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SSRN 2024年

作者： AbuGhanem, Muhammad Homid, Ali H. Obada, A.S.-F. Hendy, Ahmed S. Eleuch, Hichem Faculty of Science Ain Shams University Cairo11566 Egypt Zewail City of Science Technology and Innovation Giza12678 Egypt Mathematics Department Faculty of Science Al-Azhar University Assiut71524 Egypt Mathematics Department Faculty of Science Al-Azher University Nassr City Cairo11884 Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and Mathematics Ural Federal University Yekaterinburg Russia Department of Mathematics Faculty of Science Benha University Benha Egypt Department of Applied Physics and Astronomy University of Sharjah Sharjah27272 United Arab Emirates College of Arts and Sciences Abu Dhabi University Abu Dhabi59911 United Arab Emirates Institute for Quantum Science and Engineering Texas A&M University College StationTX77843 United States

Universal quantum gates are crucial for efficient algorithm execution on quantum computers, offering rapid and fault-tolerant manipulations. This paper presents a theoretical framework for realizing a novel entangling universal quantum gate within the circuit quantum electrodynamics (circuit QED) architecture. Our approach involves positioning two SQUIDs qubits within a resonant single-mode microwave cavity field, enabling the implementation of the SQSCZ gate, a fusion of the square root of SWAP ($\sqrt{SWAP}$) and the square root of controlled-Z ($\sqrt{CZ}$) gates. This gate serves as a fundamental building block for constructing universal quantum gates including the controlled-NOT gates. Moreover, the SQSCZ gate operates unitarily, ensuring logical reversibility, and exhibits an entangling power (EP) of 1.5/9. Quantitative analysis reveals an average gate fidelity of $60\%$. To delve deeper into the gate's performance, we conducted quantum process tomography (QPT) analysis by repeating the quantum experiment 11,000 times for each measurement basis on an IBM Quantum's quantum simulator. This rigorous approach yielded a remarkable process fidelity of $96.065616\%$. These findings offer promising implications for future research and applications. © 2024, The Authors. All rights reserved.

关键词： Qubits

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Testing topological conjugacy of time series

arXiv

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arXiv 2023年

作者： Dlotko, Pawel Lipiński, Michal Signerska-Rynkowska, Justyna Dioscuri Centre in TDA Institute of Mathematics Polish Academy of Sciences ul. Śniadeckich 8 Warszawa00-656 Poland Institute of Computer Science and Computational Mathematics Jagiellonian University ul. Lojasiewicza 6 Kraków30-348 Poland Institute of Applied Mathematics Gdańsk University of Technology ul. Narutowicza 11/12 Gdansk80-233 Poland

This paper considers a problem of testing, from a finite sample, a topological conjugacy of two trajectories coming from dynamical systems (X, f) and (Y, g). More precisely, given x1, ..., xn ⊂ X and y1, ..., yn ⊂ Y such that xi+1 = f(xi) and yi+1 = g(yi) as well as h : X → Y, we deliver a number of tests to check if f and g are topologically conjugated via h. The values of the tests are close to zero for systems conjugate by h and large for systems that are not. Convergence of the test values, in case when sample size goes to infinity, is established. We provide a number of numerical examples indicating scalability and robustness of the presented methods. In addition, we show how the presented method gives rise to a test of sufficient embedding dimension, mentioned in Takens' embedding theorem. Our methods also apply to the situation when we are given two observables of deterministic processes, of a form of one or higher dimensional time-series. In this case, their similarity can be accessed by comparing the dynamics of their Takens' reconstructions. Finally, we include a proof-of-concept study using the presented methods to search for an approximation of the homeomorphism conjugating given *** Codes 37M10, 37C15, 37B20 © 2023, CC BY.

关键词： Time series

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On the Particle Approximation of Lagged Feynman-Kac Formulae

arXiv

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arXiv 2024年

作者： Awadelkarim, Elsiddig Caffarel, Michel Moral, Pierre Del Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia University of Toulouse CNRS-Lab. de Chimie et Physique Quantiques Toulouse31062 France Centre de Recherche Inria Bordeaux Sud-Ouest Talence33405 France School of Data Science The Chinese University Hong Kong Shenzhen China

In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman-Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function. The typical application considered here is the computation of eigenvalues associated with non-negative operators as found, for example, in physics or particle simulation of rare-events. We focus on a novel lagged approximation of this invariant measure, based upon the introduction of a ratio of time-averaged Feynman-Kac marginals associated with a positive operator iterated l ∈ N times;a lagged Feynman-Kac formula. This estimator and its approximation using Diffusion Monte Carlo (DMC) have been extensively employed in the physics literature. In short, DMC is an iterative algorithm involving N ∈ N particles or walkers simulated in parallel, that undergo sampling and resampling operations. In this work, it is shown that for the DMC approximation of the lagged Feynman-Kac formula, one has an almost sure characterization of the L1-error as the time parameter (iteration) goes to infinity and this is at most of O(exp{−κl}/N), for_ κ > 0. In addition a non-asymptotic in time, and time uniform L1−bound is proved which is O(l/√N). We also prove a novel central limit theorem to give a characterization of the exact asymptotic in time variance. This analysis demonstrates that the strategy used in physics, namely, to run DMC with N and l small and, for long time enough, is mathematically justified. Our results also suggest how one should choose N and l in practice. We emphasize that these results are not restricted to physical applications;they have broad relevance to the general problem of particle simulation of the Feynman-Kac formula, which is utilized in a great variety of scientific and engineering fields. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

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Arithmetic crosscorrelation of pseudorandom binary sequences of coprime periods

arXiv

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arXiv 2022年

作者： Chen, Zhixiong Niu, Zhihua Winterhof, Arne Key Laboratory of Applied Mathematics of Fujian Province University Putian University Fujian Putian351100 China School of Computer Engineering and Science Shanghai University Shanghai200444 China Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenberger Straße 69 LinzA-4040 Austria

The (classical) crosscorrelation is an important measure of pseudorandomness of two binary sequences for applications in communications. The arithmetic crosscorrelation is another figure of merit introduced by Goresky and Klapper generalizing Mandelbaum's arithmetic autocorrelation. First we observe that the arithmetic crosscorrelation is constant for two binary sequences of coprime periods which complements the analogous result for the classical crosscorrelation. Then we prove upper bounds for the constant arithmetic crosscorrelation of two Legendre sequences of different periods and of two binary m-sequences of coprime periods, *** Codes Primary: 94A55, Secondary: 11T71, 94A05, 94A60 © 2022, CC0.

关键词： Binary sequences

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在天文学中基于机器学习的流体力学问题加速求解

在天文学中基于机器学习的流体力学问题加速求解

引用

第十三届全国流体力学学术会议

作者：毛顺元董若冰王炜琦 Kwang Moo Yi 陆路王思凡 Paris Perdikaris Department of Physics and Astronomy University of Victoria Department of Computer Science University of British Columbia Department of Statistics and Data Science Yale University Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Department ofMechanical Engineering and Applied Mechanics University of Pennsylvania

探索行星形成的过程不仅揭示了地球及其生命的起源,还为寻找地外生命提供了关键线索。行星在原行星盘中形成。原行星盘是由气体和尘埃构成的扁平盘状系统,围绕在新生恒星的周围,其跨度可达数千亿公里。近年来,通过分析行星对原行星盘的... 详细信息

探索行星形成的过程不仅揭示了地球及其生命的起源,还为寻找地外生命提供了关键线索。行星在原行星盘中形成。原行星盘是由气体和尘埃构成的扁平盘状系统,围绕在新生恒星的周围,其跨度可达数千亿公里。近年来,通过分析行星对原行星盘的引力扰动,并比较观测和数值模拟,天文学家得以推断正在盘中形成的行星的质量和轨道。然而,这种方法依赖于复杂的流体力学数值模拟,因计算成本高昂而难以普及。为了克服这一挑战,我们开发了一款基于机器学习的工具。该工具应用数据驱动的深度算子网络(DeepONet),将系统的参数映射到流体力学偏微分方程的解,从而无需昂贵的数值模拟即可实现两项功能:1)快速求解正问题,即从行星参数预测盘中物质分布和速度场;2)高效求解反问题,即从观测到的扰动图像中推断行星参数。我们展示了该工具在求解速度、精确性和鲁棒性方面的显著优势,并讨论了其在理论研究和观测中的潜在应用。我们还探索了物理信息神经网络(PINN)在这一问题的应用,特别是针对原初行星盘中旋转吸积流的时间依赖性二维可压缩Navier-Stokes方程。行星引力扰动引入显著的时间依赖性空间特征,使问题复杂化。通过对物理定律而非标注数据的训练,PINN在捕捉系统演化的空间高频特征方面展现潜力。标准PINN在此任务中存在收敛困难、预测误差随时间累积、长时间解偏离物理定律以及捕捉空间高频特征能力不足的问题。为此,我们的研究引入了自适应激活函数、时间推进策略和网络权重继承方法,以提升PINN性能。改进后的PINN模型在与标准PINN的比较中表现出显著更低的预测误差,成功再现了大部分空间高频特征,无需标注数据。这项研究为将PINN应用于类似的时间依赖性流体力学问题提供了重要参考。

关键词：天文行星形成深度学习深度算子网络物理信息神经网络

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Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws

arXiv

引用

arXiv 2021年

作者： Ranocha, Hendrik Schlottke-Lakemper, Michael Chan, Jesse Rueda-Ramírez, Andrés M. Winters, Andrew R. Hindenlang, Florian Gassner, Gregor J. Applied Mathematics University of Münster Germany High-Performance Computing Center Stuttgart University of Stuttgart Germany Computational and Applied Mathematics Rice University United States Department of Mathematics and Computer Science University of Cologne Germany Computational Mathematics Division of Applied Mathematics Linköping University Sweden Max Planck Institute for Plasma Physics NMPP division Garching Germany Department of Mathematics and Computer Science Center for Data and Simulation Science University of Cologne Germany

Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness of DG methods significantly, they are also computationally more demanding than standard weak form nodal DG methods. We present several implementation techniques to improve the efficiency of flux differencing DG methods that use tensor product quadrilateral or hexahedral elements, in 2D or 3D respectively. Focus is mostly given to CPUs and DG methods for the compressible Euler equations, although these techniques are generally also useful for GPU computing and other physical systems including the compressible Navier-Stokes and magnetohydrodynamics equations. We present results using two open source codes, *** written in Julia and FLUXO written in Fortran, to demonstrate that our proposed implementation techniques are applicable to different code bases and programming languages. Copyright © 2021, The Authors. All rights reserved.

关键词： Entropy

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Predicting convection configurations in coupled fluid-porous systems

arXiv

引用

arXiv 2022年

作者： McCurdy, Matthew Moore, Nicholas J. Wang, Xiaoming Department of Mathematics and Computer Science Ohio Wesleyan University DelawareOH43015 United States Department of Mathematics Colgate University HamiltonNY13346 United States Department of Mathematics SUSTech International Center for Mathematics National Center for Applied Mathematics Shenzhen Guangdong Provincial Key Laboratory of Computational Science and Material Design Southern University of Science and Technology Shenzhen518055 China Department of of Mathematics and Statistics Missouri University of Science and Technology RollaMO65409 United States

A ubiquitous arrangement in nature is a free-flowing fluid coupled to a porous medium, for example a river or lake lying above a porous bed. Depending on the environmental conditions, thermal convection can occur and may be confined to the clear fluid region, forming shallow convection cells, or it can penetrate into the porous medium, forming deep cells. Here, we combine three complementary approaches - linear stability analysis, fully nonlinear numerical simulations, and a coarse-grained model - to determine the circumstances that lead to each configuration. The coarse-grained model yields an explicit formula for the transition between deep and shallow convection in the physically relevant limit of small Darcy number. Near the onset of convection, all three of the approaches agree, validating the predictive capability of the explicit formula. The numerical simulations extend these results into the strongly nonlinear regime, revealing novel hybrid configurations in which the flow exhibits a dynamic shift from shallow to deep convection. This hybrid shallow-to-deep convection begins with small, random initial data, progresses through a metastable shallow state, and arrives at the preferred steady-state of deep convection. We construct a phase diagram that incorporates information from all three approaches and depicts the regions in parameter space that give rise to each convective *** Codes 76S05, 82B26, 76M10 © 2022, CC BY.

关键词： Porous materials

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Asymptotic Behaviors of Global Solutions to the Two-Dimensional Non-resistive MHD Equations with Large Initial Perturbations

arXiv

引用

arXiv 2021年

作者： Jiang, Fei Jiang, Song College of Mathematics and Computer Science Fuzhou University Fuzhou350108 China Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China

This paper is concerned with the asymptotic behaviors of global strong solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in two-dimensional periodic domains in Lagrangian coordinates. First, motivated by the odevity conditions imposed in [Arch. Ration. Mech. Anal. 227 (2018), 637–662], we prove the existence and uniqueness of strong solutions under some class of large initial perturbations, where the strength of impressive magnetic fields depends increasingly on the H2-norm of the initial perturbation values of both velocity and magnetic field. Then, we establish time-decay rates of strong solutions. Moreover, we find that H2-norm of the velocity decays faster than the perturbed magnetic field. Finally, by developing some new analysis techniques, we show that the strong solution convergence in a rate of the field strength to the solution of the corresponding linearized problem as the strength of the impressive magnetic field goes to infinity. In addition, an extension of similar results to the corresponding inviscid case with damping is presented. Copyright © 2021, The Authors. All rights reserved.

关键词： Damping

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A FLOW ARTIST FOR HIGH-DIMENSIONAL CELLULAR DATA

arXiv

引用

arXiv 2023年

作者： MacDonald, Kincaid Bhaskar, Dhananjay Thampakkul, Guy Nguyen, Nhi Zhang, Joia Perlmutter, Michael Adelstein, Ian Krishnaswamy, Smita Department of Mathematics Yale University United States Department of Genetics Yale School of Medicine United States Department of Computer Science Yale University United States Department of Mathematics Pomona College United States Applied Mathematics Program Yale University United States Department of Statistics University of Washington United States Department of Mathematics Boise State University United States Computational Biology and Bioinformatics Program Yale University United States

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data. © 2023, CC BY.

关键词： RNA

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Design and Development of a Research Integrated Geoinformation System with a Fuzzy Expert System

Design and Development of a Research Integrated Geoinformati...

引用

Annual Siberian Russian Workshop on Electron Devices and Materials (EDM)

作者： Rustam A. Burnashev Bulat M. Khairullin Nikolai A. Prokopyev Rustam A. Farahov Marina V. Bolsunovskaya Arslan I. Enikeev Institute of Computational Mathematics and Information Technologies Kazan Federal University Kazan Russia Institute of Applied Semiotics of the Academy of Sciences Of Tatarstan Republic Kazan Federal University Kazan Russia Institute of Computer Science and Technology Peter the Great St. Petersburg Polytechnic University St. Petersburg Russia

The paper presents a software toolkit that includes components of a fuzzy expert system and a geographic information system. Fuzzy expert system methods were applied to improve the decision-making efficiency when working with incomplete and inconsistent data. Geographic information technologies were used to distribute and visualize spatial data on the map. The interaction of both components will increase the efficiency of scientific projects in solving various tasks in research processes. Access to the knowledge base replenishment and processing is carried out by a subject-matter expert (administrator), while a common user has an access to elements of an intelligent fuzzy search and a visualizer (map). The software tool is a web resource capable of functioning on all modern platforms. Our research is aimed at improving the efficiency of decision-making in challenging circumstances.

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