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Achieving the KS threshold in the general stochastic block model with linearized acyclic belief propagation 30

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Achieving the KS threshold in the general stochastic block m...

30th Annual Conference on Neural Information Processing Systems, NIPS 2016

作者： Abbe, Emmanuel Sandon, Colin Applied and Computational Mathematics EE Dept. Princeton University United States Department of Mathematics Princeton University United States

The stochastic block model (SBM) has long been studied in machine learning and network science as a canonical model for clustering and community detection. In the recent years, new developments have demonstrated the presence of threshold phenomena for this model, which have set new challenges for algorithms. For the detection problem in symmetric SBMs, Decelle et al. conjectured that the so-called Kesten-Stigum (KS) threshold can be achieved efficiently. This was proved for two communities, but remained open for three and more communities. We prove this conjecture here, obtaining a general result that applies to arbitrary SBMs with linear size communities. The developed algorithm is a linearized acyclic belief propagation (ABP) algorithm, which mitigates the effects of cycles while provably achieving the KS threshold in O(n ln n) time. This extends prior methods by achieving universally the KS threshold while reducing or preserving the computational complexity. ABP is also connected to a power iteration method on a generalized nonbacktracking operator, formalizing the spectral-message passing interplay described in Krzakala et al., and extending results from Bordenave et al. © 2016 NIPS Foundation - All Rights Reserved.

关键词： Belief propagation

Understanding the origin of bandgap problem in transition and post-transition metal oxides

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arXiv 2018年

作者： Tan, Hengxin Liu, Haitao Li, Yuanchang Duan, Wenhui Zhang, Shengbai State Key Laboratory of Low-Dimensional Quantum Physics and Collaborative Innovation Center of Quantum Matter Department of Physics Tsinghua University Beijing100084 China Institute of Applied Physics and Computational Mathematics PO Box 8009 Beijing100088 China Advanced Research Institute of Multidisciplinary Science Beijing Institute of Technology Beijing100081 China Institute for Advanced Study Tsinghua University Beijing100084 China Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute TroyNY12180 United States

Improving electronic structure calculations for practical and technologically-important materials has been a never-ending pursue. This is especially true for transition and post-transition metal oxides for which the current first-principles approaches still suffer various drawbacks. Here we present a hierarchical-hybrid functional approach built on the use of pseudopotentials. The key is to introduce a discontinuity in the exchange functional between core and valence electrons. It allows for treating the localization errors of sp and d electrons differently, which have been known to be an important source of error for the band structure. Using ZnO as a prototype, we show the approach is successful in simultaneously reproducing the band gap and d-band position. Remarkably, the same approach, without having to change the hybrid mixing parameters from those of Zn, works reasonably well for other binary 3d transition and post-transition metal oxides across board. Our findings point to a new direction of systematically improving the exchange functional in first-principles calculations. Copyright © 2018, The Authors. All rights reserved.

关键词： Transition metal oxides

Sharp rates of convergence for accumulated spectrograms

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arXiv 2017年

作者： Abreu, Luis Daniel Pereira, Joao Romero, Jose Luis Acoustics Research Institute Austrian Academy of Science Wohllebengasse 12-14 ViennaA-1040 Austria Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the spectrograms corresponding to large eigenvalues). We derive a sharp bound for the rate of convergence of the accumulated spectrogram, improving on recent *** Codes 65F18, 94A12, 65N21, 42C25 Copyright © 2017, The Authors. All rights reserved.

关键词： Spectrographs

Rigorous mathematical analysis of the quasispecies model: From Manfred Eigen to the recent developments

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arXiv 2017年

作者： Bratus, Alexander S. Novozhilov, Artem S. Semenov, Yuri S. Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow119992 Russia Applied Mathematics1 Moscow State University of Railway Engineering Moscow127994 Department of Mathematics North Dakota State University FargoND58108 United States

We review the major progress in the rigorous analysis of the classical quasispecies model that usually comes in two related but different forms: the Eigen model and the CrowKimura model. The model itself was formulated almost 50 years ago, and in its stationary form represents an easy to formulate eigenvalue problem. Notwithstanding the simplicity of the problem statement, we still lack full understanding of the behavior of the mean population fitness and the quasispecies distribution for an arbitrary fitness landscape. Our main goal in this review is two-fold: First, to highlight a number of impressive mathematical results, including some of the recent ones, which pertain to the mathematical development of the quasispecies theory. Second, to emphasize that despite these 50 years of vigorous research, there are still very natural both biological and mathematical questions that remain to be addressed within the quasispecies framework. Our hope is that at least some of the approaches we review in this text can be of help for anyone embarking on further analysis of the quasispecies model. Copyright © 2017, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

A NEW NUMERICAL APPROACH TO INVERSE TRANSPORT EQUATION WITH ERROR ANALYSIS

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arXiv 2017年

作者： Li, Qin Shu, Ruiwen Wang, Li Mathematics Department University of Wisconsin-Madison 480 Lincoln Dr. MadisonWI53705 United States Department of Mathematics Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo 244 Mathematics Building BuffaloNY14206 United States

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering coefficient of the media, through the source-measurement pairs. A typical computational approach is to form the inverse problem as a PDE-constraint optimization, with the minimizer being the to-be-recovered coefficients. The method is tested to be efficient in practice, but lacks analytical justification: there is no guarantee of the existence or uniqueness of the minimizer, and the error is hard to quantify. In this paper, we provide a different algorithm by levering the ideas from singular decomposition analysis. Our approach is to decompose the measurements into three components, two out of which encode the information of the two coefficients respectively. We then split the optimization problem into two subproblems and use those two components to recover the absorption and scattering coefficients separately. In this regard, we prove the well-posedness of the new optimization, and the error could be quantified with better precision. In the end, we incorporate the diffusive scaling and show that the error is harder to control in the diffusive limit. Copyright © 2017, The Authors. All rights reserved.

关键词： Recovery

Comparative study of inelastic squared form factors of the vibronic states of B1Σu+, C1Πu, and EF1Σg+ for molecular hydrogen: Inelastic x-ray and electron scattering

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Physical Review A 2018年第3期97卷 032503-032503页

作者： Long-Quan Xu Xu Kang Yi-Geng Peng Xin Xu Ya-Wei Liu Yong Wu Ke Yang Nozomu Hiraoka Ku-Ding Tsuei Jian-Guo Wang Lin-Fan Zhu Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of China Hefei Anhui 230026 People's Republic of China Synergetic Innovation Center of Quantum Information and Quantum Physics University of Science and Technology of China Hefei Anhui 230026 People's Republic of China Institute of Applied Physics and Computational Mathematics Beijing 100088 People's Republic of China Shanghai Institute of Applied Physics Chinese Academy of Sciences Shanghai 201204 People's Republic of China National Synchrotron Radiation Research Center Hsinchu 30076 Taiwan Republic of China

A joint experimental and theoretical investigation of the valence-shell excitations of hydrogen has been performed by the high-resolution inelastic x-ray scattering and electron scattering as well as the multireference single- and double-excitation configuration-interaction method. Momentum-transfer-dependent inelastic squared form factors for the vibronic series belonging to the B1Σu+,C1Πu, and EF1Σg+ electronic states of molecular hydrogen have been derived from the inelastic x-ray scattering method at an impact photon energy around 10 keV, and the electron energy-loss spectra measured at an incident electron energy of 1500 eV. It is found that both the present and the previous calculations cannot satisfactorily reproduce the inelastic squared form-factor profiles for the higher vibronic transitions of the B1Σu+ state of molecular hydrogen, which may be due to the electronic-vibrational coupling for the higher vibronic states. For the C1Πu state and some vibronic excitations of EF1Σg+ state, the present experimental results are in good agreement with the present and previous calculations, while the slight differences between the inelastic x-ray scattering and electron energy-loss spectroscopy results in the larger squared momentum-transfer region may be attributed to the increasing role of the higher-order Born terms in the electron-scattering process.

关键词： Electron & positron scattering Electronic excitation & ionization Electronic structure of atoms & molecules Electronic transitions Resonant inelastic x-ray scattering

Quantum dynamics of atomic Rydberg excitation in strong laser fields

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arXiv 2019年

作者： Hu, Shilin Hao., Xiaolei Lv, Hang Liu, Mingqing Yang, Tianxiang Xu, Haifeng Jin, Mingxing Ding, Dajun Li, Qianguang Li, Weidong Becker, Wilhelm Chen, Jing Laboratory of Quantum Engineering and Quantum Metrology School of Physics and Astronomy Sun Yat-Sen University Zhuhai Campus Zhuhai519082 China Institute of Theoretical Physics and Department of Physics Shanxi University Taiyuan030006 China Institute of atomic and molecular physics Jinlin University Changchun130012 China Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy Jilin University Changchun130012 China Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing100088 China School of Physics and Electronic-information Engineering Hubei Engineering University Xiaogan432000 China Max-Born-Institut Max-Born-Strasse 2a Berlin12489 Germany National Research Nuclear University MEPhI Moscow115409 Russia Center for Advanced Material Diagnostic Technology Shenzhen Technology University Shenzhen518118 China

Neutral atoms have been observed to survive intense laser pulses in high Rydberg states with surprisingly large probability. Only with this Rydberg-state excitation (RSE) included is the picture of intense-laser-atom interaction complete. Various mechanisms have been proposed to explain the underlying physics. However, neither one can explain all the features observed in experiments and in time-dependent Schrödinger equation (TDSE) simulations. Here we propose a fully quantummechanical model based on the strong-field approximation (SFA). It well reproduces the intensity dependence of RSE obtained by the TDSE, which exhibits a series of modulated peaks. They are due to recapture of the liberated electron and the fact that the pertinent probability strongly depends on the position and the parity of the Rydberg state. We also present measurements of RSE in xenon at 800 nm, which display the peak structure consistent with the calculations. Copyright © 2019, The Authors. All rights reserved.

关键词： Rydberg states

The Simons Observatory: Modeling optical systematics in the large aperture telescope

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arXiv 2020年

作者： Gudmundsson, Jon E. Gallardo, Patricio A. Puddu, Roberto Dicker, Simon R. Adler, Alexandre E. Ali, Aamir M. Bazarko, Andrew Chesmore, Grace E. Coppi, Gabriele Cothard, Nicholas F. Dachlythra, Nadia Devlin, Mark Dünner, Rolando Fabbian, Giulio Galitzki, Nicholas Golec, Joseph E. Patty Ho, Shuay-Pwu Hargrave, Peter C. Kofman, Anna M. Lee, Adrian T. Limon, Michele Matsuda, Frederick T. Mauskopf, Philip D. Moodley, Kavilan Nati, Federico Niemack, Michael D. Orlowski-Scherer, John Page, Lyman A. Partridge, Bruce Puglisi, Giuseppe Reichardt, Christian L. Sierra, Carlos E. Simon, Sara M. Teply, Grant P. Tucker, Carole Wollack, Edward J. Xu, Zhilei Zhu, Ningfeng The Oskar Klein Centre Department of Physics Stockholm University StockholmSE-106 91 Sweden Department of Physics Cornell University IthacaNY14853 United States Instituto de Astrofísica Centro de Astro-Ingeniería Facultad de Física Pontificia Universidad Católica de Chile Macul Santiago Chile Department of Physics and Astronomy University of Pennsylvania PhiladelphiaPA19104 United States Department of Physics University of California BerkeleyCA94720 United States Joseph Henry Laboratories of Physics Jadwin Hall Princeton University PrincetonNJ08544 United States Department of Astronomy and Astrophysics The University of Chicago ChicagoIL60637 United States Department of Applied and Engineering Physics Cornell University IthacaNY14853 United States Department of Physics & Astronomy University of Sussex BrightonBN1 9QH United Kingdom Department of Physics University of California San Diego San diegoCA92093 United States Department of Physics University of Chicago ChicagoIL60637 United States School of Physics and Astronomy Cardiff University CardiffCF24 3AA United Kingdom The University of Tokyo Institutes for Advanced Study The University of Tokyo KashiwaChiba277-8583 Japan School of Earth and Space Exploration Department of Physics Arizona State University TempeAZ85281 United States Astrophysics Research Centre University of KwaZulu-Natal Westville Campus Durban4041 South Africa School of Mathematics Statistics & Computer Science University of KwaZulu-Natal Westville Campus Durban4041 South Africa Department of Physics University of Milano-Bicocca Milano Italy Department of Astronomy Cornell University IthacaNY14853 United States Department of Astronomy Haverford College HaverfordPA19041 United States Computational Cosmology Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States School of Physics University of Melbourne ParkvilleVIC3010 Australia Fermi National Accelerator Laboratory MS2

We present geometrical and physical optics simulation results for the Simons Observatory Large Aperture Telescope. This work was developed as part of the general design process for the telescope;allowing us to evaluate the impact of various design choices on performance metrics and potential systematic effects. The primary goal of the simulations was to evaluate the final design of the reflectors and the cold optics which are now being built. We describe non-sequential ray tracing used to inform the design of the cold optics, including absorbers internal to each optics tube. We discuss ray tracing simulations of the telescope structure that allow us to determine geometries that minimize detector loading and mitigate spurious near-field effects that have not been resolved by the internal baffling. We also describe physical optics simulations, performed over a range of frequencies and field locations, that produce estimates of monochromatic far field beam patterns which in turn are used to gauge general optical performance. Finally, we describe simulations that shed light on beam sidelobes from panel gap diffraction. Copyright © 2020, The Authors. All rights reserved.

关键词： Physical optics

Covariance estimation via fiducial inference

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arXiv 2017年

作者： Shi, W. Jenny Hannig, Jan Lai, Randy C.S. Lee, Thomas C.M. Computational Bioscience Program University of Colorado Department of Statistics & Operations Research University of North Carolina Department of Mathematics & Statistics University of Maine Department of Statistics University of California

As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the uncertainty of the estimators without having to choose a prior, we have developed a fiducial approach to the estimation of covariance matrix. Built upon the Fiducial Berstein-von Mises Theorem (Sonderegger and Hannig 2014), we show that the fiducial distribution of the covariate matrix is consistent under our framework. Consequently, the samples generated from this fiducial distribution are good estimators to the true covariance matrix, which enable us to define a meaningful confidence region for the covariance matrix. Lastly, we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.62J10, 62E20, 62F25, 62F12 Copyright © 2017, The Authors. All rights reserved.

关键词： Covariance matrix