[{"file":[{"date_created":"2018-12-12T10:08:57Z","relation":"main_file","file_id":"4720","content_type":"application/pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:52Z","checksum":"a15a3ba22df9445731507f3e06c9fcee","file_size":403013,"creator":"system","file_name":"IST-2016-547-v1+1_2013-P-08-MedusaII.pdf"}],"date_published":"2013-01-01T00:00:00Z","_id":"2906","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"}],"publication_status":"published","oa":1,"file_date_updated":"2020-07-14T12:45:52Z","pubrep_id":"547","publist_id":"3841","year":"2013","oa_version":"Submitted Version","has_accepted_license":"1","scopus_import":1,"date_updated":"2021-01-12T07:00:36Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"70 - 77","month":"01","date_created":"2018-12-11T12:00:16Z","publisher":"Society of Industrial and Applied Mathematics","publication":"2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments","quality_controlled":"1","department":[{"_id":"HeEd"}],"status":"public","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>.","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>.","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.","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>","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>","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."},"title":"3D kinetic alpha complexes and their implementation","conference":{"location":"New Orleans, LA, United States","name":"ALENEX: Algorithm Engineering and Experiments","start_date":"2013-01-07","end_date":"2013-01-07"},"day":"01","type":"conference","author":[{"last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"alternative_title":["ALENEX"],"language":[{"iso":"eng"}],"ddc":["500"],"doi":"10.1137/1.9781611972931.6"},{"month":"05","date_created":"2018-12-11T12:00:27Z","_id":"2939","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 &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)."}],"date_published":"2013-05-01T00:00:00Z","page":"435 - 447","issue":"4","publication":"Computational Geometry: Theory and Applications","quality_controlled":"1","department":[{"_id":"HeEd"}],"status":"public","intvolume":"        46","volume":46,"publisher":"Elsevier","publication_status":"published","publist_id":"3796","day":"01","type":"journal_article","author":[{"last_name":"Chen","first_name":"Chao","full_name":"Chen, Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"}],"oa_version":"None","year":"2013","citation":{"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>.","ista":"Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 46(4), 435–447.","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.","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>.","short":"C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013) 435–447.","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>","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>"},"title":"An output sensitive algorithm for persistent homology","scopus_import":1,"date_updated":"2023-02-23T11:24:10Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2012.02.010","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"3367"}]},"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."},{"day":"01","type":"conference","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"citation":{"mla":"Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” <i>Graph-Based Representations in Pattern Recognition</i>, vol. 7877, Springer Nature, 2013, pp. 182–83, doi:<a href=\"https://doi.org/10.1007/978-3-642-38221-5_19\">10.1007/978-3-642-38221-5_19</a>.","chicago":"Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” In <i>Graph-Based Representations in Pattern Recognition</i>, 7877:182–83. LNCS. Berlin, Heidelberg: Springer Nature, 2013. <a href=\"https://doi.org/10.1007/978-3-642-38221-5_19\">https://doi.org/10.1007/978-3-642-38221-5_19</a>.","ieee":"H. Edelsbrunner, “Persistent homology in image processing,” in <i>Graph-Based Representations in Pattern Recognition</i>, 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.","ama":"Edelsbrunner H. Persistent homology in image processing. In: <i>Graph-Based Representations in Pattern Recognition</i>. Vol 7877. LNCS. Berlin, Heidelberg: Springer Nature; 2013:182-183. doi:<a href=\"https://doi.org/10.1007/978-3-642-38221-5_19\">10.1007/978-3-642-38221-5_19</a>","apa":"Edelsbrunner, H. (2013). Persistent homology in image processing. In <i>Graph-Based Representations in Pattern Recognition</i> (Vol. 7877, pp. 182–183). Berlin, Heidelberg: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-642-38221-5_19\">https://doi.org/10.1007/978-3-642-38221-5_19</a>","short":"H. Edelsbrunner, in:, Graph-Based Representations in Pattern Recognition, Springer Nature, Berlin, Heidelberg, 2013, pp. 182–183."},"ec_funded":1,"title":"Persistent homology in image processing","conference":{"location":"Vienna, Austria","name":"GbRPR: Graph-based Representations in Pattern Recognition","start_date":"2013-05-15","end_date":"2013-05-17"},"language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-38221-5_19","project":[{"grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"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.","month":"06","place":"Berlin, Heidelberg","date_created":"2022-03-21T07:30:33Z","series_title":"LNCS","page":"182-183","publication":"Graph-Based Representations in Pattern Recognition","department":[{"_id":"HeEd"}],"quality_controlled":"1","intvolume":"      7877","status":"public","publisher":"Springer Nature","year":"2013","oa_version":"None","scopus_import":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2023-09-05T15:10:20Z","publication_identifier":{"eisbn":["9783642382215"],"issn":["0302-9743"],"isbn":["9783642382208"],"eissn":["1611-3349"]},"_id":"10897","date_published":"2013-06-01T00:00:00Z","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"}],"article_processing_charge":"No","volume":7877,"publication_status":"published"},{"publist_id":"4763","day":"01","year":"2013","oa_version":"None","alternative_title":["2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) "],"author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"last_name":"Held","full_name":"Held, Martin","first_name":"Martin"},{"last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814"}],"type":"conference","citation":{"chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. <a href=\"https://doi.org/10.1109/ISVD.2013.11\">https://doi.org/10.1109/ISVD.2013.11</a>.","ista":"Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) , , 37–46.","ieee":"T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.","mla":"Biedl, Therese, et al. <i>Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input</i>. IEEE, 2013, pp. 37–46, doi:<a href=\"https://doi.org/10.1109/ISVD.2013.11\">10.1109/ISVD.2013.11</a>.","short":"T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46.","ama":"Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: IEEE; 2013:37-46. doi:<a href=\"https://doi.org/10.1109/ISVD.2013.11\">10.1109/ISVD.2013.11</a>","apa":"Biedl, T., Held, M., &#38; 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. <a href=\"https://doi.org/10.1109/ISVD.2013.11\">https://doi.org/10.1109/ISVD.2013.11</a>"},"conference":{"location":"St. Petersburg, Russia","start_date":"2013-07-08","end_date":"2013-07-10","name":"ISVD: Voronoi Diagrams in Science and Engineering"},"title":"Recognizing straight skeletons and Voronoi diagrams and reconstructing their input","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:56:00Z","scopus_import":1,"doi":"10.1109/ISVD.2013.11","publication_identifier":{"eisbn":["978-0-7695-5037-4 "]},"month":"12","_id":"2209","date_published":"2013-12-01T00:00:00Z","date_created":"2018-12-11T11:56:20Z","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 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"}],"page":"37 - 46","quality_controlled":"1","department":[{"_id":"HeEd"}],"status":"public","publisher":"IEEE","publication_status":"published"},{"citation":{"ama":"Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons. In: <i>29th European Workshop on Computational Geometry</i>. TU Braunschweig; 2013:95-98.","apa":"Biedl, T., Held, M., &#38; Huber, S. (2013). Reconstructing polygons from embedded straight skeletons. In <i>29th European Workshop on Computational Geometry</i> (pp. 95–98). Braunschweig, Germany: TU Braunschweig.","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.” <i>29th European Workshop on Computational Geometry</i>, TU Braunschweig, 2013, pp. 95–98.","chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons from Embedded Straight Skeletons.” In <i>29th European Workshop on Computational Geometry</i>, 95–98. TU Braunschweig, 2013.","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.","ieee":"T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight skeletons,” in <i>29th European Workshop on Computational Geometry</i>, Braunschweig, Germany, 2013, pp. 95–98."},"conference":{"name":"EuroCG: European Workshop on Computational Geometry","start_date":"2013-03-17","end_date":"2013-03-20","location":"Braunschweig, Germany"},"title":"Reconstructing polygons from embedded straight skeletons","day":"01","publist_id":"4762","oa_version":"Submitted Version","year":"2013","type":"conference","author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"last_name":"Held","full_name":"Held, Martin","first_name":"Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","full_name":"Huber, Stefan","last_name":"Huber"}],"language":[{"iso":"eng"}],"date_updated":"2021-01-12T06:56:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"95 - 98","month":"03","date_created":"2018-12-11T11:56:21Z","_id":"2210","abstract":[{"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.","lang":"eng"}],"date_published":"2013-03-01T00:00:00Z","publisher":"TU Braunschweig","publication_status":"published","oa":1,"main_file_link":[{"open_access":"1","url":"http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf"}],"department":[{"_id":"HeEd"}],"publication":"29th European Workshop on Computational Geometry","status":"public"},{"citation":{"short":"F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50.","apa":"Pausinger, F. (2013). Van der Corput sequences and linear permutations. <i>Electronic Notes in Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.endm.2013.07.008\">https://doi.org/10.1016/j.endm.2013.07.008</a>","ama":"Pausinger F. Van der Corput sequences and linear permutations. <i>Electronic Notes in Discrete Mathematics</i>. 2013;43:43-50. doi:<a href=\"https://doi.org/10.1016/j.endm.2013.07.008\">10.1016/j.endm.2013.07.008</a>","ista":"Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 43, 43–50.","ieee":"F. Pausinger, “Van der Corput sequences and linear permutations,” <i>Electronic Notes in Discrete Mathematics</i>, vol. 43. Elsevier, pp. 43–50, 2013.","chicago":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” <i>Electronic Notes in Discrete Mathematics</i>. Elsevier, 2013. <a href=\"https://doi.org/10.1016/j.endm.2013.07.008\">https://doi.org/10.1016/j.endm.2013.07.008</a>.","mla":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” <i>Electronic Notes in Discrete Mathematics</i>, vol. 43, Elsevier, 2013, pp. 43–50, doi:<a href=\"https://doi.org/10.1016/j.endm.2013.07.008\">10.1016/j.endm.2013.07.008</a>."},"title":"Van der Corput sequences and linear permutations","day":"05","publist_id":"4623","oa_version":"None","year":"2013","author":[{"last_name":"Pausinger","full_name":"Pausinger, Florian","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"type":"journal_article","acknowledgement":"This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria).","language":[{"iso":"eng"}],"date_updated":"2021-01-12T06:56:39Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"doi":"10.1016/j.endm.2013.07.008","page":"43 - 50","month":"09","_id":"2304","date_published":"2013-09-05T00:00:00Z","date_created":"2018-12-11T11:56:53Z","abstract":[{"lang":"eng","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."}],"publication_status":"published","publisher":"Elsevier","quality_controlled":"1","department":[{"_id":"HeEd"}],"publication":"Electronic Notes in Discrete Mathematics","volume":43,"status":"public","intvolume":"        43"},{"publist_id":"3943","has_accepted_license":"1","year":"2012","oa_version":"Submitted Version","scopus_import":1,"date_updated":"2021-01-12T07:00:13Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","issue":"6","file":[{"file_name":"IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf","creator":"system","file_size":392021,"checksum":"44ee8d173487e8ed41a51136816bbeb4","date_updated":"2020-07-14T12:45:51Z","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_id":"5078","date_created":"2018-12-12T10:14:26Z"}],"date_published":"2012-01-01T00:00:00Z","_id":"2849","publication_status":"published","oa":1,"file_date_updated":"2020-07-14T12:45:51Z","pubrep_id":"546","volume":67,"citation":{"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>.","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.","ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 67(6), 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>.","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>","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."},"title":"On the configuration space of Steiner minimal trees","day":"01","type":"journal_article","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Strelkova","first_name":"Nataliya","full_name":"Strelkova, Nataliya"}],"language":[{"iso":"eng"}],"ddc":["000"],"doi":"10.1070/RM2012v067n06ABEH004820","page":"1167 - 1168","month":"01","date_created":"2018-12-11T11:59:55Z","publisher":"IOP Publishing Ltd.","publication":"Russian Mathematical Surveys","quality_controlled":"1","department":[{"_id":"HeEd"}],"intvolume":"        67","status":"public"},{"issue":"6","article_processing_charge":"No","page":"152 - 160","_id":"2902","abstract":[{"text":"We present an algorithm for simplifying linear cartographic objects and results obtained with a computer program implementing this algorithm. ","lang":"eng"}],"date_published":"2012-12-01T00:00:00Z","date_created":"2018-12-11T12:00:15Z","month":"12","oa":1,"main_file_link":[{"url":"http://mi.mathnet.ru/eng/mais280","open_access":"1"}],"publication_status":"published","publisher":"Russian Academy of Sciences","volume":19,"intvolume":"        19","status":"public","quality_controlled":"1","department":[{"_id":"HeEd"}],"publication":"Modeling and Analysis of Information Systems","title":"Fractal and computational geometry for generalizing cartographic objects","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.","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.","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.","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.","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."},"oa_version":"Published Version","year":"2012","type":"journal_article","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Musin, Oleg","first_name":"Oleg","last_name":"Musin"},{"full_name":"Ukhalov, Alexey","first_name":"Alexey","last_name":"Ukhalov"},{"last_name":"Yakimova","full_name":"Yakimova, Olga","first_name":"Olga"},{"full_name":"Alexeev, Vladislav","first_name":"Vladislav","last_name":"Alexeev"},{"full_name":"Bogaevskaya, Victoriya","first_name":"Victoriya","last_name":"Bogaevskaya"},{"full_name":"Gorohov, Andrey","first_name":"Andrey","last_name":"Gorohov"},{"first_name":"Margarita","full_name":"Preobrazhenskaya, Margarita","last_name":"Preobrazhenskaya"}],"publist_id":"3845","day":"01","article_type":"original","language":[{"iso":"rus"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-10-18T07:34:45Z"},{"scopus_import":1,"date_updated":"2021-01-12T07:00:35Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"3844","year":"2012","oa_version":"Submitted Version","has_accepted_license":"1","file_date_updated":"2020-07-14T12:45:52Z","pubrep_id":"545","publication_status":"published","oa":1,"file":[{"date_created":"2018-12-12T10:09:41Z","content_type":"application/pdf","relation":"main_file","file_id":"4765","date_updated":"2020-07-14T12:45:52Z","access_level":"open_access","checksum":"444869a4e8abf07834f88b6e5cb5e9c3","file_name":"IST-2016-545-v1+1_2012-P-10-AdaptiveTopology.pdf","file_size":760548,"creator":"system"}],"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."}],"_id":"2903","date_published":"2012-08-06T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1109/ISVD.2012.11","ddc":["000"],"day":"06","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Symonova, Olga","first_name":"Olga","last_name":"Symonova","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"}],"type":"conference","citation":{"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.","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.","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>.","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>.","short":"H. Edelsbrunner, O. Symonova, in:, IEEE, 2012, pp. 41–48.","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>","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>"},"title":"The adaptive topology of a digital image","conference":{"location":"New Brunswick, NJ, USA ","start_date":"2012-06-27","end_date":"2012-06-29","name":"ISVD: International Symposium on Voronoi Diagrams in Science and Engineering"},"department":[{"_id":"HeEd"},{"_id":"MaJö"}],"quality_controlled":"1","status":"public","publisher":"IEEE","month":"08","date_created":"2018-12-11T12:00:15Z","page":"41 - 48"},{"article_type":"original","publist_id":"3843","has_accepted_license":"1","oa_version":"Published Version","year":"2012","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-10-18T07:53:47Z","publication_identifier":{"eissn":["2118-8572"],"issn":["1246-7405"]},"file":[{"date_created":"2020-05-11T12:40:39Z","file_id":"7819","relation":"main_file","content_type":"application/pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:52Z","checksum":"6954bfe9d7f4119fbdda7a11cf0f5c67","file_size":819275,"creator":"dernst","file_name":"JTNB_2012__24_3_729_0.pdf"}],"_id":"2904","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."}],"date_published":"2012-01-01T00:00:00Z","article_processing_charge":"No","issue":"3","file_date_updated":"2020-07-14T12:45:52Z","volume":24,"publication_status":"published","oa":1,"day":"01","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","last_name":"Pausinger","full_name":"Pausinger, Florian","first_name":"Florian"}],"type":"journal_article","citation":{"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.","ista":"Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.","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>.","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>.","short":"F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749.","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>","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>"},"title":"Weak multipliers for generalized van der Corput sequences","language":[{"iso":"eng"}],"doi":"10.5802/jtnb.819","ddc":["510"],"month":"01","date_created":"2018-12-11T12:00:15Z","page":"729 - 749","publication":"Journal de Theorie des Nombres des Bordeaux","quality_controlled":"1","department":[{"_id":"HeEd"}],"status":"public","intvolume":"        24","publisher":"Université de Bordeaux"},{"day":"01","publist_id":"3831","oa_version":"None","year":"2012","type":"journal_article","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Strelkova","first_name":"Nataliya","full_name":"Strelkova, Nataliya"}],"citation":{"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>","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>","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.” <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>.","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.","ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space for the shortest networks. Russian Mathematical Surveys. 67(6), 1167–1168.","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>."},"title":"On the configuration space for the shortest networks","date_updated":"2023-10-17T11:40:39Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"doi":"10.4213/rm9503","month":"10","_id":"2912","date_created":"2018-12-11T12:00:18Z","date_published":"2012-10-01T00:00:00Z","page":"1167–1168","issue":"6","article_processing_charge":"No","department":[{"_id":"HeEd"}],"quality_controlled":"1","publication":"Russian Mathematical Surveys","volume":67,"status":"public","intvolume":"        67","publisher":"Russian Academy of Sciences","publication_status":"published"},{"ddc":["510"],"doi":"10.1070/RM2012v067n04ABEH004807","language":[{"iso":"eng"}],"type":"journal_article","author":[{"last_name":"Dolbilin","first_name":"Nikolai","full_name":"Dolbilin, Nikolai"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"}],"day":"01","title":"On the optimality of functionals over triangulations of Delaunay sets","citation":{"short":"N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012) 781–783.","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>","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>","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.","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>.","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>."},"intvolume":"        67","status":"public","quality_controlled":"1","department":[{"_id":"HeEd"}],"publication":"Russian Mathematical Surveys","publisher":"IOP Publishing","date_created":"2018-12-11T12:00:28Z","month":"11","page":"781 - 783","date_updated":"2021-01-12T07:39:55Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"year":"2012","oa_version":"Submitted Version","has_accepted_license":"1","publist_id":"3792","volume":67,"pubrep_id":"132","file_date_updated":"2020-07-14T12:45:55Z","oa":1,"publication_status":"published","date_published":"2012-11-01T00:00:00Z","_id":"2941","file":[{"checksum":"389a5ae53d6347de36c3468034f2821d","date_updated":"2020-07-14T12:45:55Z","access_level":"open_access","file_name":"IST-2013-132-v1+1_2012-J-04-Functional-E.pdf","file_size":253816,"creator":"system","date_created":"2018-12-12T10:16:49Z","content_type":"application/pdf","file_id":"5239","relation":"main_file"}],"issue":"4"},{"publication_status":"published","publisher":"Springer","quality_controlled":"1","department":[{"_id":"HeEd"}],"volume":7476,"status":"public","intvolume":"      7476","page":"11 - 20","month":"01","date_created":"2018-12-11T12:00:37Z","_id":"2971","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"}],"date_published":"2012-01-01T00:00:00Z","date_updated":"2021-01-12T07:40:10Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"scopus_import":1,"doi":"10.1007/978-3-642-32717-9_2","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>.","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.","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>.","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>","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>","short":"G. Zankl, Y. Haxhimusa, A. Ion, in:, Springer, 2012, pp. 11–20."},"conference":{"start_date":"2012-08-28","end_date":"2012-08-31","name":"Pattern Recognition","location":"Graz, Austria"},"title":"Interactive labeling of image segmentation hierarchies","publist_id":"3737","day":"01","oa_version":"None","year":"2012","type":"conference","author":[{"last_name":"Zankl","full_name":"Zankl, Georg","first_name":"Georg"},{"last_name":"Haxhimusa","first_name":"Yll","full_name":"Haxhimusa, Yll"},{"last_name":"Ion","full_name":"Ion, Adrian","first_name":"Adrian","id":"29F89302-F248-11E8-B48F-1D18A9856A87"}]},{"publisher":"Springer","status":"public","intvolume":"        48","department":[{"_id":"HeEd"}],"quality_controlled":"1","publication":"Discrete & Computational Geometry","page":"964 - 989","date_created":"2018-12-11T12:01:28Z","month":"12","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","related_material":{"record":[{"relation":"earlier_version","id":"3329","status":"public"}]},"doi":"10.1007/s00454-012-9441-5","language":[{"iso":"eng"}],"title":"Deconstructing approximate offsets","citation":{"short":"E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete &#38; Computational Geometry 48 (2012) 964–989.","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>","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>","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>.","ista":"Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate offsets. Discrete &#38; Computational Geometry. 48(4), 964–989.","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.","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>."},"type":"journal_article","author":[{"last_name":"Berberich","first_name":"Eric","full_name":"Berberich, Eric"},{"last_name":"Halperin","full_name":"Halperin, Dan","first_name":"Dan"},{"orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"},{"first_name":"Roza","full_name":"Pogalnikova, Roza","last_name":"Pogalnikova"}],"day":"01","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.2158"}],"oa":1,"publication_status":"published","volume":48,"issue":"4","arxiv":1,"date_published":"2012-12-01T00:00:00Z","_id":"3115","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-02-23T11:22:30Z","scopus_import":1,"external_id":{"arxiv":["1109.2158"]},"year":"2012","oa_version":"Preprint","publist_id":"3584"},{"title":"Fano 3 folds in codimension 4 Tom and Jerry Part I","citation":{"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>","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>","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.” <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>.","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.","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.","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":[{"last_name":"Brown","full_name":"Brown, Gavin","first_name":"Gavin"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael"},{"last_name":"Reid","first_name":"Miles","full_name":"Reid, Miles"}],"type":"journal_article","day":"01","acknowledgement":"This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.","doi":"10.1112/S0010437X11007226","language":[{"iso":"eng"}],"page":"1171 - 1194","date_created":"2018-12-11T12:01:30Z","month":"07","publisher":"Cambridge University Press","intvolume":"       148","status":"public","publication":"Compositio Mathematica","quality_controlled":"1","department":[{"_id":"HeEd"}],"oa_version":"Preprint","year":"2012","publist_id":"3579","scopus_import":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T07:41:12Z","issue":"4","_id":"3120","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."}],"date_published":"2012-07-01T00:00:00Z","main_file_link":[{"url":"http://arxiv.org/abs/1009.4313","open_access":"1"}],"oa":1,"publication_status":"published","volume":148},{"scopus_import":"1","language":[{"iso":"eng"}],"date_updated":"2023-10-17T11:55:06Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The most persistent soft-clique in a set of sampled graphs","conference":{"location":"Edinburgh, United Kingdom","start_date":"2012-06-26","end_date":"2012-07-01","name":"ICML: International Conference on Machine Learning"},"citation":{"short":"N. Quadrianto, C. Lampert, C. Chen, in:, Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 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.","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.","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.","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.","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.","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."},"author":[{"last_name":"Quadrianto","first_name":"Novi","full_name":"Quadrianto, Novi"},{"last_name":"Lampert","first_name":"Christoph","full_name":"Lampert, Christoph","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Chen","first_name":"Chao","full_name":"Chen, Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"}],"type":"conference","oa_version":"Preprint","year":"2012","publist_id":"3572","day":"01","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1206.4652","open_access":"1"}],"publisher":"ML Research Press","publication_status":"published","status":"public","publication":"Proceedings of the 29th International Conference on Machine Learning","department":[{"_id":"ChLa"},{"_id":"HeEd"}],"quality_controlled":"1","article_processing_charge":"No","page":"211-218","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."}],"_id":"3127","date_published":"2012-06-01T00:00:00Z","date_created":"2018-12-11T12:01:33Z","month":"06"},{"volume":7357,"publication_status":"published","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1107.3793"}],"date_published":"2012-06-19T00:00:00Z","_id":"3129","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"}],"arxiv":1,"scopus_import":1,"external_id":{"arxiv":["1107.3793"]},"date_updated":"2021-01-12T07:41:15Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"3569","oa_version":"Preprint","year":"2012","department":[{"_id":"HeEd"}],"quality_controlled":"1","intvolume":"      7357","status":"public","publisher":"Springer","month":"06","date_created":"2018-12-11T12:01:33Z","page":"189 - 200","language":[{"iso":"eng"}],"doi":"10.1007/978-3-642-31155-0_17","day":"19","type":"conference","author":[{"first_name":"Oleksiy","full_name":"Busaryev, Oleksiy","last_name":"Busaryev"},{"full_name":"Cabello, Sergio","first_name":"Sergio","last_name":"Cabello"},{"first_name":"Chao","full_name":"Chen, Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Dey","first_name":"Tamal","full_name":"Dey, Tamal"},{"full_name":"Wang, Yusu","first_name":"Yusu","last_name":"Wang"}],"alternative_title":["LNCS"],"citation":{"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>.","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>.","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>","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>","short":"O. Busaryev, S. Cabello, C. Chen, T. Dey, Y. Wang, in:, Springer, 2012, pp. 189–200."},"title":"Annotating simplices with a homology basis and its applications","conference":{"start_date":"2012-07-04","end_date":"2012-07-06","name":"SWAT: Symposium and Workshops on Algorithm Theory","location":"Helsinki, Finland"}},{"type":"conference","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Preprint","year":"2012","publist_id":"3564","day":"20","title":"Alexander duality for functions: The persistent behavior of land and water and shore","conference":{"location":"Chapel Hill, NC, USA","name":"SCG: Symposium on Computational Geometry","end_date":"2012-06-20","start_date":"2012-06-17"},"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>.","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>.","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.","ista":"Edelsbrunner H, Kerber M. 2012. Alexander duality for functions: The persistent behavior of land and water and shore. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 249–258.","ama":"Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: <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>","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>","short":"H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–258."},"doi":"10.1145/2261250.2261287","scopus_import":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"date_updated":"2021-01-12T07:41:17Z","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":[{"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. "}],"_id":"3133","date_published":"2012-06-20T00:00:00Z","date_created":"2018-12-11T12:01:35Z","month":"06","page":"249 - 258","status":"public","publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","quality_controlled":"1","department":[{"_id":"HeEd"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.5052"}],"oa":1,"publication_status":"published","publisher":"ACM"},{"publisher":"ACM","publication_status":"published","status":"public","publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","department":[{"_id":"HeEd"}],"quality_controlled":"1","page":"91 - 100","_id":"3134","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. "}],"date_created":"2018-12-11T12:01:35Z","date_published":"2012-06-20T00:00:00Z","month":"06","related_material":{"record":[{"relation":"later_version","id":"2815","status":"public"}]},"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.","doi":"10.1145/2261250.2261265","scopus_import":1,"date_updated":"2023-02-23T10:59:27Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","conference":{"location":"Chapel Hill, NC, USA","start_date":"2012-06-17","end_date":"2012-06-20","name":"SCG: 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.","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>","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>","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>.","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.","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.","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>."},"type":"conference","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Fasy, Brittany","first_name":"Brittany","last_name":"Fasy"},{"last_name":"Rote","full_name":"Rote, Günter","first_name":"Günter"}],"oa_version":"None","year":"2012","day":"20","publist_id":"3563"},{"scopus_import":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T07:41:28Z","has_accepted_license":"1","year":"2012","oa_version":"Published Version","publist_id":"3530","pubrep_id":"385","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":7,"file_date_updated":"2020-07-14T12:46:01Z","oa":1,"publication_status":"published","_id":"3159","date_published":"2012-06-06T00:00:00Z","abstract":[{"text":"The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the &quot;root&quot; of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. In doing so, we show that the ordering of the reticular edges is more robust to noise in weight estimation than is the ordering of the tree edges. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks.","lang":"eng"}],"article_number":"e36715","file":[{"creator":"kschuh","file_size":541583,"file_name":"2012_PLoS_Mileyko.PDF","checksum":"515a98ad72e470752f03f13663dcaff8","access_level":"open_access","date_updated":"2020-07-14T12:46:01Z","relation":"main_file","file_id":"5922","content_type":"application/pdf","date_created":"2019-02-05T12:38:43Z"}],"issue":"6","ddc":["510"],"doi":"10.1371/journal.pone.0036715","language":[{"iso":"eng"}],"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.","author":[{"last_name":"Mileyko","full_name":"Mileyko, Yuriy","first_name":"Yuriy"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Price","full_name":"Price, Charles","first_name":"Charles"},{"full_name":"Weitz, Joshua","first_name":"Joshua","last_name":"Weitz"}],"type":"journal_article","day":"06","title":"Hierarchical ordering of reticular networks","citation":{"mla":"Mileyko, Yuriy, et al. “Hierarchical Ordering of Reticular Networks.” <i>PLoS One</i>, vol. 7, no. 6, e36715, Public Library of Science, 2012, doi:<a href=\"https://doi.org/10.1371/journal.pone.0036715\">10.1371/journal.pone.0036715</a>.","chicago":"Mileyko, Yuriy, Herbert Edelsbrunner, Charles Price, and Joshua Weitz. “Hierarchical Ordering of Reticular Networks.” <i>PLoS One</i>. Public Library of Science, 2012. <a href=\"https://doi.org/10.1371/journal.pone.0036715\">https://doi.org/10.1371/journal.pone.0036715</a>.","ista":"Mileyko Y, Edelsbrunner H, Price C, Weitz J. 2012. Hierarchical ordering of reticular networks. PLoS One. 7(6), e36715.","ieee":"Y. Mileyko, H. Edelsbrunner, C. Price, and J. Weitz, “Hierarchical ordering of reticular networks,” <i>PLoS One</i>, vol. 7, no. 6. Public Library of Science, 2012.","ama":"Mileyko Y, Edelsbrunner H, Price C, Weitz J. Hierarchical ordering of reticular networks. <i>PLoS One</i>. 2012;7(6). doi:<a href=\"https://doi.org/10.1371/journal.pone.0036715\">10.1371/journal.pone.0036715</a>","apa":"Mileyko, Y., Edelsbrunner, H., Price, C., &#38; Weitz, J. (2012). Hierarchical ordering of reticular networks. <i>PLoS One</i>. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pone.0036715\">https://doi.org/10.1371/journal.pone.0036715</a>","short":"Y. Mileyko, H. Edelsbrunner, C. Price, J. Weitz, PLoS One 7 (2012)."},"status":"public","intvolume":"         7","publication":"PLoS One","quality_controlled":"1","department":[{"_id":"HeEd"}],"publisher":"Public Library of Science","date_created":"2018-12-11T12:01:44Z","month":"06"}]