• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.209-229
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• 2004

Let $\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha},\;z\;{\in}\;{\mathbb{C}}^n$ be a unimodular m-homogeneous polynomial in n variables (i.e. $$\mid$s_{\alpha}$\mid$\;=\;1$ for all multi indices $\alpha$), and let $R\;{\subset}\;{\mathbb{C}}^n$ be a (bounded complete) Reinhardt domain. We give lower bounds for the maximum modules $sup_{z\;{\in}\;R\;$\mid$\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha}$\mid$$, and upper estimates for the average of these maximum moduli taken over all possible m-homogeneous Bernoulli polynomials (i.e. $s_{\alpha}\;=\;{\pm}1$ for all multi indices $\alpha$). Examples show that for a fixed degree m our estimates, for rather large classes of domains R, are asymptotically optimal in the dimension n.

• Journal of the Korea Society of Computer and Information
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• v.17 no.2
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• pp.149-157
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• 2012

In this thesis, the problem of computing approximate answers to continuous sliding-window joins over data streams when the available memory may be insufficient to keep the entire join state. One approximation scenario is to provide a maximum subset of the result, with the objective of losing as few result tuples as possible. An alternative scenario is to provide a random sample of the join result, e.g., if the output of the join is being aggregated. It is shown formally that neither approximation can be addressed effectively for a sliding-window join of arbitrary input streams. Previous work has addressed only the maximum-subset problem, and has implicitly used a frequency based model of stream arrival. There exists a sampling problem for this model. More importantly, it is shown that a broad class of applications for which an age-based model of stream arrival is more appropriate, and both approximation scenarios under this new model are addressed. Finally, for the case of multiple joins being executed with an overall memory constraint, an algorithm for memory allocation across the join that optimizes a combined measure of approximation in all scenarios considered is provided.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.413-428
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• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.525-534
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• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.229-238
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• 2009

We propose a simple algorithm for obtaining MTL(maximum trimmed likelihood) estimates. The algorithm finds the subset to use to obtain the global maximum in the series of eliminating process which depends on the likelihood of cells in a contingency table. To evaluate the performance of the algorithm for MTL estimators, we conducted simulation studies. The results showed that the algorithm is very competitive in terms of computational burdens required to get the same or the similar results in comparison with the complete enumeration.

• Journal of KIISE:Computer Systems and Theory
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• v.28 no.9
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• pp.479-490
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• 2001

In this paper, we consider the method of partitioning a sphere into faces with a set of spherical convex polygons $\Gamma$=$｛P_1...P_n｝$ for determining the maximum of minimum intersection. This problem is commonly related with five geometric problems that fin the densest hemisphere containing the maximum subset of $\Gamma$, a great circle separating $\Gamma$, a great circle bisecting $\Gamma$ and a great circle intersecting the minimum or maximum subset of $\Gamma$. In order to efficiently compute the minimum or maximum intersection of spherical polygons. we take the approach of edge-based partition, in which the ownerships of edges rather than faces are manipulated as the sphere is incrementally partitioned by each of the polygons. Finally, by gathering the unordered split edges with the maximum number of ownerships. we approximately obtain the centroids of the solution faces without constructing their boundaries. Our algorithm for finding the maximum intersection is analyzed to have an efficient time complexity O(nv) where n and v respectively, are the numbers of polygons and all vertices. Furthermore, it is practical from the view of implementation, since it computes numerical values. robustly and deals with all the degenerate cases, Using the similar approach, the boundary of a general intersection can be constructed in O(nv+LlogL) time, where : is the output-senstive number of solution edges.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.208-212
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• 1998

This paper suggests the method to recognize the various defect patterns of cold mill strip using binary decision tree constructed by genetic algorithm automatically. In case of classifying the complex the complex patterns with high similarity like the defect patterns of cold mill strip, the selection of the optimal feature set and the structure of recognizer is important for high recognition rate. In this paper genetic algorithm is used to select a subset of the suitable features at each node in binary decision tree. The feature subset of maximum fitness is chosen and the patterns are classified into two classes by linear decision function. After this process is repeated at each node until all the patterns are classified respectively into individual classes. In this way , binary decision tree classifier is constructed automatically. After construction binary decision tree, the final recognizer is accomplished by the learning process of neural network using a set of standard p tterns at each node. In this paper, binary decision tree classifier is applied to recognition of the defect patterns of cold mill strip and the experimental results are given to show the usefulness of the proposed scheme.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.237-242
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• 1994

One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.

• Proceedings of the KIEE Conference
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• 1998.07g
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• pp.2330-2332
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• 1998

This paper suggests a method to recognize the various defect patterns of cold mill strip using binary decision tree automatically constructed by genetic algorithm. The genetic algorithm and K-means algorithm were used to select a subset of the suitable features at each node in binary decision tree. The feature subset with maximum fitness is chosen and the patterns are classified into two classes by a linear decision boundary. This process was repeated at each node until all the patterns are classified into individual classes. The final recognizer is accomplished by neural network learning of a set of standard patterns at each node. Binary decision tree classifier was applied to the recognition of the defect patterns of cold mill strip and the experimental results were given to demonstrate the usefulness of the proposed scheme.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.1
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• pp.98-103
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• 2000

This paper suggests a method to recognize the various defect patterns of a cold mill strip using a binary decision tree automatically constructed by a genetic algorithm(GA). In classifying complex patterns with high similarity like the defect patterns of a cold mill stirp, the selection of an optimal feature set and an appropriate recognizer is important to achieve high recognition rate. In this paper a GA is used to select a subset of the suitable features at each node in the binary decision tree. The feature subset with maximum fitness is chosen and the patterns are classified into two classes using a linear decision function. This process is repeated at each node until all the patterns are classified into individual classes. In this way, the classifier using the binary decision tree is constructed automatically. After constructing the binary decision tree, the final recognizer is accomplished by having neural network learning sits of standard patterns at each node. In this paper, the classifier using the binary decision tree is applied to the recognition of defect patterns of a cold mill strip, and the experimental results are given to demonstrate the usefulness of the proposed scheme.