• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.5
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• pp.451-461
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• 2002

Differential evolution(DE) has been preyed to be an efficient method for optimizing real-valued multi-modal objective functions. DE's main assets are its conceptual simplicity and ease of use. However, the convergence properties are deeply dependent on the control parameters of DE. This paper proposes an adaptive differential evolution(ADE) method which combines with a variant of DE and an adaptive mechanism of the control parameters. ADE contributes to the robustness and the easy use of the DE without deteriorating the convergence. 12 optimization problems is considered to test ADE. As an application of ADE the paper presents a supervised clustering method for predicting events, what is called, an evolutionary event clustering(EEC). EEC is tested for 4 cases used widely for the validation of data modeling.

• The Transactions of the Korea Information Processing Society
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• v.4 no.7
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• pp.1759-1769
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• 1997

The Error BackPropagation (EBP) algorithm for multi-layered neural networks is widely used in various areas such as associative memory, speech recognition, pattern recognition and robotics, etc. Nevertheless, many researchers have continuously published papers about improvements over the original EBP algorithm. The main reason for this research activity is that EBP is exceeding slow when the number of neurons and the size of training set is large. In this study, we developed new learning speed acceleration methods using variable learning rate, variable momentum rate and variable slope for the sigmoid function. During the learning process, these parameters should be adjusted continuously according to the total error of network, and it has been shown that these methods significantly reduced learning time over the original EBP. In order to show the efficiency of the proposed methods, first we have used binary data which are made by random number generator and showed the vast improvements in terms of epoch. Also, we have applied our methods to the binary-valued Monk's data, 4, 5, 6, 7-bit parity checker and real-valued Iris data which are famous benchmark training sets for machine learning.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.323-342
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.709-723
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• 2016

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}{\mathbb{R}}^n$ by $Zn(x)=(\int_{0}^{t_1}h(s)dx(s),{\cdots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $t_n$ < t is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function $Z_n$ and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function $F(x)=f(\int_{0}^{t}e(s)dx(s))$ for $x{\in}C[0,t]$, where $f{\in}L_p(\mathbb{R})(1{\leq}p{\leq}{\infty})$ and e is a unit element in $L_2[0,t]$. Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of $L_2[0,t]$ used in the transformation is independent of e and the conditioning function $Z_n$ does not contain the present positions of the generalized Wiener paths.

• Korean Journal of Computational Design and Engineering
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• v.3 no.1
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• pp.57-67
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• 1998

Genetic programming (GP) is an extension of a genetic algoriths paradigm, deals with tree structures representing computer programs as individuals. In recent, there have been many research activities on applications of GP to various engineering problems including system identification, data mining, function approximation, and so forth. However, standard GP suffers from the lack of the estimation techniques for numerical parameters of the GP tree that is an essential element in treating various engineering applications involving real-valued function approximations. Unlike the other research activities, where nonlinear optimization methods are employed, I adopt the use of a weighted linear associative memory for estimation of these parameters under GP algorithm. This approach can significantly reduce computational cost while the reasonable accurate value for parameters can be obtained. Due to the fact that the GP algorithm is likely to fall into a local minimum, the GP algorithm often fails to generate the tree with the desired accuracy. This motivates to devise a group of additive genetic programming trees (GAGPT) which consists of a primary tree and a set of auxiliary trees. The output of the GAGPT is the summation of outputs of the primary tree and all auxiliary trees. The addition of auxiliary trees makes it possible to improve both the teaming and generalization capability of the GAGPT, since the auxiliary tree evolves toward refining the quality of the GAGPT by optimizing its fitness function. The effectiveness of this approach is verified by applying the GAGPT to the estimation of the principal dimensions of bulk cargo ships and engine torque of the passenger car.

• Journal of Advanced Marine Engineering and Technology
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• v.32 no.6
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• pp.955-963
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• 2008

In this paper, we propose an improved practical encryption and fault-tolerance decryption method using a non-negative value key and random function obtained with a white noise by using iterative phase wrapping method. A phase wrapping operating key, which is generated by the product of arbitrary random phase images and an original phase image. is zero-padded and Fourier transformed. Fourier operating key is then obtained by taking the real-valued data from this Fourier transformed image. Also the random phase wrapping operating key is made from these arbitrary random phase images and the same iterative phase wrapping method. We obtain a Fourier random operating key through the same method in the encryption process. For practical transmission of encryption and decryption keys via Internet, these keys should be intensity maps with non-negative values. The encryption key and the decryption key to meet this requirement are generated by the addition of the absolute of its minimum value to each of Fourier keys, respectively. The decryption based on 2-f setup with spatial filter is simply performed by the inverse Fourier transform of the multiplication between the encryption key and the decryption key and also can be used as a current spatial light modulator technology by phase encoding of the non-negative values. Computer simulations show the validity of the encryption method and the robust decryption system in the proposed technique.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.2
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• pp.191-201
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• 2010

This paper presents a new global optimization algorithm based on the branch-and-bound principle using Bspline approximation techniques. It describes the algorithmic components and details on their implementation. The key components include the subdivision of a design space into mutually disjoint subspaces and the bound calculation of the subspaces, which are all established by a real-valued B-spline volume model. The proposed approach was demonstrated with various test problems to reveal computational performances such as the solution accuracy, number of function evaluations, running time, memory usage, and algorithm convergence. The results showed that the proposed algorithm is complete without using heuristics and has a good possibility for application in large-scale NP-hard optimization.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.777-789
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• 2016

In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term $$(r(t)x^{\Delta}(t))^{\Delta}+q({\sigma}(t))x^{\Delta}(t)+p(t)f(x({\tau}(t)))=e(t)$$, and $$(r(t)x^{\Delta}(t))^{\Delta}+q(t)x^{\Delta}(t)+p(t)f(x({\sigma}(t)))=e(t)$$, on a time scale ${\mathbb{T}}$, where r(t), p(t) and q(t) are real-valued right-dense continuous (rd-continuous) functions [1] defined on ${\mathbb{T}}$ with p(t) < 0 and ${\tau}:{\mathbb{T}}{\rightarrow}{\mathbb{T}}$ is a strictly increasing differentiable function and ${\lim}_{t{\rightarrow}{\infty}}{\tau}(t)={\infty}$. No restriction is imposed on the forcing term e(t) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.

• The Journal of the Acoustical Society of Korea
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• v.38 no.6
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• pp.716-723
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• 2019

Fingerprint matching accuracy is essential in deploying a music search service. This paper deals with a method to improve fingerprint matching accuracy by utilizing an auxiliary information which is called power weight. Power weight is an expected robustness of each hash bit. While the previous power mask binarizes the expected robustness into strong and weak bits, the proposed method utilizes a real-valued function of the expected robustness as weights for fingerprint matching. As a countermeasure to the increased storage cost, we propose a compression method for the power weight which has strong temporal correlation. Experiments on the publicly-available music datasets confirmed that the proposed power weight is effective in improving fingerprint matching performance.