[{"month":"09","day":"01","date_published":"2012-09-01T00:00:00Z","doi":"10.1007/s00220-012-1527-7","citation":{"ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues,” Communications in Mathematical Physics, vol. 314, no. 3. Springer, pp. 587–640, 2012.","apa":"Erdös, L., Knowles, A., Yau, H., & Yin, J. (2012). Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1527-7","ista":"Erdös L, Knowles A, Yau H, Yin J. 2012. Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics. 314(3), 587–640.","ama":"Erdös L, Knowles A, Yau H, Yin J. Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues. Communications in Mathematical Physics. 2012;314(3):587-640. doi:10.1007/s00220-012-1527-7","chicago":"Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues.” Communications in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1527-7.","short":"L. Erdös, A. Knowles, H. Yau, J. Yin, Communications in Mathematical Physics 314 (2012) 587–640.","mla":"Erdös, László, et al. “Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues.” Communications in Mathematical Physics, vol. 314, no. 3, Springer, 2012, pp. 587–640, doi:10.1007/s00220-012-1527-7."},"publication":"Communications in Mathematical Physics","page":"587 - 640","quality_controlled":0,"publist_id":"4114","issue":"3","abstract":[{"lang":"eng","text":"We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e. 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. Under the assumption pN≫N2/3 , we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we prove (1) that the eigenvalue spacing of the Erdős-Rényi graph in the bulk of the spectrum has the same distribution as that of the Gaussian orthogonal ensemble; and (2) that the second largest eigenvalue of the Erdős-Rényi graph has the same distribution as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application of our method, we prove the bulk universality of generalized Wigner matrices under the assumption that the matrix entries have at least 4 + ε moments."}],"extern":1,"type":"journal_article","author":[{"full_name":"László Erdös","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Antti","last_name":"Knowles","full_name":"Knowles, Antti"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng-Tzer"},{"full_name":"Yin, Jun","last_name":"Yin","first_name":"Jun"}],"volume":314,"date_created":"2018-12-11T11:59:32Z","date_updated":"2021-01-12T06:59:37Z","year":"2012","_id":"2776","publisher":"Springer","intvolume":" 314","publication_status":"published","title":"Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues","status":"public"},{"day":"01","month":"06","doi":"10.1007/s00220-012-1468-1","date_published":"2012-06-01T00:00:00Z","page":"847 - 882","quality_controlled":0,"citation":{"ama":"Erdös L, Fournais S, Solovej J. Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics. 2012;312(3):847-882. doi:10.1007/s00220-012-1468-1","ieee":"L. Erdös, S. Fournais, and J. Solovej, “Scott correction for large atoms and molecules in a self-generated magnetic field,” Communications in Mathematical Physics, vol. 312, no. 3. Springer, pp. 847–882, 2012.","apa":"Erdös, L., Fournais, S., & Solovej, J. (2012). Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-012-1468-1","ista":"Erdös L, Fournais S, Solovej J. 2012. Scott correction for large atoms and molecules in a self-generated magnetic field. Communications in Mathematical Physics. 312(3), 847–882.","short":"L. Erdös, S. Fournais, J. Solovej, Communications in Mathematical Physics 312 (2012) 847–882.","mla":"Erdös, László, et al. “Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field.” Communications in Mathematical Physics, vol. 312, no. 3, Springer, 2012, pp. 847–82, doi:10.1007/s00220-012-1468-1.","chicago":"Erdös, László, Søren Fournais, and Jan Solovej. “Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field.” Communications in Mathematical Physics. Springer, 2012. https://doi.org/10.1007/s00220-012-1468-1."},"publication":"Communications in Mathematical Physics","extern":1,"publist_id":"4116","issue":"3","abstract":[{"lang":"eng","text":"We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Zα 2 ≤ κ 0 for a sufficiently small κ 0, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κ = Zα 2 is fixed, the ground state energy of the system is given by a two term expansion c 1Z 7/3 + c 2(κ) Z 2 + o(Z 2). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion."}],"type":"journal_article","volume":312,"date_created":"2018-12-11T11:59:31Z","date_updated":"2021-01-12T06:59:36Z","author":[{"full_name":"László Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"last_name":"Fournais","first_name":"Søren","full_name":"Fournais, Søren"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan P"}],"publisher":"Springer","intvolume":" 312","title":"Scott correction for large atoms and molecules in a self-generated magnetic field","status":"public","publication_status":"published","year":"2012","_id":"2774"},{"intvolume":" 17","publisher":"Institute of Mathematical Statistics","title":"A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices","publication_status":"published","status":"public","_id":"2773","year":"2012","volume":17,"date_updated":"2021-01-12T06:59:36Z","date_created":"2018-12-11T11:59:31Z","author":[{"full_name":"László Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng-Tzer"}],"type":"journal_article","extern":1,"publist_id":"4117","abstract":[{"text":"Recently we proved [3, 4, 6, 7, 9, 10, 11] that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu [15] gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our work [2].","lang":"eng"}],"quality_controlled":0,"citation":{"short":"L. Erdös, H. Yau, Electronic Journal of Probability 17 (2012).","mla":"Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability, vol. 17, Institute of Mathematical Statistics, 2012, doi:10.1214/EJP.v17-1779.","chicago":"Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2012. https://doi.org/10.1214/EJP.v17-1779.","ama":"Erdös L, Yau H. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 2012;17. doi:10.1214/EJP.v17-1779","ieee":"L. Erdös and H. Yau, “A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices,” Electronic Journal of Probability, vol. 17. Institute of Mathematical Statistics, 2012.","apa":"Erdös, L., & Yau, H. (2012). A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v17-1779","ista":"Erdös L, Yau H. 2012. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 17."},"publication":"Electronic Journal of Probability","date_published":"2012-04-10T00:00:00Z","doi":"10.1214/EJP.v17-1779","day":"10","month":"04"},{"type":"journal_article","extern":1,"abstract":[{"lang":"eng","text":"We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erdos and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis."}],"issue":"5","publist_id":"4119","publication_status":"published","title":"Anderson localization at band edges for random magnetic fields","status":"public","publisher":"Springer","intvolume":" 146","_id":"2771","year":"2012","date_updated":"2021-01-12T06:59:35Z","date_created":"2018-12-11T11:59:31Z","volume":146,"author":[{"full_name":"László Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"first_name":"David","last_name":"Hasler","full_name":"Hasler, David G"}],"month":"03","day":"01","quality_controlled":0,"page":"900 - 923","publication":"Journal of Statistical Physics","citation":{"ama":"Erdös L, Hasler D. Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. 2012;146(5):900-923. doi:10.1007/s10955-012-0445-6","apa":"Erdös, L., & Hasler, D. (2012). Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-012-0445-6","ieee":"L. Erdös and D. Hasler, “Anderson localization at band edges for random magnetic fields,” Journal of Statistical Physics, vol. 146, no. 5. Springer, pp. 900–923, 2012.","ista":"Erdös L, Hasler D. 2012. Anderson localization at band edges for random magnetic fields. Journal of Statistical Physics. 146(5), 900–923.","short":"L. Erdös, D. Hasler, Journal of Statistical Physics 146 (2012) 900–923.","mla":"Erdös, László, and David Hasler. “Anderson Localization at Band Edges for Random Magnetic Fields.” Journal of Statistical Physics, vol. 146, no. 5, Springer, 2012, pp. 900–23, doi:10.1007/s10955-012-0445-6.","chicago":"Erdös, László, and David Hasler. “Anderson Localization at Band Edges for Random Magnetic Fields.” Journal of Statistical Physics. Springer, 2012. https://doi.org/10.1007/s10955-012-0445-6."},"date_published":"2012-03-01T00:00:00Z","doi":"10.1007/s10955-012-0445-6"},{"date_published":"2012-09-28T00:00:00Z","doi":"10.1063/1.4751478","quality_controlled":0,"publication":"Journal of Mathematical Physics","citation":{"chicago":"Bourgade, Paul, László Erdös, and Horng Yau. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics. American Institute of Physics, 2012. https://doi.org/10.1063/1.4751478.","mla":"Bourgade, Paul, et al. “Bulk Universality of General β-Ensembles with Non-Convex Potential.” Journal of Mathematical Physics, vol. 53, no. 9, American Institute of Physics, 2012, doi:10.1063/1.4751478.","short":"P. Bourgade, L. Erdös, H. Yau, Journal of Mathematical Physics 53 (2012).","ista":"Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 53(9).","apa":"Bourgade, P., Erdös, L., & Yau, H. (2012). Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4751478","ieee":"P. Bourgade, L. Erdös, and H. Yau, “Bulk universality of general β-ensembles with non-convex potential,” Journal of Mathematical Physics, vol. 53, no. 9. American Institute of Physics, 2012.","ama":"Bourgade P, Erdös L, Yau H. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 2012;53(9). doi:10.1063/1.4751478"},"day":"28","month":"09","date_created":"2018-12-11T11:59:33Z","date_updated":"2021-01-12T06:59:38Z","volume":53,"author":[{"full_name":"Bourgade, Paul","first_name":"Paul","last_name":"Bourgade"},{"full_name":"László Erdös","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Yau","first_name":"Horng","full_name":"Yau, Horng-Tzer"}],"publication_status":"published","title":"Bulk universality of general β-ensembles with non-convex potential","status":"public","intvolume":" 53","publisher":"American Institute of Physics","_id":"2778","year":"2012","extern":1,"abstract":[{"text":"We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [P. Bourgade, L. Erdös, and H.-T. Yau, Universality of general β-ensembles, preprint arXiv:0907.5605 (2011)]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a "convexified measure" so that the local statistics are preserved under this convexification.","lang":"eng"}],"issue":"9","publist_id":"4112","type":"journal_article"},{"doi":"10.1007/s00023-012-0177-9","date_published":"2012-12-01T00:00:00Z","publication":"Annales Henri Poincare","citation":{"ista":"Erdös L, Hasler D. 2012. Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. 13(8), 1719–1731.","ieee":"L. Erdös and D. Hasler, “Wegner estimate for random magnetic Laplacian on ℤ 2,” Annales Henri Poincare, vol. 13, no. 8. Birkhäuser, pp. 1719–1731, 2012.","apa":"Erdös, L., & Hasler, D. (2012). Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-012-0177-9","ama":"Erdös L, Hasler D. Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. 2012;13(8):1719-1731. doi:10.1007/s00023-012-0177-9","chicago":"Erdös, László, and David Hasler. “Wegner Estimate for Random Magnetic Laplacian on ℤ 2.” Annales Henri Poincare. Birkhäuser, 2012. https://doi.org/10.1007/s00023-012-0177-9.","mla":"Erdös, László, and David Hasler. “Wegner Estimate for Random Magnetic Laplacian on ℤ 2.” Annales Henri Poincare, vol. 13, no. 8, Birkhäuser, 2012, pp. 1719–31, doi:10.1007/s00023-012-0177-9.","short":"L. Erdös, D. Hasler, Annales Henri Poincare 13 (2012) 1719–1731."},"quality_controlled":0,"page":"1719 - 1731","month":"12","day":"01","author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"László Erdös"},{"last_name":"Hasler","first_name":"David","full_name":"Hasler, David G"}],"date_created":"2018-12-11T11:59:33Z","date_updated":"2021-01-12T06:59:38Z","volume":13,"year":"2012","_id":"2779","publication_status":"published","title":"Wegner estimate for random magnetic Laplacian on ℤ 2","status":"public","intvolume":" 13","publisher":"Birkhäuser","abstract":[{"text":"We consider a two-dimensional magnetic Schrödinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate that does not rely on the monotonicity of the energy on the random parameters.","lang":"eng"}],"issue":"8","publist_id":"4111","extern":1,"type":"journal_article"},{"publication_status":"published","status":"public","title":"Particle tracking for polydisperse sedimenting droplets in phase separation","publisher":"Springer","intvolume":" 52","year":"2012","_id":"2802","date_updated":"2021-01-12T06:59:49Z","date_created":"2018-12-11T11:59:40Z","volume":52,"author":[{"full_name":"Lapp, Tobias","last_name":"Lapp","first_name":"Tobias"},{"last_name":"Rohloff","first_name":"Martin","full_name":"Rohloff, Martin"},{"full_name":"Vollmer, Jürgen T","last_name":"Vollmer","first_name":"Jürgen"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754","first_name":"Björn","last_name":"Hof","full_name":"Björn Hof"}],"type":"journal_article","extern":1,"abstract":[{"lang":"eng","text":"When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase-separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4-40 μm are detected and tracked. Based on these data, we resolve the oscillations in the droplet size distribution that are coupled to the convective flow."}],"publist_id":"4087","issue":"5","quality_controlled":0,"page":"1187 - 1200","publication":"Experiments in Fluids","citation":{"ama":"Lapp T, Rohloff M, Vollmer J, Hof B. Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. 2012;52(5):1187-1200. doi:10.1007/s00348-011-1243-7","ista":"Lapp T, Rohloff M, Vollmer J, Hof B. 2012. Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. 52(5), 1187–1200.","ieee":"T. Lapp, M. Rohloff, J. Vollmer, and B. Hof, “Particle tracking for polydisperse sedimenting droplets in phase separation,” Experiments in Fluids, vol. 52, no. 5. Springer, pp. 1187–1200, 2012.","apa":"Lapp, T., Rohloff, M., Vollmer, J., & Hof, B. (2012). Particle tracking for polydisperse sedimenting droplets in phase separation. Experiments in Fluids. Springer. https://doi.org/10.1007/s00348-011-1243-7","mla":"Lapp, Tobias, et al. “Particle Tracking for Polydisperse Sedimenting Droplets in Phase Separation.” Experiments in Fluids, vol. 52, no. 5, Springer, 2012, pp. 1187–200, doi:10.1007/s00348-011-1243-7.","short":"T. Lapp, M. Rohloff, J. Vollmer, B. Hof, Experiments in Fluids 52 (2012) 1187–1200.","chicago":"Lapp, Tobias, Martin Rohloff, Jürgen Vollmer, and Björn Hof. “Particle Tracking for Polydisperse Sedimenting Droplets in Phase Separation.” Experiments in Fluids. Springer, 2012. https://doi.org/10.1007/s00348-011-1243-7."},"doi":"10.1007/s00348-011-1243-7","date_published":"2012-05-05T00:00:00Z","day":"05","month":"05"},{"extern":1,"abstract":[{"lang":"eng","text":"Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border."}],"issue":"21","publist_id":"4086","type":"journal_article","date_created":"2018-12-11T11:59:41Z","date_updated":"2021-01-12T06:59:49Z","volume":108,"author":[{"full_name":"de Lózar, Alberto","last_name":"De Lózar","first_name":"Alberto"},{"first_name":"Fernando","last_name":"Mellibovsky","full_name":"Mellibovsky, Fernando"},{"last_name":"Avila","first_name":"Marc","full_name":"Avila, Marc"},{"full_name":"Björn Hof","id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754","first_name":"Björn","last_name":"Hof"}],"title":"Edge state in pipe flow experiments","status":"public","publication_status":"published","publisher":"American Physical Society","intvolume":" 108","year":"2012","_id":"2803","month":"05","day":"21","date_published":"2012-05-21T00:00:00Z","doi":"10.1103/PhysRevLett.108.214502","quality_controlled":0,"publication":"Physical Review Letters","citation":{"mla":"De Lózar, Alberto, et al. “Edge State in Pipe Flow Experiments.” Physical Review Letters, vol. 108, no. 21, American Physical Society, 2012, doi:10.1103/PhysRevLett.108.214502.","short":"A. De Lózar, F. Mellibovsky, M. Avila, B. Hof, Physical Review Letters 108 (2012).","chicago":"De Lózar, Alberto, Fernando Mellibovsky, Marc Avila, and Björn Hof. “Edge State in Pipe Flow Experiments.” Physical Review Letters. American Physical Society, 2012. https://doi.org/10.1103/PhysRevLett.108.214502.","ama":"De Lózar A, Mellibovsky F, Avila M, Hof B. Edge state in pipe flow experiments. Physical Review Letters. 2012;108(21). doi:10.1103/PhysRevLett.108.214502","ista":"De Lózar A, Mellibovsky F, Avila M, Hof B. 2012. Edge state in pipe flow experiments. Physical Review Letters. 108(21).","ieee":"A. De Lózar, F. Mellibovsky, M. Avila, and B. Hof, “Edge state in pipe flow experiments,” Physical Review Letters, vol. 108, no. 21. American Physical Society, 2012.","apa":"De Lózar, A., Mellibovsky, F., Avila, M., & Hof, B. (2012). Edge state in pipe flow experiments. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.108.214502"}},{"month":"08","day":"10","doi":"10.1103/PhysRevLett.109.068701","date_published":"2012-08-10T00:00:00Z","quality_controlled":0,"publication":"Physical Review Letters","citation":{"short":"J. Blaschke, T. Lapp, B. Hof, J. Vollmer, Physical Review Letters 109 (2012).","mla":"Blaschke, Johannes, et al. “Breath Figures: Nucleation, Growth, Coalescence, and the Size Distribution of Droplets.” Physical Review Letters, vol. 109, no. 6, American Physical Society, 2012, doi:10.1103/PhysRevLett.109.068701.","chicago":"Blaschke, Johannes, Tobias Lapp, Björn Hof, and Jürgen Vollmer. “Breath Figures: Nucleation, Growth, Coalescence, and the Size Distribution of Droplets.” Physical Review Letters. American Physical Society, 2012. https://doi.org/10.1103/PhysRevLett.109.068701.","ama":"Blaschke J, Lapp T, Hof B, Vollmer J. Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets. Physical Review Letters. 2012;109(6). doi:10.1103/PhysRevLett.109.068701","ieee":"J. Blaschke, T. Lapp, B. Hof, and J. Vollmer, “Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets,” Physical Review Letters, vol. 109, no. 6. American Physical Society, 2012.","apa":"Blaschke, J., Lapp, T., Hof, B., & Vollmer, J. (2012). Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.109.068701","ista":"Blaschke J, Lapp T, Hof B, Vollmer J. 2012. Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets. Physical Review Letters. 109(6)."},"extern":1,"abstract":[{"lang":"eng","text":"The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth mechanisms of the droplets. This finding establishes a gateway connecting nucleation and growth of the smallest droplets on surfaces to gross features of the evolution of the droplet size distribution"}],"issue":"6","publist_id":"4085","type":"journal_article","date_created":"2018-12-11T11:59:41Z","date_updated":"2021-01-12T06:59:50Z","volume":109,"author":[{"full_name":"Blaschke, Johannes","first_name":"Johannes","last_name":"Blaschke"},{"last_name":"Lapp","first_name":"Tobias","full_name":"Lapp, Tobias"},{"full_name":"Björn Hof","first_name":"Björn","last_name":"Hof","id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754"},{"full_name":"Vollmer, Jürgen T","first_name":"Jürgen","last_name":"Vollmer"}],"publication_status":"published","title":"Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets","status":"public","intvolume":" 109","publisher":"American Physical Society","year":"2012","_id":"2804"},{"citation":{"chicago":"Lampert, Christoph. “Dynamic Pruning of Factor Graphs for Maximum Marginal Prediction,” 1:82–90. Neural Information Processing Systems, 2012.","short":"C. Lampert, in:, Neural Information Processing Systems, 2012, pp. 82–90.","mla":"Lampert, Christoph. Dynamic Pruning of Factor Graphs for Maximum Marginal Prediction. Vol. 1, Neural Information Processing Systems, 2012, pp. 82–90.","apa":"Lampert, C. (2012). Dynamic pruning of factor graphs for maximum marginal prediction (Vol. 1, pp. 82–90). Presented at the NIPS: Neural Information Processing Systems, Lake Tahoe, NV, United States: Neural Information Processing Systems.","ieee":"C. Lampert, “Dynamic pruning of factor graphs for maximum marginal prediction,” presented at the NIPS: Neural Information Processing Systems, Lake Tahoe, NV, United States, 2012, vol. 1, pp. 82–90.","ista":"Lampert C. 2012. Dynamic pruning of factor graphs for maximum marginal prediction. NIPS: Neural Information Processing Systems vol. 1, 82–90.","ama":"Lampert C. Dynamic pruning of factor graphs for maximum marginal prediction. In: Vol 1. Neural Information Processing Systems; 2012:82-90."},"page":"82 - 90","quality_controlled":"1","date_published":"2012-12-01T00:00:00Z","conference":{"location":"Lake Tahoe, NV, United States","start_date":"2012-12-03","end_date":"2012-12-06","name":"NIPS: Neural Information Processing Systems"},"language":[{"iso":"eng"}],"scopus_import":1,"month":"12","day":"01","_id":"2825","year":"2012","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Neural Information Processing Systems","department":[{"_id":"ChLa"}],"intvolume":" 1","title":"Dynamic pruning of factor graphs for maximum marginal prediction","status":"public","publication_status":"published","author":[{"full_name":"Lampert, Christoph","first_name":"Christoph","last_name":"Lampert","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8622-7887"}],"volume":1,"oa_version":"None","date_updated":"2021-01-12T06:59:59Z","date_created":"2018-12-11T11:59:48Z","type":"conference","publist_id":"3975","abstract":[{"lang":"eng","text":"We study the problem of maximum marginal prediction (MMP) in probabilistic graphical models, a task that occurs, for example, as the Bayes optimal decision rule under a Hamming loss. MMP is typically performed as a two-stage procedure: one estimates each variable's marginal probability and then forms a prediction from the states of maximal probability. In this work we propose a simple yet effective technique for accelerating MMP when inference is sampling-based: instead of the above two-stage procedure we directly estimate the posterior probability of each decision variable. This allows us to identify the point of time when we are sufficiently certain about any individual decision. Whenever this is the case, we dynamically prune the variables we are confident about from the underlying factor graph. Consequently, at any time only samples of variables whose decision is still uncertain need to be created. Experiments in two prototypical scenarios, multi-label classification and image inpainting, show that adaptive sampling can drastically accelerate MMP without sacrificing prediction accuracy."}]}]