--- _id: '2776' 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. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Antti full_name: Knowles, Antti last_name: Knowles - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau - first_name: Jun full_name: Yin, Jun last_name: Yin citation: 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' 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' 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.' 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.' 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.' 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.' short: L. Erdös, A. Knowles, H. Yau, J. Yin, Communications in Mathematical Physics 314 (2012) 587–640. date_created: 2018-12-11T11:59:32Z date_published: 2012-09-01T00:00:00Z date_updated: 2021-01-12T06:59:37Z day: '01' doi: 10.1007/s00220-012-1527-7 extern: 1 intvolume: ' 314' issue: '3' month: '09' page: 587 - 640 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4114' quality_controlled: 0 status: public title: 'Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues' type: journal_article volume: 314 year: '2012' ... --- _id: '2774' 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. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Søren full_name: Fournais, Søren last_name: Fournais - first_name: Jan full_name: Solovej, Jan P last_name: Solovej 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 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 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. 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. 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. 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. short: L. Erdös, S. Fournais, J. Solovej, Communications in Mathematical Physics 312 (2012) 847–882. date_created: 2018-12-11T11:59:31Z date_published: 2012-06-01T00:00:00Z date_updated: 2021-01-12T06:59:36Z day: '01' doi: 10.1007/s00220-012-1468-1 extern: 1 intvolume: ' 312' issue: '3' month: '06' page: 847 - 882 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4116' quality_controlled: 0 status: public title: Scott correction for large atoms and molecules in a self-generated magnetic field type: journal_article volume: 312 year: '2012' ... --- _id: '2773' abstract: - lang: eng 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]. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau citation: 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 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 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. 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. ista: Erdös L, Yau H. 2012. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 17. 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. short: L. Erdös, H. Yau, Electronic Journal of Probability 17 (2012). date_created: 2018-12-11T11:59:31Z date_published: 2012-04-10T00:00:00Z date_updated: 2021-01-12T06:59:36Z day: '10' doi: 10.1214/EJP.v17-1779 extern: 1 intvolume: ' 17' month: '04' publication: Electronic Journal of Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '4117' quality_controlled: 0 status: public title: A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices type: journal_article volume: 17 year: '2012' ... --- _id: '2771' 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. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: David full_name: Hasler, David G last_name: Hasler 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 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. 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. 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. short: L. Erdös, D. Hasler, Journal of Statistical Physics 146 (2012) 900–923. date_created: 2018-12-11T11:59:31Z date_published: 2012-03-01T00:00:00Z date_updated: 2021-01-12T06:59:35Z day: '01' doi: 10.1007/s10955-012-0445-6 extern: 1 intvolume: ' 146' issue: '5' month: '03' page: 900 - 923 publication: Journal of Statistical Physics publication_status: published publisher: Springer publist_id: '4119' quality_controlled: 0 status: public title: Anderson localization at band edges for random magnetic fields type: journal_article volume: 146 year: '2012' ... --- _id: '2778' abstract: - lang: eng 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. author: - first_name: Paul full_name: Bourgade, Paul last_name: Bourgade - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng-Tzer last_name: Yau citation: 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 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 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. 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. ista: Bourgade P, Erdös L, Yau H. 2012. Bulk universality of general β-ensembles with non-convex potential. Journal of Mathematical Physics. 53(9). 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). date_created: 2018-12-11T11:59:33Z date_published: 2012-09-28T00:00:00Z date_updated: 2021-01-12T06:59:38Z day: '28' doi: 10.1063/1.4751478 extern: 1 intvolume: ' 53' issue: '9' month: '09' publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '4112' quality_controlled: 0 status: public title: Bulk universality of general β-ensembles with non-convex potential type: journal_article volume: 53 year: '2012' ... --- _id: '2779' abstract: - lang: eng 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. author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: David full_name: Hasler, David G last_name: Hasler citation: 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 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 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. 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. ista: Erdös L, Hasler D. 2012. Wegner estimate for random magnetic Laplacian on ℤ 2. Annales Henri Poincare. 13(8), 1719–1731. 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. date_created: 2018-12-11T11:59:33Z date_published: 2012-12-01T00:00:00Z date_updated: 2021-01-12T06:59:38Z day: '01' doi: 10.1007/s00023-012-0177-9 extern: 1 intvolume: ' 13' issue: '8' month: '12' page: 1719 - 1731 publication: Annales Henri Poincare publication_status: published publisher: Birkhäuser publist_id: '4111' quality_controlled: 0 status: public title: Wegner estimate for random magnetic Laplacian on ℤ 2 type: journal_article volume: 13 year: '2012' ... --- _id: '2802' 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. author: - first_name: Tobias full_name: Lapp, Tobias last_name: Lapp - first_name: Martin full_name: Rohloff, Martin last_name: Rohloff - first_name: Jürgen full_name: Vollmer, Jürgen T last_name: Vollmer - first_name: Björn full_name: Björn Hof id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:59:40Z date_published: 2012-05-05T00:00:00Z date_updated: 2021-01-12T06:59:49Z day: '05' doi: 10.1007/s00348-011-1243-7 extern: 1 intvolume: ' 52' issue: '5' month: '05' page: 1187 - 1200 publication: Experiments in Fluids publication_status: published publisher: Springer publist_id: '4087' quality_controlled: 0 status: public title: Particle tracking for polydisperse sedimenting droplets in phase separation type: journal_article volume: 52 year: '2012' ... --- _id: '2803' 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. author: - first_name: Alberto full_name: de Lózar, Alberto last_name: De Lózar - first_name: Fernando full_name: Mellibovsky, Fernando last_name: Mellibovsky - first_name: Marc full_name: Avila, Marc last_name: Avila - first_name: Björn full_name: Björn Hof id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 citation: 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 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 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. 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. ista: De Lózar A, Mellibovsky F, Avila M, Hof B. 2012. Edge state in pipe flow experiments. Physical Review Letters. 108(21). 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). date_created: 2018-12-11T11:59:41Z date_published: 2012-05-21T00:00:00Z date_updated: 2021-01-12T06:59:49Z day: '21' doi: 10.1103/PhysRevLett.108.214502 extern: 1 intvolume: ' 108' issue: '21' month: '05' publication: Physical Review Letters publication_status: published publisher: American Physical Society publist_id: '4086' quality_controlled: 0 status: public title: Edge state in pipe flow experiments type: journal_article volume: 108 year: '2012' ... --- _id: '2804' 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 author: - first_name: Johannes full_name: Blaschke, Johannes last_name: Blaschke - first_name: Tobias full_name: Lapp, Tobias last_name: Lapp - first_name: Björn full_name: Björn Hof id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 - first_name: Jürgen full_name: Vollmer, Jürgen T last_name: Vollmer citation: 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' 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' 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.' 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.' 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).' 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.' short: J. Blaschke, T. Lapp, B. Hof, J. Vollmer, Physical Review Letters 109 (2012). date_created: 2018-12-11T11:59:41Z date_published: 2012-08-10T00:00:00Z date_updated: 2021-01-12T06:59:50Z day: '10' doi: 10.1103/PhysRevLett.109.068701 extern: 1 intvolume: ' 109' issue: '6' month: '08' publication: Physical Review Letters publication_status: published publisher: American Physical Society publist_id: '4085' quality_controlled: 0 status: public title: 'Breath figures: Nucleation, growth, coalescence, and the size distribution of droplets' type: journal_article volume: 109 year: '2012' ... --- _id: '2825' 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.' author: - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Lampert C. Dynamic pruning of factor graphs for maximum marginal prediction. In: Vol 1. Neural Information Processing Systems; 2012:82-90.' 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.' chicago: Lampert, Christoph. “Dynamic Pruning of Factor Graphs for Maximum Marginal Prediction,” 1:82–90. Neural Information Processing Systems, 2012. 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.' mla: Lampert, Christoph. Dynamic Pruning of Factor Graphs for Maximum Marginal Prediction. Vol. 1, Neural Information Processing Systems, 2012, pp. 82–90. short: C. Lampert, in:, Neural Information Processing Systems, 2012, pp. 82–90. conference: end_date: 2012-12-06 location: Lake Tahoe, NV, United States name: 'NIPS: Neural Information Processing Systems' start_date: 2012-12-03 date_created: 2018-12-11T11:59:48Z date_published: 2012-12-01T00:00:00Z date_updated: 2021-01-12T06:59:59Z day: '01' department: - _id: ChLa intvolume: ' 1' language: - iso: eng month: '12' oa_version: None page: 82 - 90 publication_status: published publisher: Neural Information Processing Systems publist_id: '3975' quality_controlled: '1' scopus_import: 1 status: public title: Dynamic pruning of factor graphs for maximum marginal prediction type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 1 year: '2012' ...