[{"abstract":[{"lang":"eng","text":"We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the\r\noscillations with respect to fluctuations and noise."}],"oa_version":"Preprint","publication_status":"published","day":"15","status":"public","date_updated":"2023-08-03T11:55:06Z","external_id":{"isi":["000917225500013"],"arxiv":["2103.09481"]},"title":"Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics","publication":"Journal of Computational Physics","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2103.09481"}],"arxiv":1,"citation":{"apa":"Kalinov, A., Osinskiy, A. I., Matveev, S. A., Otieno, W., &#38; Brilliantov, N. V. (2022). Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics. <i>Journal of Computational Physics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcp.2022.111439\">https://doi.org/10.1016/j.jcp.2022.111439</a>","short":"A. Kalinov, A.I. Osinskiy, S.A. Matveev, W. Otieno, N.V. Brilliantov, Journal of Computational Physics 467 (2022).","mla":"Kalinov, Aleksei, et al. “Direct Simulation Monte Carlo for New Regimes in Aggregation-Fragmentation Kinetics.” <i>Journal of Computational Physics</i>, vol. 467, 111439, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jcp.2022.111439\">10.1016/j.jcp.2022.111439</a>.","ista":"Kalinov A, Osinskiy AI, Matveev SA, Otieno W, Brilliantov NV. 2022. Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics. Journal of Computational Physics. 467, 111439.","ama":"Kalinov A, Osinskiy AI, Matveev SA, Otieno W, Brilliantov NV. Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics. <i>Journal of Computational Physics</i>. 2022;467. doi:<a href=\"https://doi.org/10.1016/j.jcp.2022.111439\">10.1016/j.jcp.2022.111439</a>","chicago":"Kalinov, Aleksei, A.I. Osinskiy, S.A. Matveev, W. Otieno, and N.V. Brilliantov. “Direct Simulation Monte Carlo for New Regimes in Aggregation-Fragmentation Kinetics.” <i>Journal of Computational Physics</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jcp.2022.111439\">https://doi.org/10.1016/j.jcp.2022.111439</a>.","ieee":"A. Kalinov, A. I. Osinskiy, S. A. Matveev, W. Otieno, and N. V. Brilliantov, “Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics,” <i>Journal of Computational Physics</i>, vol. 467. Elsevier, 2022."},"date_published":"2022-10-15T00:00:00Z","oa":1,"_id":"11556","author":[{"id":"44b7120e-eb97-11eb-a6c2-e1557aa81d02","last_name":"Kalinov","orcid":"0000-0003-2189-3904","first_name":"Aleksei","full_name":"Kalinov, Aleksei"},{"last_name":"Osinskiy","first_name":"A.I.","full_name":"Osinskiy, A.I."},{"last_name":"Matveev","full_name":"Matveev, S.A.","first_name":"S.A."},{"last_name":"Otieno","full_name":"Otieno, W.","first_name":"W."},{"full_name":"Brilliantov, N.V.","first_name":"N.V.","last_name":"Brilliantov"}],"type":"journal_article","publisher":"Elsevier","year":"2022","language":[{"iso":"eng"}],"doi":"10.1016/j.jcp.2022.111439","volume":467,"article_type":"original","isi":1,"quality_controlled":"1","publication_identifier":{"issn":["0021-9991"]},"month":"10","keyword":["Computer Science Applications","Physics and Astronomy (miscellaneous)","Applied Mathematics","Computational Mathematics","Modeling and Simulation","Numerical Analysis"],"intvolume":"       467","article_processing_charge":"No","ddc":["518"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"Zhores supercomputer of Skolkovo Institute of Science and Technology [68] has been used in the present research. S.A.M. was supported by Moscow Center for Fundamental and Applied Mathematics (the agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2019-1624). A.I.O. acknowledges RFBR project No. 20-31-90022. N.V.B. acknowledges the support of the Analytical Center (subsidy agreement 000000D730321P5Q0002, Grant No. 70-2021-00145 02.11.2021).","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"article_number":"111439","date_created":"2022-07-11T12:19:59Z"},{"article_type":"original","volume":10,"isi":1,"quality_controlled":"1","publication_identifier":{"eissn":["2050-5094"]},"month":"01","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"intvolume":"        10","article_processing_charge":"Yes","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"file_date_updated":"2022-01-19T09:27:43Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","date_created":"2022-01-18T16:18:51Z","article_number":"e4","date_published":"2022-01-18T00:00:00Z","oa":1,"_id":"10643","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha"},{"last_name":"Teufel","first_name":"Stefan","full_name":"Teufel, Stefan"}],"type":"journal_article","publisher":"Cambridge University Press","year":"2022","language":[{"iso":"eng"}],"doi":"10.1017/fms.2021.80","external_id":{"isi":["000743615000001"],"arxiv":["2012.15239"]},"file":[{"creator":"cchlebak","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_size":705323,"file_name":"2022_ForumMathSigma_Henheik.pdf","date_updated":"2022-01-19T09:27:43Z","success":1,"file_id":"10646","date_created":"2022-01-19T09:27:43Z","checksum":"87592a755adcef22ea590a99dc728dd3"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"citation":{"chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e4, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>.","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>"},"arxiv":1,"ec_funded":1,"abstract":[{"lang":"eng","text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"}],"publication_status":"published","oa_version":"Published Version","day":"18","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2023-08-02T13:53:11Z"},{"date_updated":"2023-08-04T09:00:35Z","status":"public","abstract":[{"lang":"eng","text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables."}],"ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"27","oa_version":"Published Version","publication_status":"published","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>."},"project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"has_accepted_license":"1","scopus_import":"1","title":"Rank-uniform local law for Wigner matrices","file":[{"file_size":817089,"file_name":"2022_ForumMath_Cipolloni.pdf","success":1,"date_updated":"2023-01-24T10:02:40Z","checksum":"94a049aeb1eea5497aa097712a73c400","date_created":"2023-01-24T10:02:40Z","file_id":"12356","creator":"dernst","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"external_id":{"isi":["000873719200001"]},"publication":"Forum of Mathematics, Sigma","year":"2022","publisher":"Cambridge University Press","doi":"10.1017/fms.2022.86","language":[{"iso":"eng"}],"type":"journal_article","_id":"12148","oa":1,"author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Dominik J","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856"}],"date_published":"2022-10-27T00:00:00Z","acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","department":[{"_id":"LaEr"}],"date_created":"2023-01-12T12:07:30Z","article_number":"e96","intvolume":"        10","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"file_date_updated":"2023-01-24T10:02:40Z","article_processing_charge":"No","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["2050-5094"]},"quality_controlled":"1","month":"10","article_type":"original","volume":10,"isi":1},{"citation":{"ieee":"H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 114–172, 2022.","chicago":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21m1424925\">https://doi.org/10.1137/21m1424925</a>.","ama":"Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(1):114-172. doi:<a href=\"https://doi.org/10.1137/21m1424925\">10.1137/21m1424925</a>","mla":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:<a href=\"https://doi.org/10.1137/21m1424925\">10.1137/21m1424925</a>.","apa":"Abels, H., &#38; Moser, M. (2022). Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21m1424925\">https://doi.org/10.1137/21m1424925</a>","ista":"Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. SIAM Journal on Mathematical Analysis. 54(1), 114–172.","short":"H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172."},"arxiv":1,"issue":"1","scopus_import":"1","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2105.08434"}],"external_id":{"arxiv":["2105.08434"],"isi":["000762768000004"]},"title":"Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°","publication":"SIAM Journal on Mathematical Analysis","date_updated":"2023-08-04T10:34:56Z","status":"public","abstract":[{"text":"This paper is concerned with the sharp interface limit for the Allen--Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain Ω⊂\\R2. We assume that a diffuse interface already has developed and that it is in contact with the boundary ∂Ω. The boundary condition is designed in such a way that the limit problem is given by the mean curvature flow with constant α-contact angle. For α close to 90° we prove a local in time convergence result for well-prepared initial data for times when a smooth solution to the limit problem exists. Based on the latter we construct a suitable curvilinear coordinate system and carry out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear Robin boundary condition. Moreover, we show a spectral estimate for the corresponding linearized Allen--Cahn operator and with its aid we derive strong norm estimates for the difference of the exact and approximate solutions using a Gronwall-type argument.","lang":"eng"}],"publication_status":"published","page":"114-172","oa_version":"Preprint","day":"04","department":[{"_id":"JuFi"}],"date_created":"2023-01-16T10:07:00Z","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"intvolume":"        54","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"month":"01","volume":54,"article_type":"original","isi":1,"publisher":"Society for Industrial and Applied Mathematics","year":"2022","language":[{"iso":"eng"}],"doi":"10.1137/21m1424925","type":"journal_article","oa":1,"_id":"12305","author":[{"full_name":"Abels, Helmut","first_name":"Helmut","last_name":"Abels"},{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser","full_name":"Moser, Maximilian","first_name":"Maximilian"}],"date_published":"2022-01-04T00:00:00Z"},{"date_updated":"2023-09-05T14:13:57Z","status":"public","oa_version":"Published Version","publication_status":"published","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"17","abstract":[{"lang":"eng","text":"We study the problem of recovering an unknown signal 𝑥𝑥 given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator 𝑥𝑥^L and a spectral estimator 𝑥𝑥^s. The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine 𝑥𝑥^L and 𝑥𝑥^s. At the heart of our analysis is the exact characterization of the empirical joint distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of 𝑥𝑥^L and 𝑥𝑥^s, given the limiting distribution of the signal 𝑥𝑥. When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form 𝜃𝑥𝑥^L+𝑥𝑥^s and we derive the optimal combination coefficient. In order to establish the limiting distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s), we design and analyze an approximate message passing algorithm whose iterates give 𝑥𝑥^L and approach 𝑥𝑥^s. Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately."}],"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"citation":{"chicago":"Mondelli, Marco, Christos Thrampoulidis, and Ramji Venkataramanan. “Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models.” <i>Foundations of Computational Mathematics</i>. Springer, 2021. <a href=\"https://doi.org/10.1007/s10208-021-09531-x\">https://doi.org/10.1007/s10208-021-09531-x</a>.","ieee":"M. Mondelli, C. Thrampoulidis, and R. Venkataramanan, “Optimal combination of linear and spectral estimators for generalized linear models,” <i>Foundations of Computational Mathematics</i>. Springer, 2021.","apa":"Mondelli, M., Thrampoulidis, C., &#38; Venkataramanan, R. (2021). Optimal combination of linear and spectral estimators for generalized linear models. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-021-09531-x\">https://doi.org/10.1007/s10208-021-09531-x</a>","short":"M. Mondelli, C. Thrampoulidis, R. Venkataramanan, Foundations of Computational Mathematics (2021).","mla":"Mondelli, Marco, et al. “Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models.” <i>Foundations of Computational Mathematics</i>, Springer, 2021, doi:<a href=\"https://doi.org/10.1007/s10208-021-09531-x\">10.1007/s10208-021-09531-x</a>.","ista":"Mondelli M, Thrampoulidis C, Venkataramanan R. 2021. Optimal combination of linear and spectral estimators for generalized linear models. Foundations of Computational Mathematics.","ama":"Mondelli M, Thrampoulidis C, Venkataramanan R. Optimal combination of linear and spectral estimators for generalized linear models. <i>Foundations of Computational Mathematics</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s10208-021-09531-x\">10.1007/s10208-021-09531-x</a>"},"arxiv":1,"scopus_import":"1","has_accepted_license":"1","publication":"Foundations of Computational Mathematics","external_id":{"isi":["000685721000001"],"arxiv":["2008.03326"]},"file":[{"access_level":"open_access","content_type":"application/pdf","relation":"main_file","creator":"alisjak","date_created":"2021-12-13T15:47:54Z","checksum":"9ea12dd8045a0678000a3a59295221cb","file_id":"10542","success":1,"date_updated":"2021-12-13T15:47:54Z","file_name":"2021_Springer_Mondelli.pdf","file_size":2305731}],"title":"Optimal combination of linear and spectral estimators for generalized linear models","language":[{"iso":"eng"}],"doi":"10.1007/s10208-021-09531-x","publisher":"Springer","year":"2021","type":"journal_article","author":[{"first_name":"Marco","full_name":"Mondelli, Marco","orcid":"0000-0002-3242-7020","last_name":"Mondelli","id":"27EB676C-8706-11E9-9510-7717E6697425"},{"last_name":"Thrampoulidis","first_name":"Christos","full_name":"Thrampoulidis, Christos"},{"last_name":"Venkataramanan","first_name":"Ramji","full_name":"Venkataramanan, Ramji"}],"oa":1,"_id":"10211","date_published":"2021-08-17T00:00:00Z","date_created":"2021-11-03T10:59:08Z","acknowledgement":"M. Mondelli would like to thank Andrea Montanari for helpful discussions. All the authors would like to thank the anonymous reviewers for their helpful comments.","department":[{"_id":"MaMo"}],"ddc":["510"],"article_processing_charge":"Yes (via OA deal)","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file_date_updated":"2021-12-13T15:47:54Z","keyword":["Applied Mathematics","Computational Theory and Mathematics","Computational Mathematics","Analysis"],"month":"08","quality_controlled":"1","publication_identifier":{"eissn":["1615-3383"],"issn":["1615-3375"]},"isi":1,"article_type":"original"},{"quality_controlled":"1","publication_identifier":{"eissn":["1367-4811"]},"month":"12","volume":36,"article_type":"original","pmid":1,"department":[{"_id":"FrLo"}],"date_created":"2023-08-21T12:28:20Z","keyword":["Computational Mathematics","Computational Theory and Mathematics","Computer Science Applications","Molecular Biology","Biochemistry","Statistics and Probability"],"intvolume":"        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Van"},{"first_name":"Marcus","full_name":"Vetter, Marcus","last_name":"Vetter"},{"last_name":"Vlajnic","full_name":"Vlajnic, Tatjana","first_name":"Tatjana"},{"last_name":"Weber","first_name":"Sandra","full_name":"Weber, Sandra"},{"last_name":"Weber","full_name":"Weber, Walter P","first_name":"Walter P"},{"last_name":"Wegmann","first_name":"Rebekka","full_name":"Wegmann, Rebekka"},{"first_name":"Michael","full_name":"Weller, Michael","last_name":"Weller"},{"first_name":"Fabian","full_name":"Wendt, Fabian","last_name":"Wendt"},{"first_name":"Norbert","full_name":"Wey, Norbert","last_name":"Wey"},{"last_name":"Wicki","first_name":"Andreas","full_name":"Wicki, Andreas"},{"last_name":"Wollscheid","full_name":"Wollscheid, Bernd","first_name":"Bernd"},{"last_name":"Yu","first_name":"Shuqing","full_name":"Yu, Shuqing"},{"full_name":"Ziegler, Johanna","first_name":"Johanna","last_name":"Ziegler"},{"last_name":"Zimmermann","full_name":"Zimmermann, Marc","first_name":"Marc"},{"last_name":"Zoche","full_name":"Zoche, Martin","first_name":"Martin"},{"full_name":"Zuend, Gregor","first_name":"Gregor","last_name":"Zuend"},{"last_name":"Rätsch","first_name":"Gunnar","full_name":"Rätsch, Gunnar"},{"full_name":"Lehmann, Kjong-Van","first_name":"Kjong-Van","last_name":"Lehmann"}],"date_published":"2020-12-01T00:00:00Z","publisher":"Oxford University Press","year":"2020","language":[{"iso":"eng"}],"doi":"10.1093/bioinformatics/btaa843","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1093/bioinformatics/btaa843"}],"related_material":{"link":[{"relation":"software","url":"https://github.com/ratschlab/scim"}]},"external_id":{"pmid":["33381818"]},"title":"SCIM: Universal single-cell matching with unpaired feature sets","publication":"Bioinformatics","citation":{"chicago":"Stark, Stefan G, Joanna Ficek, Francesco Locatello, Ximena Bonilla, Stéphane Chevrier, Franziska Singer, Rudolf Aebersold, et al. “SCIM: Universal Single-Cell Matching with Unpaired Feature Sets.” <i>Bioinformatics</i>. Oxford University Press, 2020. <a href=\"https://doi.org/10.1093/bioinformatics/btaa843\">https://doi.org/10.1093/bioinformatics/btaa843</a>.","ieee":"S. G. Stark <i>et al.</i>, “SCIM: Universal single-cell matching with unpaired feature sets,” <i>Bioinformatics</i>, vol. 36, no. Supplement_2. Oxford University Press, pp. i919–i927, 2020.","ista":"Stark SG et al. 2020. SCIM: Universal single-cell matching with unpaired feature sets. Bioinformatics. 36(Supplement_2), i919–i927.","apa":"Stark, S. G., Ficek, J., Locatello, F., Bonilla, X., Chevrier, S., Singer, F., … Lehmann, K.-V. (2020). SCIM: Universal single-cell matching with unpaired feature sets. <i>Bioinformatics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/bioinformatics/btaa843\">https://doi.org/10.1093/bioinformatics/btaa843</a>","mla":"Stark, Stefan G., et al. “SCIM: Universal Single-Cell Matching with Unpaired Feature Sets.” <i>Bioinformatics</i>, vol. 36, no. Supplement_2, Oxford University Press, 2020, pp. i919–27, doi:<a href=\"https://doi.org/10.1093/bioinformatics/btaa843\">10.1093/bioinformatics/btaa843</a>.","short":"S.G. Stark, J. Ficek, F. Locatello, X. Bonilla, S. Chevrier, F. Singer, R. Aebersold, F.S. Al-Quaddoomi, J. Albinus, I. Alborelli, S. Andani, P.-O. Attinger, M. Bacac, D. Baumhoer, B. Beck-Schimmer, N. Beerenwinkel, C. Beisel, L. Bernasconi, A. Bertolini, B. Bodenmiller, X. Bonilla, R. Casanova, S. Chevrier, N. Chicherova, M. D’Costa, E. Danenberg, N. Davidson, M.-A.D. gan, R. Dummer, S. Engler, M. Erkens, K. Eschbach, C. Esposito, A. Fedier, P. Ferreira, J. Ficek, A.L. Frei, B. Frey, S. Goetze, L. Grob, G. Gut, D. Günther, M. Haberecker, P. Haeuptle, V. Heinzelmann-Schwarz, S. Herter, R. Holtackers, T. Huesser, A. Irmisch, F. Jacob, A. Jacobs, T.M. Jaeger, K. Jahn, A.R. James, P.M. Jermann, A. Kahles, A. Kahraman, V.H. Koelzer, W. Kuebler, J. Kuipers, C.P. Kunze, C. Kurzeder, K.-V. Lehmann, M. Levesque, S. Lugert, G. Maass, M. Manz, P. Markolin, J. Mena, U. Menzel, J.M. Metzler, N. Miglino, E.S. Milani, H. Moch, S. Muenst, R. Murri, C.K. Ng, S. Nicolet, M. Nowak, P.G. Pedrioli, L. Pelkmans, S. Piscuoglio, M. Prummer, M. Ritter, C. Rommel, M.L. Rosano-González, G. Rätsch, N. Santacroce, J.S. del Castillo, R. Schlenker, P.C. Schwalie, S. Schwan, T. Schär, G. Senti, F. Singer, S. Sivapatham, B. Snijder, B. Sobottka, V.T. Sreedharan, S. Stark, D.J. Stekhoven, A.P. Theocharides, T.M. Thomas, M. Tolnay, V. Tosevski, N.C. Toussaint, M.A. Tuncel, M. Tusup, A.V. Drogen, M. Vetter, T. Vlajnic, S. Weber, W.P. Weber, R. Wegmann, M. Weller, F. Wendt, N. Wey, A. Wicki, B. Wollscheid, S. Yu, J. Ziegler, M. Zimmermann, M. Zoche, G. Zuend, G. Rätsch, K.-V. Lehmann, Bioinformatics 36 (2020) i919–i927.","ama":"Stark SG, Ficek J, Locatello F, et al. SCIM: Universal single-cell matching with unpaired feature sets. <i>Bioinformatics</i>. 2020;36(Supplement_2):i919-i927. doi:<a href=\"https://doi.org/10.1093/bioinformatics/btaa843\">10.1093/bioinformatics/btaa843</a>"},"issue":"Supplement_2","scopus_import":"1","abstract":[{"lang":"eng","text":"Motivation: Recent technological advances have led to an increase in the production and availability of single-cell data. The ability to integrate a set of multi-technology measurements would allow the identification of biologically or clinically meaningful observations through the unification of the perspectives afforded by each technology. In most cases, however, profiling technologies consume the used cells and thus pairwise correspondences between datasets are lost. Due to the sheer size single-cell datasets can acquire, scalable algorithms that are able to universally match single-cell measurements carried out in one cell to its corresponding sibling in another technology are needed.\r\nResults: We propose Single-Cell data Integration via Matching (SCIM), a scalable approach to recover such correspondences in two or more technologies. SCIM assumes that cells share a common (low-dimensional) underlying structure and that the underlying cell distribution is approximately constant across technologies. It constructs a technology-invariant latent space using an autoencoder framework with an adversarial objective. Multi-modal datasets are integrated by pairing cells across technologies using a bipartite matching scheme that operates on the low-dimensional latent representations. We evaluate SCIM on a simulated cellular branching process and show that the cell-to-cell matches derived by SCIM reflect the same pseudotime on the simulated dataset. Moreover, we apply our method to two real-world scenarios, a melanoma tumor sample and a human bone marrow sample, where we pair cells from a scRNA dataset to their sibling cells in a CyTOF dataset achieving 90% and 78% cell-matching accuracy for each one of the samples, respectively."}],"page":"i919-i927","publication_status":"published","oa_version":"Published Version","day":"01","date_updated":"2023-09-11T10:21:00Z","status":"public"},{"date_published":"2020-02-12T00:00:00Z","_id":"9781","oa":1,"author":[{"last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","first_name":"Dario"},{"full_name":"Seiringer, Robert","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"type":"journal_article","year":"2020","publisher":"Society for Industrial & Applied Mathematics ","doi":"10.1137/19m126284x","language":[{"iso":"eng"}],"article_type":"original","volume":52,"isi":1,"publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"quality_controlled":"1","month":"02","intvolume":"        52","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"department":[{"_id":"RoSe"}],"acknowledgement":"We are grateful for the hospitality at the Mittag-Leffler Institute, where part of this work has been done. The work of the authors was supported by the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme grant 694227.","date_created":"2021-08-06T07:34:16Z","abstract":[{"text":"We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from nondegeneracy of the Hessian at the minimum.","lang":"eng"}],"ec_funded":1,"tmp":{"image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"day":"12","oa_version":"Preprint","page":"605-622","publication_status":"published","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","status":"public","date_updated":"2023-09-07T13:30:11Z","title":"Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball","external_id":{"isi":["000546967700022"],"arxiv":["1904.08647 "]},"related_material":{"record":[{"id":"9733","status":"public","relation":"dissertation_contains"}]},"publication":"SIAM Journal on Mathematical Analysis","main_file_link":[{"url":"https://arxiv.org/abs/1904.08647","open_access":"1"}],"has_accepted_license":"1","scopus_import":"1","issue":"1","citation":{"ieee":"D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 1. Society for Industrial &#38; Applied Mathematics , pp. 605–622, 2020.","chicago":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics , 2020. <a href=\"https://doi.org/10.1137/19m126284x\">https://doi.org/10.1137/19m126284x</a>.","ama":"Feliciangeli D, Seiringer R. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>. 2020;52(1):605-622. doi:<a href=\"https://doi.org/10.1137/19m126284x\">10.1137/19m126284x</a>","mla":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 1, Society for Industrial &#38; Applied Mathematics , 2020, pp. 605–22, doi:<a href=\"https://doi.org/10.1137/19m126284x\">10.1137/19m126284x</a>.","short":"D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020) 605–622.","apa":"Feliciangeli, D., &#38; Seiringer, R. (2020). Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics . <a href=\"https://doi.org/10.1137/19m126284x\">https://doi.org/10.1137/19m126284x</a>","ista":"Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1), 605–622."},"arxiv":1,"project":[{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"}]},{"language":[{"iso":"eng"}],"doi":"10.1145/2716312","publisher":"Association for Computing Machinery","year":"2015","type":"journal_article","author":[{"last_name":"Dütting","full_name":"Dütting, Paul","first_name":"Paul"},{"first_name":"Monika H","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"Ingmar","full_name":"Weber, Ingmar","last_name":"Weber"}],"_id":"11670","date_published":"2015-12-02T00:00:00Z","article_number":"1","date_created":"2022-07-27T12:43:18Z","acknowledgement":"We would like to thank Veronika Loitzenbauer and the anonymous referees for their valuable feedback.","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","keyword":["Computational Mathematics","Marketing","Economics and Econometrics","Statistics and Probability","Computer Science (miscellaneous)"],"intvolume":"         4","month":"12","quality_controlled":"1","publication_identifier":{"issn":["2167-8375"],"eissn":["2167-8383"]},"volume":4,"article_type":"original","date_updated":"2023-02-09T10:08:41Z","status":"public","publication_status":"published","oa_version":"None","day":"02","abstract":[{"lang":"eng","text":"Auctions are widely used on the Web. Applications range from sponsored search to platforms such as eBay. In these and in many other applications the auctions in use are single-/multi-item auctions with unit demand. The main drawback of standard mechanisms for this type of auctions, such as VCG and GSP, is the limited expressiveness that they offer to the bidders. The General Auction Mechanism (GAM) of Aggarwal et al. [2009] takes a first step toward addressing the problem of limited expressiveness by computing a bidder optimal, envy-free outcome for linear utility functions with identical slopes and a single discontinuity per bidder-item pair. We show that in many practical situations this does not suffice to adequately model the preferences of the bidders, and we overcome this problem by presenting the first mechanism for piecewise linear utility functions with nonidentical slopes and multiple discontinuities. Our mechanism runs in polynomial time. Like GAM it is incentive compatible for inputs that fulfill a certain nondegeneracy assumption, but our requirement is more general than the requirement of GAM. For discontinuous utility functions that are nondegenerate as well as for continuous utility functions the outcome of our mechanism is a competitive equilibrium. We also show how our mechanism can be used to compute approximately bidder optimal, envy-free outcomes for a general class of continuous utility functions via piecewise linear approximation. Finally, we prove hardness results for even more expressive settings."}],"citation":{"short":"P. Dütting, M.H. Henzinger, I. Weber, ACM Transactions on Economics and Computation 4 (2015).","apa":"Dütting, P., Henzinger, M. H., &#38; Weber, I. (2015). An expressive mechanism for auctions on the web. <i>ACM Transactions on Economics and Computation</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/2716312\">https://doi.org/10.1145/2716312</a>","ista":"Dütting P, Henzinger MH, Weber I. 2015. An expressive mechanism for auctions on the web. ACM Transactions on Economics and Computation. 4(1), 1.","mla":"Dütting, Paul, et al. “An Expressive Mechanism for Auctions on the Web.” <i>ACM Transactions on Economics and Computation</i>, vol. 4, no. 1, 1, Association for Computing Machinery, 2015, doi:<a href=\"https://doi.org/10.1145/2716312\">10.1145/2716312</a>.","ama":"Dütting P, Henzinger MH, Weber I. An expressive mechanism for auctions on the web. <i>ACM Transactions on Economics and Computation</i>. 2015;4(1). doi:<a href=\"https://doi.org/10.1145/2716312\">10.1145/2716312</a>","chicago":"Dütting, Paul, Monika H Henzinger, and Ingmar Weber. “An Expressive Mechanism for Auctions on the Web.” <i>ACM Transactions on Economics and Computation</i>. Association for Computing Machinery, 2015. <a href=\"https://doi.org/10.1145/2716312\">https://doi.org/10.1145/2716312</a>.","ieee":"P. Dütting, M. H. Henzinger, and I. Weber, “An expressive mechanism for auctions on the web,” <i>ACM Transactions on Economics and Computation</i>, vol. 4, no. 1. Association for Computing Machinery, 2015."},"issue":"1","scopus_import":"1","publication":"ACM Transactions on Economics and Computation","title":"An expressive mechanism for auctions on the web"},{"doi":"10.1093/bioinformatics/btu166","language":[{"iso":"eng"}],"year":"2014","publisher":"Oxford University Press","type":"journal_article","author":[{"last_name":"Morin","full_name":"Morin, Sébastien","first_name":"Sébastien"},{"last_name":"Linnet","full_name":"Linnet, Troels E","first_name":"Troels E"},{"last_name":"Lescanne","first_name":"Mathilde","full_name":"Lescanne, Mathilde"},{"orcid":"0000-0002-9350-7606","last_name":"Schanda","id":"7B541462-FAF6-11E9-A490-E8DFE5697425","first_name":"Paul","full_name":"Schanda, Paul"},{"last_name":"Thompson","first_name":"Gary S","full_name":"Thompson, Gary S"},{"last_name":"Tollinger","first_name":"Martin","full_name":"Tollinger, Martin"},{"last_name":"Teilum","first_name":"Kaare","full_name":"Teilum, Kaare"},{"full_name":"Gagné, Stéphane","first_name":"Stéphane","last_name":"Gagné"},{"full_name":"Marion, Dominique","first_name":"Dominique","last_name":"Marion"},{"last_name":"Griesinger","first_name":"Christian","full_name":"Griesinger, Christian"},{"last_name":"Blackledge","first_name":"Martin","full_name":"Blackledge, Martin"},{"full_name":"d’Auvergne, Edward J","first_name":"Edward J","last_name":"d’Auvergne"}],"_id":"8459","date_published":"2014-08-01T00:00:00Z","date_created":"2020-09-18T10:08:07Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","extern":"1","intvolume":"        30","keyword":["Statistics and Probability","Computational Theory and Mathematics","Biochemistry","Molecular Biology","Computational Mathematics","Computer Science Applications"],"month":"08","publication_identifier":{"issn":["1367-4803","1460-2059"]},"quality_controlled":"1","volume":30,"article_type":"original","date_updated":"2021-01-12T08:19:25Z","status":"public","day":"01","page":"2219-2220","oa_version":"None","publication_status":"published","abstract":[{"text":"Nuclear magnetic resonance (NMR) is a powerful tool for observing the motion of biomolecules at the atomic level. One technique, the analysis of relaxation dispersion phenomenon, is highly suited for studying the kinetics and thermodynamics of biological processes. Built on top of the relax computational environment for NMR dynamics is a new dispersion analysis designed to be comprehensive, accurate and easy-to-use. The software supports more models, both numeric and analytic, than current solutions. An automated protocol, available for scripting and driving the graphical user interface (GUI), is designed to simplify the analysis of dispersion data for NMR spectroscopists. Decreases in optimization time are granted by parallelization for running on computer clusters and by skipping an initial grid search by using parameters from one solution as the starting point for another —using analytic model results for the numeric models, taking advantage of model nesting, and using averaged non-clustered results for the clustered analysis.","lang":"eng"}],"citation":{"ama":"Morin S, Linnet TE, Lescanne M, et al. Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data. <i>Bioinformatics</i>. 2014;30(15):2219-2220. doi:<a href=\"https://doi.org/10.1093/bioinformatics/btu166\">10.1093/bioinformatics/btu166</a>","mla":"Morin, Sébastien, et al. “Relax: The Analysis of Biomolecular Kinetics and Thermodynamics Using NMR Relaxation Dispersion Data.” <i>Bioinformatics</i>, vol. 30, no. 15, Oxford University Press, 2014, pp. 2219–20, doi:<a href=\"https://doi.org/10.1093/bioinformatics/btu166\">10.1093/bioinformatics/btu166</a>.","ista":"Morin S, Linnet TE, Lescanne M, Schanda P, Thompson GS, Tollinger M, Teilum K, Gagné S, Marion D, Griesinger C, Blackledge M, d’Auvergne EJ. 2014. Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data. Bioinformatics. 30(15), 2219–2220.","apa":"Morin, S., Linnet, T. E., Lescanne, M., Schanda, P., Thompson, G. S., Tollinger, M., … d’Auvergne, E. J. (2014). Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data. <i>Bioinformatics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/bioinformatics/btu166\">https://doi.org/10.1093/bioinformatics/btu166</a>","short":"S. Morin, T.E. Linnet, M. Lescanne, P. Schanda, G.S. Thompson, M. Tollinger, K. Teilum, S. Gagné, D. Marion, C. Griesinger, M. Blackledge, E.J. d’Auvergne, Bioinformatics 30 (2014) 2219–2220.","ieee":"S. Morin <i>et al.</i>, “Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data,” <i>Bioinformatics</i>, vol. 30, no. 15. Oxford University Press, pp. 2219–2220, 2014.","chicago":"Morin, Sébastien, Troels E Linnet, Mathilde Lescanne, Paul Schanda, Gary S Thompson, Martin Tollinger, Kaare Teilum, et al. “Relax: The Analysis of Biomolecular Kinetics and Thermodynamics Using NMR Relaxation Dispersion Data.” <i>Bioinformatics</i>. Oxford University Press, 2014. <a href=\"https://doi.org/10.1093/bioinformatics/btu166\">https://doi.org/10.1093/bioinformatics/btu166</a>."},"issue":"15","publication":"Bioinformatics","title":"Relax: The analysis of biomolecular kinetics and thermodynamics using NMR relaxation dispersion data","related_material":{"link":[{"url":"https://doi.org/10.1093/bioinformatics/btz397","relation":"erratum"}]}},{"doi":"10.1137/070703235","language":[{"iso":"eng"}],"year":"2008","publisher":"Society for Industrial & Applied Mathematics","date_updated":"2021-01-12T08:19:46Z","status":"public","type":"journal_article","author":[{"full_name":"Kaloshin, Vadim","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","orcid":"0000-0002-6051-2628"},{"last_name":"Levi","full_name":"Levi, Mark","first_name":"Mark"}],"_id":"8509","day":"05","page":"702-720","oa_version":"None","publication_status":"published","date_published":"2008-11-05T00:00:00Z","abstract":[{"lang":"eng","text":"The goal of this paper is to present to nonspecialists what is perhaps the simplest possible geometrical picture explaining the mechanism of Arnold diffusion. We choose to speak of a specific model—that of geometric rays in a periodic optical medium. This model is equivalent to that of a particle in a periodic potential in ${\\mathbb R}^{n}$ with energy prescribed and to the geodesic flow in a Riemannian metric on ${\\mathbb R}^{n} $."}],"date_created":"2020-09-18T10:48:12Z","citation":{"chicago":"Kaloshin, Vadim, and Mark Levi. “Geometry of Arnold Diffusion.” <i>SIAM Review</i>. Society for Industrial &#38; Applied Mathematics, 2008. <a href=\"https://doi.org/10.1137/070703235\">https://doi.org/10.1137/070703235</a>.","ieee":"V. Kaloshin and M. Levi, “Geometry of Arnold diffusion,” <i>SIAM Review</i>, vol. 50, no. 4. Society for Industrial &#38; Applied Mathematics, pp. 702–720, 2008.","short":"V. Kaloshin, M. Levi, SIAM Review 50 (2008) 702–720.","mla":"Kaloshin, Vadim, and Mark Levi. “Geometry of Arnold Diffusion.” <i>SIAM Review</i>, vol. 50, no. 4, Society for Industrial &#38; Applied Mathematics, 2008, pp. 702–20, doi:<a href=\"https://doi.org/10.1137/070703235\">10.1137/070703235</a>.","ista":"Kaloshin V, Levi M. 2008. Geometry of Arnold diffusion. SIAM Review. 50(4), 702–720.","apa":"Kaloshin, V., &#38; Levi, M. (2008). Geometry of Arnold diffusion. <i>SIAM Review</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/070703235\">https://doi.org/10.1137/070703235</a>","ama":"Kaloshin V, Levi M. Geometry of Arnold diffusion. <i>SIAM Review</i>. 2008;50(4):702-720. doi:<a href=\"https://doi.org/10.1137/070703235\">10.1137/070703235</a>"},"issue":"4","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","article_processing_charge":"No","intvolume":"        50","keyword":["Theoretical Computer Science","Applied Mathematics","Computational Mathematics"],"month":"11","publication_identifier":{"issn":["0036-1445","1095-7200"]},"quality_controlled":"1","publication":"SIAM Review","title":"Geometry of Arnold diffusion","volume":50,"article_type":"original"},{"date_created":"2022-07-28T08:56:10Z","keyword":["Computational Theory and Mathematics","Computational Mathematics","Control and Optimization"],"intvolume":"        34","extern":"1","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publication_identifier":{"issn":["0196-6774"]},"month":"02","volume":34,"article_type":"original","publisher":"Elsevier","year":"2000","language":[{"iso":"eng"}],"doi":"10.1006/jagm.1999.1055","type":"journal_article","_id":"11683","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H"},{"first_name":"Satish","full_name":"Rao, Satish","last_name":"Rao"},{"last_name":"Gabow","first_name":"Harold N.","full_name":"Gabow, Harold N."}],"date_published":"2000-02-01T00:00:00Z","citation":{"chicago":"Henzinger, Monika H, Satish Rao, and Harold N. Gabow. “Computing Vertex Connectivity: New Bounds from Old Techniques.” <i>Journal of Algorithms</i>. Elsevier, 2000. <a href=\"https://doi.org/10.1006/jagm.1999.1055\">https://doi.org/10.1006/jagm.1999.1055</a>.","ieee":"M. H. Henzinger, S. Rao, and H. N. Gabow, “Computing vertex connectivity: New bounds from old techniques,” <i>Journal of Algorithms</i>, vol. 34, no. 2. Elsevier, pp. 222–250, 2000.","apa":"Henzinger, M. H., Rao, S., &#38; Gabow, H. N. (2000). Computing vertex connectivity: New bounds from old techniques. <i>Journal of Algorithms</i>. Elsevier. <a href=\"https://doi.org/10.1006/jagm.1999.1055\">https://doi.org/10.1006/jagm.1999.1055</a>","mla":"Henzinger, Monika H., et al. “Computing Vertex Connectivity: New Bounds from Old Techniques.” <i>Journal of Algorithms</i>, vol. 34, no. 2, Elsevier, 2000, pp. 222–50, doi:<a href=\"https://doi.org/10.1006/jagm.1999.1055\">10.1006/jagm.1999.1055</a>.","ista":"Henzinger MH, Rao S, Gabow HN. 2000. Computing vertex connectivity: New bounds from old techniques. Journal of Algorithms. 34(2), 222–250.","short":"M.H. Henzinger, S. Rao, H.N. Gabow, Journal of Algorithms 34 (2000) 222–250.","ama":"Henzinger MH, Rao S, Gabow HN. Computing vertex connectivity: New bounds from old techniques. <i>Journal of Algorithms</i>. 2000;34(2):222-250. doi:<a href=\"https://doi.org/10.1006/jagm.1999.1055\">10.1006/jagm.1999.1055</a>"},"issue":"2","scopus_import":"1","title":"Computing vertex connectivity: New bounds from old techniques","publication":"Journal of Algorithms","date_updated":"2022-09-12T09:06:48Z","status":"public","abstract":[{"text":"The vertex connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{κ3 + n, κn}m); for an undirected graph the term m can be replaced by κn. A randomized algorithm finds κ with error probability 1/2 in time O(nm). If the vertices have nonnegative weights the weighted vertex connectivity is found in time O(κ1nmlog(n2/m)) where κ1 ≤ m/n is the unweighted vertex connectivity or in expected time O(nmlog(n2/m)) with error probability 1/2. The main algorithm combines two previous vertex connectivity algorithms and a generalization of the preflow-push algorithm of Hao and Orlin (1994, J. Algorithms17, 424–446) that computes edge connectivity.","lang":"eng"}],"page":"222-250","publication_status":"published","oa_version":"None","day":"01"}]