• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권1호
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• pp.63-77
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• 2003

Some inequalities for the $Csisz{\acute{a}}r\;{\Phi}-divergence$ and applications for the Kullback-Leibler, $R{\acute{e}}nyi$, Hellinger and Bhattacharyya distances in Information Theory are given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권2호
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• pp.31-42
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• 2002

Applications of a result by Andrica and Raşa involving twice differentiable mappings for Shannon's and R$\acute{e}$nyi's entropy are given.

• 대한수학회논문집
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• 제26권1호
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• pp.151-161
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• 2011

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

• Communications for Statistical Applications and Methods
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• 제24권4호
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• pp.353-365
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• 2017

In this article, we proposed a new three-parameter distribution called generalized half-logistic Poisson distribution with a failure rate function that can be increasing, decreasing or upside-down bathtub-shaped depending on its parameters. The new model extends the half-logistic Poisson distribution and has exponentiated half-logistic as its limiting distribution. A comprehensive mathematical and statistical treatment of the new distribution is provided. We provide an explicit expression for the $r^{th}$ moment, moment generating function, Shannon entropy and $R{\acute{e}}nyi$ entropy. The model parameter estimation was conducted via a maximum likelihood method; in addition, the existence and uniqueness of maximum likelihood estimations are analyzed under potential conditions. Finally, an application of the new distribution to a real dataset shows the flexibility and potentiality of the proposed distribution.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2014년도 추계학술발표대회
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• pp.849-852
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• 2014

Reverse engineering of gene regulatory network is a challenging task in computational biology. To detect a regulatory relationship among genes from time series data is called reverse engineering. Reverse engineering helps to discover the architecture of the underlying gene regulatory network. Besides, it insights into the disease process, biological process and drug discovery. There are many statistical approaches available for reverse engineering of gene regulatory network. In our paper, we propose pairwise mutual information for the reverse engineering of a gene regulatory network from time series data. Firstly, we create random boolean networks by the well-known $Erd{\ddot{o}}s-R{\acute{e}}nyi$ model. Secondly, we generate artificial time series data from that network. Then, we calculate pairwise mutual information for predicting the network. We implement of our system on java platform. To visualize the random boolean network graphically we use cytoscape plugins 2.8.0.

• 대한수학회지
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• 제54권4호
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• 정보보호학회논문지
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• 제30권5호
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• pp.945-956
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• 2020

많은 응용프로그램들로부터 양질의 서비스를 제공받기 위해서 데이터 공개는 필수적이다. 하지만 원본 데이터를 그대로 공개할 경우 개인의 민감한 정보(정치적 성향, 질병 등)가 드러날 위험이 있기 때문에 원본 데이터가 아닌 재현 데이터를 생성하여 공개함으로써 프라이버시를 보존하는 많은 연구들이 제안되어왔다. 그러나 단순히 재현 데이터를 생성하여 공개하는 것은 여러 공격들(연결공격, 추론공격 등)에 의해 여전히 프라이버시 유출 위험이 존재한다. 본 논문에서는 이러한 민감한 정보의 유출을 방지하기 위해, 재현 데이터 생성 모델로 주목받고 있는 GAN에 최신 프라이버시 보호 기술인 차분 프라이버시를 적용하여 프라이버시가 보존되는 재현 데이터 생성 알고리즘을 제안한다. 생성 모델은 레이블이 있는 데이터의 효율적인 학습을 위해 CGAN을 사용하였고, 데이터의 유용성 측면을 고려하여 기존 차분 프라이버시보다 프라이버시가 완화된 Rényi 차분 프라이버시를 적용하였다. 그리고 생성된 데이터의 유용성에 대한 검증을 다양한 분류기를 통해 실시하고 비교분석하였다.