[{"date_published":"2019-08-01T00:00:00Z","ec_funded":1,"date_created":"2019-07-12T08:34:57Z","page":"275-279","day":"01","file":[{"date_created":"2019-07-12T08:32:46Z","file_name":"IntrinsicExtrinsicCCCG2019.pdf","creator":"mwintrae","date_updated":"2020-07-14T12:47:34Z","file_size":321176,"file_id":"6629","checksum":"ceabd152cfa55170d57763f9c6c60a53","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication":"The 31st Canadian Conference in Computational Geometry","has_accepted_license":"1","year":"2019","publication_status":"published","month":"08","quality_controlled":"1","scopus_import":1,"oa":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise flat triangular meshes with a given number of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and d is the dimension of Euclidean space. Moreover the pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension. We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space."}],"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:34Z","author":[{"last_name":"Vegter","full_name":"Vegter, Gert","first_name":"Gert"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"ddc":["004"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:08:16Z","citation":{"mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–79.","ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational Geometry. ; 2019:275-279.","apa":"Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In The 31st Canadian Conference in Computational Geometry (pp. 275–279). Edmonton, Canada.","ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in The 31st Canadian Conference in Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In The 31st Canadian Conference in Computational Geometry, 275–79, 2019.","ista":"Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. The 31st Canadian Conference in Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279."},"status":"public","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"type":"conference","conference":{"name":"CCCG: Canadian Conference in Computational Geometry","start_date":"2019-08-08","location":"Edmonton, Canada","end_date":"2019-08-10"},"_id":"6628"},{"volume":129,"publication_status":"published","publication_identifier":{"isbn":["9783959771047"]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2020-07-14T12:47:35Z","file_size":1355179,"date_created":"2019-07-24T06:40:01Z","file_name":"2019_LIPICS_Edelsbrunner.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"6666","checksum":"8ec8720730d4c789bf7b06540f1c29f4"}],"scopus_import":1,"alternative_title":["LIPIcs"],"intvolume":" 129","month":"06","abstract":[{"lang":"eng","text":"Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory\r\nneeded for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context."}],"oa_version":"Published Version","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:35Z","date_updated":"2021-01-12T08:08:23Z","ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"name":"SoCG 2019: Symposium on Computational Geometry","start_date":"2019-06-18","location":"Portland, OR, United States","end_date":"2019-06-21"},"type":"conference","status":"public","_id":"6648","page":"31:1-31:14","date_created":"2019-07-17T10:36:09Z","doi":"10.4230/LIPICS.SOCG.2019.31","date_published":"2019-06-01T00:00:00Z","year":"2019","has_accepted_license":"1","publication":"35th International Symposium on Computational Geometry","day":"01","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","external_id":{"arxiv":["1903.08510"]},"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"}],"title":"Topological data analysis in information space","citation":{"short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis in information space. In 35th International Symposium on Computational Geometry (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:10.4230/LIPICS.SOCG.2019.31.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” In 35th International Symposium on Computational Geometry, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.31."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}]},{"_id":"6659","status":"public","article_type":"original","type":"journal_article","ddc":["570"],"date_updated":"2021-01-12T08:08:26Z","file_date_updated":"2020-10-02T08:49:58Z","department":[{"_id":"RySh"}],"oa_version":"Published Version","abstract":[{"text":"Chemical labeling of proteins with synthetic molecular probes offers the possibility to probe the functions of proteins of interest in living cells. However, the methods for covalently labeling targeted proteins using complementary peptide tag-probe pairs are still limited, irrespective of the versatility of such pairs in biological research. Herein, we report the new CysHis tag-Ni(II) probe pair for the specific covalent labeling of proteins. A broad-range evaluation of the reactivity profiles of the probe and the CysHis peptide tag afforded a tag-probe pair with an optimized and high labeling selectivity and reactivity. In particular, the labeling specificity of this pair was notably improved compared to the previously reported one. This pair was successfully utilized for the fluorescence imaging of membrane proteins on the surfaces of living cells, demonstrating its potential utility in biological research.","lang":"eng"}],"intvolume":" 92","month":"05","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"186de511d6e0ca93f5d981e2443eb8cd","file_id":"8594","success":1,"date_updated":"2020-10-02T08:49:58Z","file_size":2464903,"creator":"dernst","date_created":"2020-10-02T08:49:58Z","file_name":"2019_BCSJ_Zenmyo.pdf"}],"publication_status":"published","publication_identifier":{"issn":["00092673"]},"ec_funded":1,"issue":"5","volume":92,"project":[{"_id":"25CA28EA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694539","name":"In situ analysis of single channel subunit composition in neurons: physiological implication in synaptic plasticity and behaviour"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Zenmyo, Naoki, Hiroki Tokumaru, Shohei Uchinomiya, Hirokazu Fuchida, Shigekazu Tabata, Itaru Hamachi, Ryuichi Shigemoto, and Akio Ojida. “Optimized Reaction Pair of the CysHis Tag and Ni(II)-NTA Probe for Highly Selective Chemical Labeling of Membrane Proteins.” Bulletin of the Chemical Society of Japan. Bulletin of the Chemical Society of Japan, 2019. https://doi.org/10.1246/bcsj.20190034.","ista":"Zenmyo N, Tokumaru H, Uchinomiya S, Fuchida H, Tabata S, Hamachi I, Shigemoto R, Ojida A. 2019. Optimized reaction pair of the CysHis tag and Ni(II)-NTA probe for highly selective chemical labeling of membrane proteins. Bulletin of the Chemical Society of Japan. 92(5), 995–1000.","mla":"Zenmyo, Naoki, et al. “Optimized Reaction Pair of the CysHis Tag and Ni(II)-NTA Probe for Highly Selective Chemical Labeling of Membrane Proteins.” Bulletin of the Chemical Society of Japan, vol. 92, no. 5, Bulletin of the Chemical Society of Japan, 2019, pp. 995–1000, doi:10.1246/bcsj.20190034.","ama":"Zenmyo N, Tokumaru H, Uchinomiya S, et al. Optimized reaction pair of the CysHis tag and Ni(II)-NTA probe for highly selective chemical labeling of membrane proteins. Bulletin of the Chemical Society of Japan. 2019;92(5):995-1000. doi:10.1246/bcsj.20190034","apa":"Zenmyo, N., Tokumaru, H., Uchinomiya, S., Fuchida, H., Tabata, S., Hamachi, I., … Ojida, A. (2019). Optimized reaction pair of the CysHis tag and Ni(II)-NTA probe for highly selective chemical labeling of membrane proteins. Bulletin of the Chemical Society of Japan. Bulletin of the Chemical Society of Japan. https://doi.org/10.1246/bcsj.20190034","short":"N. Zenmyo, H. Tokumaru, S. Uchinomiya, H. Fuchida, S. Tabata, I. Hamachi, R. Shigemoto, A. Ojida, Bulletin of the Chemical Society of Japan 92 (2019) 995–1000.","ieee":"N. Zenmyo et al., “Optimized reaction pair of the CysHis tag and Ni(II)-NTA probe for highly selective chemical labeling of membrane proteins,” Bulletin of the Chemical Society of Japan, vol. 92, no. 5. Bulletin of the Chemical Society of Japan, pp. 995–1000, 2019."},"title":"Optimized reaction pair of the CysHis tag and Ni(II)-NTA probe for highly selective chemical labeling of membrane proteins","article_processing_charge":"No","author":[{"first_name":"Naoki","last_name":"Zenmyo","full_name":"Zenmyo, Naoki"},{"full_name":"Tokumaru, Hiroki","last_name":"Tokumaru","first_name":"Hiroki"},{"first_name":"Shohei","last_name":"Uchinomiya","full_name":"Uchinomiya, Shohei"},{"first_name":"Hirokazu","full_name":"Fuchida, Hirokazu","last_name":"Fuchida"},{"first_name":"Shigekazu","id":"4427179E-F248-11E8-B48F-1D18A9856A87","last_name":"Tabata","full_name":"Tabata, Shigekazu"},{"full_name":"Hamachi, Itaru","last_name":"Hamachi","first_name":"Itaru"},{"id":"499F3ABC-F248-11E8-B48F-1D18A9856A87","first_name":"Ryuichi","last_name":"Shigemoto","full_name":"Shigemoto, Ryuichi","orcid":"0000-0001-8761-9444"},{"full_name":"Ojida, Akio","last_name":"Ojida","first_name":"Akio"}],"acknowledgement":"his work was supported by the Grant-in-Aid for Scientific Research B (JSPS KAKENHI grant no. JP17H03090 to A. O.); the Scientific Research on Innovative Areas “Chemistry for Multimolecular Crowding Biosystems” (JSPS KAKENHI grant no. JP17H06349 to A. O.); and the European Union (European Research Council Advanced grant no. 694539 and Human Brain Project Ref. 720270 to R. S.). A. O. acknowledges the financial support of the Takeda Science Foundation.","oa":1,"publisher":"Bulletin of the Chemical Society of Japan","quality_controlled":"1","publication":"Bulletin of the Chemical Society of Japan","day":"15","year":"2019","has_accepted_license":"1","date_created":"2019-07-21T21:59:16Z","date_published":"2019-05-15T00:00:00Z","doi":"10.1246/bcsj.20190034","page":"995-1000"},{"publication":"Foundations of Computational Mathematics","day":"01","year":"2019","date_created":"2019-07-22T13:23:48Z","doi":"10.1007/s10208-018-9395-y","date_published":"2019-06-01T00:00:00Z","page":"703-773","oa":1,"publisher":"Springer","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Mondelli M, Montanari A. 2019. Fundamental limits of weak recovery with applications to phase retrieval. Foundations of Computational Mathematics. 19(3), 703–773.","chicago":"Mondelli, Marco, and Andrea Montanari. “Fundamental Limits of Weak Recovery with Applications to Phase Retrieval.” Foundations of Computational Mathematics. Springer, 2019. https://doi.org/10.1007/s10208-018-9395-y.","short":"M. Mondelli, A. Montanari, Foundations of Computational Mathematics 19 (2019) 703–773.","ieee":"M. Mondelli and A. Montanari, “Fundamental limits of weak recovery with applications to phase retrieval,” Foundations of Computational Mathematics, vol. 19, no. 3. Springer, pp. 703–773, 2019.","apa":"Mondelli, M., & Montanari, A. (2019). Fundamental limits of weak recovery with applications to phase retrieval. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-018-9395-y","ama":"Mondelli M, Montanari A. Fundamental limits of weak recovery with applications to phase retrieval. Foundations of Computational Mathematics. 2019;19(3):703-773. doi:10.1007/s10208-018-9395-y","mla":"Mondelli, Marco, and Andrea Montanari. “Fundamental Limits of Weak Recovery with Applications to Phase Retrieval.” Foundations of Computational Mathematics, vol. 19, no. 3, Springer, 2019, pp. 703–73, doi:10.1007/s10208-018-9395-y."},"title":"Fundamental limits of weak recovery with applications to phase retrieval","external_id":{"arxiv":["1708.05932"]},"author":[{"full_name":"Mondelli, Marco","orcid":"0000-0002-3242-7020","last_name":"Mondelli","first_name":"Marco","id":"27EB676C-8706-11E9-9510-7717E6697425"},{"last_name":"Montanari","full_name":"Montanari, Andrea","first_name":"Andrea"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1615-3383"]},"volume":19,"issue":"3","oa_version":"Preprint","abstract":[{"text":"In phase retrieval, we want to recover an unknown signal 𝑥∈ℂ𝑑 from n quadratic measurements of the form 𝑦𝑖=|⟨𝑎𝑖,𝑥⟩|2+𝑤𝑖, where 𝑎𝑖∈ℂ𝑑 are known sensing vectors and 𝑤𝑖 is measurement noise. We ask the following weak recovery question: What is the minimum number of measurements n needed to produce an estimator 𝑥^(𝑦) that is positively correlated with the signal 𝑥? We consider the case of Gaussian vectors 𝑎𝑎𝑖. We prove that—in the high-dimensional limit—a sharp phase transition takes place, and we locate the threshold in the regime of vanishingly small noise. For 𝑛≤𝑑−𝑜(𝑑), no estimator can do significantly better than random and achieve a strictly positive correlation. For 𝑛≥𝑑+𝑜(𝑑), a simple spectral estimator achieves a positive correlation. Surprisingly, numerical simulations with the same spectral estimator demonstrate promising performance with realistic sensing matrices. Spectral methods are used to initialize non-convex optimization algorithms in phase retrieval, and our approach can boost the performance in this setting as well. Our impossibility result is based on classical information-theoretic arguments. The spectral algorithm computes the leading eigenvector of a weighted empirical covariance matrix. We obtain a sharp characterization of the spectral properties of this random matrix using tools from free probability and generalizing a recent result by Lu and Li. Both the upper bound and lower bound generalize beyond phase retrieval to measurements 𝑦𝑖 produced according to a generalized linear model. As a by-product of our analysis, we compare the threshold of the proposed spectral method with that of a message passing algorithm.","lang":"eng"}],"intvolume":" 19","month":"06","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.05932"}],"extern":"1","date_updated":"2021-01-12T08:08:28Z","_id":"6662","status":"public","article_type":"original","type":"journal_article"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1703.06487"}],"oa":1,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","quality_controlled":"1","intvolume":" 48","month":"05","abstract":[{"text":"The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult problem in a practical way, we introduce the discrete Riemannian Voronoi diagram, a discrete structure that approximates the Riemannian Voronoi diagram. This structure has been implemented and was shown to lead to good triangulations in $\\mathbb{R}^2$ and on surfaces embedded in $\\mathbb{R}^3$ as detailed in our experimental companion paper. In this paper, we study theoretical aspects of our structure. Given a finite set of points $\\mathcal{P}$ in a domain $\\Omega$ equipped with a Riemannian metric, we compare the discrete Riemannian Voronoi diagram of $\\mathcal{P}$ to its Riemannian Voronoi diagram. Both diagrams have dual structures called the discrete Riemannian Delaunay and the Riemannian Delaunay complex. We provide conditions that guarantee that these dual structures are identical. It then follows from previous results that the discrete Riemannian Delaunay complex can be embedded in $\\Omega$ under sufficient conditions, leading to an anisotropic triangulation with curved simplices. Furthermore, we show that, under similar conditions, the simplices of this triangulation can be straightened.","lang":"eng"}],"oa_version":"Preprint","page":"1046-1097","date_created":"2019-07-24T08:42:12Z","doi":"10.1137/17m1152292","issue":"3","volume":48,"date_published":"2019-05-21T00:00:00Z","publication_status":"published","year":"2019","publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"publication":"SIAM Journal on Computing","language":[{"iso":"eng"}],"day":"21","type":"journal_article","status":"public","_id":"6672","external_id":{"arxiv":["1703.06487"]},"author":[{"first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat"},{"first_name":"Mael","last_name":"Rouxel-Labbé","full_name":"Rouxel-Labbé, Mael"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"title":"Anisotropic triangulations via discrete Riemannian Voronoi diagrams","date_updated":"2021-01-12T08:08:30Z","citation":{"mla":"Boissonnat, Jean-Daniel, et al. “Anisotropic Triangulations via Discrete Riemannian Voronoi Diagrams.” SIAM Journal on Computing, vol. 48, no. 3, Society for Industrial & Applied Mathematics (SIAM), 2019, pp. 1046–97, doi:10.1137/17m1152292.","short":"J.-D. Boissonnat, M. Rouxel-Labbé, M. Wintraecken, SIAM Journal on Computing 48 (2019) 1046–1097.","ieee":"J.-D. Boissonnat, M. Rouxel-Labbé, and M. Wintraecken, “Anisotropic triangulations via discrete Riemannian Voronoi diagrams,” SIAM Journal on Computing, vol. 48, no. 3. Society for Industrial & Applied Mathematics (SIAM), pp. 1046–1097, 2019.","apa":"Boissonnat, J.-D., Rouxel-Labbé, M., & Wintraecken, M. (2019). Anisotropic triangulations via discrete Riemannian Voronoi diagrams. SIAM Journal on Computing. Society for Industrial & Applied Mathematics (SIAM). https://doi.org/10.1137/17m1152292","ama":"Boissonnat J-D, Rouxel-Labbé M, Wintraecken M. Anisotropic triangulations via discrete Riemannian Voronoi diagrams. SIAM Journal on Computing. 2019;48(3):1046-1097. doi:10.1137/17m1152292","chicago":"Boissonnat, Jean-Daniel, Mael Rouxel-Labbé, and Mathijs Wintraecken. “Anisotropic Triangulations via Discrete Riemannian Voronoi Diagrams.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics (SIAM), 2019. https://doi.org/10.1137/17m1152292.","ista":"Boissonnat J-D, Rouxel-Labbé M, Wintraecken M. 2019. Anisotropic triangulations via discrete Riemannian Voronoi diagrams. SIAM Journal on Computing. 48(3), 1046–1097."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1"}]