• Journal of KIISE
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• v.43 no.8
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• pp.835-840
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• 2016

Monte Carlo ray tracing has been widely used for simulating a diverse set of photo-realistic effects. However, this technique typically produces noise when insufficient numbers of samples are used. As the number of samples allocated per pixel is increased, the rendered images converge. However, this approach of generating sufficient numbers of samples, requires prohibitive rendering time. To solve this problem, image filtering can be applied to rendered images, by filtering the noisy image rendered using low sample counts and acquiring smoothed images, instead of naively generating additional rays. In this paper, we proposed a Stein's Unbiased Risk Estimator (SURE) based $\grave{A}$-Trous wavelet to filter the noise in rendered images in a near-interactive rate. Based on SURE, we can estimate filtering errors associated with $\grave{A}$-Trous wavelet, and identify wavelet coefficients reducing filtering errors. Our approach showed improvement, up to 6:1, over the original $\grave{A}$-Trous filter on various regions in the image, while maintaining a minor computational overhead. We have integrated our propsed filtering method with the recent interactive ray tracing system, Embree, and demonstrated its benefits.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.241-252
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• 2012

Let $\{X_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ be a sequence of LNQD which are dominated randomly by another random variable X. We obtain the complete convergence and almost sure convergence of weighted sums ${\sum}^n_{i=1}a_{ni}X_{ni}$ for LNQD by using a new exponential inequality, where $\{a_{ni},\;1{\leq}i{\leq}n,\;n{\geq}1\}$ is an array of constants. As corollary, the results of some authors are extended from i.i.d. case to not necessarily identically LNQD case.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.351-358
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• 2014

In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for $$\sum_{k{\leq}N}k^{-1}f(S_k/{\sigma}\sqrt{k})$$, where $S_k$ is the partial sums of strictly stationary mixing random variables with $EX_1=0$ and ${\sigma}^2=EX^2_1+2\sum_{k=1}^{\infty}EX_1X_{1+k}$. We also establish an almost sure limit behaviors of the above sums.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.137-143
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• 2007

In this paper, a Berstein-Hoeffding type inequality is established for linearly negative quadrant dependent random variables. A condition is given for almost sure convergence and the associated rate of convergence is specified.

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.177-182
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• 2004

In this paper, we establish some results on almost sure convergence for sums and weighted sums of uniformly integrable fuzzy random sets taking values in the space of upper-semicontinuous fuzzy sets in $R^{p}$.

• The Korean Journal of Cytopathology
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• v.18 no.2
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• pp.143-152
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• 2007

Sono-guided fine needle aspiration (FNA) of the thyroid is widely used, but the aspirated samples are typically not well preserved and low cellularity makes diagnosis difficult in many cases. The object of the current study is to evaluate the adequacy and diagnostic accuracy of the use of $SurePath^{TM}$ liquid-based cytology (SP-LBC) in the sonoguided fine needle aspiration of the thyroid nodule and to compare its use with that of the use of a conventional smear (CS). A total of 172 sono-guided FNAs of thyroid nodules from April to June, 2006 were prepared by the use of the split method with either SP-LBC or CS; the samples were stained with the use of hematoxylin-eosin (H&E) and Papanicolaou (Pap) stains. A cyto-histological correlation was performed in 69 (30 SP and 39 CS) cases that had been histologically confirmed. The rate of producing unsatisfactory slides by the use of the SP-LBC method (9.3%) was less than that of the use of the CS method (20.9%). The diagnostic accuracy of the SP method (93.3%) was better than that of the CS method (85.3%). The sensitivity and specificity of the SP method (94.4% and 92.3%) was better than that of the CS method (83.3% and 70%), respectively (p < 0.05). The CS of sono-guided aspirated specimens had some unavoidable limitations related to inadequate sampling such as a bloody background, low cellularity and an indication that some clinicians smeared many useless slides (averaging four to ten slides), and that most slides showed only blood that included few follicular cells. The SP method resulted in more thinly smeared slides and showed cleaner background and greater cellularity than the use of the CS method. Each follicular cell shows superior nuclear detail, and more distinct cytoplasmic features than with the use of the CS method. SP-LBC appears to be an easy, highly accurate, and reliable cytological method for employ for a diagnostic approach of thyroid disease and thyroid nodules. The SP-LBC method is a suitable alternative to the CS method to overcome diagnostic difficulties.

• Journal of the Korean Statistical Society
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• v.35 no.3
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• pp.251-260
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• 2006

The proportional hazards model (PHM) can be associated with a non- homogeneous Markov chain (NHMC) in the sense that sample alignments in the PHM correspond to trajectories of the NHMC. As a result the partial likelihood widely used for the PHM is a probabilistic function of the trajectories of the NHMC. In this paper, we show that, as the total number of subjects involved increases, the trajectories of the NHMC, i.e. sample alignments in the PHM, converges to the solution of an ordinary differential equation which, subsequently, characterizes the almost sure limit of the partial likelihood.

• Restorative Dentistry and Endodontics
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• v.25 no.3
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• pp.446-458
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• 2000

In this study, compressive strengths of three condensable composite resins(ALERT, SureFil, Solitaire), conventional hybrid composite resin(Z-100) and amalgam(HI-Aristaloy 21) according to the 6 types of cavity design(cylinder, trapezoidal, butt-joint, round bevel, long bevel and short bevel) were measured and appearance of fracture surfaces were observed with SEM, thus evaluated clinical applications of condensable composite resins according to the cavity designs. The results were as follows; 1. Compressive strengths according to experimental materials were the highest in SureFil, and Z-100, ALERT, Solitaire, HI-Aristaloy 21 in order. 2. SureFil showed the highest compressive strength(p<0.05). compressive strengths of ALERT and Solitaire were lower than that of Z-100, hybrid composite(p<0.05). 3. Compressive strengths according to specimen design were the highest in trapezoidal shape(p<0.05) and no significant difference was detected between other specimen designs. 4. The appearance of condensable composite resin under SEM was of a diverse configuration according to component of resin matrix, shapes of filler and surface treatments between resin and filler.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.679-688
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• 2014

The notion of asymptotically negative dependence for collection of random variables is generalized to a Hilbert space and the almost sure convergence for these H-valued random variables is obtained. The result is also applied to a linear process generated by H-valued asymptotically negatively dependent random variables.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.885-893
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• 2009

In this paper we study the strong law of large numbers for weighted average of pairwise negatively quadrant dependent random variables. This result extends that of Jamison et al.(Convergence of weight averages of independent random variables Z. Wahrsch. Verw Gebiete(1965) 4 40-44) to the negative quadrant dependence.