• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.793-802
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• 1998

We apply the generalization of Levy's infinitesimal equation $\delta$X(t) = $\psi$(X(s), s $\leq$ t, $Y_{t}$, t, dt), $t\in R^1$, for a random field X (C) indexed by a contour C or by a more general set. Assume that the X(C) is homogeneous in x, say of degree n, then we can appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X (C.)

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2100-2103
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• 2003

기존의 객체 추출 및 추적 기법은 외형 변화가 없는 객체를 대상으로 하거나 배경이 고정된 영상만을 고려하였다 본 논문에서는 영역의 색상과 움직임 정보, 그리고 인접한 영역의 상관 관계를 고려한 Markov Random Field (MRF) 모델을 제안한다. MRF 모델은 영상의 시간적 공간적 상관성을 기반으로 최적의 레이블 셋을 계산함으로써 보다 정확하게 객체를 추출 및 추적할 수 있다. 또한, 블록 기반 움직임 추출 알고리즘인 Diamond Search (DS)를 분할된 영역에 적용하여 빠르게 영역의 움직임과 전역 움직임을 추정하였다. 실험 결과 제안한 방법이 객체의 외형 변화와 카메라 움직임이 있는 동영상에서 빠른 속도로 정확하게 객체를 추출 및 추적하는 것을 확인하였다.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.321-328
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• 1995

Ibragimov(1975) showed the central limit theorem and the invariance principle for $\rho$-mixing random variables satisfying $\sigma^2(n) = nh(n) \longrightarrow \infty$ and $E$\mid$\zeta_0$\mid$^{2+\delta} < \infty$ for some $\delta > 0$ where $\sigma^2(n)$ denotes the variance of the partial sum $S_n$ and h(n) is a slowly varying function.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.857-864
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• 2006

Due to the difficulties in numerical generation of random fields that satisfy not only the probabilistic distribution but the spectral characteristics as well. it is relatively hard to find an exact response variability of a structural response with a specific random field which has its features in the spatial and spectral domains. In this study. focusing on the fact that the random field assumes a constant over the domain under consideration when the correlation distance tends to infinity, a semi-theoretical solution of response variability is proposed for in-plane and plate bending structures. In this procedure, the probability density function is used directly resulting in a semi-exact solution for the random field in the state of random variable. It is particularly noteworthy that the proposed methodology provides response variability for virtually any type of probability density functions.

• Honam Mathematical Journal
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• v.9 no.1
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• pp.113-119
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• 1987

Random variables $X_1$, $X_1$, ..., $X_m$ are said to be weakly associated if whenever $\pi$ is a permutation of {1, 2,..., m}, $1{\leq}k<m$, and f: $R^{k}{\rightarrow}R$, g: $R^{m-k}{\rightarrow}R$ are coordinatewise nondecreasing functions then Cov $[f(X_{x(1)},...,\;X_{\pi(k)},\;g(X_{x(k+1)},...,\;X_{x(m)})]{\geq}0$, whenever the covariance is defined. An infinite collection of random variables is weakly associated if every finite subcollection is weakly associated. The basic properties of weak association and central limit theorem for weakly associated random variables are derived. We also extend this idea to point random fields and prove that a Cox process with a stationary weakly associated intensity rardom measure is weakly associated. Another inequalities and the fact that positive correlated normal random variables are weakly associated are also proved.

• Wind and Structures
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• v.23 no.4
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• pp.367-383
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• 2016

The influence mechanism of mean value components, noted as $P_0$, on POD applications for complete random fields $P_C(t)$ and fluctuating random fields $P_F(t)$ are illustrated mathematically. The critical philosophy of the illustration is introduction of a new matrix, defined as the correlation function matrix of $P_0$, which connect the correlation function matrix of $P_C(t)$ and $P_F(t)$, and their POD results. Then, POD analyses for several different wind pressure fields were presented comparatively as validation. It's inevitable mathematically that the first eigenmode of $P_C(t)$ resembles the distribution of $P_0$ and the first eigenvalue of $P_C(t)$ is close to the energy of $P_0$, due to similarity of the correlation function matrixs of $P_C(t)$ and $P_0$. However, the viewpoint is not rigorous mathematically that the first mode represents the mean pressure and the following modes represent the fluctuating pressure when $P_C(t)$ are employed in POD application. When $P_C(t)$ are employed, POD results of all modes would be distorted by the mean value components, and it's impossible to identify $P_0$ and $P_F(t)$ separately. Consequently, characteristics of the fluctuating component, which is always the primary concern in wind pressure field analysis, can only be precisely identified with $P_0$ excluded in POD.

• Journal of the Korean Geotechnical Society
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• v.24 no.8
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• pp.111-123
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• 2008

Geotechnical engineering problems are characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for a probabilistic analysis that considers the spatial variability of soil properties is presented to study the response of spatially random soil. The approach integrates a commercial finite difference method and random field theory into the framework of a probabilistic analysis. Two-dimensional non-Gaussian random fields are generated based on a Karhunen-$Lo{\grave{e}}ve$ expansion in a fashion consistent with a specified marginal distribution function and an autocorrelation function. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses were performed to study the effects of uncertainty due to the spatial heterogeneity on the settlement and bearing capacity of a rough strip footing. The simulations provide insight into the application of uncertainty treatment to the geotechnical problem and show the importance of the spatial variability of soil properties with regard to the outcome of a probabilistic assessment.

• 한국HCI학회:학술대회논문집
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• 2006.02a
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• pp.1252-1255
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• 2006

본 논문은 정보검색, 정보추출, 번역, 자연어처리 등의 작업을 위한 통계적 방법론에서 필요한 학습 데이터 구축을 효율적으로 하기 위한 학습 데이터 반자동 구축 장치 및 그 방법에 대하여 기술한다. 본 논문에서는 학습 데이터 구축양을 줄이기 위해서 능동 학습을 이용한다. 또한 최근 각광 받고 있는 Conditional Random Fields(CRF)를 능동학습에 이용하기 위해서 CRF를 이용한 Confidence measure를 정의한다.

• MALSORI
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• no.65
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• pp.125-141
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• 2008

In this work, we propose an automatic word spacing system for Korean using conditional random fields (CRFs) with Korean features. We map a word spacing problem into a classification problem in our work. We build a basic system which uses CRFs and Eumjeol bigram. After then, we analyze the result of inner-test. We extend a basic system added by some Korean features which are Josa, Eomi and two head Eumjeols of word extracting from lexicon. From the results of experiment, we can see that the proposed method is better than previous methods. Additionally the proposed method will be able to use mobile and speech applications because of very small size of model.

• MALSORI
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• no.66
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• pp.87-103
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• 2008

We describe a new active learning method in conditional random fields (CRFs) framework for keyphrase extraction. To save elaboration in annotation, we use diversity and representative measure. We select high diversity training candidates by sentence confidence value. We also select high representative candidates by clustering the part-of-speech patterns of contexts. In the experiments using dialog corpus, our method achieves 86.80% and saves 88% training corpus compared with those of supervised method. From the results of experiment, we can see that the proposed method shows improved performance over the previous methods. Additionally, the proposed method can be applied to other applications easily since its implementation is independent on applications.