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The sample complexity of multi-reference alignment

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arXiv 2017年

作者： Perry, Amelia Weed, Jonathan Bandeira, Afonso S. Rigollet, Philippe Singer, Amit Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA02139-4307 United States Department of Mathematics Courant Institute of Mathematical Sciences Center for Data Science New York University New YorkNY10012 United States Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA02139-4307 United States Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA02139-4307 United States Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The growing role of data-driven approaches to scientific discovery has unveiled a large class of models that involve latent transformations with a rigid algebraic constraint. Three-dimensional molecule reconstruction in Cryo-Electron Microscopy (cryo-EM) is a central problem in this class. Despite decades of algorithmic and software development, there is still little theoretical understanding of the sample complexity of this problem, that is, number of images required for 3-D reconstruction. Here we consider multi-reference alignment (MRA), a simple model that captures fundamental aspects of the statistical and algorithmic challenges arising in cryo-EM and related problems. In MRA, an unknown signal is subject to two types of corruption: a latent cyclic shift and the more traditional additive white noise. The goal is to recover the signal at a certain precision from independent samples. While at high signal-to-noise ratio (SNR), the number of observations needed to recover a generic signal is proportional to 1/SNR, we prove that it rises to a surprising 1/SNR3 in the low SNR regime. This precise phenomenon was observed empirically more than twenty years ago for cryo-EM but has remained unexplained to date. Furthermore, our techniques can easily be extended to the heterogeneous MRA model where the samples come from a mixture of signals, as is often the case in applications such as cryo-EM, where molecules may have different conformations. This provides a first step towards a statistical theory for heterogeneous cryo-EM.62B10, 92C55 Copyright © 2017, The Authors. All rights reserved.

关键词： Signal to noise ratio

Role of correlations in determining the Van Hove strain in Sr2RuO4

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Physical Review B 2019年第24期100卷 245139-245139页

作者： Mark E. Barber Frank Lechermann Sergey V. Streltsov Sergey L. Skornyakov Sayak Ghosh B. J. Ramshaw Naoki Kikugawa Dmitry A. Sokolov Andrew P. Mackenzie Clifford W. Hicks I. I. Mazin Max Planck Institute for Chemical Physics of Solids Nöthnitzer Straße 40 01187 Dresden Germany I. Institut für Theoretische Physik Universität Hamburg Jungiusstraße 9 20355 Hamburg Germany Institute of Metal Physics S. Kovalevskaya Street 18 620990 Ekaterinburg Russia Department of Theoretical Physics and Applied Mathematics Ural Federal University Mira Street 19 620002 Ekaterinburg Russia Laboratory of Atomic and Solid State Physics Cornell University Ithaca New York 14853 USA National Institute for Materials Science Tsukuba Ibaraki 305-0003 Japan Scottish Universities Physics Alliance School of Physics and Astronomy University of St. Andrews St. Andrews KY16 9SS United Kingdom Center for Computational Materials Science U.S. Naval Research Laboratory Washington D.C. 20375 USA

Uniaxial pressure applied along a Ru-O-Ru bond direction induces an elliptical distortion of the largest Fermi surface of Sr2RuO4, eventually causing a Fermi surface topological transition, also known as a Lifshitz transition, into an open Fermi surface. There are various anomalies in low-temperature properties associated with this transition, including maxima in the superconducting critical temperature and in resistivity. In the present paper, we report refined measurements of the strain at which this transition occurs, employing apparatus in which the stress on the sample is measured, and resonant ultrasound measurement of the low-temperature elastic moduli. The Lifshitz transition is found to occur at a longitudinal strain ɛxx of (−0.44±0.06)×10−2, which corresponds to a B1g strain ɛxx−ɛyy of (−0.66±0.09)×10−2. This is considerably smaller than the strain corresponding to a Lifshitz transition in density functional theory calculations, even if the spin-orbit coupling is taken into account. Using dynamical mean-field theory, we show that electronic correlations reduce the critical strain. It turns out that the orbital anisotropy of the local Coulomb interaction on the Ru site is, furthermore, important to bring this critical strain close to the experimental number and thus well into the experimentally accessible range of strains.

关键词： Fermi surface van Hove singularity Strongly correlated systems Unconventional superconductors Density functional theory Pressure techniques

Swarm intelligence scheme for pathfinding and action planning of non-player characters on a last-generation video game 3rd

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Swarm intelligence scheme for pathfinding and action plannin...

Proceedings of the 3rd International Conference on Harmony Search Algorithm, ICHSA 2017

作者： Díaz, Guillermo Iglesias, Andrés University Pompeu Fabra Balmes Building Balmes 132-134 Barcelona08008 Spain Department of Information Science Faculty of Sciences Toho University 2-2-1 Miyama Funabashi274-8510 Japan Department of Applied Mathematics and Computational Sciences University of Cantabria Avda. de los Castros s/n Santander39005 Spain

ISBN: (纸本)9789811037276

Swarm intelligence is an emerging subfield of artificial intelligence (AI) where the sophisticated collective intelligence arising from a swarm of simple, unsophisticated individuals cooperating together is used to solve difficult problems. In our opinion, video games can be dramatically improved through swarm intelligence. As an illustration, we introduce a swam intelligence-based system for the representation and animation of some behavioral routines for the AI of the non-player characters (NPCs) of the last-generation first-person shooter video game "Isolated". In this work we focus on the problems of pathfinding and action planning of the NPCs. Some computer experiments have been conducted to analyze the feasibility and performance of this approach. © Springer Nature Singapore Pte Ltd. 2017.

关键词： Swarm intelligence

Probing embedded topological modes in bulk-like GeTe-Sb2Te3 heterostructures

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arXiv 2019年

作者： Nakamura, Hisao Hofmann, Johannes Inoue, Nobuki Koelling, Sebastian Koenraad, Paul M. Mussler, Gregor Grützmacher, Detlev Narayan, Vijay 1-1-1 Umezono Tsukuba Central 2 Tsukuba Japan Department of Applied Mathematics and Theoretical Physics University of Cambridge Centre for Mathematical Sciences CambridgeCB3 0WA United Kingdom Department of Materials Science and Metallurgy University of Cambridge 27 Charles Babbage Road CambridgeCB3 0FS United Kingdom TCM Group Cavendish Laboratory University of Cambridge CambridgeCB3 0HE United Kingdom RIKEN Center for Computational Science 7-1-26 Minatojima-minami Cyuo-ku Hyogo Kobe650-0047 Japan Eindhoven University of Technology Eindhoven5600 MB Netherlands Forschungszentrum Jülich Jülich52425 Germany Department of Physics University of Cambridge J. J. Thomson Avenue CambridgeCB3 0HE United Kingdom

The interface between topological and normal insulators hosts metallic states that appear due to the change in band topology. While these topological states at a surface, i.e., a topological insulator-air/vacuum interface, have been studied intensely, topological states at a solid-solid interface have been less explored. Here we combine experiment and theory to study such embedded topological states (ETSs) in heterostructures of GeTe (normal insulator) and Sb2Te3 (topological insulator). We analyse their dependence on the interface and their confinement characteristics. To characterise the heterostructures, we evaluate the GeTe-Sb2Te3 band offset using X-ray photoemission spectroscopy, and chart the elemental composition using atom probe tomography. We then use first-principles to independently calculate the band offset and also parametrise the band structure within a four-band continuum model. Our analysis reveals, strikingly, that under realistic conditions, the interfacial topological modes are delocalised over many lattice spacings. Interestingly, the first-principles calculations indicate that the ETSs are relatively robust to disorder and this may have practical ramifications. Our study provides insights into how to manipulate topological modes in heterostructures and also provides a basis for recent experimental findings [Nguyen et al., Sci. Rep. 6, 27716 (2016)] where ETSs were seen to couple over large distances. Copyright © 2019, The Authors. All rights reserved.

关键词： Topology

Ergodicity-breaking reveals time optimal economic behavior in humans

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arXiv 2019年

作者： Meder, David Rabe, Finn Morville, Tobias Madsen, Kristoffer H. Koudahl, Magnus T. Dolan, Ray J. Siebner, Hartwig R. Hulme, Oliver J. Danish Research Centre for Magnetic Resonance Centre for Functional and Diagnostic Imaging and Research Copenhagen University Hospital Hvidovre Kettegard Allé 30 Hvidovre2650 Denmark Neural Control of Movement Lab ETH Zurich Winterthurerstrasse 190 Building Y36 Zurich8057 Switzerland Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby2800 Denmark Department of Electrical Engineering Eindhoven University of Technology Eindhoven6500 MB Netherlands Max Planck UCL Centre for Computational Psychiatry and Ageing Research 10-12 Russell Square LondonWC1B5EH United Kingdom Department of Neurology Copenhagen University Hospital Bispebjerg Bispebjerg Bakke 23 Copenhagen2400 Denmark Institute for Clinical Medicine Faculty of Medical and Health Sciences University of Copenhagen Blegdamsvej 9 Copenhagen2100 Denmark

Ergodicity describes an equivalence between the expectation value and the time average of observables. applied to human behaviour, ergodic theory reveals how individuals should tolerate risk in different environments. To optimise wealth over time, agents should adapt their utility function according to the dynamical setting they face. Linear utility is optimal for additive dynamics, whereas logarithmic utility is optimal for multiplicative dynamics. Whether humans approximate time optimal behavior across different dynamics is unknown. Here we compare the effects of additive versus multiplicative gamble dynamics on risky choice. We show that utility functions are modulated by gamble dynamics in ways not explained by prevailing economic theory. Instead, as predicted by time optimality, risk aversion increases under multiplicative dynamics, distributing close to the values that maximise the time average growth of wealth. We suggest that our findings motivate a need for explicitly grounding theories of decision-making on ergodic considerations. Copyright © 2019, The Authors. All rights reserved.

关键词： Dynamics

The Atacama Cosmology Telescope: Probing the baryon content of SDSS DR15 galaxies with the thermal and kinematic Sunyaev-Zel’dovich effects

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arXiv 2021年

作者： Vavagiakis, Eve M. Gallardo, Patricio A. Calafut, Victoria Amodeo, Stefania Aiola, Simone Austermann, Jason E. Battaglia, Nicholas Battistelli, Elia S. Beall, James A. Bean, Rachel Bond, J. Richard Calabrese, Erminia Choi, Steve K. Cothard, Nicholas F. Devlin, Mark J. Duell, Cody J. Duff, S.M. Duivenvoorden, Adriaan J. Dunkley, Jo Dunner, Rolando Ferraro, Simone Guan, Yilun Hill, J. Colin Hilton, G.C. Hilton, Matt Hložek, Renee Huber, Zachary B. Hubmayr, Johannes Huffenberger, Kevin M. Hughes, John P. Koopman, Brian J. Kosowsky, Arthur Li, Yaqiong Lokken, Martine Madhavacheril, Mathew McMahon, Jeff Moodley, Kavilan Naess, Sigurd Nati, Federico Newburgh, Laura B. Niemack, Michael D. Page, Lyman Partridge, Bruce Schaan, Emmanuel Schillaci, Alessandro Sifon, Cristobal Spergel, David N. Staggs, Suzanne T. Ullom, Joel N. Vale, Leila R. van Engelen, Alexander van Lanen, J. Wollack, Edward J. Xu, Zhilei Department of Physics Cornell University IthacaNY14853 United States Department of Astronomy Cornell University IthacaNY14853 United States Center for Computational Astrophysics Flatiron Institute New YorkNY10010 United States NIST Quantum Sensors Group 325 Broadway BoulderCO80305 United States Physics Department Sapienza University of Rome Piazzale Aldo Moro 5 RomeI-00185 Italy Canadian Institute for Theoretical Astrophysics University of Toronto TorontoONM5S 3H8 Canada School of Physics and Astronomy Cardiff University The Parade CardiffCF24 3AA United Kingdom Department of Applied and Engineering Physics Cornell University IthacaNY14853 United States Department of Physics and Astronomy University of Pennsylvania 209 South 33rd Street PhiladelphiaPA19104 United States Joseph Henry Laboratories of Physics Jadwin Hall Princeton University PrincetonNJ08544 United States Department of Astrophysical Sciences Peyton Hall Princeton University PrincetonNJ08544 United States Instituto de Astrofísica Centro de Astro-Ingeniería Facultad de Física Pontificia Universidad Católica de Chile Av. Vicuña Mackenna 4860 Macul Santiago7820436 Chile Lawrence Berkeley National Laboratory One Cyclotron Road BerkeleyCA94720 United States Berkeley Center for Cosmological Physics UC Berkeley CA94720 United States Department of Physics and Astronomy University of Pittsburgh PittsburghPA15260 United States Department of Physics Columbia University New YorkNY10027 United States Astrophysics Research Centre University of KwaZulu-Natal Westville Campus Durban4041 South Africa David A. Dunlap Department of Astronomy and Astrophysics University of Toronto 50 St. George St. TorontoONM5S 3H4 Canada Dunlap Institute for Astronomy and Astrophysics University of Toronto 50 St. George St. TorontoONM5S 3H4 Canada Department of Physics Florida State University TallahasseeFL32306 United States Department of Physics and Astronomy Rutgers The State

We present measurements of the average thermal Sunyaev Zel’dovich (tSZ) effect from optically selected galaxy groups and clusters at high signal-to-noise (up to 12σ) and estimate their baryon content within a 2.10 radius aperture. Sources from the Sloan Digital Sky Survey (SDSS) Baryon Oscillation Spectroscopic Survey (BOSS) DR15 catalog overlap with 3,700 sq. deg. of sky observed by the Atacama Cosmology Telescope (ACT) from 2008 to 2018 at 150 and 98 GHz (ACT DR5), and 2,089 sq. deg. of internal linear combination component-separated maps combining ACT and Planck data (ACT DR4). The corresponding optical depths, τ¯, which depend on the baryon content of the halos, are estimated using results from cosmological hydrodynamic simulations assuming an AGN feedback radiative cooling model. We estimate the mean mass of the halos in multiple luminosity bins, and compare the tSZ-based τ¯ estimates to theoretical predictions of the baryon content for a Navarro–Frenk–White profile. We do the same for τ¯ estimates extracted from fits to pairwise baryon momentum measurements of the kinematic Sunyaev-Zel’dovich effect (kSZ) for the same data set obtained in a companion paper. We find that the τ¯ estimates from the tSZ measurements in this work and the kSZ measurements in the companion paper agree within 1σ for two out of the three disjoint luminosity bins studied, while they differ by 2-3σ in the highest luminosity bin. The optical depth estimates account for one third to all of the theoretically predicted baryon content in the halos across luminosity bins. Potential systematic uncertainties are discussed. The tSZ and kSZ measurements provide a step towards empirical Compton-ȳ-¯ τ relationships to provide new tests of cluster formation and evolution models. Copyright © 2021, The Authors. All rights reserved.

关键词： Hadrons

Fisher information matrix of binary time series

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arXiv 2017年

作者： Gao, Xu Ombao, Hernando Gillen, Daniel Department of Statistics University of California IrvineCA United States Department of Cognitive Sciences University of California IrvineCA United States Program on Applied Mathematics and Computational Science King Abdullah University of Science and Technology Saudi Arabia

A common approach to analyzing categorical correlated time series data is to fit a gen- eralized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed using the empirical Fisher information do not fully account the auto-correlation in the data. To overcome this serious limitation, we derive the exact conditional Fisher information matrix of a general logistic autoregressive model with endogenous covariates for any series length T . Moreover, we also develop an iterative computational formula that allows for relatively easy implementation of the proposed estimator. Our simulation studies show that confidence intervals derived using the exact Fisher information matrix tend to be narrower than those utilizing the empirical Fisher information matrix while maintaining type I error rates at or below nominal levels. Further, we establish that the exact Fisher information matrix approaches, as T tends to infinity, the asymptotic Fisher information matrix previously derived for binary time series data. The developed exact conditional Fisher information matrix is applied to time-series data on respiratory rate among a cohort of expectant mothers where it is found to pro- vide narrower confidence intervals for functionals of scientific interest and lead to greater statistical power when compared to the empirical Fisher information matrix. Copyright © 2017, The Authors. All rights reserved.

关键词： Time series

The Atacama Cosmology Telescope: Detection of the pairwise kinematic Sunyaev-Zel’dovich Effect with SDSS DR15 galaxies

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arXiv 2021年

作者： Calafut, Victoria Gallardo, Patricio A. Vavagiakis, Eve M. Amodeo, Stefania Aiola, Simone Austermann, Jason E. Battaglia, Nicholas Battistelli, Elia S. Beall, James A. Bean, Rachel Bond, J. Richard Calabrese, Erminia Choi, Steve K. Cothard, Nicholas F. Devlin, Mark J. Duell, Cody J. Duff, S.M. Duivenvoorden, Adriaan J. Dunkley, Jo Dunner, Rolando Ferraro, Simone Guan, Yilun Hill, J. Colin Hilton, G.C. Hilton, Matt Hlozek, Renee Huber, Zachary B. Hubmayr, Johannes Huffenberger, Kevin M. Hughes, John P. Koopman, Brian J. Kosowsky, Arthur Li, Yaqiong Lokken, Martine Madhavacheril, Mathew McMahon, Jeff Moodley, Kavilan Naess, Sigurd Nati, Federico Newburgh, Laura B. Niemack, Michael D. Page, Lyman Partridge, Bruce Schaan, Emmanuel Schillaci, Alessandro Sifon, Cristobal Spergel, David N. Staggs, Suzanne T. Ullom, Joel N. Vale, Leila R. van Engelen, Alexander van Lanen, J. Wollack, Edward J. Xu, Zhilei Department of Astronomy Cornell University IthacaNY14853 United States Department of Physics Cornell University IthacaNY14853 United States Center for Computational Astrophysics Flatiron Institute New YorkNY10010 United States NIST Quantum Devices Group 325 Broadway Mailcode 817.03 BoulderCO80305 United States Physics Department Sapienza University of Rome Piazzale Aldo Moro 5 RomeI-00185 Italy Canadian Institute for Theoretical Astrophysics University of Toronto TorontoONM5S 3H8 Canada School of Physics and Astronomy Cardiff University The Parade CardiffCF24 3AA United Kingdom Department of Applied and Engineering Physics Cornell University IthacaNY14853 United States Department of Physics and Astronomy University of Pennsylvania 209 South 33rd Street PhiladelphiaPA19104 United States Joseph Henry Laboratories of Physics Jadwin Hall Princeton University PrincetonNJ08544 United States Department of Astrophysical Sciences Peyton Hall Princeton University PrincetonNJ08544 United States Instituto de Astrofísica Centro de Astro-Ingeniería Facultad de Física Pontificia Universidad Católica de Chile Av. Vicuña Mackenna 4860 Macul Santiago7820436 Chile Lawrence Berkeley National Laboratory One Cyclotron Road BerkeleyCA94720 United States Berkeley Center for Cosmological Physics UC Berkeley CA94720 United States Department of Physics and Astronomy University of Pittsburgh PittsburghPA15260 United States Department of Physics Columbia University New YorkNY10027 United States Astrophysics Research Centre University of KwaZulu-Natal Westville Campus Durban4041 South Africa David A. Dunlap Department of Astronomy and Astrophysics University of Toronto 50 St. George St. TorontoONM5S 3H4 Canada Dunlap Institute for Astronomy and Astrophysics University of Toronto 50 St. George St. TorontoONM5S 3H4 Canada Department of Physics Florida State University TallahasseeFL32306 United States Department of Physics and Astronomy Ru

We present a 5.4σ detection of the pairwise kinematic Sunyaev-Zel’dovich (kSZ) effect using Atacama Cosmology Telescope (ACT) and Planck CMB observations in combination with Luminous Red Galaxy samples from the Sloan Digital Sky Survey (SDSS) DR15 catalog. Results are obtained using three ACT CMB maps: co-added 150 GHz and 98 GHz maps, combining observations from 2008-2018 (ACT DR5), which overlap with SDSS DR15 over 3,700 sq. deg., and a component-separated map using night-time only observations from 2014-2015 (ACT DR4), overlapping with SDSS DR15 over 2,089 sq. deg. Comparisons of the results from these three maps provide consistency checks in relation to potential frequency-dependent foreground contamination. A total of 343,647 galaxies are used as tracers to identify and locate galaxy groups and clusters from which the kSZ signal is extracted using aperture photometry. We consider the impact of various aperture photometry assumptions and covariance estimation methods on the signal extraction. Theoretical predictions of the pairwise velocities are used to obtain best-fit, mass-averaged, optical depth estimates for each of five luminosity-selected tracer samples. A comparison of the kSZ-derived optical depth measurements obtained here to those derived from the thermal SZ effect for the same sample is presented in a companion paper. Copyright © 2021, The Authors. All rights reserved.

关键词： Kinematics

Complex best r-term approximations almost always exist in finite dimensions

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arXiv 2017年

作者： Qi, Yang Micha Lek, Mateusz Lim, Lek-Heng Computational and Applied Mathematics Initiative Department of Statistics University of Chicago ChicagoIL60637-1514 United States Max Planck Institute for Mathematics in the Sciences Leipzig04103 Germany Polish Academy of Sciences Warsaw00656 Poland

We show that in finite-dimensional nonlinear approximations, the best r-term approximant of a function f almost always exists over C but that the same is not true over R, i.e., the infimum inff1, . . . ,fr∈Y||f - f1- . . . - fr|| is almost always attainable by complex-valued functions f1, . . . , frin Y , a set of functions that have some desired structures. Our result extends to functions that possess special properties like symmetry or skew-symmetry under permutations of arguments. For the case where Y is the set of separable functions, the problem becomes that of best rank-r tensor approximations. We show that over C, any tensor almost always has a unique best rank-r approximation. This extends to other notions of tensor ranks such as symmetric rank and alternating rank, to best r-block-terms approximations, and to best approximations by tensor networks. When applied to sparse-plus-low-rank approximations, we obtain that for any given r and k, a general tensor has a unique best approximation by a sum of a rank-r tensor and a k-sparse tensor with a fixed sparsity pattern;this arises in, for example, estimation of covariance matrices of a Gaussian hidden variable model with k observed variables conditionally independent given r hidden variables. The existential (but not the uniqueness) part of our result also applies to best approximations by a sum of a rank-r tensor and a k-sparse tensor with no fixed sparsity pattern, as well as to tensor completion problems.15A69, 41A50, 41A52, 41A65, 97N50, 51M35 Copyright © 2017, The Authors. All rights reserved.

关键词： Tensors