• 대한수학회논문집
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• 제27권4호
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• pp.665-668
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• 2012

For a given graph G we consider a set S(G) of all symmetric matrices A = [$a_{ij}$] whose nonzero entries are placed according to the location of the edges of the graph, i.e., for $i{\neq}j$, $a_{ij}{\neq}0$ if and only if vertex $i$ is adjacent to vertex $j$. The minimum rank mr(G) of the graph G is defined to be the smallest rank of a matrix in S(G). In general the computation of mr(G) is complicated, and so is that of the maximum multiplicity MaxMult(G) of an eigenvalue of a matrix in S(G) which is equal to $n$ - mr(G) where n is the number of vertices in G. However, for trees T, there is a recursive formula to compute MaxMult(T). In this note we show that this recursive formula for MaxMult(T) also computes the path cover number $p$(T) of the tree T. This gives an alternative proof of the interesting result, MaxMult(T) = $p$(T).

• Steel and Composite Structures
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• 제25권2호
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• pp.127-139
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• 2017

In this paper, an exact analytical solution for simply supported sandwich plate which considers the permeation effect of adhesives is presented. The permeation layer is described as functionally graded material (FGM), the elastic modulus of which is assumed to be graded along the thickness following the exponential law. Based on the exact three-dimensional (3-D) elasticity theory, the solution of stresses and displacements for each layer is derived. By means of the recursive matrix method, the solution can be efficiently obtained for plates with many layers. The present solution obtained can be used as a benchmark to access other simplified solutions. The comparison study indicates that the finite element (FE) solution is close to the present one when the FGM layer in the FE model is divided into a series of homogeneous layers. However, the present method is more efficient than the FE method, with which the mesh division and computation are time-consuming. Moreover, the solution based on Kirchhoff-Love plate theory is greatly different from the present solution for thick plates. The influence of the thickness of the permeation layer on the stress and displacement fields of the sandwich plate is discussed in detail. It is indicated that the permeation layer can effectively relieve the discontinuity stress at the interface.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권8호
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• pp.3295-3311
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• 2020

With the wide application of hyperspectral images, it becomes more and more important to compress hyperspectral images. Conventional recursive least squares (CRLS) algorithm has great potentiality in lossless compression for hyperspectral images. The prediction accuracy of CRLS is closely related to the correlations between the reference bands and the current band, and the similarity between pixels in prediction context. According to this characteristic, we present an improved CRLS with adaptive band selection and adaptive predictor selection (CRLS-ABS-APS). Firstly, a spectral vector correlation coefficient-based k-means clustering algorithm is employed to generate clustering map. Afterwards, an adaptive band selection strategy based on inter-spectral correlation coefficient is adopted to select the reference bands for each band. Then, an adaptive predictor selection strategy based on clustering map is adopted to select the optimal CRLS predictor for each pixel. In addition, a double snake scan mode is used to further improve the similarity of prediction context, and a recursive average estimation method is used to accelerate the local average calculation. Finally, the prediction residuals are entropy encoded by arithmetic encoder. Experiments on the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) 2006 data set show that the CRLS-ABS-APS achieves average bit rates of 3.28 bpp, 5.55 bpp and 2.39 bpp on the three subsets, respectively. The results indicate that the CRLS-ABS-APS effectively improves the compression effect with lower computation complexity, and outperforms to the current state-of-the-art methods.

• 한국수학교육학회지시리즈A:수학교육
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• 제58권2호
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• pp.319-335
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• 2019

이 논문에서는 초등학교 교과서에서의 가분성(divisibility) 개념을 중심으로, 개념적 사고의 과정을 그대로 Python 언어로 코딩하고 Computational Thinking (이하, CT) 중 하나인 자동화에 따른 계산의 효율성을 고찰하였다. 이로부터 얻을 수 있는 교육적 시사점은 다음과 같다. 수학적인 개념적 사고를 CT의 관점에서 생각해 보고, 또한 역으로 컴퓨터 과학에서 중시하고 있는 CT에서 수학적 개념을 추출해 볼 수 있는 쌍방향의 활동이 수학 중심의 코딩교육에서 필요하다.

• 정보처리학회논문지B
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• 제13B권2호
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• pp.127-132
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• 2006

인스턴스 기반 학습의 대표적인 알고리즘인 k-NK(K-Nearest Neighbors)은 단순히 전체 학습패턴을 메모리에 저장한 다음, 분류할 때 학습 패턴들과의 거리를 계산하여 가장 가까운 학습패턴의 클래스로 테스트 패턴을 분류한다. K-NN 기법은 만족할 만한 분류성능을 보여주지만, 학습패턴의 개수가 늘어나면 메모리와 분류 시간이 증가하는 문제점을 가지고 있다. 그러므로, 메모리의 효율적 사용과 분류 시간을 단축시키기 위한 다양한 연구들이 발표되었으며, 그 대표적인 예로 NGE(Nested Generalized Exemplar) 이론을 들 수 있다. 본 논문에서는 학습패턴의 집합으로부터 대표패턴을 생성하는 RPA(Recursive Partition Averaging)기법과 점진적으로 대표패턴을 추출하는 IRPA(Incremental RPA)기법을 제안하였다. RPA기법은 전체 학습패턴의 공간을 재귀적으로 분할하면서 대표패턴을 생성하며, IRPA 기법은 RPA 기법의 특성상 패턴의 특징 개수가 많은 경우, 과도한 분할로 인하여 생성되는 많은 개수의 대표패턴을 줄이기 위하여 점진적으로 대표패턴을 추출하는 알고리즘이다. 본 논문에서 제안한 기법은 기존의 k-NN 기법과 비교하여 현저하게 줄어든 대표패턴을 이용하석 유사한 분류 성능을 보여주며, NGE 이론을 구현한 EACH 시스템과 비교하여 탁월한 분류 성능을 보여준다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 춘계학술대회 논문집
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• pp.956-959
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• 2005

The overall goal of this thesis is to develop a new algorithm based on the octree model for geometric and mechanistic milling operation at the same time. Most commercial machining simulators are based on the Z map model, which has several limitations in terms of achieving a high level of precision in five-axis machining simulation. Octree representation being a three-dimensional (3D) decomposition method, an octree-based algorithm is expected to be able to overcome such limitations. With the octree model, storage requirement is reduced. Moreover, recursive subdivision is processed in the boundaries, which reduces useless computations. To achieve a high level of accuracy, fast computation time and less memory consumption, the advanced octree model is suggested. By adopting the supersampling technique of computer graphics, the accuracy can be significantly improved at approximately equal computation time. The proposed algorithm can verify the NC machining process and estimate the material removal volume at the same time.

• Journal of Mechanical Science and Technology
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• 제15권8호
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• pp.1090-1096
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• 2001

In this paper, new methods for efficiently solving linear acceleration equations of multibody dynamic simulation exploiting sparsity for real-time simulation are presented. The coefficient matrix of the equations tends to have a large number of zero entries according to the relative joint coordinate numbering. By adequate joint coordinate numbering, the matrix has minimum off-diagonal terms and a block pattern of non-zero entries and can be solved efficiently. The proposed methods, using sparse Cholesky method and recursive block mass matrix method, take advantages of both the special structure and the sparsity of the coefficient matrix to reduce computation time. The first method solves the η$\times$η sparse coefficient matrix for the accelerations, where η denotes the number of relative coordinates. In the second method, for vehicle dynamic simulation, simple manipulations bring the original problem of dimension η$\times$η to an equivalent problem of dimension 6$\times$6 to be solved for the accelerations of a vehicle chassis. For vehicle dynamic simulation, the proposed solution methods are proved to be more efficient than the classical approaches using reduced Lagrangian multiplier method. With the methods computation time for real-time vehicle dynamic simulation can be reduced up to 14 per cent compared to the classical approach.

• 한국인터넷방송통신학회논문지
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• 제23권6호
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• pp.75-80
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• 2023

미래의 무선과 휴대용 계산 응용에서 DCT 대체할 수 있는 가역적인 블록 변환의 구현을 제시하였다. 이것을 binDCT라 불린다. BinDCT에서 정방향과 역방향 변환들은 이진 천이와 더하기 연산으로 구현될 수 있다. 그리고 binDCT는 바람직한 DCT 특징인(고코딩이득, DC손실 없음, 대칭적인 기저함수, 재귀적 구성)을 유지한다. 또한 binDCT는 lifting 특징인(빠른 구현, 가역적인 정수대정수 매핑, 내부 계산)을 유지한다. 따라서 복잡한 DCT 연산을 보다 빠르게 실행할 수 있는 장점을 가진다. 이 논문에서는 DCT와 binDCT의 계산비용과 성능분석을 Shapiro의 EZW을 사용하여 제시하였다.

• Journal of Platform Technology
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• 제6권3호
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• pp.23-30
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• 2018

동작 패턴 생성이란 로봇이 어떤 동작을 안정하게 수행하기 위해 미리 안정적인 동작 궤적을 계산해 내는 것을 말하며 자세 제어는 미리 생성된 동작 패턴을 이용하여 동작을 수행하는 도중 발생하는 외란을 제거하여 로봇의 자세를 안정 하게 만들어주는 것을 말한다. 본 논문에서는 수치적 방법이나 로봇의 상체 구조를 간략화하여 근사적으로 생성하는 기존의 보행 패턴 방법과는 다르게 범용적으로 사용 가능한 뉴럴네트워크 학습기법을 이용한 로봇의 동작패턴 생성방법에 대하여 연구한다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.295-298
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• 1996

In this paper, a self-tuning optimal control algorithm is proposed to retain the optimal performance of an active suspension system, when the vehicle has some time varying parameters and parameter uncertainties. We consider a 2 DOF time-varying quarter car model which has the parameter variation of sprung mass, suspension spring constant and suspension damping constant. Instead of solving algebraic riccati equation on line, we propose a neural network approach as an alternative. The optimal feedback gains obtained from the off line computation, according to parameter variations, are used as the neural network training data. When the active suspension system is on, the parameters are identified by the recursive least square method and the trained neural network controller designer finds the proper optimal feedback gains. The simulation results are represented and discussed.