• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.867-879
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• 2014

It is known that the orbifold Euler characteristic $e_{orb}(S)$ of a log del Pezzo surface S of rank one satisfies the inequality $0{\leq}e_{orb}(S){\leq}3$. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 < $e_{orb}(S)$. Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.

• Journal of Computing Science and Engineering
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• v.3 no.1
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• pp.15-26
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• 2009

Given an n-length text T over a $\sigma$-size alphabet, we present a compressed representation of T which supports retrieving queries of rank/select/access and updating queries of insert/delete. For a measure of compression, we use the empirical entropy H(T), which defines a lower bound nH(T) bits for any algorithm to compress T of n log $\sigma$ bits. Our representation takes this entropy bound of T, i.e., nH(T) $\leq$ n log $\sigma$ bits, and an additional bits less than the text size, i.e., o(n log $\sigma$) + O(n) bits. In compressed space of nH(T) + o(n log $\sigma$) + O(n) bits, our representation supports O(log n) time queries for a log n-size alphabet and its extension provides O(($1+\frac{{\log}\;{\sigma}}{{\log}\;{\log}\;n}$) log n) time queries for a $\sigma$-size alphabet.

• Proceedings of the Korean Information Science Society Conference
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• 2006.10a
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• pp.511-515
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• 2006

집합이나 배열의 원소, 트리의 노드, 그래프의 정점과 간선 등과 같은 이산 객체는 일반적으로 주기억장치의 논리적 주소 값과 같은 정수로 표현되어 왔다. Succinct 표현은 이와 같은 n개의 이산 객체를 O(n) 비트에 표현하는 방법이다. 대부분의 succinct 표현은 rank와 select라는 함수를 기본적으로 사용하며, 다양한 연구들에 의해 현재 rank와 select 함수는 o(n)?? 비트만을 사용하여 ??O(1) 시간에 수행될 뿐만 아니라, 실제로도 실용적으로 구현되었다. 본 논문에서는 $n{\times}n$ 배열, 즉 2차원 비트 스트링에 대한 Rank 및 Select 함수를 새롭게 정의한다. 또한, $O(n^2log\;n)$ 비트를 사용하여 O(1) 시간에 Rank 질의를 수행하고 O(log n) 시간에 Select 질의를 수행하는 방법과, 보다 적은 $O(n^2)$ 비트를 사용하면서 O(log n) 시간에 Rank 질의를 수행하고 $O(log^2\;n)$ 시간에 Select 질의를 수행하는 방법을 제안한다. 본 논문에서 정의하는 2차원 배열 상의 Rank와 Select 함수는 이미 개발된 2차원 상의 써픽스 트리 등을 기반으로 향후 개발될 2차원 상의 압축된 인덱스 자료구조나 이미지 프로세싱 등에 유용하게 사용된다.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.797-822
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• 2011

Log Enriques surface is a generalization of K3 and Enriques surface. We will classify all the rational log Enriques surfaces of rank 18 by giving concrete models for the realizable types of these surfaces.

• The Korean Journal of Applied Statistics
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• v.21 no.6
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• pp.933-945
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• 2008

The genetic association test on age of onset trait aims to detect the putative gene by means of linear rank tests for a significant trend of onset distributions with genotypes. However, due to the selective sampling of recruiting subjects with ages less than a pre-specified limit, the genotype groups are subject to substantially different censored distributions and thus this is one reason for the low efficiencies in the linear rank tests. In testing the equality of two survival distributions, log-rank statistic is preferred to the Wilcoxon statistic, when censored observations are nonignorable. Therefore, for more then two groups, we propose a generalized log-rank test for trend as a genetic association test. Monte Carlo studies are conducted to investigate the performances of the test statistics examined in this paper.

• Proceedings of the Korean Information Science Society Conference
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• 2012.06a
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• pp.385-387
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• 2012

Succinct 표현은 n개의 이산 객체를 정수 값으로 표현하는 대신 이진화하여 표현하는 방법으로 o(n) bit만을 사용하는 공간 효율적인 방법이다. Succinct 표현을 위한 1차원 비트스트링은 이산 객체의 저장 위치에 접근하기 위해서 rank와 select 함수를 필요로 하며, 다양한 연구들에 의해 현재 rank와 select 함수는 o(n) 비트를 사용하여 O(1) 시간에 수행되고, 실용적인 구현이 가능하다. 또한, 2차원 비트 스트링에 대한 연구도 진행되어, 현재 O($n^2$) bit를 사용하여 O(logn) 시간에 rank를, O($log^2n$) 시간에 select를 수행할 수 있다. 본 논문에서는 2차원 비트스트링 상에서의 rank 및 select 함수를 새롭게 정의하고 o($n^2$) 비트만을 사용하여 O(logn) 시간에 rank 질의를, 그리고 O($log^2n$)시간에 select 질의를 수행할 수 있는 방법을 제안한다.

• Genomics & Informatics
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• v.5 no.3
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• pp.95-101
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• 2007

In this paper, we consider the variable selection methods in the Cox model when a large number of gene expression levels are involved with survival time. Deciding which genes are associated with survival time has been a challenging problem because of the large number of genes and relatively small sample size (n<

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.79-88
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• 1994

Weighted log rank test is a widely applicable test when one is interested in detecting the differences between two groups. In man clinical trials it is common to see no differences in early experiments and does show significant differences later. We propose new weighted log rank test and illustrate it through an example. We also examine the empirical powers and show that the proposed test is more sensitive to detect late differences.

• Asian Pacific Journal of Cancer Prevention
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• v.14 no.8
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• pp.4769-4774
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• 2013

This paper is the first to present the incidence and overall survival of patients with squamous cell carcinoma of the head and neck (SCCHN) from the extreme northern part of the Philippines. We retrospectively retrieved the records of patients with histologically-confirmed squamous cell carcinoma of the oral cavity, oropharynx, hypopharynx and larynx at the Mariano Marcos Memorial Hospital and Medical Center, Ilocos Norte, Philippines, from 2003 to 2012 and analysed prognostic factors associated with survival. Of the 150 cases, only 80 (53.3%) were still living when the study was terminated. Median age at initial diagnosis was 61.5 years and the male to female ratio was 7:3. The majority of the cases had tumours in the oral cavity (50.7%), followed by the larynx (36.7%). Sex (log rank=1.94, p value/${\alpha}$=0.16), tumor site (log rank=0.02, p value/${\alpha}$=0.90), tumor grade (log rank=1.74, p value/${\alpha}$=0.42), and node stage (log rank=0.07, p value/${\alpha}$=0.80) were not shown to be associated with the survival of our cases. Only 45 (30.0%) had no regional lymph node involvement (N0) at presentation and 12 (8.0%) had already developed distant metastases. Among the 150 patients, 71 (47.3%) were not able to receive treatment of any kind. Oddly, treatment (log rank=1.65, p value/${\alpha}$=0.20) was also shown to be not associated with survival. The survival rate of those who underwent surgery, radiotherapy, or both was not statistically different from those who did not receive any treatment. Only the tumor stage (log rank=4.51, p value/${\alpha}$=0.03) was associated with patient survival. The overall mean survival was 49.3 months, with survival rate diminishing from 88.3% during the 1st year to 1.80% by end of the study. This relatively low survival rate of our cases only reflects their poor access to quality diagnostic and treatment facilities.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.75-86
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• 2002

We consider the problem of estimating the change-point in mean change model with one change-point. Gombay and Huskova(1998) derived a class of change-point estimators with the score function of rank. A change-point estimator with the log score function of rank is suggested and is shown to be involved in the class of Gombay and Huskova(1988). The simulation results show that the proposed estimator has smaller rose, larger proportion of matching the true change-point than the other estimators considered in the experiment when the change-point occurs in the middle of the sample.