[{"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"}],"publication_status":"published","department":[{"_id":"HeEd"}],"_id":"2843","doi":"10.1007/978-3-642-37067-0","related_material":{"record":[{"id":"2255","status":"public","relation":"later_version"}]},"language":[{"iso":"eng"}],"title":"Stable length estimates of tube-like shapes","publication":"17th IAPR International Conference on Discrete Geometry for Computer Imagery","year":"2013","day":"21","oa_version":"None","type":"conference","date_updated":"2023-02-23T10:35:00Z","quality_controlled":"1","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian","last_name":"Pausinger"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. In: <i>17th IAPR International Conference on Discrete Geometry for Computer Imagery</i>. Vol 7749. Springer; 2013:XV-XIX. doi:<a href=\"https://doi.org/10.1007/978-3-642-37067-0\">10.1007/978-3-642-37067-0</a>","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” in <i>17th IAPR International Conference on Discrete Geometry for Computer Imagery</i>, 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.","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” In <i>17th IAPR International Conference on Discrete Geometry for Computer Imagery</i>, 7749:XV–XIX. Springer, 2013. <a href=\"https://doi.org/10.1007/978-3-642-37067-0\">https://doi.org/10.1007/978-3-642-37067-0</a>.","short":"H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX.","apa":"Edelsbrunner, H., &#38; Pausinger, F. (2013). Stable length estimates of tube-like shapes. In <i>17th IAPR International Conference on Discrete Geometry for Computer Imagery</i> (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. <a href=\"https://doi.org/10.1007/978-3-642-37067-0\">https://doi.org/10.1007/978-3-642-37067-0</a>","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” <i>17th IAPR International Conference on Discrete Geometry for Computer Imagery</i>, vol. 7749, Springer, 2013, pp. XV–XIX, doi:<a href=\"https://doi.org/10.1007/978-3-642-37067-0\">10.1007/978-3-642-37067-0</a>."},"status":"public","conference":{"start_date":"2013-03-20","location":"Seville, Spain","end_date":"2013-03-22","name":"DGCI: Discrete Geometry for Computer Imagery"},"month":"02","date_created":"2018-12-11T11:59:53Z","scopus_import":1,"publist_id":"3952","alternative_title":["LNCS"],"intvolume":"      7749","publisher":"Springer","page":"XV - XIX","volume":7749,"date_published":"2013-02-21T00:00:00Z"},{"publisher":"International Press","volume":15,"issue":"1","date_created":"2018-12-11T11:59:58Z","month":"05","status":"public","intvolume":"        15","publist_id":"3930","year":"2013","citation":{"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.” <i>Homology, Homotopy and Applications</i>. International Press, 2013. <a href=\"https://doi.org/10.4310/HHA.2013.v15.n1.a3\">https://doi.org/10.4310/HHA.2013.v15.n1.a3</a>.","ista":"Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72.","ieee":"P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness of level and interlevel sets,” <i>Homology, Homotopy and Applications</i>, vol. 15, no. 1. International Press, pp. 51–72, 2013.","ama":"Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level and interlevel sets. <i>Homology, Homotopy and Applications</i>. 2013;15(1):51-72. doi:<a href=\"https://doi.org/10.4310/HHA.2013.v15.n1.a3\">10.4310/HHA.2013.v15.n1.a3</a>","mla":"Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.” <i>Homology, Homotopy and Applications</i>, vol. 15, no. 1, International Press, 2013, pp. 51–72, doi:<a href=\"https://doi.org/10.4310/HHA.2013.v15.n1.a3\">10.4310/HHA.2013.v15.n1.a3</a>.","apa":"Bendich, P., Edelsbrunner, H., Morozov, D., &#38; Patel, A. (2013). Homology and robustness of level and interlevel sets. <i>Homology, Homotopy and Applications</i>. International Press. <a href=\"https://doi.org/10.4310/HHA.2013.v15.n1.a3\">https://doi.org/10.4310/HHA.2013.v15.n1.a3</a>"},"main_file_link":[{"url":"https://arxiv.org/abs/1102.3389v1","open_access":"1"}],"quality_controlled":"1","author":[{"id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","full_name":"Bendich, Paul","first_name":"Paul","last_name":"Bendich"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Dmitriy","last_name":"Morozov","full_name":"Morozov, Dmitriy"},{"id":"34A254A0-F248-11E8-B48F-1D18A9856A87","full_name":"Patel, Amit","last_name":"Patel","first_name":"Amit"}],"publication_status":"published","abstract":[{"text":"Given a continuous function f:X-R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization.","lang":"eng"}],"title":"Homology and robustness of level and interlevel sets","publication":"Homology, Homotopy and Applications","oa":1,"_id":"2859","date_published":"2013-05-01T00:00:00Z","external_id":{"arxiv":["1102.3389"]},"page":"51 - 72","arxiv":1,"scopus_import":1,"type":"journal_article","date_updated":"2021-01-12T07:00:18Z","oa_version":"Preprint","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"doi":"10.4310/HHA.2013.v15.n1.a3","department":[{"_id":"HeEd"}]},{"volume":110,"issue":"7","article_type":"original","publisher":"National Academy of Sciences","publist_id":"3872","intvolume":"       110","status":"public","month":"02","date_created":"2018-12-11T12:00:09Z","author":[{"last_name":"Fang","first_name":"Suqin","full_name":"Fang, Suqin"},{"last_name":"Clark","first_name":"Randy","full_name":"Clark, Randy"},{"full_name":"Zheng, Ying","last_name":"Zheng","first_name":"Ying"},{"full_name":"Iyer Pascuzzi, Anjali","last_name":"Iyer Pascuzzi","first_name":"Anjali"},{"last_name":"Weitz","first_name":"Joshua","full_name":"Weitz, Joshua"},{"full_name":"Kochian, Leon","last_name":"Kochian","first_name":"Leon"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Liao","first_name":"Hong","full_name":"Liao, Hong"},{"full_name":"Benfey, Philip","first_name":"Philip","last_name":"Benfey"}],"quality_controlled":"1","citation":{"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.","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.” <i>PNAS</i>. National Academy of Sciences, 2013. <a href=\"https://doi.org/10.1073/pnas.1222821110\">https://doi.org/10.1073/pnas.1222821110</a>.","ieee":"S. Fang <i>et al.</i>, “Genotypic recognition and spatial responses by rice roots,” <i>PNAS</i>, vol. 110, no. 7. National Academy of Sciences, pp. 2670–2675, 2013.","ama":"Fang S, Clark R, Zheng Y, et al. Genotypic recognition and spatial responses by rice roots. <i>PNAS</i>. 2013;110(7):2670-2675. doi:<a href=\"https://doi.org/10.1073/pnas.1222821110\">10.1073/pnas.1222821110</a>","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. <i>PNAS</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.1222821110\">https://doi.org/10.1073/pnas.1222821110</a>","mla":"Fang, Suqin, et al. “Genotypic Recognition and Spatial Responses by Rice Roots.” <i>PNAS</i>, vol. 110, no. 7, National Academy of Sciences, 2013, pp. 2670–75, doi:<a href=\"https://doi.org/10.1073/pnas.1222821110\">10.1073/pnas.1222821110</a>."},"main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/","open_access":"1"}],"year":"2013","_id":"2887","oa":1,"pmid":1,"title":"Genotypic recognition and spatial responses by rice roots","publication":"PNAS","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"}],"publication_status":"published","page":"2670 - 2675","external_id":{"pmid":["23362379"]},"date_published":"2013-02-12T00:00:00Z","scopus_import":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"12","oa_version":"Published Version","date_updated":"2021-01-12T07:00:29Z","type":"journal_article","department":[{"_id":"HeEd"}],"doi":"10.1073/pnas.1222821110","language":[{"iso":"eng"}]},{"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"}],"publication_status":"published","title":"Computing the M most probable modes of a graphical model","department":[{"_id":"HeEd"},{"_id":"VlKo"},{"_id":"ChLa"}],"_id":"2901","language":[{"iso":"eng"}],"oa":1,"oa_version":"None","type":"conference","date_updated":"2021-01-12T07:00:35Z","year":"2013","day":"01","citation":{"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.","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.","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&#38;CP, vol. 31, 161–169.","chicago":"Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph Lampert. “Computing the M Most Probable Modes of a Graphical Model,” 31:161–69. JMLR, 2013.","short":"C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, JMLR, 2013, pp. 161–169.","apa":"Chen, C., Kolmogorov, V., Yan, Z., Metaxas, D., &#38; 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.","mla":"Chen, Chao, et al. <i>Computing the M Most Probable Modes of a Graphical Model</i>. Vol. 31, JMLR, 2013, pp. 161–69."},"main_file_link":[{"open_access":"1","url":"http://jmlr.org/proceedings/papers/v31/chen13a.html"}],"quality_controlled":"1","author":[{"full_name":"Chen, Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","first_name":"Chao"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","last_name":"Kolmogorov"},{"first_name":"Zhu","last_name":"Yan","full_name":"Yan, Zhu"},{"first_name":"Dimitris","last_name":"Metaxas","full_name":"Metaxas, Dimitris"},{"last_name":"Lampert","first_name":"Christoph","orcid":"0000-0001-8622-7887","full_name":"Lampert, Christoph","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"01","conference":{"end_date":"2013-05-01","name":" AISTATS: Conference on Uncertainty in Artificial Intelligence","location":"Scottsdale, AZ, United States","start_date":"2013-04-29"},"date_created":"2018-12-11T12:00:14Z","status":"public","alternative_title":[" JMLR: W&CP"],"intvolume":"        31","scopus_import":1,"publist_id":"3846","publisher":"JMLR","date_published":"2013-01-01T00:00:00Z","page":"161 - 169","volume":31},{"alternative_title":["ALENEX"],"scopus_import":1,"date_published":"2013-01-01T00:00:00Z","file":[{"date_updated":"2020-07-14T12:45:52Z","file_id":"4720","checksum":"a15a3ba22df9445731507f3e06c9fcee","file_name":"IST-2016-547-v1+1_2013-P-08-MedusaII.pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:08:57Z","creator":"system","content_type":"application/pdf","file_size":403013}],"page":"70 - 77","doi":"10.1137/1.9781611972931.6","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"}],"has_accepted_license":"1","date_updated":"2021-01-12T07:00:36Z","type":"conference","oa_version":"Submitted Version","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T12:00:16Z","conference":{"name":"ALENEX: Algorithm Engineering and Experiments","end_date":"2013-01-07","start_date":"2013-01-07","location":"New Orleans, LA, United States"},"month":"01","status":"public","publist_id":"3841","file_date_updated":"2020-07-14T12:45:52Z","publisher":"Society of Industrial and Applied Mathematics","pubrep_id":"547","publication_status":"published","abstract":[{"lang":"eng","text":"Motivated by an application in cell biology, we describe an extension of the kinetic data structures framework from Delaunay triangulations to fixed-radius alpha complexes. Our algorithm is implemented\r\nusing CGAL, following the exact geometric computation paradigm. We report on several\r\ntechniques to accelerate the computation that turn our implementation applicable to the underlying biological\r\nproblem."}],"publication":"2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments","title":"3D kinetic alpha complexes and their implementation","ddc":["500"],"oa":1,"_id":"2906","year":"2013","citation":{"mla":"Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and Their Implementation.” <i>2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments</i>, Society of Industrial and Applied Mathematics, 2013, pp. 70–77, doi:<a href=\"https://doi.org/10.1137/1.9781611972931.6\">10.1137/1.9781611972931.6</a>.","apa":"Kerber, M., &#38; Edelsbrunner, H. (2013). 3D kinetic alpha complexes and their implementation. In <i>2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments</i> (pp. 70–77). New Orleans, LA, United States: Society of Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611972931.6\">https://doi.org/10.1137/1.9781611972931.6</a>","ieee":"M. Kerber and H. Edelsbrunner, “3D kinetic alpha complexes and their implementation,” in <i>2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments</i>, New Orleans, LA, United States, 2013, pp. 70–77.","ama":"Kerber M, Edelsbrunner H. 3D kinetic alpha complexes and their implementation. In: <i>2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments</i>. Society of Industrial and Applied Mathematics; 2013:70-77. doi:<a href=\"https://doi.org/10.1137/1.9781611972931.6\">10.1137/1.9781611972931.6</a>","ista":"Kerber M, Edelsbrunner H. 2013. 3D kinetic alpha complexes and their implementation. 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, ALENEX, , 70–77.","short":"M. Kerber, H. Edelsbrunner, in:, 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2013, pp. 70–77.","chicago":"Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and Their Implementation.” In <i>2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments</i>, 70–77. Society of Industrial and Applied Mathematics, 2013. <a href=\"https://doi.org/10.1137/1.9781611972931.6\">https://doi.org/10.1137/1.9781611972931.6</a>."},"quality_controlled":"1","author":[{"last_name":"Kerber","first_name":"Michael","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"}]},{"oa_version":"None","type":"journal_article","date_updated":"2023-02-23T11:24:10Z","year":"2013","day":"01","citation":{"ama":"Chen C, Kerber M. An output sensitive algorithm for persistent homology. <i>Computational Geometry: Theory and Applications</i>. 2013;46(4):435-447. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2012.02.010\">10.1016/j.comgeo.2012.02.010</a>","ieee":"C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,” <i>Computational Geometry: Theory and Applications</i>, vol. 46, no. 4. Elsevier, pp. 435–447, 2013.","ista":"Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 46(4), 435–447.","short":"C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013) 435–447.","chicago":"Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2013. <a href=\"https://doi.org/10.1016/j.comgeo.2012.02.010\">https://doi.org/10.1016/j.comgeo.2012.02.010</a>.","mla":"Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” <i>Computational Geometry: Theory and Applications</i>, vol. 46, no. 4, Elsevier, 2013, pp. 435–47, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2012.02.010\">10.1016/j.comgeo.2012.02.010</a>.","apa":"Chen, C., &#38; Kerber, M. (2013). An output sensitive algorithm for persistent homology. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2012.02.010\">https://doi.org/10.1016/j.comgeo.2012.02.010</a>"},"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Chen, Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","first_name":"Chao"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber","first_name":"Michael"}],"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.","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 &gt; 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} &gt; 0. The space complexity of the Monte-Carlo version is bounded by O (d n) = O (n log n).","lang":"eng"}],"publication_status":"published","publication":"Computational Geometry: Theory and Applications","title":"An output sensitive algorithm for persistent homology","_id":"2939","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"3367"}]},"doi":"10.1016/j.comgeo.2012.02.010","publisher":"Elsevier","date_published":"2013-05-01T00:00:00Z","volume":46,"page":"435 - 447","issue":"4","month":"05","date_created":"2018-12-11T12:00:27Z","status":"public","intvolume":"        46","scopus_import":1,"publist_id":"3796"},{"publication_status":"published","abstract":[{"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.","lang":"eng"}],"publication":"Journal of Mathematical Physics, Analysis, Geometry","title":"Elementary solutions of the Bernstein problem on two intervals","oa":1,"_id":"6588","year":"2012","citation":{"ieee":"F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals,” <i>Journal of Mathematical Physics, Analysis, Geometry</i>, vol. 8, no. 1. B. Verkin Institute for Low Temperature Physics and Engineering, pp. 63–78, 2012.","ama":"Pausinger F. Elementary solutions of the Bernstein problem on two intervals. <i>Journal of Mathematical Physics, Analysis, Geometry</i>. 2012;8(1):63-78.","chicago":"Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” <i>Journal of Mathematical Physics, Analysis, Geometry</i>. B. Verkin Institute for Low Temperature Physics and Engineering, 2012.","short":"F. Pausinger, Journal of Mathematical Physics, Analysis, Geometry 8 (2012) 63–78.","ista":"Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78.","mla":"Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” <i>Journal of Mathematical Physics, Analysis, Geometry</i>, vol. 8, no. 1, B. Verkin Institute for Low Temperature Physics and Engineering, 2012, pp. 63–78.","apa":"Pausinger, F. (2012). Elementary solutions of the Bernstein problem on two intervals. <i>Journal of Mathematical Physics, Analysis, Geometry</i>. B. Verkin Institute for Low Temperature Physics and Engineering."},"main_file_link":[{"open_access":"1","url":"http://mi.mathnet.ru/eng/jmag525"}],"author":[{"last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","date_created":"2019-06-27T08:16:56Z","month":"01","status":"public","intvolume":"         8","isi":1,"publisher":"B. Verkin Institute for Low Temperature Physics and Engineering","article_type":"original","volume":8,"issue":"1","acknowledgement":"This work is supported by the Austrian Science Fund (FWF), Project P22025-N18.\r\n","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"}],"type":"journal_article","date_updated":"2023-10-16T09:41:31Z","oa_version":"Published Version","day":"01","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1812-9471"]},"scopus_import":"1","date_published":"2012-01-01T00:00:00Z","external_id":{"isi":["000301173600004"]},"page":"63-78"},{"date_published":"2012-01-01T00:00:00Z","file":[{"file_id":"5078","date_updated":"2020-07-14T12:45:51Z","file_name":"IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf","checksum":"44ee8d173487e8ed41a51136816bbeb4","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:14:26Z","file_size":392021,"content_type":"application/pdf","creator":"system"}],"page":"1167 - 1168","scopus_import":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","type":"journal_article","date_updated":"2021-01-12T07:00:13Z","oa_version":"Submitted Version","day":"01","language":[{"iso":"eng"}],"doi":"10.1070/RM2012v067n06ABEH004820","has_accepted_license":"1","department":[{"_id":"HeEd"}],"issue":"6","volume":67,"pubrep_id":"546","file_date_updated":"2020-07-14T12:45:51Z","publisher":"IOP Publishing Ltd.","intvolume":"        67","publist_id":"3943","date_created":"2018-12-11T11:59:55Z","month":"01","status":"public","citation":{"ieee":"H. Edelsbrunner and N. Strelkova, “On the configuration space of Steiner minimal trees,” <i>Russian Mathematical Surveys</i>, vol. 67, no. 6. IOP Publishing Ltd., pp. 1167–1168, 2012.","ama":"Edelsbrunner H, Strelkova N. On the configuration space of Steiner minimal trees. <i>Russian Mathematical Surveys</i>. 2012;67(6):1167-1168. doi:<a href=\"https://doi.org/10.1070/RM2012v067n06ABEH004820\">10.1070/RM2012v067n06ABEH004820</a>","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.” <i>Russian Mathematical Surveys</i>. IOP Publishing Ltd., 2012. <a href=\"https://doi.org/10.1070/RM2012v067n06ABEH004820\">https://doi.org/10.1070/RM2012v067n06ABEH004820</a>.","ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 67(6), 1167–1168.","apa":"Edelsbrunner, H., &#38; Strelkova, N. (2012). On the configuration space of Steiner minimal trees. <i>Russian Mathematical Surveys</i>. IOP Publishing Ltd. <a href=\"https://doi.org/10.1070/RM2012v067n06ABEH004820\">https://doi.org/10.1070/RM2012v067n06ABEH004820</a>","mla":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space of Steiner Minimal Trees.” <i>Russian Mathematical Surveys</i>, vol. 67, no. 6, IOP Publishing Ltd., 2012, pp. 1167–68, doi:<a href=\"https://doi.org/10.1070/RM2012v067n06ABEH004820\">10.1070/RM2012v067n06ABEH004820</a>."},"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Strelkova, Nataliya","first_name":"Nataliya","last_name":"Strelkova"}],"quality_controlled":"1","year":"2012","publication":"Russian Mathematical Surveys","title":"On the configuration space of Steiner minimal trees","oa":1,"ddc":["000"],"_id":"2849","publication_status":"published"},{"abstract":[{"text":"We present an algorithm for simplifying linear cartographic objects and results obtained with a computer program implementing this algorithm. ","lang":"eng"}],"publication_status":"published","department":[{"_id":"HeEd"}],"_id":"2902","language":[{"iso":"rus"}],"oa":1,"publication":"Modeling and Analysis of Information Systems","title":"Fractal and computational geometry for generalizing cartographic objects","year":"2012","day":"01","oa_version":"Published Version","date_updated":"2023-10-18T07:34:45Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","article_processing_charge":"No","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Musin, Oleg","last_name":"Musin","first_name":"Oleg"},{"first_name":"Alexey","last_name":"Ukhalov","full_name":"Ukhalov, Alexey"},{"last_name":"Yakimova","first_name":"Olga","full_name":"Yakimova, Olga"},{"full_name":"Alexeev, Vladislav","last_name":"Alexeev","first_name":"Vladislav"},{"last_name":"Bogaevskaya","first_name":"Victoriya","full_name":"Bogaevskaya, Victoriya"},{"last_name":"Gorohov","first_name":"Andrey","full_name":"Gorohov, Andrey"},{"first_name":"Margarita","last_name":"Preobrazhenskaya","full_name":"Preobrazhenskaya, Margarita"}],"main_file_link":[{"open_access":"1","url":"http://mi.mathnet.ru/eng/mais280"}],"citation":{"ama":"Edelsbrunner H, Musin O, Ukhalov A, et al. Fractal and computational geometry for generalizing cartographic objects. <i>Modeling and Analysis of Information Systems</i>. 2012;19(6):152-160.","ieee":"H. Edelsbrunner <i>et al.</i>, “Fractal and computational geometry for generalizing cartographic objects,” <i>Modeling and Analysis of Information Systems</i>, vol. 19, no. 6. Russian Academy of Sciences, pp. 152–160, 2012.","ista":"Edelsbrunner H, Musin O, Ukhalov A, Yakimova O, Alexeev V, Bogaevskaya V, Gorohov A, Preobrazhenskaya M. 2012. Fractal and computational geometry for generalizing cartographic objects. Modeling and Analysis of Information Systems. 19(6), 152–160.","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.” <i>Modeling and Analysis of Information Systems</i>. Russian Academy of Sciences, 2012.","short":"H. Edelsbrunner, O. Musin, A. Ukhalov, O. Yakimova, V. Alexeev, V. Bogaevskaya, A. Gorohov, M. Preobrazhenskaya, Modeling and Analysis of Information Systems 19 (2012) 152–160.","mla":"Edelsbrunner, Herbert, et al. “Fractal and computational geometry for generalizing cartographic objects.” <i>Modeling and Analysis of Information Systems</i>, vol. 19, no. 6, Russian Academy of Sciences, 2012, pp. 152–60.","apa":"Edelsbrunner, H., Musin, O., Ukhalov, A., Yakimova, O., Alexeev, V., Bogaevskaya, V., … Preobrazhenskaya, M. (2012). Fractal and computational geometry for generalizing cartographic objects. <i>Modeling and Analysis of Information Systems</i>. Russian Academy of Sciences."},"status":"public","month":"12","date_created":"2018-12-11T12:00:15Z","publist_id":"3845","intvolume":"        19","publisher":"Russian Academy of Sciences","article_type":"original","volume":19,"page":"152 - 160","issue":"6","date_published":"2012-12-01T00:00:00Z"},{"language":[{"iso":"eng"}],"doi":"10.1109/ISVD.2012.11","has_accepted_license":"1","department":[{"_id":"HeEd"},{"_id":"MaJö"}],"day":"06","type":"conference","date_updated":"2021-01-12T07:00:35Z","oa_version":"Submitted Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"page":"41 - 48","date_published":"2012-08-06T00:00:00Z","file":[{"creator":"system","content_type":"application/pdf","file_size":760548,"relation":"main_file","date_created":"2018-12-12T10:09:41Z","checksum":"444869a4e8abf07834f88b6e5cb5e9c3","file_name":"IST-2016-545-v1+1_2012-P-10-AdaptiveTopology.pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:52Z","file_id":"4765"}],"publication_status":"published","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."}],"oa":1,"ddc":["000"],"_id":"2903","title":"The adaptive topology of a digital image","year":"2012","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Symonova","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","full_name":"Symonova, Olga"}],"quality_controlled":"1","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.","ama":"Edelsbrunner H, Symonova O. The adaptive topology of a digital image. In: IEEE; 2012:41-48. doi:<a href=\"https://doi.org/10.1109/ISVD.2012.11\">10.1109/ISVD.2012.11</a>","chicago":"Edelsbrunner, Herbert, and Olga Symonova. “The Adaptive Topology of a Digital Image,” 41–48. IEEE, 2012. <a href=\"https://doi.org/10.1109/ISVD.2012.11\">https://doi.org/10.1109/ISVD.2012.11</a>.","short":"H. Edelsbrunner, O. Symonova, in:, IEEE, 2012, pp. 41–48.","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.","mla":"Edelsbrunner, Herbert, and Olga Symonova. <i>The Adaptive Topology of a Digital Image</i>. IEEE, 2012, pp. 41–48, doi:<a href=\"https://doi.org/10.1109/ISVD.2012.11\">10.1109/ISVD.2012.11</a>.","apa":"Edelsbrunner, H., &#38; 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. <a href=\"https://doi.org/10.1109/ISVD.2012.11\">https://doi.org/10.1109/ISVD.2012.11</a>"},"status":"public","date_created":"2018-12-11T12:00:15Z","conference":{"name":"ISVD: International Symposium on Voronoi Diagrams in Science and Engineering","end_date":"2012-06-29","location":"New Brunswick, NJ, USA ","start_date":"2012-06-27"},"month":"08","publist_id":"3844","publisher":"IEEE","file_date_updated":"2020-07-14T12:45:52Z","pubrep_id":"545"},{"file_date_updated":"2020-07-14T12:45:52Z","publisher":"Université de Bordeaux","article_type":"original","volume":24,"issue":"3","month":"01","date_created":"2018-12-11T12:00:15Z","status":"public","intvolume":"        24","publist_id":"3843","year":"2012","citation":{"chicago":"Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” <i>Journal de Theorie Des Nombres Des Bordeaux</i>. Université de Bordeaux, 2012. <a href=\"https://doi.org/10.5802/jtnb.819\">https://doi.org/10.5802/jtnb.819</a>.","short":"F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749.","ista":"Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.","ieee":"F. Pausinger, “Weak multipliers for generalized van der Corput sequences,” <i>Journal de Theorie des Nombres des Bordeaux</i>, vol. 24, no. 3. Université de Bordeaux, pp. 729–749, 2012.","ama":"Pausinger F. Weak multipliers for generalized van der Corput sequences. <i>Journal de Theorie des Nombres des Bordeaux</i>. 2012;24(3):729-749. doi:<a href=\"https://doi.org/10.5802/jtnb.819\">10.5802/jtnb.819</a>","mla":"Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” <i>Journal de Theorie Des Nombres Des Bordeaux</i>, vol. 24, no. 3, Université de Bordeaux, 2012, pp. 729–49, doi:<a href=\"https://doi.org/10.5802/jtnb.819\">10.5802/jtnb.819</a>.","apa":"Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences. <i>Journal de Theorie Des Nombres Des Bordeaux</i>. Université de Bordeaux. <a href=\"https://doi.org/10.5802/jtnb.819\">https://doi.org/10.5802/jtnb.819</a>"},"author":[{"last_name":"Pausinger","first_name":"Florian","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","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."}],"publication_status":"published","publication":"Journal de Theorie des Nombres des Bordeaux","title":"Weak multipliers for generalized van der Corput sequences","_id":"2904","oa":1,"ddc":["510"],"file":[{"file_id":"7819","date_updated":"2020-07-14T12:45:52Z","checksum":"6954bfe9d7f4119fbdda7a11cf0f5c67","file_name":"JTNB_2012__24_3_729_0.pdf","access_level":"open_access","relation":"main_file","date_created":"2020-05-11T12:40:39Z","file_size":819275,"content_type":"application/pdf","creator":"dernst"}],"date_published":"2012-01-01T00:00:00Z","page":"729 - 749","scopus_import":"1","publication_identifier":{"eissn":["2118-8572"],"issn":["1246-7405"]},"oa_version":"Published Version","type":"journal_article","date_updated":"2023-10-18T07:53:47Z","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","department":[{"_id":"HeEd"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"doi":"10.5802/jtnb.819"},{"publication_status":"published","publication":"Russian Mathematical Surveys","title":"On the configuration space for the shortest networks","language":[{"iso":"eng"}],"doi":"10.4213/rm9503","department":[{"_id":"HeEd"}],"_id":"2912","date_updated":"2023-10-17T11:40:39Z","type":"journal_article","oa_version":"None","day":"01","year":"2012","citation":{"ieee":"H. Edelsbrunner and N. Strelkova, “On the configuration space for the shortest networks,” <i>Russian Mathematical Surveys</i>, vol. 67, no. 6. Russian Academy of Sciences, pp. 1167–1168, 2012.","ama":"Edelsbrunner H, Strelkova N. On the configuration space for the shortest networks. <i>Russian Mathematical Surveys</i>. 2012;67(6):1167–1168. doi:<a href=\"https://doi.org/10.4213/rm9503\">10.4213/rm9503</a>","chicago":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space for the Shortest Networks.” <i>Russian Mathematical Surveys</i>. Russian Academy of Sciences, 2012. <a href=\"https://doi.org/10.4213/rm9503\">https://doi.org/10.4213/rm9503</a>.","short":"H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168.","ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space for the shortest networks. Russian Mathematical Surveys. 67(6), 1167–1168.","apa":"Edelsbrunner, H., &#38; Strelkova, N. (2012). On the configuration space for the shortest networks. <i>Russian Mathematical Surveys</i>. Russian Academy of Sciences. <a href=\"https://doi.org/10.4213/rm9503\">https://doi.org/10.4213/rm9503</a>","mla":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space for the Shortest Networks.” <i>Russian Mathematical Surveys</i>, vol. 67, no. 6, Russian Academy of Sciences, 2012, pp. 1167–1168, doi:<a href=\"https://doi.org/10.4213/rm9503\">10.4213/rm9503</a>."},"quality_controlled":"1","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Nataliya","last_name":"Strelkova","full_name":"Strelkova, Nataliya"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2018-12-11T12:00:18Z","month":"10","status":"public","intvolume":"        67","publist_id":"3831","publisher":"Russian Academy of Sciences","date_published":"2012-10-01T00:00:00Z","page":"1167–1168","volume":67,"issue":"6"},{"department":[{"_id":"HeEd"}],"has_accepted_license":"1","doi":"10.1070/RM2012v067n04ABEH004807","language":[{"iso":"eng"}],"day":"01","oa_version":"Submitted Version","date_updated":"2021-01-12T07:39:55Z","type":"journal_article","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"page":"781 - 783","file":[{"file_name":"IST-2013-132-v1+1_2012-J-04-Functional-E.pdf","checksum":"389a5ae53d6347de36c3468034f2821d","access_level":"open_access","file_id":"5239","date_updated":"2020-07-14T12:45:55Z","creator":"system","content_type":"application/pdf","file_size":253816,"relation":"main_file","date_created":"2018-12-12T10:16:49Z"}],"date_published":"2012-11-01T00:00:00Z","publication_status":"published","_id":"2941","ddc":["510"],"oa":1,"publication":"Russian Mathematical Surveys","title":"On the optimality of functionals over triangulations of Delaunay sets","year":"2012","author":[{"last_name":"Dolbilin","first_name":"Nikolai","full_name":"Dolbilin, Nikolai"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Musin","first_name":"Oleg","full_name":"Musin, Oleg"}],"quality_controlled":"1","citation":{"apa":"Dolbilin, N., Edelsbrunner, H., &#38; Musin, O. (2012). On the optimality of functionals over triangulations of Delaunay sets. <i>Russian Mathematical Surveys</i>. IOP Publishing. <a href=\"https://doi.org/10.1070/RM2012v067n04ABEH004807\">https://doi.org/10.1070/RM2012v067n04ABEH004807</a>","mla":"Dolbilin, Nikolai, et al. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” <i>Russian Mathematical Surveys</i>, vol. 67, no. 4, IOP Publishing, 2012, pp. 781–83, doi:<a href=\"https://doi.org/10.1070/RM2012v067n04ABEH004807\">10.1070/RM2012v067n04ABEH004807</a>.","short":"N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012) 781–783.","chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, and Oleg Musin. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” <i>Russian Mathematical Surveys</i>. IOP Publishing, 2012. <a href=\"https://doi.org/10.1070/RM2012v067n04ABEH004807\">https://doi.org/10.1070/RM2012v067n04ABEH004807</a>.","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,” <i>Russian Mathematical Surveys</i>, vol. 67, no. 4. IOP Publishing, pp. 781–783, 2012.","ama":"Dolbilin N, Edelsbrunner H, Musin O. On the optimality of functionals over triangulations of Delaunay sets. <i>Russian Mathematical Surveys</i>. 2012;67(4):781-783. doi:<a href=\"https://doi.org/10.1070/RM2012v067n04ABEH004807\">10.1070/RM2012v067n04ABEH004807</a>"},"status":"public","month":"11","date_created":"2018-12-11T12:00:28Z","publist_id":"3792","intvolume":"        67","publisher":"IOP Publishing","file_date_updated":"2020-07-14T12:45:55Z","pubrep_id":"132","issue":"4","volume":67},{"publication_status":"published","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"}],"language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-32717-9_2","department":[{"_id":"HeEd"}],"_id":"2971","title":"Interactive labeling of image segmentation hierarchies","day":"01","year":"2012","date_updated":"2021-01-12T07:40:10Z","type":"conference","oa_version":"None","quality_controlled":"1","author":[{"full_name":"Zankl, Georg","last_name":"Zankl","first_name":"Georg"},{"first_name":"Yll","last_name":"Haxhimusa","full_name":"Haxhimusa, Yll"},{"id":"29F89302-F248-11E8-B48F-1D18A9856A87","full_name":"Ion, Adrian","last_name":"Ion","first_name":"Adrian"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Zankl, Georg, et al. <i>Interactive Labeling of Image Segmentation Hierarchies</i>. Vol. 7476, Springer, 2012, pp. 11–20, doi:<a href=\"https://doi.org/10.1007/978-3-642-32717-9_2\">10.1007/978-3-642-32717-9_2</a>.","apa":"Zankl, G., Haxhimusa, Y., &#38; Ion, A. (2012). Interactive labeling of image segmentation hierarchies (Vol. 7476, pp. 11–20). Presented at the Pattern Recognition, Graz, Austria: Springer. <a href=\"https://doi.org/10.1007/978-3-642-32717-9_2\">https://doi.org/10.1007/978-3-642-32717-9_2</a>","ista":"Zankl G, Haxhimusa Y, Ion A. 2012. Interactive labeling of image segmentation hierarchies. Pattern Recognition vol. 7476, 11–20.","chicago":"Zankl, Georg, Yll Haxhimusa, and Adrian Ion. “Interactive Labeling of Image Segmentation Hierarchies,” 7476:11–20. Springer, 2012. <a href=\"https://doi.org/10.1007/978-3-642-32717-9_2\">https://doi.org/10.1007/978-3-642-32717-9_2</a>.","short":"G. Zankl, Y. Haxhimusa, A. Ion, in:, Springer, 2012, pp. 11–20.","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.","ama":"Zankl G, Haxhimusa Y, Ion A. Interactive labeling of image segmentation hierarchies. In: Vol 7476. Springer; 2012:11-20. doi:<a href=\"https://doi.org/10.1007/978-3-642-32717-9_2\">10.1007/978-3-642-32717-9_2</a>"},"status":"public","date_created":"2018-12-11T12:00:37Z","conference":{"start_date":"2012-08-28","location":"Graz, Austria","name":"Pattern Recognition","end_date":"2012-08-31"},"month":"01","publist_id":"3737","scopus_import":1,"intvolume":"      7476","publisher":"Springer","volume":7476,"page":"11 - 20","date_published":"2012-01-01T00:00:00Z"},{"abstract":[{"text":"We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(nlogn)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using the cgal library, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter δ its running time additionally depends on δ. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.","lang":"eng"}],"publication_status":"published","_id":"3115","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"3329"}]},"oa":1,"publication":"Discrete & Computational Geometry","title":"Deconstructing approximate offsets","year":"2012","quality_controlled":"1","author":[{"first_name":"Eric","last_name":"Berberich","full_name":"Berberich, Eric"},{"last_name":"Halperin","first_name":"Dan","full_name":"Halperin, Dan"},{"orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","last_name":"Kerber"},{"full_name":"Pogalnikova, Roza","last_name":"Pogalnikova","first_name":"Roza"}],"citation":{"apa":"Berberich, E., Halperin, D., Kerber, M., &#38; Pogalnikova, R. (2012). Deconstructing approximate offsets. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-012-9441-5\">https://doi.org/10.1007/s00454-012-9441-5</a>","mla":"Berberich, Eric, et al. “Deconstructing Approximate Offsets.” <i>Discrete &#38; Computational Geometry</i>, vol. 48, no. 4, Springer, 2012, pp. 964–89, doi:<a href=\"https://doi.org/10.1007/s00454-012-9441-5\">10.1007/s00454-012-9441-5</a>.","ieee":"E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” <i>Discrete &#38; Computational Geometry</i>, vol. 48, no. 4. Springer, pp. 964–989, 2012.","ama":"Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. <i>Discrete &#38; Computational Geometry</i>. 2012;48(4):964-989. doi:<a href=\"https://doi.org/10.1007/s00454-012-9441-5\">10.1007/s00454-012-9441-5</a>","ista":"Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate offsets. Discrete &#38; Computational Geometry. 48(4), 964–989.","chicago":"Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s00454-012-9441-5\">https://doi.org/10.1007/s00454-012-9441-5</a>.","short":"E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete &#38; Computational Geometry 48 (2012) 964–989."},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.2158"}],"status":"public","month":"12","date_created":"2018-12-11T12:01:28Z","publist_id":"3584","intvolume":"        48","publisher":"Springer","volume":48,"issue":"4","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","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"doi":"10.1007/s00454-012-9441-5","day":"01","oa_version":"Preprint","date_updated":"2023-02-23T11:22:30Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"scopus_import":1,"page":"964 - 989","external_id":{"arxiv":["1109.2158"]},"date_published":"2012-12-01T00:00:00Z"},{"department":[{"_id":"HeEd"}],"doi":"10.1112/S0010437X11007226","language":[{"iso":"eng"}],"acknowledgement":"This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"journal_article","date_updated":"2021-01-12T07:41:12Z","day":"01","scopus_import":1,"date_published":"2012-07-01T00:00:00Z","page":"1171 - 1194","title":"Fano 3 folds in codimension 4 Tom and Jerry Part I","publication":"Compositio Mathematica","_id":"3120","oa":1,"abstract":[{"text":"We introduce a strategy based on Kustin-Miller unprojection that allows us to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions (that is, nine equations and sixteen first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology. © 2012 Copyright Foundation Compositio Mathematica.","lang":"eng"}],"publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/1009.4313","open_access":"1"}],"citation":{"mla":"Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” <i>Compositio Mathematica</i>, vol. 148, no. 4, Cambridge University Press, 2012, pp. 1171–94, doi:<a href=\"https://doi.org/10.1112/S0010437X11007226\">10.1112/S0010437X11007226</a>.","apa":"Brown, G., Kerber, M., &#38; Reid, M. (2012). Fano 3 folds in codimension 4 Tom and Jerry Part I. <i>Compositio Mathematica</i>. Cambridge University Press. <a href=\"https://doi.org/10.1112/S0010437X11007226\">https://doi.org/10.1112/S0010437X11007226</a>","ieee":"G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry Part I,” <i>Compositio Mathematica</i>, vol. 148, no. 4. Cambridge University Press, pp. 1171–1194, 2012.","ama":"Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part I. <i>Compositio Mathematica</i>. 2012;148(4):1171-1194. doi:<a href=\"https://doi.org/10.1112/S0010437X11007226\">10.1112/S0010437X11007226</a>","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.","short":"G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194.","chicago":"Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” <i>Compositio Mathematica</i>. Cambridge University Press, 2012. <a href=\"https://doi.org/10.1112/S0010437X11007226\">https://doi.org/10.1112/S0010437X11007226</a>."},"author":[{"full_name":"Brown, Gavin","first_name":"Gavin","last_name":"Brown"},{"first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Reid, Miles","first_name":"Miles","last_name":"Reid"}],"quality_controlled":"1","year":"2012","intvolume":"       148","publist_id":"3579","month":"07","date_created":"2018-12-11T12:01:30Z","status":"public","issue":"4","volume":148,"publisher":"Cambridge University Press"},{"publisher":"ML Research Press","page":"211-218","date_published":"2012-06-01T00:00:00Z","status":"public","conference":{"end_date":"2012-07-01","name":"ICML: International Conference on Machine Learning","start_date":"2012-06-26","location":"Edinburgh, United Kingdom"},"month":"06","date_created":"2018-12-11T12:01:33Z","scopus_import":"1","publist_id":"3572","year":"2012","day":"01","oa_version":"Preprint","type":"conference","date_updated":"2023-10-17T11:55:06Z","quality_controlled":"1","author":[{"first_name":"Novi","last_name":"Quadrianto","full_name":"Quadrianto, Novi"},{"full_name":"Lampert, Christoph","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","last_name":"Lampert","first_name":"Christoph"},{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao","last_name":"Chen","first_name":"Chao"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","citation":{"mla":"Quadrianto, Novi, et al. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” <i>Proceedings of the 29th International Conference on Machine Learning</i>, ML Research Press, 2012, pp. 211–18.","apa":"Quadrianto, N., Lampert, C., &#38; Chen, C. (2012). The most persistent soft-clique in a set of sampled graphs. In <i>Proceedings of the 29th International Conference on Machine Learning</i> (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 <i>Proceedings of the 29th International Conference on Machine Learning</i>, Edinburgh, United Kingdom, 2012, pp. 211–218.","ama":"Quadrianto N, Lampert C, Chen C. The most persistent soft-clique in a set of sampled graphs. In: <i>Proceedings of the 29th International Conference on Machine Learning</i>. 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 <i>Proceedings of the 29th International Conference on Machine Learning</i>, 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.","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."},"main_file_link":[{"url":"http://arxiv.org/abs/1206.4652","open_access":"1"}],"abstract":[{"lang":"eng","text":"When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques.\r\n    We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data, we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations."}],"publication_status":"published","department":[{"_id":"ChLa"},{"_id":"HeEd"}],"_id":"3127","oa":1,"language":[{"iso":"eng"}],"title":"The most persistent soft-clique in a set of sampled graphs","publication":"Proceedings of the 29th International Conference on Machine Learning"},{"department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-31155-0_17","day":"19","oa_version":"Preprint","type":"conference","date_updated":"2021-01-12T07:41:15Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"scopus_import":1,"alternative_title":["LNCS"],"page":"189 - 200","external_id":{"arxiv":["1107.3793"]},"date_published":"2012-06-19T00:00:00Z","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 &lt; 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"}],"publication_status":"published","_id":"3129","oa":1,"title":"Annotating simplices with a homology basis and its applications","year":"2012","quality_controlled":"1","author":[{"full_name":"Busaryev, Oleksiy","first_name":"Oleksiy","last_name":"Busaryev"},{"full_name":"Cabello, Sergio","first_name":"Sergio","last_name":"Cabello"},{"first_name":"Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","full_name":"Chen, Chao"},{"first_name":"Tamal","last_name":"Dey","full_name":"Dey, Tamal"},{"first_name":"Yusu","last_name":"Wang","full_name":"Wang, Yusu"}],"citation":{"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:<a href=\"https://doi.org/10.1007/978-3-642-31155-0_17\">10.1007/978-3-642-31155-0_17</a>","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.","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. <a href=\"https://doi.org/10.1007/978-3-642-31155-0_17\">https://doi.org/10.1007/978-3-642-31155-0_17</a>.","short":"O. Busaryev, S. Cabello, C. Chen, T. Dey, Y. Wang, in:, Springer, 2012, pp. 189–200.","mla":"Busaryev, Oleksiy, et al. <i>Annotating Simplices with a Homology Basis and Its Applications</i>. Vol. 7357, Springer, 2012, pp. 189–200, doi:<a href=\"https://doi.org/10.1007/978-3-642-31155-0_17\">10.1007/978-3-642-31155-0_17</a>.","apa":"Busaryev, O., Cabello, S., Chen, C., Dey, T., &#38; 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. <a href=\"https://doi.org/10.1007/978-3-642-31155-0_17\">https://doi.org/10.1007/978-3-642-31155-0_17</a>"},"main_file_link":[{"url":"http://arxiv.org/abs/1107.3793","open_access":"1"}],"status":"public","month":"06","conference":{"end_date":"2012-07-06","name":"SWAT: Symposium and Workshops on Algorithm Theory","location":"Helsinki, Finland","start_date":"2012-07-04"},"date_created":"2018-12-11T12:01:33Z","publist_id":"3569","intvolume":"      7357","publisher":"Springer","volume":7357},{"conference":{"location":"Chapel Hill, NC, USA","start_date":"2012-06-17","end_date":"2012-06-20","name":"SCG: Symposium on Computational Geometry"},"month":"06","date_created":"2018-12-11T12:01:35Z","status":"public","scopus_import":1,"publist_id":"3564","publisher":"ACM","date_published":"2012-06-20T00:00:00Z","page":"249 - 258","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.","abstract":[{"text":"This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions. Given a perfect Morse function f: S n+1 →[0, 1 and a decomposition S n+1 = U ∪ V into two (n + 1)-manifolds with common boundary M, we prove elementary relationships between the persistence diagrams of f restricted to U, to V, and to M. ","lang":"eng"}],"publication_status":"published","publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","title":"Alexander duality for functions: The persistent behavior of land and water and shore","_id":"3133","department":[{"_id":"HeEd"}],"doi":"10.1145/2261250.2261287","oa":1,"language":[{"iso":"eng"}],"oa_version":"Preprint","type":"conference","date_updated":"2021-01-12T07:41:17Z","year":"2012","day":"20","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.5052"}],"citation":{"mla":"Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, ACM, 2012, pp. 249–58, doi:<a href=\"https://doi.org/10.1145/2261250.2261287\">10.1145/2261250.2261287</a>.","apa":"Edelsbrunner, H., &#38; Kerber, M. (2012). Alexander duality for functions: The persistent behavior of land and water and shore. In <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i> (pp. 249–258). Chapel Hill, NC, USA: ACM. <a href=\"https://doi.org/10.1145/2261250.2261287\">https://doi.org/10.1145/2261250.2261287</a>","ieee":"H. Edelsbrunner and M. Kerber, “Alexander duality for functions: The persistent behavior of land and water and shore,” in <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i>, Chapel Hill, NC, USA, 2012, pp. 249–258.","ama":"Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>. ACM; 2012:249-258. doi:<a href=\"https://doi.org/10.1145/2261250.2261287\">10.1145/2261250.2261287</a>","short":"H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–258.","chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” In <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, 249–58. ACM, 2012. <a href=\"https://doi.org/10.1145/2261250.2261287\">https://doi.org/10.1145/2261250.2261287</a>.","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."},"author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1"},{"status":"public","conference":{"name":"SCG: Symposium on Computational Geometry","end_date":"2012-06-20","start_date":"2012-06-17","location":"Chapel Hill, NC, USA"},"month":"06","date_created":"2018-12-11T12:01:35Z","scopus_import":1,"publist_id":"3563","publisher":"ACM","page":"91 - 100","date_published":"2012-06-20T00:00:00Z","abstract":[{"text":"It has been an open question whether the sum of finitely many isotropic Gaussian kernels in n ≥ 2 dimensions can have more modes than kernels, until in 2003 Carreira-Perpiñán and Williams exhibited n +1 isotropic Gaussian kernels in ℝ n with n + 2 modes. We give a detailed analysis of this example, showing that it has exponentially many critical points and that the resilience of the extra mode grows like √n. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes. ","lang":"eng"}],"publication_status":"published","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.","department":[{"_id":"HeEd"}],"_id":"3134","language":[{"iso":"eng"}],"doi":"10.1145/2261250.2261265","related_material":{"record":[{"id":"2815","status":"public","relation":"later_version"}]},"publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","year":"2012","day":"20","oa_version":"None","date_updated":"2023-02-23T10:59:27Z","type":"conference","quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Fasy, Brittany","first_name":"Brittany","last_name":"Fasy"},{"full_name":"Rote, Günter","first_name":"Günter","last_name":"Rote"}],"citation":{"apa":"Edelsbrunner, H., Fasy, B., &#38; Rote, G. (2012). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i> (pp. 91–100). Chapel Hill, NC, USA: ACM. <a href=\"https://doi.org/10.1145/2261250.2261265\">https://doi.org/10.1145/2261250.2261265</a>","mla":"Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, ACM, 2012, pp. 91–100, doi:<a href=\"https://doi.org/10.1145/2261250.2261265\">10.1145/2261250.2261265</a>.","ieee":"H. Edelsbrunner, B. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” in <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i>, Chapel Hill, NC, USA, 2012, pp. 91–100.","ama":"Edelsbrunner H, Fasy B, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In: <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>. ACM; 2012:91-100. doi:<a href=\"https://doi.org/10.1145/2261250.2261265\">10.1145/2261250.2261265</a>","chicago":"Edelsbrunner, Herbert, Brittany Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” In <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, 91–100. ACM, 2012. <a href=\"https://doi.org/10.1145/2261250.2261265\">https://doi.org/10.1145/2261250.2261265</a>.","short":"H. Edelsbrunner, B. Fasy, G. Rote, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100.","ista":"Edelsbrunner H, Fasy B, Rote G. 2012. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 91–100."}}]