{"acknowledgement":"This research is partially supported by the National Science Foun- dation (NSF) under grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.","department":[{"_id":"HeEd"}],"citation":{"ieee":"H. Edelsbrunner, B. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” in <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i>, Chapel Hill, NC, USA, 2012, pp. 91–100.","ama":"Edelsbrunner H, Fasy B, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In: <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>. ACM; 2012:91-100. doi:<a href=\"https://doi.org/10.1145/2261250.2261265\">10.1145/2261250.2261265</a>","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>.","short":"H. Edelsbrunner, B. Fasy, G. Rote, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100.","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>","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.","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>."},"date_created":"2018-12-11T12:01:35Z","month":"06","page":"91 - 100","year":"2012","status":"public","publisher":"ACM","day":"20","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_published":"2012-06-20T00:00:00Z","date_updated":"2023-02-23T10:59:27Z","publist_id":"3563","type":"conference","language":[{"iso":"eng"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Fasy","full_name":"Fasy, Brittany","first_name":"Brittany"},{"full_name":"Rote, Günter","first_name":"Günter","last_name":"Rote"}],"doi":"10.1145/2261250.2261265","conference":{"name":"SCG: Symposium on Computational Geometry","location":"Chapel Hill, NC, USA","end_date":"2012-06-20","start_date":"2012-06-17"},"_id":"3134","title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","related_material":{"record":[{"id":"2815","status":"public","relation":"later_version"}]},"scopus_import":1,"quality_controlled":"1","publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","publication_status":"published","oa_version":"None","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. "}]}