[{"date_published":"2013-07-18T00:00:00Z","page":"1003 - 1032","citation":{"chicago":"Erdös, László, and Brendan Farrell. “Local Eigenvalue Density for General MANOVA Matrices.” Journal of Statistical Physics. Springer, 2013. https://doi.org/10.1007/s10955-013-0807-8.","short":"L. Erdös, B. Farrell, Journal of Statistical Physics 152 (2013) 1003–1032.","mla":"Erdös, László, and Brendan Farrell. “Local Eigenvalue Density for General MANOVA Matrices.” Journal of Statistical Physics, vol. 152, no. 6, Springer, 2013, pp. 1003–32, doi:10.1007/s10955-013-0807-8.","apa":"Erdös, L., & Farrell, B. (2013). Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-013-0807-8","ieee":"L. Erdös and B. Farrell, “Local eigenvalue density for general MANOVA matrices,” Journal of Statistical Physics, vol. 152, no. 6. Springer, pp. 1003–1032, 2013.","ista":"Erdös L, Farrell B. 2013. Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. 152(6), 1003–1032.","ama":"Erdös L, Farrell B. Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. 2013;152(6):1003-1032. doi:10.1007/s10955-013-0807-8"},"publication":"Journal of Statistical Physics","day":"18","scopus_import":1,"oa_version":"Preprint","intvolume":" 152","status":"public","title":"Local eigenvalue density for general MANOVA matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2782","issue":"6","abstract":[{"text":"We consider random n×n matrices of the form (XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}, where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spectral edge, the eigenvalue density converges to the limiting density of the Jacobi ensemble even on the shortest possible scales of order 1/n (up to log n factors). This result is the analogue of the local Wigner semicircle law and the local Marchenko-Pastur law for general MANOVA matrices.","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s10955-013-0807-8","quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1207.0031","open_access":"1"}],"external_id":{"arxiv":["1207.0031"]},"oa":1,"month":"07","volume":152,"date_updated":"2021-01-12T06:59:41Z","date_created":"2018-12-11T11:59:34Z","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"last_name":"Farrell","first_name":"Brendan","full_name":"Farrell, Brendan"}],"publisher":"Springer","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2013","publist_id":"4107"},{"type":"journal_article","extern":1,"abstract":[{"text":"We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, that is, graphs on N vertices where every edge is chosen independently and with probability p = p(N). We rescale the matrix so that its bulk eigenvalues are of order one. We prove that, as long as pN→∞(with a speed at least logarithmic in N), the density of eigenvalues of the Erdős-Rényi ensemble is given by the Wigner semicircle law for spectral windows of length larger than N-1 (up to logarithmic corrections). As a consequence, all eigenvectors are proved to be completely delocalized in the sense that the ℓ∞-norms of the ℓ2-normalized eigenvectors are at most of order N-1/2 with a very high probability. The estimates in this paper will be used in the companion paper [Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues (2011) Preprint] to prove the universality of eigenvalue distributions both in the bulk and at the spectral edges under the further restriction that pN »N2/3.","lang":"eng"}],"issue":"3 B","publist_id":"4109","title":"Spectral statistics of Erdős-Rényi graphs I: Local semicircle law","publication_status":"published","status":"public","publisher":"Institute of Mathematical Statistics","intvolume":" 41","year":"2013","_id":"2781","date_created":"2018-12-11T11:59:34Z","date_updated":"2021-01-12T06:59:41Z","volume":41,"author":[{"full_name":"László Erdös","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Knowles","first_name":"Antti","full_name":"Knowles, Antti"},{"last_name":"Yau","first_name":"Horng","full_name":"Yau, Horng-Tzer"},{"last_name":"Yin","first_name":"Jun","full_name":"Yin, Jun"}],"month":"05","day":"01","quality_controlled":0,"page":"2279 - 2375","publication":"Annals of Probability","citation":{"apa":"Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). Spectral statistics of Erdős-Rényi graphs I: Local semicircle law. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/11-AOP734","ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi graphs I: Local semicircle law,” Annals of Probability, vol. 41, no. 3 B. Institute of Mathematical Statistics, pp. 2279–2375, 2013.","ista":"Erdös L, Knowles A, Yau H, Yin J. 2013. Spectral statistics of Erdős-Rényi graphs I: Local semicircle law. Annals of Probability. 41(3 B), 2279–2375.","ama":"Erdös L, Knowles A, Yau H, Yin J. Spectral statistics of Erdős-Rényi graphs I: Local semicircle law. Annals of Probability. 2013;41(3 B):2279-2375. doi:10.1214/11-AOP734","chicago":"Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “Spectral Statistics of Erdős-Rényi Graphs I: Local Semicircle Law.” Annals of Probability. Institute of Mathematical Statistics, 2013. https://doi.org/10.1214/11-AOP734.","short":"L. Erdös, A. Knowles, H. Yau, J. Yin, Annals of Probability 41 (2013) 2279–2375.","mla":"Erdös, László, et al. “Spectral Statistics of Erdős-Rényi Graphs I: Local Semicircle Law.” Annals of Probability, vol. 41, no. 3 B, Institute of Mathematical Statistics, 2013, pp. 2279–375, doi:10.1214/11-AOP734."},"main_file_link":[{"url":"http://arxiv.org/abs/1103.1919","open_access":"1"}],"oa":1,"doi":"10.1214/11-AOP734","date_published":"2013-05-01T00:00:00Z"},{"page":"1837 - 1926","quality_controlled":0,"main_file_link":[{"url":"http://arxiv.org/abs/1205.5664","open_access":"1"}],"citation":{"ista":"Erdös L, Knowles A, Yau H. 2013. Averaging fluctuations in resolvents of random band matrices. Annales Henri Poincare. 14(8), 1837–1926.","apa":"Erdös, L., Knowles, A., & Yau, H. (2013). Averaging fluctuations in resolvents of random band matrices. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-013-0235-y","ieee":"L. Erdös, A. Knowles, and H. Yau, “Averaging fluctuations in resolvents of random band matrices,” Annales Henri Poincare, vol. 14, no. 8. Birkhäuser, pp. 1837–1926, 2013.","ama":"Erdös L, Knowles A, Yau H. Averaging fluctuations in resolvents of random band matrices. Annales Henri Poincare. 2013;14(8):1837-1926. doi:10.1007/s00023-013-0235-y","chicago":"Erdös, László, Antti Knowles, and Horng Yau. “Averaging Fluctuations in Resolvents of Random Band Matrices.” Annales Henri Poincare. Birkhäuser, 2013. https://doi.org/10.1007/s00023-013-0235-y.","mla":"Erdös, László, et al. “Averaging Fluctuations in Resolvents of Random Band Matrices.” Annales Henri Poincare, vol. 14, no. 8, Birkhäuser, 2013, pp. 1837–926, doi:10.1007/s00023-013-0235-y.","short":"L. Erdös, A. Knowles, H. Yau, Annales Henri Poincare 14 (2013) 1837–1926."},"oa":1,"publication":"Annales Henri Poincare","doi":"10.1007/s00023-013-0235-y","date_published":"2013-12-01T00:00:00Z","month":"12","day":"01","intvolume":" 14","publisher":"Birkhäuser","title":"Averaging fluctuations in resolvents of random band matrices","publication_status":"published","status":"public","year":"2013","_id":"2780","volume":14,"date_created":"2018-12-11T11:59:33Z","date_updated":"2021-01-12T06:59:40Z","author":[{"full_name":"László Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"first_name":"Antti","last_name":"Knowles","full_name":"Knowles, Antti"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng-Tzer"}],"type":"journal_article","extern":1,"issue":"8","publist_id":"4110","abstract":[{"lang":"eng","text":"We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix entries. Our results generalize the previous results of Erdős et al. (Ann Probab, arXiv:1103.1919, 2013; Commun Math Phys, arXiv:1103.3869, 2013; J Combin 1(2):15-85, 2011) which constituted a key step in the proof of the local semicircle law with optimal error bound in mean-field random matrix models. Our bounds apply to random band matrices and improve previous estimates from order 2 to order 4 in the cases relevant to applications. In particular, they lead to a proof of the diffusion approximation for the magnitude of the resolvent of random band matrices. This, in turn, implies new delocalization bounds on the eigenvectors. The applications are presented in a separate paper (Erdős et al., arXiv:1205.5669, 2013)."}]},{"month":"06","conference":{"start_date":"2013-06-01","location":"Palo Alto, CA, United States","end_date":"2013-06-04","name":"STOC: Symposium on the Theory of Computing"},"doi":"10.1145/2488608.2488683","language":[{"iso":"eng"}],"oa":1,"quality_controlled":"1","file_date_updated":"2020-07-14T12:45:48Z","publist_id":"4078","author":[{"full_name":"Čadek, Martin","last_name":"Čadek","first_name":"Martin"},{"last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek"},{"first_name":"Jiří","last_name":"Matoušek","full_name":"Matoušek, Jiří"},{"first_name":"Lukáš","last_name":"Vokřínek","full_name":"Vokřínek, Lukáš"},{"full_name":"Wagner, Uli","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:59:42Z","date_updated":"2021-01-12T06:59:51Z","year":"2013","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"ACM","day":"01","has_accepted_license":"1","scopus_import":1,"date_published":"2013-06-01T00:00:00Z","publication":"45th Annual ACM Symposium on theory of computing","citation":{"ista":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of computing. STOC: Symposium on the Theory of Computing, 595–604.","ieee":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory of computing, Palo Alto, CA, United States, 2013, pp. 595–604.","apa":"Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013). Extending continuous maps: Polynomiality and undecidability. In 45th Annual ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United States: ACM. https://doi.org/10.1145/2488608.2488683","ama":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps: Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner. “Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683.","mla":"Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.” 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604, doi:10.1145/2488608.2488683.","short":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604."},"page":"595 - 604","abstract":[{"text":"We consider several basic problems of algebraic topology, with connections to combinatorial and geometric questions, from the point of view of computational complexity. The extension problem asks, given topological spaces X; Y , a subspace A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X → Y . For computational purposes, we assume that X and Y are represented as finite simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map. In this generality the problem is undecidable, as follows from Novikov's result from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected; informally, this means that Y has \\no holes up to dimension k-1" (a basic example of such a Y is the sphere Sk). We prove that, on the one hand, this problem is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2, we obtain an algorithm that solves the extension problem in polynomial time assuming Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides a classification of all extensions up to homotopy (continuous deformation). This relies on results of our SODA 2012 paper, and the main new ingredient is a machinery of objects with polynomial-time homology, which is a polynomial-time analog of objects with effective homology developed earlier by Sergeraert et al. We also consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected Y . Their computability was established by Brown in 1957; we show that πk(Y ) can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where Y is a cell complex with certain rather compact encoding. We strengthen his result to #P-hardness for Y given as a simplicial complex. ","lang":"eng"}],"type":"conference","pubrep_id":"533","file":[{"creator":"system","content_type":"application/pdf","file_size":447945,"file_name":"IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf","access_level":"open_access","date_created":"2018-12-12T10:14:29Z","date_updated":"2020-07-14T12:45:48Z","checksum":"06c2ce5c1135fbc1f71ca15eeb242dcf","file_id":"5081","relation":"main_file"}],"oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2807","ddc":["510"],"status":"public","title":"Extending continuous maps: Polynomiality and undecidability"},{"publisher":"American Society of Plant Biologists","department":[{"_id":"JiFr"}],"publication_status":"published","pmid":1,"year":"2013","volume":162,"date_updated":"2021-01-12T06:59:51Z","date_created":"2018-12-11T11:59:42Z","author":[{"last_name":"Landberg","first_name":"Katarina","full_name":"Landberg, Katarina"},{"full_name":"Pederson, Eric","first_name":"Eric","last_name":"Pederson"},{"full_name":"Viaene, Tom","first_name":"Tom","last_name":"Viaene"},{"first_name":"Behruz","last_name":"Bozorg","full_name":"Bozorg, Behruz"},{"full_name":"Friml, Jirí","orcid":"0000-0002-8302-7596","id":"4159519E-F248-11E8-B48F-1D18A9856A87","last_name":"Friml","first_name":"Jirí"},{"full_name":"Jönsson, Henrik","last_name":"Jönsson","first_name":"Henrik"},{"last_name":"Thelander","first_name":"Mattias","full_name":"Thelander, Mattias"},{"last_name":"Sundberg","first_name":"Eva","full_name":"Sundberg, Eva"}],"publist_id":"4079","quality_controlled":"1","external_id":{"pmid":["23669745"]},"oa":1,"main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3707547/","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1104/pp.113.214023","month":"07","intvolume":" 162","status":"public","title":"The moss physcomitrella patens reproductive organ development is highly organized, affected by the two SHI/STY genes and by the level of active auxin in the SHI/STY expression domain","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2808","oa_version":"Submitted Version","type":"journal_article","issue":"3","abstract":[{"text":"In order to establish a reference for analysis of the function of auxin and the auxin biosynthesis regulators SHORT INTERNODE/ STYLISH (SHI/STY) during Physcomitrella patens reproductive development, we have described male (antheridial) and female (archegonial) development in detail, including temporal and positional information of organ initiation. This has allowed us to define discrete stages of organ morphogenesis and to show that reproductive organ development in P. patens is highly organized and that organ phyllotaxis differs between vegetative and reproductive development. Using the PpSHI1 and PpSHI2 reporter and knockout lines, the auxin reporters GmGH3pro:GUS and PpPINApro:GFP-GUS, and the auxin-conjugating transgene PpSHI2pro:IAAL, we could show that the PpSHI genes, and by inference also auxin, play important roles for reproductive organ development in moss. The PpSHI genes are required for the apical opening of the reproductive organs, the final differentiation of the egg cell, and the progression of canal cells into a cell death program. The apical cells of the archegonium, the canal cells, and the egg cell are also sites of auxin responsiveness and are affected by reduced levels of active auxin, suggesting that auxin mediates PpSHI function in the reproductive organs.","lang":"eng"}],"page":"1406 - 1419","citation":{"ista":"Landberg K, Pederson E, Viaene T, Bozorg B, Friml J, Jönsson H, Thelander M, Sundberg E. 2013. The moss physcomitrella patens reproductive organ development is highly organized, affected by the two SHI/STY genes and by the level of active auxin in the SHI/STY expression domain. Plant Physiology. 162(3), 1406–1419.","apa":"Landberg, K., Pederson, E., Viaene, T., Bozorg, B., Friml, J., Jönsson, H., … Sundberg, E. (2013). The moss physcomitrella patens reproductive organ development is highly organized, affected by the two SHI/STY genes and by the level of active auxin in the SHI/STY expression domain. Plant Physiology. American Society of Plant Biologists. https://doi.org/10.1104/pp.113.214023","ieee":"K. Landberg et al., “The moss physcomitrella patens reproductive organ development is highly organized, affected by the two SHI/STY genes and by the level of active auxin in the SHI/STY expression domain,” Plant Physiology, vol. 162, no. 3. American Society of Plant Biologists, pp. 1406–1419, 2013.","ama":"Landberg K, Pederson E, Viaene T, et al. The moss physcomitrella patens reproductive organ development is highly organized, affected by the two SHI/STY genes and by the level of active auxin in the SHI/STY expression domain. Plant Physiology. 2013;162(3):1406-1419. doi:10.1104/pp.113.214023","chicago":"Landberg, Katarina, Eric Pederson, Tom Viaene, Behruz Bozorg, Jiří Friml, Henrik Jönsson, Mattias Thelander, and Eva Sundberg. “The Moss Physcomitrella Patens Reproductive Organ Development Is Highly Organized, Affected by the Two SHI/STY Genes and by the Level of Active Auxin in the SHI/STY Expression Domain.” Plant Physiology. American Society of Plant Biologists, 2013. https://doi.org/10.1104/pp.113.214023.","mla":"Landberg, Katarina, et al. “The Moss Physcomitrella Patens Reproductive Organ Development Is Highly Organized, Affected by the Two SHI/STY Genes and by the Level of Active Auxin in the SHI/STY Expression Domain.” Plant Physiology, vol. 162, no. 3, American Society of Plant Biologists, 2013, pp. 1406–19, doi:10.1104/pp.113.214023.","short":"K. Landberg, E. Pederson, T. Viaene, B. Bozorg, J. Friml, H. Jönsson, M. Thelander, E. Sundberg, Plant Physiology 162 (2013) 1406–1419."},"publication":"Plant Physiology","date_published":"2013-07-03T00:00:00Z","scopus_import":1,"day":"03"}]