--- _id: '6648' 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." alternative_title: - LIPIcs author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Ziga full_name: Virk, Ziga last_name: Virk - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: 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' 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. 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. 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.' 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. 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. conference: end_date: 2019-06-21 location: Portland, OR, United States name: 'SoCG 2019: Symposium on Computational Geometry' start_date: 2019-06-18 date_created: 2019-07-17T10:36:09Z date_published: 2019-06-01T00:00:00Z date_updated: 2021-01-12T08:08:23Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPICS.SOCG.2019.31 external_id: arxiv: - '1903.08510' file: - access_level: open_access checksum: 8ec8720730d4c789bf7b06540f1c29f4 content_type: application/pdf creator: dernst date_created: 2019-07-24T06:40:01Z date_updated: 2020-07-14T12:47:35Z file_id: '6666' file_name: 2019_LIPICS_Edelsbrunner.pdf file_size: 1355179 relation: main_file file_date_updated: 2020-07-14T12:47:35Z has_accepted_license: '1' intvolume: ' 129' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 31:1-31:14 project: - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: 35th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771047' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Topological data analysis in information space tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 129 year: '2019' ... --- _id: '6659' abstract: - lang: eng 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. 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. article_processing_charge: No article_type: original author: - first_name: Naoki full_name: Zenmyo, Naoki last_name: Zenmyo - first_name: Hiroki full_name: Tokumaru, Hiroki last_name: Tokumaru - first_name: Shohei full_name: Uchinomiya, Shohei last_name: Uchinomiya - first_name: Hirokazu full_name: Fuchida, Hirokazu last_name: Fuchida - first_name: Shigekazu full_name: Tabata, Shigekazu id: 4427179E-F248-11E8-B48F-1D18A9856A87 last_name: Tabata - first_name: Itaru full_name: Hamachi, Itaru last_name: Hamachi - first_name: Ryuichi full_name: Shigemoto, Ryuichi id: 499F3ABC-F248-11E8-B48F-1D18A9856A87 last_name: Shigemoto orcid: 0000-0001-8761-9444 - first_name: Akio full_name: Ojida, Akio last_name: Ojida citation: 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 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. 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. 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. 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. date_created: 2019-07-21T21:59:16Z date_published: 2019-05-15T00:00:00Z date_updated: 2021-01-12T08:08:26Z day: '15' ddc: - '570' department: - _id: RySh doi: 10.1246/bcsj.20190034 ec_funded: 1 file: - access_level: open_access checksum: 186de511d6e0ca93f5d981e2443eb8cd content_type: application/pdf creator: dernst date_created: 2020-10-02T08:49:58Z date_updated: 2020-10-02T08:49:58Z file_id: '8594' file_name: 2019_BCSJ_Zenmyo.pdf file_size: 2464903 relation: main_file success: 1 file_date_updated: 2020-10-02T08:49:58Z has_accepted_license: '1' intvolume: ' 92' issue: '5' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 995-1000 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' publication: Bulletin of the Chemical Society of Japan publication_identifier: issn: - '00092673' publication_status: published publisher: Bulletin of the Chemical Society of Japan quality_controlled: '1' scopus_import: '1' status: public title: Optimized reaction pair of the CysHis tag and Ni(II)-NTA probe for highly selective chemical labeling of membrane proteins type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 92 year: '2019' ... --- _id: '6662' abstract: - lang: eng text: "In phase retrieval, we want to recover an unknown signal \U0001D465∈ℂ\U0001D451 from n quadratic measurements of the form \U0001D466\U0001D456=|⟨\U0001D44E\U0001D456,\U0001D465⟩|2+\U0001D464\U0001D456, where \U0001D44E\U0001D456∈ℂ\U0001D451 are known sensing vectors and \U0001D464\U0001D456 is measurement noise. We ask the following weak recovery question: What is the minimum number of measurements n needed to produce an estimator \U0001D465^(\U0001D466) that is positively correlated with the signal \U0001D465? We consider the case of Gaussian vectors \U0001D44E\U0001D44E\U0001D456. 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 \U0001D45B≤\U0001D451−\U0001D45C(\U0001D451), no estimator can do significantly better than random and achieve a strictly positive correlation. For \U0001D45B≥\U0001D451+\U0001D45C(\U0001D451), 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 \U0001D466\U0001D456 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." article_type: original author: - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 - first_name: Andrea full_name: Montanari, Andrea last_name: Montanari citation: 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 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 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. 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. ista: Mondelli M, Montanari A. 2019. Fundamental limits of weak recovery with applications to phase retrieval. Foundations of Computational Mathematics. 19(3), 703–773. 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. short: M. Mondelli, A. Montanari, Foundations of Computational Mathematics 19 (2019) 703–773. date_created: 2019-07-22T13:23:48Z date_published: 2019-06-01T00:00:00Z date_updated: 2021-01-12T08:08:28Z day: '01' doi: 10.1007/s10208-018-9395-y extern: '1' external_id: arxiv: - '1708.05932' intvolume: ' 19' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.05932 month: '06' oa: 1 oa_version: Preprint page: 703-773 publication: Foundations of Computational Mathematics publication_identifier: eissn: - 1615-3383 publication_status: published publisher: Springer quality_controlled: '1' status: public title: Fundamental limits of weak recovery with applications to phase retrieval type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 19 year: '2019' ... --- _id: '6672' abstract: - lang: eng 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. author: - first_name: Jean-Daniel full_name: Boissonnat, Jean-Daniel last_name: Boissonnat - first_name: Mael full_name: Rouxel-Labbé, Mael last_name: Rouxel-Labbé - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: 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 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 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. 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. 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. 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. date_created: 2019-07-24T08:42:12Z date_published: 2019-05-21T00:00:00Z date_updated: 2021-01-12T08:08:30Z day: '21' doi: 10.1137/17m1152292 extern: '1' external_id: arxiv: - '1703.06487' intvolume: ' 48' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1703.06487 month: '05' oa: 1 oa_version: Preprint page: 1046-1097 publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial & Applied Mathematics (SIAM) quality_controlled: '1' status: public title: Anisotropic triangulations via discrete Riemannian Voronoi diagrams type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2019' ... --- _id: '6725' abstract: - lang: eng text: "A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective function to be minimized. This function is represented as a sum of terms where each term depends on a subset of the variables. To obtain different classes of optimization problems, one can restrict all terms to come from a fixed set Γ of cost functions, called a language. \r\nRecent breakthrough results have established a complete complexity classification of such classes with respect to language Γ: if all cost functions in Γ satisfy a certain algebraic condition then all Γ-instances can be solved in polynomial time, otherwise the problem is NP-hard. Unfortunately, testing this condition for a given language Γ is known to be NP-hard. We thus study exponential algorithms for this meta-problem. We show that the tractability condition of a finite-valued language Γ can be tested in O(3‾√3|D|⋅poly(size(Γ))) time, where D is the domain of Γ and poly(⋅) is some fixed polynomial. We also obtain a matching lower bound under the Strong Exponential Time Hypothesis (SETH). More precisely, we prove that for any constant δ<1 there is no O(3‾√3δ|D|) algorithm, assuming that SETH holds." alternative_title: - LIPIcs author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Kolmogorov V. Testing the complexity of a valued CSP language. In: 46th International Colloquium on Automata, Languages and Programming. Vol 132. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:77:1-77:12. doi:10.4230/LIPICS.ICALP.2019.77' apa: 'Kolmogorov, V. (2019). Testing the complexity of a valued CSP language. In 46th International Colloquium on Automata, Languages and Programming (Vol. 132, p. 77:1-77:12). Patras, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ICALP.2019.77' chicago: Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” In 46th International Colloquium on Automata, Languages and Programming, 132:77:1-77:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.ICALP.2019.77. ieee: V. Kolmogorov, “Testing the complexity of a valued CSP language,” in 46th International Colloquium on Automata, Languages and Programming, Patras, Greece, 2019, vol. 132, p. 77:1-77:12. ista: 'Kolmogorov V. 2019. Testing the complexity of a valued CSP language. 46th International Colloquium on Automata, Languages and Programming. ICALP 2019: International Colloquim on Automata, Languages and Programming, LIPIcs, vol. 132, 77:1-77:12.' mla: Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” 46th International Colloquium on Automata, Languages and Programming, vol. 132, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12, doi:10.4230/LIPICS.ICALP.2019.77. short: V. Kolmogorov, in:, 46th International Colloquium on Automata, Languages and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12. conference: end_date: 2019-07-12 location: Patras, Greece name: 'ICALP 2019: International Colloquim on Automata, Languages and Programming' start_date: 2019-07-08 date_created: 2019-07-29T12:23:29Z date_published: 2019-07-01T00:00:00Z date_updated: 2021-01-12T08:08:40Z day: '01' ddc: - '000' department: - _id: VlKo doi: 10.4230/LIPICS.ICALP.2019.77 ec_funded: 1 external_id: arxiv: - '1803.02289' file: - access_level: open_access checksum: f5ebee8eec6ae09e30365578ee63a492 content_type: application/pdf creator: dernst date_created: 2019-07-31T07:01:45Z date_updated: 2020-07-14T12:47:38Z file_id: '6738' file_name: 2019_LIPICS_Kolmogorov.pdf file_size: 575475 relation: main_file file_date_updated: 2020-07-14T12:47:38Z has_accepted_license: '1' intvolume: ' 132' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 77:1-77:12 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: 46th International Colloquium on Automata, Languages and Programming publication_identifier: isbn: - 978-3-95977-109-2 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Testing the complexity of a valued CSP language tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 132 year: '2019' ... --- _id: '6726' abstract: - lang: eng text: Randomness is an essential part of any secure cryptosystem, but many constructions rely on distributions that are not uniform. This is particularly true for lattice based cryptosystems, which more often than not make use of discrete Gaussian distributions over the integers. For practical purposes it is crucial to evaluate the impact that approximation errors have on the security of a scheme to provide the best possible trade-off between security and performance. Recent years have seen surprising results allowing to use relatively low precision while maintaining high levels of security. A key insight in these results is that sampling a distribution with low relative error can provide very strong security guarantees. Since floating point numbers provide guarantees on the relative approximation error, they seem a suitable tool in this setting, but it is not obvious which sampling algorithms can actually profit from them. While previous works have shown that inversion sampling can be adapted to provide a low relative error (Pöppelmann et al., CHES 2014; Prest, ASIACRYPT 2017), other works have called into question if this is possible for other sampling techniques (Zheng et al., Eprint report 2018/309). In this work, we consider all sampling algorithms that are popular in the cryptographic setting and analyze the relationship of floating point precision and the resulting relative error. We show that all of the algorithms either natively achieve a low relative error or can be adapted to do so. article_processing_charge: No author: - first_name: Michael full_name: Walter, Michael id: 488F98B0-F248-11E8-B48F-1D18A9856A87 last_name: Walter orcid: 0000-0003-3186-2482 citation: ama: 'Walter M. Sampling the integers with low relative error. In: Buchmann J, Nitaj A, Rachidi T, eds. Progress in Cryptology – AFRICACRYPT 2019. Vol 11627. LNCS. Cham: Springer Nature; 2019:157-180. doi:10.1007/978-3-030-23696-0_9' apa: 'Walter, M. (2019). Sampling the integers with low relative error. In J. Buchmann, A. Nitaj, & T. Rachidi (Eds.), Progress in Cryptology – AFRICACRYPT 2019 (Vol. 11627, pp. 157–180). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-23696-0_9' chicago: 'Walter, Michael. “Sampling the Integers with Low Relative Error.” In Progress in Cryptology – AFRICACRYPT 2019, edited by J Buchmann, A Nitaj, and T Rachidi, 11627:157–80. LNCS. Cham: Springer Nature, 2019. https://doi.org/10.1007/978-3-030-23696-0_9.' ieee: 'M. Walter, “Sampling the integers with low relative error,” in Progress in Cryptology – AFRICACRYPT 2019, vol. 11627, J. Buchmann, A. Nitaj, and T. Rachidi, Eds. Cham: Springer Nature, 2019, pp. 157–180.' ista: 'Walter M. 2019.Sampling the integers with low relative error. In: Progress in Cryptology – AFRICACRYPT 2019. vol. 11627, 157–180.' mla: Walter, Michael. “Sampling the Integers with Low Relative Error.” Progress in Cryptology – AFRICACRYPT 2019, edited by J Buchmann et al., vol. 11627, Springer Nature, 2019, pp. 157–80, doi:10.1007/978-3-030-23696-0_9. short: M. Walter, in:, J. Buchmann, A. Nitaj, T. Rachidi (Eds.), Progress in Cryptology – AFRICACRYPT 2019, Springer Nature, Cham, 2019, pp. 157–180. conference: end_date: 2019-07-11 location: Rabat, Morocco name: 'AFRICACRYPT: International Conference on Cryptology in Africa' start_date: 2019-07-09 date_created: 2019-07-29T12:25:31Z date_published: 2019-06-29T00:00:00Z date_updated: 2023-02-23T12:50:15Z day: '29' department: - _id: KrPi doi: 10.1007/978-3-030-23696-0_9 ec_funded: 1 editor: - first_name: J full_name: Buchmann, J last_name: Buchmann - first_name: A full_name: Nitaj, A last_name: Nitaj - first_name: T full_name: Rachidi, T last_name: Rachidi intvolume: ' 11627' language: - iso: eng main_file_link: - open_access: '1' url: https://eprint.iacr.org/2019/068 month: '06' oa: 1 oa_version: Preprint page: 157-180 place: Cham project: - _id: 258AA5B2-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '682815' name: Teaching Old Crypto New Tricks publication: Progress in Cryptology – AFRICACRYPT 2019 publication_identifier: eisbn: - 978-3-0302-3696-0 isbn: - 978-3-0302-3695-3 issn: - 0302-9743 - 1611-3349 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: LNCS status: public title: Sampling the integers with low relative error type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 11627 year: '2019' ... --- _id: '6663' abstract: - lang: eng text: Consider the problem of constructing a polar code of block length N for a given transmission channel W. Previous approaches require one to compute the reliability of the N synthetic channels and then use only those that are sufficiently reliable. However, we know from two independent works by Schürch and by Bardet et al. that the synthetic channels are partially ordered with respect to degradation. Hence, it is natural to ask whether the partial order can be exploited to reduce the computational burden of the construction problem. We show that, if we take advantage of the partial order, we can construct a polar code by computing the reliability of roughly a fraction 1/ log 3/2 N of the synthetic channels. In particular, we prove that N/ log 3/2 N is a lower bound on the number of synthetic channels to be considered and such a bound is tight up to a multiplicative factor log log N. This set of roughly N/ log 3/2 N synthetic channels is universal, in the sense that it allows one to construct polar codes for any W, and it can be identified by solving a maximum matching problem on a bipartite graph. Our proof technique consists of reducing the construction problem to the problem of computing the maximum cardinality of an antichain for a suitable partially ordered set. As such, this method is general, and it can be used to further improve the complexity of the construction problem, in case a refined partial order on the synthetic channels of polar codes is discovered. author: - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 - first_name: Hamed full_name: Hassani, Hamed last_name: Hassani - first_name: Rudiger full_name: Urbanke, Rudiger last_name: Urbanke citation: ama: Mondelli M, Hassani H, Urbanke R. Construction of polar codes with sublinear complexity. IEEE. 2019;65(5):2782-2791. doi:10.1109/tit.2018.2889667 apa: Mondelli, M., Hassani, H., & Urbanke, R. (2019). Construction of polar codes with sublinear complexity. IEEE. IEEE. https://doi.org/10.1109/tit.2018.2889667 chicago: Mondelli, Marco, Hamed Hassani, and Rudiger Urbanke. “Construction of Polar Codes with Sublinear Complexity.” IEEE. IEEE, 2019. https://doi.org/10.1109/tit.2018.2889667. ieee: M. Mondelli, H. Hassani, and R. Urbanke, “Construction of polar codes with sublinear complexity,” IEEE, vol. 65, no. 5. IEEE, pp. 2782–2791, 2019. ista: Mondelli M, Hassani H, Urbanke R. 2019. Construction of polar codes with sublinear complexity. IEEE. 65(5), 2782–2791. mla: Mondelli, Marco, et al. “Construction of Polar Codes with Sublinear Complexity.” IEEE, vol. 65, no. 5, IEEE, 2019, pp. 2782–91, doi:10.1109/tit.2018.2889667. short: M. Mondelli, H. Hassani, R. Urbanke, IEEE 65 (2019) 2782–2791. date_created: 2019-07-23T07:32:57Z date_published: 2019-05-01T00:00:00Z date_updated: 2023-02-23T12:50:20Z day: '01' doi: 10.1109/tit.2018.2889667 extern: '1' external_id: arxiv: - '1612.05295' intvolume: ' 65' issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1612.05295 month: '05' oa: 1 oa_version: Preprint page: 2782-2791 publication: IEEE publication_status: published publisher: IEEE quality_controlled: '1' related_material: record: - id: '6729' relation: earlier_version status: public status: public title: Construction of polar codes with sublinear complexity type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 65 year: '2019' ... --- _id: '6747' abstract: - lang: eng text: "We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors x∈ℝd, r hidden units with weights {wi}1≤i≤r and output y∈ℝ, i.e., y=∑ri=1σ(w\U0001D5B3ix), with activation functions given by low-degree polynomials. In particular, if σ(x)=a0+a1x+a3x3, we prove that no polynomial-time learning algorithm can outperform the trivial predictor that assigns to each example the response variable \U0001D53C(y), when d3/2≪r≪d2. Our conclusion holds for a `natural data distribution', namely standard Gaussian feature vectors x, and output distributed according to a two-layer neural network with random isotropic weights, and under a certain complexity-theoretic assumption on tensor decomposition. Roughly speaking, we assume that no polynomial-time algorithm can substantially outperform current methods for tensor decomposition based on the sum-of-squares hierarchy. We also prove generalizations of this statement for higher degree polynomial activations, and non-random weight vectors. Remarkably, several existing algorithms for learning two-layer networks with rigorous guarantees are based on tensor decomposition. Our results support the idea that this is indeed the core computational difficulty in learning such networks, under the stated generative model for the data. As a side result, we show that under this model learning the network requires accurate learning of its weights, a property that does not hold in a more general setting. " article_processing_charge: No author: - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 - first_name: Andrea full_name: Montanari, Andrea last_name: Montanari citation: ama: 'Mondelli M, Montanari A. On the connection between learning two-layers neural networks and tensor  decomposition. In: Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics. Vol 89. Proceedings of Machine Learning Research; 2019:1051-1060.' apa: 'Mondelli, M., & Montanari, A. (2019). On the connection between learning two-layers neural networks and tensor  decomposition. In Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (Vol. 89, pp. 1051–1060). Naha, Okinawa, Japan: Proceedings of Machine Learning Research.' chicago: Mondelli, Marco, and Andrea Montanari. “On the Connection between Learning Two-Layers Neural Networks and Tensor  Decomposition.” In Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, 89:1051–60. Proceedings of Machine Learning Research, 2019. ieee: M. Mondelli and A. Montanari, “On the connection between learning two-layers neural networks and tensor  decomposition,” in Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, Naha, Okinawa, Japan, 2019, vol. 89, pp. 1051–1060. ista: 'Mondelli M, Montanari A. 2019. On the connection between learning two-layers neural networks and tensor  decomposition. Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics. AISTATS: Artificial Intelligence and Statistics vol. 89, 1051–1060.' mla: Mondelli, Marco, and Andrea Montanari. “On the Connection between Learning Two-Layers Neural Networks and Tensor  Decomposition.” Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, vol. 89, Proceedings of Machine Learning Research, 2019, pp. 1051–60. short: M. Mondelli, A. Montanari, in:, Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, 2019, pp. 1051–1060. conference: end_date: 2019-04-18 location: Naha, Okinawa, Japan name: 'AISTATS: Artificial Intelligence and Statistics' start_date: 2019-04-16 date_created: 2019-07-31T09:31:26Z date_published: 2019-04-01T00:00:00Z date_updated: 2021-01-12T08:08:49Z day: '01' extern: '1' external_id: arxiv: - '1802.07301' intvolume: ' 89' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1802.07301 month: '04' oa: 1 oa_version: Preprint page: 1051-1060 publication: Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics publication_status: published publisher: Proceedings of Machine Learning Research quality_controlled: '1' status: public title: On the connection between learning two-layers neural networks and tensor decomposition type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 89 year: '2019' ... --- _id: '6750' abstract: - lang: eng text: 'Polar codes have gained extensive attention during the past few years and recently they have been selected for the next generation of wireless communications standards (5G). Successive-cancellation-based (SC-based) decoders, such as SC list (SCL) and SC flip (SCF), provide a reasonable error performance for polar codes at the cost of low decoding speed. Fast SC-based decoders, such as Fast-SSC, Fast-SSCL, and Fast-SSCF, identify the special constituent codes in a polar code graph off-line, produce a list of operations, store the list in memory, and feed the list to the decoder to decode the constituent codes in order efficiently, thus increasing the decoding speed. However, the list of operations is dependent on the code rate and as the rate changes, a new list is produced, making fast SC-based decoders not rate-flexible. In this paper, we propose a completely rate-flexible fast SC-based decoder by creating the list of operations directly in hardware, with low implementation complexity. We further propose a hardware architecture implementing the proposed method and show that the area occupation of the rate-flexible fast SC-based decoder in this paper is only 38% of the total area of the memory-based base-line decoder when 5G code rates are supported. ' article_number: '8854897' article_processing_charge: No article_type: original author: - first_name: Seyyed Ali full_name: Hashemi, Seyyed Ali last_name: Hashemi - first_name: Carlo full_name: Condo, Carlo last_name: Condo - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 - first_name: Warren J full_name: Gross, Warren J last_name: Gross citation: ama: Hashemi SA, Condo C, Mondelli M, Gross WJ. Rate-flexible fast polar decoders. IEEE Transactions on Signal Processing. 2019;67(22). doi:10.1109/TSP.2019.2944738 apa: Hashemi, S. A., Condo, C., Mondelli, M., & Gross, W. J. (2019). Rate-flexible fast polar decoders. IEEE Transactions on Signal Processing. IEEE. https://doi.org/10.1109/TSP.2019.2944738 chicago: Hashemi, Seyyed Ali, Carlo Condo, Marco Mondelli, and Warren J Gross. “Rate-Flexible Fast Polar Decoders.” IEEE Transactions on Signal Processing. IEEE, 2019. https://doi.org/10.1109/TSP.2019.2944738. ieee: S. A. Hashemi, C. Condo, M. Mondelli, and W. J. Gross, “Rate-flexible fast polar decoders,” IEEE Transactions on Signal Processing, vol. 67, no. 22. IEEE, 2019. ista: Hashemi SA, Condo C, Mondelli M, Gross WJ. 2019. Rate-flexible fast polar decoders. IEEE Transactions on Signal Processing. 67(22), 8854897. mla: Hashemi, Seyyed Ali, et al. “Rate-Flexible Fast Polar Decoders.” IEEE Transactions on Signal Processing, vol. 67, no. 22, 8854897, IEEE, 2019, doi:10.1109/TSP.2019.2944738. short: S.A. Hashemi, C. Condo, M. Mondelli, W.J. Gross, IEEE Transactions on Signal Processing 67 (2019). date_created: 2019-07-31T09:51:14Z date_published: 2019-11-15T00:00:00Z date_updated: 2021-01-12T08:08:51Z day: '15' department: - _id: MaMo doi: 10.1109/TSP.2019.2944738 external_id: arxiv: - '1903.09203' intvolume: ' 67' issue: '22' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1903.09203 month: '11' oa: 1 oa_version: Preprint publication: IEEE Transactions on Signal Processing publication_identifier: issn: - 1053587X publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: 1 status: public title: Rate-flexible fast polar decoders type: journal_article user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 67 year: '2019' ... --- _id: '6759' abstract: - lang: eng text: "We consider the graph class Grounded-L corresponding to graphs that admit an intersection representation by L-shaped curves, where additionally the topmost points of each curve are assumed to belong to a common horizontal line. We prove that Grounded-L graphs admit an equivalent characterisation in terms of vertex ordering with forbidden patterns. \r\nWe also compare this class to related intersection classes, such as the grounded segment graphs, the monotone L-graphs (a.k.a. max point-tolerance graphs), or the outer-1-string graphs. We give constructions showing that these classes are all distinct and satisfy only trivial or previously known inclusions." article_number: P3.17 article_processing_charge: No article_type: original author: - first_name: Vít full_name: Jelínek, Vít last_name: Jelínek - first_name: Martin full_name: Töpfer, Martin id: 4B865388-F248-11E8-B48F-1D18A9856A87 last_name: Töpfer citation: ama: Jelínek V, Töpfer M. On grounded L-graphs and their relatives. Electronic Journal of Combinatorics. 2019;26(3). doi:10.37236/8096 apa: Jelínek, V., & Töpfer, M. (2019). On grounded L-graphs and their relatives. Electronic Journal of Combinatorics. Electronic Journal of Combinatorics. https://doi.org/10.37236/8096 chicago: Jelínek, Vít, and Martin Töpfer. “On Grounded L-Graphs and Their Relatives.” Electronic Journal of Combinatorics. Electronic Journal of Combinatorics, 2019. https://doi.org/10.37236/8096. ieee: V. Jelínek and M. Töpfer, “On grounded L-graphs and their relatives,” Electronic Journal of Combinatorics, vol. 26, no. 3. Electronic Journal of Combinatorics, 2019. ista: Jelínek V, Töpfer M. 2019. On grounded L-graphs and their relatives. Electronic Journal of Combinatorics. 26(3), P3.17. mla: Jelínek, Vít, and Martin Töpfer. “On Grounded L-Graphs and Their Relatives.” Electronic Journal of Combinatorics, vol. 26, no. 3, P3.17, Electronic Journal of Combinatorics, 2019, doi:10.37236/8096. short: V. Jelínek, M. Töpfer, Electronic Journal of Combinatorics 26 (2019). date_created: 2019-08-04T21:59:20Z date_published: 2019-07-19T00:00:00Z date_updated: 2022-03-18T12:32:02Z day: '19' ddc: - '510' department: - _id: DaAl doi: 10.37236/8096 ec_funded: 1 external_id: arxiv: - '1808.04148' file: - access_level: open_access checksum: 20fc366fc6683ef0b074a019b73a663a content_type: application/pdf creator: dernst date_created: 2019-08-05T06:46:55Z date_updated: 2020-07-14T12:47:39Z file_id: '6764' file_name: 2019_eJourCombinatorics_Jelinek.pdf file_size: 533697 relation: main_file file_date_updated: 2020-07-14T12:47:39Z has_accepted_license: '1' intvolume: ' 26' issue: '3' language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: Electronic Journal of Combinatorics publication_identifier: eissn: - '10778926' publication_status: published publisher: Electronic Journal of Combinatorics quality_controlled: '1' scopus_import: '1' status: public title: On grounded L-graphs and their relatives tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2019' ...