[{"status":"public","article_processing_charge":"No","day":"01","publisher":"Springer Nature","_id":"18360","oa":1,"date_created":"2024-10-15T11:20:54Z","publication_identifier":{"issn":["0920-5691"],"eissn":["1573-1405"]},"abstract":[{"lang":"eng","text":"Many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space. The embedding process usually relies on distances between neighboring features, mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non-convexity. Distortions resulting from using long geodesics indiscriminately lead to a known limitation of the Isomap algorithm when used to map non-convex manifolds. Presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries. The resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold, thus avoiding an inherent limitation of the Isomap algorithm. Since the proposed algorithm matches non-local structures, it is robust to strong noise. We show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques, both global and local in nature."}],"date_updated":"2024-11-12T08:25:56Z","doi":"10.1007/s11263-010-0322-1","citation":{"short":"G. Rosman, M.M. Bronstein, A.M. Bronstein, R. Kimmel, International Journal of Computer Vision 89 (2010) 56–68.","mla":"Rosman, Guy, et al. “Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding.” <i>International Journal of Computer Vision</i>, vol. 89, Springer Nature, 2010, pp. 56–68, doi:<a href=\"https://doi.org/10.1007/s11263-010-0322-1\">10.1007/s11263-010-0322-1</a>.","ieee":"G. Rosman, M. M. Bronstein, A. M. Bronstein, and R. Kimmel, “Nonlinear dimensionality reduction by topologically constrained isometric embedding,” <i>International Journal of Computer Vision</i>, vol. 89. Springer Nature, pp. 56–68, 2010.","chicago":"Rosman, Guy, Michael M. Bronstein, Alex M. Bronstein, and Ron Kimmel. “Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding.” <i>International Journal of Computer Vision</i>. Springer Nature, 2010. <a href=\"https://doi.org/10.1007/s11263-010-0322-1\">https://doi.org/10.1007/s11263-010-0322-1</a>.","apa":"Rosman, G., Bronstein, M. M., Bronstein, A. M., &#38; Kimmel, R. (2010). Nonlinear dimensionality reduction by topologically constrained isometric embedding. <i>International Journal of Computer Vision</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11263-010-0322-1\">https://doi.org/10.1007/s11263-010-0322-1</a>","ista":"Rosman G, Bronstein MM, Bronstein AM, Kimmel R. 2010. Nonlinear dimensionality reduction by topologically constrained isometric embedding. International Journal of Computer Vision. 89, 56–68.","ama":"Rosman G, Bronstein MM, Bronstein AM, Kimmel R. Nonlinear dimensionality reduction by topologically constrained isometric embedding. <i>International Journal of Computer Vision</i>. 2010;89:56-68. doi:<a href=\"https://doi.org/10.1007/s11263-010-0322-1\">10.1007/s11263-010-0322-1</a>"},"volume":89,"language":[{"iso":"eng"}],"OA_type":"free access","OA_place":"publisher","title":"Nonlinear dimensionality reduction by topologically constrained isometric embedding","date_published":"2010-08-01T00:00:00Z","publication":"International Journal of Computer Vision","scopus_import":"1","type":"journal_article","oa_version":"Published Version","publication_status":"published","page":"56-68","intvolume":"        89","author":[{"last_name":"Rosman","full_name":"Rosman, Guy","first_name":"Guy"},{"first_name":"Michael M.","full_name":"Bronstein, Michael M.","last_name":"Bronstein"},{"last_name":"Bronstein","orcid":"0000-0001-9699-8730","full_name":"Bronstein, Alexander","first_name":"Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6"},{"first_name":"Ron","full_name":"Kimmel, Ron","last_name":"Kimmel"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s11263-010-0322-1"}],"month":"08","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","year":"2010","article_type":"original"},{"year":"2010","title":"Data fusion through cross-modality metric learning using similarity-sensitive hashing","quality_controlled":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","month":"08","type":"conference","scopus_import":"1","conference":{"end_date":"2010-06-18","name":"2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition","start_date":"2010-06-13","location":"San Francisco, CA, USA"},"publication":"2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition","date_published":"2010-08-05T00:00:00Z","date_created":"2024-10-15T11:20:54Z","page":"3594 - 3601","_id":"18376","publication_status":"published","publisher":"IEEE","day":"05","article_processing_charge":"No","status":"public","oa_version":"None","language":[{"iso":"eng"}],"doi":"10.1109/cvpr.2010.5539928","citation":{"mla":"Bronstein, Michael M., et al. “Data Fusion through Cross-Modality Metric Learning Using Similarity-Sensitive Hashing.” <i>2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i>, IEEE, 2010, pp. 3594–601, doi:<a href=\"https://doi.org/10.1109/cvpr.2010.5539928\">10.1109/cvpr.2010.5539928</a>.","short":"M.M. Bronstein, A.M. Bronstein, F. Michel, N. Paragios, in:, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, 2010, pp. 3594–3601.","ista":"Bronstein MM, Bronstein AM, Michel F, Paragios N. 2010. Data fusion through cross-modality metric learning using similarity-sensitive hashing. 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 3594–3601.","ama":"Bronstein MM, Bronstein AM, Michel F, Paragios N. Data fusion through cross-modality metric learning using similarity-sensitive hashing. In: <i>2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i>. IEEE; 2010:3594-3601. doi:<a href=\"https://doi.org/10.1109/cvpr.2010.5539928\">10.1109/cvpr.2010.5539928</a>","chicago":"Bronstein, Michael M., Alex M. Bronstein, Fabrice Michel, and Nikos Paragios. “Data Fusion through Cross-Modality Metric Learning Using Similarity-Sensitive Hashing.” In <i>2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i>, 3594–3601. IEEE, 2010. <a href=\"https://doi.org/10.1109/cvpr.2010.5539928\">https://doi.org/10.1109/cvpr.2010.5539928</a>.","apa":"Bronstein, M. M., Bronstein, A. M., Michel, F., &#38; Paragios, N. (2010). Data fusion through cross-modality metric learning using similarity-sensitive hashing. In <i>2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i> (pp. 3594–3601). San Francisco, CA, USA: IEEE. <a href=\"https://doi.org/10.1109/cvpr.2010.5539928\">https://doi.org/10.1109/cvpr.2010.5539928</a>","ieee":"M. M. Bronstein, A. M. Bronstein, F. Michel, and N. Paragios, “Data fusion through cross-modality metric learning using similarity-sensitive hashing,” in <i>2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition</i>, San Francisco, CA, USA, 2010, pp. 3594–3601."},"author":[{"last_name":"Bronstein","full_name":"Bronstein, Michael M.","first_name":"Michael M."},{"full_name":"Bronstein, Alexander","first_name":"Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","orcid":"0000-0001-9699-8730","last_name":"Bronstein"},{"last_name":"Michel","first_name":"Fabrice","full_name":"Michel, Fabrice"},{"full_name":"Paragios, Nikos","first_name":"Nikos","last_name":"Paragios"}],"date_updated":"2024-12-02T14:00:22Z","abstract":[{"lang":"eng","text":"Visual understanding is often based on measuring similarity between observations. Learning similarities specific to a certain perception task from a set of examples has been shown advantageous in various computer vision and pattern recognition problems. In many important applications, the data that one needs to compare come from different representations or modalities, and the similarity between such data operates on objects that may have different and often incommensurable structure and dimensionality. In this paper, we propose a framework for supervised similarity learning based on embedding the input data from two arbitrary spaces into the Hamming space. The mapping is expressed as a binary classification problem with positive and negative examples, and can be efficiently learned using boosting algorithms. The utility and efficiency of such a generic approach is demonstrated on several challenging applications including cross-representation shape retrieval and alignment of multi-modal medical images."}],"publication_identifier":{"issn":["1063-6919 "]}},{"publication":"Proceedings of the ACM workshop on 3D object retrieval","conference":{"name":"ACM Workshop on 3D Object Retrieval","start_date":"2010-10-25","location":"Firenze, Italy","end_date":"2010-10-25"},"date_published":"2010-10-25T00:00:00Z","type":"conference","scopus_import":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"10","extern":"1","title":"Volumetric heat kernel signatures","year":"2010","quality_controlled":"1","abstract":[{"lang":"eng","text":"Invariant shape descriptors are instrumental in numerous shape analysis tasks including deformable shape comparison, registration, classification, and retrieval. Most existing constructions model a 3D shape as a two-dimensional surface describing the shape boundary, typically represented as a triangular mesh or a point cloud. Using intrinsic properties of the surface, invariant descriptors can be designed. One such example is the recently introduced heat kernel signature, based on the Laplace-Beltrami operator of the surface. In many applications, however, a volumetric shape model is more natural and convenient. Moreover, modeling shape deformations as approximate isometries of the volume of an object, rather than its boundary, better captures natural behavior of non-rigid deformations in many cases. Here, we extend the idea of heat kernel signature to robust isometry-invariant volumetric descriptors, and show their utility in shape retrieval. The proposed approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark."}],"date_updated":"2024-12-19T09:27:03Z","publication_identifier":{"isbn":["9781450301602"]},"language":[{"iso":"eng"}],"author":[{"last_name":"Raviv","first_name":"Dan","full_name":"Raviv, Dan"},{"last_name":"Bronstein","first_name":"Michael M.","full_name":"Bronstein, Michael M."},{"full_name":"Bronstein, Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","first_name":"Alexander","orcid":"0000-0001-9699-8730","last_name":"Bronstein"},{"first_name":"Ron","full_name":"Kimmel, Ron","last_name":"Kimmel"}],"citation":{"mla":"Raviv, Dan, et al. “Volumetric Heat Kernel Signatures.” <i>Proceedings of the ACM Workshop on 3D Object Retrieval</i>, ACM, 2010, pp. 39–44, doi:<a href=\"https://doi.org/10.1145/1877808.1877817\">10.1145/1877808.1877817</a>.","short":"D. Raviv, M.M. Bronstein, A.M. Bronstein, R. Kimmel, in:, Proceedings of the ACM Workshop on 3D Object Retrieval, ACM, 2010, pp. 39–44.","ista":"Raviv D, Bronstein MM, Bronstein AM, Kimmel R. 2010. Volumetric heat kernel signatures. Proceedings of the ACM workshop on 3D object retrieval. ACM Workshop on 3D Object Retrieval, 39–44.","ama":"Raviv D, Bronstein MM, Bronstein AM, Kimmel R. Volumetric heat kernel signatures. In: <i>Proceedings of the ACM Workshop on 3D Object Retrieval</i>. ACM; 2010:39-44. doi:<a href=\"https://doi.org/10.1145/1877808.1877817\">10.1145/1877808.1877817</a>","chicago":"Raviv, Dan, Michael M. Bronstein, Alex M. Bronstein, and Ron Kimmel. “Volumetric Heat Kernel Signatures.” In <i>Proceedings of the ACM Workshop on 3D Object Retrieval</i>, 39–44. ACM, 2010. <a href=\"https://doi.org/10.1145/1877808.1877817\">https://doi.org/10.1145/1877808.1877817</a>.","apa":"Raviv, D., Bronstein, M. M., Bronstein, A. M., &#38; Kimmel, R. (2010). Volumetric heat kernel signatures. In <i>Proceedings of the ACM workshop on 3D object retrieval</i> (pp. 39–44). Firenze, Italy: ACM. <a href=\"https://doi.org/10.1145/1877808.1877817\">https://doi.org/10.1145/1877808.1877817</a>","ieee":"D. Raviv, M. M. Bronstein, A. M. Bronstein, and R. Kimmel, “Volumetric heat kernel signatures,” in <i>Proceedings of the ACM workshop on 3D object retrieval</i>, Firenze, Italy, 2010, pp. 39–44."},"doi":"10.1145/1877808.1877817","status":"public","article_processing_charge":"No","oa_version":"None","page":"39 - 44","date_created":"2024-10-15T11:20:55Z","publication_status":"published","publisher":"ACM","day":"25","_id":"18432"},{"oa_version":"Preprint","page":"945-987","publication_status":"published","intvolume":"        35","external_id":{"arxiv":["0812.2084"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.0812.2084","open_access":"1"}],"author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"}],"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"6","month":"06","keyword":["critical regularity","Nonlinear Schrödinger equations"],"extern":"1","year":"2010","quality_controlled":"1","article_type":"original","status":"public","article_processing_charge":"No","date_created":"2026-06-19T07:41:22Z","oa":1,"publisher":"Informa UK Limited","day":"01","_id":"22029","abstract":[{"lang":"eng","text":"We consider two classes of defocusing energy-supercritical nonlinear Schrödinger equations in dimensions d ≥ 5. We prove that if the solution u is a priori bounded in the critical Sobolev space, that is, {mathematical formular} , then u is global and scatters."}],"date_updated":"2026-06-29T06:32:07Z","publication_identifier":{"issn":["0360-5302"],"eissn":["1532-4133"]},"volume":35,"language":[{"iso":"eng"}],"citation":{"mla":"Killip, Rowan, and Monica Vişan. “Energy-Supercritical NLS: Critical [Hdot]^s-Bounds Imply Scattering.” <i>Communications in Partial Differential Equations</i>, vol. 35, no. 6, Informa UK Limited, 2010, pp. 945–87, doi:<a href=\"https://doi.org/10.1080/03605301003717084\">10.1080/03605301003717084</a>.","short":"R. Killip, M. Vişan, Communications in Partial Differential Equations 35 (2010) 945–987.","ama":"Killip R, Vişan M. Energy-supercritical NLS: Critical [Hdot]^s-bounds imply scattering. <i>Communications in Partial Differential Equations</i>. 2010;35(6):945-987. doi:<a href=\"https://doi.org/10.1080/03605301003717084\">10.1080/03605301003717084</a>","ista":"Killip R, Vişan M. 2010. Energy-supercritical NLS: Critical [Hdot]^s-bounds imply scattering. Communications in Partial Differential Equations. 35(6), 945–987.","apa":"Killip, R., &#38; Vişan, M. (2010). Energy-supercritical NLS: Critical [Hdot]^s-bounds imply scattering. <i>Communications in Partial Differential Equations</i>. Informa UK Limited. <a href=\"https://doi.org/10.1080/03605301003717084\">https://doi.org/10.1080/03605301003717084</a>","chicago":"Killip, Rowan, and Monica Vişan. “Energy-Supercritical NLS: Critical [Hdot]^s-Bounds Imply Scattering.” <i>Communications in Partial Differential Equations</i>. Informa UK Limited, 2010. <a href=\"https://doi.org/10.1080/03605301003717084\">https://doi.org/10.1080/03605301003717084</a>.","ieee":"R. Killip and M. Vişan, “Energy-supercritical NLS: Critical [Hdot]^s-bounds imply scattering,” <i>Communications in Partial Differential Equations</i>, vol. 35, no. 6. Informa UK Limited, pp. 945–987, 2010."},"doi":"10.1080/03605301003717084","OA_type":"green","title":"Energy-supercritical NLS: Critical [Hdot]^s-bounds imply scattering","OA_place":"repository","publication":"Communications in Partial Differential Equations","date_published":"2010-06-01T00:00:00Z","type":"journal_article","scopus_import":"1"},{"external_id":{"arxiv":["0804.1018"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.0804.1018"}],"author":[{"first_name":"Rowan","full_name":"Killip, Rowan","last_name":"Killip"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica","full_name":"Visan, Monica","last_name":"Visan"}],"arxiv":1,"intvolume":"       132","page":"361-424","publication_status":"published","oa_version":"Preprint","article_type":"original","year":"2010","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","month":"04","extern":"1","volume":132,"language":[{"iso":"eng"}],"doi":"10.1353/ajm.0.0107","citation":{"short":"R. Killip, M. Vişan, American Journal of Mathematics 132 (2010) 361–424.","mla":"Killip, Rowan, and Monica Vişan. “The Focusing Energy-Critical Nonlinear Schrödinger Equation in Dimensions Five and Higher.” <i>American Journal of Mathematics</i>, vol. 132, no. 2, Johns Hopkins University Press, 2010, pp. 361–424, doi:<a href=\"https://doi.org/10.1353/ajm.0.0107\">10.1353/ajm.0.0107</a>.","ieee":"R. Killip and M. Vişan, “The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher,” <i>American Journal of Mathematics</i>, vol. 132, no. 2. Johns Hopkins University Press, pp. 361–424, 2010.","chicago":"Killip, Rowan, and Monica Vişan. “The Focusing Energy-Critical Nonlinear Schrödinger Equation in Dimensions Five and Higher.” <i>American Journal of Mathematics</i>. Johns Hopkins University Press, 2010. <a href=\"https://doi.org/10.1353/ajm.0.0107\">https://doi.org/10.1353/ajm.0.0107</a>.","apa":"Killip, R., &#38; Vişan, M. (2010). The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher. <i>American Journal of Mathematics</i>. Johns Hopkins University Press. <a href=\"https://doi.org/10.1353/ajm.0.0107\">https://doi.org/10.1353/ajm.0.0107</a>","ista":"Killip R, Vişan M. 2010. The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher. American Journal of Mathematics. 132(2), 361–424.","ama":"Killip R, Vişan M. The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher. <i>American Journal of Mathematics</i>. 2010;132(2):361-424. doi:<a href=\"https://doi.org/10.1353/ajm.0.0107\">10.1353/ajm.0.0107</a>"},"abstract":[{"lang":"eng","text":"We consider the focusing energy-critical nonlinear Schr\\\"odinger equation \r\n$iu_t+\\Delta u = - |u|^{4\\over{d-2}}u$ in dimensions $d\\geq 5$. We prove \r\nthat if a maximal-lifespan solution $u\\colon \\ I\\times {\\Bbb R}^d\\to {\\Bbb C}$ obeys $\\sup_{t\\in I}\\|\\nabla u(t)\\|_2&lt;\\|\\nabla W\\|_2$, then it is \r\nglobal and scatters both forward and backward in time. Here $W$ denotes \r\nthe ground state, which is a stationary solution of the equation. In \r\nparticular, if a solution has both energy and kinetic energy less than \r\nthose of the ground state $W$ at some point in time, then the solution is \r\nglobal and scatters. We also show that any solution that blows up with \r\nbounded kinetic energy must concentrate at least the kinetic energy of the \r\nground state. Similar results were obtained by Kenig and Merle for \r\nspherically symmetric initial data and dimensions $d=3,4,5$.\r\n</jats:p>"}],"date_updated":"2026-07-01T12:52:05Z","publication_identifier":{"eissn":["1080-6377"]},"date_created":"2026-06-19T08:48:46Z","oa":1,"day":"01","publisher":"Johns Hopkins University Press","_id":"22089","status":"public","article_processing_charge":"No","type":"journal_article","scopus_import":"1","publication":"American Journal of Mathematics","date_published":"2010-04-01T00:00:00Z","das_tickbox":"1","title":"The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher","OA_place":"repository","OA_type":"green"},{"ddc":["000","004"],"has_accepted_license":"1","title":"Expressiveness and closure properties for quantitative languages","pubrep_id":"504","scopus_import":"1","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"4540"}]},"type":"journal_article","date_published":"2010-08-30T00:00:00Z","das_tickbox":"1","publication":"Logical Methods in Computer Science","ec_funded":1,"day":"30","publisher":"International Federation for Computational Logic","_id":"3867","corr_author":"1","oa":1,"license":"https://creativecommons.org/licenses/by-nd/4.0/","date_created":"2018-12-11T12:05:36Z","status":"public","article_processing_charge":"No","citation":{"mla":"Chatterjee, Krishnendu, et al. “Expressiveness and Closure Properties for Quantitative Languages.” <i>Logical Methods in Computer Science</i>, vol. 6, no. 3, International Federation for Computational Logic, 2010, pp. 1–23, doi:<a href=\"https://doi.org/10.2168/LMCS-6(3:10)2010\">10.2168/LMCS-6(3:10)2010</a>.","short":"K. Chatterjee, L. Doyen, T.A. Henzinger, Logical Methods in Computer Science 6 (2010) 1–23.","ama":"Chatterjee K, Doyen L, Henzinger TA. Expressiveness and closure properties for quantitative languages. <i>Logical Methods in Computer Science</i>. 2010;6(3):1-23. doi:<a href=\"https://doi.org/10.2168/LMCS-6(3:10)2010\">10.2168/LMCS-6(3:10)2010</a>","ista":"Chatterjee K, Doyen L, Henzinger TA. 2010. Expressiveness and closure properties for quantitative languages. Logical Methods in Computer Science. 6(3), 1–23.","apa":"Chatterjee, K., Doyen, L., &#38; Henzinger, T. A. (2010). Expressiveness and closure properties for quantitative languages. <i>Logical Methods in Computer Science</i>. International Federation for Computational Logic. <a href=\"https://doi.org/10.2168/LMCS-6(3:10)2010\">https://doi.org/10.2168/LMCS-6(3:10)2010</a>","chicago":"Chatterjee, Krishnendu, Laurent Doyen, and Thomas A Henzinger. “Expressiveness and Closure Properties for Quantitative Languages.” <i>Logical Methods in Computer Science</i>. International Federation for Computational Logic, 2010. <a href=\"https://doi.org/10.2168/LMCS-6(3:10)2010\">https://doi.org/10.2168/LMCS-6(3:10)2010</a>.","ieee":"K. Chatterjee, L. Doyen, and T. A. Henzinger, “Expressiveness and closure properties for quantitative languages,” <i>Logical Methods in Computer Science</i>, vol. 6, no. 3. International Federation for Computational Logic, pp. 1–23, 2010."},"file_date_updated":"2020-07-14T12:46:19Z","doi":"10.2168/LMCS-6(3:10)2010","volume":6,"language":[{"iso":"eng"}],"abstract":[{"text":"Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit-average, or discounted-sum of the transition weights. The value of a word w is the supremum of the values of the runs over w. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the omega-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the discounted-sum case. Third, for quantitative languages L-1 and L-2, we consider the operations max(L-1, L-2), min(L-1, L-2), and 1 - L-1, which generalize the boolean operations on languages, as well as the sum L-1 + L-2. We establish the closure properties of all classes of quantitative languages with respect to these four operations.","lang":"eng"}],"date_updated":"2026-07-06T13:24:40Z","publist_id":"2311","quality_controlled":"1","year":"2010","month":"08","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"isi":1,"publication_status":"published","page":"1 - 23","oa_version":"Published Version","file":[{"file_size":216598,"relation":"main_file","file_id":"5312","access_level":"open_access","creator":"system","checksum":"0243da726476817f2ea33b48b78be696","file_name":"IST-2012-55-v1+1_Expressiveness_Closure_Properties_Quantitative_Languages.pdf","date_created":"2018-12-12T10:17:54Z","content_type":"application/pdf","date_updated":"2020-07-14T12:46:19Z"},{"content_type":"application/pdf","date_updated":"2020-07-14T12:46:19Z","file_size":302416,"relation":"main_file","file_id":"5313","access_level":"open_access","creator":"system","checksum":"5e512b8503a9cb263de26331c4ee9cf2","file_name":"IST-2016-55-v2+1_1007.4018.pdf","date_created":"2018-12-12T10:17:55Z"}],"author":[{"last_name":"Chatterjee","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu"},{"first_name":"Laurent","full_name":"Doyen, Laurent","last_name":"Doyen"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","full_name":"Henzinger, Thomas A","last_name":"Henzinger","orcid":"0000−0002−2985−7724"}],"external_id":{"isi":["000282653500010"]},"project":[{"name":"Design for Embedded Systems","_id":"25F1337C-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"214373"},{"name":"COMponent-Based Embedded Systems design Techniques","_id":"25EFB36C-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"215543"}],"intvolume":"         6"},{"intvolume":"         6","author":[{"full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X"},{"full_name":"De Alfaro, Luca","first_name":"Luca","last_name":"De Alfaro"},{"first_name":"Ritankar","full_name":"Majumdar, Ritankar","last_name":"Majumdar"},{"last_name":"Raman","full_name":"Raman, Vishwanath","first_name":"Vishwanath"}],"external_id":{"isi":["000282653500013"]},"oa_version":"Published Version","file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:46:19Z","date_created":"2018-12-12T10:08:11Z","checksum":"a18988135fef3016c93808ecb15b55f5","file_name":"IST-2015-370-v1+1_0809.4326.pdf","file_size":346527,"relation":"main_file","creator":"system","access_level":"open_access","file_id":"4671"}],"publication_status":"published","page":"1 - 27","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)"},"isi":1,"department":[{"_id":"KrCh"}],"month":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","publist_id":"2312","quality_controlled":"1","year":"2010","abstract":[{"lang":"eng","text":"Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative mu-calculus and related probabilistic logics. We first show that the metrics provide a bound for the difference in long-run average and discounted average behavior across states, indicating that the metrics can be used both in system verification, and in performance evaluation. For turn-based games and MDPs, we provide a polynomial-time algorithm for the computation of the one-step metric distance between states. The algorithm is based on linear programming; it improves on the previous known exponential-time algorithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known algorithms for Markov chains. For the bisimulation kernel of the metric our algorithm works in time O(n(4)) for both turn-based games and MDPs; improving the previously best known O(n(9).log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing the exact distance be tween states is at least as hard as computing the value of concurrent reachability games and the square-root-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational r, can be done via a reduction to the theory of real closed fields, involving a formula with three quantifier alternations, yielding O(vertical bar G vertical bar(O(vertical bar G vertical bar 5))) time complexity, improving the previously known reduction, which yielded O(vertical bar G vertical bar(O(vertical bar G vertical bar 7))) time complexity. These algorithms can be iterated to approximate the metrics using binary search"}],"date_updated":"2026-07-06T13:25:11Z","doi":"10.2168/LMCS-6(3:13)2010","file_date_updated":"2020-07-14T12:46:19Z","citation":{"ama":"Chatterjee K, De Alfaro L, Majumdar R, Raman V. Algorithms for game metrics. <i>Logical Methods in Computer Science</i>. 2010;6(3):1-27. doi:<a href=\"https://doi.org/10.2168/LMCS-6(3:13)2010\">10.2168/LMCS-6(3:13)2010</a>","ista":"Chatterjee K, De Alfaro L, Majumdar R, Raman V. 2010. Algorithms for game metrics. Logical Methods in Computer Science. 6(3), 1–27.","apa":"Chatterjee, K., De Alfaro, L., Majumdar, R., &#38; Raman, V. (2010). Algorithms for game metrics. <i>Logical Methods in Computer Science</i>. International Federation for Computational Logic. <a href=\"https://doi.org/10.2168/LMCS-6(3:13)2010\">https://doi.org/10.2168/LMCS-6(3:13)2010</a>","chicago":"Chatterjee, Krishnendu, Luca De Alfaro, Ritankar Majumdar, and Vishwanath Raman. “Algorithms for Game Metrics.” <i>Logical Methods in Computer Science</i>. International Federation for Computational Logic, 2010. <a href=\"https://doi.org/10.2168/LMCS-6(3:13)2010\">https://doi.org/10.2168/LMCS-6(3:13)2010</a>.","ieee":"K. Chatterjee, L. De Alfaro, R. Majumdar, and V. Raman, “Algorithms for game metrics,” <i>Logical Methods in Computer Science</i>, vol. 6, no. 3. International Federation for Computational Logic, pp. 1–27, 2010.","mla":"Chatterjee, Krishnendu, et al. “Algorithms for Game Metrics.” <i>Logical Methods in Computer Science</i>, vol. 6, no. 3, International Federation for Computational Logic, 2010, pp. 1–27, doi:<a href=\"https://doi.org/10.2168/LMCS-6(3:13)2010\">10.2168/LMCS-6(3:13)2010</a>.","short":"K. Chatterjee, L. De Alfaro, R. Majumdar, V. Raman, Logical Methods in Computer Science 6 (2010) 1–27."},"language":[{"iso":"eng"}],"volume":6,"status":"public","article_processing_charge":"No","publisher":"International Federation for Computational Logic","day":"01","_id":"3868","corr_author":"1","oa":1,"date_created":"2018-12-11T12:05:36Z","date_published":"2010-09-01T00:00:00Z","das_tickbox":"1","publication":"Logical Methods in Computer Science","related_material":{"record":[{"status":"public","id":"3504","relation":"earlier_version"}]},"scopus_import":"1","type":"journal_article","pubrep_id":"370","ddc":["000"],"title":"Algorithms for game metrics","has_accepted_license":"1"},{"abstract":[{"lang":"eng","text":"In cortex surface segmentation, the extracted surface is required to have a particular topology, namely, a two-sphere. We present a new method for removing topology noise of a curve or surface within the level set framework, and thus produce a cortical surface with correct topology. We define a new energy term which quantifies topology noise. We then show how to minimize this term by computing its functional derivative with respect to the level set function. This method differs from existing methods in that it is inherently continuous and not digital; and in the way that our energy directly relates to the topology of the underlying curve or surface, versus existing knot-based measures which are related in a more indirect fashion. The proposed flow is validated empirically."}],"date_updated":"2026-07-07T13:07:08Z","doi":"10.1007/978-3-642-18421-5_4","citation":{"ieee":"C. Chen and D. Freedman, “Topology noise removal for curve  and surface evolution,” in <i>Conference proceedings MCV 2010</i>, Beijing, China, 2010, vol. 6533, pp. 31–42.","ama":"Chen C, Freedman D. Topology noise removal for curve  and surface evolution. In: <i>Conference Proceedings MCV 2010</i>. Vol 6533. Springer; 2010:31-42. doi:<a href=\"https://doi.org/10.1007/978-3-642-18421-5_4\">10.1007/978-3-642-18421-5_4</a>","ista":"Chen C, Freedman D. 2010. Topology noise removal for curve  and surface evolution. Conference proceedings MCV 2010. MCV: Medical Computer Vision, LNCS, vol. 6533, 31–42.","apa":"Chen, C., &#38; Freedman, D. (2010). Topology noise removal for curve  and surface evolution. In <i>Conference proceedings MCV 2010</i> (Vol. 6533, pp. 31–42). Beijing, China: Springer. <a href=\"https://doi.org/10.1007/978-3-642-18421-5_4\">https://doi.org/10.1007/978-3-642-18421-5_4</a>","chicago":"Chen, Chao, and Daniel Freedman. “Topology Noise Removal for Curve  and Surface Evolution.” In <i>Conference Proceedings MCV 2010</i>, 6533:31–42. Springer, 2010. <a href=\"https://doi.org/10.1007/978-3-642-18421-5_4\">https://doi.org/10.1007/978-3-642-18421-5_4</a>.","short":"C. Chen, D. Freedman, in:, Conference Proceedings MCV 2010, Springer, 2010, pp. 31–42.","mla":"Chen, Chao, and Daniel Freedman. “Topology Noise Removal for Curve  and Surface Evolution.” <i>Conference Proceedings MCV 2010</i>, vol. 6533, Springer, 2010, pp. 31–42, doi:<a href=\"https://doi.org/10.1007/978-3-642-18421-5_4\">10.1007/978-3-642-18421-5_4</a>."},"language":[{"iso":"eng"}],"volume":6533,"status":"public","acknowledgement":"Partially supported by the Austri an Science Fund unde r grant P20134-N13.\r\nWe thank Helena Molina-Abril for very helpful discussion. We thank anonymous reviewers for helpful comments.","article_processing_charge":"No","publisher":"Springer","day":"31","_id":"3782","date_created":"2018-12-11T12:05:08Z","date_published":"2010-12-31T00:00:00Z","publication":"Conference proceedings MCV 2010","scopus_import":"1","type":"conference","title":"Topology noise removal for curve  and surface evolution","intvolume":"      6533","author":[{"last_name":"Chen","full_name":"Chen, Chao","first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Daniel","full_name":"Freedman, Daniel","last_name":"Freedman"}],"oa_version":"None","publication_status":"published","page":"31 - 42","conference":{"end_date":"2010-09-20","start_date":"2010-09-20","location":"Beijing, China","name":"MCV: Medical Computer Vision"},"alternative_title":["LNCS"],"department":[{"_id":"HeEd"}],"month":"12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publist_id":"2445","year":"2010"},{"day":"09","publisher":"Cell Press","_id":"3789","corr_author":"1","date_created":"2018-12-11T12:05:11Z","oa":1,"acknowledgement":"This work was supported by grants from the Fundacion Caja Madrid to E.Q.H. and the Institute of Science and Technology Austria, the Max-Planck-Society, and the Deutsche Forschungsgemeinschaft to C.P.H.\r\nWe are grateful to Jon Clarke, Andy Oates, and Garrett Greenan for reading earlier versions of this manuscript. We thank J. Peychl, H. Ibarra, and P. Pitrone for excellent assistance and advice in multi-photon microscopy and D. White for assistance during the image-processing steps. We also thank D. Panhans for technical assistance, the whole Heisenberg laboratory for useful comments and discussions, and E. Lehmann, J. Hückmann, and G. Junghans for excellent fish care. ","status":"public","article_processing_charge":"No","citation":{"short":"E. Quesada-Hernández, L. Caneparo, S. Schneider, S. Winkler, M. Liebling, S. Fraser, C.-P.J. Heisenberg, Current Biology 20 (2010) 1966–1972.","mla":"Quesada-Hernández, Elena, et al. “Stereotypical Cell Division Orientation Controls Neural Rod Midline Formation in Zebrafish.” <i>Current Biology</i>, vol. 20, no. 21, Cell Press, 2010, pp. 1966–72, doi:<a href=\"https://doi.org/10.1016/j.cub.2010.10.009\">10.1016/j.cub.2010.10.009</a>.","ieee":"E. Quesada-Hernández <i>et al.</i>, “Stereotypical cell division orientation controls neural rod midline formation in zebrafish,” <i>Current Biology</i>, vol. 20, no. 21. Cell Press, pp. 1966–1972, 2010.","ista":"Quesada-Hernández E, Caneparo L, Schneider S, Winkler S, Liebling M, Fraser S, Heisenberg C-PJ. 2010. Stereotypical cell division orientation controls neural rod midline formation in zebrafish. Current Biology. 20(21), 1966–1972.","ama":"Quesada-Hernández E, Caneparo L, Schneider S, et al. Stereotypical cell division orientation controls neural rod midline formation in zebrafish. <i>Current Biology</i>. 2010;20(21):1966-1972. doi:<a href=\"https://doi.org/10.1016/j.cub.2010.10.009\">10.1016/j.cub.2010.10.009</a>","apa":"Quesada-Hernández, E., Caneparo, L., Schneider, S., Winkler, S., Liebling, M., Fraser, S., &#38; Heisenberg, C.-P. J. (2010). Stereotypical cell division orientation controls neural rod midline formation in zebrafish. <i>Current Biology</i>. Cell Press. <a href=\"https://doi.org/10.1016/j.cub.2010.10.009\">https://doi.org/10.1016/j.cub.2010.10.009</a>","chicago":"Quesada-Hernández, Elena, Luca Caneparo, Sylvia Schneider, Sylke Winkler, Michael Liebling, Scott Fraser, and Carl-Philipp J Heisenberg. “Stereotypical Cell Division Orientation Controls Neural Rod Midline Formation in Zebrafish.” <i>Current Biology</i>. Cell Press, 2010. <a href=\"https://doi.org/10.1016/j.cub.2010.10.009\">https://doi.org/10.1016/j.cub.2010.10.009</a>."},"doi":"10.1016/j.cub.2010.10.009","volume":20,"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"The development of multicellular organisms is dependent on the tight coordination between tissue growth and morphogenesis. The stereotypical orientation of cell divisions has been proposed to be a fundamental mechanism by which proliferating and growing tissues take shape. However, the actual contribution of stereotypical division orientation (SDO) to tissue morphogenesis is unclear. In zebrafish, cell divisions with stereotypical orientation have been implicated in both body-axis elongation and neural rod formation [1, 2], although there is little direct evidence for a critical function of SDO in either of these processes. Here we show that SDO is required for formation of the neural rod midline during neurulation but dispensable for elongation of the body axis during gastrulation. Our data indicate that SDO during both gastrulation and neurulation is dependent on the noncanonical Wnt receptor Frizzled 7 (Fz7) and that interfering with cell division orientation leads to severe defects in neural rod midline formation but not body-axis elongation. These findings suggest a novel function for Fz7-controlled cell division orientation in neural rod midline formation during neurulation. "}],"date_updated":"2026-07-28T08:03:47Z","OA_place":"publisher","title":"Stereotypical cell division orientation controls neural rod midline formation in zebrafish","OA_type":"free access","scopus_import":"1","type":"journal_article","date_published":"2010-11-09T00:00:00Z","das_tickbox":"1","publication":"Current Biology","publication_status":"published","page":"1966 - 1972","oa_version":"Published Version","author":[{"last_name":"Quesada-Hernández","id":"EA35229E-E909-11E9-8DF8-C90C5D5AF86E","first_name":"Elena","full_name":"Quesada-Hernández, Elena"},{"last_name":"Caneparo","full_name":"Caneparo, Luca","first_name":"Luca"},{"last_name":"Schneider","full_name":"Schneider, Sylvia","id":"1FAC36B0-E90A-11E9-9D2F-EF31CE0C9C2F","first_name":"Sylvia"},{"last_name":"Winkler","first_name":"Sylke","full_name":"Winkler, Sylke"},{"first_name":"Michael","full_name":"Liebling, Michael","last_name":"Liebling"},{"last_name":"Fraser","first_name":"Scott","full_name":"Fraser, Scott"},{"full_name":"Heisenberg, Carl-Philipp J","first_name":"Carl-Philipp J","id":"39427864-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0912-4566","last_name":"Heisenberg"}],"external_id":{"isi":["000284193900032"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.cub.2010.10.009"}],"intvolume":"        20","quality_controlled":"1","publist_id":"2438","year":"2010","month":"11","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"21","department":[{"_id":"CaHe"}],"article_type":"original","isi":1},{"article_type":"original","article_number":"W09521","year":"2010","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"9","month":"09","extern":"1","main_file_link":[{"url":"https://doi.org/10.1029/2009WR008611","open_access":"1"}],"author":[{"last_name":"Ivanov","full_name":"Ivanov, Valeriy Y.","first_name":"Valeriy Y."},{"full_name":"Fatichi, Simone","first_name":"Simone","id":"cf8e546b-a9b0-11f0-a43b-aa89ed1b56d6","last_name":"Fatichi"},{"last_name":"Jenerette","first_name":"G. Darrel","full_name":"Jenerette, G. Darrel"},{"last_name":"Espeleta","full_name":"Espeleta, Javier F.","first_name":"Javier F."},{"first_name":"Peter A.","full_name":"Troch, Peter A.","last_name":"Troch"},{"last_name":"Huxman","first_name":"Travis E.","full_name":"Huxman, Travis E."}],"intvolume":"        46","publication_status":"published","oa_version":"Published Version","type":"journal_article","scopus_import":"1","publication":"Water Resources Research","date_published":"2010-09-01T00:00:00Z","das_tickbox":"1","title":"Hysteresis of soil moisture spatial heterogeneity and the “homogenizing” effect of vegetation","OA_type":"free access","volume":46,"language":[{"iso":"eng"}],"citation":{"chicago":"Ivanov, Valeriy Y., Simone Fatichi, G. Darrel Jenerette, Javier F. Espeleta, Peter A. Troch, and Travis E. Huxman. “Hysteresis of Soil Moisture Spatial Heterogeneity and the ‘Homogenizing’ Effect of Vegetation.” <i>Water Resources Research</i>. American Geophysical Union, 2010. <a href=\"https://doi.org/10.1029/2009wr008611\">https://doi.org/10.1029/2009wr008611</a>.","apa":"Ivanov, V. Y., Fatichi, S., Jenerette, G. D., Espeleta, J. F., Troch, P. A., &#38; Huxman, T. E. (2010). Hysteresis of soil moisture spatial heterogeneity and the “homogenizing” effect of vegetation. <i>Water Resources Research</i>. American Geophysical Union. <a href=\"https://doi.org/10.1029/2009wr008611\">https://doi.org/10.1029/2009wr008611</a>","ista":"Ivanov VY, Fatichi S, Jenerette GD, Espeleta JF, Troch PA, Huxman TE. 2010. Hysteresis of soil moisture spatial heterogeneity and the “homogenizing” effect of vegetation. Water Resources Research. 46(9), W09521.","ama":"Ivanov VY, Fatichi S, Jenerette GD, Espeleta JF, Troch PA, Huxman TE. Hysteresis of soil moisture spatial heterogeneity and the “homogenizing” effect of vegetation. <i>Water Resources Research</i>. 2010;46(9). doi:<a href=\"https://doi.org/10.1029/2009wr008611\">10.1029/2009wr008611</a>","ieee":"V. Y. Ivanov, S. Fatichi, G. D. Jenerette, J. F. Espeleta, P. A. Troch, and T. E. Huxman, “Hysteresis of soil moisture spatial heterogeneity and the ‘homogenizing’ effect of vegetation,” <i>Water Resources Research</i>, vol. 46, no. 9. American Geophysical Union, 2010.","mla":"Ivanov, Valeriy Y., et al. “Hysteresis of Soil Moisture Spatial Heterogeneity and the ‘Homogenizing’ Effect of Vegetation.” <i>Water Resources Research</i>, vol. 46, no. 9, W09521, American Geophysical Union, 2010, doi:<a href=\"https://doi.org/10.1029/2009wr008611\">10.1029/2009wr008611</a>.","short":"V.Y. Ivanov, S. Fatichi, G.D. Jenerette, J.F. Espeleta, P.A. Troch, T.E. Huxman, Water Resources Research 46 (2010)."},"doi":"10.1029/2009wr008611","abstract":[{"text":"<jats:p>By partitioning mass and energy fluxes, soil moisture exerts a fundamental control on basin hydrological response. Using the design characteristics of the Biosphere 2 hillslope experiment, this study investigates aspects of soil moisture spatial and temporal variability in a zero‐order catchment of a semiarid climate. The hydrological response of the domain exhibits a particular structure, which depends on whether topography‐induced subsurface stormflow is triggered. The occurrence of the latter is conditioned by topography, soil depth, and pre‐storm spatial distribution of moisture. As a result, a non‐unique behavior of soil moisture spatial heterogeneity emerges, manifested through a hysteretic dependence of variability metrics on mean water content. Further, it is argued that vegetation dynamics impose a “homogenizing” effect on pre‐storm moisture states, decreasing the likelihood that a rainfall event will result in topographic redistribution of soil water. Consequently, post‐rainfall soil moisture dynamics associated with the effect of topography that could lead to the enhancement of spatial heterogeneity are suppressed; a potential “attractor” of catchment states emerges. The study thus proposes several hypotheses that will be testable within the framework of long‐term hillslope experiments.</jats:p>","lang":"eng"}],"date_updated":"2026-07-30T05:53:53Z","publication_identifier":{"issn":["0043-1397"],"eissn":["1944-7973"]},"date_created":"2026-07-27T12:30:23Z","oa":1,"day":"01","publisher":"American Geophysical Union","_id":"22446","status":"public","article_processing_charge":"No"}]