[{"ddc":["000"],"department":[{"_id":"AlBr"}],"abstract":[{"text":"Cardiac T1 mapping provides critical quantitative insights into myocardial tissue composition, enabling the assessment of pathologies such as fibrosis, inflammation, and edema.\r\nHowever, the inherently dynamic nature of the heart imposes strict limits on acquisition\r\ntimes, making high-resolution T1 mapping a persistent challenge. Compressed sensing (CS)\r\napproaches have reduced scan durations by undersampling k-space and reconstructing images from partial data, and recent studies show that jointly optimizing the undersampling\r\npatterns with the reconstruction network can substantially improve performance. Still,\r\nmost current T1 mapping pipelines rely on static, hand-crafted masks that do not exploit\r\nthe full acceleration and accuracy potential. Furthermore, most existing methods do not\r\nlevarage the physical T1 decay model in optimization. In this work, we introduce T1-\r\nPILOT: an end-to-end method that explicitly incorporates the T1 signal relaxation model\r\ninto the sampling–reconstruction framework to guide the learning of non-Cartesian trajectories, cross-frame alignment, and T1 decay estimation. Through extensive experiments\r\non the CMRxRecon dataset, T1-PILOT significantly outperforms several baseline strategies (including learned single-mask and fixed radial or golden-angle sampling schemes),\r\nachieving higher T1 map fidelity at greater acceleration factors. In particular, we observe consistent gains in PSNR and VIF relative to existing methods, along with marked\r\nimprovements in delineating finer myocardial structures. Our results highlight that optimizing sampling trajectories in tandem with the physical relaxation model leads to both\r\nenhanced quantitative accuracy and reduced acquisition times. Code for reproducing all\r\nexperiments and results is available at https://github.com/tamirshor7/T1-PILOT","lang":"eng"}],"type":"conference","OA_type":"gold","page":"1969-1982","status":"public","title":"T1-PILOT: Physics-informed learned optimized trajectories for T1 mapping acceleration","date_published":"2026-03-17T00:00:00Z","author":[{"first_name":"Tamir","full_name":"Shor, Tamir","last_name":"Shor"},{"last_name":"Freiman","first_name":"Moti","full_name":"Freiman, Moti"},{"full_name":"Baskin, Chaim","first_name":"Chaim","last_name":"Baskin"},{"first_name":"Alexander","full_name":"Bronstein, Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","last_name":"Bronstein","orcid":"0000-0001-9699-8730"}],"publisher":"ML Research Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Shor T, Freiman M, Baskin C, Bronstein AM. T1-PILOT: Physics-informed learned optimized trajectories for T1 mapping acceleration. In: <i>Medical Imaging with Deep Learning</i>. Vol 315. ML Research Press; :1969-1982.","ista":"Shor T, Freiman M, Baskin C, Bronstein AM. T1-PILOT: Physics-informed learned optimized trajectories for T1 mapping acceleration. Medical Imaging with Deep Learning. MIDL: Medical Imaging with Deep Learning, PMLR, vol. 315, 1969–1982.","apa":"Shor, T., Freiman, M., Baskin, C., &#38; Bronstein, A. M. (n.d.). T1-PILOT: Physics-informed learned optimized trajectories for T1 mapping acceleration. In <i>Medical Imaging with Deep Learning</i> (Vol. 315, pp. 1969–1982). Taipei, Taiwan: ML Research Press.","ieee":"T. Shor, M. Freiman, C. Baskin, and A. M. Bronstein, “T1-PILOT: Physics-informed learned optimized trajectories for T1 mapping acceleration,” in <i>Medical Imaging with Deep Learning</i>, Taipei, Taiwan, vol. 315, pp. 1969–1982.","chicago":"Shor, Tamir, Moti Freiman, Chaim Baskin, and Alex M. Bronstein. “T1-PILOT: Physics-Informed Learned Optimized Trajectories for T1 Mapping Acceleration.” In <i>Medical Imaging with Deep Learning</i>, 315:1969–82. ML Research Press, n.d.","short":"T. Shor, M. Freiman, C. Baskin, A.M. Bronstein, in:, Medical Imaging with Deep Learning, ML Research Press, n.d., pp. 1969–1982.","mla":"Shor, Tamir, et al. “T1-PILOT: Physics-Informed Learned Optimized Trajectories for T1 Mapping Acceleration.” <i>Medical Imaging with Deep Learning</i>, vol. 315, ML Research Press, pp. 1969–82."},"oa_version":"Published Version","OA_place":"publisher","publication_status":"accepted","oa":1,"has_accepted_license":"1","publication":"Medical Imaging with Deep Learning","quality_controlled":"1","month":"03","volume":315,"date_updated":"2026-06-08T08:05:24Z","year":"2026","date_created":"2026-06-07T22:01:36Z","conference":{"name":"MIDL: Medical Imaging with Deep Learning","start_date":"2026-07-08","end_date":"2026-07-10","location":"Taipei, Taiwan"},"main_file_link":[{"url":"https://openreview.net/forum?id=nZaPtHbd6N#discussion","open_access":"1"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"corr_author":"1","related_material":{"link":[{"url":"https://github.com/tamirshor7/T1-PILOT","relation":"software"}]},"keyword":["Cardiac T1 Mapping","Trajectory Optimization and Reconstruction","PhysicsInformed Deep-Learning"],"day":"17","_id":"21949","language":[{"iso":"eng"}],"intvolume":"       315","publication_identifier":{"eissn":["2640-3498"]},"license":"https://creativecommons.org/licenses/by/4.0/","scopus_import":"1","alternative_title":["PMLR"],"article_processing_charge":"No"},{"project":[{"grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"article_processing_charge":"Yes (via OA deal)","das_tickbox":"0","scopus_import":"1","publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]},"intvolume":"        26","_id":"14703","language":[{"iso":"eng"}],"keyword":["Optimal transport","Hamilton-Jacobi equation","convex optimization"],"day":"01","corr_author":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"file_name":"2026_FoundCompMath_Ishida.pdf","date_updated":"2026-07-23T05:37:52Z","creator":"dernst","file_id":"22384","success":1,"relation":"main_file","date_created":"2026-07-23T05:37:52Z","file_size":1240012,"access_level":"open_access","checksum":"30671f88e792e8b75ae3e698ac4c131c","content_type":"application/pdf"}],"date_created":"2023-12-21T10:14:37Z","year":"2026","isi":1,"arxiv":1,"quality_controlled":"1","month":"02","publication":"Foundations of Computational Mathematics","date_updated":"2026-07-23T05:39:38Z","volume":26,"oa":1,"supplementarymaterial":"no","file_date_updated":"2026-07-23T05:37:52Z","publication_status":"published","has_accepted_license":"1","acknowledgement":"The authors would like to thank Chris Wojtan for his continuous support and several interesting discussions. Part of this research was performed during two visits: one of SI to the BIDSA research center at Bocconi University, and one of HL to the Institute of Science and Technology Austria. Both host institutions are warmly acknowledged for the hospitality. HL is partially supported by the MUR-Prin 2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with Applications to Optimization and Machine Learning”, funded by the European Union - Next Generation EU. SI is supported in part by ERC Consolidator Grant 101045083 “CoDiNA” funded by the European Research Council. Open access funding provided by Institute of Science and Technology (IST Austria).","PlanS_conform":"1","external_id":{"isi":["001352503300001"],"arxiv":["2312.12213"]},"title":"Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation","date_published":"2026-02-01T00:00:00Z","status":"public","researchdata_availability":"no","doi":"10.1007/s10208-024-09686-3","OA_place":"publisher","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation,” <i>Foundations of Computational Mathematics</i>, vol. 26. Springer Nature, pp. 349–384, 2026.","apa":"Ishida, S., &#38; Lavenant, H. (2026). Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. <i>Foundations of Computational Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10208-024-09686-3\">https://doi.org/10.1007/s10208-024-09686-3</a>","ista":"Ishida S, Lavenant H. 2026. Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. Foundations of Computational Mathematics. 26, 349–384.","ama":"Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. <i>Foundations of Computational Mathematics</i>. 2026;26:349-384. doi:<a href=\"https://doi.org/10.1007/s10208-024-09686-3\">10.1007/s10208-024-09686-3</a>","short":"S. Ishida, H. Lavenant, Foundations of Computational Mathematics 26 (2026) 349–384.","mla":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” <i>Foundations of Computational Mathematics</i>, vol. 26, Springer Nature, 2026, pp. 349–84, doi:<a href=\"https://doi.org/10.1007/s10208-024-09686-3\">10.1007/s10208-024-09686-3</a>.","chicago":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” <i>Foundations of Computational Mathematics</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s10208-024-09686-3\">https://doi.org/10.1007/s10208-024-09686-3</a>."},"publisher":"Springer Nature","author":[{"id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","last_name":"Ishida","orcid":"0000-0002-3121-3100","first_name":"Sadashige","full_name":"Ishida, Sadashige"},{"full_name":"Lavenant, Hugo","first_name":"Hugo","last_name":"Lavenant"}],"type":"journal_article","abstract":[{"lang":"eng","text":"We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton-Jacobi equation."}],"ddc":["000"],"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"OA_type":"hybrid","page":"349-384","article_type":"original"},{"article_type":"original","page":"2077-2087","OA_type":"green","ddc":["530"],"type":"journal_article","abstract":[{"text":"We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (e.g., the object can be described by a small number of nonzero values, but the positions of these values are unknown). We nest an iterative, unapproximated compressed sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting in an interpretable, data-efficient method for maximally leveraging metaoptics to exploit object sparsity. We apply our framework to super-resolution imaging and high-resolution depth imaging with a phase-change material. In both situations, our end-to-end framework effectively optimizes metasurface structures for compressed sensing recovery, automatically balancing a number of complicated design considerations to select an imaging measurement matrix from a complex, physically constrained manifold with millions of dimensions. The optimized metasurface imaging systems are robust to noise, significantly improving over random scattering surfaces and approaching the ideal compressed sensing performance of a Gaussian matrix, showing how a physical metasurface system can demonstrably approach the mathematical limits of compressed sensing.","lang":"eng"}],"OA_place":"repository","oa_version":"Preprint","doi":"10.1021/acsphotonics.4c00259","author":[{"last_name":"Arya","full_name":"Arya, Gaurav","first_name":"Gaurav"},{"full_name":"Li, William F.","first_name":"William F.","last_name":"Li"},{"full_name":"Roques-Carmes, Charles","first_name":"Charles","id":"e2e68fc9-6505-11ef-a541-eb4e72cc3e82","last_name":"Roques-Carmes"},{"first_name":"Marin","full_name":"Soljačić, Marin","last_name":"Soljačić"},{"full_name":"Johnson, Steven G.","first_name":"Steven G.","last_name":"Johnson"},{"last_name":"Lin","first_name":"Zin","full_name":"Lin, Zin"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","citation":{"chicago":"Arya, Gaurav, William F. Li, Charles Roques-Carmes, Marin Soljačić, Steven G. Johnson, and Zin Lin. “End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing.” <i>ACS Photonics</i>. American Chemical Society, 2024. <a href=\"https://doi.org/10.1021/acsphotonics.4c00259\">https://doi.org/10.1021/acsphotonics.4c00259</a>.","mla":"Arya, Gaurav, et al. “End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing.” <i>ACS Photonics</i>, vol. 11, no. 5, American Chemical Society, 2024, pp. 2077–87, doi:<a href=\"https://doi.org/10.1021/acsphotonics.4c00259\">10.1021/acsphotonics.4c00259</a>.","short":"G. Arya, W.F. Li, C. Roques-Carmes, M. Soljačić, S.G. Johnson, Z. Lin, ACS Photonics 11 (2024) 2077–2087.","ama":"Arya G, Li WF, Roques-Carmes C, Soljačić M, Johnson SG, Lin Z. End-to-end optimization of metasurfaces for imaging with compressed sensing. <i>ACS Photonics</i>. 2024;11(5):2077-2087. doi:<a href=\"https://doi.org/10.1021/acsphotonics.4c00259\">10.1021/acsphotonics.4c00259</a>","ieee":"G. Arya, W. F. Li, C. Roques-Carmes, M. Soljačić, S. G. Johnson, and Z. Lin, “End-to-end optimization of metasurfaces for imaging with compressed sensing,” <i>ACS Photonics</i>, vol. 11, no. 5. American Chemical Society, pp. 2077–2087, 2024.","ista":"Arya G, Li WF, Roques-Carmes C, Soljačić M, Johnson SG, Lin Z. 2024. End-to-end optimization of metasurfaces for imaging with compressed sensing. ACS Photonics. 11(5), 2077–2087.","apa":"Arya, G., Li, W. F., Roques-Carmes, C., Soljačić, M., Johnson, S. G., &#38; Lin, Z. (2024). End-to-end optimization of metasurfaces for imaging with compressed sensing. <i>ACS Photonics</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/acsphotonics.4c00259\">https://doi.org/10.1021/acsphotonics.4c00259</a>"},"publisher":"American Chemical Society","title":"End-to-end optimization of metasurfaces for imaging with compressed sensing","date_published":"2024-04-23T00:00:00Z","external_id":{"arxiv":["2201.12348"]},"status":"public","oa":1,"publication_status":"published","date_updated":"2026-04-27T09:03:21Z","volume":11,"month":"04","quality_controlled":"1","arxiv":1,"publication":"ACS Photonics","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2201.12348","open_access":"1"}],"year":"2024","date_created":"2026-03-30T12:22:47Z","keyword":["end-to-end","optimization","metasurface","imaging","compressed sensing"],"day":"23","_id":"21528","language":[{"iso":"eng"}],"intvolume":"        11","issue":"5","scopus_import":"1","publication_identifier":{"eissn":["2330-4022"]},"article_processing_charge":"No","extern":"1"},{"publication_status":"published","oa":1,"publication":"ACS Photonics","arxiv":1,"quality_controlled":"1","month":"04","date_updated":"2026-04-27T09:23:04Z","type":"journal_article","abstract":[{"lang":"eng","text":"We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (i.e. the object can be described by a small number of non-zero values, but the positions of these values are unknown). We nest an iterative, unapproximated compressed sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting in an interpretable, data-efficient method for maximally leveraging metaoptics to exploit object sparsity. We apply our framework to super-resolution imaging and high-resolution depth imaging with a phase-change material. In both situations, our end-to-end framework computationally discovers optimal metasurface structures for compressed sensing recovery, automatically balancing a number of complicated design considerations to select an imaging measurement matrix from a complex, physically constrained manifold with millions ofdimensions. The optimized metasurface imaging systems are robust to noise, significantly improving over random scattering surfaces and approaching the ideal compressed sensing performance of a Gaussian matrix, showing how a physical metasurface system can demonstrably approach the mathematical limits of compressed sensing."}],"ddc":["530"],"OA_type":"green","article_type":"original","status":"public","external_id":{"arxiv":["2201.12348"]},"title":"End-to-end optimization of metasurfaces for imaging with compressed sensing","date_published":"2024-04-23T00:00:00Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publisher":"American Chemical Society","citation":{"ama":"Arya G, Li WF, Roques-Carmes C, Soljačić M, Johnson SG, Lin Z. End-to-end optimization of metasurfaces for imaging with compressed sensing. <i>ACS Photonics</i>. 2024. doi:<a href=\"https://doi.org/10.1021/acsphotonics.4c00259\">10.1021/acsphotonics.4c00259</a>","ieee":"G. Arya, W. F. Li, C. Roques-Carmes, M. Soljačić, S. G. Johnson, and Z. Lin, “End-to-end optimization of metasurfaces for imaging with compressed sensing,” <i>ACS Photonics</i>. American Chemical Society, 2024.","apa":"Arya, G., Li, W. F., Roques-Carmes, C., Soljačić, M., Johnson, S. G., &#38; Lin, Z. (2024). End-to-end optimization of metasurfaces for imaging with compressed sensing. <i>ACS Photonics</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/acsphotonics.4c00259\">https://doi.org/10.1021/acsphotonics.4c00259</a>","ista":"Arya G, Li WF, Roques-Carmes C, Soljačić M, Johnson SG, Lin Z. 2024. End-to-end optimization of metasurfaces for imaging with compressed sensing. ACS Photonics.","chicago":"Arya, Gaurav, William F. Li, Charles Roques-Carmes, Marin Soljačić, Steven G. Johnson, and Zin Lin. “End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing.” <i>ACS Photonics</i>. American Chemical Society, 2024. <a href=\"https://doi.org/10.1021/acsphotonics.4c00259\">https://doi.org/10.1021/acsphotonics.4c00259</a>.","short":"G. Arya, W.F. Li, C. Roques-Carmes, M. Soljačić, S.G. Johnson, Z. Lin, ACS Photonics (2024).","mla":"Arya, Gaurav, et al. “End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing.” <i>ACS Photonics</i>, American Chemical Society, 2024, doi:<a href=\"https://doi.org/10.1021/acsphotonics.4c00259\">10.1021/acsphotonics.4c00259</a>."},"author":[{"first_name":"Gaurav","full_name":"Arya, Gaurav","last_name":"Arya"},{"last_name":"Li","full_name":"Li, William F.","first_name":"William F."},{"last_name":"Roques-Carmes","id":"e2e68fc9-6505-11ef-a541-eb4e72cc3e82","full_name":"Roques-Carmes, Charles","first_name":"Charles"},{"first_name":"Marin","full_name":"Soljačić, Marin","last_name":"Soljačić"},{"first_name":"Steven G.","full_name":"Johnson, Steven G.","last_name":"Johnson"},{"last_name":"Lin","first_name":"Zin","full_name":"Lin, Zin"}],"doi":"10.1021/acsphotonics.4c00259","oa_version":"Preprint","OA_place":"repository","publication_identifier":{"eissn":["2330-4022"]},"scopus_import":"1","extern":"1","article_processing_charge":"No","date_created":"2026-04-09T09:10:41Z","year":"2024","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2201.12348","open_access":"1"}],"_id":"21672","language":[{"iso":"eng"}],"day":"23","keyword":["end-to-end","optimization","metasurface","imaging","compressed sensing"]},{"publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"scopus_import":"1","issue":"4","article_processing_charge":"Yes (via OA deal)","project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"conference":{"start_date":"2024-07-28","location":"Denver, Colorado","end_date":"2024-08-01"},"isi":1,"year":"2024","date_created":"2024-07-05T12:08:57Z","corr_author":"1","file":[{"file_name":"sif-final.pdf","creator":"chafner","success":1,"file_id":"17204","date_updated":"2024-07-05T12:05:17Z","date_created":"2024-07-05T12:05:17Z","file_size":7225150,"relation":"main_file","access_level":"open_access","content_type":"application/pdf","checksum":"0dc9f5a6422b8a49a79026900f349ee5"},{"date_updated":"2024-07-05T12:06:03Z","creator":"chafner","file_id":"17205","file_name":"sif-supp-final.pdf","access_level":"open_access","checksum":"cde433c6a40688d5f1187fb5721f6f94","content_type":"application/pdf","relation":"supplementary_material","date_created":"2024-07-05T12:06:03Z","file_size":397262},{"file_size":170001305,"date_created":"2024-07-17T09:29:13Z","relation":"supplementary_material","access_level":"open_access","checksum":"c0457a09c2ab9a1c2935c995dcc84907","content_type":"video/mp4","file_name":"sif-video-final.mp4","title":"Submission Video","file_id":"17276","creator":"chafner","date_updated":"2024-07-17T09:29:13Z"}],"_id":"17203","language":[{"iso":"eng"}],"intvolume":"        43","keyword":["Topology Optimization","Mass Moments","Computational Geometry"],"day":"01","has_accepted_license":"1","acknowledgement":"We thank Gianmarco Cherchi for his help in tailoring the Mesh Booleans code for this project, Stefan Jeschke for his help with the photographs, Malina Strugaru and Aleksei Kalinov for their help with the samples, and the anonymous reviewers as well as the members of the ISTA Visual Computing Group for their feedback. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).","publication_status":"published","oa":1,"file_date_updated":"2024-07-17T09:29:13Z","volume":43,"date_updated":"2025-09-08T08:29:09Z","publication":"Transactions on Graphics","month":"07","quality_controlled":"1","article_type":"original","type":"journal_article","abstract":[{"text":"The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found.\r\n\r\nIn this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes.\r\n\r\nThis insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.","lang":"eng"}],"department":[{"_id":"ChWo"}],"ddc":["516"],"citation":{"ieee":"C. Hafner, M. Ly, and C. Wojtan, “Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments,” <i>Transactions on Graphics</i>, vol. 43, no. 4. Association for Computing Machinery, 2024.","apa":"Hafner, C., Ly, M., &#38; Wojtan, C. (2024). Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. <i>Transactions on Graphics</i>. Denver, Colorado: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3658194\">https://doi.org/10.1145/3658194</a>","ista":"Hafner C, Ly M, Wojtan C. 2024. Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. Transactions on Graphics. 43(4), 78.","ama":"Hafner C, Ly M, Wojtan C. Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments. <i>Transactions on Graphics</i>. 2024;43(4). doi:<a href=\"https://doi.org/10.1145/3658194\">10.1145/3658194</a>","short":"C. Hafner, M. Ly, C. Wojtan, Transactions on Graphics 43 (2024).","mla":"Hafner, Christian, et al. “Spin-It Faster: Quadrics Solve All Topology Optimization Problems That Depend Only on Mass Moments.” <i>Transactions on Graphics</i>, vol. 43, no. 4, 78, Association for Computing Machinery, 2024, doi:<a href=\"https://doi.org/10.1145/3658194\">10.1145/3658194</a>.","chicago":"Hafner, Christian, Mickaël Ly, and Chris Wojtan. “Spin-It Faster: Quadrics Solve All Topology Optimization Problems That Depend Only on Mass Moments.” <i>Transactions on Graphics</i>. Association for Computing Machinery, 2024. <a href=\"https://doi.org/10.1145/3658194\">https://doi.org/10.1145/3658194</a>."},"publisher":"Association for Computing Machinery","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"first_name":"Christian","full_name":"Hafner, Christian","id":"400429CC-F248-11E8-B48F-1D18A9856A87","last_name":"Hafner"},{"first_name":"Mickaël","full_name":"Ly, Mickaël","id":"6340d7f0-b48d-11eb-b10d-b7487e71d9f1","last_name":"Ly"},{"orcid":"0000-0001-6646-5546","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","last_name":"Wojtan","first_name":"Christopher J","full_name":"Wojtan, Christopher J"}],"doi":"10.1145/3658194","oa_version":"Published Version","status":"public","external_id":{"isi":["001289270900045"]},"date_published":"2024-07-01T00:00:00Z","article_number":"78","title":"Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments"},{"acknowledged_ssus":[{"_id":"ScienComp"}],"year":"2024","date_created":"2024-07-09T09:14:24Z","_id":"17208","language":[{"iso":"eng"}],"keyword":["Quantum computing","Variational Quantum Algorithms","Optimization"],"day":"09","corr_author":"1","related_material":{"record":[{"id":"10545","status":"public","relation":"part_of_dissertation"},{"id":"10067","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"17222"},{"status":"public","relation":"part_of_dissertation","id":"13125"},{"status":"public","relation":"part_of_dissertation","id":"11471"}]},"file":[{"access_level":"closed","checksum":"6f45273d04f4418bc2adc018baed0525","content_type":"application/zip","relation":"source_file","date_created":"2024-07-09T09:21:44Z","file_size":"14218691","date_updated":"2024-07-10T11:34:09Z","creator":"rmedinar","file_id":"17212","file_name":"Raimel_Thesis-Final.zip"},{"file_name":"Raimel_Thesis-20_pdfa.pdf","creator":"rmedinar","file_id":"17275","success":1,"date_updated":"2024-07-17T09:23:24Z","file_size":11253627,"date_created":"2024-07-17T09:23:24Z","relation":"main_file","access_level":"open_access","checksum":"6724a95bec772dbabc0111b9f08a805e","content_type":"application/pdf"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ec_funded":1,"publication_identifier":{"issn":["2663-337X"]},"project":[{"_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","grant_number":"850899","call_identifier":"H2020","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control"}],"alternative_title":["ISTA Thesis"],"article_processing_charge":"No","abstract":[{"lang":"eng","text":"Can current quantum computers provide a speedup over their classical counterparts for some kinds of problems? In this thesis, with a focus on ground state search/preparation, we address some of the challenges that both quantum annealing and variational quantum algorithms suffer from, hindering any possible practical speedup in comparison to the best classical counterparts. \r\n\r\nIn the first part of the thesis, we study the performance of quantum annealing for solving a particular combinatorial optimization problem called 3-XOR satisfability (3-XORSAT). The classical problem is mapped into a ground state search of a 3-local classical Hamiltonian $H_C$. We consider how modifying the initial problem, by adding more interaction terms to the corresponding Hamiltonian, leads to the emergence of a first-order phase transition during the annealing process. This phenomenon causes the total annealing duration, $T$, required to prepare the ground state of $H_C$ with a high probability to increase exponentially with the size of the problem. Our findings indicate that with the growing complexity of problem instances, the likelihood of encountering first-order phase transitions also increases, making quantum annealing an impractical solution for these types of combinatorial optimization problems.\r\n\r\nIn the second part, we focus on the problem of barren plateaus in generic variational quantum algorithms. Barren plateaus correspond to flat regions in the parameter space where the gradient of the cost function is zero in expectation, and with the variance decaying exponentially with the system size, thus obstructing an efficient parameter optimization.  We propose an algorithm to circumvent Barren Plateaus by monitoring the entanglement entropy of k-local reduced density matrices, alongside a method for estimating entanglement entropy via classical shadow tomography. We illustrate the approach with the paradigmatic example of the variational quantum eigensolver, and show that our algorithm effectively avoids barren plateaus in the initialization as well as during the optimization stage. \r\n\r\nLastly, in the last two Chapters of this thesis, we focus on the quantum approximate optimization algorithm (QAOA), originally introduced as an algorithm for solving generic combinatorial optimization problems in near-term quantum devices. Specifically, we focus on how to develop rigorous initialization strategies with guarantee improvement. Our motivation for this study lies in that for random initialization, the optimization typically leads to local minima with poor performance. Our main result corresponds to the analytical construction of index-1 saddle points or transition states, stationary points with a single direction of descent, as a tool for systematically exploring the QAOA optimization landscape. This leads us to propose a novel greedy parameter initialization strategy that guarantees for the energy to decrease with an increasing number of circuit layers. Furthermore, with precise estimates for the negative Hessian eigenvalue and its eigenvector, we establish a lower bound for energy improvement following a QAOA iteration."}],"type":"dissertation","ddc":["539"],"department":[{"_id":"GradSch"},{"_id":"MaSe"}],"page":"133","supervisor":[{"first_name":"Maksym","full_name":"Serbyn, Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","last_name":"Serbyn","orcid":"0000-0002-2399-5827"}],"date_published":"2024-07-09T00:00:00Z","title":"Exploring the optimization landscape of variational quantum algorithms","status":"public","doi":"10.15479/at:ista:17208","oa_version":"Published Version","OA_place":"publisher","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publisher":"Institute of Science and Technology Austria","citation":{"chicago":"Medina Ramos, Raimel A. “Exploring the Optimization Landscape of Variational Quantum Algorithms.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17208\">https://doi.org/10.15479/at:ista:17208</a>.","short":"R.A. Medina Ramos, Exploring the Optimization Landscape of Variational Quantum Algorithms, Institute of Science and Technology Austria, 2024.","mla":"Medina Ramos, Raimel A. <i>Exploring the Optimization Landscape of Variational Quantum Algorithms</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17208\">10.15479/at:ista:17208</a>.","ama":"Medina Ramos RA. Exploring the optimization landscape of variational quantum algorithms. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17208\">10.15479/at:ista:17208</a>","apa":"Medina Ramos, R. A. (2024). <i>Exploring the optimization landscape of variational quantum algorithms</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17208\">https://doi.org/10.15479/at:ista:17208</a>","ista":"Medina Ramos RA. 2024. Exploring the optimization landscape of variational quantum algorithms. Institute of Science and Technology Austria.","ieee":"R. A. Medina Ramos, “Exploring the optimization landscape of variational quantum algorithms,” Institute of Science and Technology Austria, 2024."},"author":[{"orcid":"0000-0002-5383-2869","last_name":"Medina Ramos","id":"CE680B90-D85A-11E9-B684-C920E6697425","full_name":"Medina Ramos, Raimel A","first_name":"Raimel A"}],"oa":1,"file_date_updated":"2024-07-17T09:23:24Z","degree_awarded":"PhD","publication_status":"published","has_accepted_license":"1","month":"07","date_updated":"2026-04-07T12:43:22Z"},{"date_updated":"2025-04-15T07:43:53Z","volume":42,"month":"07","quality_controlled":"1","publication":"ACM Transactions on Graphics","acknowledgement":"We thank Todor Asenov and the Miba Machine Shop for their help in assembling the tattoo machine and manufacturing the substrates. We thank Geysler Rodrigues for the insightful discussions on tattooing practices from a professional artist's perspective. We thank Maria Fernanda Portugal for sharing a doctor's perspective on medical applications of tattoos. This work is graciously supported by the FWF Lise Meitner (Grant M 3319).","has_accepted_license":"1","file_date_updated":"2024-04-16T05:52:18Z","oa":1,"publication_status":"published","oa_version":"Published Version","doi":"10.1145/3592432","author":[{"full_name":"Piovarci, Michael","first_name":"Michael","id":"62E473F4-5C99-11EA-A40E-AF823DDC885E","last_name":"Piovarci","orcid":"0000-0002-5062-4474"},{"first_name":"Alexandre","full_name":"Chapiro, Alexandre","last_name":"Chapiro"},{"orcid":"0000-0001-6511-9385","id":"49876194-F248-11E8-B48F-1D18A9856A87","last_name":"Bickel","full_name":"Bickel, Bernd","first_name":"Bernd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Piovarci M, Chapiro A, Bickel B. Skin-Screen: A computational fabrication framework for color tattoos. <i>ACM Transactions on Graphics</i>. 2023;42(4). doi:<a href=\"https://doi.org/10.1145/3592432\">10.1145/3592432</a>","apa":"Piovarci, M., Chapiro, A., &#38; Bickel, B. (2023). Skin-Screen: A computational fabrication framework for color tattoos. <i>ACM Transactions on Graphics</i>. Los Angeles, CA, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3592432\">https://doi.org/10.1145/3592432</a>","ista":"Piovarci M, Chapiro A, Bickel B. 2023. Skin-Screen: A computational fabrication framework for color tattoos. ACM Transactions on Graphics. 42(4), 67.","ieee":"M. Piovarci, A. Chapiro, and B. Bickel, “Skin-Screen: A computational fabrication framework for color tattoos,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4. Association for Computing Machinery, 2023.","chicago":"Piovarci, Michael, Alexandre Chapiro, and Bernd Bickel. “Skin-Screen: A Computational Fabrication Framework for Color Tattoos.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3592432\">https://doi.org/10.1145/3592432</a>.","short":"M. Piovarci, A. Chapiro, B. Bickel, ACM Transactions on Graphics 42 (2023).","mla":"Piovarci, Michael, et al. “Skin-Screen: A Computational Fabrication Framework for Color Tattoos.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, 67, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3592432\">10.1145/3592432</a>."},"publisher":"Association for Computing Machinery","article_number":"67","title":"Skin-Screen: A computational fabrication framework for color tattoos","date_published":"2023-07-26T00:00:00Z","external_id":{"isi":["001044671300033"]},"status":"public","article_type":"original","department":[{"_id":"BeBi"}],"ddc":["004"],"type":"journal_article","abstract":[{"text":"Tattoos are a highly popular medium, with both artistic and medical applications. Although the mechanical process of tattoo application has evolved historically, the results are reliant on the artisanal skill of the artist. This can be especially challenging for some skin tones, or in cases where artists lack experience. We provide the first systematic overview of tattooing as a computational fabrication technique. We built an automated tattooing rig and a recipe for the creation of silicone sheets mimicking realistic skin tones, which allowed us to create an accurate model predicting tattoo appearance. This enables several exciting applications including tattoo previewing, color retargeting, novel ink spectra optimization, color-accurate prosthetics, and more.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","project":[{"grant_number":"M03319","_id":"eb901961-77a9-11ec-83b8-f5c883a62027","name":"Perception-Aware Appearance Fabrication"}],"issue":"4","scopus_import":"1","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"day":"26","keyword":["appearance","modeling","reproduction","tattoo","skin color","gamut mapping","ink-optimization","prosthetic"],"language":[{"iso":"eng"}],"_id":"12984","intvolume":"        42","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"relation":"main_file","file_size":30817343,"date_created":"2023-05-16T09:38:25Z","content_type":"application/pdf","checksum":"5f0a6867689e025a661bd0b4fd90b821","access_level":"open_access","file_name":"Piovarci2023.pdf","date_updated":"2023-05-16T09:38:25Z","file_id":"12985","success":1,"creator":"mpiovarc"},{"date_updated":"2024-04-16T05:52:18Z","creator":"dernst","file_id":"15324","success":1,"file_name":"2023_ACM_Piovarci.pdf","access_level":"open_access","checksum":"6dd371de5b517e5f184f9c2cbea4b8b3","content_type":"application/pdf","relation":"main_file","date_created":"2024-04-16T05:52:18Z","file_size":30281676}],"corr_author":"1","isi":1,"conference":{"start_date":"2023-08-06","name":"SIGGRAPH: Computer Graphics and Interactive Techniques Conference","end_date":"2023-08-10","location":"Los Angeles, CA, United States"},"acknowledged_ssus":[{"_id":"M-Shop"}],"year":"2023","date_created":"2023-05-16T09:39:14Z"},{"article_processing_charge":"No","extern":"1","scopus_import":"1","issue":"1","publication_identifier":{"eissn":["2330-4022"]},"language":[{"iso":"eng"}],"_id":"21527","intvolume":"         9","day":"07","keyword":["metasurfaces","inverse design","multilayered metaoptics","3D printing","topology optimization"],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.11326","open_access":"1"}],"date_created":"2026-03-30T12:22:47Z","year":"2022","date_updated":"2026-04-27T09:14:46Z","volume":9,"arxiv":1,"quality_controlled":"1","month":"01","publication":"ACS Photonics","oa":1,"publication_status":"published","doi":"10.1021/acsphotonics.1c01442","oa_version":"Preprint","OA_place":"repository","citation":{"ista":"Roques-Carmes C, Lin Z, Christiansen RE, Salamin Y, Kooi SE, Joannopoulos JD, Johnson SG, Soljačić M. 2022. Toward 3D-printed inverse-designed metaoptics. ACS Photonics. 9(1), 43–51.","apa":"Roques-Carmes, C., Lin, Z., Christiansen, R. E., Salamin, Y., Kooi, S. E., Joannopoulos, J. D., … Soljačić, M. (2022). Toward 3D-printed inverse-designed metaoptics. <i>ACS Photonics</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/acsphotonics.1c01442\">https://doi.org/10.1021/acsphotonics.1c01442</a>","ieee":"C. Roques-Carmes <i>et al.</i>, “Toward 3D-printed inverse-designed metaoptics,” <i>ACS Photonics</i>, vol. 9, no. 1. American Chemical Society, pp. 43–51, 2022.","ama":"Roques-Carmes C, Lin Z, Christiansen RE, et al. Toward 3D-printed inverse-designed metaoptics. <i>ACS Photonics</i>. 2022;9(1):43-51. doi:<a href=\"https://doi.org/10.1021/acsphotonics.1c01442\">10.1021/acsphotonics.1c01442</a>","short":"C. Roques-Carmes, Z. Lin, R.E. Christiansen, Y. Salamin, S.E. Kooi, J.D. Joannopoulos, S.G. Johnson, M. Soljačić, ACS Photonics 9 (2022) 43–51.","mla":"Roques-Carmes, Charles, et al. “Toward 3D-Printed Inverse-Designed Metaoptics.” <i>ACS Photonics</i>, vol. 9, no. 1, American Chemical Society, 2022, pp. 43–51, doi:<a href=\"https://doi.org/10.1021/acsphotonics.1c01442\">10.1021/acsphotonics.1c01442</a>.","chicago":"Roques-Carmes, Charles, Zin Lin, Rasmus E. Christiansen, Yannick Salamin, Steven E. Kooi, John D. Joannopoulos, Steven G. Johnson, and Marin Soljačić. “Toward 3D-Printed Inverse-Designed Metaoptics.” <i>ACS Photonics</i>. American Chemical Society, 2022. <a href=\"https://doi.org/10.1021/acsphotonics.1c01442\">https://doi.org/10.1021/acsphotonics.1c01442</a>."},"publisher":"American Chemical Society","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","author":[{"full_name":"Roques-Carmes, Charles","first_name":"Charles","last_name":"Roques-Carmes","id":"e2e68fc9-6505-11ef-a541-eb4e72cc3e82"},{"full_name":"Lin, Zin","first_name":"Zin","last_name":"Lin"},{"last_name":"Christiansen","full_name":"Christiansen, Rasmus E.","first_name":"Rasmus E."},{"full_name":"Salamin, Yannick","first_name":"Yannick","last_name":"Salamin"},{"last_name":"Kooi","first_name":"Steven E.","full_name":"Kooi, Steven E."},{"first_name":"John D.","full_name":"Joannopoulos, John D.","last_name":"Joannopoulos"},{"last_name":"Johnson","full_name":"Johnson, Steven G.","first_name":"Steven G."},{"full_name":"Soljačić, Marin","first_name":"Marin","last_name":"Soljačić"}],"external_id":{"arxiv":["2105.11326"]},"date_published":"2022-01-07T00:00:00Z","title":"Toward 3D-printed inverse-designed metaoptics","status":"public","page":"43-51","OA_type":"green","article_type":"letter_note","type":"journal_article","abstract":[{"text":"Optical metasurfaces have been heralded as the platform to integrate multiple functionalities in a compact form-factor, with the potential to replace bulky optical components. A central stepping stone toward realizing this promise is the demonstration of multifunctionality under several constraints (e.g., at multiple incident wavelengths and/or angles) in a single device, an achievement being hampered by design limitations inherent to single-layer planar geometries. Here, we propose a framework for the inverse design of multilayer metaoptics via topology optimization, showing that even few-wavelength thick devices can achieve high-efficiency multifunctionality, such as multiangle light concentration and plan-achromaticity. We embody our framework in multiple closely spaced patterned layers of a low-index polymer, with fabrication constraints specific to this platform enforced in the optimization process. We experimentally demonstrate our approach with an inverse-designed 3D-printed light concentrator working at five different nonparaxial angles of incidence. Our framework paves the way toward realizing multifunctional ultracompact 3D nanophotonic devices.","lang":"eng"}],"ddc":["530"]},{"day":"19","keyword":["Computing methodologies","shape modeling","modeling and simulation","theory of computation","computational geometry","mathematics of computing","mathematical optimization"],"language":[{"iso":"eng"}],"_id":"9817","intvolume":"        40","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"date_created":"2021-10-18T10:42:15Z","file_size":17064290,"relation":"main_file","access_level":"open_access","checksum":"7e5d08ce46b0451b3102eacd3d00f85f","content_type":"application/pdf","file_name":"elastic-curves-paper.pdf","creator":"chafner","success":1,"file_id":"10150","date_updated":"2021-10-18T10:42:15Z"},{"date_updated":"2021-10-18T10:42:22Z","file_id":"10151","creator":"chafner","file_name":"elastic-curves-supp.pdf","content_type":"application/pdf","checksum":"0088643478be7c01a703b5b10767348f","access_level":"open_access","relation":"supplementary_material","file_size":547156,"date_created":"2021-10-18T10:42:22Z"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"12897"}],"link":[{"url":"https://ist.ac.at/en/news/designing-with-elastic-structures/","description":"News on IST Website","relation":"press_release"}]},"isi":1,"conference":{"name":"SIGGRAF: Special Interest Group on Computer Graphics and Interactive Techniques","start_date":"2021-08-09","end_date":"2021-08-13","location":"Virtual"},"date_created":"2021-08-08T22:01:26Z","year":"2021","article_processing_charge":"No","project":[{"_id":"24F9549A-B435-11E9-9278-68D0E5697425","grant_number":"715767","call_identifier":"H2020","name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling"}],"issue":"4","scopus_import":"1","publication_identifier":{"issn":["0730-0301"],"eissn":["1557-7368"]},"ec_funded":1,"oa_version":"Published Version","doi":"10.1145/3450626.3459800","author":[{"first_name":"Christian","full_name":"Hafner, Christian","last_name":"Hafner","id":"400429CC-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-6511-9385","last_name":"Bickel","id":"49876194-F248-11E8-B48F-1D18A9856A87","full_name":"Bickel, Bernd","first_name":"Bernd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Association for Computing Machinery","citation":{"ista":"Hafner C, Bickel B. 2021. The design space of plane elastic curves. ACM Transactions on Graphics. 40(4), 126.","apa":"Hafner, C., &#38; Bickel, B. (2021). The design space of plane elastic curves. <i>ACM Transactions on Graphics</i>. Virtual: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3450626.3459800\">https://doi.org/10.1145/3450626.3459800</a>","ieee":"C. Hafner and B. Bickel, “The design space of plane elastic curves,” <i>ACM Transactions on Graphics</i>, vol. 40, no. 4. Association for Computing Machinery, 2021.","ama":"Hafner C, Bickel B. The design space of plane elastic curves. <i>ACM Transactions on Graphics</i>. 2021;40(4). doi:<a href=\"https://doi.org/10.1145/3450626.3459800\">10.1145/3450626.3459800</a>","mla":"Hafner, Christian, and Bernd Bickel. “The Design Space of Plane Elastic Curves.” <i>ACM Transactions on Graphics</i>, vol. 40, no. 4, 126, Association for Computing Machinery, 2021, doi:<a href=\"https://doi.org/10.1145/3450626.3459800\">10.1145/3450626.3459800</a>.","short":"C. Hafner, B. Bickel, ACM Transactions on Graphics 40 (2021).","chicago":"Hafner, Christian, and Bernd Bickel. “The Design Space of Plane Elastic Curves.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2021. <a href=\"https://doi.org/10.1145/3450626.3459800\">https://doi.org/10.1145/3450626.3459800</a>."},"date_published":"2021-07-19T00:00:00Z","title":"The design space of plane elastic curves","article_number":"126","external_id":{"isi":["000674930900091"]},"status":"public","article_type":"original","ddc":["516"],"department":[{"_id":"BeBi"}],"type":"journal_article","abstract":[{"text":"Elastic bending of initially flat slender elements allows the realization and economic fabrication of intriguing curved shapes. In this work, we derive an intuitive but rigorous geometric characterization of the design space of plane elastic rods with variable stiffness. It enables designers to determine which shapes are physically viable with active bending by visual inspection alone. Building on these insights, we propose a method for efficiently designing the geometry of a flat elastic rod that realizes a target equilibrium curve, which only requires solving a linear program. We implement this method in an interactive computational design tool that gives feedback about the feasibility of a design, and computes the geometry of the structural elements necessary to realize it within an instant. The tool also offers an iterative optimization routine that improves the fabricability of a model while modifying it as little as possible. In addition, we use our geometric characterization to derive an algorithm for analyzing and recovering the stability of elastic curves that would otherwise snap out of their unstable equilibrium shapes by buckling. We show the efficacy of our approach by designing and manufacturing several physical models that are assembled from flat elements.","lang":"eng"}],"date_updated":"2026-08-21T22:30:05Z","volume":40,"quality_controlled":"1","month":"07","publication":"ACM Transactions on Graphics","has_accepted_license":"1","acknowledgement":"We thank the anonymous reviewers for their generous feedback, and Michal Piovarči for his help in producing the supplemental video. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 715767).\r\n","file_date_updated":"2021-10-18T10:42:22Z","oa":1,"publication_status":"published"},{"oa_version":"Preprint","doi":"10.1088/1742-5468/ab16c8","author":[{"first_name":"Ryan J","full_name":"Cubero, Ryan J","orcid":"0000-0003-0002-1867","last_name":"Cubero","id":"850B2E12-9CD4-11E9-837F-E719E6697425"},{"last_name":"Jo","first_name":"Junghyo","full_name":"Jo, Junghyo"},{"first_name":"Matteo","full_name":"Marsili, Matteo","last_name":"Marsili"},{"first_name":"Yasser","full_name":"Roudi, Yasser","last_name":"Roudi"},{"first_name":"Juyong","full_name":"Song, Juyong","last_name":"Song"}],"citation":{"chicago":"Cubero, Ryan J, Junghyo Jo, Matteo Marsili, Yasser Roudi, and Juyong Song. “Statistical Criticality Arises in Most Informative Representations.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2019. <a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">https://doi.org/10.1088/1742-5468/ab16c8</a>.","short":"R.J. Cubero, J. Jo, M. Marsili, Y. Roudi, J. Song, Journal of Statistical Mechanics: Theory and Experiment 2019 (2019).","mla":"Cubero, Ryan J., et al. “Statistical Criticality Arises in Most Informative Representations.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6, 063402, IOP Publishing, 2019, doi:<a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">10.1088/1742-5468/ab16c8</a>.","ama":"Cubero RJ, Jo J, Marsili M, Roudi Y, Song J. Statistical criticality arises in most informative representations. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2019;2019(6). doi:<a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">10.1088/1742-5468/ab16c8</a>","ieee":"R. J. Cubero, J. Jo, M. Marsili, Y. Roudi, and J. Song, “Statistical criticality arises in most informative representations,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6. IOP Publishing, 2019.","apa":"Cubero, R. J., Jo, J., Marsili, M., Roudi, Y., &#38; Song, J. (2019). Statistical criticality arises in most informative representations. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">https://doi.org/10.1088/1742-5468/ab16c8</a>","ista":"Cubero RJ, Jo J, Marsili M, Roudi Y, Song J. 2019. Statistical criticality arises in most informative representations. Journal of Statistical Mechanics: Theory and Experiment. 2019(6), 063402."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"IOP Publishing","date_published":"2019-06-17T00:00:00Z","title":"Statistical criticality arises in most informative representations","article_number":"063402","external_id":{"arxiv":["1808.00249"]},"status":"public","article_type":"original","type":"journal_article","abstract":[{"lang":"eng","text":"We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify the frequency with which different outcomes occur in a sample, as the variable carrying useful information on the generative process. The entropy of the frequency, that we call relevance, provides an upper bound to the number of informative bits. This differs from the entropy of the data, that we take as a measure of resolution. Samples that maximise relevance at a given resolution—that we call maximally informative samples—exhibit statistical criticality. In particular, Zipf's law arises at the optimal trade-off between resolution (i.e. compression) and relevance. As a byproduct, we derive a bound of the maximal number of parameters that can be estimated from a dataset, in the absence of prior knowledge on the generative model.\r\n\r\nFurthermore, we relate criticality to the statistical properties of the representation of the data generating process. We show that, as a consequence of the concentration property of the asymptotic equipartition property, representations that are maximally informative about the data generating process are characterised by an exponential distribution of energy levels. This arises from a principle of minimal entropy, that is conjugate of the maximum entropy principle in statistical mechanics. This explains why statistical criticality requires no parameter fine tuning in maximally informative samples."}],"date_updated":"2021-01-12T08:11:57Z","volume":2019,"quality_controlled":"1","month":"06","arxiv":1,"publication":"Journal of Statistical Mechanics: Theory and Experiment","acknowledgement":"We acknowledge interesting discussions with M Abbott, E Aurell, J Barbier, R Monasson, T Mora, I Nemenman, N Tishby and R Zecchina. This research was supported by the Kavli Foundation and the Centre of Excellence scheme of the Research Council of Norway (Centre for Neural Computation) (RJC and YR), by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2016R1D1A1B03932264) (JJ), and, in part, by the ICTP through the OEA-AC-98 (JS).","oa":1,"publication_status":"published","day":"17","keyword":["optimization under uncertainty","source coding","large deviation"],"language":[{"iso":"eng"}],"_id":"7130","intvolume":"      2019","main_file_link":[{"url":"https://arxiv.org/abs/1808.00249","open_access":"1"}],"date_created":"2019-11-26T22:36:09Z","year":"2019","article_processing_charge":"No","extern":"1","issue":"6","publication_identifier":{"issn":["1742-5468"]}},{"publication_status":"published","publication":"Journal of Algorithms","month":"02","quality_controlled":"1","volume":34,"date_updated":"2024-11-04T11:42:08Z","type":"journal_article","abstract":[{"lang":"eng","text":"The vertex connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{κ3 + n, κn}m); for an undirected graph the term m can be replaced by κn. A randomized algorithm finds κ with error probability 1/2 in time O(nm). If the vertices have nonnegative weights the weighted vertex connectivity is found in time O(κ1nmlog(n2/m)) where κ1 ≤ m/n is the unweighted vertex connectivity or in expected time O(nmlog(n2/m)) with error probability 1/2. The main algorithm combines two previous vertex connectivity algorithms and a generalization of the preflow-push algorithm of Hao and Orlin (1994, J. Algorithms17, 424–446) that computes edge connectivity."}],"page":"222-250","article_type":"original","status":"public","date_published":"2000-02-01T00:00:00Z","title":"Computing vertex connectivity: New bounds from old techniques","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","citation":{"short":"M. Henzinger, S. Rao, H.N. Gabow, Journal of Algorithms 34 (2000) 222–250.","mla":"Henzinger, Monika, et al. “Computing Vertex Connectivity: New Bounds from Old Techniques.” <i>Journal of Algorithms</i>, vol. 34, no. 2, Elsevier, 2000, pp. 222–50, doi:<a href=\"https://doi.org/10.1006/jagm.1999.1055\">10.1006/jagm.1999.1055</a>.","chicago":"Henzinger, Monika, Satish Rao, and Harold N. Gabow. “Computing Vertex Connectivity: New Bounds from Old Techniques.” <i>Journal of Algorithms</i>. Elsevier, 2000. <a href=\"https://doi.org/10.1006/jagm.1999.1055\">https://doi.org/10.1006/jagm.1999.1055</a>.","apa":"Henzinger, M., Rao, S., &#38; Gabow, H. N. (2000). Computing vertex connectivity: New bounds from old techniques. <i>Journal of Algorithms</i>. Elsevier. <a href=\"https://doi.org/10.1006/jagm.1999.1055\">https://doi.org/10.1006/jagm.1999.1055</a>","ista":"Henzinger M, Rao S, Gabow HN. 2000. Computing vertex connectivity: New bounds from old techniques. Journal of Algorithms. 34(2), 222–250.","ieee":"M. Henzinger, S. Rao, and H. N. Gabow, “Computing vertex connectivity: New bounds from old techniques,” <i>Journal of Algorithms</i>, vol. 34, no. 2. Elsevier, pp. 222–250, 2000.","ama":"Henzinger M, Rao S, Gabow HN. Computing vertex connectivity: New bounds from old techniques. <i>Journal of Algorithms</i>. 2000;34(2):222-250. doi:<a href=\"https://doi.org/10.1006/jagm.1999.1055\">10.1006/jagm.1999.1055</a>"},"author":[{"orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","first_name":"Monika H","full_name":"Henzinger, Monika H"},{"first_name":"Satish","full_name":"Rao, Satish","last_name":"Rao"},{"full_name":"Gabow, Harold N.","first_name":"Harold N.","last_name":"Gabow"}],"doi":"10.1006/jagm.1999.1055","oa_version":"None","publication_identifier":{"issn":["0196-6774"]},"scopus_import":"1","issue":"2","extern":"1","article_processing_charge":"No","date_created":"2022-07-28T08:56:10Z","year":"2000","language":[{"iso":"eng"}],"intvolume":"        34","_id":"11683","day":"01","keyword":["Computational Theory and Mathematics","Computational Mathematics","Control and Optimization"]}]