[{"date_created":"2021-01-10T23:01:18Z","date_published":"2021-09-01T00:00:00Z","doi":"10.1109/TIT.2020.3038806","page":"5693-5710","publication":"IEEE Transactions on Information Theory","day":"01","year":"2021","publisher":"IEEE","quality_controlled":"1","title":"Binary linear codes with optimal scaling: Polar codes with large kernels","article_processing_charge":"No","external_id":{"arxiv":["1711.01339"]},"author":[{"first_name":"Arman","full_name":"Fazeli, Arman","last_name":"Fazeli"},{"last_name":"Hassani","full_name":"Hassani, Hamed","first_name":"Hamed"},{"last_name":"Mondelli","orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco","first_name":"Marco","id":"27EB676C-8706-11E9-9510-7717E6697425"},{"first_name":"Alexander","last_name":"Vardy","full_name":"Vardy, Alexander"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Fazeli, Arman, Hamed Hassani, Marco Mondelli, and Alexander Vardy. “Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” IEEE Transactions on Information Theory. IEEE, 2021. https://doi.org/10.1109/TIT.2020.3038806.","ista":"Fazeli A, Hassani H, Mondelli M, Vardy A. 2021. Binary linear codes with optimal scaling: Polar codes with large kernels. IEEE Transactions on Information Theory. 67(9), 5693–5710.","mla":"Fazeli, Arman, et al. “Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” IEEE Transactions on Information Theory, vol. 67, no. 9, IEEE, 2021, pp. 5693–710, doi:10.1109/TIT.2020.3038806.","apa":"Fazeli, A., Hassani, H., Mondelli, M., & Vardy, A. (2021). Binary linear codes with optimal scaling: Polar codes with large kernels. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2020.3038806","ama":"Fazeli A, Hassani H, Mondelli M, Vardy A. Binary linear codes with optimal scaling: Polar codes with large kernels. IEEE Transactions on Information Theory. 2021;67(9):5693-5710. doi:10.1109/TIT.2020.3038806","short":"A. Fazeli, H. Hassani, M. Mondelli, A. Vardy, IEEE Transactions on Information Theory 67 (2021) 5693–5710.","ieee":"A. Fazeli, H. Hassani, M. Mondelli, and A. Vardy, “Binary linear codes with optimal scaling: Polar codes with large kernels,” IEEE Transactions on Information Theory, vol. 67, no. 9. IEEE, pp. 5693–5710, 2021."},"volume":67,"issue":"9","related_material":{"record":[{"id":"6665","status":"public","relation":"earlier_version"}]},"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1557-9654"],"issn":["0018-9448"]},"intvolume":" 67","month":"09","scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":" We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a function of the gap to capacity. This result exhibits the first known family of binary codes that attain both optimal scaling and quasi-linear complexity of encoding and decoding. Our proof is based on the construction and analysis of binary polar codes with large kernels. When communicating reliably at rates within ε>0 of capacity, the code length n often scales as O(1/εμ), where the constant μ is called the scaling exponent. It is known that the optimal scaling exponent is μ=2, and it is achieved by random linear codes. The scaling exponent of conventional polar codes (based on the 2×2 kernel) on the BEC is μ=3.63. This falls far short of the optimal scaling guaranteed by random codes. Our main contribution is a rigorous proof of the following result: for the BEC, there exist ℓ×ℓ binary kernels, such that polar codes constructed from these kernels achieve scaling exponent μ(ℓ) that tends to the optimal value of 2 as ℓ grows. We furthermore characterize precisely how large ℓ needs to be as a function of the gap between μ(ℓ) and 2. The resulting binary codes maintain the recursive structure of conventional polar codes, and thereby achieve construction complexity O(n) and encoding/decoding complexity O(nlogn)."}],"department":[{"_id":"MaMo"}],"date_updated":"2024-03-07T12:18:50Z","status":"public","article_type":"original","type":"journal_article","_id":"9002"},{"project":[{"_id":"B6FC0238-B512-11E9-945C-1524E6697425","call_identifier":"H2020","name":"Coordination of Patterning And Growth In the Spinal Cord","grant_number":"680037"},{"_id":"267AF0E4-B435-11E9-9278-68D0E5697425","name":"The role of morphogens in the regulation of neural tube growth"},{"name":"Morphogen control of growth and pattern in the spinal cord","grant_number":"F07802","_id":"059DF620-7A3F-11EA-A408-12923DDC885E"}],"article_number":"e383","author":[{"full_name":"Kuzmicz-Kowalska, Katarzyna","last_name":"Kuzmicz-Kowalska","first_name":"Katarzyna","id":"4CED352A-F248-11E8-B48F-1D18A9856A87"},{"id":"3959A2A0-F248-11E8-B48F-1D18A9856A87","first_name":"Anna","orcid":"0000-0003-4509-4998","full_name":"Kicheva, Anna","last_name":"Kicheva"}],"external_id":{"pmid":["32391980"],"isi":["000531419400001"]},"article_processing_charge":"Yes (via OA deal)","title":"Regulation of size and scale in vertebrate spinal cord development","citation":{"ista":"Kuzmicz-Kowalska K, Kicheva A. 2021. Regulation of size and scale in vertebrate spinal cord development. Wiley Interdisciplinary Reviews: Developmental Biology., e383.","chicago":"Kuzmicz-Kowalska, Katarzyna, and Anna Kicheva. “Regulation of Size and Scale in Vertebrate Spinal Cord Development.” Wiley Interdisciplinary Reviews: Developmental Biology. Wiley, 2021. https://doi.org/10.1002/wdev.383.","apa":"Kuzmicz-Kowalska, K., & Kicheva, A. (2021). Regulation of size and scale in vertebrate spinal cord development. Wiley Interdisciplinary Reviews: Developmental Biology. Wiley. https://doi.org/10.1002/wdev.383","ama":"Kuzmicz-Kowalska K, Kicheva A. Regulation of size and scale in vertebrate spinal cord development. Wiley Interdisciplinary Reviews: Developmental Biology. 2021. doi:10.1002/wdev.383","short":"K. Kuzmicz-Kowalska, A. Kicheva, Wiley Interdisciplinary Reviews: Developmental Biology (2021).","ieee":"K. Kuzmicz-Kowalska and A. Kicheva, “Regulation of size and scale in vertebrate spinal cord development,” Wiley Interdisciplinary Reviews: Developmental Biology. Wiley, 2021.","mla":"Kuzmicz-Kowalska, Katarzyna, and Anna Kicheva. “Regulation of Size and Scale in Vertebrate Spinal Cord Development.” Wiley Interdisciplinary Reviews: Developmental Biology, e383, Wiley, 2021, doi:10.1002/wdev.383."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Wiley","quality_controlled":"1","oa":1,"acknowledgement":"Austrian Academy of Sciences, Grant/Award Number: DOC fellowship for Katarzyna Kuzmicz-Kowalska; Austrian Science Fund, Grant/Award Number: F78 (Stem Cell Modulation); H2020 European Research Council, Grant/Award Number: 680037","doi":"10.1002/wdev.383","date_published":"2021-04-15T00:00:00Z","date_created":"2020-05-24T22:01:00Z","isi":1,"has_accepted_license":"1","year":"2021","day":"15","publication":"Wiley Interdisciplinary Reviews: Developmental Biology","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"7883","department":[{"_id":"AnKi"}],"file_date_updated":"2020-11-24T13:11:39Z","date_updated":"2024-03-07T15:03:00Z","ddc":["570"],"scopus_import":"1","month":"04","abstract":[{"lang":"eng","text":"All vertebrates have a spinal cord with dimensions and shape specific to their species. Yet how species‐specific organ size and shape are achieved is a fundamental unresolved question in biology. The formation and sculpting of organs begins during embryonic development. As it develops, the spinal cord extends in anterior–posterior direction in synchrony with the overall growth of the body. The dorsoventral (DV) and apicobasal lengths of the spinal cord neuroepithelium also change, while at the same time a characteristic pattern of neural progenitor subtypes along the DV axis is established and elaborated. At the basis of these changes in tissue size and shape are biophysical determinants, such as the change in cell number, cell size and shape, and anisotropic tissue growth. These processes are controlled by global tissue‐scale regulators, such as morphogen signaling gradients as well as mechanical forces. Current challenges in the field are to uncover how these tissue‐scale regulatory mechanisms are translated to the cellular and molecular level, and how regulation of distinct cellular processes gives rise to an overall defined size. Addressing these questions will help not only to achieve a better understanding of how size is controlled, but also of how tissue size is coordinated with the specification of pattern."}],"pmid":1,"oa_version":"Published Version","related_material":{"record":[{"relation":"dissertation_contains","id":"14323","status":"public"}]},"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","publication_identifier":{"eissn":["17597692"],"issn":["17597684"]},"publication_status":"published","file":[{"date_created":"2020-11-24T13:11:39Z","file_name":"2020_WIREs_DevBio_KuzmiczKowalska.pdf","date_updated":"2020-11-24T13:11:39Z","file_size":2527276,"creator":"dernst","file_id":"8800","checksum":"f0a7745d48afa09ea7025e876a0145a8","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}]},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198.","chicago":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00206-y.","short":"A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.","ieee":"A. Brown and B. Wang, “Sheaf-theoretic stratification learning from geometric and topological perspectives,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1166–1198, 2021.","ama":"Brown A, Wang B. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 2021;65:1166-1198. doi:10.1007/s00454-020-00206-y","apa":"Brown, A., & Wang, B. (2021). Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00206-y","mla":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1166–98, doi:10.1007/s00454-020-00206-y."},"title":"Sheaf-theoretic stratification learning from geometric and topological perspectives","external_id":{"arxiv":["1712.07734"],"isi":["000536324700001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","full_name":"Brown, Adam"},{"first_name":"Bei","last_name":"Wang","full_name":"Wang, Bei"}],"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication":"Discrete and Computational Geometry","day":"01","year":"2021","has_accepted_license":"1","isi":1,"date_created":"2020-05-30T10:26:04Z","date_published":"2021-06-01T00:00:00Z","doi":"10.1007/s00454-020-00206-y","page":"1166-1198","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was partially supported by NSF IIS-1513616 and NSF ABI-1661375. The authors would like to thank the anonymous referees for their insightful comments.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","ddc":["510"],"date_updated":"2024-03-07T15:01:58Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-11-25T09:06:41Z","_id":"7905","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"file":[{"checksum":"487a84ea5841b75f04f66d7ebd71b67e","file_id":"8803","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2020-11-25T09:06:41Z","file_name":"2020_DiscreteCompGeometry_Brown.pdf","date_updated":"2020-11-25T09:06:41Z","file_size":1013730,"creator":"dernst"}],"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"volume":65,"oa_version":"Published Version","abstract":[{"text":"We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms.","lang":"eng"}],"intvolume":" 65","month":"06","scopus_import":"1"},{"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"title":"Edge universality for non-Hermitian random matrices","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2021.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-020-01003-7","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields."},"oa":1,"quality_controlled":"1","publisher":"Springer Nature","date_created":"2020-10-04T22:01:37Z","doi":"10.1007/s00440-020-01003-7","date_published":"2021-02-01T00:00:00Z","publication":"Probability Theory and Related Fields","day":"01","year":"2021","isi":1,"has_accepted_license":"1","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"8601","file_date_updated":"2020-10-05T14:53:40Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2024-03-07T15:07:53Z","month":"02","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble."}],"ec_funded":1,"language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"611ae28d6055e1e298d53a57beb05ef4","file_id":"8612","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2020_ProbTheory_Cipolloni.pdf","date_created":"2020-10-05T14:53:40Z","file_size":497032,"date_updated":"2020-10-05T14:53:40Z","creator":"dernst"}],"publication_status":"published","publication_identifier":{"eissn":["14322064"],"issn":["01788051"]}},{"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"7925","department":[{"_id":"VlKo"}],"file_date_updated":"2024-03-07T14:58:51Z","date_updated":"2024-03-07T15:00:43Z","ddc":["510"],"scopus_import":"1","month":"09","intvolume":" 15","abstract":[{"lang":"eng","text":"In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method."}],"oa_version":"Published Version","volume":15,"ec_funded":1,"publication_identifier":{"eissn":["1862-4480"],"issn":["1862-4472"]},"publication_status":"published","file":[{"success":1,"checksum":"63c5f31cd04626152a19f97a2476281b","file_id":"15089","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2021_OptimizationLetters_Shehu.pdf","date_created":"2024-03-07T14:58:51Z","file_size":2148882,"date_updated":"2024-03-07T14:58:51Z","creator":"kschuh"}],"language":[{"iso":"eng"}],"project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"author":[{"last_name":"Shehu","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gibali, Aviv","last_name":"Gibali","first_name":"Aviv"}],"external_id":{"isi":["000537342300001"]},"article_processing_charge":"Yes (via OA deal)","title":"New inertial relaxed method for solving split feasibilities","citation":{"mla":"Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split Feasibilities.” Optimization Letters, vol. 15, Springer Nature, 2021, pp. 2109–26, doi:10.1007/s11590-020-01603-1.","ieee":"Y. Shehu and A. Gibali, “New inertial relaxed method for solving split feasibilities,” Optimization Letters, vol. 15. Springer Nature, pp. 2109–2126, 2021.","short":"Y. Shehu, A. Gibali, Optimization Letters 15 (2021) 2109–2126.","apa":"Shehu, Y., & Gibali, A. (2021). New inertial relaxed method for solving split feasibilities. Optimization Letters. Springer Nature. https://doi.org/10.1007/s11590-020-01603-1","ama":"Shehu Y, Gibali A. New inertial relaxed method for solving split feasibilities. Optimization Letters. 2021;15:2109-2126. doi:10.1007/s11590-020-01603-1","chicago":"Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split Feasibilities.” Optimization Letters. Springer Nature, 2021. https://doi.org/10.1007/s11590-020-01603-1.","ista":"Shehu Y, Gibali A. 2021. New inertial relaxed method for solving split feasibilities. Optimization Letters. 15, 2109–2126."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are grateful to the referees for their insightful comments which have improved the earlier version of the manuscript greatly. The first author has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160).","page":"2109-2126","date_published":"2021-09-01T00:00:00Z","doi":"10.1007/s11590-020-01603-1","date_created":"2020-06-04T11:28:33Z","has_accepted_license":"1","isi":1,"year":"2021","day":"01","publication":"Optimization Letters"}]