• Title, Summary, Keyword: R ${\acute{e}}nyi\

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SOME INEQUALITIES FOR THE $CSISZ{\acute{A}}R\;{\Phi}-DIVERGENCE$

  • Dragomir, S.S.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.7 no.1
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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.

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MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES

  • Xuejun, Wang;Shuhe, Hu;Xiaoqin, Li;Wenzhi, Yang
    • Communications of the Korean Mathematical Society
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    • v.26 no.1
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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.

Generalized half-logistic Poisson distributions

  • Muhammad, Mustapha
    • Communications for Statistical Applications and Methods
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    • v.24 no.4
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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.

Reverse Engineering of a Gene Regulatory Network from Time-Series Data Using Mutual Information

  • Barman, Shohag;Kwon, Yung-Keun
    • Proceedings of the Korea Information Processing Society Conference
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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.

Finite-Size Scaling in q-Coloring Problems

  • Ha, Meesoon
    • New Physics: Sae Mulli
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    • v.67 no.8
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    • pp.1023-1027
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    • 2017
  • We numerically investigate q-coloring (q-COL) problems in random networks in terms of a stochastic-local-search (SLS) algorithm. Random q-COL problems involve finding solutions where all nodes consist of different colors from their neighbors' colors, among q colors. For a fixed number of colors, say q = 3 or larger, various phase transitions have been reported as the average degree of links (the number density of constraints), c = , increases. This is because the set of solutions undergoes several types of phase transitions similar to those observed in the mean-field theory of spin glasses at zero temperature. Eventually, a dynamic coloring threshold is found to exist, above which no more solutions exist. Using the finite-size scaling (FSS) technique for nonequilibrium absorbing phase transitions, we analyze critical behaviors in the dynamic phase transition of q-COL problems by using the SLS algorithm, where we test both $Erd{\ddot{o}}s-R{\acute{e}}nyi$ and regular random networks. Finally, we discuss the extended FSS in q-COL problems compared to random k-satisfiability ones.

THE PROBABILISTIC METHOD MEETS GO

  • Farr, Graham
    • Journal of the Korean Mathematical Society
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    • v.54 no.4
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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.

A Study on Synthetic Data Generation Based Safe Differentially Private GAN (차분 프라이버시를 만족하는 안전한 GAN 기반 재현 데이터 생성 기술 연구)

  • Kang, Junyoung;Jeong, Sooyong;Hong, Dowon;Seo, Changho
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.30 no.5
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    • pp.945-956
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    • 2020
  • The publication of data is essential in order to receive high quality services from many applications. However, if the original data is published as it is, there is a risk that sensitive information (political tendency, disease, ets.) may reveal. Therefore, many research have been proposed, not the original data but the synthetic data generating and publishing to privacy preserve. but, there is a risk of privacy leakage still even if simply generate and publish the synthetic data by various attacks (linkage attack, inference attack, etc.). In this paper, we propose a synthetic data generation algorithm in which privacy preserved by applying differential privacy the latest privacy protection technique to GAN, which is drawing attention as a synthetic data generative model in order to prevent the leakage of such sensitive information. The generative model used CGAN for efficient learning of labeled data, and applied Rényi differential privacy, which is relaxation of differential privacy, considering the utility aspects of the data. And validation of the utility of the generated data is conducted and compared through various classifiers.