• Journal of the Korean Statistical Society
• /
• 제30권2호
• /
• pp.231-246
• /
• 2001

Local linear smoothing enjoys several excellent theoretical and numerical properties, an in a range of applications is the method most frequently chosen for fitting curves to noisy data. Nevertheless, it suffers numerical problems in places where the distribution of design points(often called predictors, or explanatory variables) is spares. In the case of univariate design, several remedies have been proposed for overcoming this problem, of which one involves adding additional ″pseudo″ design points in places where the orignal design points were too widely separated. This approach is particularly well suited to treating sparse bivariate design problem, and in fact attractive, elegant geometric analogues of unvariate imputation and interpolation rules are appropriate for that case. In the present paper we introduce and develop pseudo dta rules for bivariate design, and apply them to real data.

• 전기학회논문지
• /
• 제56권3호
• /
• pp.615-622
• /
• 2007

In general, Harris detector is commonly used for finding salient points in watermarking systems using feature points. Harris detector is a kind of combined comer and edge detector which is based on neighboring image data distribution, therefore it has some limitation to find accurate salient points after watermark embedding or any kinds of digital attacks. In this paper, we have used cross reference points which use not data distribution but geometrical structure of a normalized image in order to avoid pointing error caused by the distortion of image data. After normalization, we find cross reference points and take inverse normalization of these points. Next, we construct a group of triangles using tessellation with inversely normalized cross reference points. The watermarks are affine transformed and transformed-watermarks are embedded into not normalized image but original one. Only locations of watermarks are determined on the normalized image. Therefore, we can reduce data loss of watermark which is caused by inverse normalization. As a result, we can detect watermarks with high correlation after several digital attacks.

• 대한수학회보
• /
• 제46권5호
• /
• pp.823-833
• /
• 2009

It is well-known that if a convex hyperbolic polygon is constructed as a fundamental domain for a subgroup of the modular group, then its translates by the group elements form a locally finite tessellation and its side-pairing transformations form a system of generators for the group. Such hyperbolically convex polygons can be obtained by using Dirichlet's and Ford's polygon constructions. Another method of obtaining a fundamental domain for subgroups of the modular group is through the use of a right coset decomposition and we call such domains standard fundamental domains. In this paper we give subgroups of the modular group which do not have hyperbolically convex standard fundamental domain containing only inequivalent cusps.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제13권2호
• /
• pp.141-159
• /
• 2009

In this article, we consider a weighted CVT-based reduced-order modelling for Burgers equation. Brief review of the CVT (centroidal Voronoi tessellation) approaches to reduced-order bases are provided. In CVT-reduced order modelling, we start with a snapshot set just as is done in a POD (Proper Orthogonal Decomposition)-based setting. So far, the CVT was researched with uniform density ($\rho$(y) = 1) to determine the basis elements for the approximatin subspaces. Here, we shall investigate the technique of CVT with nonuniform density as a procedure to determine the basis elements for the approximating subspaces. Some numerical experiments including comparison of two CVT (CVT-uniform and CVT-nonuniform)-based algorithm with numerical results obtained from FEM(finite element method) and POD-based algorithm are reported.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제9권3호
• /
• pp.275-284
• /
• 2005

Tessellations are the pattern of iterations of geometric symmetry and translation. We can find them in the works of Escher who is the famous Dutch artist, and the American Indean life. Also, we can find the beauty of tessellations in the Korean traditional house door, Buddist temple architecture, palace's fence, etc. In the article, the figures of patterns we present are bird, fish, cat, pig, elephant, penguin, child and horse riding man, including Escher's, which are constructed using the computer geometric program, GSP (Geometer's Sketchpad). We want to talk about girl's disposition toward mathematics related to the figures. If they are supported by this kind of interesting figures constructed by their own hands, students will have more interest in learning geometric figures.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제7권9호
• /
• pp.2173-2193
• /
• 2013

In order to reduce the distribution cost of sensor nodes, a mobile sensor deployment has been proposed. The mobile sensor deployment can be solved by finding the optimal layout and planning the movement of sensor nodes with minimum energy consumption. However, previous studies have not sufficiently addressed these issues with an efficient way. Therefore, we propose a new deployment approach satisfying these features, namely a tree-based approach. In the tree-based approach, we propose three matching schemes. These matching schemes match each sensor node to a vertex in a rake tree, which can be trivially transformed to the target layout. In our experiments, the tree-based approach successfully deploys the sensor nodes in the optimal layout and consumes less energy than previous works.

• Computers and Concrete
• /
• 제7권1호
• /
• pp.39-51
• /
• 2010

The system of pores of autoclaved aerated concrete (AAC) is described by the so-called cherry-pit model, a random system of partially interpenetrating spheres. For the simulation of fracture processes, the solid phase is approximated by an irregular spatial network of beams obtained by means of the so-called radical tessellation with respect to the pore spheres. FE calculations using standard software (ANSYS) yield the strain energies of the beams. These energies are used as fracture criterion according to which highly loaded beams are considered as broken and are removed from the network. The paper investigates the relationship between mean fracture strength and microstructure for structures close to real AAC samples and virtual structures with particular geometrical properties.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2007년도 하계종합학술대회 논문집
• /
• pp.43-44
• /
• 2007

The Underwater Wireless Sensor Network (UWSN) consists of sensor nodes equipped with a small battery of limited energy resource. Hence, the energy efficiency is a key design issue that needs to be addressed in order to improve the lifetime of the network. In this paper, we use a hexagon tessellation with and ideal cell size to deploy the underwater sensor nodes for the UWSN and propose an enhanced hybrid transmission method that considers the load balancing once the data transmission occurs.

• 충청수학회지
• /
• 제32권3호
• /
• pp.261-280
• /
• 2019

We apply a reduced-order method based on B-spline Galerkin finite elements formulation to Rosenau-RLW equation for the first time and explain their process in detail. The ensemble of snapshots is very large generally, and it is difficult to apply POD to the ensemble of snapshots directly. Hence, we try to pick up important snapshots among the whole data. In this paper, we represent three different reduced-order schemes. First, the classical POD technique is examined. Second, (equally sampled snapshots) are exploited for POD technique. Finally, afterward sampling snapshots by CVT, for those snapshots, POD technique is implemented again.

• 대한전자공학회논문지TC
• /
• 제43권1호
• /
• pp.57-70
• /
• 2006

센싱, 데이터 가공, 통신이 가능한 소형의 센서 노드로 구성된 무선 센서 네트워크는 다양한 환경 변화를 측정할 수 있는 유용한 수단이다. 센서 노드에서 측정된 데이터는 모든 데이터를 수집, 처리하며 사용자에게 전달하는 기능을 가진 프로세싱 센터에 전송된다. 이러한 과정은 에너지 제약을 가진 센서 노드를 고려하여 설계되어야 한다. 일반적으로 인접한 센서 노드는 유사한 정보를 가지므로, 로컬 클러스터를 형성하고 클러스터 헤드에 의해 집약된 데이터를 프로세싱 센터에 전송하는 클러스터링 기법이 저전력 구동에 효과적이다. 자동 구성능력을 지닌 기존의 다중 홉 클러스터 에너지 소비량 모델링 기법은 개별 센서 노드의 정확한 에너지 소비량을 예측할 수 없는 문제를 가지고 있었다. 따라서 본 논문에서는 이러한 문제를 보완한 새로운 클러스터 에너지 소비량 모델링 기법을 제안한다. 제안된 모델링 기법은 보로노이 배열(Voronoi tessellation)을 이용하여 클러스터 헤드의 수에 따른 에너지 소비량을 모델링한다. 즉, 센서 필드의 면적, 분포된 센서 노드의 수와 통신 범위를 이용하여 전체 네트워크의 에너지 소비량을 클러스터 헤드의 수에 따라 정량적으로 나타낸다. 본 모델링 기법을 통해 전체 네트워크의 에너지 소비량이 최소가 되는 클러스터의 수를 예측함으로써 저전력을 실현할 수 있다. 본 논문에서 제안하는 모델링 기법은 시뮬레이션을 통해 구성한 실제 네트워크의 에너지 소비량과 $90\%$ 이상의 정확도를 가지며, 기존 모델링의 $60\%$대에 비춰볼 때 상당히 우수한 정확도를 지니고 있다. 또한, 센서 노드의 밀도가 증가할수록 에너지 소비량 정확도가 증가하는 효과를 확인하였다.