Browsing by Author "Hwang, F. K."

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A new construction of 3-separable matrices via an improved decoding of Macula's construction
(2008-11-01)
Fu, Hung-Lin
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Hwang, F. K.
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應用數學系
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Department of Applied Mathematics
Macula proposed a novel construction of pooling designs which can effectively identify positive clones and also proposed a decoding method. However, the probability of all unresolved positive clone is hard to analyze. In this paper we propose an improved decoding method and show that ford d = 3 an exact probability analysis is possible. Further, we derive necessary and Sufficient conditions for a positive clone to be unresolved and gave a modified construction which avoids this necessary condition, thus resulting; in a 3-separable matrix. (c) 2008 Elsevier B.V. All rights reserved.
An unexpected meeting of four seemingly unrelated problems: graph testing, DNA complex screening, superimposed codes and secure key distribution
(2007-10-01)
Chen, H. B.
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Du, D. Z.
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Hwang, F. K.
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應用數學系
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Department of Applied Mathematics
This paper discusses the relation among four problems: graph testing, DNA complex screening, superimposed codes and secure key distribution. We prove a surprising equivalence relation among these four problems, and use this equivalence to improve current results on graph testing. In the rest of this paper, we give a lower bound for the minimum number of tests on DNA complex screening model.
Bounding the number of columns which appear only in positive pools
(2006-06-01)
Chen, H. B.
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Hwang, F. K.
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Li, C. M.
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應用數學系
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Department of Applied Mathematics
d-separable, (d) over bar -separable and d-disjunct matrices are the major tools in constructing pooling designs which has many applications to DNA experiments, for example, the clone library screening problem. While there exists a simple decoding for d-disjunct matrices, only brute-force methods are known for the other two. In this paper we identify structures in these two matrices which lead to significant improvements for decoding.
Construction of d(H)-disjunct matrix for group testing in hypergraphs
(2006-11-01)
Gao, Hong
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Hwang, F. K.
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Thai, My T.
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Wu, Weili
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Znati, Taieb
Given a hypergraph with at most d positive edges, identify all positive edges with the minimum number of tests each of which tests on a subset of nodes, called a pool, and the outcome is positive if and only if the pool contains a positive edge. This problem is called the group testing in hypergraphs, which has been found to have many applications in molecular biology, such as the interactions between bait proteins and prey proteins, the complexes of eukaryotic DNA transcription and RNA translation. In this paper, we present a general construction for constructions of nonadaptive algorithms for group testing in hypergraphs.
Improved construction for pooling design
(2008-01-01)
Deng, Ping
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Hwang, F. K.
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Wu, Weili
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MacCallum, David
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Wang, Feng
Pooling design is a mathematical tool with many applications in molecular biology, specially to reduce the number of tests for DNA library screening. In this note, we study construction of pooling design and present an improvement to a recent new construction given by Du et al.
The identification of positive clones in a general inhibitor model
(2007-11-01)
Hwang, F. K.
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Chang, F. H.
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應用數學系
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Department of Applied Mathematics
In using pooling designs to identify clones containing a specific subsequence called positive clones, sometimes there exist nonpositive clones which can cancel the effect of positive clones. Various models have been studied which differ in the power of cancellation. Although the various models pose interesting mathematical problems, and ingenious constructions of pooling designs have been proposed, in practice we rarely are sure about the true model and thus about which pooling design to use. In this paper we give a pooling design which fits all inhibitor models, and does not use more tests than in the more specific models. In particular, we obtain a I-round pooling design for the k-inhibitor model for which only sequential designs are currently known. (c) 2007 Elsevier Inc. All rights reserved.
The minimum number of e-vertex-covers among hypergraphs with e edges of given ranks
(2009-01-06)
Chang, F. H.
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Fu, H. L.
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Hwang, F. K.
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Lin, B. C.
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應用數學系
We study the problem that among all hypergraphs with e edges of ranks l(1), ..., l(e) an v vertices, which hypergraph has the least number of vertex-covers of size e. The problem is very difficult and we only get some partial answers. We show an application of our results to improve the error-tolerance of a pooling design proposed in the literature. (c) 2008 Elsevier B.V. All rights reserved.