• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.2019-2022
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• 2002

This paper presents design of spreading codes for asynchronous DS-CDMA systems. We have been trying to generate maximal-period sequences based on one-dimensional maps with finite bits whose shapes are similar to piecewise linear chaotic maps. We propose an efficient search algorithm finding such mammal-period sequences. This algorithm makes it possible to find many kinds of maximal-period sequences with sufficiently long period for CDMA applications. We also investigate bit error rate(BER) in asynchronous DS-CDMA systems using the maximal-period binary sequences by computer simulations.

• Genomics & Informatics
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• v.10 no.1
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• pp.51-57
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• 2012

Mining interesting patterns from DNA sequences is one of the most challenging tasks in bioinformatics and computational biology. Maximal contiguous frequent patterns are preferable for expressing the function and structure of DNA sequences and hence can capture the common data characteristics among related sequences. Biologists are interested in finding frequent orderly arrangements of motifs that are responsible for similar expression of a group of genes. In order to reduce mining time and complexity, however, most existing sequence mining algorithms either focus on finding short DNA sequences or require explicit specification of sequence lengths in advance. The challenge is to find longer sequences without specifying sequence lengths in advance. In this paper, we propose an efficient approach to mining maximal contiguous frequent patterns from large DNA sequence datasets. The experimental results show that our proposed approach is memory-efficient and mines maximal contiguous frequent patterns within a reasonable time.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.3
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• pp.627-633
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• 2013

An important problem in the transmission performance and efficiency is to find the values and the number of the cross-correlation function between two different maximal sequences. In this paper, we present the new maximal sequences which are obtained by the new decimations $d=\frac{2^{m-st-1}}{2^s-1}(2^n+2^{st+s+1}-2^{m+st+1}-1)$ from some maximal sequences. We will also find the values and the number of occurrences of each value of the cross-correlation function from the proposed decimations.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.567-570
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• 2000

A design method of nonlinear feedback shift registers that can produce maximal-period sequences is given. Such a design is based on one-to-one mappings which are similar to well-known chaotic maps. Some properties of generated binary sequences are investigated and discussed.

• International Journal of Contents
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• v.3 no.2
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• pp.18-24
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• 2007

Biological sequences such as DNA and amino acid sequences typically contain a large number of items. They have contiguous sequences that ordinarily consist of more than hundreds of frequent items. In biological sequences analysis(BSA), a frequent contiguous sequence search is one of the most important operations. Many studies have been done for mining sequential patterns efficiently. Most of the existing methods for mining sequential patterns are based on the Apriori algorithm. In particular, the prefixSpan algorithm is one of the most efficient sequential pattern mining schemes based on the Apriori algorithm. However, since the algorithm expands the sequential patterns from frequent patterns with length-1, it is not suitable for biological datasets with long frequent contiguous sequences. In recent years, the MacosVSpan algorithm was proposed based on the idea of the prefixSpan algorithm to significantly reduce its recursive process. However, the algorithm is still inefficient for mining frequent contiguous sequences from long biological data sequences. In this paper, we propose an efficient method to mine maximal frequent contiguous sequences in large biological data sequences by constructing the spanning tree with a fixed length. To verify the superiority of the proposed method, we perform experiments in various environments. The experiments show that the proposed method is much more efficient than MacosVSpan in terms of retrieval performance.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1882-1885
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• 2002

This paper shows design of maximal-period sequences with prescribed constant auto-correlation values based on one-dimensional (1-D) maps with (mite bits. We construct such 1-D maps based on piecewise linear onto chaotic maps. Theoretical analyses and some design examples are given.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.6
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• pp.891-897
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• 2013

The spectrum and the number of the values of the cross-correlation function between the maximal period binary sequences have been extensively studied because of their importance in communications applications. In this paper, we propose the new family of the sequences using the decimation $d=2^{m-1}(3{\cdot}2^{m}-1)$. And we find the spectrum of the cross-correlation function of the sequences and analyze the number of times each value occurs for $0{\leq}{\tau}{\leq}2^{n}-2$.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.83-116
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• 2020

Let G be a finite group. By a sequence over G, we mean a finite unordered sequence of terms from G, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals the identity element of G. The large Davenport constant D(G) is the maximal length of a minimal product-one sequence, that is, a product-one sequence which cannot be factored into two non-trivial product-one subsequences. We provide explicit characterizations of all minimal product-one sequences of length D(G) over dihedral and dicyclic groups. Based on these characterizations we study the unions of sets of lengths of the monoid of product-one sequences over these groups.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.515-525
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• 1998

In this paper we obtain a "compactness" result that asserts the existence, in certain sets of sequences, of a sequence which has a maximal reciprocal sum. We derive this result from a much more general theorem which will be proved by introducing a metric into the set of sequences and using a topological argument.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.57-72
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• 2016

We establish maximal moment inequalities of partial sums under ${\psi}$-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with ${\psi}$-weakly dependent innovations.