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Chang’e 3 lunar mission and upper limit on stochastic background of gravitational wave around the 0.01 Hz band

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arXiv 2017年

作者： Tang, Wenlin Xu, Peng Hu, Songjie Cao, Jianfeng Dong, Peng Bu, Yanlong Chena, Lue Han, Songtao Gong, Xuefei Lie, Wenxiao Ping, Jinsong Lau, Yun-Kau Tang, Geshi Science and Technology on Aerospace Flight Dynamics Laboratory Beijing Aerospace Control Center Beijing China Institute of Applied Mathematics Morningside Center of Mathematics and LESC Institute of Computational Mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing China Department of Aerospace Guidance Navigation and Control School of Astronautics Beihang University Beijing China Beijing Institute of Aerospace Control Devices Beijing China National astronomical observatories Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China

The Doppler tracking data of the Chang’e 3 lunar mission is used to constrain the stochastic background of gravitational wave in cosmology within the 1 mHz to 0.05 Hz frequency band. Our result improves on the upper bound on the energy density of the stochastic background of gravitational wave in the 0.02 Hz to 0.05 Hz band obtained by the Apollo missions, with the improvement reaching almost one order of magnitude at around 0.05 Hz. Detailed noise analysis of the Doppler tracking data is also presented, with the prospect that these noise sources will be mitigated in future Chinese deep space missions. A feasibility study is also undertaken to understand the scientific capability of the Chang’e 4 mission, due to be launched in 2018, in relation to the stochastic gravitational wave background around 0.01 Hz. Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

OPERATORS ON ANTI-DUAL PAIRS: LEBESGUE DECOMPOSITION VIA ARLINSKII’S ITERATION

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arXiv 2024年

作者： Göde, Ábel Tarcsay, Zsigmond Department of Applied Analysis and Computational Mathematics Eötvös Loránd University Pázmány Péter sétány 1/c. BudapestH-1117 Hungary Department of Mathematics Corvinus University of Budapest IX. Fővám tér 13-15. BudapestH-1093 Hungary

The aim of this paper is to prove a general Lebesgue decomposition theorem for positive operators on so-called anti-dual pairs, following the iterative approach introduced by Arlinskii. This procedure and the resulting theorem encompass several special cases, including positive operators on Hilbert spaces, non-negative forms on vector spaces, and representable functionals over *-*** Codes 47B65, 47A07 Copyright © 2024, The Authors. All rights reserved.

关键词： Vector spaces

Stable reconstruction of simple riemannian manifolds from unknown interior sources

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arXiv 2021年

作者： de Hoop, Maarten V. Ilmavirta, Joonas Lassas, Matti Saksala, Teemu Department of Computational and Applied Mathematics Rice University 6100 Main MS-134 HoustonTX77005-1892 United States Unit of Computing Sciences Tampere University Kalevantie 4 FI-33014 Finland FI-00014 Finland Department of Mathematics North Carolina State University 2311 Stinson Drive RaleighNC27695-8205 United States

Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to get an approximate reconstruction, and we indeed provide a discrete metric approximation to the manifold with explicit data-driven error bounds when the manifold is simple. This is the geometrization of a seismological inverse problem where we measure the arrival times on the surface of waves from an unknown number of unknown interior microseismic events at unknown times. The closeness of two metric spaces with a marked boundary is measured by a labeled Gromov–Hausdorff distance. If measurements are done for infinite time and spatially dense sources, our construction produces the true Riemannian manifold and the finite-time approximations converge to it in the metric sense. Copyright © 2021, The Authors. All rights reserved.

关键词： Geometry

Interplay of network dynamics and heterogeneity of ties on spreading dynamics

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Physical Review E 2014年第1期90卷 012812-012812页

作者： Luca Ferreri Paolo Bajardi Mario Giacobini Silvia Perazzo Ezio Venturino GECO-Computational Epidemiology Group Department of Veterinary Sciences University of Torino largo Braccini 2 IT-10095 Grugliasco (TO) ARCS - Applied Research on Computational Complex Systems Group Department of Computer Science University of Torino corso Svizzera 185 IT-10149 Torino CSU-Complex Systems Unit Molecular Biotechnology Centre University of Torino via Nizza 52 IT-10126 Torino Department of Mathematics “Giuseppe Peano” University of Torino via Carlo Alberto 10 IT-10123 Torino

The structure of a network dramatically affects the spreading phenomena unfolding upon it. The contact distribution of the nodes has long been recognized as the key ingredient in influencing the outbreak events. However, limited knowledge is currently available on the role of the weight of the edges on the persistence of a pathogen. At the same time, recent works showed a strong influence of temporal network dynamics on disease spreading. In this work we provide an analytical understanding, corroborated by numerical simulations, about the conditions for infected stable state in weighted networks. In particular, we reveal the role of heterogeneity of edge weights and of the dynamic assignment of weights on the ties in the network in driving the spread of the epidemic. In this context we show that when weights are dynamically assigned to ties in the network, a heterogeneous distribution is able to hamper the diffusion of the disease, contrary to what happens when weights are fixed in time.

关键词： Dynamics

Biofluid mechanics of special organs and the issue of system control: Sixth international bio-fluid mechanics symposium and workshop, March 28-30, 2008 Pasadena, California

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Biofluid mechanics of special organs and the issue of system...

作者： Zamir, Mair Moore Jr., James E. Fujioka, Hideki Gaver III, Donald P. Department of Applied Mathematics University of Western Ontario 1151 Richmond Street London ON N6A 3K7 Canada Department of Medical Biophysics University of Western Ontario London ON N6A 3K7 Canada Department of Biomedical Engineering Texas A and M University College Station TX United States Center for Computational Science Tulane University New Orleans LA United States Department of Biomedical Engineering Tulane University New Orleans LA United States

In the field of fluid flow within the human body, focus has been placed on the transportation of blood in the systemic circulation since the discovery of that system;but, other fluids and fluid flow phenomena pervade the body. Some of the most fascinating fluid flow phenomena within the human body involve fluids other than blood and a service other than transport-the lymphatic and pulmonary systems are two striking examples. While transport is still involved in both cases, this is not the only service which they provide and blood is not the only fluid involved. In both systems, filtration, extraction, enrichment, and in general some "treatment" of the fluid itself is the primary function. The study of the systemic circulation has also been conventionally limited to treating the system as if it were an open-loop system governed by the laws of fluid mechanics alone, independent of physiological controls and regulations. This implies that system failures can be explained fully in terms of the laws of fluid mechanics, which of course is not the case. In this paper we examine the clinical implications of these issues and of the special biofluid mechanics issues involved in the lymphatic and pulmonary systems. © 2010 Biomedical Engineering Society.

关键词： Flow of fluids

Alignment of density maps in Wasserstein distance

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Biological imaging 2024年 4卷 e5页

作者： Amit Singer Ruiyi Yang Department of Mathematics Princeton University Princeton NJ USA. Program in Applied and Computational Mathematics Princeton University Princeton NJ USA.

In this article, we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance between the density maps after a rigid transformation. The induced loss function enjoys a more benign landscape than its Euclidean counterpart and Bayesian optimization is employed for computation. Numerical experiments show improved accuracy and efficiency over existing algorithms on the alignment of real protein molecules. In the context of aligning heterogeneous pairs, we illustrate a potential need for new distance functions.

关键词： Bayesian optimization Wasserstein distance cryogenic electron microscopy heterogeneity analysis volume alignment

Setting the physical scale of dimensional reduction in causal dynamical triangulations

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Physical Review D 2019年第2期100卷 026014-026014页

作者： Joshua H. Cooperman Manuchehr Dorghabekov Department of Physics and Astronomy Bucknell University Lewisburg Pennsylvania 17837 USA Physics Program Bard College Annandale-on-Hudson New York 12504 USA* Applied Mathematics and Informatics Program American University of Central Asia Bishkek Kyrgyz Republic*

Within the causal dynamical triangulations approach to the quantization of gravity, striking evidence has emerged for the dynamical reduction of spacetime dimension on sufficiently small scales. Specifically, the spectral dimension decreases from the topological value of 4 toward a value near 2 as the scale being probed decreases. The physical scales over which this dimensional reduction occurs have not previously been ascertained. We present and implement a method to determine these scales in units of either the Planck length or the quantum spacetime geometry’s effective de Sitter length. We find that dynamical reduction of the spectral dimension occurs over physical scales of the order of 10 Planck lengths, which, for the numerical simulation considered below, corresponds to the order of 10−1 de Sitter lengths.

关键词： Quantum gravity

The ESPRIT algorithm under high noise: Optimal error scaling and noisy super-resolution

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arXiv 2024年

作者： Ding, Zhiyan Epperly, Ethan N. Lin, Lin Zhang, Ruizhe Department of Mathematics University of California Berkeley United States Department of Computing and Mathematical Sciences California Institute of Technology PasadenaCA United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory United States Challenge Institute for Quantum Computation University of California Berkeley United States Simons Institute for the Theory of Computing United States

Subspace-based signal processing techniques, such as the Estimation of Signal Parameters via Rotational Invariant Techniques (ESPRIT) algorithm, are popular methods for spectral estimation. These algorithms can achieve the so-called super-resolution scaling under low noise conditions, surpassing the well-known Nyquist limit. However, the performance of these algorithms under high-noise conditions is not as well understood. Existing state-of-the-art analysis indicates that ESPRIT and related algorithms can be resilient even for signals where each observation is corrupted by statistically independent, mean-zero noise of size O(1), but these analyses only show that the error ∊ decays at a slow rate ∊ = O͂(n−1/2) with respect to the cutoff frequency n (i.e., the maximum frequency of the measurements). In this work, we prove that under certain assumptions, the ESPRIT algorithm can attain a significantly improved error scaling ∊ = O͂(n−3/2), exhibiting noisy super-resolution scaling beyond the Nyquist limit ∊ = O(n−1) given by the Nyquist-–Shannon sampling theorem. We further establish a theoretical lower bound and show that this scaling is optimal. Our analysis introduces novel matrix perturbation results, which could be of independent interest. © 2024, CC BY.

关键词： Cutoff frequency

Imaging atomic-scale chemistry from fused multi-modal electron microscopy

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npj computational Materials 2022年第1期8卷 164-171页

作者： Jonathan Schwartz Zichao Wendy Di Yi Jiang Alyssa J.Fielitz Don-Hyung Ha Sanjaya D.Perera Ismail El Baggari Richard D.Robinson Jeffrey A.Fessler Colin Ophus Steve Rozeveld Robert Hovden Department of Materials Science and Engineering University of MichiganAnn ArborMIUSA Mathematics and Computer Science Division Argonne National LaboratoryLemontILUSA Advanced Photon Source Facility Argonne National LaboratoryLemontILUSA Dow Chemical Co. MidlandMIUSA Department of Material Science and Engineering Cornell UniversityIthacaNew YorkUSA School of Integrative Engineering Chung-Ang UniversitySeoulRepublic of Korea Department of Physics Cornell UniversityIthacaNYUSA The Rowland Institute at Harvard CambridgeMAUSA Department of Electrical Engineering and Computer Science University of MichiganAnn ArborMIUSA National Center for Electron Microscopy Lawrence Berkeley National LaboratoryMolecular FoundryBerkeleyCAUSA Applied Physics Program University of MIchiganAnn ArborMIUnited States

Efforts to map atomic-scale chemistry at low doses with minimal noise using electron microscopes are fundamentally limited by inelastic ***,fused multi-modal electron microscopy offers high signal-to-noise ratio(SNR)recovery of material chemistry at nano-and atomic-resolution by coupling correlated information encoded within both elastic scattering(high-angle annular dark-field(HAADF))and inelastic spectroscopic signals(electron energy loss(EELS)or energy-dispersive x-ray(EDX)).By linking these simultaneously acquired signals,or modalities,the chemical distribution within nanomaterials can be imaged at significantly lower doses with existing detector *** many cases,the dose requirements can be reduced by over one order of *** high SNR recovery of chemistry is tested against simulated and experimental atomic resolution data of heterogeneous nanomaterials.

关键词： materials chemistry fused