology","intvolume":" 203","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1929","abstract":[{"lang":"eng","text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales."}],"issue":"6","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s10958-014-2165-8","quality_controlled":"1","month":"11","publication_identifier":{"issn":["1072-3374"],"eissn":["1573-8795"]},"date_created":"2018-12-11T11:54:46Z","date_updated":"2022-05-24T10:39:06Z","volume":203,"author":[{"full_name":"Alexeev, V V","first_name":"V V","last_name":"Alexeev"},{"full_name":"Bogaevskaya, V G","first_name":"V G","last_name":"Bogaevskaya"},{"first_name":"M M","last_name":"Preobrazhenskaya","full_name":"Preobrazhenskaya, M M"},{"full_name":"Ukhalov, A Y","last_name":"Ukhalov","first_name":"A Y"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Yakimova, Olga","first_name":"Olga","last_name":"Yakimova"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","year":"2014","acknowledgement":"We would like to offer our special thanks to students of the Department of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev for participation in developing the program and assistance in preparation of test data. This work was supported by grant 11.G34.31.0053 from the government of the Russian Federation.","publist_id":"5165"},{"scopus_import":1,"month":"12","day":"31","page":"2585 - 2594","quality_controlled":"1","citation":{"mla":"Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:10.1109/TVCG.2014.2346432.","short":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T. Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.","chicago":"Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics. IEEE, 2014. https://doi.org/10.1109/TVCG.2014.2346432.","ama":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 2014;20(12):2585-2594. doi:10.1109/TVCG.2014.2346432","ista":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.","apa":"Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O., & Weinkauf, T. (2014). Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. IEEE. https://doi.org/10.1109/TVCG.2014.2346432","ieee":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar fields,” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12. IEEE, pp. 2585–2594, 2014."},"publication":"IEEE Transactions on Visualization and Computer Graphics","language":[{"iso":"eng"}],"doi":"10.1109/TVCG.2014.2346432","date_published":"2014-12-31T00:00:00Z","type":"journal_article","issue":"12","publist_id":"5164","abstract":[{"text":"(Figure Presented) Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations. Removing this noise is often necessary for efficient analysis and visualization of this data, yet many denoising techniques change the minima and maxima of a scalar field. For example, the extrema can appear or disappear, spatially move, and change their value. This can lead to wrong interpretations of the data, e.g., when the maximum temperature over an area is falsely reported being a few degrees cooler because the denoising method is unaware of these features. Recently, a topological denoising technique based on a global energy optimization was proposed, which allows the topology-controlled denoising of 2D scalar fields. While this method preserves the minima and maxima, it is constrained by the size of the data. We extend this work to large 2D data and medium-sized 3D data by introducing a novel domain decomposition approach. It allows processing small patches of the domain independently while still avoiding the introduction of new critical points. Furthermore, we propose an iterative refinement of the solution, which decreases the optimization energy compared to the previous approach and therefore gives smoother results that are closer to the input. We illustrate our technique on synthetic and real-world 2D and 3D data sets that highlight potential applications.","lang":"eng"}],"department":[{"_id":"HeEd"}],"intvolume":" 20","publisher":"IEEE","publication_status":"published","status":"public","title":"Fast and memory-efficient topological denoising of 2D and 3D scalar fields","year":"2014","_id":"1930","acknowledgement":"RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship; MPC-VCC","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa_version":"None","volume":20,"date_updated":"2021-01-12T06:54:09Z","date_created":"2018-12-11T11:54:46Z","author":[{"full_name":"Günther, David","first_name":"David","last_name":"Günther"},{"full_name":"Jacobson, Alec","last_name":"Jacobson","first_name":"Alec"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"full_name":"Seidel, Hans","last_name":"Seidel","first_name":"Hans"},{"first_name":"Olga","last_name":"Sorkine Hornung","full_name":"Sorkine Hornung, Olga"},{"last_name":"Weinkauf","first_name":"Tino","full_name":"Weinkauf, Tino"}]},{"language":[{"iso":"eng"}],"conference":{"start_date":"2014-01-05","location":"Portland, USA","end_date":"2014-01-05","name":"ALENEX: Algorithm Engineering and Experiments"},"doi":"10.1137/1.9781611973198.4","quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.0710"}],"oa":1,"month":"01","date_updated":"2021-01-12T06:54:56Z","date_created":"2018-12-11T11:55:23Z","author":[{"full_name":"Bauer, Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer"},{"orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"},{"last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"}],"publication_status":"published","publisher":"Society of Industrial and Applied Mathematics","editor":[{"full_name":" McGeoch, Catherine","last_name":" McGeoch","first_name":"Catherine"},{"first_name":"Ulrich","last_name":"Meyer","full_name":"Meyer, Ulrich"}],"department":[{"_id":"HeEd"}],"year":"2014","ec_funded":1,"publist_id":"5008","date_published":"2014-01-01T00:00:00Z","page":"31 - 38","publication":"Proceedings of the Workshop on Algorithm Engineering and Experiments","citation":{"mla":"Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” Proceedings of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch and Ulrich Meyer, Society of Industrial and Applied Mathematics, 2014, pp. 31–38, doi:10.1137/1.9781611973198.4.","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, C. McGeoch, U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2014, pp. 31–38.","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation of Persistent Homology.” In Proceedings of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch and Ulrich Meyer, 31–38. Society of Industrial and Applied Mathematics, 2014. https://doi.org/10.1137/1.9781611973198.4.","ama":"Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology. In: McGeoch C, Meyer U, eds. Proceedings of the Workshop on Algorithm Engineering and Experiments. Society of Industrial and Applied Mathematics; 2014:31-38. doi:10.1137/1.9781611973198.4","ista":"Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent homology. Proceedings of the Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, 31–38.","apa":"Bauer, U., Kerber, M., & Reininghaus, J. (2014). Distributed computation of persistent homology. In C. McGeoch & U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments (pp. 31–38). Portland, USA: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973198.4","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent homology,” in Proceedings of the Workshop on Algorithm Engineering and Experiments, Portland, USA, 2014, pp. 31–38."},"day":"01","scopus_import":1,"oa_version":"Submitted Version","status":"public","title":"Distributed computation of persistent homology","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2043","abstract":[{"lang":"eng","text":"Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically – as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems [1], we demonstrate that a simple adaption of the standard reduction algorithm leads to a variant for distributed systems. Our algorithmic design ensures that the data is distributed over the nodes without redundancy; this permits the computation of much larger instances than on a single machine. Moreover, we observe that the parallelism at least compensates for the overhead caused by communication between nodes, and often even speeds up the computation compared to sequential and even parallel shared memory algorithms. In our experiments, we were able to compute the persistent homology of filtrations with more than a billion (109) elements within seconds on a cluster with 32 nodes using less than 6GB of memory per node."}],"type":"conference"},{"date_published":"2014-03-19T00:00:00Z","publication":"Topological Methods in Data Analysis and Visualization III","citation":{"ista":"Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent Homology in Chunks. In: Topological Methods in Data Analysis and Visualization III. , 103–117.","apa":"Bauer, U., Kerber, M., & Reininghaus, J. (2014). Clear and Compress: Computing Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (pp. 103–117). Springer. https://doi.org/10.1007/978-3-319-04099-8_7","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent Homology in Chunks,” in Topological Methods in Data Analysis and Visualization III, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014, pp. 103–117.","ama":"Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer; 2014:103-117. doi:10.1007/978-3-319-04099-8_7","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress: Computing Persistent Homology in Chunks.” In Topological Methods in Data Analysis and Visualization III, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_7.","mla":"Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in Chunks.” Topological Methods in Data Analysis and Visualization III, edited by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:10.1007/978-3-319-04099-8_7.","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III, Springer, 2014, pp. 103–117."},"page":"103 - 117","day":"19","scopus_import":1,"series_title":"Mathematics and Visualization","oa_version":"Submitted Version","_id":"2044","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","title":"Clear and Compress: Computing Persistent Homology in Chunks","status":"public","abstract":[{"text":"We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation.","lang":"eng"}],"type":"book_chapter","doi":"10.1007/978-3-319-04099-8_7","language":[{"iso":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1303.0477","open_access":"1"}],"oa":1,"quality_controlled":"1","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"month":"03","author":[{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich"},{"full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"}],"date_updated":"2021-01-12T06:54:56Z","date_created":"2018-12-11T11:55:23Z","year":"2014","publication_status":"published","editor":[{"full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo","last_name":"Bremer"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"first_name":"Valerio","last_name":"Pascucci","full_name":"Pascucci, Valerio"},{"first_name":"Ronald","last_name":"Peikert","full_name":"Peikert, Ronald"}],"department":[{"_id":"HeEd"}],"publisher":"Springer","publist_id":"5007","ec_funded":1},{"month":"06","day":"01","scopus_import":1,"date_published":"2014-06-01T00:00:00Z","doi":"10.1145/2582112.2582168","conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Kyoto, Japan","start_date":"2014-06-08","end_date":"2014-06-11"},"language":[{"iso":"eng"}],"citation":{"ama":"Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:355-364. doi:10.1145/2582112.2582168","apa":"Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In Proceedings of the Annual Symposium on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168","ieee":"U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 355–364.","ista":"Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic stability of persistence. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 355–364.","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364.","mla":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168.","chicago":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168."},"main_file_link":[{"url":"http://arxiv.org/abs/1311.3681","open_access":"1"}],"oa":1,"publication":"Proceedings of the Annual Symposium on Computational Geometry","page":"355 - 364","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"quality_controlled":"1","publist_id":"4853","ec_funded":1,"abstract":[{"text":"We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s).","lang":"eng"}],"type":"conference","author":[{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich"},{"last_name":"Lesnick","first_name":"Michael","full_name":"Lesnick, Michael"}],"oa_version":"Submitted Version","date_updated":"2021-01-12T06:55:38Z","date_created":"2018-12-11T11:56:01Z","year":"2014","_id":"2153","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publisher":"ACM","department":[{"_id":"HeEd"}],"title":"Induced matchings of barcodes and the algebraic stability of persistence","publication_status":"published","status":"public"},{"month":"06","language":[{"iso":"eng"}],"doi":"10.1145/2582112.2582169","conference":{"end_date":"2014-06-11","location":"Kyoto, Japan","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry"},"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1307.2839","open_access":"1"}],"oa":1,"ec_funded":1,"publist_id":"4850","date_updated":"2021-01-12T06:55:39Z","date_created":"2018-12-11T11:56:02Z","author":[{"full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"},{"last_name":"Ge","first_name":"Xiaoyin","full_name":"Ge, Xiaoyin"},{"first_name":"Yusu","last_name":"Wang","full_name":"Wang, Yusu"}],"department":[{"_id":"HeEd"}],"publisher":"ACM","publication_status":"published","year":"2014","acknowledgement":"National Science Foundation under grants CCF-1319406, CCF-1116258.","day":"01","scopus_import":1,"date_published":"2014-06-01T00:00:00Z","page":"464 - 473","citation":{"short":"U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473.","mla":"Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73, doi:10.1145/2582112.2582169.","chicago":"Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In Proceedings of the Annual Symposium on Computational Geometry, 464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169.","ama":"Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169","ieee":"U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 464–473.","apa":"Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb graphs. In Proceedings of the Annual Symposium on Computational Geometry (pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169","ista":"Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473."},"publication":"Proceedings of the Annual Symposium on Computational Geometry","abstract":[{"lang":"eng","text":"We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s)."}],"type":"conference","oa_version":"Submitted Version","title":"Measuring distance between Reeb graphs","status":"public","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2156"},{"day":"01","scopus_import":1,"date_published":"2014-06-01T00:00:00Z","publication":"Proceedings of the Annual Symposium on Computational Geometry","citation":{"chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” In Proceedings of the Annual Symposium on Computational Geometry, 484–90. ACM, 2014. https://doi.org/10.1145/2582112.2582167.","short":"U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490.","mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–90, doi:10.1145/2582112.2582167.","ieee":"U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 484–490.","apa":"Bauer, U., & Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay filtrations. In Proceedings of the Annual Symposium on Computational Geometry (pp. 484–490). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582167","ista":"Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 484–490.","ama":"Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:484-490. doi:10.1145/2582112.2582167"},"page":"484 - 490","abstract":[{"lang":"eng","text":"Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s)."}],"type":"conference","oa_version":"Submitted Version","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2155","title":"The morse theory of Čech and Delaunay filtrations","status":"public","month":"06","conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Kyoto, Japan","start_date":"2014-06-08","end_date":"2014-06-11"},"doi":"10.1145/2582112.2582167","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1312.1231"}],"oa":1,"quality_controlled":"1","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"publist_id":"4851","author":[{"full_name":"Bauer, Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2021-01-12T06:55:38Z","date_created":"2018-12-11T11:56:01Z","acknowledgement":"This research is partially supported by ESF under the ACAT Research Network Programme, and by the Russian Government under mega project 11.G34.31.0053","year":"2014","publication_status":"published","publisher":"ACM","department":[{"_id":"HeEd"}]},{"day":"01","month":"01","scopus_import":1,"language":[{"iso":"eng"}],"date_published":"2014-01-01T00:00:00Z","doi":"10.1137/1.9781611973402.11","conference":{"name":"SODA: Symposium on Discrete Algorithms","location":"Portland, USA","start_date":"2014-01-05","end_date":"2014-01-07"},"page":"152 - 160","quality_controlled":"1","citation":{"ama":"Edelsbrunner H, Parsa S. On the computational complexity of betti numbers reductions from matrix rank. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11","ista":"Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.","apa":"Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity of betti numbers reductions from matrix rank. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 152–160). Portland, USA: SIAM. https://doi.org/10.1137/1.9781611973402.11","ieee":"H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers reductions from matrix rank,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Portland, USA, 2014, pp. 152–160.","mla":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–60, doi:10.1137/1.9781611973402.11.","short":"H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–160.","chicago":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 152–60. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.11."},"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","publist_id":"4805","abstract":[{"text":"We give evidence for the difficulty of computing Betti numbers of simplicial complexes over a finite field. We do this by reducing the rank computation for sparse matrices with to non-zero entries to computing Betti numbers of simplicial complexes consisting of at most a constant times to simplices. Together with the known reduction in the other direction, this implies that the two problems have the same computational complexity.","lang":"eng"}],"type":"conference","oa_version":"None","date_updated":"2021-01-12T06:55:48Z","date_created":"2018-12-11T11:56:09Z","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Parsa, Salman","id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87","first_name":"Salman","last_name":"Parsa"}],"department":[{"_id":"HeEd"}],"publisher":"SIAM","publication_status":"published","title":"On the computational complexity of betti numbers reductions from matrix rank","status":"public","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2177","year":"2014"},{"main_file_link":[{"url":"http://arxiv.org/abs/1105.6257","open_access":"1"}],"oa":1,"quality_controlled":"1","doi":"10.1145/2597629","language":[{"iso":"eng"}],"month":"05","acknowledgement":"The research by M. K. was supported by project GAUK 49209. The research by M. K. was also supported by project 1M0545 by the Ministry of Education of the Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague (project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).","year":"2014","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"ACM","author":[{"last_name":"Čadek","first_name":"Martin","full_name":"Čadek, Martin"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál","full_name":"Krcál, Marek"},{"full_name":"Matoušek, Jiří","last_name":"Matoušek","first_name":"Jiří"},{"full_name":"Sergeraert, Francis","last_name":"Sergeraert","first_name":"Francis"},{"last_name":"Vokřínek","first_name":"Lukáš","full_name":"Vokřínek, Lukáš"},{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"date_created":"2018-12-11T11:56:12Z","date_updated":"2021-01-12T06:55:50Z","volume":61,"article_number":"17 ","publist_id":"4797","publication":"Journal of the ACM","citation":{"ama":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. Journal of the ACM. 2014;61(3). doi:10.1145/2597629","apa":"Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner, U. (2014). Computing all maps into a sphere. Journal of the ACM. ACM. https://doi.org/10.1145/2597629","ieee":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” Journal of the ACM, vol. 61, no. 3. ACM, 2014.","ista":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing all maps into a sphere. Journal of the ACM. 61(3), 17.","short":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal of the ACM 61 (2014).","mla":"Čadek, Martin, et al. “Computing All Maps into a Sphere.” Journal of the ACM, vol. 61, no. 3, 17, ACM, 2014, doi:10.1145/2597629.","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere.” Journal of the ACM. ACM, 2014. https://doi.org/10.1145/2597629."},"date_published":"2014-05-01T00:00:00Z","scopus_import":1,"day":"01","_id":"2184","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","title":"Computing all maps into a sphere","status":"public","intvolume":" 61","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X→ Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools from effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X,Y] is known to be uncomputable for general X,Y, since for X = S1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, and extended to other problems, such as the extension problem, where we are given a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or computing the Z2-index-everything in the stable range. Outside the stable range, the extension problem is undecidable."}],"issue":"3"},{"oa":1,"quality_controlled":"1","doi":"10.4171/120-1/3","conference":{"end_date":"2012-07-07","start_date":"2012-07-02","location":"Kraków, Poland","name":"ECM: European Congress of Mathematics"},"language":[{"iso":"eng"}],"month":"01","year":"2014","acknowledgement":"This research is partially supported by NSF under grant DBI-0820624, by ESF under the Research Networking Programme, and by the Russian Government Project 11.G34.31.0053.","department":[{"_id":"HeEd"}],"publisher":"European Mathematical Society Publishing House","publication_status":"published","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Morozovy, Dmitriy","first_name":"Dmitriy","last_name":"Morozovy"}],"date_created":"2018-12-11T12:00:16Z","date_updated":"2021-01-12T07:00:36Z","publist_id":"3842","file_date_updated":"2020-07-14T12:45:52Z","citation":{"apa":"Edelsbrunner, H., & Morozovy, D. (2014). Persistent homology: Theory and practice (pp. 31–50). Presented at the ECM: European Congress of Mathematics, Kraków, Poland: European Mathematical Society Publishing House. https://doi.org/10.4171/120-1/3","ieee":"H. Edelsbrunner and D. Morozovy, “Persistent homology: Theory and practice,” presented at the ECM: European Congress of Mathematics, Kraków, Poland, 2014, pp. 31–50.","ista":"Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.","ama":"Edelsbrunner H, Morozovy D. Persistent homology: Theory and practice. In: European Mathematical Society Publishing House; 2014:31-50. doi:10.4171/120-1/3","chicago":"Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory and Practice,” 31–50. European Mathematical Society Publishing House, 2014. https://doi.org/10.4171/120-1/3.","short":"H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing House, 2014, pp. 31–50.","mla":"Edelsbrunner, Herbert, and Dmitriy Morozovy. Persistent Homology: Theory and Practice. European Mathematical Society Publishing House, 2014, pp. 31–50, doi:10.4171/120-1/3."},"page":"31 - 50","date_published":"2014-01-01T00:00:00Z","has_accepted_license":"1","article_processing_charge":"No","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2905","title":"Persistent homology: Theory and practice","status":"public","ddc":["000"],"pubrep_id":"544","file":[{"creator":"system","file_size":435320,"content_type":"application/pdf","access_level":"open_access","file_name":"IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf","checksum":"1d4a046f1af945c407c5c4d411d4c5e4","date_created":"2018-12-12T10:16:43Z","date_updated":"2020-07-14T12:45:52Z","file_id":"5232","relation":"main_file"}],"oa_version":"Submitted Version","type":"conference","abstract":[{"text":"Persistent homology is a recent grandchild of homology that has found use in\r\nscience and engineering as well as in mathematics. This paper surveys the method as well\r\nas the applications, neglecting completeness in favor of highlighting ideas and directions.","lang":"eng"}]},{"date_published":"2014-11-08T00:00:00Z","publication":"25th International Symposium, ISAAC 2014","citation":{"ista":"Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 8889, 117–127.","apa":"Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889, pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” in 25th International Symposium, ISAAC 2014, Jeonju, Korea, 2014, vol. 8889, pp. 117–127.","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature; 2014:117-127. doi:10.1007/978-3-319-13075-0_10","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” In 25th International Symposium, ISAAC 2014, 8889:117–27. Springer Nature, 2014. https://doi.org/10.1007/978-3-319-13075-0_10.","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” 25th International Symposium, ISAAC 2014, vol. 8889, Springer Nature, 2014, pp. 117–27, doi:10.1007/978-3-319-13075-0_10.","short":"T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127."},"page":"117-127","day":"08","article_processing_charge":"No","scopus_import":"1","oa_version":"None","_id":"10892","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Planar matchings for weighted straight skeletons","status":"public","intvolume":" 8889","abstract":[{"text":"In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.\r\nUsing our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"conference":{"name":"ISAAC: International Symposium on Algorithms and Computation","location":"Jeonju, Korea","start_date":"2014-12-15","end_date":"2014-12-17"},"doi":"10.1007/978-3-319-13075-0_10","language":[{"iso":"eng"}],"quality_controlled":"1","month":"11","publication_identifier":{"isbn":["9783319130743"],"eissn":["1611-3349"],"eisbn":["9783319130750"],"issn":["0302-9743"]},"author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber"},{"first_name":"Peter","last_name":"Palfrader","full_name":"Palfrader, Peter"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"481"}]},"date_updated":"2023-02-23T12:20:55Z","date_created":"2022-03-21T07:09:03Z","volume":8889,"acknowledgement":"T. Biedl was supported by NSERC and the Ross and Muriel Cheriton Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.","year":"2014","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature"},{"quality_controlled":"1","page":"IX, 110","citation":{"mla":"Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0.","short":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed., Springer Nature, Cham, 2014.","chicago":"Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-05957-0.","ama":"Edelsbrunner H. A Short Course in Computational Geometry and Topology. 1st ed. Cham: Springer Nature; 2014. doi:10.1007/978-3-319-05957-0","ista":"Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p.","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","ieee":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed. Cham: Springer Nature, 2014."},"language":[{"iso":"eng"}],"date_published":"2014-01-01T00:00:00Z","doi":"10.1007/978-3-319-05957-0","series_title":"SpringerBriefs in Applied Sciences and Technology","scopus_import":"1","month":"01","day":"01","article_processing_charge":"No","publication_identifier":{"isbn":["9-783-3190-5956-3"],"eissn":["2191-5318"],"eisbn":["9-783-3190-5957-0"],"issn":["2191-530X"]},"publication_status":"published","title":"A Short Course in Computational Geometry and Topology","status":"public","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6853","year":"2014","date_created":"2019-09-06T09:22:33Z","date_updated":"2022-03-04T07:47:54Z","oa_version":"None","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"related_material":{"link":[{"url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106","relation":"other","description":"available as eBook via catalog IST BookList"},{"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","place":"Cham","alternative_title":["SpringerBriefs in Applied Sciences and Technology"],"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."}]},{"alternative_title":["Mathematics and Visualization"],"type":"conference","abstract":[{"lang":"eng","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."}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10886","year":"2014","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","oa_version":"None","date_updated":"2023-09-05T14:13:16Z","date_created":"2022-03-18T13:05:39Z","author":[{"first_name":"Valentin","last_name":"Zobel","full_name":"Zobel, Valentin"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"last_name":"Hotz","first_name":"Ingrid","full_name":"Hotz, Ingrid"}],"scopus_import":"1","article_processing_charge":"No","publication_identifier":{"issn":["1612-3786"],"eisbn":["9783319040998"],"eissn":["2197-666X"],"isbn":["9783319040981"]},"month":"03","day":"19","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","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","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.","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"},{"oa_version":"None","title":"Notes on the simplification of the Morse-Smale complex","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10817","abstract":[{"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.","lang":"eng"}],"type":"book_chapter","date_published":"2014-03-19T00:00:00Z","page":"135-150","publication":"Topological Methods in Data Analysis and Visualization III.","citation":{"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","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.","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","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.","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.","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.","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."},"day":"19","article_processing_charge":"No","series_title":"Mathematics and Visualization","scopus_import":"1","date_updated":"2023-09-05T15:33:45Z","date_created":"2022-03-04T08:33:57Z","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"},{"last_name":"Seidel","first_name":"Hans-Peter","full_name":"Seidel, Hans-Peter"},{"last_name":"Weinkauf","first_name":"Tino","full_name":"Weinkauf, Tino"}],"publication_status":"published","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","last_name":"Pascucci","first_name":"Valerio"},{"first_name":"Ronald","last_name":"Peikert","full_name":"Peikert, Ronald"}],"year":"2014","acknowledgement":"This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.","ec_funded":1,"place":"Cham","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-04099-8_9","quality_controlled":"1","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}],"month":"03","publication_identifier":{"eissn":["2197-666X"],"isbn":["9783319040981"],"issn":["1612-3786"],"eisbn":["9783319040998"]}},{"publist_id":"4691","ec_funded":1,"file_date_updated":"2020-07-14T12:45:35Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"2843"},{"id":"1399","relation":"dissertation_contains","status":"public"}]},"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger"}],"volume":50,"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:56:36Z","year":"2014","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","publication_identifier":{"issn":["09249907"]},"month":"09","doi":"10.1007/s10851-013-0468-x","language":[{"iso":"eng"}],"oa":1,"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"quality_controlled":"1","issue":"1","abstract":[{"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.","lang":"eng"}],"type":"journal_article","pubrep_id":"549","oa_version":"Submitted Version","file":[{"access_level":"open_access","file_name":"IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf","file_size":3941391,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"5204","checksum":"2f93f3e63a38a85cd4404d7953913b14","date_created":"2018-12-12T10:16:18Z","date_updated":"2020-07-14T12:45:35Z"}],"_id":"2255","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 50","title":"Stable length estimates of tube-like shapes","ddc":["000"],"status":"public","has_accepted_license":"1","day":"01","scopus_import":1,"date_published":"2014-09-01T00:00:00Z","citation":{"ista":"Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.","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","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.","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","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."},"publication":"Journal of Mathematical Imaging and Vision","page":"164 - 177"},{"date_updated":"2023-09-20T09:42:40Z","date_created":"2022-03-21T07:12:16Z","volume":8592,"author":[{"last_name":"Bauer","first_name":"Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"full_name":"Wagner, Hubert","first_name":"Hubert","last_name":"Wagner"}],"related_material":{"record":[{"id":"1433","relation":"later_version","status":"public"}]},"publication_status":"published","publisher":"Springer Berlin Heidelberg","department":[{"_id":"HeEd"}],"year":"2014","place":"Berlin, Heidelberg","language":[{"iso":"eng"}],"conference":{"name":"ICMS: International Congress on Mathematical Software","location":"Seoul, South Korea","start_date":"2014-08-05","end_date":"2014-08-09"},"doi":"10.1007/978-3-662-44199-2_24","quality_controlled":"1","month":"09","publication_identifier":{"issn":["0302-9743"],"eisbn":["9783662441992"],"eissn":["1611-3349"],"isbn":["9783662441985"]},"oa_version":"None","status":"public","title":"PHAT – Persistent Homology Algorithms Toolbox","intvolume":" 8592","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10894","abstract":[{"lang":"eng","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."}],"type":"conference","date_published":"2014-09-01T00:00:00Z","page":"137-143","publication":"ICMS 2014: International Congress on Mathematical Software","citation":{"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","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.","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","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.","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.","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."},"day":"01","article_processing_charge":"No","series_title":"LNCS","scopus_import":"1"},{"article_processing_charge":"No","day":"01","month":"01","doi":"10.48550/arXiv.1401.0468","date_published":"2014-01-01T00:00:00Z","language":[{"iso":"eng"}],"oa":1,"citation":{"ama":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. doi:10.48550/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. .","ista":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv, 1401.0468.","short":"M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.).","mla":"Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, 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."},"main_file_link":[{"open_access":"1","url":"http://cccg.ca/proceedings/2014/papers/paper23.pdf"}],"external_id":{"arxiv":["1401.0468"]},"publication":"arXiv","publist_id":"5064","abstract":[{"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.","lang":"eng"}],"type":"preprint","article_number":"1401.0468","author":[{"first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299"},{"full_name":"Uhler, Caroline","orcid":"0000-0002-7008-0216","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","last_name":"Uhler","first_name":"Caroline"}],"oa_version":"Submitted Version","date_updated":"2023-10-18T08:06:45Z","date_created":"2018-12-11T11:55:12Z","_id":"2012","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","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2014","department":[{"_id":"HeEd"},{"_id":"CaUh"}],"title":"Sphere packing with limited overlap","publication_status":"submitted","status":"public"},{"conference":{"name":"ISVD: Voronoi Diagrams in Science and Engineering","location":"St. Petersburg, Russia","start_date":"2013-07-08","end_date":"2013-07-10"},"doi":"10.1109/ISVD.2013.11","date_published":"2013-12-01T00:00:00Z","language":[{"iso":"eng"}],"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.","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","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."},"quality_controlled":"1","page":"37 - 46","day":"01","month":"12","publication_identifier":{"eisbn":["978-0-7695-5037-4 "]},"scopus_import":1,"author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan"}],"date_updated":"2021-01-12T06:56:00Z","date_created":"2018-12-11T11:56:20Z","oa_version":"None","_id":"2209","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","status":"public","title":"Recognizing straight skeletons and Voronoi diagrams and reconstructing their input","publisher":"IEEE","department":[{"_id":"HeEd"}],"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","type":"conference","alternative_title":["2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) "]},{"day":"01","month":"03","conference":{"name":"EuroCG: European Workshop on Computational Geometry","start_date":"2013-03-17","location":"Braunschweig, Germany","end_date":"2013-03-20"},"date_published":"2013-03-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"29th European Workshop on Computational Geometry","main_file_link":[{"url":"http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf","open_access":"1"}],"oa":1,"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.","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.","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.","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."},"page":"95 - 98","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."}],"publist_id":"4762","type":"conference","author":[{"full_name":"Biedl, Therese","last_name":"Biedl","first_name":"Therese"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber","full_name":"Huber, Stefan"}],"date_updated":"2021-01-12T06:56:00Z","date_created":"2018-12-11T11:56:21Z","oa_version":"Submitted Version","_id":"2210","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Reconstructing polygons from embedded straight skeletons","status":"public","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"TU Braunschweig"},{"day":"05","month":"09","scopus_import":1,"language":[{"iso":"eng"}],"date_published":"2013-09-05T00:00:00Z","doi":"10.1016/j.endm.2013.07.008","quality_controlled":"1","page":"43 - 50","publication":"Electronic Notes in Discrete Mathematics","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","ieee":"F. Pausinger, “Van der Corput sequences and linear permutations,” Electronic Notes in Discrete Mathematics, vol. 43. Elsevier, pp. 43–50, 2013.","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","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."},"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"}],"publist_id":"4623","type":"journal_article","date_created":"2018-12-11T11:56:53Z","date_updated":"2021-01-12T06:56:39Z","volume":43,"oa_version":"None","author":[{"first_name":"Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian"}],"status":"public","publication_status":"published","title":"Van der Corput sequences and linear permutations","intvolume":" 43","publisher":"Elsevier","department":[{"_id":"HeEd"}],"acknowledgement":"This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria).","_id":"2304","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2013"},{"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"},"month":"06","publisher":"ACM","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"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"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál","full_name":"Krcál, Marek"},{"full_name":"Matoušek, Jiří","first_name":"Jiří","last_name":"Matoušek"},{"full_name":"Vokřínek, Lukáš","last_name":"Vokřínek","first_name":"Lukáš"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli"}],"publist_id":"4078","file_date_updated":"2020-07-14T12:45:48Z","page":"595 - 604","citation":{"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.","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","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.","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","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."},"publication":"45th Annual ACM Symposium on theory of computing","date_published":"2013-06-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01","title":"Extending continuous maps: Polynomiality and undecidability","status":"public","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2807","file":[{"relation":"main_file","file_id":"5081","checksum":"06c2ce5c1135fbc1f71ca15eeb242dcf","date_created":"2018-12-12T10:14:29Z","date_updated":"2020-07-14T12:45:48Z","access_level":"open_access","file_name":"IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf","file_size":447945,"content_type":"application/pdf","creator":"system"}],"oa_version":"Submitted Version","pubrep_id":"533","type":"conference","abstract":[{"lang":"eng","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. "}]},{"related_material":{"record":[{"id":"1805","status":"public","relation":"later_version"}]},"author":[{"full_name":"Attali, Dominique","last_name":"Attali","first_name":"Dominique"},{"last_name":"Bauer","first_name":"Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, 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"}],"oa_version":"Submitted Version","date_updated":"2023-02-23T10:15:15Z","date_created":"2018-12-11T11:59:44Z","_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).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2013","department":[{"_id":"HeEd"}],"publisher":"ACM","status":"public","title":"Homological reconstruction and simplification in R3","publication_status":"published","publist_id":"4072","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."}],"type":"conference","doi":"10.1145/2462356.2462373","date_published":"2013-06-01T00:00:00Z","conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Rio de Janeiro, Brazil","start_date":"2013-06-17","end_date":"2013-06-20"},"language":[{"iso":"eng"}],"main_file_link":[{"url":"http://hal.archives-ouvertes.fr/hal-00833791/","open_access":"1"}],"oa":1,"citation":{"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.","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."},"publication":"Proceedings of the 29th annual symposium on Computational Geometry","page":"117 - 125","quality_controlled":"1","month":"06","day":"01","scopus_import":1},{"page":"E1695 - E1704","citation":{"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.","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","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","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."},"publication":"PNAS","date_published":"2013-04-30T00:00:00Z","scopus_import":1,"day":"30","intvolume":" 110","status":"public","title":"3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2822","oa_version":"Submitted Version","type":"journal_article","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."}],"quality_controlled":"1","oa":1,"external_id":{"pmid":["25673779"]},"main_file_link":[{"open_access":"1","url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/"}],"language":[{"iso":"eng"}],"doi":"10.1073/pnas.1304354110","month":"04","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"publisher":"National Academy of Sciences","publication_status":"published","pmid":1,"year":"2013","volume":110,"date_updated":"2021-01-12T06:59:58Z","date_created":"2018-12-11T11:59:47Z","author":[{"last_name":"Topp","first_name":"Christopher","full_name":"Topp, Christopher"},{"first_name":"Anjali","last_name":"Iyer Pascuzzi","full_name":"Iyer Pascuzzi, Anjali"},{"first_name":"Jill","last_name":"Anderson","full_name":"Anderson, Jill"},{"last_name":"Lee","first_name":"Cheng","full_name":"Lee, Cheng"},{"last_name":"Zurek","first_name":"Paul","full_name":"Zurek, Paul"},{"id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","last_name":"Symonova","first_name":"Olga","full_name":"Symonova, Olga"},{"first_name":"Ying","last_name":"Zheng","full_name":"Zheng, Ying"},{"full_name":"Bucksch, Alexander","first_name":"Alexander","last_name":"Bucksch"},{"last_name":"Mileyko","first_name":"Yuriy","full_name":"Mileyko, Yuriy"},{"full_name":"Galkovskyi, Taras","last_name":"Galkovskyi","first_name":"Taras"},{"last_name":"Moore","first_name":"Brad","full_name":"Moore, Brad"},{"last_name":"Harer","first_name":"John","full_name":"Harer, John"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Mitchell Olds, Thomas","first_name":"Thomas","last_name":"Mitchell Olds"},{"first_name":"Joshua","last_name":"Weitz","full_name":"Weitz, Joshua"},{"last_name":"Benfey","first_name":"Philip","full_name":"Benfey, Philip"}],"publist_id":"3979"},{"abstract":[{"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.","lang":"eng"}],"publist_id":"3952","alternative_title":["LNCS"],"type":"conference","date_updated":"2023-02-23T10:35:00Z","date_created":"2018-12-11T11:59:53Z","oa_version":"None","volume":7749,"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"2255"}]},"title":"Stable length estimates of tube-like shapes","status":"public","publication_status":"published","department":[{"_id":"HeEd"}],"intvolume":" 7749","publisher":"Springer","year":"2013","_id":"2843","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"21","month":"02","scopus_import":1,"language":[{"iso":"eng"}],"conference":{"end_date":"2013-03-22","start_date":"2013-03-20","location":"Seville, Spain","name":"DGCI: Discrete Geometry for Computer Imagery"},"date_published":"2013-02-21T00:00:00Z","doi":"10.1007/978-3-642-37067-0","quality_controlled":"1","page":"XV - XIX","publication":"17th IAPR International Conference on Discrete Geometry for Computer Imagery","citation":{"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","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.","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.","short":"H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX.","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.","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."}},{"publisher":"International Press","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2013","volume":15,"date_created":"2018-12-11T11:59:58Z","date_updated":"2021-01-12T07:00:18Z","author":[{"full_name":"Bendich, Paul","first_name":"Paul","last_name":"Bendich","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Morozov, Dmitriy","first_name":"Dmitriy","last_name":"Morozov"},{"full_name":"Patel, Amit","id":"34A254A0-F248-11E8-B48F-1D18A9856A87","first_name":"Amit","last_name":"Patel"}],"publist_id":"3930","quality_controlled":"1","oa":1,"external_id":{"arxiv":["1102.3389"]},"main_file_link":[{"url":"https://arxiv.org/abs/1102.3389v1","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.4310/HHA.2013.v15.n1.a3","month":"05","intvolume":" 15","status":"public","title":"Homology and robustness of level and interlevel sets","_id":"2859","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"journal_article","issue":"1","abstract":[{"lang":"eng","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."}],"page":"51 - 72","citation":{"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","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.","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","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.","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.","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."},"publication":"Homology, Homotopy and Applications","date_published":"2013-05-01T00:00:00Z","scopus_import":1,"day":"01"},{"publication":"PNAS","citation":{"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","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.","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","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.","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."},"article_type":"original","page":"2670 - 2675","date_published":"2013-02-12T00:00:00Z","scopus_import":1,"day":"12","article_processing_charge":"No","_id":"2887","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Genotypic recognition and spatial responses by rice roots","intvolume":" 110","oa_version":"Published Version","type":"journal_article","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"}],"issue":"7","oa":1,"external_id":{"pmid":["23362379"]},"main_file_link":[{"open_access":"1","url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/"}],"quality_controlled":"1","doi":"10.1073/pnas.1222821110","language":[{"iso":"eng"}],"month":"02","year":"2013","pmid":1,"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"National Academy of Sciences","author":[{"full_name":"Fang, Suqin","last_name":"Fang","first_name":"Suqin"},{"last_name":"Clark","first_name":"Randy","full_name":"Clark, Randy"},{"last_name":"Zheng","first_name":"Ying","full_name":"Zheng, Ying"},{"first_name":"Anjali","last_name":"Iyer Pascuzzi","full_name":"Iyer Pascuzzi, Anjali"},{"full_name":"Weitz, Joshua","first_name":"Joshua","last_name":"Weitz"},{"full_name":"Kochian, Leon","last_name":"Kochian","first_name":"Leon"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Liao","first_name":"Hong","full_name":"Liao, Hong"},{"last_name":"Benfey","first_name":"Philip","full_name":"Benfey, Philip"}],"date_updated":"2021-01-12T07:00:29Z","date_created":"2018-12-11T12:00:09Z","volume":110,"publist_id":"3872"},{"intvolume":" 31","department":[{"_id":"HeEd"},{"_id":"VlKo"},{"_id":"ChLa"}],"publisher":"JMLR","status":"public","publication_status":"published","title":"Computing the M most probable modes of a graphical model","_id":"2901","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2013","volume":31,"oa_version":"None","date_created":"2018-12-11T12:00:14Z","date_updated":"2021-01-12T07:00:35Z","author":[{"first_name":"Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao"},{"first_name":"Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"},{"full_name":"Yan, Zhu","first_name":"Zhu","last_name":"Yan"},{"full_name":"Metaxas, Dimitris","last_name":"Metaxas","first_name":"Dimitris"},{"last_name":"Lampert","first_name":"Christoph","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","full_name":"Lampert, Christoph"}],"alternative_title":[" JMLR: W&CP"],"type":"conference","publist_id":"3846","abstract":[{"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. ","lang":"eng"}],"page":"161 - 169","quality_controlled":"1","main_file_link":[{"url":"http://jmlr.org/proceedings/papers/v31/chen13a.html","open_access":"1"}],"citation":{"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.","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."},"oa":1,"language":[{"iso":"eng"}],"date_published":"2013-01-01T00:00:00Z","conference":{"end_date":"2013-05-01","location":"Scottsdale, AZ, United States","start_date":"2013-04-29","name":" AISTATS: Conference on Uncertainty in Artificial Intelligence"},"scopus_import":1,"day":"01","month":"01"},{"oa":1,"quality_controlled":"1","conference":{"end_date":"2013-01-07","start_date":"2013-01-07","location":"New Orleans, LA, United States","name":"ALENEX: Algorithm Engineering and Experiments"},"doi":"10.1137/1.9781611972931.6","language":[{"iso":"eng"}],"month":"01","year":"2013","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Society of Industrial and Applied Mathematics","author":[{"full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"date_created":"2018-12-11T12:00:16Z","date_updated":"2021-01-12T07:00:36Z","file_date_updated":"2020-07-14T12:45:52Z","publist_id":"3841","publication":"2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments","citation":{"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.","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.","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.","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","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.","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."},"page":"70 - 77","date_published":"2013-01-01T00:00:00Z","scopus_import":1,"day":"01","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2906","title":"3D kinetic alpha complexes and their implementation","status":"public","ddc":["500"],"pubrep_id":"547","oa_version":"Submitted Version","file":[{"file_size":403013,"content_type":"application/pdf","creator":"system","access_level":"open_access","file_name":"IST-2016-547-v1+1_2013-P-08-MedusaII.pdf","checksum":"a15a3ba22df9445731507f3e06c9fcee","date_created":"2018-12-12T10:08:57Z","date_updated":"2020-07-14T12:45:52Z","relation":"main_file","file_id":"4720"}],"type":"conference","alternative_title":["ALENEX"],"abstract":[{"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.","lang":"eng"}]},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-013-9517-x"}],"oa":1,"quality_controlled":"1","doi":"10.1007/s00454-013-9517-x","language":[{"iso":"eng"}],"month":"06","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"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.","year":"2013","publication_status":"published","publisher":"Springer","department":[{"_id":"HeEd"}],"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"id":"F65D502E-E68D-11E9-9252-C644099818F6","last_name":"Fasy","first_name":"Brittany Terese","full_name":"Fasy, Brittany Terese"},{"last_name":"Rote","first_name":"Günter","full_name":"Rote, Günter"}],"related_material":{"record":[{"id":"3134","relation":"earlier_version","status":"public"}]},"date_created":"2018-12-11T11:59:44Z","date_updated":"2023-02-23T11:13:49Z","volume":49,"publist_id":"3991","publication":"Discrete & Computational Geometry","citation":{"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.","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.","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","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","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.","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."},"article_type":"original","page":"797 - 822","date_published":"2013-06-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2815","title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","status":"public","intvolume":" 49","oa_version":"Published Version","type":"journal_article","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."}],"issue":"4"},{"scopus_import":1,"day":"01","month":"05","publication":"Computational Geometry: Theory and Applications","citation":{"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.","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.","short":"C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013) 435–447.","ista":"Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 46(4), 435–447.","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","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.","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"},"quality_controlled":"1","page":"435 - 447","date_published":"2013-05-01T00:00:00Z","doi":"10.1016/j.comgeo.2012.02.010","language":[{"iso":"eng"}],"type":"journal_article","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"}],"issue":"4","publist_id":"3796","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.","_id":"2939","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","status":"public","title":"An output sensitive algorithm for persistent homology","intvolume":" 46","department":[{"_id":"HeEd"}],"publisher":"Elsevier","author":[{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","first_name":"Chao","full_name":"Chen, Chao"},{"full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"3367"}]},"date_created":"2018-12-11T12:00:27Z","date_updated":"2023-02-23T11:24:10Z","oa_version":"None","volume":46},{"abstract":[{"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.","lang":"eng"}],"type":"conference","oa_version":"None","intvolume":" 7877","title":"Persistent homology in image processing","status":"public","_id":"10897","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","day":"01","series_title":"LNCS","scopus_import":"1","date_published":"2013-06-01T00:00:00Z","page":"182-183","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."},"publication":"Graph-Based Representations in Pattern Recognition","ec_funded":1,"place":"Berlin, Heidelberg","volume":7877,"date_updated":"2023-09-05T15:10:20Z","date_created":"2022-03-21T07:30:33Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","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.","publication_identifier":{"issn":["0302-9743"],"eisbn":["9783642382215"],"eissn":["1611-3349"],"isbn":["9783642382208"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-38221-5_19","conference":{"location":"Vienna, Austria","start_date":"2013-05-15","end_date":"2013-05-17","name":"GbRPR: Graph-based Representations in Pattern Recognition"},"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1"},{"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"IOP Publishing Ltd.","year":"2012","date_updated":"2021-01-12T07:00:13Z","date_created":"2018-12-11T11:59:55Z","volume":67,"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Strelkova","first_name":"Nataliya","full_name":"Strelkova, Nataliya"}],"file_date_updated":"2020-07-14T12:45:51Z","publist_id":"3943","quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"doi":"10.1070/RM2012v067n06ABEH004820","month":"01","status":"public","title":"On the configuration space of Steiner minimal trees","ddc":["000"],"intvolume":" 67","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"2849","oa_version":"Submitted Version","file":[{"file_id":"5078","relation":"main_file","date_created":"2018-12-12T10:14:26Z","date_updated":"2020-07-14T12:45:51Z","checksum":"44ee8d173487e8ed41a51136816bbeb4","file_name":"IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf","access_level":"open_access","creator":"system","content_type":"application/pdf","file_size":392021}],"pubrep_id":"546","type":"journal_article","issue":"6","page":"1167 - 1168","publication":"Russian Mathematical Surveys","citation":{"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","ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 67(6), 1167–1168.","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.","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","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.","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."},"date_published":"2012-01-01T00:00:00Z","scopus_import":1,"day":"01","has_accepted_license":"1"},{"file":[{"date_updated":"2020-07-14T12:45:52Z","date_created":"2018-12-12T10:09:41Z","checksum":"444869a4e8abf07834f88b6e5cb5e9c3","file_id":"4765","relation":"main_file","creator":"system","content_type":"application/pdf","file_size":760548,"file_name":"IST-2016-545-v1+1_2012-P-10-AdaptiveTopology.pdf","access_level":"open_access"}],"oa_version":"Submitted Version","pubrep_id":"545","status":"public","title":"The adaptive topology of a digital image","ddc":["000"],"_id":"2903","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. 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","date_published":"2012-08-06T00:00:00Z","page":"41 - 48","citation":{"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.","ama":"Edelsbrunner H, Symonova O. The adaptive topology of a digital image. In: IEEE; 2012:41-48. doi:10.1109/ISVD.2012.11","chicago":"Edelsbrunner, Herbert, and Olga Symonova. “The Adaptive Topology of a Digital Image,” 41–48. IEEE, 2012. https://doi.org/10.1109/ISVD.2012.11.","short":"H. Edelsbrunner, O. Symonova, in:, IEEE, 2012, pp. 41–48.","mla":"Edelsbrunner, Herbert, and Olga Symonova. The Adaptive Topology of a Digital Image. IEEE, 2012, pp. 41–48, doi:10.1109/ISVD.2012.11."},"has_accepted_license":"1","day":"06","scopus_import":1,"date_updated":"2021-01-12T07:00:35Z","date_created":"2018-12-11T12:00:15Z","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","first_name":"Olga","last_name":"Symonova","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","language":[{"iso":"eng"}],"doi":"10.1109/ISVD.2012.11","conference":{"name":"ISVD: International Symposium on Voronoi Diagrams in Science and Engineering","location":"New Brunswick, NJ, USA ","start_date":"2012-06-27","end_date":"2012-06-29"},"quality_controlled":"1","oa":1,"month":"08"},{"scopus_import":1,"has_accepted_license":"1","day":"01","page":"781 - 783","citation":{"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.","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.","short":"N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012) 781–783.","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.","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.","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","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"},"publication":"Russian Mathematical Surveys","date_published":"2012-11-01T00:00:00Z","type":"journal_article","issue":"4","intvolume":" 67","ddc":["510"],"title":"On the optimality of functionals over triangulations of Delaunay sets","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"2941","file":[{"relation":"main_file","file_id":"5239","date_updated":"2020-07-14T12:45:55Z","date_created":"2018-12-12T10:16:49Z","checksum":"389a5ae53d6347de36c3468034f2821d","file_name":"IST-2013-132-v1+1_2012-J-04-Functional-E.pdf","access_level":"open_access","file_size":253816,"content_type":"application/pdf","creator":"system"}],"oa_version":"Submitted Version","pubrep_id":"132","month":"11","quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"doi":"10.1070/RM2012v067n04ABEH004807","publist_id":"3792","file_date_updated":"2020-07-14T12:45:55Z","publisher":"IOP Publishing","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2012","volume":67,"date_updated":"2021-01-12T07:39:55Z","date_created":"2018-12-11T12:00:28Z","author":[{"full_name":"Dolbilin, Nikolai","last_name":"Dolbilin","first_name":"Nikolai"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Musin, Oleg","last_name":"Musin","first_name":"Oleg"}]},{"abstract":[{"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. ","lang":"eng"}],"publist_id":"3737","type":"conference","date_created":"2018-12-11T12:00:37Z","date_updated":"2021-01-12T07:40:10Z","volume":7476,"oa_version":"None","author":[{"first_name":"Georg","last_name":"Zankl","full_name":"Zankl, Georg"},{"last_name":"Haxhimusa","first_name":"Yll","full_name":"Haxhimusa, Yll"},{"id":"29F89302-F248-11E8-B48F-1D18A9856A87","last_name":"Ion","first_name":"Adrian","full_name":"Ion, Adrian"}],"status":"public","publication_status":"published","title":"Interactive labeling of image segmentation hierarchies","department":[{"_id":"HeEd"}],"intvolume":" 7476","publisher":"Springer","year":"2012","_id":"2971","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"01","day":"01","scopus_import":1,"language":[{"iso":"eng"}],"conference":{"name":"Pattern Recognition","end_date":"2012-08-31","location":"Graz, Austria","start_date":"2012-08-28"},"doi":"10.1007/978-3-642-32717-9_2","date_published":"2012-01-01T00:00:00Z","quality_controlled":"1","page":"11 - 20","citation":{"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.","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.","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.","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"}},{"oa_version":"Preprint","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"3120","status":"public","title":"Fano 3 folds in codimension 4 Tom and Jerry Part I","intvolume":" 148","abstract":[{"lang":"eng","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."}],"issue":"4","type":"journal_article","date_published":"2012-07-01T00:00:00Z","publication":"Compositio Mathematica","citation":{"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","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.","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","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."},"page":"1171 - 1194","day":"01","scopus_import":1,"author":[{"first_name":"Gavin","last_name":"Brown","full_name":"Brown, Gavin"},{"last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael"},{"last_name":"Reid","first_name":"Miles","full_name":"Reid, Miles"}],"date_created":"2018-12-11T12:01:30Z","date_updated":"2021-01-12T07:41:12Z","volume":148,"acknowledgement":"This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.","year":"2012","publication_status":"published","publisher":"Cambridge University Press","department":[{"_id":"HeEd"}],"publist_id":"3579","doi":"10.1112/S0010437X11007226","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1009.4313","open_access":"1"}],"quality_controlled":"1","month":"07"},{"day":"20","month":"06","scopus_import":1,"language":[{"iso":"eng"}],"conference":{"name":"SCG: Symposium on Computational Geometry","end_date":"2012-06-20","start_date":"2012-06-17","location":"Chapel Hill, NC, USA"},"date_published":"2012-06-20T00:00:00Z","doi":"10.1145/2261250.2261287","quality_controlled":"1","page":"249 - 258","publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","citation":{"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","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.","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","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.","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.","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."},"main_file_link":[{"url":"http://arxiv.org/abs/1109.5052","open_access":"1"}],"oa":1,"abstract":[{"lang":"eng","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. "}],"publist_id":"3564","type":"conference","date_created":"2018-12-11T12:01:35Z","date_updated":"2021-01-12T07:41:17Z","oa_version":"Preprint","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael"}],"publication_status":"published","status":"public","title":"Alexander duality for functions: The persistent behavior of land and water and shore","department":[{"_id":"HeEd"}],"publisher":"ACM","_id":"3133","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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.","year":"2012"},{"abstract":[{"lang":"eng","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. "}],"publist_id":"3563","type":"conference","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Fasy, Brittany","first_name":"Brittany","last_name":"Fasy"},{"full_name":"Rote, Günter","first_name":"Günter","last_name":"Rote"}],"related_material":{"record":[{"id":"2815","relation":"later_version","status":"public"}]},"date_updated":"2023-02-23T10:59:27Z","date_created":"2018-12-11T12:01:35Z","oa_version":"None","_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.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2012","status":"public","title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","publication_status":"published","publisher":"ACM","department":[{"_id":"HeEd"}],"month":"06","day":"20","scopus_import":1,"conference":{"name":"SCG: Symposium on Computational Geometry","location":"Chapel Hill, NC, USA","start_date":"2012-06-17","end_date":"2012-06-20"},"doi":"10.1145/2261250.2261265","date_published":"2012-06-20T00:00:00Z","language":[{"iso":"eng"}],"publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","citation":{"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.","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.","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","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.","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","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."},"quality_controlled":"1","page":"91 - 100"},{"type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"2","_id":"3256","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"title":"Dual complexes of cubical subdivisions of ℝn","status":"public","intvolume":" 47","pubrep_id":"543","file":[{"file_name":"IST-2016-543-v1+1_2012-J-08-HierarchyCubeComplex.pdf","access_level":"open_access","creator":"system","content_type":"application/pdf","file_size":203636,"file_id":"4675","relation":"main_file","date_updated":"2020-07-14T12:46:05Z","date_created":"2018-12-12T10:08:15Z","checksum":"76486f3b2c9e7fd81342f3832ca387e7"}],"oa_version":"Submitted Version","scopus_import":1,"day":"01","has_accepted_license":"1","publication":"Discrete & Computational Geometry","citation":{"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.","short":"H. Edelsbrunner, M. Kerber, Discrete & Computational Geometry 47 (2012) 393–414.","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.","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","ista":"Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 47(2), 393–414.","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","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."},"page":"393 - 414","date_published":"2012-03-01T00:00:00Z","file_date_updated":"2020-07-14T12:46:05Z","publist_id":"3398","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","department":[{"_id":"HeEd"}],"publisher":"Springer","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"}],"date_updated":"2021-01-12T07:42:10Z","date_created":"2018-12-11T12:02:17Z","volume":47,"month":"03","oa":1,"quality_controlled":"1","doi":"10.1007/s00454-011-9382-4","language":[{"iso":"eng"}]},{"conference":{"name":"ICCV: International Conference on Computer Vision","start_date":"2011-11-06","location":"Barcelona, Spain","end_date":"2011-11-13"},"date_published":"2012-01-12T00:00:00Z","doi":"10.1109/ICCV.2011.6126486","language":[{"iso":"eng"}],"citation":{"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","ista":"Ion A, Carreira J, Sminchisescu C. 2012. Image segmentation by figure-ground composition into maximal cliques. ICCV: International Conference on Computer Vision, 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.","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","mla":"Ion, Adrian, et al. Image Segmentation by Figure-Ground Composition into Maximal Cliques. 6126486, IEEE, 2012, doi:10.1109/ICCV.2011.6126486.","short":"A. Ion, J. Carreira, C. Sminchisescu, in:, IEEE, 2012.","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."},"quality_controlled":"1","month":"01","day":"12","author":[{"id":"29F89302-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian","last_name":"Ion","full_name":"Ion, Adrian"},{"first_name":"Joao","last_name":"Carreira","full_name":"Carreira, Joao"},{"full_name":"Sminchisescu, Cristian","last_name":"Sminchisescu","first_name":"Cristian"}],"date_created":"2018-12-11T12:02:21Z","date_updated":"2021-01-12T07:42:15Z","oa_version":"None","_id":"3265","year":"2012","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publication_status":"published","status":"public","title":"Image segmentation by figure-ground composition into maximal cliques","department":[{"_id":"HeEd"}],"publisher":"IEEE","abstract":[{"lang":"eng","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."}],"publist_id":"3382","article_number":"6126486","type":"conference"},{"date_published":"2012-12-01T00:00:00Z","page":"964 - 989","citation":{"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.","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","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.","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."},"publication":"Discrete & Computational Geometry","day":"01","scopus_import":1,"oa_version":"Preprint","intvolume":" 48","title":"Deconstructing approximate offsets","status":"public","_id":"3115","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"4","abstract":[{"lang":"eng","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."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00454-012-9441-5","quality_controlled":"1","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1109.2158","open_access":"1"}],"external_id":{"arxiv":["1109.2158"]},"month":"12","volume":48,"date_created":"2018-12-11T12:01:28Z","date_updated":"2023-02-23T11:22:30Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"3329"}]},"author":[{"first_name":"Eric","last_name":"Berberich","full_name":"Berberich, Eric"},{"full_name":"Halperin, Dan","last_name":"Halperin","first_name":"Dan"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299"},{"full_name":"Pogalnikova, Roza","first_name":"Roza","last_name":"Pogalnikova"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","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","publist_id":"3584"},{"_id":"3331","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2012","publisher":"Elsevier","intvolume":" 47","department":[{"_id":"HeEd"}],"title":"A worst case bound for topology computation of algebraic curves","publication_status":"published","status":"public","author":[{"first_name":"Michael","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael"},{"first_name":"Michael","last_name":"Sagraloff","full_name":"Sagraloff, Michael"}],"volume":47,"oa_version":"Preprint","date_updated":"2021-01-12T07:42:43Z","date_created":"2018-12-11T12:02:43Z","type":"journal_article","issue":"3","publist_id":"3303","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"}],"citation":{"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.","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.","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","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."},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1104.1510"}],"oa":1,"publication":" Journal of Symbolic Computation","page":"239 - 258","quality_controlled":"1","doi":"10.1016/j.jsc.2011.11.001","date_published":"2012-03-01T00:00:00Z","language":[{"iso":"eng"}],"scopus_import":1,"month":"03","day":"01"},{"day":"19","scopus_import":1,"date_published":"2012-06-19T00:00:00Z","page":"189 - 200","citation":{"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.","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.","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","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.","short":"O. Busaryev, S. Cabello, C. Chen, T. Dey, Y. Wang, in:, Springer, 2012, pp. 189–200.","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."},"abstract":[{"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","lang":"eng"}],"alternative_title":["LNCS"],"type":"conference","oa_version":"Preprint","intvolume":" 7357","status":"public","title":"Annotating simplices with a homology basis and its applications","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"3129","month":"06","language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-31155-0_17","conference":{"location":"Helsinki, Finland","start_date":"2012-07-04","end_date":"2012-07-06","name":"SWAT: Symposium and Workshops on Algorithm Theory"},"quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1107.3793","open_access":"1"}],"external_id":{"arxiv":["1107.3793"]},"oa":1,"publist_id":"3569","volume":7357,"date_created":"2018-12-11T12:01:33Z","date_updated":"2021-01-12T07:41:15Z","author":[{"last_name":"Busaryev","first_name":"Oleksiy","full_name":"Busaryev, Oleksiy"},{"last_name":"Cabello","first_name":"Sergio","full_name":"Cabello, Sergio"},{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","first_name":"Chao","full_name":"Chen, Chao"},{"last_name":"Dey","first_name":"Tamal","full_name":"Dey, Tamal"},{"first_name":"Yusu","last_name":"Wang","full_name":"Wang, Yusu"}],"department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","year":"2012"},{"type":"journal_article","issue":"6","abstract":[{"lang":"eng","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."}],"_id":"3159","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 7","title":"Hierarchical ordering of reticular networks","status":"public","ddc":["510"],"pubrep_id":"385","file":[{"file_size":541583,"content_type":"application/pdf","creator":"kschuh","file_name":"2012_PLoS_Mileyko.PDF","access_level":"open_access","date_updated":"2020-07-14T12:46:01Z","date_created":"2019-02-05T12:38:43Z","checksum":"515a98ad72e470752f03f13663dcaff8","relation":"main_file","file_id":"5922"}],"oa_version":"Published Version","scopus_import":1,"has_accepted_license":"1","day":"06","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","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","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.","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","date_published":"2012-06-06T00:00:00Z","article_number":"e36715","publist_id":"3530","file_date_updated":"2020-07-14T12:46:01Z","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.","year":"2012","department":[{"_id":"HeEd"}],"publisher":"Public Library of Science","publication_status":"published","author":[{"last_name":"Mileyko","first_name":"Yuriy","full_name":"Mileyko, Yuriy"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Price, Charles","first_name":"Charles","last_name":"Price"},{"first_name":"Joshua","last_name":"Weitz","full_name":"Weitz, Joshua"}],"volume":7,"date_updated":"2021-01-12T07:41:28Z","date_created":"2018-12-11T12:01:44Z","month":"06","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","doi":"10.1371/journal.pone.0036715","language":[{"iso":"eng"}]},{"publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"Research by the third author is partially supported by the National Science Foundation (NSF) under grant DBI-0820624.","year":"2012","volume":33,"date_created":"2018-12-11T12:02:36Z","date_updated":"2021-01-12T07:42:34Z","author":[{"last_name":"Bendich","first_name":"Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","full_name":"Bendich, Paul"},{"first_name":"Sergio","last_name":"Cabello","full_name":"Cabello, Sergio"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"publist_id":"3330","file_date_updated":"2020-07-14T12:46:06Z","quality_controlled":"1","oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.patrec.2011.10.007","month":"08","intvolume":" 33","title":"A point calculus for interlevel set homology","ddc":["000"],"status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"3310","oa_version":"Submitted Version","file":[{"file_name":"IST-2016-542-v1+1_2012-J-01-Poinculus.pdf","access_level":"open_access","file_size":280280,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"5116","date_updated":"2020-07-14T12:46:06Z","date_created":"2018-12-12T10:15:00Z","checksum":"d65f79775b51258a604ca5ec741297cc"}],"pubrep_id":"542","type":"journal_article","issue":"11","abstract":[{"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.","lang":"eng"}],"page":"1436 - 1444","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.","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.","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","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"},"publication":"Pattern Recognition Letters","date_published":"2012-08-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01"},{"date_created":"2019-06-27T08:16:56Z","date_updated":"2023-10-16T09:41:31Z","volume":8,"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":"B. Verkin Institute for Low Temperature Physics and Engineering","year":"2012","acknowledgement":"This work is supported by the Austrian Science Fund (FWF), Project P22025-N18.\r\n","month":"01","publication_identifier":{"issn":["1812-9471"]},"language":[{"iso":"eng"}],"isi":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://mi.mathnet.ru/eng/jmag525"}],"external_id":{"isi":["000301173600004"]},"oa":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."}],"issue":"1","type":"journal_article","oa_version":"Published Version","status":"public","title":"Elementary solutions of the Bernstein problem on two intervals","intvolume":" 8","_id":"6588","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2012-01-01T00:00:00Z","article_type":"original","page":"63-78","publication":"Journal of Mathematical Physics, Analysis, Geometry","citation":{"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.","short":"F. Pausinger, Journal of Mathematical Physics, Analysis, Geometry 8 (2012) 63–78.","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.","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.","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.","ista":"Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78.","ama":"Pausinger F. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 2012;8(1):63-78."}},{"_id":"2912","year":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On the configuration space for the shortest networks","publication_status":"published","status":"public","intvolume":" 67","publisher":"Russian Academy of Sciences","department":[{"_id":"HeEd"}],"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Strelkova, Nataliya","first_name":"Nataliya","last_name":"Strelkova"}],"date_created":"2018-12-11T12:00:18Z","date_updated":"2023-10-17T11:40:39Z","oa_version":"None","volume":67,"type":"journal_article","issue":"6","publist_id":"3831","publication":"Russian Mathematical Surveys","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","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","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.","ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space for the shortest networks. Russian Mathematical Surveys. 67(6), 1167–1168."},"quality_controlled":"1","page":"1167–1168","date_published":"2012-10-01T00:00:00Z","doi":"10.4213/rm9503","language":[{"iso":"eng"}],"month":"10","day":"01","article_processing_charge":"No"},{"type":"conference","publist_id":"3572","abstract":[{"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.","lang":"eng"}],"publisher":"ML Research Press","department":[{"_id":"ChLa"},{"_id":"HeEd"}],"title":"The most persistent soft-clique in a set of sampled graphs","publication_status":"published","status":"public","_id":"3127","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2012","oa_version":"Preprint","date_updated":"2023-10-17T11:55:06Z","date_created":"2018-12-11T12:01:33Z","author":[{"full_name":"Quadrianto, Novi","first_name":"Novi","last_name":"Quadrianto"},{"full_name":"Lampert, Christoph","last_name":"Lampert","first_name":"Christoph","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87"},{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao","last_name":"Chen","full_name":"Chen, Chao"}],"scopus_import":"1","article_processing_charge":"No","day":"01","month":"06","page":"211-218","quality_controlled":"1","oa":1,"citation":{"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.","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.","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.","short":"N. Quadrianto, C. Lampert, C. Chen, in:, Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 211–218.","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."},"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":{"name":"ICML: International Conference on Machine Learning","end_date":"2012-07-01","location":"Edinburgh, United Kingdom","start_date":"2012-06-26"}},{"oa":1,"quality_controlled":"1","doi":"10.5802/jtnb.819","language":[{"iso":"eng"}],"month":"01","publication_identifier":{"eissn":["2118-8572"],"issn":["1246-7405"]},"year":"2012","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Université de Bordeaux","author":[{"full_name":"Pausinger, Florian","first_name":"Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768"}],"date_updated":"2023-10-18T07:53:47Z","date_created":"2018-12-11T12:00:15Z","volume":24,"file_date_updated":"2020-07-14T12:45:52Z","publist_id":"3843","publication":"Journal de Theorie des Nombres des Bordeaux","citation":{"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","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."},"article_type":"original","page":"729 - 749","date_published":"2012-01-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2904","status":"public","ddc":["510"],"title":"Weak multipliers for generalized van der Corput sequences","intvolume":" 24","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"7819","checksum":"6954bfe9d7f4119fbdda7a11cf0f5c67","date_updated":"2020-07-14T12:45:52Z","date_created":"2020-05-11T12:40:39Z","access_level":"open_access","file_name":"JTNB_2012__24_3_729_0.pdf","content_type":"application/pdf","file_size":819275,"creator":"dernst"}],"type":"journal_article","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."},{"lang":"fre","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."}],"issue":"3"},{"year":"2012","_id":"2902","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","title":"Fractal and computational geometry for generalizing cartographic objects","status":"public","department":[{"_id":"HeEd"}],"intvolume":" 19","publisher":"Russian Academy of Sciences","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"},{"full_name":"Ukhalov, Alexey","last_name":"Ukhalov","first_name":"Alexey"},{"last_name":"Yakimova","first_name":"Olga","full_name":"Yakimova, Olga"},{"full_name":"Alexeev, Vladislav","first_name":"Vladislav","last_name":"Alexeev"},{"last_name":"Bogaevskaya","first_name":"Victoriya","full_name":"Bogaevskaya, Victoriya"},{"first_name":"Andrey","last_name":"Gorohov","full_name":"Gorohov, Andrey"},{"full_name":"Preobrazhenskaya, Margarita","first_name":"Margarita","last_name":"Preobrazhenskaya"}],"date_updated":"2023-10-18T07:34:45Z","date_created":"2018-12-11T12:00:15Z","oa_version":"Published Version","volume":19,"type":"journal_article","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","publication":"Modeling and Analysis of Information Systems","oa":1,"citation":{"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.","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.","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.","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.","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.","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."},"main_file_link":[{"open_access":"1","url":"http://mi.mathnet.ru/eng/mais280"}],"article_type":"original","quality_controlled":"1","page":"152 - 160","date_published":"2012-12-01T00:00:00Z","language":[{"iso":"rus"}],"month":"12","day":"01","article_processing_charge":"No"},{"date_published":"2011-12-01T00:00:00Z","conference":{"location":"Granada, Spain","start_date":"2011-12-12","end_date":"2011-12-14","name":"NIPS: Neural Information Processing Systems"},"language":[{"iso":"eng"}],"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","page":"1827 - 1835","quality_controlled":"1","day":"01","month":"12","scopus_import":1,"author":[{"full_name":"Ion, Adrian","id":"29F89302-F248-11E8-B48F-1D18A9856A87","last_name":"Ion","first_name":"Adrian"},{"first_name":"Joao","last_name":"Carreira","full_name":"Carreira, Joao"},{"full_name":"Sminchisescu, Cristian","first_name":"Cristian","last_name":"Sminchisescu"}],"volume":24,"oa_version":"None","date_created":"2018-12-11T12:02:21Z","date_updated":"2021-01-12T07:42:15Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"3266","year":"2011","publisher":"Neural Information Processing Systems Foundation","department":[{"_id":"HeEd"}],"intvolume":" 24","title":"Probabilistic joint image segmentation and labeling","publication_status":"published","status":"public","publist_id":"3381","abstract":[{"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.","lang":"eng"}],"type":"conference"},{"main_file_link":[{"open_access":"1","url":"http://www.cs.cmu.edu/%7Eshengyu/download/egsr2011_paper.pdf"}],"oa":1,"quality_controlled":"1","doi":"10.1111/j.1467-8659.2011.01985.x","language":[{"iso":"eng"}],"month":"07","year":"2011","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Wiley-Blackwell","author":[{"full_name":"Sheng, Yu","last_name":"Sheng","first_name":"Yu"},{"first_name":"Barbara","last_name":"Cutler","full_name":"Cutler, Barbara"},{"last_name":"Chen","first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao"},{"last_name":"Nasman","first_name":"Joshua","full_name":"Nasman, Joshua"}],"date_updated":"2021-01-12T07:42:16Z","date_created":"2018-12-11T12:02:22Z","volume":30,"publist_id":"3377","publication":"Computer Graphics Forum","citation":{"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.","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.","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.","short":"Y. Sheng, B. Cutler, C. Chen, J. Nasman, Computer Graphics Forum 30 (2011) 1261–1268.","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."},"article_type":"original","page":"1261 - 1268","date_published":"2011-07-19T00:00:00Z","scopus_import":1,"day":"19","article_processing_charge":"No","_id":"3269","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Perceptual global illumination cancellation in complex projection environments","intvolume":" 30","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"},{"author":[{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao","last_name":"Chen","full_name":"Chen, Chao"},{"last_name":"Freedman","first_name":"Daniel","full_name":"Freedman, Daniel"}],"related_material":{"record":[{"id":"10909","status":"public","relation":"earlier_version"}]},"date_created":"2018-12-11T12:02:21Z","date_updated":"2023-02-21T16:07:10Z","oa_version":"None","volume":45,"_id":"3267","year":"2011","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Hardness results for homology localization","publication_status":"published","status":"public","publisher":"Springer","department":[{"_id":"HeEd"}],"intvolume":" 45","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."}],"issue":"3","publist_id":"3379","type":"journal_article","date_published":"2011-01-14T00:00:00Z","doi":"10.1007/s00454-010-9322-8","language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","citation":{"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.","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","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.","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."},"quality_controlled":"1","page":"425 - 448","month":"01","day":"14","scopus_import":1},{"publist_id":"3295","year":"2011","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","editor":[{"full_name":"Gavrilova, Marina","first_name":"Marina","last_name":"Gavrilova"},{"last_name":"Tan","first_name":"Kenneth","full_name":"Tan, Kenneth"},{"full_name":"Mostafavi, Mir","last_name":"Mostafavi","first_name":"Mir"}],"author":[{"full_name":"Van De Weygaert, Rien","first_name":"Rien","last_name":"Van De Weygaert"},{"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"},{"full_name":"Jones, Bernard","last_name":"Jones","first_name":"Bernard"},{"last_name":"Pranav","first_name":"Pratyush","full_name":"Pranav, Pratyush"},{"last_name":"Park","first_name":"Changbom","full_name":"Park, Changbom"},{"last_name":"Hellwing","first_name":"Wojciech","full_name":"Hellwing, Wojciech"},{"last_name":"Eldering","first_name":"Bob","full_name":"Eldering, Bob"},{"full_name":"Kruithof, Nico","last_name":"Kruithof","first_name":"Nico"},{"first_name":"Patrick","last_name":"Bos","full_name":"Bos, Patrick"},{"full_name":"Hidding, Johan","last_name":"Hidding","first_name":"Johan"},{"last_name":"Feldbrugge","first_name":"Job","full_name":"Feldbrugge, Job"},{"full_name":"Ten Have, Eline","last_name":"Ten Have","first_name":"Eline"},{"full_name":"Van Engelen, Matti","first_name":"Matti","last_name":"Van Engelen"},{"full_name":"Caroli, Manuel","last_name":"Caroli","first_name":"Manuel"},{"first_name":"Monique","last_name":"Teillaud","full_name":"Teillaud, Monique"}],"date_created":"2018-12-11T12:02:44Z","date_updated":"2021-01-12T07:42:44Z","volume":6970,"month":"11","external_id":{"arxiv":["1306.3640"]},"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1306.3640"}],"quality_controlled":"1","doi":"10.1007/978-3-642-25249-5_3","language":[{"iso":"eng"}],"type":"book_chapter","alternative_title":["LNCS"],"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."}],"_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","oa_version":"Preprint","scopus_import":1,"series_title":"Special Issue on Voronoi Diagrams and Delaunay Triangulation","day":"09","publication":"Transactions on Computational Science XIV","citation":{"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.","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","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.","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."},"page":"60 - 101","date_published":"2011-11-09T00:00:00Z"},{"scopus_import":1,"month":"06","day":"13","page":"187 - 196","quality_controlled":"1","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1109.2158","open_access":"1"}],"citation":{"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","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","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.","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."},"publication":"Proceedings of the twenty-seventh annual symposium on Computational geometry","language":[{"iso":"eng"}],"doi":"10.1145/1998196.1998225","date_published":"2011-06-13T00:00:00Z","conference":{"start_date":"2011-06-13","location":"Paris, France","end_date":"2011-06-15","name":"SCG: Symposium on Computational Geometry"},"type":"conference","publist_id":"3306","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"}],"publisher":"ACM","department":[{"_id":"HeEd"}],"status":"public","publication_status":"published","title":"Deconstructing approximate offsets","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"3329","year":"2011","oa_version":"Preprint","date_updated":"2023-02-23T11:12:57Z","date_created":"2018-12-11T12:02:42Z","related_material":{"record":[{"relation":"later_version","status":"public","id":"3115"}]},"author":[{"last_name":"Berberich","first_name":"Eric","full_name":"Berberich, Eric"},{"full_name":"Halperin, Dan","first_name":"Dan","last_name":"Halperin"},{"last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael"},{"full_name":"Pogalnikova, Roza","last_name":"Pogalnikova","first_name":"Roza"}]},{"doi":"10.1007/s00373-011-1020-7","language":[{"iso":"eng"}],"oa":1,"quality_controlled":"1","month":"03","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","last_name":"Sagraloff","first_name":"Michael"}],"volume":27,"date_updated":"2021-01-12T07:42:43Z","date_created":"2018-12-11T12:02:43Z","year":"2011","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","publist_id":"3301","file_date_updated":"2020-07-14T12:46:08Z","date_published":"2011-03-17T00:00:00Z","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.","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","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.","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","has_accepted_license":"1","article_processing_charge":"No","day":"17","scopus_import":1,"file":[{"file_size":143976,"content_type":"application/pdf","creator":"dernst","file_name":"2011_GraphsCombi_Kerber.pdf","access_level":"open_access","date_updated":"2020-07-14T12:46:08Z","date_created":"2020-05-19T16:11:36Z","checksum":"a63a1e3e885dcc68f1e3dea68dfbe213","relation":"main_file","file_id":"7869"}],"oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"3332","intvolume":" 27","status":"public","ddc":["500"],"title":"A note on the complexity of real algebraic hypersurfaces","issue":"3","abstract":[{"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.","lang":"eng"}],"type":"journal_article"},{"language":[{"iso":"eng"}],"doi":"10.1145/1993886.1993920","date_published":"2011-06-08T00:00:00Z","conference":{"name":"ISSAC: International Symposium on Symbolic and Algebraic Computation","location":"California, USA","start_date":"2011-06-08","end_date":"2011-06-11"},"page":"209 - 216","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1104.1362"}],"citation":{"ama":"Kerber M, Sagraloff M. Root refinement for real polynomials. In: Springer; 2011:209-216. doi:10.1145/1993886.1993920","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","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.","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."},"oa":1,"external_id":{"arxiv":["1104.1362"]},"article_processing_charge":"No","month":"06","day":"08","scopus_import":1,"oa_version":"Preprint","date_created":"2018-12-11T12:02:43Z","date_updated":"2021-01-12T07:42:42Z","author":[{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"},{"last_name":"Sagraloff","first_name":"Michael","full_name":"Sagraloff, Michael"}],"department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","status":"public","title":"Root refinement for real polynomials","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"3330","year":"2011","publist_id":"3304","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."}],"type":"conference"},{"citation":{"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.","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"},"main_file_link":[{"url":"https://hal.inria.fr/inria-00480031/file/RR-7274.pdf","open_access":"1"}],"oa":1,"page":"179 - 186","quality_controlled":"1","doi":"10.1145/1998196.1998224","date_published":"2011-06-13T00:00:00Z","conference":{"location":"Paris, France","start_date":"2011-06-13","end_date":"2011-06-15","name":"SCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"scopus_import":1,"article_processing_charge":"No","month":"06","day":"13","_id":"3328","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2011","department":[{"_id":"HeEd"}],"publisher":"ACM","status":"public","title":"A generic algebraic kernel for non linear geometric applications","publication_status":"published","author":[{"last_name":"Berberich","first_name":"Eric","full_name":"Berberich, Eric"},{"first_name":"Michael","last_name":"Hemmer","full_name":"Hemmer, Michael"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"}],"oa_version":"Published Version","date_created":"2018-12-11T12:02:42Z","date_updated":"2021-01-12T07:42:41Z","type":"conference","publist_id":"3307","abstract":[{"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.","lang":"eng"}]},{"publist_id":"3297","issue":"1","type":"journal_article","volume":45,"oa_version":"None","date_created":"2018-12-11T12:02:44Z","date_updated":"2021-01-12T07:42:44Z","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Pach, János","last_name":"Pach","first_name":"János"},{"first_name":"Günter","last_name":"Ziegler","full_name":"Ziegler, Günter"}],"department":[{"_id":"HeEd"}],"intvolume":" 45","publisher":"Springer","title":"Letter from the new editors-in-chief","status":"public","publication_status":"published","_id":"3334","year":"2011","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","month":"01","scopus_import":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00454-010-9313-9","date_published":"2011-01-01T00:00:00Z","page":"1 - 2","quality_controlled":"1","article_type":"letter_note","citation":{"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.","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.","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","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"},"publication":"Discrete & Computational Geometry"},{"year":"2011","_id":"3367","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"ACM","department":[{"_id":"HeEd"}],"title":"An output sensitive algorithm for persistent homology","status":"public","publication_status":"published","related_material":{"record":[{"status":"public","relation":"later_version","id":"2939"}]},"author":[{"first_name":"Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao"},{"first_name":"Michael","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael"}],"oa_version":"None","date_updated":"2023-02-23T11:05:04Z","date_created":"2018-12-11T12:02:56Z","type":"conference","publist_id":"3245","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."}],"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.","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.","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","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."},"page":"207 - 216","quality_controlled":"1","doi":"10.1145/1998196.1998228","date_published":"2011-06-13T00:00:00Z","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2011-06-15","start_date":"2011-06-13","location":"Paris, France"},"language":[{"iso":"eng"}],"scopus_import":1,"article_processing_charge":"No","day":"13","month":"06"},{"type":"journal_article","publist_id":"2446","issue":"1-2","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"}],"_id":"3781","acknowledgement":"Funded by Graduate Aid in Areas of National Need (GAANN) Fellowship.","year":"2011","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Szegedi Tudományegyetem","department":[{"_id":"HeEd"}],"intvolume":" 77","title":"The difference in length of curves in R^n","status":"public","publication_status":"published","author":[{"last_name":"Fasy","first_name":"Brittany Terese","id":"F65D502E-E68D-11E9-9252-C644099818F6","full_name":"Fasy, Brittany Terese"}],"oa_version":"None","volume":77,"date_updated":"2021-01-12T07:52:09Z","date_created":"2018-12-11T12:05:08Z","month":"01","day":"01","citation":{"chicago":"Fasy, Brittany Terese. “The Difference in Length of Curves in R^n.” Acta Sci. Math. (Szeged). Szegedi Tudományegyetem, 2011.","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.","ista":"Fasy BT. 2011. The difference in length of curves in R^n. Acta Sci. Math. (Szeged). 77(1–2), 359–367.","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.","apa":"Fasy, B. T. (2011). The difference in length of curves in R^n. Acta Sci. Math. (Szeged). Szegedi Tudományegyetem.","ama":"Fasy BT. The difference in length of curves in R^n. Acta Sci Math (Szeged). 2011;77(1-2):359-367."},"publication":"Acta Sci. Math. (Szeged)","page":"359 - 367","quality_controlled":"1","date_published":"2011-01-01T00:00:00Z","language":[{"iso":"eng"}]},{"file_date_updated":"2020-07-14T12:46:16Z","publist_id":"2427","date_created":"2018-12-11T12:05:13Z","date_updated":"2021-01-12T07:52:15Z","volume":6570,"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299"}],"publication_status":"published","editor":[{"full_name":"Calude, Cristian","first_name":"Cristian","last_name":"Calude"},{"last_name":"Rozenberg","first_name":"Grzegorz","full_name":"Rozenberg, Grzegorz"},{"first_name":"Arto","last_name":"Salomaa","full_name":"Salomaa, Arto"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"year":"2011","month":"05","language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-19391-0_2","quality_controlled":"1","oa":1,"abstract":[{"lang":"eng","text":"We address the problem of covering ℝ n with congruent balls, while minimizing the number of balls that contain an average point. Considering the 1-parameter family of lattices defined by stretching or compressing the integer grid in diagonal direction, we give a closed formula for the covering density that depends on the distortion parameter. We observe that our family contains the thinnest lattice coverings in dimensions 2 to 5. We also consider the problem of packing congruent balls in ℝ n , for which we give a closed formula for the packing density as well. Again we observe that our family contains optimal configurations, this time densest packings in dimensions 2 and 3."}],"alternative_title":["LNCS"],"type":"book_chapter","oa_version":"Submitted Version","file":[{"file_size":436875,"content_type":"application/pdf","creator":"system","access_level":"open_access","file_name":"IST-2016-539-v1+1_2011-B-01-CoveringPacking.pdf","checksum":"aaf22b4d7bd4277ffe8db532119cf474","date_updated":"2020-07-14T12:46:16Z","date_created":"2018-12-12T10:07:42Z","relation":"main_file","file_id":"4640"}],"pubrep_id":"539","title":"Covering and packing with spheres by diagonal distortion in R^n","status":"public","ddc":["000"],"intvolume":" 6570","_id":"3796","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","day":"03","has_accepted_license":"1","series_title":"Dedicated to Hermann Maurer on the Occasion of His 70th Birthday","date_published":"2011-05-03T00:00:00Z","page":"20 - 35","publication":"Rainbow of Computer Science","citation":{"ista":"Edelsbrunner H, Kerber M. 2011.Covering and packing with spheres by diagonal distortion in R^n. In: Rainbow of Computer Science. LNCS, vol. 6570, 20–35.","ieee":"H. Edelsbrunner and M. Kerber, “Covering and packing with spheres by diagonal distortion in R^n,” in Rainbow of Computer Science, vol. 6570, C. Calude, G. Rozenberg, and A. Salomaa, Eds. Springer, 2011, pp. 20–35.","apa":"Edelsbrunner, H., & Kerber, M. (2011). Covering and packing with spheres by diagonal distortion in R^n. In C. Calude, G. Rozenberg, & A. Salomaa (Eds.), Rainbow of Computer Science (Vol. 6570, pp. 20–35). Springer. https://doi.org/10.1007/978-3-642-19391-0_2","ama":"Edelsbrunner H, Kerber M. Covering and packing with spheres by diagonal distortion in R^n. In: Calude C, Rozenberg G, Salomaa A, eds. Rainbow of Computer Science. Vol 6570. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday. Springer; 2011:20-35. doi:10.1007/978-3-642-19391-0_2","chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Covering and Packing with Spheres by Diagonal Distortion in R^n.” In Rainbow of Computer Science, edited by Cristian Calude, Grzegorz Rozenberg, and Arto Salomaa, 6570:20–35. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday. Springer, 2011. https://doi.org/10.1007/978-3-642-19391-0_2.","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Covering and Packing with Spheres by Diagonal Distortion in R^n.” Rainbow of Computer Science, edited by Cristian Calude et al., vol. 6570, Springer, 2011, pp. 20–35, doi:10.1007/978-3-642-19391-0_2.","short":"H. Edelsbrunner, M. Kerber, in:, C. Calude, G. Rozenberg, A. Salomaa (Eds.), Rainbow of Computer Science, Springer, 2011, pp. 20–35."}},{"type":"journal_article","issue":"2.2","publist_id":"2161","abstract":[{"text":"The elevation function on a smoothly embedded 2-manifold in R-3 reflects the multiscale topography of cavities and protrusions as local maxima. The function has been useful in identifying coarse docking configurations for protein pairs. Transporting the concept from the smooth to the piecewise linear category, this paper describes an algorithm for finding all local maxima. While its worst-case running time is the same as of the algorithm used in prior work, its performance in practice is orders of magnitudes superior. We cast light on this improvement by relating the running time to the total absolute Gaussian curvature of the 2-manifold.","lang":"eng"}],"department":[{"_id":"HeEd"}],"intvolume":" 16","publisher":"ACM","publication_status":"published","title":"Computing elevation maxima by searching the Gauss sphere","status":"public","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"3965","year":"2011","volume":16,"oa_version":"None","date_created":"2018-12-11T12:06:09Z","date_updated":"2021-01-12T07:53:31Z","author":[{"first_name":"Bei","last_name":"Wang","full_name":"Wang, Bei"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Morozov, Dmitriy","first_name":"Dmitriy","last_name":"Morozov"}],"scopus_import":1,"day":"01","month":"05","page":"1 - 13","quality_controlled":"1","citation":{"ista":"Wang B, Edelsbrunner H, Morozov D. 2011. Computing elevation maxima by searching the Gauss sphere. Journal of Experimental Algorithmics. 16(2.2), 1–13.","ieee":"B. Wang, H. Edelsbrunner, and D. Morozov, “Computing elevation maxima by searching the Gauss sphere,” Journal of Experimental Algorithmics, vol. 16, no. 2.2. ACM, pp. 1–13, 2011.","apa":"Wang, B., Edelsbrunner, H., & Morozov, D. (2011). Computing elevation maxima by searching the Gauss sphere. Journal of Experimental Algorithmics. ACM. https://doi.org/10.1145/1963190.1970375","ama":"Wang B, Edelsbrunner H, Morozov D. Computing elevation maxima by searching the Gauss sphere. Journal of Experimental Algorithmics. 2011;16(2.2):1-13. doi:10.1145/1963190.1970375","chicago":"Wang, Bei, Herbert Edelsbrunner, and Dmitriy Morozov. “Computing Elevation Maxima by Searching the Gauss Sphere.” Journal of Experimental Algorithmics. ACM, 2011. https://doi.org/10.1145/1963190.1970375.","mla":"Wang, Bei, et al. “Computing Elevation Maxima by Searching the Gauss Sphere.” Journal of Experimental Algorithmics, vol. 16, no. 2.2, ACM, 2011, pp. 1–13, doi:10.1145/1963190.1970375.","short":"B. Wang, H. Edelsbrunner, D. Morozov, Journal of Experimental Algorithmics 16 (2011) 1–13."},"publication":"Journal of Experimental Algorithmics","language":[{"iso":"eng"}],"doi":"10.1145/1963190.1970375","date_published":"2011-05-01T00:00:00Z"},{"department":[{"_id":"HeEd"}],"editor":[{"last_name":"Peikert","first_name":"Ronald","full_name":"Peikert, Ronald"},{"first_name":"Helwig","last_name":"Hauser","full_name":"Hauser, Helwig"},{"full_name":"Carr, Hamish","first_name":"Hamish","last_name":"Carr"},{"full_name":"Fuchs, Raphael","last_name":"Fuchs","first_name":"Raphael"}],"publisher":"Springer","status":"public","title":"Efficient computation of persistent homology for cubical data","publication_status":"published","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"3271","year":"2011","oa_version":"None","date_updated":"2021-01-12T07:42:18Z","date_created":"2018-12-11T12:02:23Z","author":[{"full_name":"Wagner, Hubert","first_name":"Hubert","last_name":"Wagner"},{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","first_name":"Chao","full_name":"Chen, Chao"},{"first_name":"Erald","last_name":"Vuçini","full_name":"Vuçini, Erald"}],"alternative_title":["Theory, Algorithms, and Applications"],"type":"book_chapter","publist_id":"3375","abstract":[{"lang":"eng","text":"In this paper we present an efficient framework for computation of persis- tent homology of cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is adapted to the setting of cubical complexes. The proposed approach enables efficient application of persistent homology in domains where the data is naturally given in a cubical form. By avoiding triangulation of the data, we significantly reduce the size of the complex. We also present a data-structure de- signed to compactly store and quickly manipulate cubical complexes. By means of numerical experiments, we show high speed and memory efficiency of our ap- proach. We compare our framework to other available implementations, showing its superiority. Finally, we report performance on selected 3D and 4D data-sets."}],"page":"91 - 106","quality_controlled":"1","citation":{"chicago":"Wagner, Hubert, Chao Chen, and Erald Vuçini. “Efficient Computation of Persistent Homology for Cubical Data.” In Topological Methods in Data Analysis and Visualization II, edited by Ronald Peikert, Helwig Hauser, Hamish Carr, and Raphael Fuchs, 91–106. Springer, 2011. https://doi.org/10.1007/978-3-642-23175-9_7.","short":"H. Wagner, C. Chen, E. Vuçini, in:, R. Peikert, H. Hauser, H. Carr, R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II, Springer, 2011, pp. 91–106.","mla":"Wagner, Hubert, et al. “Efficient Computation of Persistent Homology for Cubical Data.” Topological Methods in Data Analysis and Visualization II, edited by Ronald Peikert et al., Springer, 2011, pp. 91–106, doi:10.1007/978-3-642-23175-9_7.","apa":"Wagner, H., Chen, C., & Vuçini, E. (2011). Efficient computation of persistent homology for cubical data. In R. Peikert, H. Hauser, H. Carr, & R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II (pp. 91–106). Springer. https://doi.org/10.1007/978-3-642-23175-9_7","ieee":"H. Wagner, C. Chen, and E. Vuçini, “Efficient computation of persistent homology for cubical data,” in Topological Methods in Data Analysis and Visualization II, R. Peikert, H. Hauser, H. Carr, and R. Fuchs, Eds. Springer, 2011, pp. 91–106.","ista":"Wagner H, Chen C, Vuçini E. 2011.Efficient computation of persistent homology for cubical data. In: Topological Methods in Data Analysis and Visualization II. Theory, Algorithms, and Applications, , 91–106.","ama":"Wagner H, Chen C, Vuçini E. Efficient computation of persistent homology for cubical data. In: Peikert R, Hauser H, Carr H, Fuchs R, eds. Topological Methods in Data Analysis and Visualization II. Springer; 2011:91-106. doi:10.1007/978-3-642-23175-9_7"},"publication":"Topological Methods in Data Analysis and Visualization II","language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-23175-9_7","date_published":"2011-11-14T00:00:00Z","scopus_import":1,"day":"14","month":"11"},{"day":"01","month":"01","page":"197 - 200","quality_controlled":"1","citation":{"mla":"Chen, Chao, and Michael Kerber. Persistent Homology Computation with a Twist. TU Dortmund, 2011, pp. 197–200.","short":"C. Chen, M. Kerber, in:, TU Dortmund, 2011, pp. 197–200.","chicago":"Chen, Chao, and Michael Kerber. “Persistent Homology Computation with a Twist,” 197–200. TU Dortmund, 2011.","ama":"Chen C, Kerber M. Persistent homology computation with a twist. In: TU Dortmund; 2011:197-200.","ista":"Chen C, Kerber M. 2011. Persistent homology computation with a twist. EuroCG: European Workshop on Computational Geometry, 197–200.","apa":"Chen, C., & Kerber, M. (2011). Persistent homology computation with a twist (pp. 197–200). Presented at the EuroCG: European Workshop on Computational Geometry, Morschach, Switzerland: TU Dortmund.","ieee":"C. Chen and M. Kerber, “Persistent homology computation with a twist,” presented at the EuroCG: European Workshop on Computational Geometry, Morschach, Switzerland, 2011, pp. 197–200."},"language":[{"iso":"eng"}],"date_published":"2011-01-01T00:00:00Z","conference":{"name":"EuroCG: European Workshop on Computational Geometry","location":"Morschach, Switzerland","start_date":"2011-03-28","end_date":"2011-03-30"},"type":"conference","publist_id":"3376","abstract":[{"text":"The persistence diagram of a filtered simplicial com- plex is usually computed by reducing the boundary matrix of the complex. We introduce a simple op- timization technique: by processing the simplices of the complex in decreasing dimension, we can “kill” columns (i.e., set them to zero) without reducing them. This technique completely avoids reduction on roughly half of the columns. We demonstrate that this idea significantly improves the running time of the reduction algorithm in practice. We also give an output-sensitive complexity analysis for the new al- gorithm which yields to sub-cubic asymptotic bounds under certain assumptions.","lang":"eng"}],"department":[{"_id":"HeEd"}],"publisher":"TU Dortmund","status":"public","title":"Persistent homology computation with a twist","publication_status":"published","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"3270","year":"2011","oa_version":"None","date_created":"2018-12-11T12:02:22Z","date_updated":"2021-01-12T07:42:17Z","author":[{"full_name":"Chen, Chao","last_name":"Chen","first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael"}]},{"date_updated":"2020-07-14T23:03:43Z","date_created":"2018-12-11T12:02:36Z","author":[{"first_name":"Ying","last_name":"Zheng","full_name":"Zheng, Ying"},{"last_name":"Gu","first_name":"Steve","full_name":"Gu, Steve"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Tomasi, Carlo","first_name":"Carlo","last_name":"Tomasi"},{"first_name":"Philip","last_name":"Benfey","full_name":"Benfey, Philip"}],"publication_status":"published","publisher":"IEEE","department":[{"_id":"HeEd"}],"year":"2011","acknowledgement":"This research is supported by the National Science Foundation (NSF) under grant DBI-0820624.","file_date_updated":"2020-07-14T12:46:07Z","publist_id":"3328","article_number":"6126475","language":[{"iso":"eng"}],"conference":{"name":"ICCV: International Conference on Computer Vision","end_date":"2011-11-13","start_date":"2011-11-06","location":"Barcelona, Spain"},"doi":"10.1109/ICCV.2011.6126475","quality_controlled":"1","oa":1,"month":"12","oa_version":"Submitted Version","file":[{"content_type":"application/pdf","file_size":5622728,"creator":"system","access_level":"open_access","file_name":"IST-2016-541-v1+1_2011-P-07-RootReconstruction.pdf","checksum":"30a33564b7b45a7ee31610898267fd0e","date_updated":"2020-07-14T12:46:07Z","date_created":"2018-12-12T10:09:04Z","relation":"main_file","file_id":"4727"}],"pubrep_id":"541","ddc":["000"],"status":"public","title":"Detailed reconstruction of 3D plant root shape","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"3312","abstract":[{"lang":"eng","text":"We study the 3D reconstruction of plant roots from multiple 2D images. To meet the challenge caused by the delicate nature of thin branches, we make three innovations to cope with the sensitivity to image quality and calibration. First, we model the background as a harmonic function to improve the segmentation of the root in each 2D image. Second, we develop the concept of the regularized visual hull which reduces the effect of jittering and refraction by ensuring consistency with one 2D image. Third, we guarantee connectedness through adjustments to the 3D reconstruction that minimize global error. Our software is part of a biological phenotype/genotype study of agricultural root systems. It has been tested on more than 40 plant roots and results are promising in terms of reconstruction quality and efficiency."}],"type":"conference_poster","date_published":"2011-12-31T00:00:00Z","publication":"Proceedings of the IEEE International Conference on Computer Vision","citation":{"ama":"Zheng Y, Gu S, Edelsbrunner H, Tomasi C, Benfey P. Detailed Reconstruction of 3D Plant Root Shape. IEEE; 2011. doi:10.1109/ICCV.2011.6126475","ieee":"Y. Zheng, S. Gu, H. Edelsbrunner, C. Tomasi, and P. Benfey, Detailed reconstruction of 3D plant root shape. IEEE, 2011.","apa":"Zheng, Y., Gu, S., Edelsbrunner, H., Tomasi, C., & Benfey, P. (2011). Detailed reconstruction of 3D plant root shape. Proceedings of the IEEE International Conference on Computer Vision. Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126475","ista":"Zheng Y, Gu S, Edelsbrunner H, Tomasi C, Benfey P. 2011. Detailed reconstruction of 3D plant root shape, IEEE,p.","short":"Y. Zheng, S. Gu, H. Edelsbrunner, C. Tomasi, P. Benfey, Detailed Reconstruction of 3D Plant Root Shape, IEEE, 2011.","mla":"Zheng, Ying, et al. “Detailed Reconstruction of 3D Plant Root Shape.” Proceedings of the IEEE International Conference on Computer Vision, 6126475, IEEE, 2011, doi:10.1109/ICCV.2011.6126475.","chicago":"Zheng, Ying, Steve Gu, Herbert Edelsbrunner, Carlo Tomasi, and Philip Benfey. Detailed Reconstruction of 3D Plant Root Shape. Proceedings of the IEEE International Conference on Computer Vision. IEEE, 2011. https://doi.org/10.1109/ICCV.2011.6126475."},"day":"31","has_accepted_license":"1","article_processing_charge":"No"},{"file_date_updated":"2020-07-14T12:46:07Z","publist_id":"3327","article_number":"6126271","date_updated":"2021-01-12T07:42:35Z","date_created":"2018-12-11T12:02:37Z","author":[{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","first_name":"Chao","full_name":"Chen, Chao"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"IEEE","year":"2011","month":"11","language":[{"iso":"eng"}],"conference":{"start_date":"2011-11-06","location":"Barcelona, Spain","end_date":"2011-11-13","name":"ICCV: International Conference on Computer Vision"},"doi":"10.1109/ICCV.2011.6126271","quality_controlled":"1","oa":1,"abstract":[{"text":"Interpreting an image as a function on a compact sub- set of the Euclidean plane, we get its scale-space by diffu- sion, spreading the image over the entire plane. This gener- ates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian ker- nel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods.","lang":"eng"}],"type":"conference","oa_version":"Submitted Version","file":[{"date_created":"2018-12-12T10:17:28Z","date_updated":"2020-07-14T12:46:07Z","checksum":"6984684081ba123808b344f9f2e64a8f","file_id":"5282","relation":"main_file","creator":"system","file_size":614050,"content_type":"application/pdf","file_name":"IST-2016-540-v1+1_2011-P-08-RunEmpty.pdf","access_level":"open_access"}],"pubrep_id":"540","title":"Diffusion runs low on persistence fast","ddc":["000"],"status":"public","_id":"3313","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"06","has_accepted_license":"1","scopus_import":1,"date_published":"2011-11-06T00:00:00Z","publication":"Proceedings of the IEEE International Conference on Computer Vision","citation":{"ama":"Chen C, Edelsbrunner H. Diffusion runs low on persistence fast. In: Proceedings of the IEEE International Conference on Computer Vision. IEEE; 2011. doi:10.1109/ICCV.2011.6126271","ista":"Chen C, Edelsbrunner H. 2011. Diffusion runs low on persistence fast. Proceedings of the IEEE International Conference on Computer Vision. ICCV: International Conference on Computer Vision, 6126271.","ieee":"C. Chen and H. Edelsbrunner, “Diffusion runs low on persistence fast,” in Proceedings of the IEEE International Conference on Computer Vision, Barcelona, Spain, 2011.","apa":"Chen, C., & Edelsbrunner, H. (2011). Diffusion runs low on persistence fast. In Proceedings of the IEEE International Conference on Computer Vision. Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126271","mla":"Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.” Proceedings of the IEEE International Conference on Computer Vision, 6126271, IEEE, 2011, doi:10.1109/ICCV.2011.6126271.","short":"C. Chen, H. Edelsbrunner, in:, Proceedings of the IEEE International Conference on Computer Vision, IEEE, 2011.","chicago":"Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.” In Proceedings of the IEEE International Conference on Computer Vision. IEEE, 2011. https://doi.org/10.1109/ICCV.2011.6126271."}},{"file_date_updated":"2022-05-24T07:55:05Z","abstract":[{"text":"Alpha shapes have been conceived in 1981 as an attempt to define the shape of a finite set of point in the plane. Since then, connections to diverse areas in the sciences and engineering have developed, including to pattern recognition, digital shape sampling and processing, and structural molecular biology. This survey begins with a historical account and discusses geometric, algorithmic, topological, and combinatorial aspects of alpha shapes in this sequence.","lang":"eng"}],"publist_id":"3329","type":"book_chapter","date_updated":"2022-05-24T07:56:30Z","date_created":"2018-12-11T12:02:36Z","oa_version":"Submitted Version","file":[{"file_size":475254,"content_type":"application/pdf","creator":"dernst","file_name":"2010_AlphaShapes.pdf","access_level":"open_access","date_created":"2022-05-24T07:55:05Z","date_updated":"2022-05-24T07:55:05Z","checksum":"a592ea438351e7280eea993a7713ab8f","success":1,"relation":"main_file","file_id":"11408"}],"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"ddc":["510"],"publication_status":"inpress","status":"public","title":"Alpha shapes - a survey","publisher":"Springer","department":[{"_id":"HeEd"}],"editor":[{"first_name":"R","last_name":"van de Weygaert","full_name":"van de Weygaert, R"},{"full_name":"Vegter, G","first_name":"G","last_name":"Vegter"},{"full_name":"Ritzerveld, J","first_name":"J","last_name":"Ritzerveld"},{"full_name":"Icke, V","last_name":"Icke","first_name":"V"}],"_id":"3311","year":"2011","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"31","month":"12","article_processing_charge":"No","has_accepted_license":"1","language":[{"iso":"eng"}],"date_published":"2011-12-31T00:00:00Z","quality_controlled":"1","publication":"Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings","citation":{"short":"H. Edelsbrunner, in:, R. van de Weygaert, G. Vegter, J. Ritzerveld, V. Icke (Eds.), Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, Springer, n.d.","mla":"Edelsbrunner, Herbert. “Alpha Shapes - a Survey.” Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, edited by R van de Weygaert et al., Springer.","chicago":"Edelsbrunner, Herbert. “Alpha Shapes - a Survey.” In Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, edited by R van de Weygaert, G Vegter, J Ritzerveld, and V Icke. Springer, n.d.","ama":"Edelsbrunner H. Alpha shapes - a survey. In: van de Weygaert R, Vegter G, Ritzerveld J, Icke V, eds. Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. Springer.","apa":"Edelsbrunner, H. (n.d.). Alpha shapes - a survey. In R. van de Weygaert, G. Vegter, J. Ritzerveld, & V. Icke (Eds.), Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. Springer.","ieee":"H. Edelsbrunner, “Alpha shapes - a survey,” in Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, R. van de Weygaert, G. Vegter, J. Ritzerveld, and V. Icke, Eds. Springer.","ista":"Edelsbrunner H.Alpha shapes - a survey. In: Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. ."},"oa":1},{"day":"01","scopus_import":1,"date_published":"2011-06-01T00:00:00Z","publication":"Foundations of Computational Mathematics","citation":{"ama":"Edelsbrunner H, Morozov D, Patel A. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 2011;11(3):345-361. doi:10.1007/s10208-011-9090-8","ista":"Edelsbrunner H, Morozov D, Patel A. 2011. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 11(3), 345–361.","apa":"Edelsbrunner, H., Morozov, D., & Patel, A. (2011). Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-011-9090-8","ieee":"H. Edelsbrunner, D. Morozov, and A. Patel, “Quantifying transversality by measuring the robustness of intersections,” Foundations of Computational Mathematics, vol. 11, no. 3. Springer, pp. 345–361, 2011.","mla":"Edelsbrunner, Herbert, et al. “Quantifying Transversality by Measuring the Robustness of Intersections.” Foundations of Computational Mathematics, vol. 11, no. 3, Springer, 2011, pp. 345–61, doi:10.1007/s10208-011-9090-8.","short":"H. Edelsbrunner, D. Morozov, A. Patel, Foundations of Computational Mathematics 11 (2011) 345–361.","chicago":"Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “Quantifying Transversality by Measuring the Robustness of Intersections.” Foundations of Computational Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-011-9090-8."},"page":"345 - 361","abstract":[{"text":"By definition, transverse intersections are stable under in- finitesimal perturbations. Using persistent homology, we ex- tend this notion to sizeable perturbations. Specifically, we assign to each homology class of the intersection its robust- ness, the magnitude of a perturbation necessary to kill it, and prove that robustness is stable. Among the applications of this result is a stable notion of robustness for fixed points of continuous mappings and a statement of stability for con- tours of smooth mappings.","lang":"eng"}],"issue":"3","type":"journal_article","oa_version":"Submitted Version","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"3377","title":"Quantifying transversality by measuring the robustness of intersections","status":"public","intvolume":" 11","month":"06","doi":"10.1007/s10208-011-9090-8","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/0911.2142","open_access":"1"}],"quality_controlled":"1","publist_id":"3230","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Morozov","first_name":"Dmitriy","full_name":"Morozov, Dmitriy"},{"id":"34A254A0-F248-11E8-B48F-1D18A9856A87","first_name":"Amit","last_name":"Patel","full_name":"Patel, Amit"}],"date_updated":"2021-01-12T07:43:04Z","date_created":"2018-12-11T12:02:59Z","volume":11,"year":"2011","acknowledgement":"This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057.","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer"},{"month":"06","day":"01","scopus_import":1,"language":[{"iso":"eng"}],"doi":"10.1007/s10208-010-9081-1","date_published":"2011-06-01T00:00:00Z","quality_controlled":"1","page":"305 - 336","publication":"Foundations of Computational Mathematics","citation":{"short":"P. Bendich, J. Harer, Foundations of Computational Mathematics 11 (2011) 305–336.","mla":"Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics, vol. 11, no. 3, Springer, 2011, pp. 305–36, doi:10.1007/s10208-010-9081-1.","chicago":"Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-010-9081-1.","ama":"Bendich P, Harer J. Persistent intersection homology. Foundations of Computational Mathematics. 2011;11(3):305-336. doi:10.1007/s10208-010-9081-1","apa":"Bendich, P., & Harer, J. (2011). Persistent intersection homology. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-010-9081-1","ieee":"P. Bendich and J. Harer, “Persistent intersection homology,” Foundations of Computational Mathematics, vol. 11, no. 3. Springer, pp. 305–336, 2011.","ista":"Bendich P, Harer J. 2011. Persistent intersection homology. Foundations of Computational Mathematics. 11(3), 305–336."},"abstract":[{"lang":"eng","text":"The theory of intersection homology was developed to study the singularities of a topologically stratified space. This paper in- corporates this theory into the already developed framework of persistent homology. We demonstrate that persistent intersec- tion homology gives useful information about the relationship between an embedded stratified space and its singularities. We give, and prove the correctness of, an algorithm for the computa- tion of the persistent intersection homology groups of a filtered simplicial complex equipped with a stratification by subcom- plexes. We also derive, from Poincare ́ Duality, some structural results about persistent intersection homology."}],"publist_id":"3229","issue":"3","type":"journal_article","date_created":"2018-12-11T12:02:59Z","date_updated":"2021-01-12T07:43:04Z","volume":11,"oa_version":"None","author":[{"full_name":"Bendich, Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","first_name":"Paul","last_name":"Bendich"},{"full_name":"Harer, John","first_name":"John","last_name":"Harer"}],"title":"Persistent intersection homology","status":"public","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","intvolume":" 11","_id":"3378","acknowledgement":"This research was partially supported by the Defense Advanced Research Projects Agency (DARPA) under grant HR0011-05-1-0007.","year":"2011","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87"},{"citation":{"ieee":"C. Chen, D. Freedman, and C. Lampert, “Enforcing topological constraints in random field image segmentation,” in CVPR: Computer Vision and Pattern Recognition, Colorado Springs, CO, United States, 2011, pp. 2089–2096.","apa":"Chen, C., Freedman, D., & Lampert, C. (2011). Enforcing topological constraints in random field image segmentation. In CVPR: Computer Vision and Pattern Recognition (pp. 2089–2096). Colorado Springs, CO, United States: IEEE. https://doi.org/10.1109/CVPR.2011.5995503","ista":"Chen C, Freedman D, Lampert C. 2011. Enforcing topological constraints in random field image segmentation. CVPR: Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition, 2089–2096.","ama":"Chen C, Freedman D, Lampert C. Enforcing topological constraints in random field image segmentation. In: CVPR: Computer Vision and Pattern Recognition. IEEE; 2011:2089-2096. doi:10.1109/CVPR.2011.5995503","chicago":"Chen, Chao, Daniel Freedman, and Christoph Lampert. “Enforcing Topological Constraints in Random Field Image Segmentation.” In CVPR: Computer Vision and Pattern Recognition, 2089–96. IEEE, 2011. https://doi.org/10.1109/CVPR.2011.5995503.","short":"C. Chen, D. Freedman, C. Lampert, in:, CVPR: Computer Vision and Pattern Recognition, IEEE, 2011, pp. 2089–2096.","mla":"Chen, Chao, et al. “Enforcing Topological Constraints in Random Field Image Segmentation.” CVPR: Computer Vision and Pattern Recognition, IEEE, 2011, pp. 2089–96, doi:10.1109/CVPR.2011.5995503."},"publication":"CVPR: Computer Vision and Pattern Recognition","page":"2089 - 2096","quality_controlled":"1","date_published":"2011-07-22T00:00:00Z","doi":"10.1109/CVPR.2011.5995503","conference":{"name":"CVPR: Conference on Computer Vision and Pattern Recognition","location":"Colorado Springs, CO, United States","start_date":"2011-06-20","end_date":"2011-06-25"},"language":[{"iso":"eng"}],"scopus_import":"1","publication_identifier":{"isbn":["978-1-4577-0394-2"],"eisbn":["978-1-4577-0395-9"]},"article_processing_charge":"No","day":"22","month":"07","_id":"3336","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2011","acknowledgement":"The first author is supported by the Austrian Science Fund (FWF) grant No. P20134-N13. The authors would like to thank Sebastian Nowozin for helpful discussions.","department":[{"_id":"HeEd"},{"_id":"ChLa"}],"publisher":"IEEE","publication_status":"published","status":"public","title":"Enforcing topological constraints in random field image segmentation","related_material":{"record":[{"id":"5386","status":"public","relation":"earlier_version"}]},"author":[{"first_name":"Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao"},{"full_name":"Freedman, Daniel","last_name":"Freedman","first_name":"Daniel"},{"id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8622-7887","first_name":"Christoph","last_name":"Lampert","full_name":"Lampert, Christoph"}],"oa_version":"None","date_created":"2018-12-11T12:02:45Z","date_updated":"2023-02-23T12:23:56Z","type":"conference","publist_id":"3294","abstract":[{"text":"We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.","lang":"eng"}]}]