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Verifiable and visually meaningful image encryption scheme based on two-stage data fusion in the encrypted domain

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Journal of Electronic Imaging 2025年第2期34卷

作者： Li, Haojie Li, Meng Chongqing Technology and Business University School of Mathematics and Statistics Chongqing China Chongqing Technology and Business University Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring Chongqing China

Visually meaningful image encryption (VMIE) schemes disguise the secret image as another common image, effectively avoiding hackers' notice and suspicion. Most existing schemes embed pre-encrypted secret images into the plaintext domain of host images. This may lead to the following security risks: (1) the easy accessibility of embedded data through direct statistical analysis of ciphertext images and (2) visual quality degradation caused by direct embedding images with different distribution features. In addition, existing schemes rarely consider identity verification for the data-sharing party. Motivated by these shortcomings, we develop a verifiable VMIE framework based on data fusion in the encrypted domain. First, an improved chaos system is designed to effectively pre-encrypt the digitalized handwritten signature, secret image, and host image. Then, an embedding strategy of two-stage data fusion in the encrypted domain is proposed to integrate the handwritten signature, secret image, and host image by least significant bit-based data hiding. Finally, the ciphertext image is reconstructed by applying the reverse operation of pre-encryption to the fusion result. Different from general schemes that directly embed noise-like images into the plaintext domain, our data fusion is completed in the encrypted domain. Due to the similarity of images in the ciphertext domain to noise images, the secret and host images after pre-encryption have close distribution and texture features. Thus, it reduces disturbance to the host image caused by secret embedding, thereby improving the visual quality of the ciphertext image and the security of the secret data. Moreover, the introduction of digitalized handwritten signatures has brought a more convenient user experience for identity verification. Experiments show that the proposed scheme can recover the secret image and handwritten signature even after undertaking various attacks. Compared with the state-of-the-art algorithms, th

关键词： chaos system data fusion digital signature encrypted domain visually meaningful image encryption

Convergence and applications of novel FISTA-like algorithms

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Communications in Nonlinear Science and Numerical Simulation 2025年 148卷

作者： Zhang, Yeyu Liu, Hongwei Tang, Yan School of Mathematics and Statistics Xidian University Shaanxi710126 China School of Mathematics and Statistics Chongqing Technology and Business University Chongqing400067 China Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring China

In this paper, a novel unified framework of fast iterative shrinkage-thresholding algorithm (FISTA)-like algorithms is proposed for nonsmooth convex minimization problems in real Hilbert spaces, which includes several variants (e.g., forward–backward splitting methods, inertial forward–backward algorithms, and FISTA). The convergence rates of the objective function and the iterative algorithm are studied, and the strong convergence is obtained provided that the objective function is uniformly convex. Secondly, a perturbed version of the FISTA-like algorithms is presented. Two strategies for the selection of the step size and improvement measures for the local oscillation behavior of the algorithm are introduced, which greatly improves the practical application performance. In addition, the model of the continuous dynamical system is established, and also the asymptotic property is obtained. Finally, the effectiveness and superiority of the proposed algorithms are verified by LASSO problems, image deblurring, and signal recovery. © 2025 Elsevier B.V.

关键词： Hilbert spaces

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

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Applied Mathematics(A Journal of Chinese Universities) 2024年第3期39卷 438-447页

作者： SUN Rong School of Mathematics and Statistics Chongqing Technology and Business UniversityChongqing 400067China Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring Chongqing Technology and Business UniversityChongqing 400067China

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy ***,the concept of fuzzy concave integral on a fuzzy set is ***,some important properties of s... 详细信息

关键词： convergence theorems fuzzy concave integral fuzzyσ-algebra

Impact of Us–China Tensions on the Volatility, Correlation, and Hedging Effects of Gold and Crude Oil Prices

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SSRN

SSRN 2025年

作者： Liu, Ping Li Lü, Zheng Yoon, Seong-Min School of Mathematics and Statistics Chongqing Technology and Business University Chongqing China Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring Chongqing Technology and Business University Chongqing China Limited Shanghai China China Foreign Exchange Trade System China Department of Economics Pusan National University Busan Korea Republic of

In the context of the global economy facing complex challenges and the increasing tension in US–China relations, studying the effect of these tensions on the volatility, correlation, and hedging effects of gold and crude oil prices is particularly important. This study explores three main aspects of this issue. First, the GARCH-MIDAS approach is implemented to assess the impact of the US–China Tensions Index (UCT) on the long-term volatility of gold and crude oil. Second, the DCC-MIDAS-UCT model is constructed to explore the impact of US–China tensions on the dynamics between gold and crude oil. Finally, the time-varying correlation and covariance matrices estimated by the DCC-MIDAS-UCT model are applied to a portfolio to assess the effectiveness of the model in enhancing the hedging effect of gold against oil. These findings indicate that UCT exerts a statistically significant positive influence on long-term volatility in international crude oil prices. However, its transmission mechanism to gold price fluctuations is more complex. When examining its long-term impact on gold prices exclusively, a notably positive correlation emerges;however, upon incorporating the control variables, this relationship turns negative. This suggests that the gold market may be hedging against the impact of UCT through the risk-premium channel. Furthermore, the DCC-MIDAS-UCT model, which considers UCT, significantly improves the hedging effect of gold against oil in risk management. This study not only enriches our understanding of market dynamics but also serves as an effective guide for investors and policymakers to better cope with market risks. © 2025, The Authors. All rights reserved.

关键词： Risk management

AN INERTIAL ALGORITHM FOR SOLVING SPLIT VARIATIONAL INCLUSION PROBLEM

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UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 2024年第4期86卷 103-112页

作者： Guan, Jin-Lin Tang, Yan Zhang, Ye-Yu School of Mathematics and Statistics Chongqing Technology and Business University Chongqing400067 China Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring Chongqing400067 China

This paper aims to investigate a new inertial algorithm for solving a split variational inclusion problem in real Hilbert spaces. Under very mild conditions, we prove a strong convergence theorem for the proposed algorithm by using self-adaptive stepsizes and demiclosedness principle. Furthermore, an application is given to illustrate the effectiveness of the algorithm. The results improve and extend the corresponding ones announced by some others in the earlier and recent literature. © 2024, Politechnica University of Bucharest. All rights reserved.

关键词： Consensus algorithm

Inertial primal-dual dynamics with Hessian-driven damping and Tikhonov regularization for convex-concave bilinear saddle point problems

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arXiv 2024年

作者： Sun, Xiangkai He, Liang Long, Xian-Jun Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring College of Mathematics and Statistics Chongqing Technology and Business University Chongqing400067 China

This paper deals with a second-order primal-dual dynamical system with Hessian-driven damping and Tikhonov regularization terms in connection with a convex-concave bilinear saddle point problem. We first obtain a fast convergence rate of the primal-dual gap along the trajectory generated by the dynamical system, and provide some integral estimates. Then, based on the setting of the parameters involved, we demonstrate that both the convergence rate of the primal-dual gap and the strong convergence of the trajectory can be achieved simultaneously. Furthermore, we evaluate the performance of the proposed system using two numerical *** Codes 34D05(Primary) 37N40, 46N10, 90C25 (Secondary) Copyright © 2024, The Authors. All rights reserved.

关键词： Damping

Tikhonov regularized inertial primal-dual dynamics for convex-concave bilinear saddle point problems

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arXiv 2024年

In this paper, for a convex-concave bilinear saddle point problem, we propose a Tikhonov regularized second-order primal-dual dynamical system with slow damping, extrapolation and general time scaling parameters. Depending on the vanishing speed of the rescaled regularization parameter (i.e., the product of Tikhonov regularization parameter and general time scaling parameter), we analyze the convergence properties of the trajectory generated by the dynamical system. When the rescaled regularization parameter decreases rapidly to zero, we obtain convergence rates of the primal-dual gap and velocity vector along the trajectory generated by the dynamical system. In the case that the rescaled regularization parameter tends slowly to zero, we show the strong convergence of the trajectory towards the minimal norm solution of the convex-concave bilinear saddle point problem. Further, we also present some numerical experiments to illustrate the theoretical *** Codes 34D05, 37N40, 46N10, 90C25 Copyright © 2024, The Authors. All rights reserved.

关键词： Trajectories

Tikhonov regularization of second-order plus first-order primal-dual dynamical systems for separable convex optimization

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arXiv 2024年

作者： Sun, Xiangkai Zheng, Lijuan Teo, Kok Lay Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring College of Mathematics and Statistics Chongqing Technology and Business University Chongqing400067 China School of Mathematical Sciences Sunway University Bandar Sunway Selangor Darul Ehsan47500 Malaysia

This paper deals with a Tikhonov regularized second-order plus first-order primaldual dynamical system with time scaling for separable convex optimization problems with linear equality constraints. This system consists of two second-order ordinary differential equations for the primal variables and one first-order ordinary differential equation for the dual variable. By utilizing the Lyapunov analysis approach, we obtain the convergence properties of the primal-dual gap, the objective function error, the feasibility measure and the gradient norm of the objective function along the trajectory. We also establish the strong convergence of the primal trajectory generated by the dynamical system towards the minimal norm solution of the separable convex optimization problem. Furthermore, we give numerical experiments to illustrate the theoretical results, showing that our dynamical system performs better than those in the literature in terms of convergence *** Codes 90C25, 37N40, 34D05 Copyright © 2024, The Authors. All rights reserved.

关键词： Ordinary differential equations

Linear-quadratic Stochastic Stackelberg Differential Games with Affine Constraints

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arXiv 2024年

作者： Gou, Zhun Huang, Nan-Jing Long, Xian-Jun Kang, Jian-Hao School of Mathematics and Statistics Chongqing Technology and Business University Chongqing400067 China Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring Chongqing Technology and Business University Chongqing400067 China Department of Mathematics Sichuan University Sichuan Chengdu610064 China School of Mathematics Southwest Jiaotong University Sichuan Chengdu610031 China

This paper investigates the non-zero-sum linear-quadratic stochastic Stackelberg differential games with affine constraints, which depend on both the follower’s response and the leader’s strategy. With the help of the stochastic Riccati equations and the Lagrangian duality theory, the feedback expressions of optimal strategies of the follower and the leader are obtained and the dual problem of the leader’s problem is established. Under the Slater condition, the equivalence is proved between the solutions to the dual problem and the leader’s problem, and the KKT condition is also provided for solving the dual problem. Then, the feedback Stackelberg equilibrium is provided for the linear-quadratic stochastic Stackelberg differential games with affine constraints, and a new positive definite condition is proposed for ensuring the uniqueness of solutions to the dual problem. Finally, two non-degenerate examples with indefinite coefficients are provided to illustrate and to support our main results. © 2024, CC BY.

关键词： Riccati equations