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Symmetric Private Shortest Path Retrieval for LM-Enabled Route Services on Consumer Devices

IEEE Transactions on Consumer Electronics 2025年

作者： Liu, Xuefeng Lyu, Fake Lei, Jing Yang, Mengmeng Yau, Kok-Lim Alvin Lin, Yangfei Xidian University School of Cyber Engineering Shaanxi Xi’an710071 China Shaanxi Key Laboratory of Blockchain and Secure Computing China Commonwealth Scientific and Industrial Research Organization Data61 Black MountainACT2601 Australia Universiti Tunku Abdul Rahman Department of Internet Engineering and Computer Science Selangor Kajang43200 Malaysia University of Tsukuba Department of Computer Science Tsukuba305-8577 Japan

Route optimization is widely utilized in consumer electronics like Google Maps and Facebook connections. However, due to the limitations of consumer devices, users often rely on online service providers to process large-model-enabled route services, which may involve sensitive information such as location and social relationships. This raises privacy concerns, necessitating the need for a system that ensures expected utility while protecting the privacy of both consumers and service providers. This problem, known as Symmetric Private Shortest Path Retrieval, has been studied in the literature, either focusing on specific data types or a simple private setting where the data user and owner are the same. In this paper, we propose a low-latency symmetric private shortest path query for generic graph data in a more realistic public service model. We propose several novel techniques, including a chained encryption method and an oblivious key transfer mechanism to efficiently reveal the queried shortest path without leaking additional information to either the consumers or service provider. Experimental results demonstrate that our scheme outperforms the state-of-the-art by being approximately 46 to 53 times faster and consuming roughly 36 to 74 times less bandwidth for a city navigation service. © 1975-2011 IEEE.

关键词： Sensitive data

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Asymptotic Behavior of the Principal Eigenvalue of a Linear Second Order Elliptic Operator with Large Advection and General Boundary Conditions

SSRN

引用

SSRN 2023年

作者： Peng, Rui Zhang, Guanghui Zhou, Maolin School of Mathematical Sciences Zhejiang Normal University Zhejiang Jinhua321004 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Chern Institute of Mathematics LPMC Nankai University Tianjin300071 China

In this paper, we consider asymptotic behavior of the principal eigenvalue of some second order elliptic operator with general boundary conditions. For $N=1$, we provide a complete characterization of the asymptotic behavior, assuming that $m'$ changes sign at most finitely many times. Our findings not only improve upon the previous work in \cite{BHN2005,CL2008,PZ2018}, but also partially address some of the open questions posed in \cite{BHN2005}. Furthermore, our results elucidate the novel influence of boundary conditions on such asymptotics. To achieve these results, we develop several sophisticated techniques to overcome the new difficulties posed by the problems under consideration. © 2023, The Authors. All rights reserved.

关键词： Advection

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ASYMPTOTIC BEHAVIOR OF THE PRINCIPAL EIGENVALUE OF A LINEAR SECOND ORDER ELLIPTIC OPERATOR WITH LARGE ADVECTION AND GENERAL BOUNDARY CONDITIONS

arXiv

引用

arXiv 2023年

Consider the eigenvalue problem of a linear second order elliptic operator: − D∆ − 2α∇m(x) · ∇ + V (x) = λ in Ω, complemented by the Dirichlet boundary condition or the following general Robin boundary condition: (Formula Presented) is a bounded smooth domain, n(x) is the unit exterior normal to ∂Ω at x ∈ ∂Ω, D > 0 and α > 0 are, respectively, the diffusion and advection coefficients, m ∈ C2(Ω), V ∈ C(Ω), β ∈ C(∂Ω) are given functions, and β allows to be positive, sign-changing or negative. In [41], the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as D → 0 or D → ∞ was studied. In this paper, when N ≥ 2, under proper conditions on the advection function m, we establish the asymptotic behavior of the principal eigenvalue as α → ∞, and when N = 1, we obtain a complete characterization for such asymptotic behavior provided m0 changes sign at most finitely many times. Our results complement or improve those in [4, 7, 44] and also partially answer some questions raised in [4]. © 2023, CC0.

关键词： Advection

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The macroscopic finite-difference scheme and modified equations of the general propagation multiple-relaxation-time lattice Boltzmann model

arXiv

引用

arXiv 2023年

作者： Chen, Ying Liu, Xi Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Organization Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Organization Hubei Wuhan430074 China

In this paper, we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations (MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation (NACDE) and Navier-Stokes equations (NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, two benchmark problems, Gauss hill problem and Poiseuille flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results are not only in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

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An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling

arXiv

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arXiv 2022年

作者： Shi, Bin Sun, Guodong State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing100029 China University of Chinese Academy of Sciences Beijing100049 China

In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods.1 Specifically, the traditional approach is unavailable in practice, which requires numerically computing the gradient (first-order information) such that the computation cost is expensive since it needs a large number of times to run numerical models. However, the sampling approach directly reduces the gradient to the objective function value (zeroth-order information), which also avoids using the adjoint technique that is unusable for many atmosphere and ocean models and requires large amounts of storage. We show an intuitive analysis for the sampling algorithm from the law of large numbers and further present a Chernoff-type concentration inequality to rigorously characterize the degree to which the sample average probabilistically approximates the exact gradient. The experiments are implemented to obtain the CNOPs for two numerical models, the Burgers equation with small viscosity and the Lorenz-96 model. We demonstrate the CNOPs obtained with their spatial patterns, objective values, computation times and nonlinear error growth. Compared with the performance of the three approaches, all the characters for quantifying the CNOPs are nearly consistent, while the computation time using the sampling approach with fewer samples is extremely shorter. In other words, the new sampling algorithm shortens the computation time to the utmost at the cost of losing little accuracy. © 2022, CC BY-NC-SA.

关键词： Numerical models

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A Multi-scale Generalized Shrinkage Threshold Network for Image Blind Deblurring in Remote Sensing

arXiv

引用

arXiv 2023年

作者： Feng, Yujie Yang, Yin Fan, Xiaohong Zhang, Zhengpeng Zhang, Jianping School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory for Intelligent Computing and Information Processing The Ministry of Education Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Xiangtan411105 China School of Automation and Electronic Information Xiangtan University Xiangtan411105 China

MSC Codes 54H30, 68U10, 94A08Remote sensing images are essential for many applications of the earth’s sciences, but their quality can usually be degraded due to limitations in sensor technology and complex imaging environments. To address this, various remote sensing image deblurring methods have been developed to restore sharp and high-quality images from degraded observational data. However, most traditional model-based deblurring methods usually require predefined hand-crafted prior assumptions, which are difficult to handle in complex applications. On the other hand, deep learning-based deblurring methods are often considered as black boxes, lacking transparency and interpretability. In this work, we propose a new blind deblurring learning framework that utilizes alternating iterations of shrinkage thresholds. This framework involves updating blurring kernels and images, with a theoretical foundation in network design. Additionally, we propose a learnable blur kernel proximal mapping module to improve the accuracy of the blur kernel reconstruction. Furthermore, we propose a deep proximal mapping module in the image domain, which combines a generalized shrinkage threshold with a multi-scale prior feature extraction block. This module also incorporates an attention mechanism to learn adaptively the importance of prior information, improving the flexibility and robustness of prior terms, and avoiding limitations similar to hand-crafted image prior terms. Consequently, we design a novel multi-scale generalized shrinkage threshold network (MGSTNet) that focuses specifically on learning deep geometric prior features to enhance image restoration. Experimental results on real and synthetic remote sensing image datasets demonstrate the superiority of our MGSTNet framework compared to existing deblurring methods. Copyright © 2023, The Authors. All rights reserved.

关键词： Shrinkage

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Covariance-Based Joint Device Activity and Delay Detection in Asynchronous mMTC

arXiv

引用

arXiv 2021年

作者： Wang, Zhaorui Liu, Ya-Feng Liu, Liang The Department of Information Engineering The Chinese University of Hong Kong Hong Kong The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong

In this letter, we study the joint device activity and delay detection problem in asynchronous massive machine-type communications (mMTC), where all active devices asynchronously transmit their preassigned preamble sequences to the base station (BS) for device identification and delay detection. We first formulate this joint detection problem as a maximum likelihood estimation problem, which depends on the received signal only through its sample covariance, and then propose efficient coordinate descent type of algorithms to solve the formulated problem. Our proposed covariance-based approach is sharply different from the existing compressed sensing (CS) approach for the same problem. Numerical results show that our proposed covariance-based approach significantly outperforms the CS approach in terms of the detection performance since our proposed approach can make better use of the BS antennas than the CS approach. © 2021, CC BY.

关键词： Compressed sensing

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Random-batch list algorithm for short-range molecular dynamics simulations

arXiv

引用

arXiv 2021年

作者： Liang, Jiuyang Xu, Zhenli Zhao, Yue School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences MoE Key Lab of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China

We propose a fast method for the calculation of short-range interactions in molecular dynamics simulations. The so-called random-batch list method is a stochastic version of the classical neighborlist method to avoid the construction of a full Verlet list, which introduces two-level neighbor lists for each particle such that the neighboring particles are located in core and shell regions, respectively. Direct interactions are performed in the core region. For the shell zone, we employ a random batch of interacting particles to reduce the number of interaction pairs. The error estimate of the algorithm is provided. We investigate the Lennard-Jones fluid by molecular dynamics simulations, and show that this novel method can significantly accelerate the simulations with a factor of several fold without loss of the accuracy. This method is simple to implement, can be well combined with any linked cell methods to further speed up and scale up the simulation systems, and can be straightforwardly extended to other interactions such as Ewald short-range part, and thus it is promising for large-scale molecular dynamics simulations. Copyright © 2021, The Authors. All rights reserved.

关键词： Molecular dynamics

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Quantum simulation of Maxwell's equations via Schrödingersation

arXiv

引用

arXiv 2023年

作者： Jin, Shi Liu, Nana Ma, Chuwen School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China Shanghai Artificial Intelligence Laboratory Shanghai China

We present quantum algorithms for electromagnetic fields governed by Maxwell’s equations. The algorithms are based on the Schrödingerisation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system evolving under unitary dynamics, via a warped phase transformation that maps the equation into one higher dimension. In this paper, our quantum algorithms are based on either a direct approximation of Maxwell’s equations combined with Yee’s algorithm, or a matrix representation in terms of Riemann-Silberstein vectors combined with a spectral approach and an upwind scheme. We implement these algorithms with physical boundary conditions, including perfect conductor and impedance boundaries. We also solve Maxwell’s equations for a linear inhomogeneous medium, specifically the interface problem. Several numerical experiments are performed to demonstrate the validity of this approach. In addition, instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework, which allows the quantum simulation of Maxwell’s equations in analog quantum simulation. Copyright © 2023, The Authors. All rights reserved.

关键词： Maxwell equations

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Quantum simulation for time-dependent Hamiltonians – with applications to non-autonomous ordinary and partial differential equations

arXiv

引用

arXiv 2023年

作者： Cao, Yu Jin, Shi Liu, Nana School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China Shanghai Artificial Intelligence Laboratory Shanghai China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China

Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having a time-dependent Hamiltonian. However, the quantum simulation of these systems often needs to appeal to rather complicated procedures involving the Dyson series, considerations of time-ordering, requirement of time steps to be discrete and/or requiring multiple measurements and postselection. These procedures are generally much more complicated than the quantum simulation of time-independent Hamiltonians. Here we propose an alternative formalism that turns any non-autonomous unitary dynamical system into an autonomous unitary system, i.e., quantum system with a time-independent Hamiltonian, in one higher dimension, while keeping time continuous. This makes the simulation with time-dependent Hamiltonians not much more difficult than that of time-independent Hamiltonians, and can also be framed in terms of an analogue quantum system evolving continuously in time. We show how our new quantum protocol for time-dependent Hamiltonians can be performed in a resource-efficient way and without measurements, and can be made possible on either continuous-variable, qubit or hybrid systems. Combined with a technique called Schrödingerisation, this dilation technique can be applied to the quantum simulation of any linear ODEs and PDEs, and nonlinear ODEs and certain nonlinear PDEs, with time-dependent coefficients. © 2023, CC BY.

关键词： Hybrid systems

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