• Journal of Information Processing Systems
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• v.19 no.3
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• pp.275-288
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• 2023

Many image edge details are easily lost in the image denoising process, and the smooth image regions are prone to produce jagged. In this paper, we propose a wavelet-based image global k- singular value decomposition variational method to remove image noise. A layer of wavelet decomposition is applied to the noisy image first. Then, the image global k-singular value decomposition (IGK-SVD) method is used to remove the random noise of low-frequency components. Furthermore, a constructed variational denoising method (VDM) removes the random noise in the high-frequency component. Finally, the denoised image is obtained by wavelet reconstruction. The experimental results show that the proposed method's peak signal-to-noise ratio (PSNR) value is higher than other methods, and its structural similarity (SSIM) value is closer to one, indicating that the proposed method can effectively suppress image noise while retaining more image edge details. The denoised image has better denoising effects.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• Communications for Statistical Applications and Methods
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• v.30 no.6
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• pp.589-603
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• 2023

Deep generative models target to infer the underlying true data distribution, and it leads to a huge success in generating fake-but-realistic data. Regarding such a perspective, the data attributes can be a crucial factor in the data generation process since non-existent counterfactual samples can be generated by altering certain factors. For example, we can generate new portrait images by flipping the gender attribute or altering the hair color attributes. This paper proposes counterfactual disentangled variational autoencoder generative adversarial networks (CDVAE-GAN), specialized for data attribute level counterfactual data generation. The structure of the proposed CDVAE-GAN consists of variational autoencoders and generative adversarial networks. Specifically, we adopt a Gaussian variational autoencoder to extract low-dimensional disentangled data features and auxiliary Bernoulli latent variables to model the data attributes separately. Also, we utilize a generative adversarial network to generate data with high fidelity. By enjoying the benefits of the variational autoencoder with the additional Bernoulli latent variables and the generative adversarial network, the proposed CDVAE-GAN can control the data attributes, and it enables producing counterfactual data. Our experimental result on the CelebA dataset qualitatively shows that the generated samples from CDVAE-GAN are realistic. Also, the quantitative results support that the proposed model can produce data that can deceive other machine learning classifiers with the altered data attributes.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• The Journal of the Acoustical Society of Korea
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• v.41 no.3
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• pp.351-358
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• 2022

Recently, Generative Adversarial Networks (GAN) and Variational AutoEncoders (VAE) have been applied to voice conversion that can make use of non-parallel training data. Especially, Conditional Cycle-Consistent Generative Adversarial Networks (CC-GAN) and Cycle-Consistent Variational AutoEncoders (CycleVAE) show promising results in many-to-many voice conversion among multiple speakers. However, the number of speakers has been relatively small in the conventional voice conversion studies using the CC-GANs and the CycleVAEs. In this paper, we extend the number of speakers to 100, and analyze the performances of the many-to-many voice conversion methods experimentally. It has been found through the experiments that the CC-GAN shows 4.5 % less Mel-Cepstral Distortion (MCD) for a small number of speakers, whereas the CycleVAE shows 12.7 % less MCD in a limited training time for a large number of speakers.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.1-11
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• 2004

In this paper, we suggest and analyze some new classes of three step iterative algorithms for solving generalized quasivariational inclusions by using the properties of proximal maps. Our results include the Ishikawa, Mann iterations for solving variational inclusions(inequalities) as special cases. The results obtained in this paper represent an improvement and significant refinement of previously known results [3, 5-8, 10, 14-18].

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.845-860
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• 2010

In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.409-413
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• 2018

In this paper, He's Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-12
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• 1997

Complementaity problem theory developed by Lemke [10], Cottle and Dantzig [8] and others in the early 1960s and thereafter, has numerous applications in diverse fields of mathematical and engineering sciences. And it is closely related to variational inquality theory and fixed point theory. Recently, fixed point methods for the solving of nonlinear complementarity problems were considered by Noor et al. [11, 12]. Also complementarity problems related to variational inequality problems were investigated by Chang [1], Cottle [7] and others.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1433-1451
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• 2014

In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.