• Communications for Statistical Applications and Methods
• /
• v.22 no.1
• /
• pp.69-80
• /
• 2015

In this paper, the probability that a given point is covered by a random convex hull generated by independent and identically-distributed random points in a plane is studied. It is shown that such probability can be expressed in terms of an integral that can be approximated numerically by function-evaluations over the grid-points in a 2-dimensional space. The new integral representation allows such probability be computed efficiently. The computational burdens under the proposed integral representation and those in the existing literature are compared. The proposed method is illustrated through numerical examples where the random points are drawn from (i) uniform distribution over a square and (ii) bivariate normal distribution over the two-dimensional Euclidean space. The applications of the proposed method in statistics are are discussed.

• Journal of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.993-1015
• /
• 2012

In this paper, we study the quantum sl($n$) representation category using the web space. Specially, we extend sl($n$) web space for $n{\geq}4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl($n$). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial ($n=0$) and Jones polynomial ($n=2$) and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.

• Proceedings of the Korea Society for Simulation Conference
• /
• 2003.06a
• /
• pp.73-78
• /
• 2003

This paper proposes the simulator synthesis scheme which is based on the exploration of the total design space in attributed AND-OR graph. Attributed AND-OR graph is a systematic design space representation formalism which enables to represent all the design space by decomposition rule and specialization rule. In addition, attributes attached to the design entity provides flexible modeling. Based on this design space representation scheme, a pruning algorithm which can transform the total design space into sub-design space that satisfies the user requirements is given. We have shown the effectiveness of our framework by (ⅰ) constructing the design space of superscalar processor in attributed AND-OR graph (ⅱ) pruning it to obtain the ARM9 processor architecture. (ⅲ) modeling the components of the architecture and (ⅳ) simulating the ARM9 model.

• ETRI Journal
• /
• v.11 no.1
• /
• pp.109-122
• /
• 1989

We developed new quadtree and octree representation schemes which reduce the storage requirements from exponential to polynomial. The new schemes not only lessen the large storage requirements of the existing quadtree and octree representation schemes but guarantee an exact representation of the original object. These are made possible by adopting a new set of termination conditions that ensure finiteness of the quadtree and octree during the decomposition. These new data structures are analyzed theoretically and tested empirically. For space complexity, we analyzed its best case, worst case, and average case. Given an $n_e$-gon, we show that the expected number of nodes in our quadtree isO($$$n_e^1.292$) For a polyhedron with $n_f$ faces, the expected number of nodes in the new octree is O($$$n_f^1.667$). For time complexity, we again analyzed the best, worst, and average cases for constructing such quadtree and octree and find the average to be the same as those of the space complexity. Finally, random $n_e$- gons are generated as test data. Regression equations are fitted and are shown to support the claims on the average case performance.

• Journal of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.177-189
• /
• 1998

In this paper, weighted Bloch spaces $B_q (q > 0)$ are considered on the open unit ball in $C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic functions. It is proved that the functions in a weighted Bloch space admit certain integral representation. This representation formula is then used to determine the degree of growth of the functions in the space $B_q$. It is also proved that weighted Bloch space is a Banach space for each weight q > 0, and the little Bloch space $B_q,0$ associated with $B_q$ is a separable subspace of $B_q$ which is the closure of the polynomials for each $q \geq 1$.

• Korean Institute of Interior Design Journal
• /
• v.15 no.1 s.54
• /
• pp.79-87
• /
• 2006

'Fantasy' in this study is Not something fantastic in the used to be-way we can Imagine easily. This study is to figure out 'fantasy' and 'the fantastic' as a significant measure to interpret the contemporary space-time. In particular, it analyzed that fantasy have influenced on some kind of specific trend what is expressed a tendency to contemporary interior designs of informal, indeterminacy and unpredictability. Fantasy is represented as 'the fantastic space' through spatial revealing, concealing, distorting, and connoting. Representation becomes a major issue in almost many kinds of knowledge-system that start from the mind to go out to the world in a realistic or idealistic way. Therefore, the fantastic space reconstructs the reality while making itself through to representational creation-process. It is Important for fantasy and the fantastic space to help detect behind beneath the reality more than what we know.

• Journal of the Korea Institute of Building Construction
• /
• v.15 no.3
• /
• pp.317-327
• /
• 2015

Many construction projects have extensively adopted building information modeling (BIM), and various institutions and standards have been developed domestically in Korea. However, the current process that is used to calculate building space area has a significant shortcoming in that there are two different laws to apply the method of measurement considering space boundaries for building element guidelines. For example, space area can be calculated by a polygon, which is modeling using a BIM-based computer aided design program, such that the space polygon is always exported as an inner-edge type. In this paper, we developed an automated algorithm to convert coordinates of space representation using industry foundation classes based BIM data. The proposed algorithm will enable engineers responsible for space management to use a BIM-based model directly in the space programming process without having to do additional work. The proposed process can help ensure that space area is more accurately and reliably.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.19 no.9
• /
• pp.1702-1709
• /
• 1994

In the postprocessing of Hangul recognition system, the storage structure of contextual information is an important matter for the recognition rate and speed of the entire system. Trie in general is used to represent the context as word dictionary, but the memory space efficiency of the structure is low. Therefore we propose a new structure for word dictionary that has better space efficiency and the equivalent merits of trie. Because Hangul is a compound language, the language can be represented by phonemes or by characters. In the representation by phonemes(P-mode) the retrieval is fast, but the space efficiency is low. In the representation by characters(C-mode) the space efficiency is high, but the retrieval is slow. In this paper the two representation methods are combined to form a hybrid representation(H-mode). At first an optimal level for the combination is selected by two characteristic curves of node utilization and dispersion. Then the input words are represented with trie structure by P-mode from the first to the optimal level, and the rest are represented with sequentially linked list structure by C-mode. The experimental results for the six kinds of word set show that the proposed structure is more efficient. This result is based on the fact that the retrieval for H-mode is as fast as P-mode and the space efficiency is as good as C-mode.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.6
• /
• pp.2709-2729
• /
• 2016

Representation based classification, kernel method and sparse representation have received much attention in the field of face recognition. In this paper, we proposed an improved kernel principal component analysis method based on sparse representation to improve the accuracy and robustness for face recognition. First, the distances between the test sample and all training samples in kernel space are estimated based on collaborative representation. Second, S training samples with the smallest distances are selected, and Kernel Principal Component Analysis (KPCA) is used to extract the features that are exploited for classification. The proposed method implements the sparse representation under ℓ₂ regularization and performs feature extraction twice to improve the robustness. Also, we investigate the relationship between the accuracy and the sparseness coefficient, the relationship between the accuracy and the dimensionality respectively. The comparative experiments are conducted on the ORL, the GT and the UMIST face database. The experimental results show that the proposed method is more effective and robust than several state-of-the-art methods including Sparse Representation based Classification (SRC), Collaborative Representation based Classification (CRC), KCRC and Two Phase Test samples Sparse Representation (TPTSR).

• Korean Institute of Interior Design Journal
• /
• v.23 no.5
• /
• pp.41-50
• /
• 2014

In relation to spatial expression, the remediation theory of Jay David Bolter & Richard Grusin shows a sufficient possibility of providing extended idea and experience through the space of critical representation. The remediation theory discussed in the scope of new media says about the existence method and the development process of media through immersion into media and awakening, and one attribute of remediation which aims at the extension of another realistic experience and recognition through various media, contains common denominators which display diversity and complexity of installation space, and use the audience as expression elements. Therefore, this study aims to apply the remediation theory in order to interpret space using more diverse and multisensory expression methods. For achieving this purpose, this study found the connection among characteristics of hypermediacy which is an axis of installation and remediation theory, and analyzed diverse cases regarding installation space and characteristics of hypermediacy, depending on external aspects of form and expression and internal aspects of experience and cognition. The method of hypermediation expression in installation space converts the recognition about the basic custom of new experience, space and representation. This means that the logic of remediation could approach space by leading to more extended form and recognition. In conclusion, the characteristics of space and the possibility of extended expression revealed in the relationship between installation space and hypermediacy logic would provide another developmental significance for research on space design.