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arXiv 2023年

作者： Su, Q. Larson, J. Dalichaouch, T.N. Li, F. An, W. Hildebrand, L. Zhao, Y. Decyk, V. Alves, P. Wild, S.M. Mori, W.B. Department of Electrical and Computer Engineering University of California Los Angeles Los AngelesCA90095 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States Department of Physics and Astronomy University of California Los Angeles Los AngelesCA90095 United States Department of Astronomy Beijing Normal University Beijing100875 China Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. The current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the

关键词： Energy transfer

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Correction: Unbiased and multilevel methods for a class of diffusions partially observed via marked point processes

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Statistics and Computing 2024年第6期34卷 1-1页

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal Saudi Arabia School of Data Science The Chinese University of Hong Kong Shenzhen China

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Autonomous Electron Tomography Reconstruction with Machine Learning

arXiv

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arXiv 2023年

作者： Millsaps, William Schwartz, Jonathan Di, Zichao Wendy Jiang, Yi Hovden, Robert Department of Nuclear Engineering & Radiological Sciences University of Michigan Ann ArborMI United States Department of Materials Science and Engineering University of Michigan Ann ArborMI United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL United States Advanced Photon Source Facility Argonne National Laboratory LemontIL United States Applied Physics Program University of Michigan Ann ArborMI United States

This manuscript is published in Microscopy and Microanalysis (DOI: 10.1093/micmic/ozad083). Modern electron tomography has progressed to higher resolution at lower doses by leveraging compressed sensing methods that minimize total variation (TV). However, these sparsity-emphasized reconstruction algorithms introduce tunable parameters that greatly influence the reconstruction quality. Here, Pareto front analysis shows that high-quality tomograms are reproducibly achieved when TV minimization is heavily weighted. However, in excess, compressed sensing tomography creates overly smoothed 3D reconstructions. Adding momentum to the gradient descent during reconstruction reduces the risk of over-smoothing and better ensures that compressed sensing is well behaved. For simulated data, the tedious process of tomography parameter selection is efficiently solved using Bayesian optimization with Gaussian processes. In combination, Bayesian optimization with momentum-based compressed sensing greatly reduces the required compute time-an 80% reduction was observed for the 3D reconstruction of SrTiO3 nanocubes. Automated parameter selection is necessary for large scale tomographic simulations that enable the 3D characterization of a wider range of inorganic and biological materials. © 2023, CC BY.

关键词： Compressed sensing

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Unbiased Estimation using a Class of Diffusion Processes

arXiv

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arXiv 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 KSA Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (d, B(d)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}tϵ[0,1]on d, d ϵ 0. This latter process is constructed such that, starting at X0= 0, one has X1∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 16] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(ϵ2), for arbitrary ϵ > 0, the associated cost is O(ϵ-5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(ϵ2), the associated cost (which is random) is, with high probability, O(ϵ-2| log(ϵ)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse *** Codes 60J60, 62D05, 65C40 © 2022, CC BY.

关键词： Diffusion

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Weak solution for time-fractional strongly coupled three species cooperating model

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Partial Differential Equations in applied mathematics 2023年 7卷

作者： Manimaran, J. Bhuvaneswari, V. Shangerganesh, L. Division of Mathematics School of Advanced Sciences Vellore Institute of Technology Chennai Campus Chennai 600 127 India Department of Mathematics with Computer Applications PSG College of Arts & Science Coimbatore 641 014 India Department of Applied Sciences National Institute of Technology Goa Goa Farmagudi 403 401 India

This article investigates the solvability of the time-fractional strongly coupled three-species cooperating system of equations with the Dirichlet boundary conditions. This model expresses the interactions of cooperating species. First, a suitable approximation problem is considered to overcome the strong degeneracy of the original model. Then, we establish the existence of a weak solution for the proposed system using the Faedo–Galerkin method and some compactness arguments. © 2023 The Authors

关键词： Faedo Galerkin method Fractional PDE Weak solution

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Advantage of Machine Learning over Maximum Likelihood in Limited-Angle Low-Photon X-Ray Tomography

Advantage of Machine Learning over Maximum Likelihood in Lim...

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IS and T International Symposium on Electronic Imaging: Machine Learning for Scientific Imaging, MLSI 2022

作者： Guo, Zhen Song, Jung Ki Barbastathis, George Glinsky, Michael E. Vaughan, Courtenay T. Larson, Kurt W. Alpert, Bradley K. Levine, Zachary H. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States Department of Mechanical Engineering Massachusetts Institute of Technology CambridgeMA02139 United States Centre Singapore138002 Singapore Sandia National Laboratory AlbuquerqueNM87123 United States Applied and Computational Mathematics Division National Institute of Standards and Technology Boulder CO80305 United States Quantum Measurement Division National Institute of Standards and Technology GaithersburgMD20899 United States

Limited-angle X-ray tomography reconstruction is an ill-conditioned inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical algorithms such as filtered backprojection may lose fidelity and acquire artifacts due to the missing-cone problem. To obtain satisfactory reconstruction results, prior assumptions, such as total variation minimization and nonlocal image similarity, are usually incorporated within the reconstruction algorithm. In this work, we introduce deep neural networks to determine and apply a prior distribution in the reconstruction process. Our neural networks learn the prior directly from synthetic training samples. The neural nets thus obtain a prior distribution that is specific to the class of objects we are interested in reconstructing. In particular, we used deep generative models with 3D convolutional layers and 3D attention layers which are trained on 3D synthetic integrated circuit (IC) data from a model dubbed CircuitFaker. We demonstrate that, when the projection angles and photon budgets are limited, the priors from our deep generative models can dramatically improve the IC reconstruction quality on synthetic data compared with maximum likelihood estimation. Training the deep generative models with synthetic IC data from CircuitFaker illustrates the capabilities of the learned prior from machine learning. We expect that if the process were reproduced with experimental data, the advantage of the machine learning would persist. The advantages of machine learning in limited angle X-ray tomography may further enable applications in low-photon nanoscale imaging. © 2022, Society for Imaging science and Technology

关键词： Photons

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HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

arXiv

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arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

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Minuscule corrections to near-surface solar internal rotation using mode-coupling

arXiv

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arXiv 2023年

作者： Das, Srijan Bharati Kashyap, Samarth G. Oktay, Deniz Hanasoge, Shravan M. Tromp, Jeroen Department of Geosciences Princeton University PrincetonNJ United States Department of Astronomy and Astrophysics Tata Institute of Fundamental Research Mumbai India Department of Computer Science Princeton University PrincetonNJ United States Department of Geosciences and Program in Applied & Computational Mathematics Princeton University PrincetonNJ United States

The observed solar oscillation spectrum is influenced by internal perturbations such as flows and structural asphericities. These features induce splitting of characteristic frequencies and distort the resonant-mode eigenfunctions. Global axisymmertric flow — differential rotation — is a very prominent perturbation. Tightly constrained rotation profiles as a function of latitude and radius are products of established helioseismic pipelines that use observed Dopplergrams to generate frequency-splitting measurements at high precision. However, the inference of rotation using frequency-splittings do not consider the effect of mode-coupling. This approximation worsens for high-angular-degree modes, as they become increasingly proximal in frequency. Since modes with high angular degrees probe the near-surface layers of the Sun, inversions considering coupled modes could potentially lead to more accurate estimates of rotation very close to the surface. In order to investigate if this is indeed the case, we perform inversions for solar differential rotation, considering coupling of modes for angular degrees 160 ≤ ` ≤ 300 in the surface gravity f-branch and first-overtone p modes. In keeping with the character of mode coupling, we carry out a non-linear inversion using an eigenvalue solver. Differences in inverted profiles for frequency splitting measurements from MDI and HMI are compared and discussed. We find that corrections to the near-surface differential rotation profile, when accounting for mode-coupling effects, are smaller than 0.003 nHz and hence are insignificant. These minuscule corrections are found to be correlated with the solar cycle. We also present corrections to even-order splitting coefficients, which could consequently impact inversions for structure and magnetic fields. © 2023, CC BY.

关键词： Rotation

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Immersive Analysis: Enhancing Material Inspection of X-Ray Computed Tomography Datasets in Augmented Reality

arXiv

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arXiv 2024年

作者： Gall, Alexander Heim, Anja Weinberger, Patrick Fröhler, Bernhard Kastner, Johann Heinzl, Christoph Research Group Computed Tomography University of Applied Sciences Upper Austria Roseggerstraße 15 Wels4600 Austria Faculty of Computer Science and Mathematics University of Passau Innstraße 43 Passau94032 Germany Division Development Center X-ray Technology Fraunhofer Institute for Integrated Circuits IIS Flugplatzstraße 75 Fürth90768 Germany

This work introduces a novel Augmented Reality (AR) approach to visualize material data alongside real objects in order to facilitate detailed material analyses based on spatial non-destructive testing (NDT) data as generated in X-ray computed tomography (XCT) imaging. For this purpose, we introduce a framework that leverages the potential of AR devices, visualization and interaction techniques to seamlessly explore complex primary and secondary XCT data matched with real-world objects. The overall goal of the proposed analysis scheme is to enable researchers and analysts to inspect material properties and structures onsite and in-place. Coupling immersive visualization techniques with real physical objects allows for highly intuitive workflows in material analysis and inspection, which enables the identification of anomalies and accelerates informed decision making. As a result, this framework generates an immersive experience, which provides a more engaging and more natural analysis of material data. A case study on fiber-reinforced polymer datasets was used to validate the AR framework and its new workflow. Initial results revealed positive feedback from experts, in particular regarding improved understanding of spatial data and a more natural interaction with material samples, which may have significant potential when combined with conventional analysis systems. Copyright © 2024, The Authors. All rights reserved.

关键词： Nondestructive examination

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Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems

arXiv

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arXiv 2025年

作者： Wei, Lu Jia, Zhian Wang, Yufeng Kaszlikowski, Dagomir Ling, Haibin Department of Applied Mathematics & Statistics Stony Brook University Stony BrookNY11794 United States Program of Data Science Stony Brook University Stony BrookNY11794 United States Centre for Quantum Technologies National University of Singapore SG 117543 Singapore Department of Physics National University of Singapore SG 117543 Singapore Department of Computer Science Stony Brook University Stony BrookNY11794 United States

The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter physics. In this work, we propose the transformer density operator ansatz for determining the steady states of dissipative quantum many-body systems. By vectorizing the density operator as a many-body state in a doubled Hilbert space, the transformer encodes the amplitude and phase of the state’s coefficients, with its parameters serving as variational variables. Our design preserves translation invariance while leveraging attention mechanisms to capture diverse long-range correlations. We demonstrate the effectiveness of our approach by numerically calculating the steady states of dissipative Ising and Heisenberg spin chain models, showing that our method achieves excellent accuracy in predicting steady states. © 2025, CC BY.

关键词： Hilbert spaces

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