• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.825-839
• /
• 1997

The permanent function on certain faces of the polytope of doubly stochastic matrices are studied. These faces are shown to be barycentric, and the minimum values of permanent are determined.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1247-1260
• /
• 2021

We introduce the notion of barycentric transformation of Fano polytopes, from which we can assign a certain type to each Fano polytope. The type can be viewed as a measure of the extent to which the given Fano polytope is close to be Kähler-Einstein. In particular, we expect that every Kähler-Einstein Fano polytope is of type B_∞. We verify this expectation for some low dimensional cases. We emphasize that for a Fano polytope X of dimension 1, 3 or 5, X is Kähler-Einstein if and only if it is of type B_∞.

• International Journal of Precision Engineering and Manufacturing
• /
• v.3 no.1
• /
• pp.33-42
• /
• 2002

Recently, various experiments to apply reinforcement learning method to the self-learning intelligent control of continuous dynamic system have been reported in the machine learning related research community. The reports have produced mixed results of some successes and some failures, and show that the success of reinforcement learning method in application to the intelligent control of continuous control systems depends on the ability to combine proper function approximation method with temporal difference methods such as Q-learning and value iteration. One of the difficulties in using function approximation method in connection with temporal difference method is the absence of guarantee for the convergence of the algorithm. This paper provides a proof of convergence of a particular function approximation method based on \"barycentric interpolator\" which is known to be computationally more efficient than multilinear interpolation .

• Proceedings of the KOSOMBE Conference
• /
• v.1997 no.05
• /
• pp.362-365
• /
• 1997

To visualize electrical activities in the cerebral cortex, we develop the 3D topographic mapping system based on PC. For this work, we utilize OpenGL tool and an optimized interpolation method known as 3D barycentric algotithm, which has a little computational complexity. OpenGL processes the 3D coordinates, and 3D barycentric algotithm interpolates to get overall EEGs with EEGs measured from finite electrodes on 3D. To prove validity of this algorithm on the PC-based system, we developped Windows-based 3D topographic mapping program using the Barycentric algorithm. The result showed that the performance of this system is comparable to that of workstation in terms of speed and precision. Also, the result of clinical test was the same as that of a EEG technician's analysis.

• Honam Mathematical Journal
• /
• v.35 no.2
• /
• pp.211-223
• /
• 2013

We consider permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing identity submatrix. We determine the minimum permanents and minimizing matrices on the given faces of the polytope using the contraction method.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2010.05a
• /
• pp.1001-1002
• /
• 2010

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.199-211
• /
• 2004

For positive integers $\kappa$ and p$\geq$3, let(equation omitted) where $J_{p}$ is the p${\times}$p matrix whose entries are all 1. Then, we determine the minimum permanents and minimizing matrices over (1) the face of $\Omega$(D) and (2) the face of $\Omega$($D^{*}$), where (equation omitted).

• Proceedings of the IEEK Conference
• /
• 1998.06a
• /
• pp.581-584
• /
• 1998

To obtain 3-D topography of EEG records, we propose a new method based on the polygon mapping technique. The method has the low complexity to calculate the interpolation of the EEG records on the scalp and maintains the high resolution topography because the polygon technique performs the interpolation at the only vertexes of each polygon. We implemented the topographic system with 3D barycentric, 3D polynomial and spherical spline algorithms in a personal computer.

• Proceedings of the KIPE Conference
• /
• 2015.07a
• /
• pp.45-46
• /
• 2015

본 논문에서는 무게중심좌표계에 의한 공간벡터 PWM의 간단한 구현방법을 제안한다. 무게중심좌표계를 사용하면 듀티비를 계산할 때 SIN, COS의 함수계산없이 단순한 사칙연산만을 사용하고 기준벡터가 속한 섹터에 따라 서로 다른 듀티비를 정하는 식을 유도할 필요가 없으며 듀티비가 어떻게 정해지는지에 대한 직관적인 이해를 할 수 있다. 본 논문에서는 무게중심 좌표계에서 공간벡터 PWM의 듀티비를 정하는 원리에 대하여 설명한다.

• Journal of KIISE:Computer Systems and Theory
• /
• v.31 no.7
• /
• pp.414-420
• /
• 2004

Among the desirable properties of a piecewise linear parameterization, guaranteeing a one-to-one mapping (i.e., no triangle flips in the parameter plane) is often sought. A one-to-one mapping is accomplished by non-negative coefficients in the affine transformation. In the Floater's method, the coefficients were computed after the 3D mesh was flattened by geodesic polar-mapping. But using this geodesic polar map introduces unnecessary local distortion. In this paper, a simple variant of the original shape-preserving mapping technique by Floater is introduced. A new simple method for calculating barycentric coordinates by using straightest geodesics is proposed. With this method, the non-negative coefficients are computed directly on the mesh, reducing the shape distortion introduced by the previously-used polar mapping. The parameterization is then found by solving a sparse linear system, and it provides a simple and visually-smooth piecewise linear mapping, without foldovers.