[{"arxiv":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","file":[{"creator":"dernst","file_name":"2026_LIPIcSSoCG_Tinarrage.pdf","date_created":"2026-06-22T07:53:13Z","date_updated":"2026-06-22T07:53:13Z","file_size":1436035,"file_id":"22111","content_type":"application/pdf","checksum":"a468edad327962309688aa78678138da","success":1,"access_level":"open_access","relation":"main_file"}],"quality_controlled":"1","oa":1,"keyword":["Triangulation of manifolds","Simplicial approximation","CW complexes","Delaunay complexes","List homomorphism problem","Topological Data Analysis"],"external_id":{"arxiv":["2112.07573"]},"date_published":"2026-05-27T00:00:00Z","supplementarymaterial":"yes","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["500"],"article_processing_charge":"Yes","file_date_updated":"2026-06-22T07:53:13Z","das_tickbox":"0","date_created":"2026-06-14T22:01:43Z","status":"public","corr_author":"1","intvolume":"       367","year":"2026","abstract":[{"text":"Simplicial approximation provides a framework for constructing simplicial complexes that are homotopy equivalent to a given manifold, provided a CW structure is explicitly known. However, its conventional implementation quickly becomes intractable on a computer: barycentric subdivision produces poorly shaped simplices, and the star condition introduces many vertices. To address these limitations, this article develops a subdivision scheme based on spherical Delaunay triangulations, which attains better refinement properties than barycentric subdivisions. Moreover, the star condition is reframed as two independent problems, one geometric and the other combinatorial, respectively tackled in the language of locally equiconnected spaces and the list homomorphism problem, allowing an exponential reduction in the number of vertices. Via a prototype implementation, we obtain simplicial complexes homotopy equivalent to Grassmannians and Stiefel manifolds up to dimension 5.","lang":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2026.93","OA_place":"publisher","OA_type":"gold","author":[{"first_name":"Raphaël","full_name":"Tinarrage, Raphaël","last_name":"Tinarrage","id":"40ebcc9d-905f-11ef-bf0a-dc475da8a04e","orcid":"0000-0002-1404-1095"}],"volume":367,"citation":{"short":"R. Tinarrage, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","apa":"Tinarrage, R. (2026). Simplicial approximation to CW complexes with spherical Delaunay triangulations. In <i>42nd International Symposium on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.93\">https://doi.org/10.4230/LIPIcs.SoCG.2026.93</a>","chicago":"Tinarrage, Raphaël. “Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations.” In <i>42nd International Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.93\">https://doi.org/10.4230/LIPIcs.SoCG.2026.93</a>.","ama":"Tinarrage R. Simplicial approximation to CW complexes with spherical Delaunay triangulations. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.93\">10.4230/LIPIcs.SoCG.2026.93</a>","ista":"Tinarrage R. 2026. Simplicial approximation to CW complexes with spherical Delaunay triangulations. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry vol. 367, 93:1-93:22.","ieee":"R. Tinarrage, “Simplicial approximation to CW complexes with spherical Delaunay triangulations,” in <i>42nd International Symposium on Computational Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367.","mla":"Tinarrage, Raphaël. “Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367, 93:1-93:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.93\">10.4230/LIPIcs.SoCG.2026.93</a>."},"title":"Simplicial approximation to CW complexes with spherical Delaunay triangulations","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa_version":"Published Version","type":"conference","_id":"22000","publication_status":"published","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959774185"],"eissn":["1868-8969"]},"department":[{"_id":"UlWa"}],"day":"27","has_accepted_license":"1","article_number":"93:1-93:22","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2026-06-02","location":"New Brunswick, NJ, United States","end_date":"2026-06-05"},"related_material":{"link":[{"relation":"software","url":"https://doi.org/10.5281/zenodo.19251455"}]},"researchdata_availability":"no","month":"05","publication":"42nd International Symposium on Computational Geometry","date_updated":"2026-06-22T11:28:26Z"},{"language":[{"iso":"eng"}],"_id":"21954","publication_status":"published","day":"25","department":[{"_id":"UlWa"}],"publication_identifier":{"eissn":["1573-7683"],"issn":["0924-9907"]},"has_accepted_license":"1","article_number":"20","month":"05","article_type":"original","publication":"Journal of Mathematical Imaging and Vision","date_updated":"2026-06-10T08:00:52Z","doi":"10.1007/s10851-026-01300-1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","OA_type":"hybrid","author":[{"last_name":"François","full_name":"François, Anton","first_name":"Anton"},{"orcid":"0000-0002-1404-1095","first_name":"Raphaël","full_name":"Tinarrage, Raphaël","last_name":"Tinarrage","id":"40ebcc9d-905f-11ef-bf0a-dc475da8a04e"}],"OA_place":"publisher","citation":{"ieee":"A. François and R. Tinarrage, “Train-free segmentation in MRI with cubical persistent homology,” <i>Journal of Mathematical Imaging and Vision</i>, vol. 68, no. 3. Springer Nature, 2026.","mla":"François, Anton, and Raphaël Tinarrage. “Train-Free Segmentation in MRI with Cubical Persistent Homology.” <i>Journal of Mathematical Imaging and Vision</i>, vol. 68, no. 3, 20, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s10851-026-01300-1\">10.1007/s10851-026-01300-1</a>.","ista":"François A, Tinarrage R. 2026. Train-free segmentation in MRI with cubical persistent homology. Journal of Mathematical Imaging and Vision. 68(3), 20.","ama":"François A, Tinarrage R. Train-free segmentation in MRI with cubical persistent homology. <i>Journal of Mathematical Imaging and Vision</i>. 2026;68(3). doi:<a href=\"https://doi.org/10.1007/s10851-026-01300-1\">10.1007/s10851-026-01300-1</a>","chicago":"François, Anton, and Raphaël Tinarrage. “Train-Free Segmentation in MRI with Cubical Persistent Homology.” <i>Journal of Mathematical Imaging and Vision</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s10851-026-01300-1\">https://doi.org/10.1007/s10851-026-01300-1</a>.","apa":"François, A., &#38; Tinarrage, R. (2026). Train-free segmentation in MRI with cubical persistent homology. <i>Journal of Mathematical Imaging and Vision</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10851-026-01300-1\">https://doi.org/10.1007/s10851-026-01300-1</a>","short":"A. François, R. Tinarrage, Journal of Mathematical Imaging and Vision 68 (2026)."},"volume":68,"title":"Train-free segmentation in MRI with cubical persistent homology","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article","oa_version":"Published Version","status":"public","corr_author":"1","PlanS_conform":"1","intvolume":"        68","year":"2026","abstract":[{"lang":"eng","text":"We investigate a framework for train-free MRI segmentation based on Topological Data Analysis. The pipeline proceeds in three steps, first identifying the whole object to segment via automatic thresholding, then detecting a distinctive subset whose topology is known in advance, and finally deducing the various components of the segmentation. A key ingredient is the extraction of approximate representative cycles from persistence diagrams, which provides an interpretable link between persistent features and anatomical components. To clarify the method’s scope, we make the underlying topological and intensity assumptions explicit, quantify when they hold on real data, and analyze typical failure modes. We evaluate the approach on glioblastoma and on fetal cortical plate segmentation, with comparisons to unsupervised and deep-learning references. By operating without large annotated datasets, the method is well suited to scarce-data settings and provides an interpretable baseline and practical initialization for expert refinement or learning-based pipelines."}],"issue":"3","file":[{"checksum":"34080653e0f9c6160856a6bbca9b5248","content_type":"application/pdf","file_id":"21990","relation":"main_file","access_level":"open_access","success":1,"file_name":"2026_JourMathImaging_Francois.pdf","creator":"dernst","file_size":6070434,"date_updated":"2026-06-10T07:58:58Z","date_created":"2026-06-10T07:58:58Z"}],"publisher":"Springer Nature","arxiv":1,"external_id":{"arxiv":["2401.01160"]},"quality_controlled":"1","oa":1,"ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2026-05-25T00:00:00Z","scopus_import":"1","date_created":"2026-06-08T08:34:43Z","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2026-06-10T07:58:58Z"},{"type":"journal_article","oa_version":"Published Version","isi":1,"title":"Empirical analysis of binding precedent efficiency in Brazilian Supreme Court via case classification","citation":{"chicago":"Tinarrage, Raphaël, Henrique Ennes, Lucas Resck, Lucas T. Gomes, Jean R. Ponciano, and Jorge Poco. “Empirical Analysis of Binding Precedent Efficiency in Brazilian Supreme Court via Case Classification.” <i>Artificial Intelligence and Law</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s10506-025-09458-6\">https://doi.org/10.1007/s10506-025-09458-6</a>.","ama":"Tinarrage R, Ennes H, Resck L, Gomes LT, Ponciano JR, Poco J. Empirical analysis of binding precedent efficiency in Brazilian Supreme Court via case classification. <i>Artificial Intelligence and Law</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s10506-025-09458-6\">10.1007/s10506-025-09458-6</a>","apa":"Tinarrage, R., Ennes, H., Resck, L., Gomes, L. T., Ponciano, J. R., &#38; Poco, J. (2025). Empirical analysis of binding precedent efficiency in Brazilian Supreme Court via case classification. <i>Artificial Intelligence and Law</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10506-025-09458-6\">https://doi.org/10.1007/s10506-025-09458-6</a>","short":"R. Tinarrage, H. Ennes, L. Resck, L.T. Gomes, J.R. Ponciano, J. Poco, Artificial Intelligence and Law (2025).","ieee":"R. Tinarrage, H. Ennes, L. Resck, L. T. Gomes, J. R. Ponciano, and J. Poco, “Empirical analysis of binding precedent efficiency in Brazilian Supreme Court via case classification,” <i>Artificial Intelligence and Law</i>. Springer Nature, 2025.","mla":"Tinarrage, Raphaël, et al. “Empirical Analysis of Binding Precedent Efficiency in Brazilian Supreme Court via Case Classification.” <i>Artificial Intelligence and Law</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s10506-025-09458-6\">10.1007/s10506-025-09458-6</a>.","ista":"Tinarrage R, Ennes H, Resck L, Gomes LT, Ponciano JR, Poco J. 2025. Empirical analysis of binding precedent efficiency in Brazilian Supreme Court via case classification. Artificial Intelligence and Law."},"OA_place":"publisher","author":[{"orcid":"0000-0002-1404-1095","id":"40ebcc9d-905f-11ef-bf0a-dc475da8a04e","first_name":"Raphaël","full_name":"Tinarrage, Raphaël","last_name":"Tinarrage"},{"last_name":"Ennes","first_name":"Henrique","full_name":"Ennes, Henrique"},{"last_name":"Resck","full_name":"Resck, Lucas","first_name":"Lucas"},{"full_name":"Gomes, Lucas T.","first_name":"Lucas T.","last_name":"Gomes"},{"last_name":"Ponciano","first_name":"Jean R.","full_name":"Ponciano, Jean R."},{"first_name":"Jorge","full_name":"Poco, Jorge","last_name":"Poco"}],"OA_type":"hybrid","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","doi":"10.1007/s10506-025-09458-6","date_updated":"2026-06-18T08:34:38Z","publication":"Artificial Intelligence and Law","article_type":"original","month":"05","publication_identifier":{"eissn":["1572-8382"],"issn":["0924-8463"]},"department":[{"_id":"UlWa"}],"day":"26","publication_status":"epub_ahead","_id":"19848","language":[{"iso":"eng"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2025-06-15T22:01:31Z","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-05-26T00:00:00Z","ddc":["510"],"oa":1,"quality_controlled":"1","external_id":{"isi":["001494836700001"],"arxiv":["2407.07004"]},"arxiv":1,"publisher":"Springer Nature","abstract":[{"lang":"eng","text":"Binding precedents (súmulas vinculantes) constitute a juridical instrument unique to the Brazilian legal system and whose objectives include the protection of the Federal Supreme Court against repetitive demands. Studies of the effectiveness of these instruments in decreasing the Court’s exposure to similar cases, however, indicate that they tend to fail in such a direction, with some of the binding precedents seemingly creating new demands. We empirically assess the legal impact of five binding precedents, 11, 14, 17, 26, and 37, at the highest Court level through their effects on the legal subjects they address. This analysis is only possible through the comparison of the Court’s ruling about the precedents’ themes before they are created, which means that these decisions should be detected through techniques of Similar Case Retrieval, which we tackle from the angle of Case Classification. The contributions of this article are therefore twofold: on the mathematical side, we compare the use of different methods of Natural Language Processing — TF-IDF, LSTM, Longformer, and regex — for Case Classification, whereas on the legal side, we contrast the inefficiency of these binding precedents with a set of hypotheses that may justify their repeated usage. We observe that the TF-IDF models performed slightly better than LSTM and Longformer when compared through common metrics; however, the deep learning models were able to detect certain important legal events that TF-IDF missed. On the legal side, we argue that the reasons for binding precedents to fail in responding to repetitive demand are heterogeneous and case-dependent, making it impossible to single out a specific cause. We identify five main hypotheses, which are found in different combinations in each of the precedents studied."}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s10506-025-09458-6"}],"year":"2025","corr_author":"1","status":"public"},{"status":"public","corr_author":"1","PlanS_conform":"1","year":"2025","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s10208-025-09728-4"}],"abstract":[{"lang":"eng","text":"We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum of irreducible representations. Moreover, the knowledge of the representation type permits the reconstruction of its orbit, which is useful for identifying the Lie group that generates the action, from a finite list of candidates. Our algorithm is general for any compact Lie group, but only instantiations for SO(2), T^d, SU(2), and SO(3) are considered. Theoretical guarantees of robustness in terms of Hausdorff and Wasserstein distances are derived. Our tools are drawn from geometric measure theory, computational geometry, and optimization on matrix manifolds. The algorithm is tested for synthetic data up to dimension 32, as well as real-life applications in image analysis, harmonic analysis, density estimation, equivariant neural networks, chemical conformational spaces, and classical mechanics systems, achieving very accurate results."}],"publisher":"Springer Nature","arxiv":1,"external_id":{"arxiv":["2309.03086"],"isi":["001571197200001"]},"quality_controlled":"1","oa":1,"ddc":["500"],"scopus_import":"1","date_published":"2025-09-15T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2025-09-28T22:01:27Z","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"publication_status":"epub_ahead","_id":"20407","department":[{"_id":"UlWa"}],"day":"15","publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]},"month":"09","article_type":"original","publication":"Foundations of Computational Mathematics","date_updated":"2026-06-18T18:22:42Z","doi":"10.1007/s10208-025-09728-4","acknowledgement":"The original work behind this article was developed for HE’s master’s thesis, supervised by RT. We are mostly in debt to César Camacho, who was HE’s co-advisor, as well as the members of the thesis jury, Clément Maria, Eduardo Mendes, and Jameson Cahill, not only for agreeing to evaluate the original work but also for many valuable inputs. Finally, we are indebted to the anonymous reviewers for their important feedback and suggestions. Open access funding provided by Institute of Science and Technology (IST Austria).","OA_type":"hybrid","author":[{"last_name":"Ennes","full_name":"Ennes, Henrique","first_name":"Henrique"},{"id":"40ebcc9d-905f-11ef-bf0a-dc475da8a04e","last_name":"Tinarrage","first_name":"Raphaël","full_name":"Tinarrage, Raphaël","orcid":"0000-0002-1404-1095"}],"OA_place":"publisher","citation":{"ama":"Ennes H, Tinarrage R. LieDetect: Detection of representation orbits of compact Lie groups from point clouds. <i>Foundations of Computational Mathematics</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s10208-025-09728-4\">10.1007/s10208-025-09728-4</a>","chicago":"Ennes, Henrique, and Raphaël Tinarrage. “LieDetect: Detection of Representation Orbits of Compact Lie Groups from Point Clouds.” <i>Foundations of Computational Mathematics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s10208-025-09728-4\">https://doi.org/10.1007/s10208-025-09728-4</a>.","apa":"Ennes, H., &#38; Tinarrage, R. (2025). LieDetect: Detection of representation orbits of compact Lie groups from point clouds. <i>Foundations of Computational Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10208-025-09728-4\">https://doi.org/10.1007/s10208-025-09728-4</a>","short":"H. Ennes, R. Tinarrage, Foundations of Computational Mathematics (2025).","mla":"Ennes, Henrique, and Raphaël Tinarrage. “LieDetect: Detection of Representation Orbits of Compact Lie Groups from Point Clouds.” <i>Foundations of Computational Mathematics</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s10208-025-09728-4\">10.1007/s10208-025-09728-4</a>.","ieee":"H. Ennes and R. Tinarrage, “LieDetect: Detection of representation orbits of compact Lie groups from point clouds,” <i>Foundations of Computational Mathematics</i>. Springer Nature, 2025.","ista":"Ennes H, Tinarrage R. 2025. LieDetect: Detection of representation orbits of compact Lie groups from point clouds. Foundations of Computational Mathematics."},"title":"LieDetect: Detection of representation orbits of compact Lie groups from point clouds","type":"journal_article","oa_version":"Published Version","isi":1}]