[{"doi":"10.1039/c6nj00870d","citation":{"ista":"Koenigsmann C, Ding W, Koepf M, Batra A, Venkataraman L, Negre CFA, Brudvig GW, Crabtree RH, Batista VS, Schmuttenmaer CA. 2016. Structure–function relationships in single molecule rectification by N-phenylbenzamide derivatives. New Journal of Chemistry. 40(9), 7373–7378.","ama":"Koenigsmann C, Ding W, Koepf M, et al. Structure–function relationships in single molecule rectification by N-phenylbenzamide derivatives. <i>New Journal of Chemistry</i>. 2016;40(9):7373-7378. doi:<a href=\"https://doi.org/10.1039/c6nj00870d\">10.1039/c6nj00870d</a>","apa":"Koenigsmann, C., Ding, W., Koepf, M., Batra, A., Venkataraman, L., Negre, C. F. A., … Schmuttenmaer, C. A. (2016). Structure–function relationships in single molecule rectification by N-phenylbenzamide derivatives. <i>New Journal of Chemistry</i>. Royal Society of Chemistry. <a href=\"https://doi.org/10.1039/c6nj00870d\">https://doi.org/10.1039/c6nj00870d</a>","chicago":"Koenigsmann, Christopher, Wendu Ding, Matthieu Koepf, Arunabh Batra, Latha Venkataraman, Christian F. A. Negre, Gary W. Brudvig, Robert H. Crabtree, Victor S. Batista, and Charles A. Schmuttenmaer. “Structure–Function Relationships in Single Molecule Rectification by N-Phenylbenzamide Derivatives.” <i>New Journal of Chemistry</i>. Royal Society of Chemistry, 2016. <a href=\"https://doi.org/10.1039/c6nj00870d\">https://doi.org/10.1039/c6nj00870d</a>.","ieee":"C. Koenigsmann <i>et al.</i>, “Structure–function relationships in single molecule rectification by N-phenylbenzamide derivatives,” <i>New Journal of Chemistry</i>, vol. 40, no. 9. Royal Society of Chemistry, pp. 7373–7378, 2016.","mla":"Koenigsmann, Christopher, et al. “Structure–Function Relationships in Single Molecule Rectification by N-Phenylbenzamide Derivatives.” <i>New Journal of Chemistry</i>, vol. 40, no. 9, Royal Society of Chemistry, 2016, pp. 7373–78, doi:<a href=\"https://doi.org/10.1039/c6nj00870d\">10.1039/c6nj00870d</a>.","short":"C. Koenigsmann, W. Ding, M. Koepf, A. Batra, L. Venkataraman, C.F.A. Negre, G.W. Brudvig, R.H. Crabtree, V.S. Batista, C.A. Schmuttenmaer, New Journal of Chemistry 40 (2016) 7373–7378."},"volume":40,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1369-9261"],"issn":["1144-0546"]},"date_updated":"2024-12-18T09:37:58Z","abstract":[{"text":"We examine structure–function relationships in a series of N-phenylbenzamide (NPBA) derivatives by using computational modeling to identify molecular structures that exhibit both rectification and good conductance together with experimental studies of bias-dependent single molecule conductance and rectification behavior using the scanning tunneling microscopy break-junction technique. From a large number of computationally screened molecular diode structures, we have identified NPBA as a promising candidate, relative to the other structures that were screened. We demonstrate experimentally that conductance and rectification are both enhanced by functionalization of the NPBA 4-carboxamido-aniline moiety with electron donating methoxy groups, and are strongly correlated with the energy of the conducting frontier orbital relative to the Fermi level of the gold leads used in break-junction experiments.","lang":"eng"}],"_id":"17962","publisher":"Royal Society of Chemistry","day":"30","license":"https://creativecommons.org/licenses/by-nc/3.0/","date_created":"2024-09-09T09:36:47Z","article_processing_charge":"No","status":"public","scopus_import":"1","type":"journal_article","date_published":"2016-06-30T00:00:00Z","publication":"New Journal of Chemistry","OA_place":"publisher","title":"Structure–function relationships in single molecule rectification by N-phenylbenzamide derivatives","OA_type":"hybrid","author":[{"full_name":"Koenigsmann, Christopher","first_name":"Christopher","last_name":"Koenigsmann"},{"last_name":"Ding","first_name":"Wendu","full_name":"Ding, Wendu"},{"last_name":"Koepf","first_name":"Matthieu","full_name":"Koepf, Matthieu"},{"full_name":"Batra, Arunabh","first_name":"Arunabh","last_name":"Batra"},{"orcid":"0000-0002-6957-6089","last_name":"Venkataraman","id":"9ebb78a5-cc0d-11ee-8322-fae086a32caf","first_name":"Latha","full_name":"Venkataraman, Latha"},{"full_name":"Negre, Christian F. A.","first_name":"Christian F. A.","last_name":"Negre"},{"first_name":"Gary W.","full_name":"Brudvig, Gary W.","last_name":"Brudvig"},{"first_name":"Robert H.","full_name":"Crabtree, Robert H.","last_name":"Crabtree"},{"full_name":"Batista, Victor S.","first_name":"Victor S.","last_name":"Batista"},{"first_name":"Charles A.","full_name":"Schmuttenmaer, Charles A.","last_name":"Schmuttenmaer"}],"intvolume":"        40","publication_status":"published","page":"7373-7378","oa_version":"Published Version","article_type":"original","tmp":{"name":"Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)","short":"CC BY-NC (3.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/3.0/legalcode","image":"/images/cc_by_nc.png"},"quality_controlled":"1","year":"2016","extern":"1","month":"06","issue":"9","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"date_created":"2024-09-09T09:37:59Z","day":"30","publisher":"Royal Society of Chemistry","_id":"17963","status":"public","article_processing_charge":"Yes","volume":7,"language":[{"iso":"eng"}],"citation":{"short":"H. Li, M.H. Garner, Z. Shangguan, Q. Zheng, T.A. Su, M. Neupane, P. Li, A. Velian, M.L. Steigerwald, S. Xiao, C. Nuckolls, G.C. Solomon, L. Venkataraman, Chemical Science 7 (2016) 5657–5662.","mla":"Li, Haixing, et al. “Conformations of Cyclopentasilane Stereoisomers Control Molecular Junction Conductance.” <i>Chemical Science</i>, vol. 7, no. 9, Royal Society of Chemistry, 2016, pp. 5657–62, doi:<a href=\"https://doi.org/10.1039/c6sc01360k\">10.1039/c6sc01360k</a>.","ieee":"H. Li <i>et al.</i>, “Conformations of cyclopentasilane stereoisomers control molecular junction conductance,” <i>Chemical Science</i>, vol. 7, no. 9. Royal Society of Chemistry, pp. 5657–5662, 2016.","ista":"Li H, Garner MH, Shangguan Z, Zheng Q, Su TA, Neupane M, Li P, Velian A, Steigerwald ML, Xiao S, Nuckolls C, Solomon GC, Venkataraman L. 2016. Conformations of cyclopentasilane stereoisomers control molecular junction conductance. Chemical Science. 7(9), 5657–5662.","ama":"Li H, Garner MH, Shangguan Z, et al. Conformations of cyclopentasilane stereoisomers control molecular junction conductance. <i>Chemical Science</i>. 2016;7(9):5657-5662. doi:<a href=\"https://doi.org/10.1039/c6sc01360k\">10.1039/c6sc01360k</a>","chicago":"Li, Haixing, Marc H. Garner, Zhichun Shangguan, Qianwen Zheng, Timothy A. Su, Madhav Neupane, Panpan Li, et al. “Conformations of Cyclopentasilane Stereoisomers Control Molecular Junction Conductance.” <i>Chemical Science</i>. Royal Society of Chemistry, 2016. <a href=\"https://doi.org/10.1039/c6sc01360k\">https://doi.org/10.1039/c6sc01360k</a>.","apa":"Li, H., Garner, M. H., Shangguan, Z., Zheng, Q., Su, T. A., Neupane, M., … Venkataraman, L. (2016). Conformations of cyclopentasilane stereoisomers control molecular junction conductance. <i>Chemical Science</i>. Royal Society of Chemistry. <a href=\"https://doi.org/10.1039/c6sc01360k\">https://doi.org/10.1039/c6sc01360k</a>"},"doi":"10.1039/c6sc01360k","abstract":[{"text":"Here we examine the impact of ring conformation on the charge transport characteristics of cyclic pentasilane structures bound to gold electrodes in single molecule junctions. We investigate the conductance properties of alkylated cyclopentasilane cis and trans stereoisomers substituted in the 1,3-position with methylthiomethyl electrode binding groups using both the scanning tunneling microscope-based break junction technique and density functional theory based ab initio calculations. In contrast with the linear ones, these cyclic silanes yield lower conductance values; calculations reveal that the constrained dihedral geometries occurring within the ring are suboptimal for σ-orbital delocalization, and therefore, conductance. Theoretical calculations reproduce the measured conductance trends for both cis and trans isomers and find several distinct conformations that are likely to form stable molecular junctions at room temperature. Due to the weakened σ-conjugation in the molecule, through-space interactions are found to contribute significantly to the conductance. This manuscript details the vast conformational flexibility in cyclopentasilanes and the tremendous impact it has on controlling conductance.","lang":"eng"}],"date_updated":"2024-12-18T09:51:40Z","publication_identifier":{"issn":["2041-6520"],"eissn":["2041-6539"]},"title":"Conformations of cyclopentasilane stereoisomers control molecular junction conductance","DOAJ_listed":"1","OA_place":"publisher","OA_type":"gold","type":"journal_article","scopus_import":"1","publication":"Chemical Science","date_published":"2016-05-30T00:00:00Z","page":"5657-5662","publication_status":"published","oa_version":"Published Version","author":[{"last_name":"Li","first_name":"Haixing","full_name":"Li, Haixing"},{"first_name":"Marc H.","full_name":"Garner, Marc H.","last_name":"Garner"},{"full_name":"Shangguan, Zhichun","first_name":"Zhichun","last_name":"Shangguan"},{"full_name":"Zheng, Qianwen","first_name":"Qianwen","last_name":"Zheng"},{"last_name":"Su","full_name":"Su, Timothy A.","first_name":"Timothy A."},{"full_name":"Neupane, Madhav","first_name":"Madhav","last_name":"Neupane"},{"last_name":"Li","first_name":"Panpan","full_name":"Li, Panpan"},{"first_name":"Alexandra","full_name":"Velian, Alexandra","last_name":"Velian"},{"full_name":"Steigerwald, Michael L.","first_name":"Michael L.","last_name":"Steigerwald"},{"full_name":"Xiao, Shengxiong","first_name":"Shengxiong","last_name":"Xiao"},{"full_name":"Nuckolls, Colin","first_name":"Colin","last_name":"Nuckolls"},{"first_name":"Gemma C.","full_name":"Solomon, Gemma C.","last_name":"Solomon"},{"full_name":"Venkataraman, Latha","first_name":"Latha","id":"9ebb78a5-cc0d-11ee-8322-fae086a32caf","orcid":"0000-0002-6957-6089","last_name":"Venkataraman"}],"intvolume":"         7","year":"2016","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"9","month":"05","extern":"1","tmp":{"name":"Creative Commons Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0)","short":"CC BY-NC (3.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/3.0/legalcode","image":"/images/cc_by_nc.png"},"article_type":"original"},{"intvolume":"        18","author":[{"first_name":"Dean","full_name":"Cvetko, Dean","last_name":"Cvetko"},{"last_name":"Fratesi","full_name":"Fratesi, Guido","first_name":"Guido"},{"last_name":"Kladnik","first_name":"Gregor","full_name":"Kladnik, Gregor"},{"last_name":"Cossaro","full_name":"Cossaro, Albano","first_name":"Albano"},{"last_name":"Brivio","first_name":"Gian Paolo","full_name":"Brivio, Gian Paolo"},{"first_name":"Latha","id":"9ebb78a5-cc0d-11ee-8322-fae086a32caf","full_name":"Venkataraman, Latha","orcid":"0000-0002-6957-6089","last_name":"Venkataraman"},{"first_name":"Alberto","full_name":"Morgante, Alberto","last_name":"Morgante"}],"external_id":{"pmid":["27444572"]},"main_file_link":[{"url":"https://doi.org/10.1039/C6CP04099C","open_access":"1"}],"oa_version":"Published Version","publication_status":"published","page":"22140-22145","article_type":"original","pmid":1,"month":"07","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"32","quality_controlled":"1","year":"2016","publication_identifier":{"issn":["1463-9076"],"eissn":["1463-9084"]},"abstract":[{"lang":"eng","text":"Charge transfer rates at metal/organic interfaces affect the efficiencies of devices for organic based electronics and photovoltaics. A quantitative study of electron transfer rates, which take place on the femtosecond timescale, is often difficult, especially since in most systems the molecular adsorption geometry is unknown. Here, we use X-ray resonant photoemission spectroscopy to measure ultrafast charge transfer rates across pyridine/Au(111) interfaces while also controlling the molecular orientation on the metal. We demonstrate that a bi-directional charge transfer across the molecule/metal interface is enabled upon creation of a core-exciton on the molecule with a rate that has a strong dependence on the molecular adsorption angle. Through density functional theory calculations, we show that the alignment of molecular levels relative to the metal Fermi level is dramatically altered when a core-hole is created on the molecule, allowing the lowest unoccupied molecular orbital to fall partially below the metal Fermi level. We also calculate charge transfer rates as a function of molecular adsorption geometry and find a trend that agrees with the experiment. These findings thus give insight into the charge transfer dynamics of a photo-excited molecule on a metal surface."}],"date_updated":"2024-12-18T10:17:35Z","doi":"10.1039/c6cp04099c","citation":{"mla":"Cvetko, Dean, et al. “Ultrafast Electron Injection into Photo-Excited Organic Molecules.” <i>Physical Chemistry Chemical Physics</i>, vol. 18, no. 32, Royal Society of Chemistry, 2016, pp. 22140–45, doi:<a href=\"https://doi.org/10.1039/c6cp04099c\">10.1039/c6cp04099c</a>.","short":"D. Cvetko, G. Fratesi, G. Kladnik, A. Cossaro, G.P. Brivio, L. Venkataraman, A. Morgante, Physical Chemistry Chemical Physics 18 (2016) 22140–22145.","apa":"Cvetko, D., Fratesi, G., Kladnik, G., Cossaro, A., Brivio, G. P., Venkataraman, L., &#38; Morgante, A. (2016). Ultrafast electron injection into photo-excited organic molecules. <i>Physical Chemistry Chemical Physics</i>. Royal Society of Chemistry. <a href=\"https://doi.org/10.1039/c6cp04099c\">https://doi.org/10.1039/c6cp04099c</a>","chicago":"Cvetko, Dean, Guido Fratesi, Gregor Kladnik, Albano Cossaro, Gian Paolo Brivio, Latha Venkataraman, and Alberto Morgante. “Ultrafast Electron Injection into Photo-Excited Organic Molecules.” <i>Physical Chemistry Chemical Physics</i>. Royal Society of Chemistry, 2016. <a href=\"https://doi.org/10.1039/c6cp04099c\">https://doi.org/10.1039/c6cp04099c</a>.","ista":"Cvetko D, Fratesi G, Kladnik G, Cossaro A, Brivio GP, Venkataraman L, Morgante A. 2016. Ultrafast electron injection into photo-excited organic molecules. Physical Chemistry Chemical Physics. 18(32), 22140–22145.","ama":"Cvetko D, Fratesi G, Kladnik G, et al. Ultrafast electron injection into photo-excited organic molecules. <i>Physical Chemistry Chemical Physics</i>. 2016;18(32):22140-22145. doi:<a href=\"https://doi.org/10.1039/c6cp04099c\">10.1039/c6cp04099c</a>","ieee":"D. Cvetko <i>et al.</i>, “Ultrafast electron injection into photo-excited organic molecules,” <i>Physical Chemistry Chemical Physics</i>, vol. 18, no. 32. Royal Society of Chemistry, pp. 22140–22145, 2016."},"language":[{"iso":"eng"}],"volume":18,"status":"public","article_processing_charge":"Yes (in subscription journal)","day":"14","publisher":"Royal Society of Chemistry","_id":"17964","date_created":"2024-09-09T09:39:29Z","oa":1,"date_published":"2016-07-14T00:00:00Z","publication":"Physical Chemistry Chemical Physics","scopus_import":"1","type":"journal_article","OA_type":"hybrid","OA_place":"publisher","title":"Ultrafast electron injection into photo-excited organic molecules"},{"date_created":"2024-10-15T11:20:53Z","day":"01","publisher":"Springer International Publishing","_id":"18328","edition":"1","status":"public","article_processing_charge":"No","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-24726-7_10","citation":{"short":"J. Pokrass, A.M. Bronstein, M.M. Bronstein, P. Sprechmann, G. Sapiro, in:, M. Breuß, A. Bruckstein, P. Maragos, S. Wuhrer (Eds.), Perspectives in Shape Analysis, 1st ed., Springer International Publishing, Cham, 2016, pp. 211–230.","mla":"Pokrass, Jonathan, et al. “Sparse Models for Intrinsic Shape Correspondence.” <i>Perspectives in Shape Analysis</i>, edited by Michael Breuß et al., 1st ed., Springer International Publishing, 2016, pp. 211–30, doi:<a href=\"https://doi.org/10.1007/978-3-319-24726-7_10\">10.1007/978-3-319-24726-7_10</a>.","ieee":"J. Pokrass, A. M. Bronstein, M. M. Bronstein, P. Sprechmann, and G. Sapiro, “Sparse Models for Intrinsic Shape Correspondence,” in <i>Perspectives in Shape Analysis</i>, 1st ed., M. Breuß, A. Bruckstein, P. Maragos, and S. Wuhrer, Eds. Cham: Springer International Publishing, 2016, pp. 211–230.","ista":"Pokrass J, Bronstein AM, Bronstein MM, Sprechmann P, Sapiro G. 2016.Sparse Models for Intrinsic Shape Correspondence. In: Perspectives in Shape Analysis. Mathematics and Visualization, , 211–230.","ama":"Pokrass J, Bronstein AM, Bronstein MM, Sprechmann P, Sapiro G. Sparse Models for Intrinsic Shape Correspondence. In: Breuß M, Bruckstein A, Maragos P, Wuhrer S, eds. <i>Perspectives in Shape Analysis</i>. 1st ed. Cham: Springer International Publishing; 2016:211-230. doi:<a href=\"https://doi.org/10.1007/978-3-319-24726-7_10\">10.1007/978-3-319-24726-7_10</a>","apa":"Pokrass, J., Bronstein, A. M., Bronstein, M. M., Sprechmann, P., &#38; Sapiro, G. (2016). Sparse Models for Intrinsic Shape Correspondence. In M. Breuß, A. Bruckstein, P. Maragos, &#38; S. Wuhrer (Eds.), <i>Perspectives in Shape Analysis</i> (1st ed., pp. 211–230). Cham: Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-319-24726-7_10\">https://doi.org/10.1007/978-3-319-24726-7_10</a>","chicago":"Pokrass, Jonathan, Alex M. Bronstein, Michael M. Bronstein, Pablo Sprechmann, and Guillermo Sapiro. “Sparse Models for Intrinsic Shape Correspondence.” In <i>Perspectives in Shape Analysis</i>, edited by Michael Breuß, Alfred Bruckstein, Petros Maragos, and Stefanie Wuhrer, 1st ed., 211–30. Cham: Springer International Publishing, 2016. <a href=\"https://doi.org/10.1007/978-3-319-24726-7_10\">https://doi.org/10.1007/978-3-319-24726-7_10</a>."},"abstract":[{"lang":"eng","text":"We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor do we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to establish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non-trivial use of sparse models in shape correspondence. We formulate the problem of permuted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown correspondence in functional representation. We also propose a robust variant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects."}],"date_updated":"2024-10-22T08:17:06Z","publication_identifier":{"issn":["1612-3786"],"isbn":["9783319247243"],"eissn":["2197-666X"],"eisbn":["9783319247267"]},"title":"Sparse Models for Intrinsic Shape Correspondence","OA_type":"closed access","type":"book_chapter","scopus_import":"1","publication":"Perspectives in Shape Analysis","place":"Cham","date_published":"2016-10-01T00:00:00Z","page":"211-230","publication_status":"published","editor":[{"last_name":"Breuß","first_name":"Michael","full_name":"Breuß, Michael"},{"first_name":"Alfred","full_name":"Bruckstein, Alfred","last_name":"Bruckstein"},{"last_name":"Maragos","first_name":"Petros","full_name":"Maragos, Petros"},{"last_name":"Wuhrer","full_name":"Wuhrer, Stefanie","first_name":"Stefanie"}],"oa_version":"None","author":[{"full_name":"Pokrass, Jonathan","first_name":"Jonathan","last_name":"Pokrass"},{"orcid":"0000-0001-9699-8730","last_name":"Bronstein","first_name":"Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","full_name":"Bronstein, Alexander"},{"last_name":"Bronstein","full_name":"Bronstein, Michael M.","first_name":"Michael M."},{"last_name":"Sprechmann","full_name":"Sprechmann, Pablo","first_name":"Pablo"},{"full_name":"Sapiro, Guillermo","first_name":"Guillermo","last_name":"Sapiro"}],"year":"2016","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"10","extern":"1","alternative_title":["Mathematics and Visualization"]},{"isi":1,"department":[{"_id":"CaUh"}],"month":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","quality_controlled":"1","publist_id":"5270","year":"2016","intvolume":"       143","author":[{"first_name":"Anna","id":"31934120-F248-11E8-B48F-1D18A9856A87","full_name":"Klimova, Anna","last_name":"Klimova"},{"first_name":"Tamás","full_name":"Rudas, Tamás","last_name":"Rudas"}],"arxiv":1,"external_id":{"isi":["000366885300029"],"arxiv":["1501.00600"]},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1501.00600"}],"oa_version":"Preprint","publication_status":"published","page":"440 - 452","date_published":"2016-01-01T00:00:00Z","publication":"Journal of Multivariate Analysis","scopus_import":"1","type":"journal_article","title":"On the closure of relational models","abstract":[{"text":"Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in the table, and not necessarily containing the overall effect, that is, a common parameter in every cell. Similarly to log-linear models, relational models can be extended to non-negative distributions, but the extension requires more complex methods. An extended relational model is defined as an algebraic variety, and it turns out to be the closure of the original model with respect to the Bregman divergence. In the extended relational model, the MLE of the cell parameters always exists and is unique, but some of its properties may be different from those of the MLE under log-linear models. The MLE can be computed using a generalized iterative scaling procedure based on Bregman projections. ","lang":"eng"}],"date_updated":"2025-09-18T10:47:32Z","doi":"10.1016/j.jmva.2015.10.005","citation":{"ieee":"A. Klimova and T. Rudas, “On the closure of relational models,” <i>Journal of Multivariate Analysis</i>, vol. 143. Elsevier, pp. 440–452, 2016.","apa":"Klimova, A., &#38; Rudas, T. (2016). On the closure of relational models. <i>Journal of Multivariate Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jmva.2015.10.005\">https://doi.org/10.1016/j.jmva.2015.10.005</a>","chicago":"Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.” <i>Journal of Multivariate Analysis</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.jmva.2015.10.005\">https://doi.org/10.1016/j.jmva.2015.10.005</a>.","ista":"Klimova A, Rudas T. 2016. On the closure of relational models. Journal of Multivariate Analysis. 143, 440–452.","ama":"Klimova A, Rudas T. On the closure of relational models. <i>Journal of Multivariate Analysis</i>. 2016;143:440-452. doi:<a href=\"https://doi.org/10.1016/j.jmva.2015.10.005\">10.1016/j.jmva.2015.10.005</a>","short":"A. Klimova, T. Rudas, Journal of Multivariate Analysis 143 (2016) 440–452.","mla":"Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.” <i>Journal of Multivariate Analysis</i>, vol. 143, Elsevier, 2016, pp. 440–52, doi:<a href=\"https://doi.org/10.1016/j.jmva.2015.10.005\">10.1016/j.jmva.2015.10.005</a>."},"volume":143,"language":[{"iso":"eng"}],"status":"public","article_processing_charge":"No","day":"01","publisher":"Elsevier","_id":"1833","corr_author":"1","oa":1,"date_created":"2018-12-11T11:54:15Z"},{"_id":"18361","day":"01","publisher":"Springer Nature","oa":1,"date_created":"2024-10-15T11:20:54Z","article_processing_charge":"No","status":"public","citation":{"ieee":"D. Pickup <i>et al.</i>, “Shape retrieval of non-rigid 3D human models,” <i>International Journal of Computer Vision</i>, vol. 120, no. 2. Springer Nature, pp. 169–193, 2016.","ama":"Pickup D, Sun X, Rosin PL, et al. Shape retrieval of non-rigid 3D human models. <i>International Journal of Computer Vision</i>. 2016;120(2):169-193. doi:<a href=\"https://doi.org/10.1007/s11263-016-0903-8\">10.1007/s11263-016-0903-8</a>","ista":"Pickup D, Sun X, Rosin PL, Martin RR, Cheng Z, Lian Z, Aono M, Hamza AB, Bronstein AM, Bronstein M, Bu S, Castellani U, Cheng S, Garro V, Giachetti A, Godil A, Isaia L, Han J, Johan H, Lai L, Li B, Li C, Li H, Litman R, Liu X, Liu Z, Lu Y, Sun L, Tam G, Tatsuma A, Ye J. 2016. Shape retrieval of non-rigid 3D human models. International Journal of Computer Vision. 120(2), 169–193.","chicago":"Pickup, D., X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian, M. Aono, et al. “Shape Retrieval of Non-Rigid 3D Human Models.” <i>International Journal of Computer Vision</i>. Springer Nature, 2016. <a href=\"https://doi.org/10.1007/s11263-016-0903-8\">https://doi.org/10.1007/s11263-016-0903-8</a>.","apa":"Pickup, D., Sun, X., Rosin, P. L., Martin, R. R., Cheng, Z., Lian, Z., … Ye, J. (2016). Shape retrieval of non-rigid 3D human models. <i>International Journal of Computer Vision</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11263-016-0903-8\">https://doi.org/10.1007/s11263-016-0903-8</a>","short":"D. Pickup, X. Sun, P.L. Rosin, R.R. Martin, Z. Cheng, Z. Lian, M. Aono, A.B. Hamza, A.M. Bronstein, M. Bronstein, S. Bu, U. Castellani, S. Cheng, V. Garro, A. Giachetti, A. Godil, L. Isaia, J. Han, H. Johan, L. Lai, B. Li, C. Li, H. Li, R. Litman, X. Liu, Z. Liu, Y. Lu, L. Sun, G. Tam, A. Tatsuma, J. Ye, International Journal of Computer Vision 120 (2016) 169–193.","mla":"Pickup, D., et al. “Shape Retrieval of Non-Rigid 3D Human Models.” <i>International Journal of Computer Vision</i>, vol. 120, no. 2, Springer Nature, 2016, pp. 169–93, doi:<a href=\"https://doi.org/10.1007/s11263-016-0903-8\">10.1007/s11263-016-0903-8</a>."},"doi":"10.1007/s11263-016-0903-8","volume":120,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1573-1405"],"issn":["0920-5691"]},"date_updated":"2024-12-18T15:13:03Z","abstract":[{"lang":"eng","text":"3D models of humans are commonly used within computer graphics and vision, and so the ability to distinguish between body shapes is an important shape retrieval problem. We extend our recent paper which provided a benchmark for testing non-rigid 3D shape retrieval algorithms on 3D human models. This benchmark provided a far stricter challenge than previous shape benchmarks. We have added 145 new models for use as a separate training set, in order to standardise the training data used and provide a fairer comparison. We have also included experiments with the FAUST dataset of human scans. All participants of the previous benchmark study have taken part in the new tests reported here, many providing updated results using the new data. In addition, further participants have also taken part, and we provide extra analysis of the retrieval results. A total of 25 different shape retrieval methods are compared."}],"title":"Shape retrieval of non-rigid 3D human models","scopus_import":"1","type":"journal_article","date_published":"2016-11-01T00:00:00Z","publication":"International Journal of Computer Vision","publication_status":"published","page":"169-193","oa_version":"Published Version","author":[{"full_name":"Pickup, D.","first_name":"D.","last_name":"Pickup"},{"last_name":"Sun","full_name":"Sun, X.","first_name":"X."},{"last_name":"Rosin","full_name":"Rosin, P. L.","first_name":"P. L."},{"last_name":"Martin","first_name":"R. R.","full_name":"Martin, R. R."},{"last_name":"Cheng","first_name":"Z.","full_name":"Cheng, Z."},{"last_name":"Lian","full_name":"Lian, Z.","first_name":"Z."},{"full_name":"Aono, M.","first_name":"M.","last_name":"Aono"},{"full_name":"Hamza, A. Ben","first_name":"A. Ben","last_name":"Hamza"},{"orcid":"0000-0001-9699-8730","last_name":"Bronstein","first_name":"Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","full_name":"Bronstein, Alexander"},{"full_name":"Bronstein, M.","first_name":"M.","last_name":"Bronstein"},{"first_name":"S.","full_name":"Bu, S.","last_name":"Bu"},{"last_name":"Castellani","first_name":"U.","full_name":"Castellani, U."},{"last_name":"Cheng","full_name":"Cheng, S.","first_name":"S."},{"full_name":"Garro, V.","first_name":"V.","last_name":"Garro"},{"last_name":"Giachetti","full_name":"Giachetti, A.","first_name":"A."},{"last_name":"Godil","full_name":"Godil, A.","first_name":"A."},{"last_name":"Isaia","first_name":"L.","full_name":"Isaia, L."},{"last_name":"Han","full_name":"Han, J.","first_name":"J."},{"last_name":"Johan","first_name":"H.","full_name":"Johan, H."},{"first_name":"L.","full_name":"Lai, L.","last_name":"Lai"},{"full_name":"Li, B.","first_name":"B.","last_name":"Li"},{"full_name":"Li, C.","first_name":"C.","last_name":"Li"},{"first_name":"H.","full_name":"Li, H.","last_name":"Li"},{"last_name":"Litman","first_name":"R.","full_name":"Litman, R."},{"last_name":"Liu","first_name":"X.","full_name":"Liu, X."},{"first_name":"Z.","full_name":"Liu, Z.","last_name":"Liu"},{"full_name":"Lu, Y.","first_name":"Y.","last_name":"Lu"},{"last_name":"Sun","first_name":"L.","full_name":"Sun, L."},{"full_name":"Tam, G.","first_name":"G.","last_name":"Tam"},{"last_name":"Tatsuma","full_name":"Tatsuma, A.","first_name":"A."},{"full_name":"Ye, J.","first_name":"J.","last_name":"Ye"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s11263-016-0903-8"}],"intvolume":"       120","quality_controlled":"1","year":"2016","extern":"1","month":"11","issue":"2","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"12","extern":"1","year":"2016","quality_controlled":"1","conference":{"name":"4th International Conference on 3D Vision","start_date":"2016-10-25","location":" Stanford, CA, United States","end_date":"2016-10-28"},"article_number":"7785118","oa_version":"Preprint","publication_status":"published","external_id":{"arxiv":["1609.05434"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1609.05434"}],"author":[{"first_name":"Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","full_name":"Bronstein, Alexander","orcid":"0000-0001-9699-8730","last_name":"Bronstein"},{"first_name":"Yoni","full_name":"Choukroun, Yoni","last_name":"Choukroun"},{"last_name":"Kimmel","full_name":"Kimmel, Ron","first_name":"Ron"},{"first_name":"Matan","full_name":"Sela, Matan","last_name":"Sela"}],"arxiv":1,"title":"Consistent discretization and minimization of the L1 norm on manifolds","publication":"2016 Fourth International Conference on 3D Vision (3DV)","date_published":"2016-12-19T00:00:00Z","type":"conference","scopus_import":"1","status":"public","article_processing_charge":"No","oa":1,"date_created":"2024-10-15T11:20:54Z","day":"19","publisher":"IEEE","_id":"18374","abstract":[{"lang":"eng","text":"The L 1 norm has been tremendously popular in signal and image processing in the past two decades due to its sparsity-promoting properties. More recently, its generalization to non-Euclidean domains has been found useful in shape analysis applications. For example, in conjunction with the minimization of the Dirichlet energy, it was shown to produce a compactly supported quasi-harmonic orthonormal basis, dubbed as compressed manifold modes [14]. The continuous L 1 norm on the manifold is often replaced by the vector ℓ 1 norm applied to sampled functions. We show that such an approach is incorrect in the sense that it does not consistently discretize the continuous norm and warn against its sensitivity to the specific sampling. We propose two alternative discretizations resulting in an iteratively-reweighed ℓ 2 norm. We demonstrate the proposed strategy on the compressed modes problem, which reduces to a sequence of simple eigendecomposition problems not requiring non-convex optimization on Stiefel manifolds and producing more stable and accurate results."}],"date_updated":"2024-12-05T14:19:34Z","publication_identifier":{"isbn":["9781509054084"]},"language":[{"iso":"eng"}],"citation":{"short":"A.M. Bronstein, Y. Choukroun, R. Kimmel, M. Sela, in:, 2016 Fourth International Conference on 3D Vision (3DV), IEEE, 2016.","mla":"Bronstein, Alex M., et al. “Consistent Discretization and Minimization of the L1 Norm on Manifolds.” <i>2016 Fourth International Conference on 3D Vision (3DV)</i>, 7785118, IEEE, 2016, doi:<a href=\"https://doi.org/10.1109/3dv.2016.53\">10.1109/3dv.2016.53</a>.","ieee":"A. M. Bronstein, Y. Choukroun, R. Kimmel, and M. Sela, “Consistent discretization and minimization of the L1 norm on manifolds,” in <i>2016 Fourth International Conference on 3D Vision (3DV)</i>,  Stanford, CA, United States, 2016.","ama":"Bronstein AM, Choukroun Y, Kimmel R, Sela M. Consistent discretization and minimization of the L1 norm on manifolds. In: <i>2016 Fourth International Conference on 3D Vision (3DV)</i>. IEEE; 2016. doi:<a href=\"https://doi.org/10.1109/3dv.2016.53\">10.1109/3dv.2016.53</a>","ista":"Bronstein AM, Choukroun Y, Kimmel R, Sela M. 2016. Consistent discretization and minimization of the L1 norm on manifolds. 2016 Fourth International Conference on 3D Vision (3DV). 4th International Conference on 3D Vision, 7785118.","apa":"Bronstein, A. M., Choukroun, Y., Kimmel, R., &#38; Sela, M. (2016). Consistent discretization and minimization of the L1 norm on manifolds. In <i>2016 Fourth International Conference on 3D Vision (3DV)</i>.  Stanford, CA, United States: IEEE. <a href=\"https://doi.org/10.1109/3dv.2016.53\">https://doi.org/10.1109/3dv.2016.53</a>","chicago":"Bronstein, Alex M., Yoni Choukroun, Ron Kimmel, and Matan Sela. “Consistent Discretization and Minimization of the L1 Norm on Manifolds.” In <i>2016 Fourth International Conference on 3D Vision (3DV)</i>. IEEE, 2016. <a href=\"https://doi.org/10.1109/3dv.2016.53\">https://doi.org/10.1109/3dv.2016.53</a>."},"doi":"10.1109/3dv.2016.53"},{"status":"public","article_processing_charge":"No","date_created":"2024-10-15T11:20:54Z","oa":1,"publisher":"IEEE","day":"19","_id":"18375","abstract":[{"text":"We present a method to approximate pairwise distance on a graph, having an amortized sub-linear complexity in its size. The proposed method follows the so called heat method due to Crane et al. The only additional input are the values of the eigenfunctions of the graph Laplacian at a subset of the vertices. Using these values we estimate a random walk from the source points, and normalize the result into a unit gradient function. The eigenfunctions are then used to synthesize distance values abiding by these constraints at desired locations. We show that this method works in practice on different types of inputs ranging from triangular meshes to general graphs. We also demonstrate that the resulting approximate distance is accurate enough to be used as the input to a recent method for intrinsic shape correspondence computation.","lang":"eng"}],"date_updated":"2024-12-05T14:17:16Z","publication_identifier":{"isbn":["9781509054084"]},"language":[{"iso":"eng"}],"citation":{"apa":"Litman, R., &#38; Bronstein, A. M. (2016). SpectroMeter: Amortized sublinear spectral approximation of distance on graphs. In <i>2016 Fourth International Conference on 3D Vision (3DV)</i>. Stanford, CA, United States: IEEE. <a href=\"https://doi.org/10.1109/3dv.2016.60\">https://doi.org/10.1109/3dv.2016.60</a>","chicago":"Litman, Roee, and Alex M. Bronstein. “SpectroMeter: Amortized Sublinear Spectral Approximation of Distance on Graphs.” In <i>2016 Fourth International Conference on 3D Vision (3DV)</i>. IEEE, 2016. <a href=\"https://doi.org/10.1109/3dv.2016.60\">https://doi.org/10.1109/3dv.2016.60</a>.","ama":"Litman R, Bronstein AM. SpectroMeter: Amortized sublinear spectral approximation of distance on graphs. In: <i>2016 Fourth International Conference on 3D Vision (3DV)</i>. IEEE; 2016. doi:<a href=\"https://doi.org/10.1109/3dv.2016.60\">10.1109/3dv.2016.60</a>","ista":"Litman R, Bronstein AM. 2016. SpectroMeter: Amortized sublinear spectral approximation of distance on graphs. 2016 Fourth International Conference on 3D Vision (3DV). 4th International Conference on 3D Vision, 7785125.","ieee":"R. Litman and A. M. Bronstein, “SpectroMeter: Amortized sublinear spectral approximation of distance on graphs,” in <i>2016 Fourth International Conference on 3D Vision (3DV)</i>, Stanford, CA, United States, 2016.","mla":"Litman, Roee, and Alex M. Bronstein. “SpectroMeter: Amortized Sublinear Spectral Approximation of Distance on Graphs.” <i>2016 Fourth International Conference on 3D Vision (3DV)</i>, 7785125, IEEE, 2016, doi:<a href=\"https://doi.org/10.1109/3dv.2016.60\">10.1109/3dv.2016.60</a>.","short":"R. Litman, A.M. Bronstein, in:, 2016 Fourth International Conference on 3D Vision (3DV), IEEE, 2016."},"doi":"10.1109/3dv.2016.60","title":"SpectroMeter: Amortized sublinear spectral approximation of distance on graphs","publication":"2016 Fourth International Conference on 3D Vision (3DV)","date_published":"2016-12-19T00:00:00Z","type":"conference","scopus_import":"1","oa_version":"Preprint","publication_status":"published","external_id":{"arxiv":["1609.05715"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1609.05715","open_access":"1"}],"author":[{"last_name":"Litman","full_name":"Litman, Roee","first_name":"Roee"},{"orcid":"0000-0001-9699-8730","last_name":"Bronstein","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","first_name":"Alexander","full_name":"Bronstein, Alexander"}],"arxiv":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"12","extern":"1","year":"2016","quality_controlled":"1","conference":{"end_date":"2016-10-28","start_date":"2016-10-25","location":"Stanford, CA, United States","name":"4th International Conference on 3D Vision"},"article_number":"7785125"},{"status":"public","article_processing_charge":"No","oa":1,"date_created":"2024-10-15T11:20:54Z","publisher":"IEEE","day":"16","_id":"18388","abstract":[{"lang":"eng","text":"The pursuit of smaller pixel sizes at ever increasing resolution in digital image sensors is mainly driven by the stringent price and form-factor requirements of sensors and optics in the cellular phone market. Recently, Eric Fossum proposed a novel concept of an image sensor with dense sub-diffraction limit one-bit pixels (jots), which can be considered a digital emulation of silver halide photographic film. This idea has been recently embodied as the EPFL Gigavision camera. A major bottleneck in the design of such sensors is the image reconstruction process, producing a continuous high dynamic range image from oversampled binary measurements. The extreme quantization of the Poisson statistics is incompatible with the assumptions of most standard image processing and enhancement frameworks. The recently proposed maximum-likelihood (ML) approach addresses this difficulty, but suffers from image artefacts and has impractically high computational complexity. In this work, we study a variant of a sensor with binary threshold pixels and propose a reconstruction algorithm combining an ML data fitting term with a sparse synthesis prior. We also show an efficient hardware-friendly real-time approximation of this inverse operator. Promising results are shown on synthetic data as well as on HDR data emulated using multiple exposures of a regular CMOS sensor."}],"date_updated":"2024-12-05T14:16:11Z","publication_identifier":{"eisbn":["9781467386234"]},"language":[{"iso":"eng"}],"doi":"10.1109/iccphot.2016.7492874","citation":{"ieee":"T. Remez, O. Litany, and A. M. Bronstein, “A picture is worth a billion bits: Real-time image reconstruction from dense binary threshold pixels,” in <i>2016 IEEE International Conference on Computational Photography (ICCP)</i>, Evanston, IL, United States, 2016.","ama":"Remez T, Litany O, Bronstein AM. A picture is worth a billion bits: Real-time image reconstruction from dense binary threshold pixels. In: <i>2016 IEEE International Conference on Computational Photography (ICCP)</i>. IEEE; 2016. doi:<a href=\"https://doi.org/10.1109/iccphot.2016.7492874\">10.1109/iccphot.2016.7492874</a>","ista":"Remez T, Litany O, Bronstein AM. 2016. A picture is worth a billion bits: Real-time image reconstruction from dense binary threshold pixels. 2016 IEEE International Conference on Computational Photography (ICCP). IEEE International Conference on Computational Photography, 7492874.","chicago":"Remez, Tal, Or Litany, and Alex M. Bronstein. “A Picture Is Worth a Billion Bits: Real-Time Image Reconstruction from Dense Binary Threshold Pixels.” In <i>2016 IEEE International Conference on Computational Photography (ICCP)</i>. IEEE, 2016. <a href=\"https://doi.org/10.1109/iccphot.2016.7492874\">https://doi.org/10.1109/iccphot.2016.7492874</a>.","apa":"Remez, T., Litany, O., &#38; Bronstein, A. M. (2016). A picture is worth a billion bits: Real-time image reconstruction from dense binary threshold pixels. In <i>2016 IEEE International Conference on Computational Photography (ICCP)</i>. Evanston, IL, United States: IEEE. <a href=\"https://doi.org/10.1109/iccphot.2016.7492874\">https://doi.org/10.1109/iccphot.2016.7492874</a>","short":"T. Remez, O. Litany, A.M. Bronstein, in:, 2016 IEEE International Conference on Computational Photography (ICCP), IEEE, 2016.","mla":"Remez, Tal, et al. “A Picture Is Worth a Billion Bits: Real-Time Image Reconstruction from Dense Binary Threshold Pixels.” <i>2016 IEEE International Conference on Computational Photography (ICCP)</i>, 7492874, IEEE, 2016, doi:<a href=\"https://doi.org/10.1109/iccphot.2016.7492874\">10.1109/iccphot.2016.7492874</a>."},"title":"A picture is worth a billion bits: Real-time image reconstruction from dense binary threshold pixels","publication":"2016 IEEE International Conference on Computational Photography (ICCP)","date_published":"2016-06-16T00:00:00Z","type":"conference","scopus_import":"1","oa_version":"Preprint","publication_status":"published","external_id":{"arxiv":["1510.04601"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1510.04601","open_access":"1"}],"author":[{"full_name":"Remez, Tal","first_name":"Tal","last_name":"Remez"},{"first_name":"Or","full_name":"Litany, Or","last_name":"Litany"},{"orcid":"0000-0001-9699-8730","last_name":"Bronstein","first_name":"Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","full_name":"Bronstein, Alexander"}],"arxiv":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"06","extern":"1","year":"2016","quality_controlled":"1","conference":{"end_date":"2016-05-15","name":"IEEE International Conference on Computational Photography","start_date":"2016-05-13","location":"Evanston, IL, United States"},"article_number":"7492874"},{"date_created":"2024-10-15T11:20:55Z","oa":1,"day":"01","publisher":"IEEE","_id":"18419","status":"public","article_processing_charge":"No","volume":64,"language":[{"iso":"eng"}],"citation":{"apa":"Giryes, R., Sapiro, G., &#38; Bronstein, A. M. (2016). Deep neural networks with random Gaussian weights: A universal classification strategy? <i>IEEE Transactions on Signal Processing</i>. IEEE. <a href=\"https://doi.org/10.1109/tsp.2016.2546221\">https://doi.org/10.1109/tsp.2016.2546221</a>","chicago":"Giryes, Raja, Guillermo Sapiro, and Alex M. Bronstein. “Deep Neural Networks with Random Gaussian Weights: A Universal Classification Strategy?” <i>IEEE Transactions on Signal Processing</i>. IEEE, 2016. <a href=\"https://doi.org/10.1109/tsp.2016.2546221\">https://doi.org/10.1109/tsp.2016.2546221</a>.","ama":"Giryes R, Sapiro G, Bronstein AM. Deep neural networks with random Gaussian weights: A universal classification strategy? <i>IEEE Transactions on Signal Processing</i>. 2016;64(13):3444-3457. doi:<a href=\"https://doi.org/10.1109/tsp.2016.2546221\">10.1109/tsp.2016.2546221</a>","ista":"Giryes R, Sapiro G, Bronstein AM. 2016. Deep neural networks with random Gaussian weights: A universal classification strategy? IEEE Transactions on Signal Processing. 64(13), 3444–3457.","ieee":"R. Giryes, G. Sapiro, and A. M. Bronstein, “Deep neural networks with random Gaussian weights: A universal classification strategy?,” <i>IEEE Transactions on Signal Processing</i>, vol. 64, no. 13. IEEE, pp. 3444–3457, 2016.","mla":"Giryes, Raja, et al. “Deep Neural Networks with Random Gaussian Weights: A Universal Classification Strategy?” <i>IEEE Transactions on Signal Processing</i>, vol. 64, no. 13, IEEE, 2016, pp. 3444–57, doi:<a href=\"https://doi.org/10.1109/tsp.2016.2546221\">10.1109/tsp.2016.2546221</a>.","short":"R. Giryes, G. Sapiro, A.M. Bronstein, IEEE Transactions on Signal Processing 64 (2016) 3444–3457."},"doi":"10.1109/tsp.2016.2546221","abstract":[{"lang":"eng","text":"Three important properties of a classification machinery are i) the system preserves the core information of the input data; ii) the training examples convey information about unseen data; and iii) the system is able to treat differently points from different classes. In this paper, we show that these fundamental properties are satisfied by the architecture of deep neural networks. We formally prove that these networks with random Gaussian weights perform a distance-preserving embedding of the data, with a special treatment for in-class and out-of-class data. Similar points at the input of the network are likely to have a similar output. The theoretical analysis of deep networks here presented exploits tools used in the compressed sensing and dictionary learning literature, thereby making a formal connection between these important topics. The derived results allow drawing conclusions on the metric learning properties of the network and their relation to its structure, as well as providing bounds on the required size of the training set such that the training examples would represent faithfully the unseen data. The results are validated with state-of-the-art trained networks."}],"date_updated":"2024-12-18T11:49:18Z","publication_identifier":{"issn":["1053-587X"],"eissn":["1941-0476"]},"title":"Deep neural networks with random Gaussian weights: A universal classification strategy?","type":"journal_article","scopus_import":"1","related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1109/TSP.2019.2961228"}]},"publication":"IEEE Transactions on Signal Processing","date_published":"2016-07-01T00:00:00Z","page":"3444-3457","publication_status":"published","oa_version":"Preprint","external_id":{"arxiv":["1504.08291"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1504.08291","open_access":"1"}],"author":[{"last_name":"Giryes","first_name":"Raja","full_name":"Giryes, Raja"},{"full_name":"Sapiro, Guillermo","first_name":"Guillermo","last_name":"Sapiro"},{"full_name":"Bronstein, Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","first_name":"Alexander","last_name":"Bronstein","orcid":"0000-0001-9699-8730"}],"arxiv":1,"intvolume":"        64","year":"2016","quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","issue":"13","month":"07","extern":"1"},{"title":"Non‐rigid puzzles","type":"journal_article","scopus_import":"1","publication":"Computer Graphics Forum","date_published":"2016-08-01T00:00:00Z","oa":1,"date_created":"2024-10-15T11:20:55Z","_id":"18426","publisher":"Wiley","day":"01","article_processing_charge":"No","status":"public","volume":35,"language":[{"iso":"eng"}],"doi":"10.1111/cgf.12970","citation":{"ieee":"O. Litany, E. Rodolà, A. M. Bronstein, M. M. Bronstein, and D. Cremers, “Non‐rigid puzzles,” <i>Computer Graphics Forum</i>, vol. 35, no. 5. Wiley, pp. 135–143, 2016.","apa":"Litany, O., Rodolà, E., Bronstein, A. M., Bronstein, M. M., &#38; Cremers, D. (2016). Non‐rigid puzzles. <i>Computer Graphics Forum</i>. Wiley. <a href=\"https://doi.org/10.1111/cgf.12970\">https://doi.org/10.1111/cgf.12970</a>","chicago":"Litany, O., E. Rodolà, Alex M. Bronstein, M. M. Bronstein, and D. Cremers. “Non‐rigid Puzzles.” <i>Computer Graphics Forum</i>. Wiley, 2016. <a href=\"https://doi.org/10.1111/cgf.12970\">https://doi.org/10.1111/cgf.12970</a>.","ama":"Litany O, Rodolà E, Bronstein AM, Bronstein MM, Cremers D. Non‐rigid puzzles. <i>Computer Graphics Forum</i>. 2016;35(5):135-143. doi:<a href=\"https://doi.org/10.1111/cgf.12970\">10.1111/cgf.12970</a>","ista":"Litany O, Rodolà E, Bronstein AM, Bronstein MM, Cremers D. 2016. Non‐rigid puzzles. Computer Graphics Forum. 35(5), 135–143.","short":"O. Litany, E. Rodolà, A.M. Bronstein, M.M. Bronstein, D. Cremers, Computer Graphics Forum 35 (2016) 135–143.","mla":"Litany, O., et al. “Non‐rigid Puzzles.” <i>Computer Graphics Forum</i>, vol. 35, no. 5, Wiley, 2016, pp. 135–43, doi:<a href=\"https://doi.org/10.1111/cgf.12970\">10.1111/cgf.12970</a>."},"date_updated":"2024-12-19T14:29:56Z","abstract":[{"text":"Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non-rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non-rigid multi-part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non-rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.","lang":"eng"}],"publication_identifier":{"eissn":["1467-8659"],"issn":["0167-7055"]},"year":"2016","quality_controlled":"1","issue":"5","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","extern":"1","month":"08","page":"135-143","publication_status":"published","oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2011.13076","open_access":"1"}],"author":[{"first_name":"O.","full_name":"Litany, O.","last_name":"Litany"},{"full_name":"Rodolà, E.","first_name":"E.","last_name":"Rodolà"},{"orcid":"0000-0001-9699-8730","last_name":"Bronstein","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","first_name":"Alexander","full_name":"Bronstein, Alexander"},{"first_name":"M. M.","full_name":"Bronstein, M. M.","last_name":"Bronstein"},{"full_name":"Cremers, D.","first_name":"D.","last_name":"Cremers"}],"intvolume":"        35"},{"intvolume":"         9","date_updated":"2024-12-19T13:05:21Z","abstract":[{"text":"Sparse models in dictionary learning have been successfully applied in a wide variety of machine learning and computer vision problems, and as a result have recently attracted increased research interest. Another interesting related problem based on linear equality constraints, namely the sparse null space (SNS) problem, first appeared in 1986 and has since inspired results on sparse basis pursuit. In this paper, we investigate the relation between the SNS problem and the analysis dictionary learning (ADL) problem, and show that the SNS problem plays a central role, and may be utilized to solve dictionary learning problems. Moreover, we propose an efficient algorithm of sparse null space basis pursuit (SNS-BP) and extend it to a solution of ADL. Experimental results on numerical synthetic data and real-world data are further presented to validate the performance of our method.","lang":"eng"}],"publication_identifier":{"eissn":["1936-4954"]},"language":[{"iso":"eng"}],"volume":9,"citation":{"ieee":"X. Bian, H. Krim, A. M. Bronstein, and L. Dai, “Sparsity and nullity: Paradigms for analysis dictionary learning,” <i>SIAM Journal on Imaging Sciences</i>, vol. 9, no. 3. Society for Industrial &#38; Applied Mathematics, pp. 1107–1126, 2016.","chicago":"Bian, Xiao, Hamid Krim, Alex M. Bronstein, and Liyi Dai. “Sparsity and Nullity: Paradigms for Analysis Dictionary Learning.” <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial &#38; Applied Mathematics, 2016. <a href=\"https://doi.org/10.1137/15m1030376\">https://doi.org/10.1137/15m1030376</a>.","apa":"Bian, X., Krim, H., Bronstein, A. M., &#38; Dai, L. (2016). Sparsity and nullity: Paradigms for analysis dictionary learning. <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/15m1030376\">https://doi.org/10.1137/15m1030376</a>","ama":"Bian X, Krim H, Bronstein AM, Dai L. Sparsity and nullity: Paradigms for analysis dictionary learning. <i>SIAM Journal on Imaging Sciences</i>. 2016;9(3):1107-1126. doi:<a href=\"https://doi.org/10.1137/15m1030376\">10.1137/15m1030376</a>","ista":"Bian X, Krim H, Bronstein AM, Dai L. 2016. Sparsity and nullity: Paradigms for analysis dictionary learning. SIAM Journal on Imaging Sciences. 9(3), 1107–1126.","short":"X. Bian, H. Krim, A.M. Bronstein, L. Dai, SIAM Journal on Imaging Sciences 9 (2016) 1107–1126.","mla":"Bian, Xiao, et al. “Sparsity and Nullity: Paradigms for Analysis Dictionary Learning.” <i>SIAM Journal on Imaging Sciences</i>, vol. 9, no. 3, Society for Industrial &#38; Applied Mathematics, 2016, pp. 1107–26, doi:<a href=\"https://doi.org/10.1137/15m1030376\">10.1137/15m1030376</a>."},"doi":"10.1137/15m1030376","author":[{"last_name":"Bian","first_name":"Xiao","full_name":"Bian, Xiao"},{"full_name":"Krim, Hamid","first_name":"Hamid","last_name":"Krim"},{"full_name":"Bronstein, Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","first_name":"Alexander","orcid":"0000-0001-9699-8730","last_name":"Bronstein"},{"first_name":"Liyi","full_name":"Dai, Liyi","last_name":"Dai"}],"article_processing_charge":"No","status":"public","oa_version":"None","date_created":"2024-10-15T11:20:55Z","page":"1107-1126","_id":"18430","publisher":"Society for Industrial & Applied Mathematics","day":"09","publication_status":"published","publication":"SIAM Journal on Imaging Sciences","date_published":"2016-08-09T00:00:00Z","type":"journal_article","scopus_import":"1","issue":"3","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","extern":"1","month":"08","year":"2016","title":"Sparsity and nullity: Paradigms for analysis dictionary learning","quality_controlled":"1"},{"date_updated":"2025-02-04T15:03:47Z","abstract":[{"lang":"eng","text":"Notions of similarity and correspondence between geometric shapes and images are central to many tasks in geometry processing, computer vision, and computer graphics. The goal of this course is to familiarize the audience with a set of recent techniques that greatly facilitate the computation of mappings or correspondences between geometric datasets, such as 3D shapes or 2D images by formulating them as mappings between functions rather than points or triangles.\r\nMethods based on the functional map framework have recently led to state-of-the-art results in problems as diverse as non-rigid shape matching, image co-segmentation and even some aspects of tangent vector field design. One challenge in adopting these methods in practice, however, is that their exposition often assumes a significant amount of background in geometry processing, spectral methods and functional analysis, which can make it difficult to gain an intuition about their performance or about their applicability to real-life problems. In this course, we try to provide all the tools necessary to appreciate and use these techniques, while assuming very little background knowledge. We also give a unifying treatment of these techniques, which may be difficult to extract from the individual publications and, at the same time, hint at the generality of this point of view, which can help tackle many problems in the analysis and creation of visual content.\r\nThis course is structured as a half day course. We will assume that the participants have knowledge of basic linear algebra and some knowledge of differential geometry, to the extent of being familiar with the concepts of a manifold and a tangent vector space. We will discuss in detail the functional approach to finding correspondences between non-rigid shapes, the design and analysis of tangent vector fields on surfaces, consistent map estimation in networks of shapes and applications to shape and image segmentation, shape variability analysis, and other areas."}],"publication_identifier":{"isbn":["9781450345385"]},"language":[{"iso":"eng"}],"citation":{"ieee":"M. Ovsjanikov <i>et al.</i>, “Computing and processing correspondences with functional maps,” in <i>SIGGRAPH ASIA 2016 Courses</i>, Macau, 2016.","ista":"Ovsjanikov M, Corman E, Bronstein M, Rodolà E, Ben-Chen M, Guibas L, Chazal F, Bronstein AM. 2016. Computing and processing correspondences with functional maps. SIGGRAPH ASIA 2016 Courses. SA ’16: SIGGRAPH ASIA 2016 Courses, 9.","ama":"Ovsjanikov M, Corman E, Bronstein M, et al. Computing and processing correspondences with functional maps. In: <i>SIGGRAPH ASIA 2016 Courses</i>. ACM; 2016. doi:<a href=\"https://doi.org/10.1145/2988458.2988494\">10.1145/2988458.2988494</a>","apa":"Ovsjanikov, M., Corman, E., Bronstein, M., Rodolà, E., Ben-Chen, M., Guibas, L., … Bronstein, A. M. (2016). Computing and processing correspondences with functional maps. In <i>SIGGRAPH ASIA 2016 Courses</i>. Macau: ACM. <a href=\"https://doi.org/10.1145/2988458.2988494\">https://doi.org/10.1145/2988458.2988494</a>","chicago":"Ovsjanikov, Maks, Etienne Corman, Michael Bronstein, Emanuele Rodolà, Mirela Ben-Chen, Leonidas Guibas, Frederic Chazal, and Alex M. Bronstein. “Computing and Processing Correspondences with Functional Maps.” In <i>SIGGRAPH ASIA 2016 Courses</i>. ACM, 2016. <a href=\"https://doi.org/10.1145/2988458.2988494\">https://doi.org/10.1145/2988458.2988494</a>.","short":"M. Ovsjanikov, E. Corman, M. Bronstein, E. Rodolà, M. Ben-Chen, L. Guibas, F. Chazal, A.M. Bronstein, in:, SIGGRAPH ASIA 2016 Courses, ACM, 2016.","mla":"Ovsjanikov, Maks, et al. “Computing and Processing Correspondences with Functional Maps.” <i>SIGGRAPH ASIA 2016 Courses</i>, 9, ACM, 2016, doi:<a href=\"https://doi.org/10.1145/2988458.2988494\">10.1145/2988458.2988494</a>."},"doi":"10.1145/2988458.2988494","article_processing_charge":"No","status":"public","oa":1,"date_created":"2024-10-15T11:20:55Z","_id":"18434","publisher":"ACM","day":"28","publication":"SIGGRAPH ASIA 2016 Courses","date_published":"2016-11-28T00:00:00Z","type":"conference","scopus_import":"1","OA_type":"green","title":"Computing and processing correspondences with functional maps","OA_place":"repository","main_file_link":[{"url":"https://inria.hal.science/hal-01664767/","open_access":"1"}],"author":[{"last_name":"Ovsjanikov","first_name":"Maks","full_name":"Ovsjanikov, Maks"},{"last_name":"Corman","first_name":"Etienne","full_name":"Corman, Etienne"},{"first_name":"Michael","full_name":"Bronstein, Michael","last_name":"Bronstein"},{"last_name":"Rodolà","first_name":"Emanuele","full_name":"Rodolà, Emanuele"},{"full_name":"Ben-Chen, Mirela","first_name":"Mirela","last_name":"Ben-Chen"},{"first_name":"Leonidas","full_name":"Guibas, Leonidas","last_name":"Guibas"},{"last_name":"Chazal","full_name":"Chazal, Frederic","first_name":"Frederic"},{"orcid":"0000-0001-9699-8730","last_name":"Bronstein","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","first_name":"Alexander","full_name":"Bronstein, Alexander"}],"oa_version":"Preprint","publication_status":"published","conference":{"end_date":"2016-12-08","start_date":"2016-12-05","location":"Macau","name":"SA '16: SIGGRAPH ASIA 2016 Courses"},"article_number":"9","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","month":"11","year":"2016","quality_controlled":"1"},{"extern":"1","month":"11","keyword":["final-state problem","wave operators","cubic-quintic NLS","nonvanishing boundary conditions"],"issue":"7","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","year":"2016","article_type":"original","oa_version":"Preprint","publication_status":"published","page":"1523-1574","intvolume":"         9","arxiv":1,"author":[{"first_name":"Rowan","full_name":"Killip, Rowan","last_name":"Killip"},{"last_name":"Murphy","first_name":"Jason","full_name":"Murphy, Jason"},{"full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1506.06151","open_access":"1"}],"external_id":{"arxiv":["1506.06151"]},"OA_type":"green","OA_place":"repository","mathsc":["35Q55"],"title":"The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions","das_tickbox":"1","date_published":"2016-11-07T00:00:00Z","publication":"Analysis & PDE","scopus_import":"1","type":"journal_article","article_processing_charge":"No","status":"public","_id":"22051","day":"07","publisher":"Mathematical Sciences Publishers","oa":1,"date_created":"2026-06-19T07:54:01Z","publication_identifier":{"issn":["2157-5045"],"eissn":["1948-206X"]},"date_updated":"2026-06-25T08:23:10Z","abstract":[{"lang":"eng","text":"We construct solutions with prescribed scattering state to the cubic-quintic NLS (mathematical formular)in three spatial dimensions in the class of solutions with (mathematical formular). This models disturbances in an infinite expanse of (quantum) fluid in its quiescent state— the limiting modulus c corresponds to a local minimum in the energy density.\r\nOur arguments build on work of Gustafson, Nakanishi, and Tsai on the (defocusing) Gross–Pitaevskii equation. The presence of an energy-critical nonlinearity and changes in the geometry of the energy\r\nfunctional add several new complexities. One new ingredient in our argument is a demonstration that\r\nsolutions of such (perturbed) energy-critical equations exhibit continuous dependence on the initial data\r\nwith respect to the weak topology on H1/x."}],"citation":{"short":"R. Killip, J. Murphy, M. Vişan, Analysis &#38; PDE 9 (2016) 1523–1574.","mla":"Killip, Rowan, et al. “The Final-State Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>Analysis &#38; PDE</i>, vol. 9, no. 7, Mathematical Sciences Publishers, 2016, pp. 1523–74, doi:<a href=\"https://doi.org/10.2140/apde.2016.9.1523\">10.2140/apde.2016.9.1523</a>.","ieee":"R. Killip, J. Murphy, and M. Vişan, “The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions,” <i>Analysis &#38; PDE</i>, vol. 9, no. 7. Mathematical Sciences Publishers, pp. 1523–1574, 2016.","ama":"Killip R, Murphy J, Vişan M. The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. <i>Analysis &#38; PDE</i>. 2016;9(7):1523-1574. doi:<a href=\"https://doi.org/10.2140/apde.2016.9.1523\">10.2140/apde.2016.9.1523</a>","ista":"Killip R, Murphy J, Vişan M. 2016. The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. Analysis &#38; PDE. 9(7), 1523–1574.","chicago":"Killip, Rowan, Jason Murphy, and Monica Vişan. “The Final-State Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers, 2016. <a href=\"https://doi.org/10.2140/apde.2016.9.1523\">https://doi.org/10.2140/apde.2016.9.1523</a>.","apa":"Killip, R., Murphy, J., &#38; Vişan, M. (2016). The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/apde.2016.9.1523\">https://doi.org/10.2140/apde.2016.9.1523</a>"},"doi":"10.2140/apde.2016.9.1523","language":[{"iso":"eng"}],"volume":9},{"page":"146-180","publication_status":"published","oa_version":"Preprint","external_id":{"arxiv":["1501.05062"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1501.05062"}],"author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica","last_name":"Visan"},{"last_name":"Zhang","full_name":"Zhang, Xiaoyi","first_name":"Xiaoyi"}],"arxiv":1,"intvolume":"      2016","year":"2016","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","month":"01","extern":"1","article_type":"original","date_created":"2026-06-19T07:54:24Z","oa":1,"day":"01","publisher":"Oxford University Press","_id":"22052","status":"public","article_processing_charge":"No","language":[{"iso":"eng"}],"volume":2016,"doi":"10.1093/amrx/abv012","citation":{"ieee":"R. Killip, M. Vişan, and X. Zhang, “The focusing cubic NLS on exterior domains in three dimensions,” <i>Applied Mathematics Research eXpress</i>, vol. 2016, no. 1. Oxford University Press, pp. 146–180, 2016.","apa":"Killip, R., Vişan, M., &#38; Zhang, X. (2016). The focusing cubic NLS on exterior domains in three dimensions. <i>Applied Mathematics Research EXpress</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/amrx/abv012\">https://doi.org/10.1093/amrx/abv012</a>","chicago":"Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “The Focusing Cubic NLS on Exterior Domains in Three Dimensions.” <i>Applied Mathematics Research EXpress</i>. Oxford University Press, 2016. <a href=\"https://doi.org/10.1093/amrx/abv012\">https://doi.org/10.1093/amrx/abv012</a>.","ista":"Killip R, Vişan M, Zhang X. 2016. The focusing cubic NLS on exterior domains in three dimensions. Applied Mathematics Research eXpress. 2016(1), 146–180.","ama":"Killip R, Vişan M, Zhang X. The focusing cubic NLS on exterior domains in three dimensions. <i>Applied Mathematics Research eXpress</i>. 2016;2016(1):146-180. doi:<a href=\"https://doi.org/10.1093/amrx/abv012\">10.1093/amrx/abv012</a>","short":"R. Killip, M. Vişan, X. Zhang, Applied Mathematics Research EXpress 2016 (2016) 146–180.","mla":"Killip, Rowan, et al. “The Focusing Cubic NLS on Exterior Domains in Three Dimensions.” <i>Applied Mathematics Research EXpress</i>, vol. 2016, no. 1, Oxford University Press, 2016, pp. 146–80, doi:<a href=\"https://doi.org/10.1093/amrx/abv012\">10.1093/amrx/abv012</a>."},"abstract":[{"text":"We consider the focusing cubic nonlinear Schrödinger equation (NLS) in the exterior Ω of a smooth, compact, strictly convex obstacle in three dimensions. We prove that the threshold for global existence and scattering is the same as for the problem posed on Euclidean space. Specifically, we prove that if E(u0)M(u0)<E(Q)M(Q) and ||u0||2||u0||2<\\|\\nabla Q||2||Q||2, the corresponding solution to the initial value problem with Dirichlet boundary conditions exists globally and scatters to linear evolutions asymptotically in the future and in the past. Here, Q(x) denotes the ground state for the focusing cubic NLS in ℝ3. ","lang":"eng"}],"date_updated":"2026-06-25T08:30:19Z","publication_identifier":{"eissn":["1687-1197"],"issn":["1687-1200"]},"title":"The focusing cubic NLS on exterior domains in three dimensions","OA_place":"repository","OA_type":"green","type":"journal_article","scopus_import":"1","publication":"Applied Mathematics Research eXpress","date_published":"2016-01-01T00:00:00Z","das_tickbox":"1"},{"citation":{"mla":"Killip, Rowan, and Monica Vişan. “Scale-Invariant Strichartz Estimates on Tori and Applications.” <i>Mathematical Research Letters</i>, vol. 23, no. 2, International Press, 2016, pp. 445–72, doi:<a href=\"https://doi.org/10.4310/mrl.2016.v23.n2.a8\">10.4310/mrl.2016.v23.n2.a8</a>.","short":"R. Killip, M. Vişan, Mathematical Research Letters 23 (2016) 445–472.","ama":"Killip R, Vişan M. Scale-invariant Strichartz estimates on tori and applications. <i>Mathematical Research Letters</i>. 2016;23(2):445-472. doi:<a href=\"https://doi.org/10.4310/mrl.2016.v23.n2.a8\">10.4310/mrl.2016.v23.n2.a8</a>","ista":"Killip R, Vişan M. 2016. Scale-invariant Strichartz estimates on tori and applications. Mathematical Research Letters. 23(2), 445–472.","chicago":"Killip, Rowan, and Monica Vişan. “Scale-Invariant Strichartz Estimates on Tori and Applications.” <i>Mathematical Research Letters</i>. International Press, 2016. <a href=\"https://doi.org/10.4310/mrl.2016.v23.n2.a8\">https://doi.org/10.4310/mrl.2016.v23.n2.a8</a>.","apa":"Killip, R., &#38; Vişan, M. (2016). Scale-invariant Strichartz estimates on tori and applications. <i>Mathematical Research Letters</i>. International Press. <a href=\"https://doi.org/10.4310/mrl.2016.v23.n2.a8\">https://doi.org/10.4310/mrl.2016.v23.n2.a8</a>","ieee":"R. Killip and M. Vişan, “Scale-invariant Strichartz estimates on tori and applications,” <i>Mathematical Research Letters</i>, vol. 23, no. 2. International Press, pp. 445–472, 2016."},"doi":"10.4310/mrl.2016.v23.n2.a8","language":[{"iso":"eng"}],"volume":23,"publication_identifier":{"eissn":["1945-001X"],"issn":["1073-2780"]},"date_updated":"2026-06-30T10:59:10Z","abstract":[{"text":"We prove scale-invariant Strichartz inequalities for the Schrödinger equation on rectangular tori (rational or irrational) in all dimensions. We use these estimates to give a simpler treatment of local well-posedness of the energy-critical nonlinear Schrödinger equation in dimensions three and four.","lang":"eng"}],"_id":"22073","day":"06","publisher":"International Press","date_created":"2026-06-19T08:22:27Z","oa":1,"article_processing_charge":"No","status":"public","scopus_import":"1","type":"journal_article","das_tickbox":"1","date_published":"2016-06-06T00:00:00Z","publication":"Mathematical Research Letters","OA_place":"repository","title":"Scale-invariant Strichartz estimates on tori and applications","OA_type":"green","arxiv":1,"author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica","last_name":"Visan"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1409.3603 ","open_access":"1"}],"external_id":{"arxiv":["1409.3603"]},"intvolume":"        23","publication_status":"published","page":"445-472","oa_version":"Preprint","article_type":"original","quality_controlled":"1","year":"2016","extern":"1","month":"06","issue":"2","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"title":"Localization for transversally periodic random potentials on binary trees","das_tickbox":"1","date_published":"2016-01-01T00:00:00Z","publication":"Journal of Spectral Theory","scopus_import":"1","type":"journal_article","article_processing_charge":"No","status":"public","_id":"1223","publisher":"EMS Press","day":"01","oa":1,"date_created":"2018-12-11T11:50:48Z","date_updated":"2026-07-06T11:55:04Z","abstract":[{"text":"We consider a random Schrödinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, Qr, and a random transversally periodic potential, κQt, with coupling constant κ. Using a new one-dimensional dynamical systems approach combined with Jensen's inequality in hyperbolic space (our key estimate) we obtain a fractional moment estimate proving localization for small and large κ. Together with a previous result we therefore obtain a model with two Anderson transitions, from localization to delocalization and back to localization, when increasing κ. As a by-product we also have a partially new proof of one-dimensional Anderson localization at any disorder.","lang":"eng"}],"citation":{"ieee":"R. Froese, D. Lee, C. Sadel, W. Spitzer, and G. Stolz, “Localization for transversally periodic random potentials on binary trees,” <i>Journal of Spectral Theory</i>, vol. 6, no. 3. EMS Press, pp. 557–600, 2016.","chicago":"Froese, Richard, Darrick Lee, Christian Sadel, Wolfgang Spitzer, and Günter Stolz. “Localization for Transversally Periodic Random Potentials on Binary Trees.” <i>Journal of Spectral Theory</i>. EMS Press, 2016. <a href=\"https://doi.org/10.4171/JST/132\">https://doi.org/10.4171/JST/132</a>.","apa":"Froese, R., Lee, D., Sadel, C., Spitzer, W., &#38; Stolz, G. (2016). Localization for transversally periodic random potentials on binary trees. <i>Journal of Spectral Theory</i>. EMS Press. <a href=\"https://doi.org/10.4171/JST/132\">https://doi.org/10.4171/JST/132</a>","ama":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. Localization for transversally periodic random potentials on binary trees. <i>Journal of Spectral Theory</i>. 2016;6(3):557-600. doi:<a href=\"https://doi.org/10.4171/JST/132\">10.4171/JST/132</a>","ista":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. 2016. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 6(3), 557–600.","short":"R. Froese, D. Lee, C. Sadel, W. Spitzer, G. Stolz, Journal of Spectral Theory 6 (2016) 557–600.","mla":"Froese, Richard, et al. “Localization for Transversally Periodic Random Potentials on Binary Trees.” <i>Journal of Spectral Theory</i>, vol. 6, no. 3, EMS Press, 2016, pp. 557–600, doi:<a href=\"https://doi.org/10.4171/JST/132\">10.4171/JST/132</a>."},"doi":"10.4171/JST/132","volume":6,"language":[{"iso":"eng"}],"month":"01","issue":"3","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"6112","quality_controlled":"1","year":"2016","isi":1,"department":[{"_id":"LaEr"}],"oa_version":"Preprint","publication_status":"published","page":"557 - 600","intvolume":"         6","arxiv":1,"author":[{"first_name":"Richard","full_name":"Froese, Richard","last_name":"Froese"},{"last_name":"Lee","full_name":"Lee, Darrick","first_name":"Darrick"},{"last_name":"Sadel","orcid":"0000-0001-8255-3968","full_name":"Sadel, Christian","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","first_name":"Christian"},{"first_name":"Wolfgang","full_name":"Spitzer, Wolfgang","last_name":"Spitzer"},{"full_name":"Stolz, Günter","first_name":"Günter","last_name":"Stolz"}],"main_file_link":[{"url":"https://arxiv.org/abs/1408.3961","open_access":"1"}],"external_id":{"arxiv":["1408.3961"],"isi":["000388627000004"]}},{"date_updated":"2026-07-06T14:00:20Z","abstract":[{"text":"The increasing complexity of dynamic models in systems and synthetic biology poses computational challenges especially for the identification of model parameters. While modularization of the corresponding optimization problems could help reduce the “curse of dimensionality,” abundant feedback and crosstalk mechanisms prohibit a simple decomposition of most biomolecular networks into subnetworks, or modules. Drawing on ideas from network modularization and multiple-shooting optimization, we present here a modular parameter identification approach that explicitly allows for such interdependencies. Interfaces between our modules are given by the experimentally measured molecular species. This definition allows deriving good (initial) estimates for the inter-module communication directly from the experimental data. Given these estimates, the states and parameter sensitivities of different modules can be integrated independently. To achieve consistency between modules, we iteratively adjust the estimates for inter-module communication while optimizing the parameters. After convergence to an optimal parameter set---but not during earlier iterations---the intermodule communication as well as the individual modules\\' state dynamics agree with the dynamics of the nonmodularized network. Our modular parameter identification approach allows for easy parallelization; it can reduce the computational complexity for larger networks and decrease the probability to converge to suboptimal local minima. We demonstrate the algorithm\\'s performance in parameter estimation for two biomolecular networks, a synthetic genetic oscillator and a mammalian signaling pathway.","lang":"eng"}],"citation":{"ista":"Lang M, Stelling J. 2016. Modular parameter identification of biomolecular networks. SIAM Journal on Scientific Computing. 38(6), B988–B1008.","ama":"Lang M, Stelling J. Modular parameter identification of biomolecular networks. <i>SIAM Journal on Scientific Computing</i>. 2016;38(6):B988-B1008. doi:<a href=\"https://doi.org/10.1137/15M103306X\">10.1137/15M103306X</a>","apa":"Lang, M., &#38; Stelling, J. (2016). Modular parameter identification of biomolecular networks. <i>SIAM Journal on Scientific Computing</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/15M103306X\">https://doi.org/10.1137/15M103306X</a>","chicago":"Lang, Moritz, and Jörg Stelling. “Modular Parameter Identification of Biomolecular Networks.” <i>SIAM Journal on Scientific Computing</i>. Society for Industrial and Applied Mathematics, 2016. <a href=\"https://doi.org/10.1137/15M103306X\">https://doi.org/10.1137/15M103306X</a>.","ieee":"M. Lang and J. Stelling, “Modular parameter identification of biomolecular networks,” <i>SIAM Journal on Scientific Computing</i>, vol. 38, no. 6. Society for Industrial and Applied Mathematics, pp. B988–B1008, 2016.","mla":"Lang, Moritz, and Jörg Stelling. “Modular Parameter Identification of Biomolecular Networks.” <i>SIAM Journal on Scientific Computing</i>, vol. 38, no. 6, Society for Industrial and Applied Mathematics, 2016, pp. B988–1008, doi:<a href=\"https://doi.org/10.1137/15M103306X\">10.1137/15M103306X</a>.","short":"M. Lang, J. Stelling, SIAM Journal on Scientific Computing 38 (2016) B988–B1008."},"file_date_updated":"2025-06-25T11:26:45Z","doi":"10.1137/15M103306X","language":[{"iso":"eng"}],"volume":38,"article_processing_charge":"No","status":"public","_id":"1170","publisher":"Society for Industrial and Applied Mathematics","day":"15","oa":1,"date_created":"2018-12-11T11:50:31Z","corr_author":"1","das_tickbox":"1","date_published":"2016-11-15T00:00:00Z","publication":"SIAM Journal on Scientific Computing","scopus_import":"1","type":"journal_article","pubrep_id":"811","OA_type":"green","OA_place":"repository","ddc":["003","518","570","621"],"has_accepted_license":"1","title":"Modular parameter identification of biomolecular networks","intvolume":"        38","author":[{"id":"29E0800A-F248-11E8-B48F-1D18A9856A87","first_name":"Moritz","full_name":"Lang, Moritz","last_name":"Lang"},{"last_name":"Stelling","first_name":"Jörg","full_name":"Stelling, Jörg"}],"external_id":{"isi":["000391853100010"]},"oa_version":"Submitted Version","file":[{"date_created":"2018-12-12T10:14:41Z","file_name":"IST-2017-811-v1+1_modular_parameter_identification.pdf","checksum":"781bc3ffd30b2dd65b7727c5a285fc78","creator":"system","file_id":"5095","access_level":"open_access","relation":"main_file","file_size":871964,"date_updated":"2025-06-25T11:26:45Z","content_type":"application/pdf"}],"publication_status":"published","page":"B988 - B1008","article_type":"original","isi":1,"department":[{"_id":"CaGu"},{"_id":"GaTk"}],"month":"11","issue":"6","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publist_id":"6186","year":"2016"},{"type":"journal_article","scopus_import":"1","publication":"SIAM Journal on Imaging Sciences","ec_funded":1,"date_published":"2016-05-03T00:00:00Z","das_tickbox":"1","title":"Total variation on a tree","volume":9,"language":[{"iso":"eng"}],"citation":{"mla":"Kolmogorov, Vladimir, et al. “Total Variation on a Tree.” <i>SIAM Journal on Imaging Sciences</i>, vol. 9, no. 2, Society for Industrial and Applied Mathematics, 2016, pp. 605–36, doi:<a href=\"https://doi.org/10.1137/15M1010257\">10.1137/15M1010257</a>.","short":"V. Kolmogorov, T. Pock, M. Rolinek, SIAM Journal on Imaging Sciences 9 (2016) 605–636.","ama":"Kolmogorov V, Pock T, Rolinek M. Total variation on a tree. <i>SIAM Journal on Imaging Sciences</i>. 2016;9(2):605-636. doi:<a href=\"https://doi.org/10.1137/15M1010257\">10.1137/15M1010257</a>","ista":"Kolmogorov V, Pock T, Rolinek M. 2016. Total variation on a tree. SIAM Journal on Imaging Sciences. 9(2), 605–636.","chicago":"Kolmogorov, Vladimir, Thomas Pock, and Michal Rolinek. “Total Variation on a Tree.” <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial and Applied Mathematics, 2016. <a href=\"https://doi.org/10.1137/15M1010257\">https://doi.org/10.1137/15M1010257</a>.","apa":"Kolmogorov, V., Pock, T., &#38; Rolinek, M. (2016). Total variation on a tree. <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/15M1010257\">https://doi.org/10.1137/15M1010257</a>","ieee":"V. Kolmogorov, T. Pock, and M. Rolinek, “Total variation on a tree,” <i>SIAM Journal on Imaging Sciences</i>, vol. 9, no. 2. Society for Industrial and Applied Mathematics, pp. 605–636, 2016."},"doi":"10.1137/15M1010257","abstract":[{"text":"We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the nonconvex case and derive worst-case complexities that are equal to or better than existing methods. We show applications to total variation based two dimensional image processing and computer vision problems based on a Lagrangian decomposition approach. The resulting algorithms are very effcient, offer a high degree of parallelism, and come along with memory requirements which are only in the order of the number of image pixels.","lang":"eng"}],"date_updated":"2026-07-06T13:59:54Z","date_created":"2018-12-11T11:51:40Z","oa":1,"publisher":"Society for Industrial and Applied Mathematics","day":"03","_id":"1377","status":"public","article_processing_charge":"No","department":[{"_id":"VlKo"}],"isi":1,"year":"2016","publist_id":"5834","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","month":"05","external_id":{"isi":["000385275400005"],"arxiv":["1502.07770"]},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1502.07770"}],"author":[{"full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov"},{"full_name":"Pock, Thomas","first_name":"Thomas","last_name":"Pock"},{"first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","full_name":"Rolinek, Michal","last_name":"Rolinek"}],"arxiv":1,"intvolume":"         9","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7"}],"page":"605 - 636","publication_status":"published","oa_version":"Preprint"},{"publication_status":"published","page":"712 - 721","oa_version":"Published Version","file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:44:42Z","checksum":"c746f3a48edb62b588d92ea5d0fd2c0e","file_name":"IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf","date_created":"2018-12-12T10:16:20Z","relation":"main_file","file_size":1678369,"file_id":"5206","access_level":"open_access","creator":"system"}],"author":[{"last_name":"Held","full_name":"Held, Martin","first_name":"Martin"},{"last_name":"Huber","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"intvolume":"        13","quality_controlled":"1","publist_id":"6048","year":"2016","month":"09","issue":"5","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"_id":"1272","publisher":"Taylor & Francis","day":"02","date_created":"2018-12-11T11:51:04Z","oa":1,"article_processing_charge":"No","status":"public","acknowledgement":"This work was supported by Austrian Science Fund (FWF): P25816-N15.","file_date_updated":"2020-07-14T12:44:42Z","doi":"10.1080/16864360.2016.1150718","citation":{"mla":"Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” <i>Computer-Aided Design and Applications</i>, vol. 13, no. 5, Taylor &#38; Francis, 2016, pp. 712–21, doi:<a href=\"https://doi.org/10.1080/16864360.2016.1150718\">10.1080/16864360.2016.1150718</a>.","short":"M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721.","ista":"Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.","ama":"Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using skeletons. <i>Computer-Aided Design and Applications</i>. 2016;13(5):712-721. doi:<a href=\"https://doi.org/10.1080/16864360.2016.1150718\">10.1080/16864360.2016.1150718</a>","chicago":"Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” <i>Computer-Aided Design and Applications</i>. Taylor &#38; Francis, 2016. <a href=\"https://doi.org/10.1080/16864360.2016.1150718\">https://doi.org/10.1080/16864360.2016.1150718</a>.","apa":"Held, M., Huber, S., &#38; Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. <i>Computer-Aided Design and Applications</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/16864360.2016.1150718\">https://doi.org/10.1080/16864360.2016.1150718</a>","ieee":"M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” <i>Computer-Aided Design and Applications</i>, vol. 13, no. 5. Taylor &#38; Francis, pp. 712–721, 2016."},"volume":13,"language":[{"iso":"eng"}],"date_updated":"2026-07-07T05:34:31Z","abstract":[{"lang":"eng","text":"We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams."}],"ddc":["004","516"],"has_accepted_license":"1","title":"Generalized offsetting of planar structures using skeletons","pubrep_id":"694","scopus_import":"1","type":"journal_article","das_tickbox":"1","date_published":"2016-09-02T00:00:00Z","publication":"Computer-Aided Design and Applications"}]